**Effect of Ti/Ni Coating of Diamond Particles on Microstructure and Properties of High-Entropy Alloy/Diamond Composites**

#### **Wei Zhang 1,\*, Mingyang Zhang 1, Yingbo Peng 2, Fangzhou Liu 1, Yong Liu 1, Songhao Hu <sup>3</sup> and Yang Hu <sup>4</sup>**


Received: 31 December 2018; Accepted: 5 February 2019; Published: 10 February 2019

**Abstract:** In this study, an effective way of applying Ti/Ni deposited coating to the surface of diamond single crystal particles by magnetron sputtering was proposed and novel high-entropy alloy (HEA)/diamond composites were prepared by spark plasma sintering (SPS). The results show that the interfacial bonding state of the coated diamond composite is obviously better than that of the uncoated diamond composite. Corresponding mechanical properties such as hardness, density, transverse fracture strength and friction properties of the coated diamond composite were also found to be better than those of the uncoated diamond composite. The effects of interface structure and defects on the mechanical properties of HEA/diamond composites were investigated. The research directions for further improving the structure and properties of high-entropy alloy/diamond composites were proposed.

**Keywords:** high-entropy alloy; diamond; coating; interface; mechanical properties

#### **1. Introduction**

Multi-principal high-entropy alloys break through the traditional alloy design mode based on one kind of alloy element. By optimizing the composition design, excellent performance combinations such as high strength, high hardness, high temperature creep resistance, high temperature oxidation resistance and corrosion resistance can be obtained [1–9]. Based on the excellent properties of high-entropy alloys (HEAs) and diamond, it is of great scientific value and application significance to design a novel high-entropy metal matrix binder for diamond tools and to develop the corresponding theory and technology of heterogeneous multi-phase interface control [10–12].

Under the application conditions, improving the interface state between matrix materials and diamond particles is the key problem to be urgently solved in the research field of diamond tool materials. For diamond tools with an HEA matrix, improving the wettability between the HEA matrix and diamond particles and effectively controlling the reaction products of the HEA/diamond interface are important for improving the interface bonding and overall application performance of diamond tools. Ti, Cr, Mo, V and other strong carbide-forming elements were always selected as coating materials [13–15], which can form a carbide layer on the surface of diamond particles to realize metallurgical bonding between diamond and the matrix. Meanwhile, the direct contact between Fe, Co, Ni and diamond particles can be avoided to prevent the formation of hard and brittle carbides at the interface [16,17]. Therefore, the ideal structure of metallurgical bonding between diamond particles and a metal matrix involves avoiding the formation of carbides.

In this paper, a novel HEA/diamond composite was studied by magnetron sputtering Ti/Ni coating and the spark plasma sintering (SPS) method. A Ti/Ni coating (inner Ti and outer Ni) of diamond particles was realized by magnetron sputtering. An HEA/coated diamond interface was obtained, composed of the solid solution formed by diffusion between the HEA matrix and Ni element in the outer layer of diamond particles. The carbide formed by the reaction of Ti element with diamond particles. On the one hand, this interface can effectively reduce the interface energy between diamond and the HEA matrix and improve the bonding strength. On the other hand, the cracks and micro-holes on the interface after SPS can be filled by generated carbides to improve the density of the composites and improve the strength, toughness and other mechanical properties of the composites.

#### **2. Experimental**

Standard MBD4-type synthetic diamond single crystals of 140/170 mesh were boiled and rinsed in HNO3 and NaOH solutions for surface purification. Diamond was deposited in the magnetron sputtering coating equipment and high purity argon was introduced. The metals Ti and Ni with purity higher than 99.99% were used as targets. The diamond surface was coated by vacuum magnetron sputtering and maintained at room temperature. The vacuum of the reaction chamber was 10−<sup>4</sup> Pa, the partial pressure of argon was 10−<sup>1</sup> Pa, the ion deposition rate was 20 nm/min and the diamond was rolled by ultrasonic vibration in the diamond tray to ensure the uniformity of the coating. The thickness was controlled and was about 15 μm as shown in Figure 1. FeCoCrNiMo HEA powders prepared by gas atomization were applied as matrix materials as shown in Figure 1c, in which the average particle size was about 50 μm. Coated and uncoated diamond particles with a mass ratio of 4% were mixed with HEA powder and put into the mixer for 5 hours (mixer speed: 60 r/min). HEA/diamond composites were prepared by SPS (SPS parameters: 950 °C/35 MPa, holding time: 480 s).

**Figure 1.** Microstructure of (**a**) uncoated and (**b**) coated diamond particles and (**c**) high-entropy alloy (HEA) powders.

The density of samples was measured by the Archimedes drainage method. The transverse fracture strength of the samples (size: 12 × <sup>2</sup> × 30 mm3, span: 25 mm, loading rate: 2 mm/min) was determined by the Instron 3369 mechanical testing facility (Instron, Norwood, MA, USA) using the three-point method. The hardness of the alloy was determined using a Vickers hardness tester (200HVS-5, HuaYin, Zhengzhou) under a 200 g load for 15 s and was averaged from five measurements. The wearing behavior was measured by HRS-2M high-speed reciprocating line friction test equipment (Lanzhou Zhongke Kaihua Technology Development Co., Ltd., Lanzhou, China). The test parameters were a test time of 15 min, 50 N loading, 15 Hz frequency (900 times/min) and a 5-mm stroke. A scanning electron microscope (SEM, FEI, Quanta 250 FEG, Vlastimila Pecha, Czech Republic) equipped with an energy dispersive X-ray (EDX) analyzer was used to investigate the microstructure and chemical compositions of the sintered samples. Confocal Raman microscopy was performed on the interface of diamonds/HEA using an inVia Reflex by Renishaw with an Ar laser, using the green line (532 nm, 7.6 mW) with a resolution of 0.5 × 2 μm.

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

#### *3.1. Interface of HEA/Diamond Composite*

In the SEM analysis of the coated diamond (Figure 2 and Table 1), spot 1 at the edge of the diamond shows all C atoms. Spot 2 is in the transition zone between the diamond and the coated layer. C, Ti and Ni elements can be found in the area near the diamond, of which the content of Ni is relatively small. Spot 3 is in the coated layer, whereas that of Ni element is much more in the outer layer. This is because Ti is a strong carbide-forming element with strong chemical activity and diffusion ability. During the SPS process, Ti reacts with diamond to form a stable, chemically bonded TiC layer. At the same time, because the matrix is a five-element HEA of FeCoCrNiMo, the higher amount of Ni element in the outer layer can form a solid solution interface with the HEA matrix.

**Figure 2.** Microstructure of Ti/Ni-coated diamond particles.

**Table 1.** Chemical composition of different spots in Figure 2.


The density of coated diamond increases by about 1/3 due to its multi-layer. This is closer to the density of a high-entropy alloy matrix, which makes the mixture more uniform, reduces the number of voids and indirectly improves the density after sintering. The HEA matrix was found to form a metallurgical bonding with diamond and shows a thin layer with a width of approximately 3 μm at the interface between the diamond and the matrix. This indicates that the metallurgical bonding between the coated diamond particles and the matrix is relatively strong, as shown in Figure 3c,d, while the uncoated diamond resists mechanical bonding to a certain extent, as shown in Figure 3a,b.

**Figure 3.** Scanning Electron Microscope (SEM) and Back Scattered Electron (BSE) images of (**a**,**b**) uncoated diamond particles and (**c**,**d**) coated diamond particles.

