**New Manufacturing Process for Granular Texture Management in Polycrystalline BaM Hexaferrites through the Goethite Crystallite Laths Aspect Ratio, and a Specialized Law of Approach to the Magnetic Saturation for Partly Polarized Uniaxial Materials**

**Antoine Hoëz, Jean-Luc Mattei \* and Alexis Chevalier**

Lab-STICC, UMR CNRS 6285, 6 av. Le Gorgeu, 29238 Brest, France **\*** Correspondence: jean-luc.mattei@univ-brest.fr

**Abstract:** This study is aimed at the manufacture and the magnetic properties of polycrystalline M-type hexaferrites BaFe12O<sup>19</sup> (barium ferrite, or BaM) materials of different magnetic texturing grades, going from a random distribution of the BaM crystallites to their almost complete stacking. Our target is to optimize the value of reduced-remanence magnetization *MR*/*MS*, which is among the most significant features of the self-polarized materials. In this study, we focus on the role played by the precursors hematite (isotropic spherical shape) and goethite (anisotropic lath shape). Therefore, 11 samples with a flat cylinder shape are fabricated, with an increasing hematite to goethite ratio. We demonstrate that this ratio drives the texturization of the samples by producing self-polarized materials with different *MR*/*M<sup>S</sup>* from the simple green compaction of the precursors, followed by a heat treatment. Most importantly, our study reveals the orientation of BaM particles after compaction; therefore, *MR*/*MS*, is strongly influenced by the aspect ratio of the lath-shaped goethite crystallites. Additionally, we show that finer goethite crystallites yield higher-value *MR*/*MS*. We optimize the aspect ratio of the goethite crystallites for an improved BaM texture. The optimization of the morphology of the goethite crystallites leads to an increase in the BaM particles' orientation and stacking. The salient outcome of this work, which distinguishes it significantly from recent works, is that the particles stacking increases with the value of the shape factor η (defined as the ratio of the diameter of the laths to their length) of the goethite, evidenced by XRD results. The Rietveld refinements of powder diffractograms and the measured magnetic properties reveal a particle-stacking enhancement caused by not only the ratio of hematite: goethite but mainly by an optimal aspect ratio of the goethite crystallites. Based on this study, the BaM materials are further manufactured with a controlled magnetic texture; thus, they are partly self-polarized. They show reduced-remanence magnetization *MR*/*M<sup>S</sup>* varying from 0.5 and 0.81, while the angular dispersion of the BaM particles' easy axis of magnetization varies from 60◦ to 10◦ . The magnetic properties of the samples are further studied in microwave experiments, from which the value of the magnetocrystalline anisotropy field *H<sup>K</sup>* = 16.6 kOe is deduced. The first magnetization curves of each sample are obtained using a VSM. A law of approach to the saturation suitable for the case of the uniaxial polycrystalline materials, and for which the particle stacking is only partial, is proposed for the fitting of the magnetization process. It is suggested that by using the proposed law with a known magnetocrystalline anisotropy constant *K*<sup>1</sup> , the angular grain-dispersion can be found.

**Keywords:** barium hexaferrites; self-polarized hexaferrites; cold compaction; controlled magnetic texturization; magnetocrystalline anisotropy; law of approach to saturation

#### **1. Introduction**

In recent years, a revival in the interest in rare-earth-free permanent magnets, such as M-type hexaferrites [1–3], has been observed. Among this class of materials, strontium

**Citation:** Hoëz, A.; Mattei, J.-L.; Chevalier, A. New Manufacturing Process for Granular Texture Management in Polycrystalline BaM Hexaferrites through the Goethite Crystallite Laths Aspect Ratio, and a Specialized Law of Approach to the Magnetic Saturation for Partly Polarized Uniaxial Materials. *Magnetochemistry* **2023**, *9*, 30. https://doi.org/10.3390/ magnetochemistry9010030

Academic Editor: Carlos J. Gómez García

Received: 16 November 2022 Revised: 23 December 2022 Accepted: 30 December 2022 Published: 12 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

hexaferrites and barium hexaferrites, BaFe12O<sup>19</sup> (BaM), present intermediate performances between standard ferrite and rare-earth magnets. In addition to a strong magnetocrystalline anisotropy, the BaM hexaferrites engineered to have a sufficient magnetic texture can present the great advantage of possessing high-remanence magnetization. For these reasons, they have attracted attention for use in microwave and millimeter wave (MMW) applications [4–6]. The interest of such properties is obvious in the design of the integrated and miniature MMW devices, in which the external permanent magnet would be eliminated [7–9].

The crystals of BaM grow in a flat hexagonal platelet shape, with an aspect ratio of about 1/3. Their easy axis of magnetization is perpendicular to the basal plane. The critical single-domain size is between 0.5 and 1 µm [10]. The achievement of stacking these single-domain particles is desired in order to produce a self-polarized material.

Among the manufacturing techniques used to effectively fabricate these magnets, those operating with standard ceramic technology and mechanical processes [10] must be distinguished from those implementing soft chemistry methods [6,10–13]. The latter fabrication methods involve topotactical reactions. In addition to being inexpensive, unlike other techniques, soft chemistry methods present the notable advantage of leading to the spontaneous stacking of particles [6]. It should be made clear, however, that even if the polycrystalline material has a high-quality magnetic texture, there is always some misorientation of the easy axes of magnetization, which could hardly be limited only by applying a strong magnetic field during the compaction process. Recent works [14,15], showed that the combined use of goethite and hematite crystallites to fabricate strontium hexaferrites (SrFe12O19), allowed some degree of alignment of the crystallites after a cold compaction and a heat treatment with *MR*/*M<sup>S</sup>* = 0.71. The magnitude of this value, indicative of the degree of particle packing, is insufficient for many applications. The required *MR*/*M<sup>S</sup>* value for a self-polarized material used in a circulator, one of the major applications at present [4,16–19], should be higher than 0.83 [6,20]. In our previous work, using a coprecipitation technique, we created highly oriented bulk compacts made of BaM particles with reduced-remanence magnetization *MR*/*M<sup>S</sup>* = 0.88, which are suitable for self-biased applications [6]. In order to increase this value, we optimized several stages of the fabrication process. In the present work, we focus on the role played by the morphology of the goethite crystallites (which are used as a precursor) and on the quality of BaM particle packing. We show that the shape and aspect ratio of the goethite crystallites are critical parameters for obtaining high *MR*/*M<sup>S</sup>* values, and that they were not taken into account before [14,15].

In the case where the dispersion of the axes of easy magnetization of the material is random, i.e., when the material has no magnetic texture, the law of approach to saturation (LAS) is commonly used to describe the first magnetization curve [21]. However, when used under its most usual formulation, the LAS applies only to the specific case where the material is constituted of particles dispersed at random, and they consequently show a random distribution of their easy axes of magnetization. This state defines the lower degree of the magnetic texture. The LAS is not adapted to the case of a partly or a fully oriented material and should not be used as is. Consequently, it is desirable to have a LAS that is applicable to textured materials. Our purpose is to determine the magnetization curve of a material where the magnetic texture lies between random and perfectly oriented.

The aim of the present work is twofold. Firstly, we present a new method for manufacturing BaFe12O<sup>19</sup> materials with different magnetic texturing grades. The novelty and salient point of our method lie in the use of goethite crystallites with an optimized shape and aspect ratio. The value obtained for the remanent magnetization *MR*/*M<sup>S</sup>* of the BaM material increases from 0.54 to 0.81 when the angular dispersion of the easy axis of magnetization varies from 60◦ to 10◦ (XRD measurements). The magnetocrystalline field *H<sup>K</sup>* is measured from microwave experiments. Secondly, we propose a new formulation of the LAS, partly based on structural characterizations, where the spatial dispersion of the easy

axis of magnetization in grain-oriented polycrystals of hexagonal materials is considered, and from which the angular dispersion value of the BaM particles could be inferred.

#### **2. Experimental Details**

X-ray diffraction measurements are carried out on a Panalytical Empyrean with Chi-Phi-Z configuration using Cu Kα radiation over a 2θ range from 15◦ to 60◦ . The parameters Z, Chi, and Omega are adjusted for each sample.

The microstructures of the samples are imaged by a scanning electron microscope Hitachi-S-3200N (Japan). The hysteresis loops of the sintered samples are measured at room temperature using a Vibrating Sample Magnetometer EZ9 from MicroSense (Lowell, MA, USA), with maximum applied field intensity equal to 1500 kA/m. Each sample was maintained on a Pyrex sample holder, with its c-axis (this axis being defined by the direction of the applied pressure during compaction, as explained below) aligned firstly parallel, and then perpendicular, to the applied field, in order to measure the hysteresis loops in both directions. The sample oscillated at a frequency of 70 Hz and averaged for 3 s. The demagnetizing correction is further carried out by applying the relationship *H<sup>i</sup>* = *H*-NM, where *H<sup>i</sup>* is the internal filed and *H* the applied field. The values of the demagnetizing factor N are tabulated in [22]. The frequency evolution of the imaginary part of the magnetic permeability is extracted from S parameters measured by a ZVA67 vector network analyzer (Rohde & Schwarz, Munich, Germany) in the frequency band [10 GHz–60 GHz]. The frequency evolution of the imaginary part of the magnetic permeability is extracted in using a Rohde and Schwarz ZVA67 vector network analyzer in the frequency band [10 GHz–60 GHz]. The anisotropy field *H<sup>K</sup>* is deduced from the resonant frequency *f<sup>R</sup>* determined by the maximum of the imaginary part µ" of the intrinsic permeability of the sample from the relationship between *H<sup>K</sup>* and *fR*, which writes *<sup>f</sup><sup>R</sup>* <sup>=</sup> *<sup>γ</sup>HK*, where *<sup>γ</sup>* is the gyromagnetic ratio (*<sup>γ</sup>* = 35.12 <sup>×</sup> <sup>10</sup>−<sup>3</sup> MHz/A.m−<sup>1</sup> ).

#### **3. Results and Discussion**

#### *3.1. Manufacture of a Self-Polarized BaM Sample*

The polycrystalline BaFe12O19-oriented samples were made using barium carbonate BaCO<sup>3</sup> (Acros-organics, Nidderau, Germany, 99%) and goethite FeO(OH), which was synthetized in the laboratory from iron III hexahydrate (Sigma-Aldrich, Saint Louis, MS, USA, 98%). For the sake of confidentiality, the synthesis process is not detailed. These components were carefully mixed with a manual mortar. The mixtures obtained were pressed into cylindrical pellets (7 mm diameter and 5 mm thickness) at a pressure of 320 MPa using a uniaxial hydraulic press. The direction of the applied pressure defined the c-axis, which was normal to the upper side of the pellets. The pellets were further heated to 1040 ◦C with zero dwell time and heating and cooling rates of 3 K/min.

During compaction, the applied pressure orients the goethite crystallites along the compaction axis (Figure 1a). We first considered the synthesized goethite crystallites: they are lath-shaped, with a crystallographic axis [001] that is oriented perpendicular to the largest face of the crystallite (Figure 1d). The pressure applied during the molding step leads to a preferential orientation of the goethite crystallites, the [001] axes of which being predominantly parallel to the direction of the applied pressure. The X-ray diffraction pattern of the goethite before and after the pressing process confirm a preferential orientation of the goethite close to the direction [001]. The direction [101], which is closest to [001] among these that contribute to the diffraction pattern, is clearly the one that remains, with a strong intensity (Figure 1a,b), whereas all the others Bragg diffraction peaks are extinguished. The Rietveld analyses performed (Table 1) using Jana2020 (Institute of Physics, Prague, Czech Republic) [23] give a preferred orientation axis [001] with an r-factor of 0.39. This preferential orientation of the [001] axes is maintained during the various topotactic reactions that occur during the subsequent heat treatment leading to the formation of BaFe12O<sup>19</sup> [24–26]. The chemical processes that lead to BaFe12O<sup>19</sup> from oriented goethite crystallites are as follows:

follows:

```
2 αFeO(OH)[001] → αFe2O3[001] + H2O
   αFe2O3[001] + BaCO3 → BaFe2O4[001]
BaFe2O4[001] + αFe2O3[001] → BaFe12O19[001]
     2 αFeO(OH)[001] → αFe2O3[001] + H2O 
      αFe2O3[001] + BaCO3 → BaFe2O4[001] 
   BaFe2O4[001] + αFe2O3[001] → BaFe12O19[001]
```
occur during the subsequent heat treatment leading to the formation of BaFe12O19 [24–26]. The chemical processes that lead to BaFe12O19 from oriented goethite crystallites are as

*Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 4 of 19

**Figure 1.** *(***a**) Schematic representation of the alignment in the basal plane of goethite crystallites, observed after uniaxial pressure. (**b***,***c**) Rietveld analysis of goethite before and after pressing pro‐ cess, respectively. (**d**) TEM images of lath‐shaped goethite crystallites. **Figure 1.** (**a**) Schematic representation of the alignment in the basal plane of goethite crystallites, observed after uniaxial pressure. (**b***,***c**) Rietveld analysis of goethite before and after pressing process, respectively. (**d**) TEM images of lath-shaped goethite crystallites.


**Table 1.** Rietveld refinement values (self-polarized material). **Table 1.** Rietveld refinement values (self‐polarized material).

#### *3.2. The Aspect Ratio of the Goethite Particles: Its Major Role on the Quality of the BaM Particles Stacking 3.2. The Aspect Ratio of the Goethite Particles: Its Major Role on the Quality of the BaM Particles Stacking*

It was found that the aspect ratio of width to length η of the goethite impacts the stacking quality of the resulting BaM crystallites. The X-ray patterns of the three samples obtained with G1, G2, and G3 clearly show an improvement of the stacking quality with increasing η (Figure 2d), and the intensity ratio I(008)/I(107) increases with η (Table 2). It is expected that these results might be significantly improved by optimizing the heat treatment after compaction. Further studies are ongoing. It was found that the aspect ratio of width to length η of the goethite impacts the stacking quality of the resulting BaM crystallites. The X‐ray patterns of the three samples obtained with G1, G2, and G3 clearly show an improvement of the stacking quality with increasing η (Figure 2d), and the intensity ratio I(008)/I(107) increases with η (Table 2). It is expected that these results might be significantly improved by optimizing the heat treat‐ ment after compaction. Further studies are ongoing.

**Table 2.** Influence of the aspect ratio of the goethite on BaM particles stacking. **Table 2.** Influence of the aspect ratio of the goethite on BaM particles stacking*.*


**Figure 2.** *(***a***–***c**) Goethites G1, G2, G3, respectively. *(***d**) X‐Ray pattern of oriented BaM samples *(***1**–**3**) obtained with G1, G2, G3, respectively. **Figure 2.** (**a**–**c**) Goethites G1, G2, G3, respectively. (**d**) X-Ray pattern of oriented BaM samples (**1**–**3**) obtained with G1, G2, G3, respectively.

