**1. Introduction**

Mechanical alloying (MA) is a popular method for obtaining new materials with a controlled structure. This method can be used for the synthesis of materials with equilibrium and non-equilibrium structures, and the preparation of supersaturated, metastable crystalline, quasi-crystalline, intermetallic, nanostructured, and amorphous alloys [1,2]. The advantage of MA involves the possibility of obtaining nanocrystalline solid solutions and the occurrences of low-temperature phase transformations [2]. During the mechanical alloying process, parameters such as milling time, milling atmosphere, ball-to-powder ratio, or the size of grinding balls are selected. The milling time is one of the most important variables that affect the purity, structure, and properties of the final powder product. Therefore, many publications focus on the analysis of the properties of powders depending on the milling time [1,3–5]. Another important process parameter that affects the oxidation and contamination of powders is the milling atmosphere. Generally, an inert atmosphere, such

**Citation:** Romanczuk-Ruszuk, E.; Nowik, K.; Sztorch, B. X-ray Line Profile Analysis of Austenitic Phase Transition and Morphology of Nickel-Free Fe-18Cr-18Mn Steel Powder Synthesized by Mechanical Alloying. *Crystals* **2022**, *12*, 1233. https://doi.org/10.3390/cryst12091233

Academic Editor: Wojciech Polkowski

Received: 31 July 2022 Accepted: 23 August 2022 Published: 1 September 2022

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as argon or helium, is used. Nevertheless, when milling reactive powders, such as titanium, aluminum, iron, or iron alloys, a different protective atmosphere can be used to introduce gas from the atmosphere into the powders [1]. Mechanical alloying of iron alloy powders in a nitrogen atmosphere introduces nitrogen into the matrix in a solid–gas reaction. One interesting issue is the development of nickel-free austenitic stainless steel with nitrogen obtained by mechanical alloying in a nitrogen atmosphere and then consolidating these powders. Therefore, many studies have been carried out on nickel-free austenitic steel powders mechanically alloyed in a nitrogen atmosphere, which allows the introduction of nitrogen into the matrix. The use of nitrogen atmosphere in the mechanical alloying process leads to the transformation of ferrite into austenite. Additionally, manganese is added to these materials to increase the solubility of nitrogen [6,7].

The influence of the milling parameters and atmospheres on the Fe-α→Fe-γ phase transformation and amorphization process of the nickel-free stainless steel powder were analyzed by researchers [8–11]. However, there is no systematic analysis of the manganese (Mn) and nitrogen (N) influence and MA process parameters on the powder properties. Amini et al. [9] used elemental powders for the synthesis of Fe-18Cr-18Mn (wt. %) stainless steel under a nitrogen atmosphere. A fully fcc (Fe-γ) phase structure was achieved after 96 h of ball milling in a high-energy ball mill. Prolonging the ball milling process in this atmosphere up to 144 h resulted in an amorphous phase. Similar results, for Fe-18Cr-11Mn (wt. %) steel elemental powders mechanically alloyed in argon were reported by Haghir et al. [10]. A fully austenitic structure was achieved after 120 h of milling using a planetary high-energy ball mill (Retsch, PM100, Haan, Germany). When nitrogen atmosphere was used, a complete phase transformation occurred 20 h earlier. This emphasizes the nitrogen interstitial effect on the bcc to fcc phase transformation.

Tehrani et al. [12] reported an influence of Mn content on the Fe-α→Fe-γ phase transformation on two Fe-18Cr-7Mn and Fe-18Cr-8Mn (in wt. %) steel powder compositions mechanically alloyed in argon using a planetary high-energy ball mill (Retsch, PM100, Haan, Germany). In the higher manganese content alloy (8 wt. %), the fully austenitic structure was detected after 100 h of MA, while in the material with lower manganese content, even after 150 h of milling, the Fe-α→Fe-γ phase transformation was incomplete. This suggests that Mn content in the mechanically-alloyed austenitic steel should be higher than 7%.

The results in the literature show that the influence of manganese content from 6 to 12% on the properties of nickel-free stainless steel was usually investigated. The literature appraisal revealed that the influence of manganese content from 6 to 12% on the nickel-free stainless steel properties was usually investigated. In this study, a higher manganese content (18%) and a mixed atmosphere of mechanical alloying were used.

