Laves Phase Precipitation Behavior and the Orientation Relationship with BCC in Cr–Mo–Nb System

Abstract

The isothermal sections of the Cr–Mo–Nb ternary phase diagram have been studied. The C15 NbCr₂ Laves precipitation behavior in three different alloys has been investigated in the Cr–Mo–Nb ternary system. The orientation relationship (OR) of NbCr₂ in BCC matrix among BCC/Laves two-phase alloys and Cr-rich BCC₁/Mo-rich BCC₂/Laves three-phase alloy is different at 1473 K; OR 1: (011)_BCC // $(11\bar{1})_{\text{C15}}$, $[0\bar{1}1]_{\text{BCC}}$ // $[\bar{1}10]_{\text{C15}}$ and OR 2: $(\bar{4}11)_{\text{BCC}}$ // (111)_C15, $[0\bar{1}1]_{\text{BCC}}$ // $[\bar{1}10]_{\text{C15}}$ with low lattice mismatch are both observed in Cr-rich alloys #3 (74Cr–16Mo–10Nb) and #2 (50Cr–30Mo–20Nb). OR 3: (011)_BCC // (111)_C15, $[\bar{1}1\bar{1}]_{\text{BCC}}$ // $[01\bar{1}]_{\text{C15}}$ with a lattice mismatch relatively larger than that of OR 1 and OR 2 is only observed in alloy #2, which may be due to the presence of BCC₁ and BCC₂ interphases formed after BCC decomposition. Only discontinuous precipitation is observed at grain boundaries in Cr-lean alloy #1 (42Cr–31Mo–27Nb) without obvious OR between the BCC matrix and Laves phase.

Fig. 17 Atomic matching at three BCC/C15 interfaces.

1. Introduction

The AB₂ Laves phases have been widely studied over the past several decades because of their high melting temperatures and superior high-temperature strength.^1–8) There are three major types of Laves phases, the cubic MgCu₂ type C15 phase, the hexagonal MgZn₂ type C14 phase and the dihexagonal MgNi₂ type C36 phase. Although alloying elements have been added into the Laves phase on the basis of the atomic size ratio rule to improve the mechanical properties^9,10) and the room temperature deformability can be enhanced by adopting the pseudo binary AB₂-CB₂ Laves phase alloys,¹¹⁾ the low-temperature mechanical properties are still insufficient for application as structural materials in a single phase due to their complex structures.

Therefore, the introduction of a ductile phase into Laves phase-based materials is attractive to obtain a two-phase alloy, which may preferably balance the strength and fracture toughness, in both binary and ternary systems.¹²⁾ The mechanical properties of two-phase alloys are strongly dependent on the morphology, volume fraction and the orientation relationship (OR) of the second phase.¹³⁾ However, it is difficult to control the microstructure of two-phase alloys composed of Laves and ductile phases, especially in binary systems, because for almost all of the binary Laves systems, the two-phase microstructure is obtained by a eutectic reaction because many Laves phases are in equilibrium with the ductile BCC phase with a limited solid solubility, which is insufficient for the large volume fraction of Laves phase precipitation.

It should be noted that the Cr–Ti system is an exception, in which a continuous BCC solid solution area exists at high temperature over the entire composition range. Chen et al.¹⁴⁾ selected several Cr–Ti alloys to study the precipitation behavior of TiCr₂; however, the difference of the Laves phase precipitation behavior among the alloys is not yet well understood. The ternary system can provide a higher degree of freedom in control of the volume fraction and alloy composition of the constituent phases;^15,16) however, there are few works related to details on the precipitation behavior of Laves phase from a supersaturated ternary solid solution. Laves phases sometimes precipitate from the BCC phase, as with the Cr/NbCr₂ alloys,^1,17) and sometimes just precipitate along the grain boundaries, for example, in the Nb–20W–10Cr alloy.¹⁸⁾

To understand the Laves phase precipitation behavior in the BCC phase, the Cr–Mo–Nb system is selected in the present study. Three alloys with different compositions were prepared, which have different equilibrium BCC matrix compositions with NbCr₂ precipitates after annealing at 1473 K. The Laves precipitation behavior was investigated and the OR between the Laves and BCC phases was examined.

2. Experimental Procedure

Raw materials of Nb, Cr, and Mo with purities of 99.9, 99.99, and 99.9 mass%, respectively, were employed. Alloys with three different compositions (see Table 1) were prepared in the form of small button ingots (ca. 7 g) by arc melting. Alloys were turned over and melted more than ten times on a water-cooled copper hearth in a high purity Ar atmosphere. There are two series of heat-treatment. For the confirmation of phase equilibrium and the composition of phases at 1473 K, we applied a heat-treatment on as-cast ingots for 168 h without solution treatment. The ingots were sealed in quartz tubes with Ar and water-quenched after the heat-treatment.

Table 1 Nominal compositions of alloys for isothermal section study (at%).

In order to investigate the precipitation behavior of Laves phase in the supersaturated BCC matrix phase, solution treatment at 1973 K for 1 h was performed on alloys #1, #2 and #3 in a high-frequency furnace under vacuum, followed by furnace cooling. The samples were then encapsulated in evacuated quartz tubes and aged at 1473 K for various periods, followed by quenching.