#### *3.3. Manufacturing of BaM Samples with Differents Grades of Orientation* **Table 3.** Details on the prepared samples.

and cooling rates set to 3 °C/min.

The polycrystalline BaFe12O<sup>19</sup> samples were synthesized using barium carbonate BaCO<sup>3</sup> (Acros-organics, 99%), ferric oxide Fe2O<sup>3</sup> (Sigma-Aldrich, 99%), and goethite FeO(OH) synthetized in the laboratory from iron III hexahydrate (Sigma-Aldrich, 98%). Keeping the 1:12 molar ratio for Ba:Fe and with different molar proportions of Fe2O<sup>3</sup> and FeO(OH), a total of eleven samples were prepared. These components were carefully mixed with a mortar, with molar ratios *\$* = Fe2O3:FeO(OH) varying from 0 to 1 (Table 3). The so-obtained mixtures were pressed into cylindrical pellets (with dimensions of 7 mm diameter and 5 mm thickness) at a pressure of 320 MPa using a uniaxial hydraulic press. The direction of the applied pressure defined the c-axis, perpendicular to the upper side of the pellets. The pellets were further heated to 1040 ◦C, with zero dwell time and heating and cooling rates set to 3 ◦C/min. Goethite (% molar) 0 5 10 20 Hematite (% molar) 100 95 90 80 Notation in this paper BaM‐0 BaM‐5 BaM‐10 BaM‐20 Goethite (% molar) 30 40 50 60 Hematite (% molar) 70 60 50 40

*Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 6 of 19

*3.3. Manufacturing of BaM Samples with Differents Grades of Orientation* 

The polycrystalline BaFe12O19 samples were synthesized using barium carbonate

BaCO3 (Acros‐organics, 99%), ferric oxide Fe2O3 (Sigma‐Aldrich, 99%), and goethite

FeO(OH) synthetized in the laboratory from iron III hexahydrate (Sigma‐Aldrich, 98%).

Keeping the 1:12 molar ratio for Ba:Fe and with different molar proportions of Fe2O3 and

FeO(OH), a total of eleven samples were prepared. These components were carefully

mixed with a mortar, with molar ratios ρ = Fe2O3:FeO(OH) varying from 0 to 1 (Table 3).

The so‐obtained mixtures were pressed into cylindrical pellets (with dimensions of 7 mm

diameter and 5 mm thickness) at a pressure of 320 MPa using a uniaxial hydraulic press.

The direction of the applied pressure defined the c‐axis, perpendicular to the upper side

of the pellets. The pellets were further heated to 1040 °C, with zero dwell time and heating

**Table 3.** Details on the prepared samples. Notation in this paper BaM‐30 BaM‐40 BaM‐50 BaM‐60


The effect of the applied pressure was different on hematite particles than on goethite crystallites. This is a key point of the manufacturing process, which we will emphasize. Now we consider the hematite particles, which have a spherical shape (Figure 3): because the applied pressure does not have any effect on the orientation of these particles, their crystallographic axes remain randomly oriented. Now we consider the hematite particles, which have a spherical shape (Figure 3): because the applied pressure does not have any effect on the orientation of these particles, their crystallographic axes remain randomly oriented.

**Figure 3.** TEM images of spherical crystallites of hematite. **Figure 3.** TEM images of spherical crystallites of hematite.

The initial ratio of Fe2O3:FeO(OH) drives the amount of randomly oriented or ori‐ ented BaFe12O19 crystals. Figure 4a,b are SEM images evidencing the differences in texture The initial ratio of Fe2O3:FeO(OH) drives the amount of randomly oriented or oriented BaFe12O<sup>19</sup> crystals. Figure 4a,b are SEM images evidencing the differences in texture between randomly oriented crystallites in sample BaM-0 (prepared with hematite only) and stacked crystallites in sample BaM-100 (prepared with goethite only).

between randomly oriented crystallites in sample BaM‐0 (prepared with hematite only)

and stacked crystallites in sample BaM‐100 (prepared with goethite only).

**Figure 4.** SEM images show the evolution of the texturization between BaM‐0 (**a**) and BaM‐100 (**b**)*.* **Figure 4.** SEM images show the evolution of the texturization between BaM-0 (**a**) and BaM-100 (**b**).

#### *3.4. Crystallographic Study of BaM Samples Manufactured with Different Texturations 3.4. Crystallographic Study of BaM Samples Manufactured with Different Texturations*

*3.4. Crystallographic Study of BaM Samples Manufactured with Different Texturations*  X‐ray diffraction data were processed with HighScore Plus software (Panalytical, UK) [27] for phase analysis and Jana2020 for Rietveld analysis. The latter made it possible to examine the purity of the samples and to characterize the stacking of the crystallites. The crystallographic model used comes from the ICSD 259873 CIF file with cell parame‐ ters *a* = *b* = 5.8909 Å, *c* = 23.1882 Å and space group symmetry *P*63/*mmc*. The Rietveld anal‐ ysis shows that all samples are single‐phase (Figure 5). After refinement, the cell parame‐ ters and R factors for BaM‐0 are a = b = 5.8928 Å, c = 23.2295 Å and Robs = 3.67, wRobs = 4.47, Rall = 4.78, wRall = 4.68, GOF = 1.19, whereas and BaM‐100, they are a = b = 5.8921 Å, X-ray diffraction data were processed with HighScore Plus software (Panalytical, UK) [27] for phase analysis and Jana2020 for Rietveld analysis. The latter made it possible to examine the purity of the samples and to characterize the stacking of the crystallites. The crystallographic model used comes from the ICSD 259873 CIF file with cell parameters *a* = *b* = 5.8909 Å, *c* = 23.1882 Å and space group symmetry *P*63/*mmc*. The Rietveld analysis shows that all samples are single-phase (Figure 5). After refinement, the cell parameters and R factors for BaM-0 are a = b = 5.8928 Å, c = 23.2295 Å and Robs = 3.67, wRobs = 4.47, Rall = 4.78, wRall = 4.68, GOF = 1.19, whereas and BaM-100, they are a = b = 5.8921 Å, c = 23.2161 Å and Robs = 5.41, wRobs = 5.60, Rall = 6.42, wRall = 5.79, GOF = 1.26. X‐ray diffraction data were processed with HighScore Plus software (Panalytical, UK) [27] for phase analysis and Jana2020 for Rietveld analysis. The latter made it possible to examine the purity of the samples and to characterize the stacking of the crystallites. The crystallographic model used comes from the ICSD 259873 CIF file with cell parame‐ ters *a* = *b* = 5.8909 Å, *c* = 23.1882 Å and space group symmetry *P*63/*mmc*. The Rietveld anal‐ ysis shows that all samples are single‐phase (Figure 5). After refinement, the cell parame‐ ters and R factors for BaM‐0 are a = b = 5.8928 Å, c = 23.2295 Å and Robs = 3.67, wRobs = 4.47, Rall = 4.78, wRall = 4.68, GOF = 1.19, whereas and BaM‐100, they are a = b = 5.8921 Å, c = 23.2161 Å and Robs = 5.41, wRobs = 5.60, Rall = 6.42, wRall = 5.79, GOF = 1.26.

**Figure 5.** Diffraction pattern and Rietveld analysis of BaM‐0 (**left**) and of BaM‐100 (**right**). **Figure 5.** Diffraction pattern and Rietveld analysis of BaM-0 (**left**) and of BaM-100 (**right**).

**Figure 5.** Diffraction pattern and Rietveld analysis of BaM‐0 (**left**) and of BaM‐100 (**right**). When comparing the X‐Ray diffraction pattern of all the samples from BaM‐0 to BaM‐ When comparing the X‐Ray diffraction pattern of all the samples from BaM‐0 to BaM‐ 100, it appears that (00l) basal reflections become stronger (Figure 5). This is explained by an increasing orientation of the crystallites [28]. More specifically the (008) reflection be‐ comes stronger with the increasing goethite to hematite molar ratio, meaning that the rate of oriented BaM particles increases as well (Figure 6). When comparing the X-Ray diffraction pattern of all the samples from BaM-0 to BaM-100, it appears that (00l) basal reflections become stronger (Figure 5). This is explained by an increasing orientation of the crystallites [28]. More specifically the (008) reflection becomes stronger with the increasing goethite to hematite molar ratio, meaning that the rate of oriented BaM particles increases as well (Figure 6).

100, it appears that (00l) basal reflections become stronger (Figure 5). This is explained by an increasing orientation of the crystallites [28]. More specifically the (008) reflection be‐ comes stronger with the increasing goethite to hematite molar ratio, meaning that the rate

**Figure 6.** The intensity of XRD (008) reflection increases with the molar ratio between goethite and hematite. **Figure 6.** The intensity of XRD (008) reflection increases with the molar ratio between goethite and hematite.

XRD data make it also possible to obtain information on the distribution of the ori‐ entation of the crystallites. Among the several mathematical models available (e.g., Sasa‐ Uda [29], Capkova, and Valvoda [30]), the March–Dollase approach [31] is used for the determination of the degree of preferred orientation. The March–Dollase model, devel‐ oped to describe the compaction of platelike grains under uniaxial stress [32], states that XRD data make it also possible to obtain information on the distribution of the orientation of the crystallites. Among the several mathematical models available (e.g., Sasa-Uda [29], Capkova, and Valvoda [30]), the March–Dollase approach [31] is used for the determination of the degree of preferred orientation. The March–Dollase model, developed to describe the compaction of platelike grains under uniaxial stress [32], states that the fraction P(θ) of crystallites having the inclination angle θ between the normal to the diffraction plane and the hkl plane is defined:

$$\mathbf{P}(\theta) = \left(\mathbf{r}^2 \cos^2(\theta) + \frac{\sin^2(\theta)}{\mathbf{r}}\right)^{-\frac{3}{2}} \tag{1}$$

Pሺθሻ = ቆrଶcosଶሺθሻ + sinଶሺθሻ <sup>r</sup> <sup>ቇ</sup> ିଷ <sup>ଶ</sup> (1) The March–Dollase factor, denoted r, defines the spread of angular distribution of the crystallite inclinations. It is extracted from XRD data using Rietveld refinement with The March–Dollase factor, denoted r, defines the spread of angular distribution of the crystallite inclinations. It is extracted from XRD data using Rietveld refinement with Jana2020. If the maximum of the orientation distribution does not occur for the [001] direction, which is most often the case, the distribution is shifted so that θ = 0 represents the easy axis of magnetization [001]. Thus, for the determination of the factor r with a direction [hkl] different than [001], the relation P(θ) with ω the angle between [001] and [hkl] becomes:

$$P(\theta) = \left(\mathbf{r}^2 \cos^2(\theta - \omega) + \frac{\sin^2(\theta - \omega)}{\mathbf{r}}\right)^{-\frac{3}{2}}\tag{2}$$

16] to define the preferred orientation. The Rocking curve (Figure 7a) shows a difference of 3.6° between the maximum intensity of (008) reflection and the diffraction plane. This result confirms that the preferred orientation vector is around [1 0 16] because the angle

molar percentage of goethite (Figure 7b). This result shows that the preferential orienta‐ tion according to [001] is more important, as the initial proportion of goethite is greater. The variation of the orientation distributions as a function of the molar proportion of goe‐ thite is shown in Figure 8. Obviously, these conclusions might be directly applied to the

spatial distribution of the easy axis of the hexagonal BaM platelets in each sample.

easy axis of magnetization [001]. Thus, for the determination of the factor r with a direc‐ tion [hkl] different than [001], the relation P(θ) with ω the angle between [001] and [hkl] becomes: Pሺθሻ = ቆrଶcosଶሺθ − ωሻ + sinଶሺθ − ωሻ <sup>r</sup> <sup>ቇ</sup> ିଷ <sup>ଶ</sup> (2) Rietveld analyses are used to extract the r factor for each sample, with the vector [1 0 Rietveld analyses are used to extract the r factor for each sample, with the vector [1 0 16] to define the preferred orientation. The Rocking curve (Figure 7a) shows a difference of 3.6◦ between the maximum intensity of (008) reflection and the diffraction plane. This result confirms that the preferred orientation vector is around [1 0 16] because the angle between [1 0 16] and [0 0 1] is 3.56◦ . The r-factor decreases linearly as a function of the molar percentage of goethite (Figure 7b). This result shows that the preferential orientation according to [001] is more important, as the initial proportion of goethite is greater. The variation of the orientation distributions as a function of the molar proportion of goethite is shown in Figure 8. Obviously, these conclusions might be directly applied to the spatial distribution of the easy axis of the hexagonal BaM platelets in each sample.

*Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 9 of 19

**Figure 7.** (**a**) Rocking curve for the intensity of the (008) Bragg diffraction pic. (**b**) Evolution of the March–Dollase factor as a function of mole percentage of goethite. **Figure 7.** (**a**) Rocking curve for the intensity of the (008) Bragg diffraction pic. (**b**) Evolution of the March–Dollase factor as a function of mole percentage of goethite. March–Dollase factor as a function of mole percentage of goethite.

**Figure 8.** Probability density of crystallite orientations, from March–Dollase model. **Figure 8.** Probability density of crystallite orientations, from March–Dollase model.

#### **Figure 8.** Probability density of crystallite orientations, from March–Dollase model. *3.5. Experimental Investigations of the Magnetocrystalline Anisotropy*

*3.5. Experimental Investigations of the Magnetocrystalline Anisotropy 3.5. Experimental Investigations of the Magnetocrystalline Anisotropy*  In the case of a hexagonal crystal, and omitting higher terms than the second order, In the case of a hexagonal crystal, and omitting higher terms than the second order, the magnetocrystalline anisotropy energy is expressed as [2]:

$$E\_{\rm K}(\theta\_{\rm m}) = K\_1 \sin^2(\theta\_{\rm m}) + K\_2 \sin^4(\theta\_{\rm m}) \tag{3}$$

the magnetocrystalline anisotropy energy is expressed as [2]: ሺθ୫ሻ = ଵsinଶሺθ୫ሻ + ଶsinସሺθ୫ሻ (3) ሺθ୫ሻ = ଵsinଶሺθ୫ሻ + ଶsinସሺθ୫ሻ (3) where *K*<sup>1</sup> and *K*<sup>2</sup> are magnetic anisotropy constants and θ<sup>m</sup> is the angle between the magnetization and the c-axis (easy axis of magnetization.)

where *K*1 and *K*2 are magnetic anisotropy constants and θm is the angle between the mag‐ Then, the anisotropy field H<sup>K</sup> is given by [33]:

$$H\_K = \frac{\cdots \to \cdots \to \infty}{2K\_1 + 4K\_2} \tag{4}$$

Then, the anisotropy field HK is given by [33]: <sup>=</sup> ଶభାସమ µబெೄ (4) <sup>=</sup> ଶభାସమ µబெೄ (4) For non‐substituted BaM, *K*2 = 0. The value of *K*1 is positive, equal to 5.4 105 erg/g [34], For non-substituted BaM, *K*<sup>2</sup> = 0. The value of *K*<sup>1</sup> is positive, equal to 5.4 10<sup>5</sup> erg/g [34], meaning that the easy axis of magnetization is parallel to the hexagonal c-axis. The uniaxial anisotropy field *H<sup>K</sup>* of BaM is typically in the 1320–1360 kA/m or 16.5–17 kOe range [10,35].