It was found from the Energy Dispersive Spectrometer (EDS) analysis of the interface of coated diamond/HEA composites that, as shown in Figure 4, there is a high content of Cr and Fe elements between the diamond and the high-entropy alloy matrix, that is, the segregation of Cr, Ti, Ni and Mo elements occurs and the reaction with diamond produces a solid solution layer with a higher bonding strength than that achieved via pure mechanical bonding. It can also be seen from the image that although C atoms aggregate at the interface, they do not extend to the matrix. Although the functional metallic layer has a certain corrosion effect on diamond, it does not destroy the crystalline form of diamond to a large extent. On the contrary, the transition layer restricts the diffusion of carbon atoms to the matrix. It can be seen from Figure 3c,d that the transition layer is different from the non-functional diamond. The smooth bonding surface of diamond composites and the functional diamond composites show a fold structure. This structure increases the bonding area between diamond and the matrix in the transition layer, so that it can be better bonded with the matrix. Moreover, the EDS surface analysis of the interface between coated diamond and the matrix was carried out. As shown in Figure 4b, in accordance with the results of liner scanning, there is obvious segregation at the interface and obvious precipitation of Cr and Mo. This indicates that the interface layer may be a solid solution composed of Cr, Mo, Ti and Ni, indicating that the functionalized layer can form a metallurgical bond with the HEA matrix that will increase the interfacial bonding strength.

**Figure 4.** EDS liner scan (**a**) and element mapping (**b**) analysis on the interface of coated diamond/HEA composite.

The interface status of HEA matrix/diamond were also characterized by Raman spectroscopy, as shown in Figure 5. As shown in Figure 5a, there are diamond peaks at 1332 cm<sup>−</sup>1, graphite peaks at 1350 cm−<sup>1</sup> (D-band), 1580 cm−<sup>1</sup> (G-band) and 2700 cm−<sup>1</sup> (2D-band) and other bonds at the interface of the uncoated diamond specimens. The peak shape is sharp, the G-band strength is more than two times that of D-b (Figure 5b) and the area ratio of ID/IG (Intensity ratio of peak D to peak G) is about 0.52. The interface of the coated diamond specimens only exhibits a diamond peak at 1332 cm−1. For the peaks at 1350 cm−<sup>1</sup> (D-band) and 1580 cm−<sup>1</sup> (G-band) (Figure 5c), the peak shape is wide, the G-band strength and D-band strength are close (Figure 5d) and the area ratio of ID/IG is about 2.35, which is obviously higher than that of the uncoated diamond samples. The results show that the graphitization degree of diamond particles in uncoated diamond samples is higher [18] and the other bonds indicate that there are carbides or oxides at the interface [19]. In conclusion, coated diamond can effectively inhibit the graphitization structural transformation of diamond particles in the SPS process and improve the material properties.

**Figure 5.** Raman spectra of HEA matrix/diamond interface in (**a**) uncoated diamond and (**c**) coated diamond, as well as the corresponding fitting curves (1000 cm−<sup>1</sup> ~ 2000 cm<sup>−</sup>1) (**b**,**d**).

#### *3.2. Microstructure of the HEA/Diamond Composite*

The microstructure of the composites fabricated by SPS with coated and uncoated diamond is shown in Figure 6. Uncoated diamond particles are severely ablated. After sintering, the original diamond with a regular shape displays jagged ablation on its surface, which cannot maintain the original excellent crystal form of the diamond as shown in Figure 6a,c. The coated diamond also has a certain degree of ablation, as shown in Figure 6b,d. However, due to the passivation of the coated metal layer, which prevents the corrosion of the matrix to diamond and reduces the diffusion of C element to the matrix, a good crystal form of diamond is maintained. Meanwhile, the coating contains Ti element, while Ti element and C element form carbides and the second-phase carbides disperse in the matrix, thus improving the hardness of the FeCoCrNiMo high-entropy alloy system [20]. Therefore, the friction and wear properties of materials are also affected.

According to the X-ray diffraction (XRD) analysis of the HEA/diamond composite, as shown in Figure 7, only two strong peaks of diamond were detected, because of the low content of diamond and the close distance between the Face-Centred Cubic (FCC)peak and the diamond peak of HEA. However, no carbide and C element were detected. This indicates that there was no large amount of ablation or graphitization of the diamond in coated diamond samples. Moreover, the HEA matrix had an FCC structure and there was no complex multiphase structure and no intermetallic compound found in coated samples in Figure 7. Therefore, the excellent properties of HEA matrix could be maintained. Yet, in uncoated diamond samples, the addition of diamond particles was found to form any complex carbide phase and there existed carbides of Cr according to the powder diffraction files (PDF), such as Cr23C6 (PDF No. 04-004-1672) and Cr7C3 (PDF No. 04-005-9649). These carbides were hard and brittle, which could deteriorate the mechanical properties of the composite.

**Figure 6.** Microstructure of the composites fabricated by spark plasma sintering (SPS) with uncoated (**a**,**c**) and coated diamond (**b**,**d**).

**Figure 7.** XRD pattern of the composites fabricated by SPS with coated and uncoated diamond.

#### *3.3. Mechanical Properties*

From the density of uncoated diamond/HEA composites in Table 2, the density difference between uncoated diamond and HEA powder was found to be large, which not only causes inhomogeneity in the mixing process, but also causes a low density of green compacts. Under such circumstances, it is impossible to eliminate the inhomogeneous distribution of pressure in the sintered block caused by pores, which ultimately results in the insufficient density of composites. The surface coating of diamond can improve the density of diamond particles, make the mixture more uniform, reduce the number of pores and increase the sintering density. At the same time, the activation of diamond can promote the diffusion reaction between diamond and the matrix and produce good metallurgical bonding. According to the results of hardness tests (Table 2), it was found that the hardness of the samples of coated diamond composites is about 30 HV higher than the that of uncoated samples, because the graphitization of diamond particles (Figure 4c) in the uncoated diamond composites reduces the hardness of the matrix.

The fracture strength of coated diamond composites is 745 MPa, which is far greater than that of uncoated diamond samples, as shown in Table 2. The reason for the low fracture strength of uncoated diamond composites is the low density caused by the micro-voids in the materials, the graphitization of diamond as a hard phase and the poor bonding between diamond and the HEA matrix. It does not produce good metallurgical bonding, but is only a metallurgical bonding and mechanical bonding interface.

**Table 2.** Density, hardness and transverse fracture strength of the composites fabricated by SPS with coated and uncoated diamond.


Friction and wear performance is an important property of diamond tools. Comparing the SEM images after friction from the wear mechanism, as shown in Figure 8, there were ravines and trace debris on the surface of the both coated and uncoated diamond composites. It can be inferred that the wear mechanism is abrasive wear with partially adhesive wear. The scratches on the surface of uncoated diamond composites were obvious and diamond shedding occurred. Through the analysis of the exfoliated parts in Figure 8a,b, it was found that although the diamond and the matrix have a certain degree of metallurgical bonding, due to the loose structure and inadequate bonding, the diamond will fall off from the matrix and fail. Compared with the coated diamond composite, the coated diamond can be worn without showing signs of falling off (Figure 8c,d). This shows that the Ti/Ni coating can enhance the control ability of the HEA matrix over diamond particles, improve the bonding strength and thus enhance the service life of diamond composites.

**Figure 8.** The wearing surface of the composites fabricated by SPS with uncoated (**a**) and coated (**b**) diamond.

The friction coefficients of the two kinds of samples fabricated by SPS ranged from 0.04 to 0.06 and maintained a very stable trend, as shown in Figure 9. After 15 min of friction, the wear of the uncoated diamond samples was 0.0144 g, while the wear of the coated diamond samples was only 0.0127 g. This shows that the friction and wear properties of the two samples are both excellent, which also confirms that the hardness of the two samples is not very different. The reason for the smaller friction coefficient is that the diamond in the sample is relatively complete and bare. The agate ball only rubs on the diamond surface, while the strong control of the matrix on diamond keeps the friction

coefficient in a stable linear trend. That is, in the actual friction process, diamond plays a major role in friction, while the HEA matrix holds on the diamond. The basic type of wear is the combination of abrasive wear and adhesive wear. In general, the friction failure of diamond tools is the shedding of diamond or the wear of matrix; however, the surface coating of diamond can effectively avoid the shedding of diamond particles.

**Figure 9.** The friction coefficient curve of the composites fabricated by SPS with uncoated and coated diamond.

#### **4. Conclusions**

Diamond single crystal particles with Ti/Ni coatings were obtained by magnetron sputtering. The diamond gained more than 30% weight and the coating thickness was 10–20 μm.

The interfacial diffusion and solid solution formation in coated diamond composites led to the increase of interfacial bonding strength. The interface bonding strength and mechanical properties of the composites without diamond coating decreased, due to the occurrence of graphitization at the interface and the formation of carbides.