The main goal of this work was to analyze the phase transformation process and morphology of the Fe-18Cr-18Mn steel powder after mechanical alloying using argon followed by a nitrogen atmosphere.

## **2. Materials and Methods**

#### *2.1. Mechanical Alloying of Powders*

Iron, chromium, and manganese elemental powders (average particle size ~45 μm, 99.5% purity) supplied by Alfa Aesar (Kandel, Germany) were mixed and mechanically alloyed to obtain a nominal composition of Fe-18Cr-18Mn (in wt. %). The MA process was conducted in a planetary, high-energy ball mill Pulverisette 6 (Fritsch, Amberg, Germany) at a rotation speed of 250 rpm. Stainless steel balls (12 mm in diameter) were charged into a 500 mL stainless steel bowl with a ball to powder ratio (BPR) of 10:1. First, mixing of the powders was performed for 0.5 h at 150 rpm under argon atmosphere. For the first 30 h, the milling process was conducted under a pure argon atmosphere (>99.999%); after that, pure nitrogen (>99.999%) was applied. After 150 h of MA, the process was finished.

#### *2.2. Morphology and Microhardness of Powders*

The morphology of the powders was examined using scanning electron microscopy (SEM, Hitachi 3000N, Tokyo, Japan) with an energy dispersive spectroscopy (EDS) (Hitachi, Tokyo, Japan). Semi-quantitative chemical analysis of the main elements in the powders was performed. Figure 1 shows the SEM image of the surface area of the particle taken for the EDS analysis.

**Figure 1.** Example SEM image of a particle surface area for the SEM-EDS analysis.

Vickers microhardness (HV0.2) tests of the powders after different mechanical alloying times were performed using the PMT-3 tester (PMT Labs, Wah, Pakistan) under a load of 1.96 N (0.2 kg) for 15 s. For accurate results, at least ten indents were conducted on each sample and then the results were averaged and standard deviations determined.

#### *2.3. X-ray Diffraction of Powders*

A small amount of the MA powder was taken for the X-ray diffractometry (XRD) (Bruker, Karlsruhe, Germany) analysis after 30, 60, 90, 120, and 150 h of the milling process. To minimize the powder contamination, loading and unloading of the powder were performed in a glove box under a protection argon atmosphere. The phase structure was measured by means of X-ray diffractometry using Bruker D8 Advance equipped with Cu anode (*λ* = 0.15418 nm) radiation of 40 kV and 25 mA. For all samples, the angular range (2*θ*) of 20◦ to 100◦ with a step width of 0.01 and an acquisition time of 5 s was used. The instrumental broadening of peak profiles was determined using a corundum (Al2O3) standard (NBS SRM 1976b) and processed accordingly to the Caglioti et al. formula [13], following the procedures described widely in the literature (e.g., [14]).

It is widely known that traditional, "single-peak" methods of extracting microstructural data (e.g., Williamson–Hall method) do not take strain anisotropy effects into consideration [15], which are manifested in that the widths of the peaks do not increase monotonically with the diffraction angle *θ* [16]. For that reason, Ungár and Borbély developed an upgraded dislocation model of the mean square strain by incorporating the so-called average dislocation contrast factor *C*, which is known as the *modified* Williamson– Hall plot (MWH) [17]. The strain contribution can be expressed in terms of dislocation properties, as demonstrated in Equation (1):

$$
\Delta K = 0.9/d + \left(\pi A b^2 / 2\right)^{\frac{1}{2}} \rho^{\frac{1}{2}} K \overline{C}^{\frac{1}{2}} + O\left(K^2 \overline{C}\right) \tag{1}
$$