For non‐substituted BaM, *K*2 = 0. The value of *K*1 is positive, equal to 5.4 105 erg/g [34], meaning that the easy axis of magnetization is parallel to the hexagonal c‐axis. The uniax‐ ial anisotropy field *HK* of BaM is typically in the 1320–1360 kA/m or 16.5–17 kOe range

meaning that the easy axis of magnetization is parallel to the hexagonal c‐axis. The uniax‐ ial anisotropy field *HK* of BaM is typically in the 1320–1360 kA/m or 16.5–17 kOe range

[10,35].

[10,35].

#### *3.6. Microwave Measurement Method for Determining Anisotropy* = 2.8 MHz/kOe = 1.7608 × 1011 s−1T−1) and the magnetocrystalline anisotropy field, respec‐

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*3.6. Microwave Measurement Method for Determining Anisotropy* 

A successful way of determining the magnetocrystalline anisotropy field of a magnetic material involves the measurement of its dynamic permeability in the high-frequency range. Thus, it is established that the maximum of the imaginary part µ" of the magnetic permeability µ (µ = µ'-jµ") occurs at a frequency *f<sup>R</sup>* which, in the absence of demagnetizing effects, is written *f<sup>R</sup>* = *γHK*, with *γ* and *H<sup>K</sup>* being the gyromagnetic ratio (*<sup>γ</sup>* = 2.8 MHz/kOe = 1.7608 <sup>×</sup> <sup>10</sup><sup>11</sup> <sup>s</sup> <sup>−</sup>1T −1 ) and the magnetocrystalline anisotropy field, respectively. tively. The broadband complex permeability of the BAM‐0 sample was measured in the fre‐ quency band [10 GHz–60 GHz] by the transmission/reflection method using a Rohde and Schwarz ZVA67 vector network analyzer. The demagnetized sample was placed on the top of a high‐frequency microstrip line to measure the transmission S21 and reflection S11 parameters. First, the effective permeability of the structure (microstrip line and sample)

A successful way of determining the magnetocrystalline anisotropy field of a mag‐

netic material involves the measurement of its dynamic permeability in the high‐fre‐ quency range. Thus, it is established that the maximum of the imaginary part µ'' of the magnetic permeability µ (µ = µ'‐jµ'') occurs at a frequency *fR* which, in the absence of demagnetizing effects, is written *fR* = *γHK*, with *γ* and *HK* being the gyromagnetic ratio (*γ*

The broadband complex permeability of the BAM-0 sample was measured in the frequency band [10 GHz–60 GHz] by the transmission/reflection method using a Rohde and Schwarz ZVA67 vector network analyzer. The demagnetized sample was placed on the top of a high-frequency microstrip line to measure the transmission S21 and reflection S11 parameters. First, the effective permeability of the structure (microstrip line and sample) was calculated from the measured S-parameters using a specially written Matlab code based on the NRW equations [36]. Then, conformal mapping applied to permeability [37,38] was used to extract the intrinsic permeability of the sample from the effective multilayers structure. Finally, the anisotropy field *H<sup>K</sup>* of the hexaferrite was deduced from the resonant frequency determined by the maximum of the imaginary part µ" of the intrinsic permeability. The frequency evolution of µ"(*f*) normalized to its maximum is shown in Figure 9. The maximum of µ"(f) occurs for *f<sup>R</sup>* = 46.6 GHz, to which corresponds *H<sup>K</sup>* = 1330 kA/m (i.e., 16.6 kOe). This result agrees with the value of the anisotropy field *H<sup>K</sup>* of BaM ferrites, which is close to 1360 kA/m (i.e., 17 kOe). However, a distribution of switching fields inevitably appears in a given assembly of particles with shapes, sizes, morphological, and structural defects that vary from one particle to another, and then the anisotropy field thus determined should correspond to the higher value of the anisotropy field distribution *f*(*HK*). was calculated from the measured S‐parameters using a specially written Matlab code based on the NRW equations [36]. Then, conformal mapping applied to permeability [37,38] was used to extract the intrinsic permeability of the sample from the effective mul‐ tilayers structure. Finally, the anisotropy field *HK* of the hexaferrite was deduced from the resonant frequency determined by the maximum of the imaginary part µ" of the intrinsic permeability. The frequency evolution of µ''(*f*) normalized to its maximum is shown in Figure 9. The maximum of µ''(f) occurs for *fR* = 46.6 GHz, to which corresponds *HK* = 1330 kA/m (i.e., 16.6 kOe). This result agrees with the value of the anisotropy field *HK* of BaM ferrites, which is close to 1360 kA/m (i.e., 17 kOe). However, a distribution of switching fields inevitably appears in a given assembly of particles with shapes, sizes, morphologi‐ cal, and structural defects that vary from one particle to another, and then the anisotropy field thus determined should correspond to the higher value of the anisotropy field dis‐ tribution *f*(*HK*).

**Figure 9***.* Frequency evolution of the normalized intrinsic permeability of sample BAM‐0. **Figure 9.** Frequency evolution of the normalized intrinsic permeability of sample BAM-0.

#### *3.7. Isothermal Remanence Measurements*

*3.7. Isothermal Remanence Measurements*  In order to clarify this point, we discriminated the anisotropy field distribution *f*(*HK*) from the switching field distribution. It was established that by measuring the initial rem‐ anence curve *MR*(*H*) a switching field distribution could be calculated [39], from which In order to clarify this point, we discriminated the anisotropy field distribution *f*(*HK*) from the switching field distribution. It was established that by measuring the initial remanence curve *MR*(*H*) a switching field distribution could be calculated [39], from which the *HK*-distribution function *f*(*HK*) could be obtained [39]. The switching field distribution was similar to the anisotropy field distribution in the situation where the particles diameter

the *HK*‐distribution function *f*(*HK*) could be obtained [39]. The switching field distribution was similar to the anisotropy field distribution in the situation where the particles diam‐

was below the critical single-domain size DC. For BaM, D<sup>C</sup> is about 0.5–1 µm [10], which is much larger than the typical diameter observed in this study. Therefore, it is legitimate to admit that SFD and *f*(*HK*) are similar. In the present study, the distribution *f*(*HK*) was obtained by the isothermal remanence measurement (IRM). The IRM measures the remanent magnetization as a function of an increasing magnetizing field starting from a demagnetized state. After demagnetizing the sample, a small field was applied and subsequently removed, after which the remanent magnetization was measured. This magnetization is plotted against the previously applied field. Next, a somewhat larger field was applied and subsequently removed, after which the next remanent magnetization was measured. The resulting curve *MR*(*H*) looks comparable to the virgin curve. For a random assembly of particles with uniaxial anisotropy, the anisotropy field distribution can be obtained by differentiating the reduced IRM curve (*mR(H*) = *MR*(*H*)/*M*∞, where *M*<sup>∞</sup> is for the maximum remanent magnetization value) after considering the effects of demagnetizing fields. The distribution function *f*(*HK*) is then obtained by readjusting the field scale, and where *H<sup>i</sup>* is the internal magnetic field: *f*(*HK*) was obtained by the isothermal remanence measurement (IRM). The IRM measures the remanent magnetization as a function of an increasing magnetizing field starting from a demagnetized state. After demagnetizing the sample, a small field was applied and sub‐ sequently removed, after which the remanent magnetization was measured. This magnet‐ ization is plotted against the previously applied field. Next, a somewhat larger field was applied and subsequently removed, after which the next remanent magnetization was measured. The resulting curve *MR*(*H*) looks comparable to the virgin curve. For a random assembly of particles with uniaxial anisotropy, the anisotropy field distribution can be obtained by differentiating the reduced IRM curve (*mR(H*) = *MR*(*H*)/*M*∞, where *M*∞ is for the maximum remanent magnetization value) after considering the effects of demagnet‐ izing fields. The distribution function *f*(*HK*) is then obtained by readjusting the field scale, and where *Hi*is the internal magnetic field: ሺሻ = ቈோሺሻ 

which is much larger than the typical diameter observed in this study. Therefore, it is legitimate to admit that SFD and *f*(*HK*) are similar. In the present study, the distribution

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$$f(H\_K) = \left[\frac{d m\_R(H\_i)}{d H\_i}\right]\_{H\_i = \frac{H\_K}{2}}\tag{5}$$

(5)

Figure 10 shows *f*(*HK*) for the less-textured sample (BaM-0). In the higher fields, the distribution decreases slowly until the value ( *HK*)*Max* = 1370 kA/m (i.e. 16.6 kOe) is reached (triangle symbol in Figure 10). The behavior in the high fields is still unclear; however, it could be ascribed to dipolar interactions between grains. Figure 10 shows *f*(*HK*) for the less‐textured sample (BaM‐0). In the higher fields, the distribution decreases slowly until the value ሺሻெ௫ = 1370 kA/m ሺ. . 16.6 kOeሻ is reached (triangle symbol in Figure 10). The behavior in the high fields is still unclear; however, it could be ascribed to dipolar interactions between grains.

**Figure 10.** Anisotropy field distribution *f*(*HK*) of the sample BaM‐0. The triangle shows the value of *HK* as measured by using microwave experiment (see main text). Inset: the frequency variation of the imaginary part of permeability (µ'') shows a maximum at frequency *fR* = 46.6 GHz. To this value of *fR* corresponds the maximum value *HK* of the anisotropy field distribution (both are marked by a triangle), the relationship beween *fR* and *HK* being *fR* = *γHK*. **Figure 10.** Anisotropy field distribution *f*(*HK*) of the sample BaM-0. The triangle shows the value of *HK* as measured by using microwave experiment (see main text). Inset: the frequency variation of the imaginary part of permeability (µ") shows a maximum at frequency *fR* = 46.6 GHz. To this value of *fR* corresponds the maximum value *H<sup>K</sup>* of the anisotropy field distribution (both are marked by a triangle), the relationship beween *fR* and *HK* being *fR* = *γHK*.

The anisotropy field value obtained from microstrip experiments, ሺሻெ௫ = 16.6 kOe, is very close to the one for which *f*(*HK*) cancels. While the IRM measurements give the anisotropy field distribution, the microstrip line measurement method provides the maximum value of anisotropy field, which corresponds to the field to be applied to complete the coherent spin rotation in the Stoner and Wolfarth model [40]. The anisotropy field value obtained from microstrip experiments, (*HK*)*Max* = 16.6 kOe, is very close to the one for which *f*(*HK*) cancels. While the IRM measurements give the anisotropy field distribution, the microstrip line measurement method provides the maximum value of anisotropy field, which corresponds to the field to be applied to complete the coherent spin rotation in the Stoner and Wolfarth model [40].

#### *3.8. The First Magnetization Curve and the Law of Approach to Saturation*

*3.8. The First Magnetization Curve and the Law of Approach to Saturation*  The first magnetization curve of an isotropic polycrystalline material, as it ap‐ proaches magnetic saturation, is commonly described using the law of approach to satu‐ The first magnetization curve of an isotropic polycrystalline material, as it approaches magnetic saturation, is commonly described using the law of approach to saturation, which expresses [2,41];

$$M(H) = M\_{\mathbb{S}} \left( 1 - \frac{a}{H\_i} - \frac{b}{H\_i^2} \right) + \text{x}\_P H\_i \tag{6}$$

*M<sup>S</sup>* is the saturation magnetization and H<sup>i</sup> is the internal field (i.e., the applied field *H*<sup>0</sup> corrected from the demagnetizing field: *H<sup>i</sup>* = *H*0-*H<sup>d</sup>* ). The term *a*/*H*, which results from the presence of inclusions and defects, must vanish at high enough magnetic fields. The last term *χ<sup>P</sup>* is a small high-field susceptibility, called paraprocess. It is due to highfield band splitting, and can be neglected below moderately applied fields intensities [2]. The *b*/*H*<sup>2</sup> term arises from the magnetic moments reorientation when the anisotropy axis is misaligned with the applied field. It is directly related to the magnetocrystalline anisotropy (even *H<sup>K</sup>* or the first anisotropy constant *K*1). Then, the following relation (1) is commonly used to derived *M<sup>S</sup>* and the anisotropy field for an isotropic distribution of magnetic moments which can change direction only by rotating against the magnetic anisotropy [42,43]:

$$M(H) = M\_{\mathbb{S}} \left( 1 - \frac{b}{H^2} \right) \tag{7}$$

If such a polycrystalline ferromagnet consists of randomly oriented, single-domain crystallites having uniaxial anisotropy, the coefficient b writes:

$$b = \frac{H\_k^2}{15} \tag{8}$$

The variation of *M* as a function of 1/*H*<sup>2</sup> being linear for field values close to saturation therefore allows to determine both *MS*, and *HK*, as well as *K*<sup>1</sup> (if the constant *K*<sup>2</sup> is negligible compared to *K*1.)

The LAS can then be used to determine the magnetocrystalline anisotropy constant *K*<sup>1</sup> and the saturation magnetization *MS*, for a random distribution of uniaxial crystals, from (7):

$$M(H) = M\_S \left( 1 - \frac{4}{15} \frac{K\_1^2}{\mu\_0 M\_S^2} \frac{1}{H^2} \right) \tag{9}$$

However, the LAS as such does not apply when the spatial distribution of the particles is no longer random. This situation arises in the case of polycrystalline materials intended for the production of permanent magnets. In order to quantify more precisely the expected modifications to be applied to the LAS regarding the amount of granular texturization in the partly oriented hexaferrites used in this study, we propose to introduce in relation (9) an additional factor, which is intended to take into account the degree of disorientation of the particles, itself being a function of the initial ratio Fe2O3:FeO(OH).