Compared with the composite with uncoated diamond, the density, hardness, transverse fracture strength and interfacial bonding properties of the composite with coated diamond were significantly improved.

The wear resistance of the coated composites is obviously higher than that of the uncoated composites, because the coating on the diamond particles maintains a relatively complete crystal form in the SPS process and has a higher bonding strength with the HEA matrix. This improves the holding force of the matrix and gives full play to the excellent properties of the HEA.

**Author Contributions:** Conceptualization, W.Z. and Y.L.; Methodology, W.Z.; Validation, Y.P.; Formal Analysis, W.Z. and Y.P.; Investigation, M.Z. and F.L.; Resources, Y.L. and S.H.; Data Curation, M.Z.; Writing—Original Draft Preparation, M.Z. and F.L.; Writing—Review & Editing, W.Z. and Y.P.; Project Administration, W.Z. and Y.L.; Funding Acquisition, Y.L., S.H. and Y.H.

**Funding:** The authors wish to acknowledge the financial support of State Key Laboratory of Powder Metallurgy (CSU 621011808), the XUCHANG Fellowship Program (grant number: XW2017-40), the project of Innovation and Entrepreneur Team Introduced by Guangdong Province (201301G0105337290) and the Special Funds for Future Industrial Development of Shenzhen (No. HKHTZD20140702020004).

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

#### **References**

1. Yeh, J.W.; Chen, S.K.; Lin, S.J.; Gan, J.Y.; Chin, T.S.; Shun, T.T.; Tsau, C.H.; Chang, S.Y. Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. *Adv. Eng. Mater.* **2004**, *6*, 299–303. [CrossRef]


© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

### *Review* **Coherent Precipitation and Strengthening in Compositionally Complex Alloys: A Review**

#### **Qing Wang 1, Zhen Li 2, Shujie Pang 3, Xiaona Li 1,\*, Chuang Dong <sup>1</sup> and Peter K. Liaw 4,\***


Received: 29 October 2018; Accepted: 14 November 2018; Published: 15 November 2018

**Abstract:** High-performance conventional engineering materials (including Al alloys, Mg alloys, Cu alloys, stainless steels, Ni superalloys, etc.) and newly-developed high entropy alloys are all compositionally-complex alloys (CCAs). In these CCA systems, the second-phase particles are generally precipitated in their solid-solution matrix, in which the precipitates are diverse and can result in different strengthening effects. The present work aims at generalizing the precipitation behavior and precipitation strengthening in CCAs comprehensively. First of all, the morphology evolution of second-phase particles and precipitation strengthening mechanisms are introduced. Then, the precipitation behaviors in diverse CCA systems are illustrated, especially the coherent precipitation. The relationship between the particle morphology and strengthening effectiveness is discussed. It is addressed that the challenge in the future is to design the stable coherent microstructure in different solid-solution matrices, which will be the most effective approach for the enhancement of alloy strength.

**Keywords:** precipitation; strengthening; coherent microstructure; conventional alloys; high entropy alloys

#### **1. Introduction**

Precipitation strengthening with intermetallic compounds is the most effective approach for the enhancement of alloy strength in engineering structural materials, compared with solid-solution strengthening, grain-boundary strengthening, and work hardening [1–3]. Especially at high temperatures (HTs), the precipitation strengthening is indispensable due to the prominent long-time microstructural stabilities caused by second-phase precipitates in the solid-solution matrix [4–8]. Among them, the coherent ordered phases, such as L12-Ni3Al (*cP*4-Cu3Au) of the face-centered-cubic (FCC) solid solution [4,5], and B2-NiAl (*cP*2-ClCs) of the body-centered-cubic (BCC) solid solution [9–13], are crucial for the HT creep-resistant properties of alloys due to the perfect coherency between the ordered phase and the solid-solution matrix. It should be pointed out that the precipitation strengthening is related not only to the macroscopic properties of precipitates, but also to their microstructural morphologies. For instance, the prominent creep-resistant property of Ni-based superalloys at up to 85% of the insipient melting temperature (as high as 1100 ◦C) is primarily attributed to the special microstructure of spherical or cuboidal L12-Ni3Al nanoprecipitates coherently-precipitated into the FCC matrix [5].

In order to meet the service-performance requirements, including mechanical strength, corrosionand oxidation-resistant properties, etc., several solute elements are generally added to alloy or minor-alloy the solvent matrix constituted of one or two primary elements in conventional engineering structural materials [14]. From the viewpoint of element species, most of high-performance metallic materials, including Al alloys, Mg alloys, Cu alloys, stainless steels, and Ni superalloys, are all compositionally-complex alloys (CCAs), resulting in a uniform microstructure of diverse second-phase particles distributed in their solid-solution matrix. Recently, another kind of newly-developed CCAs are not based on one or two solvent elements, but based on the equimolar or near-equimolar mixing of multi-principal elements, which are also named high-entropy alloys (HEAs) [15–20]. HEAs have attracted more attention due to their unique properties resulted from simple crystalline structures, such as FCC, BCC, close-packed hexagonal (HCP), and their derivatives (L12, B2, etc.) [19–22]. Thus, they can also be regarded as a special kind of solid-solution alloys, similar to conventional engineering alloys.

Therefore, the present work will comprehensively generalize the precipitation behavior and precipitation strengthening in CCAs, including conventional engineering alloys and high-entropy alloys, where the coherent precipitation will be specially emphasized. The morphology evolution of second-phase particles and precipitation strengthening mechanisms will be illustrated firstly. Then, the relationship between the particle morphology (shape and particle size) and strengthening effectiveness in diverse CCAs will be discussed, respectively. Finally, several thoughts on the coherent precipitation to design and develop high-performance CCAs in the future will be suggested.

#### **2. Equilibrium Morphology of a Misfitting Particle**

In the absence of elastic stress, the equilibrium morphology of a second-phase particle embedded into a matrix is established solely by the particle-matrix interfacial energy and its dependence on crystallographic orientation [23]. However, experimentally, the particle morphology, which arises during a diffusional phase transition in many alloys, was often not the shape that minimizes the total interfacial energy. In most cases, the presence of the lattice misfit between the second phase and the matrix can induce an elastic stress field, which in turn, affects the particle morphology [24]. For instance, in Ni-based superalloys with a microstructure of ordered L12-Ni3Al particles coherently-embedded into the FCC solid-solution matrix, the particles were observed to undergo changes in shape from spheres to cuboids, and then to plates with increasing particle size [25,26], or even fission into smaller particles once they reach a critical size [27–29]. Actually, the particle equilibrium shape is determined by minimizing the total energy *Et*, the sum of interfacial energy, *Ei*, and elastic energy, *Ee*, at a constant particle volume, in which the *Ei* and *Ee* scale with the surface area and the volume of the particle, respectively [30,31]. So, the equilibrium shape of a misfitting particle is dependent on the particle size. That is to say, the particle shape should tend towards the shape that minimizes the *Ei* at a smaller particle size, and towards the shape that minimizes the *Ee* at a larger size. Furthermore, with increasing particle size, the elastic energy plays an increasingly important role in setting the shape since it is the driving force of the particle growth and coarsening.

The relative importance of the elastic energy and the interfacial energy can be evaluated through the characteristic parameter *L* [32,33], i.e., *L* = *ε*2*C*44r/s, where *ε* is the lattice misfit between the particle and matrix phases, *C*<sup>44</sup> is the elastic constant of the matrix, *r* is the average particle size, and *s* is the average specific interfacial energy. Figure 1 gives the morphology evolution of the particle with the parameter *L* [33], from which it is found that a small *L* usually corresponds to a spherical particle, which can transform to ellipsoidal or cuboidal shape when *L* increases. At a much larger *L*, the fourfold symmetry of cuboidal particles will be broken and some low symmetric shapes, like plates or needles, will begin to appear due to the elastic anisotropy. In addition, when the particle sizes are comparable, the lattice misfit *ε* will play the key role in determining the particle shape, since the parameter *L* is proportional to both the lattice misfit *ε* and the particle size *r*. Apparently, the particle morphology has a profound effect on the mechanical properties of alloys, which will be discussed in the following diverse alloy systems, respectively.