where *K* = 2 sin *θ*/*λ*, Δ*K* = 2 cos *θ*(Δ*θ*)/*λ*, *θ*, Δ*θ*, *λ* are the diffraction angle, FWHM of the reflection and the wavelength of X-rays. *C* is the average dislocation factor, where the average is made over the equally populated equivalent slip system. Other physical parameters in Equation (1) are: the dislocation density *ρ*, respectively, *A* is a constant determined by the outer cutoff radius of the strain field, *Re*, and *O* stands for noninterpreted, higher-order terms. Finally, *b* is the Burgers vector equal to *b* = *abcc*3 1 <sup>2</sup> /2 or *b* = *a f cc*2 1 <sup>2</sup> /2 for bcc and fcc crystal systems, respectively, where *a* is the lattice constant. The value of *C* depends only on the ratios of the material's elastic constants *c*11, *c*12, and *c*44, which can be further reduced to two parameters—elastic anisotropy *Ai* = 2*c*44/(*c*<sup>11</sup> − *c*12) and the ratio *c*12/*c*<sup>44</sup> [18]. In the case of cubic lattice systems, *C* is a linear function of the fourth-order invariant of the *hkl* Miller indices [19], as shown in Equation (2):

$$\overline{\mathcal{L}} = \overline{\mathsf{C}}\_{h00} \left( 1 - qH^2 \right) \tag{2}$$

where:

$$H^2 = \frac{h^2k^2 + h^2l^2 + k^2l^2}{\left(h^2 + k^2 + l^2\right)^2} \tag{3}$$

Equation (2) shows that, under the hypothesis that the sample has a random texture, which is entirely justifiable for a milled powder or randomly oriented polycrystal, *C* can be evaluated if the values of *q* and *Ch*<sup>00</sup> are known. *Ch*<sup>00</sup> is the average contrast factor corresponding to the *h*00 reflection, whereas the value of *q* determines the edge/screw type of dislocations [20].

To implement the strain anisotropy model, contrast factor coefficients had to be calculated for both Fe-bcc and Fe-fcc phases. As the austenitic transformation is caused by the continuous dissolution of Mn in the Fe matrix, it was assumed that the ferritic phase occurring at the beginning of MA was pure Fe, while the austenitic phase had the nominal composition of Fe-18Cr-18Mn. The necessary single crystal *cij* elastic constants of pure ferrite (Fe-bcc) were adopted from the literature [21], whereas Fe-18Cr-18Mn alloy elastic properties were estimated by the relations provided by Razumovskiy et al. [22]. These values were used to calculate the average contrast factors toward the *h*00 direction for edge *Ce <sup>h</sup>*<sup>00</sup> and screw the *<sup>C</sup><sup>s</sup> <sup>h</sup>*<sup>00</sup> dislocations, considering the 111{110} and 110{111} primary slip systems for bcc and fcc metals, respectively, using the online program ANIZC [23]. Similarly, the extreme values of *q*, corresponding to pure edge *qe* and pure screw *qs* dislocation characters were obtained by equations elaborated by Ungár et al. [18]. After obtaining *Ch*<sup>00</sup> and *q*, the average contrast factor can be calculated. The trend of *C* as a function of the scattering vector modulus (*s* = 2 sin *θ*/*λ*) is plotted in Figure 2. As presumed, *C* reaches its maximum towards the *h*00 direction, which is the soft crystallographic direction in both bcc and fcc Fe, along which the strain proceeds the most easily [24]. Relevant parameters needed to incorporate the dislocation model are summarized in Table 1. As can be noticed, the anisotropy of Fe-18Cr-18Mn austenitic alloy is considerably higher than in the case of pure bcc Fe, which is manifested by bigger deviations of *Ai* from unity.

**Figure 2.** The average value of anisotropic contrast factor *C* versus the scattering vector *s* calculated for bcc and fcc microstructures of the Fe-18Cr-18Mn alloy, considering pure edge and pure screw dislocation characters.


**Table 1.** Elastic parameters required to implement the strain anisotropy model.

Contrary to the classical methods of the line profile analysis (LPA), i.e., fitting peak profiles using arbitrarily defined, bell-shaped mathematical functions (top-down approach), the more sophisticated, bottom-up approach was recently developed. In the bottom-up approach, the entire diffractogram is modeled directly as a set of physical parameters affecting the peak's shape, width, and position. The size broadening calculation is based on the concept of column heights and the lognormal distribution of crystallite sizes is assumed (in contrast to the plain average obtained by classical LPA methods), which was largely verified in the case of highly deformed metals and finely dispersed powders [25]. Strain broadening was considered by the Krivoglaz–Wilkens theory of dislocations in distorted crystals [26].