To the best of our knowledge, the only work published in this area comes from Celasco et al. [44]. In [44], the saturation approach of polycrystalline magnetic materials made of randomly oriented, single-domain crystallites with cubic anisotropy and a preferential orientation was studied theoretically, and an adapted saturation-approach law was proposed. The orientation of the particles was described by an angular distribution of the axes of easy magnetization carried by the grains. The authors showed that the LAS writes:

$$M = M\_S \left( 1 - \frac{A\_{cub}(K\_1, K\_2, \tau)}{\mu\_0 \times M\_S^2} \times \frac{1}{H^2} \right) \tag{10}$$

where τ quantifies the orientation of the axes of easy magnetization. Following [45], the influence of the grain dispersion on the saturation-approach law is fully contained in the *Acub*(*K*1, *K*2, *τ*) factor. In the case of a random dispersion of grains the function *Acub*(*K*1, *K*2, *τ*) simply reduces to the usual expression for a cubic anisotropy, and to the first order [45]:

$$A\_{cub}(\mathbf{K}\_1, \mathbf{K}\_2, \tau) = \frac{8}{105} \mathbf{K}\_1^2 \tag{11}$$

However, there is no equivalent expression in the published literature for a LAS that could be used in the case where the crystallites exhibit uniaxial anisotropy. Therefore, we have adopted an experimental approach, leading to the determination of a function *Auni*(*K*1, *τ*) to the case of polycrystalline magnetic materials consisting of BaM grains of

uniaxial anisotropy and with preferential spatial orientation (*K*<sup>2</sup> = 0 for unsubstituted BaM). Hence, we assumed that the LAS can be written in a similar way as in [44]: BaM). Hence, we assumed that the LAS can be written in a similar way as in [44]: =ௌ ൬1 − ೠሺభ,ఘሻ ଵ

have adopted an experimental approach, leading to the determination of a function ௨ሺଵ, ሻ to the case of polycrystalline magnetic materials consisting of BaM grains of uniaxial anisotropy and with preferential spatial orientation (*K*2 =0 for unsubstituted

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*M* = *M<sup>S</sup>* 1 − *Auni*(*K*1, *ρ*) *µ*0*M*<sup>2</sup> *S* 1 *H*<sup>2</sup> ! (12) ఓబெೄ మ ு<sup>మ</sup>൰ (12) Our purpose is to find out the experimental variation of the factor ௨ሺଵ, ሻ, where

Our purpose is to find out the experimental variation of the factor *Auni*(*K*1, *ρ*), where *\$* is a parameter intended to take the grade of texturization into account. We made the reasonable assumption that the anisotropy field *HK*, as well as the anisotropy constant *K*1, are independent of the spatial dispersion of the platelets: the value of *H<sup>K</sup>* was supposed to be the one given in section IV: *H<sup>K</sup>* = 16.6 kOe. The value of *K*<sup>1</sup> will be derived further from Equation (4), with *K*<sup>2</sup> = 0. ρ is a parameter intended to take the grade of texturization into account. We made the reasonable assumption that the anisotropy field *HK*, as well as the anisotropy constant *K*1, are independent of the spatial dispersion of the platelets: the value of *HK* was supposed to be the one given in section IV: *HK* = 16.6 kOe. The value of *K*1 will be derived further from Equation (4), with *K*2 = 0. The direction of the normal ሬ⃗ to the basal surface of a sample defines its C axis. A

The direction of the normal <sup>→</sup> *n* to the basal surface of a sample defines its C axis. A magnetic field *H*<sup>0</sup> is applied parallel to the C axis. The magnetization M is measured along this direction. The demagnetizing effects were taken into account, the internal field *H<sup>i</sup>* being obtained by the relation *H<sup>i</sup>* = *H*0-NZM, where N<sup>Z</sup> is the macroscopic demagnetizing field coefficient along the C axis. The value of N<sup>Z</sup> is fixed by the aspect ratio of the sample (thickness: diameter), as given in [22]. As the goethite content increases, the obtained hysteresis cycles evolve steadily from that characteristic of a random dispersion of uniaxial and monodomain particles for sample BaM-0 to that characteristic of a strongly self-polarized material for sample BaM-100 (Figure 11). For BaM-0, the hysteresis loops measured along the basal plane of the sample (<sup>→</sup> *n* direction) and perpendicular to <sup>→</sup> *n* are completely identical due to the isotropy of the sample, whereas for BaM-100, these hysteresis loops are characteristic of an anisotropic material. The LAS was applied to the first magnetization curves using the relation (12) in the range of internal fields between 1384 kA/m and 1000 kA/m, typically. magnetic field *H*0 is applied parallel to the C axis. The magnetization M is measured along this direction. The demagnetizing effects were taken into account, the internal field *Hi* be‐ ing obtained by the relation *Hi*=*H*0‐NZM, where NZ is the macroscopic demagnetizing field coefficient along the C axis. The value of NZ is fixed by the aspect ratio of the sample (thickness: diameter), as given in [22]. As the goethite content increases, the obtained hys‐ teresis cycles evolve steadily from that characteristic of a random dispersion of uniaxial and monodomain particles for sample BaM‐0 to that characteristic of a strongly self‐po‐ larized material for sample BaM‐100 (Figure 11). For BaM‐0, the hysteresis loops meas‐ ured along the basal plane of the sample (ሬ⃗ direction) and perpendicular to ሬ⃗ are com‐ pletely identical due to the isotropy of the sample, whereas for BaM‐100, these hysteresis loops are characteristic of an anisotropic material. The LAS was applied to the first mag‐ netization curves using the relation (12) in the range of internal fields between 1384 kA/m and 1000 kA/m, typically.

**Figure 11.** Hysteresis cycles measured for samples BaM‐0 (**left**) and BaM‐100 (**right**). Black symbols: ሬ⃗//ሬ⃗, open symbols: ሬ⃗ ⊥ ሬ⃗. The dashed lines in red are the first magnetization curves. **Figure 11.** Hysteresis cycles measured for samples BaM-0 (**left**) and BaM-100 (**right**). Black symbols: → *H*//<sup>→</sup> *n*, open symbols: → *H*⊥ → *n*. The dashed lines in red are the first magnetization curves.

The behavior of the measured magnetization M as a function of 1/*Hi* 2 is strongly linear in this range (Figure 12), which confirms that both the constant a and the susceptibility *χ<sup>p</sup>* of Equation (6) can be neglected in the high‐field domain. The data extracted from M(H) loops and the LAS are reported in Table 4. The behavior of the measured magnetization M as a function of 1/*H<sup>i</sup>* 2 is strongly linear in this range (Figure 12), which confirms that both the constant a and the susceptibility *χ<sup>p</sup>* of Equation (6) can be neglected in the high-field domain. The data extracted from M(H) loops and the LAS are reported in Table 4.

**Figure 12***.* Law of approach to saturation of some BaM samples. The determination coefficients R2 in M vs. 1/Hi2 linear relations are better than 0.999 in any case. **Figure 12.** Law of approach to saturation of some BaM samples. The determination coefficients R2 in M vs. 1/Hi2 linear relations are better than 0.999 in any case.

**Table 4***.* Data obtained from hysteresis loops and the law of approach to saturation. *MS* is the satu‐ ration magnetization, *MR*// and *MR*⊥ the remanent magnetizations measured along the easy axis and **Table 4.** Data obtained from hysteresis loops and the law of approach to saturation. *M<sup>S</sup>* is the saturation magnetization, *MR*// and *MR*<sup>⊥</sup> the remanent magnetizations measured along the easy axis and perpendicular to the easy axis, respectively. α<sup>50</sup> is the full width at half remanence measured in ARM. For *Auni*(*K*<sup>1</sup> ,*\$*), see Equation (12) and main text.


#### *3.9. Discussion*

*3.9. Discussion* 

BaM‐50 308 203 0.66 0.69 105 0.21 BaM‐60 311 229 0.74 0.64 101 0.19 BaM‐70 313 230 0.73 0.57 93 0.17 BaM‐80 312 237 0.76 0.54 89 0.16 The variation of the remanent magnetization *MR*///*M<sup>S</sup>* with the percentage of molar mass of goethite (Figure 13) attests the evolution of the texture of the samples from a random structure towards a state of ordered alignment of the easy axes. These results suggest that the actual angular dispersion of easy axis of magnetization (as described by *MR*///*M<sup>S</sup>* in Figure 13) is significantly larger than the angular dispersion of the crystal grains (Figure 8). This difference could be due to dipolar interactions between grains, which cannot be detected by XRD measurements.

BaM‐90 303 242 0.8 0.46 87 0.12

BaM‐100 299 238 0.81 0.40 70 0.1

The variation of the remanent magnetization *MR*///*MS* with the percentage of molar

mass of goethite (Figure 13) attests the evolution of the texture of the samples from a ran‐ dom structure towards a state of ordered alignment of the easy axes. These results suggest that the actual angular dispersion of easy axis of magnetization (as described by *MR*///*MS* in Figure 13) is significantly larger than the angular dispersion of the crystal grains (Figure 8). This difference could be due to dipolar interactions between grains, which cannot be

detected by XRD measurements.

**300**

**Ms**

**350**

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**Figure 13***.* Variations of the saturation magnetization (MS) and reduced‐remanence magnetization (*MR*///*MS*) with the molar percentage of goethite. **Figure 13.** Variations of the saturation magnetization (MS) and reduced-remanence magnetization (*MR*///*MS*) with the molar percentage of goethite. From these fits, the value of *Auni*(*K*1,ρ)/*K*12 was determined for each sample (Table 4). The choice of the parameter for quantifying the spatial dispersion of the axes can be made

**0,8**

**0,85**

**0.85**

From these fits, the value of *Auni*(*K*1,ρ)/*K*12 was determined for each sample (Table 4). The choice of the parameter for quantifying the spatial dispersion of the axes can be made among the following quantities: (a) the angular dispersion of the axes of easy magnetiza‐ tion, as determined in X‐ray diffraction; (b) the ratio *MR*⊥⁄*MR*∕∕, where *MR*∕∕ and *MR*⊥ are the remanent magnetization measured perpendicular and parallel to the sample plane (i.e., presumably along the easy direction and in the magnetic hard plane, respectively) [4]; (c) the width at half height of the angular remanence measurement (ARM). The ARM measures the remanent magnetization as a function of the angle. This is achieved by turn‐ ing the sample to a certain angle, applying the maximum field, reducing the field to zero, and measuring the resulting moment. The zero crossing marks the hard axis angle. The narrower the transition, the better defined the anisotropy direction is. By taking the de‐ From these fits, the value of *Auni*(*K*1,*\$*)/*K*<sup>1</sup> <sup>2</sup> was determined for each sample (Table 4). The choice of the parameter for quantifying the spatial dispersion of the axes can be made among the following quantities: (a) the angular dispersion of the axes of easy magnetization, as determined in X-ray diffraction; (b) the ratio *MR*⊥⁄*MR*⁄⁄, where *MR*⁄⁄ and *MR*<sup>⊥</sup> are the remanent magnetization measured perpendicular and parallel to the sample plane (i.e., presumably along the easy direction and in the magnetic hard plane, respectively) [4]; (c) the width at half height of the angular remanence measurement (ARM). The ARM measures the remanent magnetization as a function of the angle. This is achieved by turning the sample to a certain angle, applying the maximum field, reducing the field to zero, and measuring the resulting moment. The zero crossing marks the hard axis angle. The narrower the transition, the better defined the anisotropy direction is. By taking the derivative of this curve, a spread in the easy axis directions can be obtained (Figure 14). It is convenient to characterize the data by the full width at half-remanence α<sup>50</sup> (see Table 4). among the following quantities: (a) the angular dispersion of the axes of easy magnetiza‐ tion, as determined in X‐ray diffraction; (b) the ratio *MR*⊥⁄*MR*∕∕, where *MR*∕∕ and *MR*⊥ are the remanent magnetization measured perpendicular and parallel to the sample plane (i.e., presumably along the easy direction and in the magnetic hard plane, respectively) [4]; (c) the width at half height of the angular remanence measurement (ARM). The ARM measures the remanent magnetization as a function of the angle. This is achieved by turn‐ ing the sample to a certain angle, applying the maximum field, reducing the field to zero, and measuring the resulting moment. The zero crossing marks the hard axis angle. The narrower the transition, the better defined the anisotropy direction is. By taking the de‐ rivative of this curve, a spread in the easy axis directions can be obtained (Figure 14). It is convenient to characterize the data by the full width at half‐remanence α50 (see Table 4).

**Figure 14***.* Measured angular dispersion and full width at half‐remanence α50 for BaM‐0 (open cir‐ cles) and BaM‐100 (full circles). **Figure 14.** Measured angular dispersion and full width at half-remanence α<sup>50</sup> for BaM-0 (open circles) and BaM-100 (full circles).

**Figure 14***.* Measured angular dispersion and full width at half‐remanence α50 for BaM‐0 (open cir‐ cles) and BaM‐100 (full circles). In [44], the angle between the cubic axis that forms the smallest angle with the direc‐ In [44], the angle between the cubic axis that forms the smallest angle with the direc‐ tion of the applied field is chosen as to represent the grain‐dispersion parameter τ (Equa‐ tion (10)). There is a strong correlation between the angular dispersion of the axes of easy magnetization and both the ratio *MR*⊥⁄*MR*∕∕ on one hand, and with the width at half height In [44], the angle between the cubic axis that forms the smallest angle with the direction of the applied field is chosen as to represent the grain-dispersion parameter τ (Equation (10)). There is a strong correlation between the angular dispersion of the axes of easy magnetization and both the ratio *MR*⊥⁄*MR*⁄⁄ on one hand, and with the width at half height α<sup>50</sup> of the ARM, on the other hand (Figure 15).

tion of the applied field is chosen as to represent the grain‐dispersion parameter τ (Equa‐ tion (10)). There is a strong correlation between the angular dispersion of the axes of easy

α50 of the ARM, on the other hand (Figure 15).

α50 of the ARM, on the other hand (Figure 15).