**Figure 1.** Particle morphology evolution with the characteristic parameter *L*, in which the vertical axis is the Fourier coefficient *aR* to represent the energy of different particle shapes. It shows that the bifurcation from the four-fold symmetric cuboid to the two-fold symmetric shapes (plate or needle) occurs at a critical value (*L* = 5.6) [33].

#### **3. Precipitation Strengthening Mechanisms**

The precipitation strengthening mechanisms can be divided into two categories [1–3], the dislocation shearing mechanism and the Orowan dislocation bypassing mechanism, depending on the interaction between moving dislocations and precipitates. The one leading to a smaller strength increment is the operative mechanism. The dislocation-shearing mechanism is generally active when the precipitates are coherent with the matrix, and the particle size is small, while the Orowan bypassing mechanism dominates when the coherent particle size exceeds a critical value or when the particles are incoherent with the matrix. For the shearing mechanism, three factors contribute to the increase in yield strength, coherency strengthening (Δ*σCS*), modulus mismatch strengthening (Δ*σMS*), and order strengthening (Δ*σOS*). The former two (Δ*σCS* and Δ*σMS*) occur before the dislocation shears the particle and the latter (Δ*σOS*) during shearing. Thereof, the larger value of (Δ*σCS* + Δ*σMS*) or Δ*σOS* is expected to be the total strength increment from the shearing mechanism. The equations available to calculate these strength increments caused by both dislocation shearing and bypassing are as follows [34–39]:

$$
\Delta \sigma\_{\rm CS} = M \times u\_{\rm \varepsilon} \times \left( G \varepsilon\_{\rm c} \right)^{\frac{3}{2}} \times \left( \frac{rf}{0.5Gb} \right)^{\frac{1}{2}} \tag{1}
$$

$$
\Delta \sigma\_{\rm MS} = M \times 0.0055 (\Delta G)^{\frac{3}{2}} \times \left(\frac{2f}{G}\right)^{\frac{1}{2}} \times \left(\frac{r}{b}\right)^{\frac{3\mu}{2}-1} \tag{2}
$$

$$
\Delta \sigma\_{\rm OS} = M \times 0.81 \times \frac{\gamma\_{\rm app}}{2b} \times \left(\frac{3\pi f}{8}\right)^{\frac{1}{2}} \tag{3}
$$

$$
\Delta \sigma\_{\text{or woman}} = M \times \frac{0.4Gb}{\pi \sqrt{1-\upsilon}} \times \frac{\ln(2\sqrt{\frac{2}{3}}r/b)}{\lambda\_p},
\lambda\_p = 2\sqrt{\frac{2}{3}}r(\sqrt{\frac{\pi}{4f}}-1) \tag{4}
$$

where *M* = 2.73 for BCC structure and *M* = 3.06 for FCC structure (Taylor Factor) [1], *αε* = 2.6 (a constant) [35,36], *m* = 0.85 (a constant) [37,38], *ε*<sup>c</sup> = 2*ε*/3 [2,35,36], the constrained lattice misfit. *G* and Δ*G* are the shear-modulus of the matrix and the shear modulus mismatch between precipitates and matrix, respectively; *b* is the Burgers vector; *r* and *f* are the average size and the volume fraction of precipitates, respectively; γ*apb* is the anti-phase boundary energy of precipitates; *v* is the Poisson ratio; and *λ<sup>p</sup>* is the inter-precipitate spacing.

Since the shearing and bypassing mechanisms occur concurrently and are independent to each other, the strengthening is determined by the smaller of Δ*σshearing* or Δ*σorowan*. In other words, the softer mechanism initiates the plastic deformation. Ideally, the largest yield strength increment could be reached when Δ*σ*shearing = Δ*σorowan* at a critical particle size *r*<sup>0</sup> with a fixed *f* [1]. Figure 2 shows the variation tendency of the yield strength increment with the particle size by competing the dislocation shearing and bypassing mechanisms, in which the maximum strength increment reaches at the critical *r*<sup>0</sup> when the volume fraction *f* is fixed.

**Figure 2.** The variation tendency of yield strength increment with the particle size [1–3], in which the strength increments caused by dislocation shearing mechanism (Δ*σshearing*) and bypassing mechanism (Δ*σorowan*) are shown, and the maximum increment reaches at a critical particle size *r*0.

#### **4. Precipitate Morphology and Precipitation Strengthening in CCAs**

In this section, the precipitation behavior and precipitation strengthening effects in each CCA system are generalized in details. Typical alloy systems with precipitation strengthening include Ni-based superalloys, Al alloys, Mg alloys, Cu alloys, stainless steels, and high-entropy alloys. The overviews are elaborated as follows.

#### *4.1. Ni-Based Superalloys*

Ni-based superalloys exhibit the most outstanding mechanical properties (especially the creep-resistance), corrosion- and oxidation-resistant properties at elevated temperatures among all the conventional structural materials. Their excellent properties are benefited from their specially coherent microstructures of spherical or cuboidal L12-γ nanoprecipitates into FCC-γ solid solution [4–6]. Especially the coherent precipitation of cuboidal L12-γ particles in single-crystal superalloys is responsible for the necessary strength at much higher temperatures near to the melting point [40,41]. However, the single-crystal superalloys with similar compositions often possess different creep-resistant properties, even containing cuboidal γ precipitates with a comparable particle size.

Figure 3 exhibits the creep curves at 1100 ◦C/137 MPa of TMS-138 (Ni-6Co-3Cr-3Mo-6W-6Al-6Ta-0.1Hf-5Re-2Ru, wt.%) and TMS-75(+Ru) (Ni-12Co-3Cr-2Mo-6W-6Al-6Ta-0.1Hf-5Re-1.5Ru, wt.%) alloys, in which the microstructural evolutions during the creep process are also shown [40]. Both superalloys have similar compositions with a minor difference in the amounts of Co, Mo, and Ru. The particle sizes of cuboidal γ nanoprecipitates in these two alloys are comparable, being *r* = 230 ± 30 nm (TMS-138) and *r* = 245 ± 25 nm (TMS-75(+Ru)), respectively, with a volume fraction of

about *f* = 65% in experiments. But the lattice misfit *ε* between γ and γ phases are different in both alloys, being *ε* = −0.33% in TMS-138 and *ε* = −0.16% in TMS-75(+Ru) at 1100 ◦C, respectively, in which the lattice misfit is calculated with the equation of *ε* = 2(*a*<sup>γ</sup> − *a*γ)/(*a*<sup>γ</sup> + *a*γ) (*a*<sup>γ</sup> and *a*γ: the lattice constants of γ and γ phases, respectively). Remarkably, TMS-138 possesses a longer creep life and a lower minimum creep rate, which is attributed to its larger γ/γ lattice misfit *ε*. Specifically, in the primary creep stage, such as the time *t* = 2 h, the larger misfit stress caused by the larger *ε* in TMS-138 drives the loops of matrix dislocations to move by cross-slip through the matrix channels, while in TMS-75(+Ru), the dislocations move by climbing around the γ cuboids due to the insufficient driving force by the relatively-smaller *ε* (as seen in the microstructures in Figure 3). With increasing creep time to *t* = 60 h, there are many superdislocations in γ cuboids in TMS-75(+Ru), while many perfect dislocation networks on the γ/γ interface are formed in TMS-138, which can effectively prevent the gliding dislocations in the γ channels from cutting the rafted γ/γ structure. More importantly, the larger lattice misfit can result in the denser γ/γ interfacial dislocation networks. Clearly, the dislocation networks are much denser in TMS-138 after rupture, which is the key for the small minimum creep rate.

**Figure 3.** Creep curves at 1100 ◦C/ 137 MPa of TMS-75(+Ru) and TMS-138 superalloys, in which the microstructures at different creep stages (primary stage, steady state and after rupture) are also presented [40].