The whole powder pattern modeling (WPPM) has been proposed as a universal technique for microstructure refinement. It provides detailed data on specimen microstructures by directly comparing model peak profiles with the entire experimental pattern, considering instrumental broadening and background [27,28]. Size and defect contributions are convoluted together with the instrumental component, and the pattern is then directly synthesized through Fourier transformation [29]. Despite the close analogy to the widely used Rietveld method, in WPPM, structural information is limited only to lattice parameters, while Rietveld refinement strictly relates integrated intensity to the structural model (atomic positions, occupancy, thermal factors, etc.) [28]. Another (but very similar to WPPM) approach is known as the convolutional multiple whole profile fitting (CWMP) [30], with the procedure of employing the instrumental profile being the only major difference. WPPM has been successfully utilized for investigating microstructural evolution in many ball-milled powders and other nanocrystalline materials [29]. Its algorithm has been implemented in a free and flexible software package, named PM2K [31], which was exploited in this study.

## **3. Results and Discussion**

#### *3.1. Morphology and Microhardness of the MA Powders*

Figure 3 shows SEM images of the powder morphology as a function of milling time. The histogram of the average particle size is presented in Figure 4. It is clear that the time of the process impacts the powder morphology. As received, an iron powder is regular and smooth in shape (Figure 3a). The chromium powder is irregular and angular in shape (Figure 3b), whereas the manganese powder (Figure 3c) has a morphology similar to chromium, with a more regular and smoother surface. The first 30 h of MA revealed an irregular shape of the powder, with an average size of 165 ± 10 μm. After replacing argon with nitrogen and prolonging the milling time up to 60 h, an average particle size continues increasing up to 213 ± 11 μm. The next 30 h of milling (30 h in argon and 60 h in nitrogen) did not change the morphology of powder particles; however, the average size of particles slightly decreased to 200 ± 10 μm. After another 30 h of MA, significant particle refinement to 81 ± 8 μm was observed. Thus, at this stage of the MA process, after 30 h of

milling in argon and 90 h of milling in nitrogen (total time of MA was 120 h), the powder fracturing took place. The MA process was performed up to a total of 150 h (30 h in argon and 120 h in nitrogen) and revealed bimodal distributions of particle, where approximately 75% of the powder had particle sizes of 51 ± 6 μm and 25% of powder had particle sizes of 10 ± 5 μm. This kind of bimodal powder distribution might have a favorable influence on the classical PM consolidation process, e.g., annealing, cold compaction, and sintering.

**Figure 3.** Morphology of the elemental powders: (**a**) Fe, (**b**), Cr and (**c**) Mn, and mechanically alloyed powder at different milling times, after: (**d**) 30 h, (**e**) 60 h, (**f**) 90 h, (**g**) 120 h, (**h**) 150 h.

**Figure 4.** The particle size and microhardness of powders at different milling times.

The mechanical alloying process consists of the repetition of cold welding, fracturing, and rewelding of powder particles occurring in the milling jar by collisions of balls against each other and the walls of the jar. The cold welding leads to an increase in particle sizes, while the fracturing leads to the fragmentation of particles [32]. Analyzing changes in the morphology of particles as a function of milling time, it can be concluded that during the first 60 h of MA, cold welding dominates, increasing the average particle size. The subsequent 30 h of milling does not cause a significant alteration in the particle size. This means that the fracturing process, resulting in the particle size decrease, is in equilibrium with the cold welding process. After 120 h of MA, the fracturing phenomenon causes a continuous decrease in the particle size, which emphasizes domination of the fracturing over cold welding. After 150 h of ball milling, the average particle sizes were almost similar to the initial sizes of the particles used at the beginning of the process (but with the bimodal distribution). Similar trends were reported by Haghir et al. [10], whereas Cisneros et al. [33] and Duan et al. [34] observed that the initial sizes of the elemental powders of ~50 μm after mechanical alloying, up to 170 h in nitrogen, were reduced to 10 μm. The authors pointed out that first the powder particles flattened and then the prolonging of milling time became equiaxed.