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**Figure 15***.* Correlation between 2θ, *MR*<sup>⊥</sup>⁄*MR*∕∕ (open symbols) and ARM (full symbols). **Figure 15.** Correlation between 2θ, *M<sup>R</sup>* ⊥⁄*M<sup>R</sup>* ⁄⁄ (open symbols) and ARM (full symbols). The variation of *Auni*(*K*1,ρ)/K12 is shown in Figure 16. Two points are added to the

Therefore, we admitted that these two parameters have a common significance, and we chose, as a parameter for quantifying the orientation of the easy axes, the half‐height Therefore, we admitted that these two parameters have a common significance, and we chose, as a parameter for quantifying the orientation of the easy axes, the half-height width of the ARM. experimental data: one corresponding to a monocrystal, for which *Auni* = 0, and the other corresponding to a polycrystal with an ideal random distribution of easy axes, for which

width of the ARM. The variation of *Auni*(*K*1,ρ)/K12 is shown in Figure 16. Two points are added to the experimental data: one corresponding to a monocrystal, for which *Auni* = 0, and the other corresponding to a polycrystal with an ideal random distribution of easy axes, for which *Auni* = 4/15. Interestingly, these variations are not linear and have a maximum. This behav‐ ior is also reported on in [44] with regard to the calculated ௨ሺଵ, ଶ, ሻ/ଵ presented as a real effect and not due to the particular distribution function used to de‐ scribe the dispersion of the grains in the polycrystal. As seen in Figure 16, it is obvious that the law of approach to saturation for isotropic crystals given by relation (9) is no longer suitable for textured crystals, even if the texture is weak. Instead, it is necessary to The variation of *Auni*(*K*1,*\$*)/K<sup>1</sup> 2 is shown in Figure 16. Two points are added to the experimental data: one corresponding to a monocrystal, for which *Auni* = 0, and the other corresponding to a polycrystal with an ideal random distribution of easy axes, for which *Auni* = 4/15. Interestingly, these variations are not linear and have a maximum. This behavior is also reported on in [44] with regard to the calculated *Acub*(*K*1, *K*2, *τ*)/*K* 2 1 . This was presented as a real effect and not due to the particular distribution function used to describe the dispersion of the grains in the polycrystal. As seen in Figure 16, it is obvious that the law of approach to saturation for isotropic crystals given by relation (9) is no longer suitable for textured crystals, even if the texture is weak. Instead, it is necessary to use a LAS of the same type as in relation (12), where the influence of the grain dispersion on the law of approach to saturation is fully contained in the *Auni*(*K*1,ρ) factor. In this present study, we found that once the constant *K*<sup>1</sup> is determined, the angular grain-dispersion can be deduced from saturation-approach measurements. *Auni* = 4/15. Interestingly, these variations are not linear and have a maximum. This behav‐ ior is also reported on in [44] with regard to the calculated ௨ሺଵ, ଶ, ሻ/ଵ presented as a real effect and not due to the particular distribution function used to de‐ scribe the dispersion of the grains in the polycrystal. As seen in Figure 16, it is obvious that the law of approach to saturation for isotropic crystals given by relation (9) is no longer suitable for textured crystals, even if the texture is weak. Instead, it is necessary to use a LAS of the same type as in relation (12), where the influence of the grain dispersion on the law of approach to saturation is fully contained in the *Auni*(*K*1,ρ) factor. In this pre‐ sent study, we found that once the constant *K*1 is determined, the angular grain‐dispersion can be deduced from saturation‐approach measurements.

<sup>ଶ</sup>. This was

<sup>ଶ</sup>. This was

**0,05 monocrystal 0.05 Figure 16.** Variation of ௨ሺଵ, ሻ/ଵ <sup>ଶ</sup> as a function of the ARM half‐height width (the full line is only a guide for the eyes). **Figure 16.** Variation of *Auni*(*K*<sup>1</sup> , *ρ*)/*K* 2 1 as a function of the ARM half-height width (the full line is only a guide for the eyes).

**0 50 100 150 200**

**ARM half-height width (degree)**

<sup>ଶ</sup> as a function of the ARM half‐height width (the full line is

BaM samples with different magnetic texturing grades are manufactured by con‐

trolled topotactical reaction by using hematite and goethite particles. It is demonstrated that the hematite: goethite ratio drives the texturization of the samples. The novelty of this study lies in the optimization of the aspect ratio of the goethite crystallites in view of an improved BaM texturization. We show that the optimization of the morphology of goe‐ thite crystallites improves the BaM particles' orientation and stacking. The salient result of this study is the demonstration that by using a single cold compression process and a

that the hematite: goethite ratio drives the texturization of the samples. The novelty of this study lies in the optimization of the aspect ratio of the goethite crystallites in view of an improved BaM texturization. We show that the optimization of the morphology of goe‐ thite crystallites improves the BaM particles' orientation and stacking. The salient result of this study is the demonstration that by using a single cold compression process and a

only a guide for the eyes).

**4. Conclusions** 

**0**

**4. Conclusions** 

width of the ARM.

**0,8**

**0.8**

**1**

**1,2**

**1.2**

**0**

#### **4. Conclusions**

BaM samples with different magnetic texturing grades are manufactured by controlled topotactical reaction by using hematite and goethite particles. It is demonstrated that the hematite: goethite ratio drives the texturization of the samples. The novelty of this study lies in the optimization of the aspect ratio of the goethite crystallites in view of an improved BaM texturization. We show that the optimization of the morphology of goethite crystallites improves the BaM particles' orientation and stacking. The salient result of this study is the demonstration that by using a single cold compression process and a heat treatment, we can organize BaM particles stacking, which increases with the value of the aspect ratio of the goethite crystallites. The Rietveld refinements of powder diffractograms clearly revealed a particles-stacking enhancement, which is dependent not only of the hematite: goethite ratio but also of the optimal aspect ratio of goethite crystallites. This optimization resulted in a significant improvement of the remanent magnetization value, increasing it to 0.82 compared with the most recent literature. Additionally, we expect in the near future to further improve this value by optimizing the heat treatment after compaction. Based on this study, BaM materials are further manufactured with a controlled magnetic texture; therefore, they are partly self-polarized. They show a reduced-remanence magnetization *MR*/*M<sup>S</sup>* varying from 0.5 to 0.81, while the angular dispersion of the BaM particles' easy axis of magnetization varies from 60◦ to 10◦ . The magnetocrystalline anisotropy field was measured: microwave measurements provided its maximum value, while its distribution function is obtained from IRM experiments. A law of approach to saturation was proposed and adapted to the case of uniaxial polycrystalline materials for which the particles stacking is only partial. In this law, the influence of the grain dispersion on the saturation approach is fully contained in an additional factor *Auni*(*K*1,*\$*). The experimental values of *Auni*(*K*1,*\$*) compare well with numerical data from the single study on this topic. It is suggested that by using the proposed law once the constant K<sup>1</sup> is determined, the angular grain-dispersion can be deduced from saturation-approach measurements.

**Author Contributions:** A.H. has carried out the synthesis and the structural characterizations of the samples, he has contributed to the writing of the paragraphs dealing with the chemical parts and more generally to the review and editing of this research article. He has also contributed to the conceptualization and analysis of the materials. A.C. has performed the microwave measurements, and he has contributed to the writing of the paragraphs dealing with microwave measurements and the law of approach to saturation, as well as to the review of the article. J.-L.M. is a supervisor of the research project, supporting the work reported in this article. He has contributed to the conceptualization, methodology, and review of the work, he performed the magnetic measurements, and contributed to the writing of the associated paragraphs. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is partially supported by a public grant overseen by the French National Research Agency (ANR-20-ASTR-0010, CONTACT project).

**Institutional Review Board Statement:** No ethical approval required.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing is not applicable to this article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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### *Article* **Shielding Effectiveness Measurement Method for Planar Nanomaterial Samples Based on CNT Materials up to 18 GHz**

**Andrea Amaro 1,\* , Adrian Suarez <sup>1</sup> , Jose Torres <sup>1</sup> , Pedro A. Martinez <sup>1</sup> , Roberto Herraiz <sup>1</sup> , Antonio Alcarria <sup>2</sup> , Adolfo Benedito <sup>3</sup> , Rocio Ruiz <sup>3</sup> , Pedro Galvez <sup>3</sup> and Antonio Penades <sup>3</sup>**


**Abstract:** The study and measurement of the shielding effectiveness (SE) of planar materials is required to predict the suitability of a certain material to form an enclosed electromagnetic shield. One of the most widely used standards for measuring the SE of planar materials is ASMT D4935-18. It is based on a coaxial sample holder (CSH) that operates up to 1.5 GHz. Due to this standard's frequency limitations, new variants with higher frequency limits have been developed by decreasing the size of the CSH conductors and the samples. However, this method and its high-frequency variants require two types of samples with very specific geometries and sizes. This method is unsuitable for certain types of nanomaterials due to their complex mechanization at such undersized scales. This contribution proposes an alternative SE measurement method based on an absorber box that mitigates the problems presented by the ASTM D4935-18 standard. The SE of rigid nanomaterial samples based on several concentrations of multi-walled carbon nanotubes (MWCNT) and two different fiber reinforcements have been obtained.

**Keywords:** shielding effectiveness (SE); nanomaterials; absorber box; electromagnetic compatibility (EMC)

#### **1. Introduction**

The fast-paced advancements in electronic devices, information technology, wearable devices, and 5G technology have significantly increased electromagnetic interference (EMI) and radiation pollution [1]. This has required developing new materials with advanced shielding capabilities to reduce the effects of EMI. Developing this kind of material aims to increase the security of sensitive devices or systems that can be susceptible to EMI. Moreover, new advanced materials must ensure the protection of human health to reduce the risk of problems derived from exposure to electromagnetic radiation. Consequently, there is a high demand for advanced materials that can significantly address the challenges posed by EMI.

The investigation of lightweight EMI shielding materials will allow the possibility of increasing safety in 5G communications. When it comes to shielding materials, one of the most determining parameters for the application of the material is shielding effectiveness (SE). The SE indicates the attenuation intensity experimented by an electromagnetic wave traveling through a medium, A, after interacting with a medium, B (shield).

Magnetic materials, which are the main ones responsible for magnetic losses, achieve electromagnetic wave (EMW) absorption through magnetic hysteresis loss, eddy current effects, and ferromagnetic resonance [2–4]. Ferrites are widely used as EMW absorbers due to their high magnetic permeability, saturation magnetization (Ms), and resistivity (Ω), as well as a significant flexibility that allows the modification of their chemical composition to

**Citation:** Amaro, A.; Suarez, A.; Torres, J.; Martinez, P.A.; Herraiz, R.; Alcarria, A.; Benedito, A.; Ruiz, R.; Galvez, P.; Penades, A. Shielding Effectiveness Measurement Method for Planar Nanomaterial Samples Based on CNT Materials up to 18 GHz. *Magnetochemistry* **2023**, *9*, 114. https://doi.org/10.3390/ magnetochemistry9050114

Academic Editor: Cătălin-Daniel Constantinescu

Received: 24 March 2023 Revised: 21 April 2023 Accepted: 23 April 2023 Published: 25 April 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

adapt their magnetic properties to specific applications [5–7]. A recent study evaluated the efficiency of magnetostatic protection using nanostructured permalloy shielding coatings, demonstrating their potential for enhancing the shielding efficiency of electronic devices achieving a maximum SE value of 29 dB [8]. On the other hand, carbonaceous materials (e.g., carbon nanotubes (CNT), MXenes, or graphene foams) are excellent candidates for enhancing the absorption of the incident EMW due to their interesting electromagnetic and molecular properties, such as a unique combination of high conductivity and low density [9,10]. Specifically, multi-walled carbon nanotubes (MWCNTs) possess a shielding effect against EMI owing to their conductivity and unique internal porous structure and morphology. Consequently, they are an excellent and cost-effective choice for the primary material in composites. Moreover, the availability of specific heteroatomic groups in MWCNTs makes them suitable for convenient modification in subsequent applications. The combination of high conductivity and the presence of numerous internal interfaces because of either their porous structure or molecular arrangement enhances the dielectric loss through interfacial polarization. This also introduces an additional absorption mechanism based on multiple reflections, consisting of the continuous reflection of the incident wave in the different interfaces of the particle; thus, enhancing the attenuation of the EMW reflections [9,11]. The dispersion of carbonaceous particles in a polymer matrix, either thermoplastic or thermosetting, entails the improvement of the SE capabilities of the matrix [12] This allows the obtaining of specific compounds for lightweight applications overcoming the limitations of metals in terms of high density and corrosion susceptibility. Increasing the content of carbonaceous particles was found to have a positive effect on the SE of the resulting compound, achieving a maximum absorption of −38 dB in the X-band with 5% wt MWCNTs [13] and −66 dB for a polystyrene (PS) compound containing 20% wt MWCNT obtained via compression molding [14].

However, further increasing the content of carbon fillers also entails the increment of the compound viscosity and, therefore, hinders its processability, as noted in [15]. Fiberreinforced polymer (FRP) composite materials are characterized by their heterogeneity and anisotropy, which imparts to them the property of not exhibiting plastic deformation. FRP composites have found widespread use in a diverse range of contemporary applications, such as space, aviation, and automotive. Carbon-fiber-reinforced polymer (CFRP) and glass-fiber-reinforced polymer (GFRP) composite materials, among other fiber-reinforced materials, have gained increasing popularity due to their outstanding strength and low specific weight properties, leading them to replace conventional materials in various applications [16]. The use of CFRP is a prominent alternative to address the manufacturing problems derived from the use of particle-based composites [17]. Although recent studies have demonstrated the feasibility of using woven prepreg laminates to produce shielding effectiveness of more than 100 dB at low frequencies (<1 GHz) [18], the specific contribution of each type of shielding mechanism and the effect of the typology of the fibers at higher frequencies remains an open question. Suitable compositions and orientation of fibers made desired properties and functional characteristics of some GFRP composites equal to steel, had higher stiffness than aluminum, and the specific gravity was one-quarter of the steel [19]. Martinez et al. performed SE measurements in the frequency range of 300 kHz–8 GHz on GF composites in combination with different conductive materials, such as MWCNT and copper mesh, reporting an attenuation of approximately −40 dB up to 1.5 GHz for the copper mesh case [20]. Another study investigated the EMI shielding performance of carbon-nanomaterial-embedded fiber-reinforced polymer composites, revealing that the EMI shielding effectiveness of the composites was significantly improved with the addition of carbon nanomaterials. A sample with 3% CNT-GNP CFRP composition demonstrated an EMI shielding effectiveness higher than 15 dB [21].

To evaluate the suitability of these novel shielding materials for integration into a 5G system or other high-frequency applications, it is necessary to perform a characterization of their SE. Due to the wide variety of applications and shapes that a shielding material can adopt, this is generally characterized as a planar material. Depending on the frequency

range where the material will operate, there are various measurement methods to determine their shielding effectiveness. Currently, the most widely used standard for measuring the effectiveness of shielding of planar materials is the ASTM D4935-18 standard [22]. However, this standard is limited in frequency to 1.5 GHz, making it significantly restricted when considering 5G technology that operates at much higher frequencies. Alternative measurement methods based on free-space measurements, such as the IEEE 299 standard, are available but are hindered by the complexity of measurement due to the dimensions of the material sample required and the infrastructure required to perform the measurements [23]. Considering these limitations, alternative measurement methods derived from existing standards are currently being developed to address these issues.

In this work, the proposed measurement method is based on an absorbing box that overcomes the limitations that standard methods present. This method eliminates the sample size and mechanization issue, as it does not require a sample that is either too large or too small. Additionally, it makes it possible to measure in a frequency range that goes further than the region defined by the method presented in the ASTM D4935-18 standard. Furthermore, this method mitigates the problems of surrounding influences as measurements are taken within a controlled, absorbing environment. The results of EMI shielding effectiveness of the developed samples are reported in the frequency range of 700 MHz–18 GHz, covering the sub-6 GHz band of the 5G spectrum and part of the mmWave band.

This manuscript is organized as follows. First, Section 2 describes the manufacturing process of the five samples and their most relevant characteristics. Section 3 illustrates the main planar material measurement methods. This section also describes the current standard methods, their limitations, and the non-standardized measurement techniques. In this section, it is described the measurement setup to determine the SE of the different samples. Subsequently, the obtained results are presented in Section 4. This section also discusses the performance of the samples in the entire frequency range in terms of the attenuation that they provide. Finally, the main conclusions obtained in this research are summarized in Section 5.