Not only the precipitate morphology, but also the strengthening effect of coherent precipitation are closely related to the lattice misfit between the ordered phase and solid-solution phase. We calculated the yield strength increments given by shearing and bypassing mechanisms according to the Equations (1)–(4) with the particle size *r*, in which the dominant (Δ*σCS* + Δ*σMS*) presents the strength increment caused by the shearing mechanism. The used parameters for strength increment calculations are *M* = 3.06, *αε* = 2.6, *G* = 81 GPa, Δ*G* = 4 GPa, *m* = 0.85, *b* = 0.254 nm, *γapb* = 0.12 J/m2, and *v* = 0.35, respectively. Figure 4 gives the variation tendencies of (Δ*σCS* + Δ*σMS*) and Δ*σorowan* as a function of the particle size *r* for TMS-138 and TMS-75(+Ru) superalloys. It was found that the optimal particle size *r*<sup>0</sup> corresponding to the maximum strength increment given by the theoretical calculation in TMS138 is *r*<sup>0</sup> = 193 nm, which is consistent with the experimental size of *r* = 230 ± 30 nm. While the experimental particle size (*r* = 245 ± 25 nm) is far away from its optimal *r*<sup>0</sup> = 406 nm in TMS-75(+Ru), indicating that the strengthening effect does not reach the maximum. Hence, the TMS-138 superalloy exhibits a much higher strength and a better creep resistance due to a larger lattice misfit. Therefore, in the case of coherent precipitation, the control of the lattice misfit between the ordered phase and its parent solid solution is significant to develop high-performance CCAs.

**Figure 4.** The variation tendency of (Δ*σCS* + Δ*σMS*) and Δ*σorowan* with the particle size *r* of TMS-138 and TMS-75(+Ru) superalloys, in which the optimal particle size *r*<sup>0</sup> from the calculation and the experimentally-measured *r* are also marked for each alloy.

#### *4.2. Al-Based Alloys*

Al alloys have been used widely as engineering structural materials due to their high specific strength, among which the high-strength Al-Zn-Mg-Cu series of alloys (7000 series) are extensively applied into aeronautical fields [42–46]. The Al-Cu binary system is a well-studied precipitation-strengthening system, since it forms the basis for many types of age-hardening alloys with technological importance [47]. The precipitation sequence during the aging process, Al SS → G.P. zone → θ"-Al3Cu → θ -Al2Cu → θ-Al2Cu, was often taken as a model for describing the fundamentals of precipitation strengthening. The coherent Guinier-Preston (G.P.) zone consisting of a single layer of pure Cu atoms was firstly precipitated from the FCC-Al solid solution (SS) matrix. Then, Al-Cu clusters with a stoichiometrical Al3Cu (θ") were formed, which is also coherent with the FCC matrix. It could transform into the metastable θ -Al2Cu phase with a body-centered-tetragonal structure, which is the main strengthening phase, but semi-coherent with the matrix. Finally, the metastable θ -Al2Cu would transform into the equilibrium tetragonal θ -Al2Cu phase, which is incoherent with the matrix [48]. In this case, the coherent relationship between the precipitated phase and the matrix could be destroyed with prolonging the aging time, which eventually leads to the formation of coarse precipitates, as a final result of weakening the strengthening effect, compared with the coherent fine precipitates. Figure 5 shows the effect of the particle morphology on the hardness variation with the aging time of Al-0.8Mg-0.79Si (wt.%, 6061) alloy [49]. The peak hardness reaches at 175 ◦C aging for 4 h, corresponding to the semi-coherent precipitation of the needle β (a monoclinic structure with a stoichiometrically MgSi) nanoparticles with a size of about 10~15 nm. Once the needle β nanoparticles are transformed to relatively-coarse rod β particles (a hexagonal structure with a stoichiometrically Mg1.7Si) at 200 ◦C aging for 20 h, the hardness will decrease due to the incoherency of β and the matrix [49].

**Figure 5.** Variation of hardness of the 6061 Al alloy with the aging time at both 175 ◦C and 200 ◦C, in which the microstructures at peak aging and over aging are also shown [49].

Recently, the coherent precipitation of ordered L12-Ni3M (M = Sc, Er, Zr, etc.) in the disordered FCC matrix of Al-Zr-Sc-Er alloy systems has attracted more attention since it can provide significant strengthening to a temperature of about 300 ◦C. Such Al alloys are excellent candidates for some high-temperature automotive and aerospace applications [50–52]. Supersaturated Al-Sc binary alloys generally possess high strength due to the coherent precipitation of L12-Al3Sc nanoparticles [53,54]. Based on it, the addition of Zr can form coarsening-resistant L12-Al3(Sc,Zr) lobed-cuboids consisting of a Sc-enriched core surrounded by a Zr-enriched shell in Al-0.06Sc-0.06Zr (wt.%) alloy [45,55] (as seen in Figure 6). More interestingly, the Er further substitution for Zr can form spheroidal Al3(Sc,Zr,Er) nanoprecipitates with a core/double-shell structure consisting of an Er-enriched core surrounded by a Sc-enriched inner shell and a Zr-enriched outer shell in the Al-0.06Sc-0.04Zr-0.02Er (wt.%) alloy (Figure 6), which are stable and difficult to be coarsened even at a higher temperature of 400 ◦C for 64 days [42]. Resultantly, it is due to the particle size that renders the two alloys with a remarkable difference in microhardness, as shown in Figure 6. The particle size of lobed-cuboidal Al3(Sc,Zr) precipitates is about 25 nm in the former alloy, while the spheroidal Al3(Sc,Zr,Er) nanoprecipitates with a particle size of 3~8 nm result in a drastic improvement of the alloy strength, from a peak harness of 243 MPa in the former alloy to 451 MPa in the later one at 400 ◦C aging. Therefore, more and more interests have been focused on the coherent precipitation in Al alloys to develop new light-weight materials that can be applied in high-temperature environments (>300 ◦C).

**Figure 6.** Variation of Vickers hardness of Al-Zr-Sc-Er alloys with the aging time at 400 ◦C, in which the precipitate morphologies of coherent Al3(Sc,Zr) after aging 24 h and Al3(Sc,Zr,Er) after aging 64 days are also presented [50].

#### *4.3. Mg-Based Alloys*

Mg alloys with a close-packed-hexagonal (HCP) matrix are the lightest among all the commonly-used structural materials and have great potentials for application in the automotive, aircraft, aerospace, and electronic industries [56]. Their useful mechanical properties were generally achieved via age-hardening process to form high-strength precipitates, which is similar to the precipitation in Al alloys. Actually, it is more difficult to keep the coherency between the precipitates and the matrix due to the HCP structure of the matrix. The structure, morphology, and orientation of precipitates, precipitation sequence, and hardening response in various Mg alloy systems have been generalized, in which the effects of precipitate shapes on strengthening and the rational design of microstructures for higher strengths were also emphasized [57,58]. For the most widely-used Mg-Al-based alloys, such as AZ91 (Mg-8.7Al-0.7Zn-0.1Mn, wt.%), the final stable incoherent β-Mg17Al12 phase with a BCC structure precipitates directly from the supersaturated HCP-Mg solid solution without any coherent G.P. zones, which could not result in an appreciable strengthening response due to the existence of relatively-coarse plate/lath-like β particles [59–61]. For most of the high-strength Mg alloy series, the precipitation usually follows the sequence of Mg SS → G.P. zone → coherent metastable phase → incoherent stable phase [62–71]. A typical Mg-Gd(-Y)-based Mg-15Gd-0.5Zr (wt.%) alloy was taken for an instance [72]. Firstly, the coherent G.P. zone precipitated from the HCP-Mg solid solution at the initial stage of aging at 250 ◦C. Then the metastable β-Mg3Gd phase with an ordered DO19 structure of the HCP solid solution appeared after aging for 0.5 h, which keeps the perfect coherent orientation with the matrix and exhibits a hexagonal prism morphology. Another metastable orthorhombic β -Mg3Gd phase with a lenticular particle morphology would substitute for the β when the aging time increased to 8 h, resulting in a peak strengthening. Figure 7 shows the microhardness variation with the aging time, from which an obvious improvement of microhardness is attributed to the precipitation of metastable β and β phases. Further prolonging the aging time, β will transform into a FCC β1-Mg3Gd with a DO3-L21 structure, and then to the

final stable β-Mg5Gd with a FCC structure, which can weaken the strengthening response due to the plate-like morphology of β<sup>1</sup> and β particles [72,73].