Coarser particle sizes observed here, in comparison with the literature data [33,34], are due to the different milling devices and process parameters, including atmospheres. For instance, decreasing the ball to the powder weight ratio from 10:1 to 5:1 can cause a significant increase in the crystallite and particle size of the obtained powder [32]. Cisneros et al. [33] used an attritor ball mill with the ball to powder weight ratio of 30:1, the rotation speed of 300 rpm, and nitrogen. Duan et al. [34] used a planetary ball mill, for instance, with a rotation speed of 350 rpm, and with three different types of ball diameters. This explains the differences between the literature data and the results presented here. Moreover, the atmosphere used here differs from the literature cited. The powder obtained here is softer in comparison to the hardness measurements presented by the other authors. This suggests that nitrogen content in the bulk powder is lower and, therefore, the number density of hard nitride precipitations can be reduced. This is clearly observed especially when argon atmosphere is used.

Figure 4 depicts the microhardness variation of the as-milled powder as a function of the milling time. The average microhardness of the powder increased from 450 ± 35 HV0.2 (after 0.5 h of powder blending) to 523 ± 45 HV0.2 after the first 30 h of MA. Note that when the atmosphere changed from argon to nitrogen, the hardness of the powder abruptly increased from 523 ± 45 up to 731 ± 52 HV0.2 within the same period of time. By further prolonging the milling time, an average hardness almost linearly increased, reaching 1068 ± 56 HV0.2 after 150 h of milling.

The mechanical alloying process, due to collisions of the powder with the balls and jar wall, generated microstructure defects, which caused the hardening effect and a continuous increase in hardness. As expected, a greater increase in the hardness of the powder was measured after changing the milling atmosphere from argon to nitrogen. However, the final hardness measured in this work was about 5% lower in comparison with the literature data [7], where the nominal composition of the tested powder was Fe-18Cr-4Mn (in % wt.), a 2.5 times lower percent of manganese in comparison with this work [7]. It is worth noting that Salahinejad et al. [7] applied different mechanical alloying process parameters (e.g., the ball to powder weight ratio was 30:1) and nitrogen atmosphere through the whole period of MA. After 153 h of mechanical alloying, a fully amorphous phase was obtained. Moreover, the microhardness of powder after 99 h of milling, when the phase structure was crystalline, was 1070 HV similar to the value obtained in this work after 150 h of MA.

#### *3.2. Chemical Composition of Powders*

In this work, the nominal composition of the alloy (Fe-18Cr-18Mn-N) was selected based on the modified Schaeffler's diagram for austenitic stainless steel. The percentage of manganese used in this study was higher in comparison to the literature data [6,33,35–37]. Higher Mn content stabilizes γ-Fe phase and alters the final powder's properties. We calculated both the Ni and Cr equivalents assuming that the steel possessed 18% of Mn and 18% of Cr, to find out the minimum N content that ensured the austenitic structure. From these calculations, it followed that 0.75% of N content was enough to obtain the austenite phase structure at room temperature. This N content can also be diminished when the equivalent carbon in the powder is included. From the literature, it is known that 0.9 ÷ 1.2% of N and 0.02 ÷ 0.03% of C content in austenitic steel powder after 120–150 h of MA was measured [33,36].

Table 2 presents the changes in the main element composition of the steel powder as a function of the milling time. These results reveal that, with up to 90 h of MA, the Mn and Cr content continuously increase; however, after this time of milling, the concentrations of these elements are almost unaffected. Therefore, taking into account the optimization process, the expected composition of the alloy was achieved after 90 h of milling, which suggests that the process of MA should be interrupted. The MA process was continued for up to 150 h to find out whether—after such a long time of milling—an amorphous phase would occur. The content of nitrogen and carbon increased gradually with the increasing milling time. After 150 h of mechanical alloying, the nitrogen content was 0.9% and carbon was 0.03%; the content of N and C were similar to the data from the literature.


**Table 2.** SEM-EDS analysis of the iron, chromium, and manganese concentrations in the MA powders at different milling times.