#### **2. Material Characterization**

#### *2.1. Material Selection*

Before thermoplastics were extended, thermosets were widely used for various applications. However, as the industry evolves, thermosets have some serious limitations. When heating a thermoset once, it becomes irreversibly hardened when cured due to heating. Once cured, a thermoset plastic cannot be modified in shape by applying heat or pressure because the curing process has set a permanent chemical bond. The only way to break that chemical bond is by exposing it to a high-temperature source where the thermoset plastic is burned off. Hence the recyclability is zero compared to thermoplastic polymers, which can be repeatedly heated and remolded into desired shapes or forms [24].

Acrylonitrile butadiene styrene (ABS) is an amorphous thermoplastic copolymer built by polymerizing styrene and acrylonitrile in the presence of polybutadiene. The combination of the three confers to ABS a wide range of characteristics, such as impact resistance, toughness, heat resistance, or weather and chemical resistance [24]. ABS is widely used in the plastic industry for modern processes such as plastic injection molding for end products such as protective housings, stiff packaging, and structurally robust parts, as well as in the production of polymer blends, such as polycarbonate + ABS or polyamide + ABS, and can be regularly found in the automotive sector [25–27]. Additionally, the use of ABS has also been reported for EMI shielding applications throughout the manufacturing of ABS/MWCNT compounds, due to its processability and dimensional stability [28,29]. Raw ABS 118HF pellets supplied by Elix Polymers are used in this study in the production of seven samples containing different MWCNT concentrations and reinforcements. These samples are summarized in Table 1. A CNT Masterbatch from Nanocyl, the Plasticyl ABS1501, is used to manufacture Sample 7.


**Sample ID Description Particle Type Particle Percentage**

samples are summarized in Table 1. A CNT Masterbatch from Nanocyl, the Plasticyl

**Table 1.** List of samples. 1 ABS NA <sup>1</sup> NA

**Table 1.** List of samples.

ABS1501, is used to manufacture Sample 7.

*Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 4 of 18

<sup>1</sup> NA: Not applicable. <sup>2</sup> MB: Masterbatch *2.2. Samples Manufacturing*

#### *2.2. Samples Manufacturing* The samples studied to determine their SE to prevent EMI has been manufactured following a two-step process encompassing the production of the raw thermoplastic com-

The samples studied to determine their SE to prevent EMI has been manufactured following a two-step process encompassing the production of the raw thermoplastic compounds and the subsequent obtention of the testing samples. The compounding stage included using an extruder setup with ABS/CNT pellets and a thermoplastic pultrusion line for LFP production. Finally, the samples underwent compression molding to produce the final rectangular specimens. pounds and the subsequent obtention of the testing samples. The compounding stage included using an extruder setup with ABS/CNT pellets and a thermoplastic pultrusion line for LFP production. Finally, the samples underwent compression molding to produce the final rectangular specimens. 2.2.1. Compounding

#### 2.2.1. Compounding The initial stage consists of obtaining the raw compounds used in manufacturing the

The initial stage consists of obtaining the raw compounds used in manufacturing the testing samples. These initial compounds carry diverse concentrations of multi-walled carbon nanotube (MWCNT) particles. Furthermore, a sample consisting of 100% raw ABS (Sample 1) allowed the definition of a minimum reference value of EMI shielding. The compounds are obtained following three different and independent techniques. testing samples. These initial compounds carry diverse concentrations of multi-walled carbon nanotube (MWCNT) particles. Furthermore, a sample consisting of 100% raw ABS (Sample 1) allowed the definition of a minimum reference value of EMI shielding. The compounds are obtained following three different and independent techniques. The compounds used in the manufacturing of Samples 2 to 5 are produced by means

The compounds used in the manufacturing of Samples 2 to 5 are produced by means of a PRISM 16 L/D 25 twin screw extruder and located at the compounding facilities at AIMPLAS (Figure 1a). In this process, ABS pellets and particles are fed together into the extruder via a specific hopper. During the extrusion process, the raw materials are mixed due to the effect of temperature and the shearing forces exerted by the twin screws. Taking into consideration 240 ◦C as the processing temperature of the ABS matrix used, a flat temperature profile of 260 ◦C is settled to process the compounds to ensure good processability of the materials (Table 2). Then, at the end of the extruder, a continuous filament with a pre-defined diameter is obtained and cooled down. Finally, a cutting unit located at the end of the setup generates the ABS/CNT pellets with the desired length. of a PRISM 16 L/D 25 twin screw extruder and located at the compounding facilities at AIMPLAS (Figure 1a). In this process, ABS pellets and particles are fed together into the extruder via a specific hopper. During the extrusion process, the raw materials are mixed due to the effect of temperature and the shearing forces exerted by the twin screws. Taking into consideration 240 °C as the processing temperature of the ABS matrix used, a flat temperature profile of 260 °C is seled to process the compounds to ensure good processability of the materials (Table 2). Then, at the end of the extruder, a continuous filament with a pre-defined diameter is obtained and cooled down. Finally, a cuing unit located at the end of the setup generates the ABS/CNT pellets with the desired length.

**Figure 1.** *Cont.*

**Figure 1.** Compounding process. (**a**) Schematic of the extruder setup. (**b**) Schematic of the LFP production line. **Figure 1.** Compounding process. (**a**) Schematic of the extruder setup. (**b**) Schematic of the LFP production line.

**Table 2.** Extrusion parameters. **Table 2.** Extrusion parameters.


by AIMPLAS, allowing Ø4mm unidirectional threads of glass or carbon fiber impregnated by the ABS/CNT compounds previously developed (Figure 1b). In this process, the pellets produced in the previous step are fed to the same extruder described previously in order to melt the polymer and facilitate the subsequent impregnation of the fiber. A temperature profile of 270 °C is used to process the ABS/CNT compound in the extruder to ensure good processability and further fiber impregnation. The resulting melted polymer matrix compound is then transferred to the impregnation die to impregnate the fiber thread effectively. The continuous thread of thermoplastic impregnated fiber leaving the impregnation die at a rate of 600 g/h is cooled down and cut into 12 mm pellets reinforced with oriented and continuous either carbon or glass fiber. The resulting carbon and glass LFP are used to manufacture Samples 4 and 5, respectively. Long fiber pellets (LFP) are produced in a thermoplastic pultrusion line developed by AIMPLAS, allowing Ø4 mm unidirectional threads of glass or carbon fiber impregnated by the ABS/CNT compounds previously developed (Figure 1b). In this process, the pellets produced in the previous step are fed to the same extruder described previously in order to melt the polymer and facilitate the subsequent impregnation of the fiber. A temperature profile of 270 ◦C is used to process the ABS/CNT compound in the extruder to ensure good processability and further fiber impregnation. The resulting melted polymer matrix compound is then transferred to the impregnation die to impregnate the fiber thread effectively. The continuous thread of thermoplastic impregnated fiber leaving the impregnation die at a rate of 600 g/h is cooled down and cut into 12 mm pellets reinforced with oriented and continuous either carbon or glass fiber. The resulting carbon and glass LFP are used to manufacture Samples 4 and 5, respectively.

Long fiber pellets (LFP) are produced in a thermoplastic pultrusion line developed

#### Following the production of the pellets, rectangular specimens of dimensions 210 2.2.2. Compression Molding

2.2.2. Compression Molding

mm × 297 mm × 2 mm are obtained (Figure 2) via compression molding using a CUYMA PH1000 hot press. In this process, the pellets obtained in Section 2.2.1 are placed in a mold of pre-defined dimensions and located between two rigid and hot plates. The effect of the temperature and pressure upon the closure of the mold induced the melting of the pellets and obtaining testing samples with the required dimensions (Figure 3). For all specimens, the temperature is kept constant at 250 °C through the entire compression cycle, which accounted for an initial force of 60 kN for 5 min, followed by an increase in the force to 100 kN and holding for 10 min (Table 3). Following the production of the pellets, rectangular specimens of dimensions 210 mm × 297 mm × 2 mm are obtained (Figure 2) via compression molding using a CUYMA PH1000 hot press. In this process, the pellets obtained in Section 2.2.1 are placed in a mold of pre-defined dimensions and located between two rigid and hot plates. The effect of the temperature and pressure upon the closure of the mold induced the melting of the pellets and obtaining testing samples with the required dimensions (Figure 3). For all specimens, the temperature is kept constant at 250 ◦C through the entire compression cycle, which accounted for an initial force of 60 kN for 5 min, followed by an increase in the force to 100 kN and holding for 10 min (Table 3).

Seven testing samples are produced, one per each type of compound. An additional specimen is produced with the same formulation as used for the manufacturing of Sample 6. Coupling these two specimens together (Sample 7) would shed light on the relationship between the increase in the thickness by a factor of 2 and the EMI shielding.

*Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 6 of 18

(**a**) (**b**) **Figure 3.** CF LFP ABS + 3% CNT sample. (**a**) Front side. (**b**) Back side. **Figure 3.** CF LFP ABS + 3% CNT sample. (**a**) Front side. (**b**) Back side. **Figure 3.** CF LFP ABS + 3% CNT sample. (**a**) Front side. (**b**) Back side.

**Table 3.** Hot press molding parameters. **Table 3.** Hot press molding parameters.


#### Seven testing samples are produced, one per each type of compound. An additional *2.3. Dispersion Analysis*

Seven testing samples are produced, one per each type of compound. An additional specimen is produced with the same formulation as used for the manufacturing of Sample 6. Coupling these two specimens together (Sample 7) would shed light on the relationship between the increase in the thickness by a factor of 2 and the EMI shielding. *2.3. Dispersion Analysis* Following the preparation of the samples, an analysis of the dispersion of the EMI specimen is produced with the same formulation as used for the manufacturing of Sample 6. Coupling these two specimens together (Sample 7) would shed light on the relationship between the increase in the thickness by a factor of 2 and the EMI shielding. *2.3. Dispersion Analysis* Following the preparation of the samples, an analysis of the dispersion of the EMI shielding particles in the polymeric matrix is deemed necessary to assess the quality of Following the preparation of the samples, an analysis of the dispersion of the EMI shielding particles in the polymeric matrix is deemed necessary to assess the quality of the manufacturing process. Scanning electron microscopy (SEM) imaging is performed using a Hitachi S-4800 Scanning Electron Microscope which allowed the characterization of the surface of Samples 2, 4, and 7, generated in Section 2.2 (Figure 4). The selected samples are representative of each of the three manufacturing processes and materials described previously.

shielding particles in the polymeric matrix is deemed necessary to assess the quality of the manufacturing process. Scanning electron microscopy (SEM) imaging is performed using a Hitachi S-4800 Scanning Electron Microscope which allowed the characterization of the surface of Samples 2, 4, and 7, generated in Section 2.2 (Figure 4). The selected samples are representative of each of the three manufacturing processes and materials described previously. the manufacturing process. Scanning electron microscopy (SEM) imaging is performed using a Hitachi S-4800 Scanning Electron Microscope which allowed the characterization of the surface of Samples 2, 4, and 7, generated in Section 2.2 (Figure 4). The selected samples are representative of each of the three manufacturing processes and materials described previously. CNTs appear as thin and elongated structures and are homogeneously distributed across the three samples, indicating a high-quality manufacturing process. Sample 7 contains the highest concentration of CNTs after visual assessment, confirming the nominal specifications of this sample (Figure 4a,b). It is worth noting that the combined effect of the low apparent density of the CNTs (~0.23 g/cm<sup>3</sup> ) and the high weight percentage of CNTs (15%) contained by this sample, results in a dense network of CNT that hinders the visualization of the polymeric matrix.

**Figure 4.** SEM images of three of the developed samples. General view (**left**). Detailed view (**right**). (**a,b**) MB ABS + 15% CNT (**c,d**) ABS + 5%CNT (**e,f**) CF LFP ABS + 3% CNT. **Figure 4.** SEM images of three of the developed samples. General view (**left**). Detailed view (**right**). (**a,b**) MB ABS + 15% CNT (**c,d**) ABS + 5%CNT (**e,f**) CF LFP ABS + 3% CNT.

CNTs appear as thin and elongated structures and are homogeneously distributed across the three samples, indicating a high-quality manufacturing process. Sample 7 contains the highest concentration of CNTs after visual assessment, confirming the nominal specifications of this sample (Figure 4a,b). It is worth noting that the combined effect of As the concentration of CNT decreases (Samples 2 and 4), the polymeric matrix is rendered visible, and the network of CNT becomes less dense (Figure 4c,d). Additionally, the correct impregnation of the carbon fibers by the polymer matrix can be observed in Figure 4e, ruling out the delamination of the fibers produced by the sample preparation.

the low apparent density of the CNTs (~0.23 g/cm3) and the high weight percentage of CNTs (15%) contained by this sample, results in a dense network of CNT that hinders the visualization of the polymeric matrix. As the concentration of CNT decreases (Samples 2 and 4), the polymeric matrix is rendered visible, and the network of CNT becomes less dense (Figure 4c,d). Additionally, Regarding the CNT distribution, it can be observed that a similar distribution is obtained across the samples included in Figure 4. This effect indicates a high level of reproducibility of the manufacturing process. Following a visual examination, empty spaces and aggregates are not appreciated, and CNTs are homogeneously dispersed in the polymer matrix.

#### the correct impregnation of the carbon fibers by the polymer matrix can be observed in **3. Planar Material Measurement Methods**

Figure 4e, ruling out the delamination of the fibers produced by the sample preparation. Regarding the CNT distribution, it can be observed that a similar distribution is obtained across the samples included in Figure 4. This effect indicates a high level of reproducibility of the manufacturing process. Following a visual examination, empty spaces and aggregates are not appreciated, and CNTs are homogeneously dispersed in the polymer matrix. The current standard method that defines the measurement procedure to determine the shielding effectiveness of planar materials is the ASTM 4935-18. Nevertheless, the frequency region of this measurement method is limited in frequency (up to 1.5 GHz). Other measurement techniques used to analyze the performance of planar materials are based on the IEEE 299 standard. Due to the wide variety of applications that need to be shielded by using housing with a specific size and shape, planar materials are generally characterized, considering different field conditions. Thereby, depending on the frequency range and the sample features, different measurement techniques may be used to cover the

entire frequency range of interest. The 5G operates in a wide range of frequencies. Currently, two different frequency ranges are available for the 5G technology, FR1 and FR2. The bands in the FR1 spectrum are envisaged for the operation of traditional cellular communication, whereas FR2 bands aim to provide short-range very high data rate capability. The 5G FR1 range covers frequencies up to 7.125 GHz, and FR2 encompasses frequencies above 24.5 GHz.