**Figure 7.** Variation of Vickers hardness of the Mg-15Gd-0.5Zr alloy with the aging time at 250 ◦C, in which the morphologies of coherent β and β precipitates are also shown [72,73].

It is emphasized that the DO3-L21 β<sup>1</sup> phase often exists in many high-strength Mg alloys, which is a highly-ordered superstructure of the BCC solid solution, consisting of eight BCC unit cells. If the HCP-Mg matrix is changed to a BCC structure, the coherency will be achieved between the L21 phase and BCC-Mg solid solution. It is fascinating that the ordered L21-Li2MgAl phase was coherently-precipitated into the BCC-Mg matrix in the recently-reported Mg-11Li-3Al (wt.%) alloy, which renders the alloy with high strength, good ductility, and excellent corrosion resistance [74]. Figure 8 compared the room-temperature mechanical tensile properties (yield strength and elongation to fracture) of Mg-11Li-3Al alloy with several traditional Mg alloys. It is found that this BCC-based alloy exhibits not only a higher strength, but also a much better ductility with an elongation to fracture of about 27%, which is attributed to the coherent precipitation of spherical L21 nanoparticles with a particle size of 2~20 nm (as shown in Figure 8).

**Figure 8.** Comparison of the mechanical properties (yield strength and elongation) of the BCC-based Mg-11Li-3Al alloy in traditional HCP Mg alloys, in which the spherical L21 nanoparticles of the former BCC Mg alloy are also presented [74].

#### *4.4. Cu-Based Alloys*

The precipitates in various Cu alloys generally show different phase structures, in which the coherent precipitation of metastable ordered L12 in the FCC-Cu solid solution matrix can appear in the commonly-used Cu-Ni-Sn alloy system [75–77]. The model alloy is the Cu-15Ni-8Sn (wt.%, C72900), in which the (Cu,Ni)3Sn precipitates have four crystal structures, FCC-DO3, tetragonal DO22, ordered L12, and orthorhombic δ. The phase evolution sequence from high to low temperatures is similar to that in aged Al alloys for different times. When aging at above 550 ◦C, discontinuous and intragranular DO3-γ precipitates (plate-like shape) appeared in the FCC matrix, as seen in Figure 9a. Spinodal decomposition often occurred during the early stage of the decomposition below ~500 ◦C, followed by the DO22 ordering (as seen in Figure 9b) and then L12 ordering (the inset of Figure 9c) [77]. With decreasing aging temperature, spherical L12 nanoparticles could be coherently-precipitated into the FCC matrix, compared with the rod-like DO22 precipitates. The particle morphology can affect the mechanical property of this alloy, as seen in Figure 9c, being the variation tendency of the tensile yield strength with the aging time [77–79]. It was found that the coherent precipitation of spherical L12 nanoprecipitates corresponds to the highest strength.

**Figure 9.** Morphologies of ordered DO3-(**a**), DO22-(**b**), and L12-(Cu,Ni)3Sn precipitates (**c**), as well as the variation tendency of the tensile yield strength of Cu-15Ni-8Sn alloy with the aging time at 350 ◦C (**c**) [77,78].

#### *4.5. Fe-Based Stainless Steels*

It is well known that the most common strengthening precipitates are carbides, being Cr23C6 and MC (M = Nb, Ti, V, etc.) [7,8]. For some special stainless steels (SSs), there also exist other kinds of precipitates, such as Laves phases (Fe2M), Ni3M, B2-NiAl, σ-FeCr, and Z-CrNbN, to strengthen the FCC or BCC matrix [7]. For instance, austenitic SSs for the use in high-temperature (600~800 ◦C) and oxidation environment are generally strengthened by MC, Cr23Cr6, Z, Fe2M, or B2-NiAl [80,81]. However, it is noted that these phases are not coherent with the FCC austenite matrix, which can lead to the coarsening of second phase precipitates, as a final result of softeness or embrittlement (the latter mainly caused by the σ phase). Very interestingly, another kind of high-temperature ferritic SSs with a coherent microstructure of ordered B2 phase precipitation into BCC matrix have been developed [12,13,82–88]. As shown in Figure 10a, the Fe-6.5Al-10Ni-10Cr-3.4Mo-0.25Zr-0.005B (wt.%, FBB8) alloy exhibits a prominent creep resistance at 700 ◦C, better than the conventional P92, P122, T122, and 12CR steels [12,84]. It is attributed to the coherent precipitation of spherical B2 nanoparticles into BCC ferritic matrix (Figure 10b), similar to that in FCC Ni-based superalloys [5]. The further addition of 2 wt.% Ti into FBB8 induces another ordered L21-Ni2AlTi phase of the BCC solid solution,

forming a coherent microstructure with cuboidal B2/L21 hierarchical precipitates (Figure 10c) [89,90]. We calculated the lattice misfit between BCC and B2/L21 phases with the formulas of *ε* = 2(*a*B2 − *a*BCC)/(*a*B2 + *a*BCC) and *ε* = 2(*a*L21 − 2*a*BCC)/(*a*L21 + 2*a*BCC), in which *a*B2, *a*L21, and *a*BCC are the lattice constants of B2, L21, and BCC solid solution phases, respectively. It was found that the cuboidal precipitation of B2/L21 phases mainly resulted from the larger lattice misfit of *ε* = 0.7% between the BCC and L21 phases in the Ti-modified FBB8, while the smaller value of *ε* = 0.06% promotes the formation of spherical B2 precipitates in FBB8. More importantly, it is due to the cuboidal precipitation that further improves the creep-resistant property of the Ti-modified FBB8 alloy at 700 ◦C (Figure 10a), possessing a better creep life than FBB8.

**Figure 10.** (**a**) Larson-Miller parameters (LMP) for FBB8, Ti-modified FBB8, and several conventional steels (P92, P122, T122, and 12CR) [89]; (**b**,**c**) morphologies of spherical B2 nanoprecipitates in FBB8 [12] and cuboidal L21 nanoprecipitates in Ti-modified FBB8 [89,90], respectively.

Moreover, the precipitation of intermetallic compound Ni3M in the BCC martensite matrix can make maraging stainless steels with a much higher strength (tensile yield strength of σ<sup>y</sup> = 1.2~1.5 GPa) [91–94]. Very recently, the coherent precipitation of spherical B2 nanoparticles with a particle size of 3~5 nm, rather than the Ni3M, in the BCC martensite rendered a Fe-17Ni-6.2Al-2.3Mo-0.48Nb-0.37C-0.05B (wt.%) steel with a superhigh strength (σ<sup>y</sup> > 1.9 GPa) [9], as shown in Figure 11. It is attributed to the smaller lattice misfit (*ε* = 0.17%) that permits the dislocations cutting through the B2 nanoparticles, in which the high anti-phase boundary (APB) energy can promote the ordering strengthening by increasing the dislocation shear resistance in the particles.

**Figure 11.** Tensile engineering stress-strain curve of the aged Fe-17Ni-6.2Al-2.3Mo-0.48Nb- 0.37C-0.05B steel, in which the microstructures of B2 nanoparticles with a size about 3~5 nm and dislocations are also shown [9].

#### *4.6. High-Entropy Alloys*

High-entropy alloys (HEAs) with equimolar or near-equimolar mixing of multiple elements have been found in diverse alloy systems and have attracted more attention due to their interesting properties and associated scientific understandings. Especially, CoCrFeNi-based HEAs [95–104], composed of late transition metals (LTMs), were widely investigated due to their exceptional mechanical properties and potential industrial applications. For instance, the single FCC CoCrFeNiMn HEA displays an excellent damage tolerance with higher tensile strength and remarkable fracture toughness than traditional engineering stainless steels at cryogenic temperatures down to −196 ◦C, which resulted from the microstructural diversity caused by the twinning-induced plasticity (TWIP) effect [98].