#### *3.1. Standard Measurement Methods*

The main techniques for the measurement of the SE of planar materials are based on using mono-mode coaxial TEM cells, according to the standard ASTM D4935-18, or the use of emitting and receiving antennas as in the IEEE 299 standard. The first method has a frequency limit of about 1.5 GHz; the last one applies for higher frequencies, but it requires large sheet samples, which is a disadvantage when dealing with novel materials that rely on rare raw materials. The cost of the shielding particles can be very high, making unfeasible the manufacturing of large-scale samples. Consequently, measuring these materials using a method that requires covering the entire door of an anechoic chamber becomes impractical.

The ASTM D4935-18 is the standard test method for measuring the electromagnetic shielding effectiveness of planar materials. This method allows measuring planar samples in a narrow frequency range from 30 MHz to 1.5 GHz. The technique measures the insertion loss (IL) that results when introducing test samples in a coaxial two-conductor transmission line holder, supporting transverse electromagnetic (TEM) propagation mode. The procedure requires two types of specimens with the same thickness to make SE measurements: the reference and the load specimens (Figure 5). The difference between the measurements of the load and the reference specimen provides the measurement of the SE, caused by the reflection and absorption of the material between the two flanks of the coaxial probe. The upper-frequency limit that can be measured with this method depends on the cut-off frequency for the transverse electric propagation mode of the coaxial cell holder. At frequencies higher than the cut-off, higher-order modes other than TEM can propagate, changing the field distribution inside the cell and causing resonances in the measured results, which have an adverse effect on the accuracy of the measured results. Therefore, the main disadvantage of the fixture is the narrow frequency band of operation, which is limited, considering the operating frequencies of current electronic devices and systems. *Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 9 of 18

**Figure 5.** Measurement test setup based on the ASTM D4935-18 procedure and sample geometries and dimensions. **Figure 5.** Measurement test setup based on the ASTM D4935-18 procedure and sample geometries and dimensions.

The IEEE 299 standard defines how to measure the effectiveness of electromagnetic shielding enclosures. This method is carried out by placing a sample of the material under test between two antennas connected to a vector network analyzer equipment (VNA) that provides the emiing signal to one of the antennas and receives the field measured by the receiving antenna (Figure 6). Thereby, it is possible to obtain the shielding effectiveness of The IEEE 299 standard defines how to measure the effectiveness of electromagnetic shielding enclosures. This method is carried out by placing a sample of the material under test between two antennas connected to a vector network analyzer equipment (VNA) that provides the emitting signal to one of the antennas and receives the field measured by the receiving antenna (Figure 6). Thereby, it is possible to obtain the shielding effectiveness

the material under test by analyzing the S-parameters obtained through a reference measurement (without the material sample) and a load measurement (by placing the material

aperture in an anechoic chamber wall. The SE is obtained by taking the difference between the received field strength (in dB units) with the sample absent and with the sample present. The nature of the illuminating field varies with frequency and the type of antenna

To these limitations is added the high influence between the characteristics of the anechoic chamber as well as the proper location/orientation of the antennas and the sam-

Due to the increase in operating frequencies and the evolution of 5G towards FR2, it is important to develop non-standardized measurement methods through setups, fixtures, and techniques compatible with the operating frequencies of 5G technologies and

From the standards, some derivative methods can be highlighted: nested reverberation chambers [30], vibrating intrinsic reverberation chambers [31], TEM cell methods [32],

**Figure 6.** Measurement test setup based on the IEEE 299 standard procedure.

*3.2. Non-Standardized Measurement Methods*

the samples manufactured.

used.

ple in the space.

of the material under test by analyzing the S-parameters obtained through a reference measurement (without the material sample) and a load measurement (by placing the material between the two antennas). The reference can be taken in free space or through an open aperture in an anechoic chamber wall. The SE is obtained by taking the difference between the received field strength (in dB units) with the sample absent and with the sample present. The nature of the illuminating field varies with frequency and the type of antenna used. aperture in an anechoic chamber wall. The SE is obtained by taking the difference between the received field strength (in dB units) with the sample absent and with the sample present. The nature of the illuminating field varies with frequency and the type of antenna used. To these limitations is added the high influence between the characteristics of the anechoic chamber as well as the proper location/orientation of the antennas and the sample in the space.

**Figure 5.** Measurement test setup based on the ASTM D4935-18 procedure and sample geometries

The IEEE 299 standard defines how to measure the effectiveness of electromagnetic shielding enclosures. This method is carried out by placing a sample of the material under test between two antennas connected to a vector network analyzer equipment (VNA) that provides the emiing signal to one of the antennas and receives the field measured by the receiving antenna (Figure 6). Thereby, it is possible to obtain the shielding effectiveness of the material under test by analyzing the S-parameters obtained through a reference measurement (without the material sample) and a load measurement (by placing the material between the two antennas). The reference can be taken in free space or through an open

*Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 9 of 18

and dimensions.

*3.2. Non-Standardized Measurement Methods* Due to the increase in operating frequencies and the evolution of 5G towards FR2, it is important to develop non-standardized measurement methods through setups, fix-To these limitations is added the high influence between the characteristics of the anechoic chamber as well as the proper location/orientation of the antennas and the sample in the space.

#### tures, and techniques compatible with the operating frequencies of 5G technologies and *3.2. Non-Standardized Measurement Methods*

the samples manufactured. From the standards, some derivative methods can be highlighted: nested reverberation chambers [30], vibrating intrinsic reverberation chambers [31], TEM cell methods [32], Due to the increase in operating frequencies and the evolution of 5G towards FR2, it is important to develop non-standardized measurement methods through setups, fixtures, and techniques compatible with the operating frequencies of 5G technologies and the samples manufactured.

From the standards, some derivative methods can be highlighted: nested reverberation chambers [30], vibrating intrinsic reverberation chambers [31], TEM cell methods [32], ASTM D4935-18 high-frequency variants [33–35], or absorber box methods [36,37]. The last one proposes an alternative to free space measurements in an anechoic chamber, where the sample size is significantly reduced, and no complex sample preparation is required. Moreover, the equipment and the sample size determine the cutoff frequency, so the method is considerably adaptable to the type of material to be measured. This alternative also eliminates the main problems that the other techniques present, making this method suitable for this study.

As some bibliographic sources indicate, extending the upper-frequency limit of the ASTM D4935-18 standard could be possible. Some institutions have modified this standard coaxial cell holder to perform SE measurements at higher frequencies and on smaller-size materials under test [34,35]. Basically, as the cut-off frequency, and consequently the upperfrequency limit, depends on cell dimensions, new versions of coaxial sample holders can be designed and fabricated, reducing the inner radius of the outer conductor and the radius of the center one.

On the other hand, the measurements based on the IEEE 299 standard are another interesting line of research since they can be performed with RF antennas (inside an anechoic chamber), extending the frequency region defined by the ASTM D4935-18 standard. The upper frequency for IEEE 299 methods is limited by the chamber leakage and the need for the sample to be large enough to minimize edge diffraction effects. Nevertheless, test-to-test variations arise from normal differences between instruments, from discrepancies between transmitting and receiving antennas, including their positions, and primarily from differences between test techniques. Most of the methods based on free space require sample dimensions too large, in addition to being strongly conditioned by the environmental conditions and the directivity of the antennas. Consequently, the proposed alternative method is based on an EMI absorber box lined with absorbent material and two antennas: one transmitter and one receiver.

#### *3.3. Proposed Shielding Effectiveness Measurement System*

The proposed measurement method is an adaptation of one of the methods included in the P2715 standard, a guide for the characterization of the shielding effectiveness of planar materials. This method provides the SE of planar materials, adapting to the specific requirements of the study. The main advantage is that the sample machining is simple, which represents a significant breakthrough when dealing with rigid and delicate materials that cannot be machined with very specific geometries or tiny dimensions. Furthermore, no electrical connection to the sample is required, which allows the measurement of samples with low conductivity, contrary to the measurement method proposed in the ASTM D4935 standard. These facts mean that a wide range of measurements can be made with reasonable speed due to the easiness of the measurement procedure. Another notable advantage is the elimination of frequency limitation, making it a suitable method for measurements in the frequency range where 5G technology operates.

The scheme of the proposed prototype is shown in Figure 7. The receiving antenna embedded in the absorber and the receiving antenna are commercial 700 MHz to 18 GHz A-Info LB-7180 ridged waveguide horns. The dimensions of the cavity are 300 × 500 mm, thus, adapting to the rectangular shape of the horn antennas [38]. In one of the sides of the box, a hole has been drilled where an SMA-type connector is placed and connected to the transmitting antenna inside the cavity. The laminated absorber is arranged inside the cavity of the absorber box cut to fit the geometry and dimensions of the antenna. The absorber material is a commercial series made from polyurethane foam that is treated with carbon and assembled in a laminate construction to generate a controlled conductivity gradient. The upper layers above the emitting antenna have a square opening of 100 × 100 mm where the sample is placed to measure the SE of the sample. Assuming no contact exists between the equipment and the sample, two more sheets of absorbent material are placed on top of the sample to mitigate diffraction losses due to the edge effect and to flatten the sample in case it has a concave or convex shape due to the manufacturing process. These top layers of absorbers have an opening of the same dimensions as the sample layer to illuminate the sample as uniformly as possible. *Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 11 of 18 process. These top layers of absorbers have an opening of the same dimensions as the sample layer to illuminate the sample as uniformly as possible. The selected size of the developed samples is 210 × 297 mm. These dimensions correspond to a fairly standard size for sample prototyping, although it is possible to perform measurements with samples up to 300 × 500 mm, which corresponds to the maximum dimensions of the cavity. Furthermore, with this size, the samples aim to be large enough to reduce the edge effect previously mentioned, but at the same time, small enough to ensure that production is simple and cost-effective. The antennas are connected to port 1 (emiing channel) and port 2 (receiving channel) of a VNA measuring equipment through an SMA-type connector and two cables Megaphase KB18-S1S1-48 SMA. The frequency range of the final system is 700 MHz–18 GHz, limited by the maximum and minimum operating frequencies of the antennas.

The procedure to obtain the shielding effectiveness of the different samples is based on measuring the scaering parameter S21 by taking the transmission ratio through the system without any sample (S21,ref), and with the sample present in the cavity (S21,sample).

The prototype and the final measurement setup are shown in Figure 8, where the receiving horn antenna is situated above a material under test and connected to the VNA

**Figure 8.** Experimental measurement setup. (**a**) Sample window layer. (**b**) Experimental setup per-

SE (dB) = S21,sample − S21,ref (1)

**Figure 7.** Cross-sectional view of the prototype system. **Figure 7.** Cross-sectional view of the prototype system.

(**a**) (**b**)

forming a sample measurement.

equipment.

Subsequently, the SE is calculated according to Equation 1:

The selected size of the developed samples is 210 × 297 mm. These dimensions correspond to a fairly standard size for sample prototyping, although it is possible to perform measurements with samples up to 300 × 500 mm, which corresponds to the maximum dimensions of the cavity. Furthermore, with this size, the samples aim to be large enough to reduce the edge effect previously mentioned, but at the same time, small enough to ensure that production is simple and cost-effective.

process. These top layers of absorbers have an opening of the same dimensions as the

The selected size of the developed samples is 210 × 297 mm. These dimensions correspond to a fairly standard size for sample prototyping, although it is possible to perform measurements with samples up to 300 × 500 mm, which corresponds to the maximum dimensions of the cavity. Furthermore, with this size, the samples aim to be large enough to reduce the edge effect previously mentioned, but at the same time, small enough to

The antennas are connected to port 1 (emiing channel) and port 2 (receiving channel) of a VNA measuring equipment through an SMA-type connector and two cables Megaphase KB18-S1S1-48 SMA. The frequency range of the final system is 700 MHz–18

GHz, limited by the maximum and minimum operating frequencies of the antennas.

The antennas are connected to port 1 (emitting channel) and port 2 (receiving channel) of a VNA measuring equipment through an SMA-type connector and two cables Megaphase KB18-S1S1-48 SMA. The frequency range of the final system is 700 MHz– 18 GHz, limited by the maximum and minimum operating frequencies of the antennas. **Figure 7.** Cross-sectional view of the prototype system. The procedure to obtain the shielding effectiveness of the different samples is based

The procedure to obtain the shielding effectiveness of the different samples is based on measuring the scattering parameter S<sup>21</sup> by taking the transmission ratio through the system without any sample (S21,ref), and with the sample present in the cavity (S21,sample). Subsequently, the SE is calculated according to Equation 1: on measuring the scaering parameter S21 by taking the transmission ratio through the system without any sample (S21,ref), and with the sample present in the cavity (S21,sample). Subsequently, the SE is calculated according to Equation 1:

$$\text{SE (dB)} = \text{S}\_{\text{21,sample}} - \text{S}\_{\text{21,ref}} \tag{1}$$

The prototype and the final measurement setup are shown in Figure 8, where the receiving horn antenna is situated above a material under test and connected to the VNA equipment. The prototype and the final measurement setup are shown in Figure 8, where the receiving horn antenna is situated above a material under test and connected to the VNA equipment.

*Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 11 of 18

sample layer to illuminate the sample as uniformly as possible.

ensure that production is simple and cost-effective.

**Figure 8.** Experimental measurement setup. (**a**) Sample window layer. (**b**) Experimental setup performing a sample measurement. **Figure 8.** Experimental measurement setup. (**a**) Sample window layer. (**b**) Experimental setup performing a sample measurement.

To characterize the system, the measurement of the dynamic range of the proposed method has been carried out. The SE of the cavity without a sample has been compared with the SE resulting from placing a perfect electric conductor (PEC) with the maximum size of the cavity (300 × 500 mm) to avoid the effect of diffraction at the edges. In this case, the sample is an aluminum sheet with a thickness of *t* = 2 mm. Figure 9 shows the resulting dynamic range of the system, which is approximately -100 dB and is expected to be suitable to measure the SE of the developed materials according to the values obtained in previous studies of composites with similar characteristics [20,39].

The most notable features of the measurement method used to evaluate the developed samples are summarized in Table 4.

vious studies of composites with similar characteristics [20,39].

**Figure 9.** Measured dynamic range of the system with a 2 mm thick aluminum sample. **Figure 9.** Measured dynamic range of the system with a 2 mm thick aluminum sample.