A further addition of Al or Ti into these LTMs-based HEAs can produce phase transformations [105–131], and then lead to microstructural diversities due to the strong interactions between Al/Ti and LTMs, resulting in an enhancement of strength. It is primarily attributed to the coherent precipitation of intermetallic phases, such as L12-Ni3Al from the FCC matrix [125,126], and B2-NiAl [110,118–124] and L21-Ni2AlTi [107–109] from the BCC matrix. As example, the (NiCoFeCr)94Ti2Al4 (at.%) HEA possesses a special coherent microstructure with fine spherical L12-(Ni3(Al,Ti)) nanoprecipitates in the FCC matrix, resulting in a significant strength improvement with a yield strength over 1 GPa [125]. A newly-developed kind of high entropy Ni-based alloys, such as Ni48.6Al10.3Co17Cr7.5Fe9.0Ti5.8Ta0.6Mo0.8W0.4 (at.%), exhibit a higher high-temperature hardness resulted from the γ -L12 precipitation-strengthening of γ-FCC matrix, where the coherent γ/γ microstructure can be thermodynamically stable after aging from 700 ◦C to 1100 ◦C for at least 500 h [126]. It is noted that a small amount of Al addition in HEAs (e.g., Al0.3FeCoNiCr [115–117] and Al8Co17Cr17Cu8Fe17Ni33 [127]) generally renders spherical L12-Ni3Al particles precipitated in the FCC matrix, resulting in high strength and good ductility, similar to that in Ni-based superalloys [5,132]. With increasing Al content, not only the FCC matrix of AlxFeCoNiCr series of HEAs transforms into the BCC phase, but also the precipitates change from L12-Ni3Al to B2-NiAl, as a result of an enhancement of strength drastically [114–118]. In addition, fixing Al content, the mutation of transition metals can also change the phase transition from FCC to BCC, as evidenced by the two HEAs of the FCC-based Fe36Co21Cr18Ni15Al10 (at.%) and the BCC-based Fe36Mn21Cr18Ni15Al10 (at.%) HEA with cuboidal B2 nanoprecipitates [109,123]. Furthermore, a minor addition of Ti (4 at.%) into these two HEAs leads to the formation of L21-Ni2AlTi phase, rather than the B2, but the L21 precipitates exhibit different morphologies, being plate-like shape in the former alloy and cuboidal shape in the latter, respectively [109].

Experimentally, it is difficult to obtain cuboidal or spherical morphology of coherent B2 or L21 precipitates in BCC-based HEAs, which is primarily attributed to a large lattice misfit between BCC and B2 phases caused by the large composition difference. Thus, a weave-like microstructure of BCC and B2/L21 always occurred in these BCC-based HEAs, since it is sensitive to the Al/Ti content, such as the AlFeCoNiCr HEA, leading to a serious brittleness [114]. Massive efforts have been done to research for the cuboidal or spherical B2/L21 precipitation in various systems through adjusting both Al and transition metals [107–109,118–124,128,129]. It is fascinating that spherical or cuboidal B2/L21 nanoprecipitates are coherently-existed not only in Al/Ti-LTM HEAs (e.g., Fe34Cr34Ni14Al14Co4 at.% [121]), but also in refractory HEAs consisted of Al and early transition metals [111,128,129]. For instance, the coherent precipitation of spherical B2 nanoparticles in BCC matrix improves the room- temperature compressive ductility on a large extent of refractory Al0.5NbTa0.8Ti1.5V0.2Zr HEA, while maintains high yield strength at both room and elevated temperatures [129].

Table 1 lists the mechanical properties (yield strength *σ*<sup>y</sup> and ductility *δ*) at room and elevated temperatures of some precipitation-strengthened HEAs, including L12-strengthed FCC-based HEAs and B2/L21-strenthened BCC-based HEAs. The mechanical properties of commercial boiler steel HR3C (Fe54.73Cr24.01Ni20.6C0.05Nb0.37N0.24, wt.%) [133,134], newly-developed Ti-modified FBB8 ferritic stainless steel [89,90], and commercial Ni-based polycrystalline superalloy Inconel 718 (Ni53Fe18.5Cr19Nb5.1Mo3.0Ti0.9Al0.5 wt.%) [135,136] were also listed in Table 1 for reference. Compared with the HR3C austenitic stainless steel strengthened by MC-type carbides and Z-NbCrN nanoparticles, the FCC-based HEAs containing coherent spherical L12 nanoprecipitates generally exhibit higher yield strengths at both room and elevated temperatures, in which the particle size must exceed a certain value to ensure high strength according to the strengthening mechanism. In fact, the high-temperature strength has been improved in the newly-developed Ti-modified FBB8 ferritic stainless steel due to the coherent precipitation of cuboidal L21 nanoparticles [89,90]. The higher room-temperature strengths of BCC-based HEAs with cuboidal B2/L21 precipitation are comparable to that of Ni-based Inconel 718 superalloy. Especially for the Al-contained refractory HEAs [128,129], the yield strengths at both room and elevated temperatures (up to 1200 ◦C) are all much higher than that of Inconel 718, which will be softened at the temperature above 900 ◦C.

**Table 1.** Data summary for some typical precipitation-strengthened HEAs, including alloy composition, matrix phase, particle size and morphology of precipitated phase at room temperature (RT), and mechanical properties (yield strength *σ*<sup>y</sup> and ductility *δ*) at both room and elevated temperatures. The mechanical properties of commercial HR3C steel and Inconel 718 superalloy, as well as Ti-modified FBB8, are also listed for reference.



**Table 1.** *Cont*.

In our recent work, we obtained spherical or cuboidal B2 nanoprecipitates in the BCC matrix of Al-TM HEAs with the composition formula of Al2M14 (=Al0.7M5 in molar fraction), in which Al is fixed and M represents different mutations of Ni, Co, Fe, and Cr [119,120]. The Al2M14 was designed with the guide of a cluster formula approach through mutating the combinations of TMs, rather than the Al. It is noted that the addition of a much more amount of BCC stabilizers (Fe and Cr) can favor to the formation of the BCC/B2 structures without any FCC phase in alloys. More significantly, the cuboidal B2 nanoprecipitation in alloys with M = NiCoFe2Cr and M = NiCoFeCr2 is strongly attributed to a moderate lattice misfit (*ε* ~0.4%) between BCC and B2 phases, as seen in Figure 12a [120]. It is due to the cuboidal B2 nanoparticles in the BCC matrix that produces a prominent mechanical property with higher strength (*σ*<sup>y</sup> = 1.1~1.7 GPa) and good ductility. Besides, these cuboidal B2 nanoprecipitates in these two alloys are very stable and could not be coarsened even after a long-time aging at 773 K for 1080 h [137]. In addition, the Ti substitution for Al in Al2M14 HEAs can change the phase structures of ordered precipitates, from B2-NiAl to L21-Ni2AlTi. Furthermore, a minor amount of Ti substitution with a ratio of Al/Ti ≥ 2/1 can still keep the cuboidal morphology of L21 nanoprecipitates for the achievement of a higher strength (*σ*<sup>y</sup> = 1.8 GPa) due to a moderate lattice misfit (Figure 12b) [107,108]. Figure 12c shows the variation tendencies of (Δ*σCS* + Δ*σMS*) and Δ*σorowan* with the particle size *r* in typical (Al,Ti)2M14 alloys at a fixed *f*. The used parameters for yield strength increment calculations are *M* = 2.73, *αε* = 2.6, *G*BCC = 83 GPa, *G*B2 = 80 GPa, *G*L21 = 73.6 GPa, *m* = 0.85, *b* = 0.254 nm, (*γapb*)B2 = 0.25 J/m2, (*γapb*)L21 = 0.04 J/m2, and *v* =0.3, respectively. The optimal particle size *r0*, corresponding to the largest strength increment, is calculated by the equation of (Δ*σCS* + Δ*σMS*) = Δ*σorowan* in light of the precipitation strengthening mechanism. It is noted that when the particle size of B2 or L21 nanoprecipitates exceeds a certain value (about 40 nm), the (Δ*σCS* + Δ*σMS*), rather than the Δ*σOR*, will dominates the dislocation-shearing mechanism, compared with the phenomenon in the above-mentioned superhigh strength Fe-17Ni-6.2Al-2.3Mo-0.48Nb-0.37C-0.05B (wt.%) alloy [9]. More importantly, it can be demonstrated that the higher strength of (Al,Ti)2M14 HEAs is primarily attributed to the fact that the experimental particle size (50~120 nm) of B2 or L21 cuboids is close to the optimal size *r*<sup>0</sup> for the maximum strength increment from theoretical calculations.