The most notable features of the measurement method used to evaluate the devel-**Table 4.** Hot press molding parameters.


mm

700 MHz–18

GHz −100 dB

To characterize the system, the measurement of the dynamic range of the proposed method has been carried out. The SE of the cavity without a sample has been compared with the SE resulting from placing a perfect electric conductor (PEC) with the maximum size of the cavity (300 × 500 mm) to avoid the effect of diffraction at the edges. In this case, the sample is an aluminum sheet with a thickness of *t* = 2 mm. Figure 9 shows the resulting dynamic range of the system, which is approximately -100 dB and is expected to be suitable to measure the SE of the developed materials according to the values obtained in pre-

#### effectiveness dB 300 × 500 mm 210 × 297 **4. Results and Discussion**

Shielding

**4. Results and Discussion** This section is focused on showing the results corresponding to the measurement of seven sample composites under test. Firstly, it is compared the different composite samples based on ABS (samples 1, 2, 3, and 7) to analyze how the increase in the concentration of CNT is turned into an improvement of the SE parameter. Subsequently, the influence of the reinforcement material used to manufacture the composite is studied by comparing This section is focused on showing the results corresponding to the measurement of seven sample composites under test. Firstly, it is compared the different composite samples based on ABS (samples 1, 2, 3, and 7) to analyze how the increase in the concentration of CNT is turned into an improvement of the SE parameter. Subsequently, the influence of the reinforcement material used to manufacture the composite is studied by comparing the samples based on glass fiber and carbon fiber (samples 4 and 5). Finally, the effect of introducing a thicker carbon fiber reinforcement in the composite is analyzed (samples 4 and 6).

the samples based on glass fiber and carbon fiber (samples 4 and 5). Finally, the effect of introducing a thicker carbon fiber reinforcement in the composite is analyzed (samples 4 and 6). Figure 10 shows the results obtained in terms of SE of different composites with an ABS matrix without fiber reinforcement and three different concentrations of %w CNT. The ABS trace represents the outcome of the SE measurement conducted on the ABS matrix without any filler material. This particular measurement is used as a reference to compare the SE values obtained from the other samples. It can be observed how this trace does not provide considerable aenuation but the increase in CNT filler leads to a rise in the SE provided by the material. If we take the value of 7.125 GHz as a reference, which corresponds to the upper limit of the FR1 band in the 5G spectrum, a value of −24.75 dB is Figure 10 shows the results obtained in terms of SE of different composites with an ABS matrix without fiber reinforcement and three different concentrations of %w CNT. The ABS trace represents the outcome of the SE measurement conducted on the ABS matrix without any filler material. This particular measurement is used as a reference to compare the SE values obtained from the other samples. It can be observed how this trace does not provide considerable attenuation but the increase in CNT filler leads to a rise in the SE provided by the material. If we take the value of 7.125 GHz as a reference, which corresponds to the upper limit of the FR1 band in the 5G spectrum, a value of −24.75 dB is obtained for the trace with a concentration of 5w%CNT. For the sample with twice the weight concentration of CNT, the SE value increases to −39.65 dB. In the last case, for the 15w%CNT sample at the reference frequency, the SE value obtained is −81.30 dB.

Below the reference frequency, the behavior of the traces is slightly different. The red trace corresponding to sample 2 shows a linear behavior, whereas the traces corresponding to the samples with the highest CNT concentration (samples 3 and 7) show an increase in SE as the frequency increases. On the other hand, starting at approximately 14 GHz, it can be observed that the red trace (sample 2) continues to exhibit a flat behavior, whereas the blue trace (sample 3) continues to decrease. However, the black trace (sample 7) shows a change in slope, taking an ascending trend. This fact leaves the door open for further study at higher frequencies to determine if, at a given frequency, the sample with the highest concentration of CNT may not necessarily present the greatest attenuation.

**Figure 10.** Comparison of ABS polymer samples with three different w%CNT concentrations. **Figure 10.** Comparison of ABS polymer samples with three different w%CNT concentrations.

obtained for the trace with a concentration of 5w%CNT. For the sample with twice the weight concentration of CNT, the SE value increases to −39.65 dB. In the last case, for the

Below the reference frequency, the behavior of the traces is slightly different. The red trace corresponding to sample 2 shows a linear behavior, whereas the traces corresponding to the samples with the highest CNT concentration (samples 3 and 7) show an increase in SE as the frequency increases. On the other hand, starting at approximately 14 GHz, it can be observed that the red trace (sample 2) continues to exhibit a flat behavior, whereas the blue trace (sample 3) continues to decrease. However, the black trace (sample 7) shows a change in slope, taking an ascending trend. This fact leaves the door open for further study at higher frequencies to determine if, at a given frequency, the sample with the highest concentration of CNT may not necessarily present the greatest aenuation.

15w%CNT sample at the reference frequency, the SE value obtained is −81.30 dB.

It has been observed that to achieve higher levels of aenuation, it is necessary to increase the concentration of CNT. However, this presents a challenge during the machining process as the addition of CNT increases the viscosity of the composite. To address this issue, two compounds have been developed with the addition of different reinforcements, one based on CF and the other based on GF. These reinforcements provide rigidity to the material, thereby improving its mechanical properties. It has been observed that to achieve higher levels of attenuation, it is necessary to increase the concentration of CNT. However, this presents a challenge during the machining process as the addition of CNT increases the viscosity of the composite. To address this issue, two compounds have been developed with the addition of different reinforcements, one based on CF and the other based on GF. These reinforcements provide rigidity to the material, thereby improving its mechanical properties.

Figure 11 shows the shielding effectiveness provided by the CF reinforcement sample comparing it with the GF reinforcement sample (samples 4 and 5, respectively) with a 3w%CNT. It can be observed that the CF sample exhibits considerably higher aenuation compared to the GF sample when the same %w filler is introduced. Quantitatively comparing the results, for the selected reference frequency of 7.125 GHz, it can be observed that the SE value of the CF sample is −60.03 dB. In contrast, the SE value obtained for the GF sample is −14.24 dB, which significantly differs from the CF sample, even though the weight percentage of CNT is the same for both samples. This is aributed to the nature of the fiber reinforcements, as carbon fiber alone exhibits a certain level of shielding depending on the fiber density due to the highly conductive nature of carbon fibers, whereas fiberglass does not cause significant aenuation. Figure 11 shows the shielding effectiveness provided by the CF reinforcement sample comparing it with the GF reinforcement sample (samples 4 and 5, respectively) with a 3w%CNT. It can be observed that the CF sample exhibits considerably higher attenuation compared to the GF sample when the same %w filler is introduced. Quantitatively comparing the results, for the selected reference frequency of 7.125 GHz, it can be observed that the SE value of the CF sample is −60.03 dB. In contrast, the SE value obtained for the GF sample is −14.24 dB, which significantly differs from the CF sample, even though the weight percentage of CNT is the same for both samples. This is attributed to the nature of the fiber reinforcements, as carbon fiber alone exhibits a certain level of shielding depending on the fiber density due to the highly conductive nature of carbon fibers, whereas fiberglass does not cause significant attenuation. *Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 14 of 18 reinforcement chosen will depend on the final application of the composite and the required level of aenuation.

> Figure 12 shows the influence of the sample thickness in the measurement of the SE. To achieve this, a CF reinforcement sample (sample 4) with a thickness of *t* = 2 mm and 3w%CNT filling is compared with two stacked sheets of the sample (sample 6). On the

> capability of the material. Below the reference frequency, the behavior of the traces is similar up to approximately 3.5 GHz, where the two traces diverge. It can be observed how the CF sample (black trace) presents considerable attenuation, particularly from 4 GHz. From this point up to 7.125 GHz, the black trace (sample 2) shows a linear behavior with a slightly decreasing slope, whereas the red trace (sample 6) shows a more abrupt decrease until the reference frequency, where it flattens out. Comparing the results for the selected frequency of 7.125 GHz, it can be observed that the SE value of the single-layer CF sample is −60.03 dB, whereas the SE value of the double-layer CF sample shows an increase of 21.29 dB, reaching a SE value of −81.32 dB. Moreover, it is noted that the red trace shows an increase in slope starting at approximately 16 GHz. This phenomenon may

be attributed to multiple reflections that occur between the two sheets of material.

**Figure 12.** Carbon-fiber-reinforced polymers. Comparison of one sample (black trace) and two

superposed samples (red trace).

**Figure 11.** Carbon-fiber- and glass-fiber-reinforced polymers. **Figure 11.** Carbon-fiber- and glass-fiber-reinforced polymers.

Although GF does not provide a significant attenuation by itself, these two compounds have been compared due to the fact that GF provides some advantages in terms of cost, production, and machining. GF is generally more affordable because the materials used to produce it are widely available. Additionally, the manufacturing of GF is simpler and requires fewer processing steps. On the other hand, this type of reinforcement is easier to manipulate and has a longer lifespan than CF reinforcement. Therefore, the type of reinforcement chosen will depend on the final application of the composite and the required level of attenuation. **Figure 11.** Carbon-fiber- and glass-fiber-reinforced polymers. Figure 12 shows the influence of the sample thickness in the measurement of the SE. To achieve this, a CF reinforcement sample (sample 4) with a thickness of *t* = 2 mm and

reinforcement chosen will depend on the final application of the composite and the re-

*Magnetochemistry* **2023**, *9*, x FOR PEER REVIEW 14 of 18

quired level of aenuation.

Figure 12 shows the influence of the sample thickness in the measurement of the SE. To achieve this, a CF reinforcement sample (sample 4) with a thickness of *t* = 2 mm and 3w%CNT filling is compared with two stacked sheets of the sample (sample 6). On the other hand, the red trace shows the measurement result of the two overlapping sheets. These observations suggest that the sample thickness significantly affects the shielding capability of the material. Below the reference frequency, the behavior of the traces is similar up to approximately 3.5 GHz, where the two traces diverge. It can be observed how the CF sample (black trace) presents considerable attenuation, particularly from 4 GHz. From this point up to 7.125 GHz, the black trace (sample 2) shows a linear behavior with a slightly decreasing slope, whereas the red trace (sample 6) shows a more abrupt decrease until the reference frequency, where it flattens out. Comparing the results for the selected frequency of 7.125 GHz, it can be observed that the SE value of the single-layer CF sample is −60.03 dB, whereas the SE value of the double-layer CF sample shows an increase of 21.29 dB, reaching a SE value of −81.32 dB. Moreover, it is noted that the red trace shows an increase in slope starting at approximately 16 GHz. This phenomenon may be attributed to multiple reflections that occur between the two sheets of material. 3w%CNT filling is compared with two stacked sheets of the sample (sample 6). On the other hand, the red trace shows the measurement result of the two overlapping sheets. These observations suggest that the sample thickness significantly affects the shielding capability of the material. Below the reference frequency, the behavior of the traces is similar up to approximately 3.5 GHz, where the two traces diverge. It can be observed how the CF sample (black trace) presents considerable attenuation, particularly from 4 GHz. From this point up to 7.125 GHz, the black trace (sample 2) shows a linear behavior with a slightly decreasing slope, whereas the red trace (sample 6) shows a more abrupt decrease until the reference frequency, where it flattens out. Comparing the results for the selected frequency of 7.125 GHz, it can be observed that the SE value of the single-layer CF sample is −60.03 dB, whereas the SE value of the double-layer CF sample shows an increase of 21.29 dB, reaching a SE value of −81.32 dB. Moreover, it is noted that the red trace shows an increase in slope starting at approximately 16 GHz. This phenomenon may be attributed to multiple reflections that occur between the two sheets of material.

**Figure 12.** Carbon-fiber-reinforced polymers. Comparison of one sample (black trace) and two superposed samples (red trace). **Figure 12.** Carbon-fiber-reinforced polymers. Comparison of one sample (black trace) and two superposed samples (red trace).

The following Table 5 provides a summary of the most representative results for each of the seven samples in three different frequency ranges. This table shows the maximum and minimum SE values in decibels.

The ability to detect these variations is essential for optimizing the performance of shielding materials in a given application. By identifying the frequency ranges in which a material provides the most significant attenuation in terms of attenuation, it is possible to design more effective shielding systems. These results demonstrate how this method is capable of detecting variations in the shielding performance of the material across different frequency ranges.


**Table 5.** Summary of the most representative results in three different frequency ranges.

#### **5. Conclusions**

The proposed measurement methodology shows significant advantages, including the simplicity of the sample machining, which means that very specific geometries or tiny dimensions are not required. This method allows the measurement of samples with low conductivity, contrary to the measurement method proposed in the ASTM D4935 standard. The sample insertion and removal process can be completed within a matter of seconds, which supposes that a wide range of measurements can be made with reasonable speed due to the easiness of the measurement procedure. The measured dynamic range is approximately −100 dB, allowing us to analyze the samples developed in this study in the frequency range where 5G technology operates.

On the other hand, EMI shielding effectiveness in the 700 MHz–18 GHz frequency range has been studied. Two types of materials have been compared, depending on the presence of fiber reinforcement. It has been observed the performance of the materials studied in a wider frequency spectrum than specified by ASTM4935-18 standard and controlling the surrounding effects by using the absorber box method.

Some of the samples analyzed have demonstrated to provide a significant attenuation. For those composites based on a polymer matrix with different concentrations of CNT, a value of −81.30 dB has been obtained for the frequency of 7.125 GHz for the 15w%CNT composite, which is a very significant SE value considering the nature of these materials. Whilst it is true that an increased volume fraction of filler may lead to a decrease in the mechanical performance of the host matrix by means of deterioration of its inherent morphology, it is necessary to incorporate a higher filler content in order to achieve higher SE. It is desirable to employ CNT/polymer composites at low filler loadings to produce cost-effective and versatile conductive composites.

The inclusion of a carbon fiber reinforcement has proven to be an effective strategy for achieving significant attenuation in composite materials, providing higher attenuation than the GF-reinforced composite with the same CNT concentration. This approach offers an advantage over using a high percentage of filler, which may lead to undesirable mechanical properties. This is due to the highly conductive nature of carbon fibers, which can effectively attenuate electromagnetic radiation. Furthermore, using CF reinforcement can also provide additional benefits such as increased stiffness and strength, as well as reduced weight. This, in turn, makes these materials an excellent alternative to replace traditional shielding materials.

It has to be highlighted that these types of characterizations are very relevant from a technological and industrial point of view. Specifically, for those sectors related to 5G technology, since the use of EMI shielding based on plastic materials has many advantages, such as manufacturing cost reduction.

**Author Contributions:** Conceptualization, A.S., J.T., A.B. and R.R.; Methodology, A.A. (Andrea Amaro), P.A.M. and A.A. (Antonio Alcarria); Validation, A.S., J.T. and P.A.M.; Formal analysis, A.A. (Andrea Amaro), R.H. and A.A. (Antonio Alcarria); Investigation, A.A. (Andrea Amaro), A.S. and R.H.; Resources, A.B., R.R., P.G. and A.P.; Writing—original draft, A.A. (Andrea Amaro), A.S., R.H., P.G. and A.P.; Writing—review & editing, J.T., P.A.M, A.B. and R.R.; Project administration, J.T.; Funding acquisition, J.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** The project with reference PLEC2021-007994 has been funded by MCIN/AEI/10.13039/ 501100011033 and by the European Union NextGenerationEU/PRTR.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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