**Figure 12.** Computations of (Δ*σCS* + Δ*σMS*) and Δ*σorowan* as a function of particle size *r* for the present Al0.7Ni1Co1Fe1Cr2, Al0.7Ni1Co1Fe2Cr1, and (Al2Ti)0.7Ni1Co1Fe1Cr2 HEAs (**c**), in which the morphologies of the coherent cuboidal B2 (**a**) and L21 (**b**) precipitates are also presented [107,108,120]. The optimal particle size *r0* from the calculation and the experimentally-measured *r* are also marked for each alloy.

#### **5. Thoughts on the Coherent Precipitation Strengthening**

The coherent precipitation of ordered L12-γ' nanoprecipitates into the FCC-γ matrix renders the Ni-based superalloys with prominent mechanical properties at elevated temperatures close to melting points, which is hard to realize in other conventional alloy systems. The main reason is that in most conventional alloy systems, such as Al alloys, Mg alloys, and Cu alloys, the finally-stable precipitated phases are not the ordered superstructures of their parent solid solutions. In fact, the precipitation sequence of G.P. zones → metastable coherent ordered phases → stable non-coherent intermetallic phases often appears during the aging process, in which only the coherent precipitation corresponds to the peak strength. Therefore, many researchers have been exploring how to maintain the long-term stability of coherent precipitates through adjusting the amount of alloying elements or changing element species. Take the Mg alloys for instance. Based on the Mg-Al binary alloys without any ordered phases, the addition of a superlarge-size element Ca can form an ordered G.P. zone on the basal plane of the HCP matrix, i.e., clusters induced by Ca atoms, which can improve the creep resistance, but cannot enhance the strength [65]. So, in order to further improve the alloy strength, Mg-Gd-, Mg-Y-, and Mg-Nd-based alloys have been developed, in which several typical alloys, such as

Mg-18.2Gd-1.9Ag-0.3Zr, Mg-6Y-4.9Zn, and Mg-10Gd-5.7Y-1.6Zn-0.7Zr (wt.%), possess a much higher ultimate tensile strength of above 400 MPa [57]. An obvious feature in these alloy systems is that the interplanar distance of G.P. zones (*d* = 0.37 nm) is getting closer to the lattice constant (*a*~0.32 nm) of the basal plane of HCP-Mg matrix, compared with that (*d* = 0.556 nm) in Mg-Al-Ca alloys. Hence, the much better coherency between the G.P. zones and the Mg matrix promotes the formation of ordered superstructure (DO19-Mg3(Gd,Nd)) of the HCP solid solution, resulting in a higher strength. From the viewpoint of alloying element species, it can be found that the key factor for the better coherency is that the super large-size elements (Gd, Y, etc.) and small-size elements (Zn, Ag, etc.) must be added simultaneously to balance the interplanar distance of G.P. zones close to the lattice constant of Mg matrix. Till recently, the HCP-Mg matrix was changed into the BCC-Mg matrix in Mg-Li-Al system, in which the coherent precipitation of ordered superstructure of L21-Li2MgAl improves the tensile ductility, besides the higher strength of alloys [74]. It demonstrates sufficiently the important role of coherent precipitation in the development of high-strength structural materials.

In addition, in the case of coherent precipitation, the morphology of the coherent precipitates is also important to the mechanical properties of alloys, which has been identified by the presence of cuboidal L12-γ nanoprecipitates in Ni-based single-crystal superalloys [5]. It is known that the precipitate morphology (shape and size) is primarily controlled by the lattice misfit between the ordered phase and its parent solid solution. A moderate lattice misfit for cuboidal nanoprecipitates should be achieved by mutating the lattice constants of these two phases simultaneously. For the γ/γ coherent microstructure, it is relatively easy to adjust the lattice misfit because there exists a relatively-small composition difference between γ and γ phases. In contrast, it is difficult to adjust the lattice misfit between the B2 or L21 phase and the BCC matrix rationally in conventional alloy systems due to the relatively-larger composition difference between these two phases. In most cases, there often exhibits a weave-like microstructure induced by spinodal decomposition. The recent development of high-entropy alloys shows a bright insight to achieve the ideal (cuboidal) coherent microstructure since the phase compositions can be adjusted within a wide range in multi-principal alloy systems. Actually, all of the Ni-based single-crystal superalloys are concentratedly-complex alloys, generally containing more than ten elements, which favors the mutation of lattice misfit. So, some new BCC-based superalloys with superhigh strength and/or better creep resistance have been developed recently, which is derived from the coherent precipitation of spherical/cuboidal B2 or L21 nanoprecipitates in the BCC matrix [9,89,90,108,120].

It is emphasized that whether the formation of coherent phases or the morphology of coherent precipitates is considered, both are closely related to the chemical composition. However, the rational matching of solute elements in the ordered phase and the solid solution was seldom considered when designing alloy compositions, since the solute distribution in the parent solid solution has not been clear until now. Actually, the local chemical structural units (chemical short range orders, CSROs) induced by solute elements are crucial to the stability of parent solid solution at high temperatures [138,139], which decides the precipitation of ordered phase during the aging or as-cast state. The recently-proposed cluster-plus-glue-atom model has defined such local chemical structure units in solid solutions [120,140–142], in which the cluster is the nearest-neighbor polyhedron centered by a solute atom having the strong interaction with the base solvent atoms to represent the strongest CSRO, and some other solute atoms (i.e., glue atoms) with weak interactions are certainly required to fill the space between the clusters to balance the atomic-packing density. Thus, a composition formula of [cluster] (glue atom) *x* (*x* being the glue-atom number) can be obtained from the cluster model. So, the phase compositions of ordered phase and their parent solid solution could be considered in light of the chemical structural units, respectively. Combined with the volume fraction of coherent precipitates, it would provide a new approach of composition design to develop high-performance compositionally-complex alloys with coherent precipitation.

#### **6. Conclusions**

In the present work, the precipitation behavior and precipitation strengthening in compositionally-complex alloys were generalized comprehensively, including high-performance conventional engineering materials (Ni superalloys, Al alloys, Mg alloys, Cu alloys, and stainless steels), and newly-developed high entropy alloys. The morphology evolution of second-phase particles and precipitation strengthening mechanism were introduced firstly. Then, the precipitation behaviors in diverse compositionally-complex alloy systems are illustrated, respectively. After discussing the relationship between the particle morphology and strengthening effectiveness, alloys with the coherent microstructure of the ordered phase precipitated in the disordered solid solution matrix were specially emphasized, since they exhibit prominent mechanical properties (superhigh strength/toughness and excellent high-temperature creep resistance). The universal feature existed in all compositionally-complex alloys is the coherent precipitation, which will be the most effective approach for the enhancement of alloy strength.

**Author Contributions:** Conceptualization, P.K.L. and Q.W.; methodology, Q.W., Z.L. and C.D.; validation, X.L. and P.K.L.; formal analysis, Q.W. and S.P.; investigation, X.L.; resources, C.D.; writing—original draft preparation, Q.W.; writing—review and editing, C.D. and P.K.L.

**Funding:** This research was funded by the National Key Research and Development Plan, grant number 2017YFB0702400; the Science Challenge Project, grant number TZ2016004; the National Magnetic Confinement Fusion Energy Research Project, grant number 2015GB121004.

**Acknowledgments:** P.K.L. would like to acknowledge the Department of Energy (DOE), Office of Fossil Energy, National Energy Technology Laboratory, grant number DE-FE-0011194; the U.S. Army Research Office project, grant number W911NF-13-1-0438; the National Science Foundation, grant number DMR-1611180 and 1809640.

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

#### **References**


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