The samples were cut and mounted for polishing. The microstructure was observed using field emission scanning electron microscope (FE-SEM, JEOL JXA-8530F) equipped with an electron probe micro-analyzer. Wavelength dispersive spectroscopy (WDS) was employed to determine the average composition of the alloys with a large spot size of ca. 20 µm. X-ray diffraction (XRD, PANalytical X’Pert PRO, Cu-Kα) with 2θ scans from 30° to 80° were also performed to identify the crystal structures of the constituent phases at a current of 40 mA and a voltage of 40 kV. The microstructure was also characterized using scanning electron microscope (SEM, JEOL JAMP-9500F) equipped with an electron backscatter diffraction (EBSD) system.

3. Results and Discussion

3.1 Annealed microstructure and phase diagram

Figure 1 shows an SEM image and XRD pattern of alloy #2 heat-treated at 1473 K for 168 h. The XRD pattern confirmed that the alloy consists of Cr-rich BCC₁ phase, Mo-rich BCC₂ phase, and C15 Laves phase NbCr₂ at 1473 K. Based on the WDS results (Table 2), the bright phase (B) is the Mo-rich BCC₂ phase, the gray phase (C) is the Laves phase and the dark particles (A) are the Cr-rich BCC₁ phase in Fig. 1(a).

Fig. 1

(a) Microstructure and (b) XRD pattern of alloy #2 heat-treated at 1473 K for 168 h.

Table 2 WDS results for each phase in alloy #2 at 1473 K, plotted in Fig. 1(a) (at%).

Figure 2 shows isothermal sections of the Cr-rich corner of the Cr–Mo–Nb ternary system at 1473 K. Zakharova and Prokoshkin¹⁹⁾ reported the isothermal section of the Cr–Mo–Nb ternary system at 1473 K, as shown in Fig. 2(a). The composition of each phase in the three-phase region was mainly determined by coupling XRD results and composition of alloys investigated. The Cr-rich BCC₁ phase has almost the same composition with the present result shown in Fig. 2(b), however, the composition of the Mo-rich BCC₂ phase is far different from the that of the present work which is determined on the basis of the WDS results. Each alloy is also plotted with a triangle in Fig. 2(b). It should also be noted that according to the ternary phase diagram reported by Zakharova and Prokoshkin¹⁹⁾ alloy #1 is in the three-phase region. However, it is in BCC-Laves two-phase region as will be discussed in the following sections.

Fig. 2

Cr-rich corner of Cr–Mo–Nb isothermal sections at 1473 K. (a) Reported by Zakharova and Prokoshkin.¹⁹⁾ (b) Present work.

Homogenous structures were obtained for three alloys (#1–3) at 1973 K, as shown in Fig. 3(a,c,g), which was determined to be single BCC phase, according to the XRD results in Fig. 4. For alloy #3, it should be noted that a limited amount of Laves phase precipitated along the grain boundaries, but no precipitates were observed in the grain interior. Thus the discontinuous precipitation may occur during cooling.

Fig. 3

Microstructure of alloy #3 (a,b), alloy #2 (c–f), and alloy #1 (g,h) heat-treated at different conditions. (a), (c) and (g): solution-treated at 1973 K for 1 h. (b), (d), (e), (f) and (h): heat-treated at 1473 K for various duration after the solution treatment.

Fig. 4

XRD patterns corresponding to the alloys in Fig. 3.

After subsequent annealing at 1473 K, each of the three alloys had different precipitation morphologies, as shown in Fig. 3(b,d,e,f,h). Black precipitates appear at the grain boundaries and cellular structures are formed in alloy #1, while precipitates appear not only at the grain boundaries but also in the grain interior in alloy #3 in which the needle-like precipitates tend to grow in certain directions. The precipitates in both alloys were confirmed to be Laves phases from the XRD patterns shown in Fig. 4. However, in alloy #2, BCC phase decomposes into two BCC phases (BCC₁ and BCC₂) during 12 h heat-treatment (Fig. 3(d) and Fig. 4(b)) in a manner of a lamellar-like structure, then blocky gray Laves phase appears in sample heat-treated for 100 h (Fig. 3(e,f) and Fig. 4(b)). It is noteworthy that the Laves phase in alloy #2 seems to be surrounded by bright BCC₂ phase. These microstructures of alloys are consistent with the 1473 K isothermal section (Fig. 2(b)) proposed in the present study.

3.2 Crystallographic orientation relationship (OR) between phases

In this study, EBSD was adopted instead of TEM to further understand the precipitation behavior in alloys #3 and #2 because EBSD enables the crystallographic OR between many Laves precipitates and BCC matrix phase to be simultaneously examined over a wide area (approximately several tens of square micrometers).

Figure 5 shows an SEM image, phase map, corresponding inverse pole figure (IPF) maps, and pole figures (PF) for C15 #3-1&#3-2 of alloy #3. Compared to the {011}_BCC plane traces shown in Fig. 5(c), the interphase boundaries between the BCC and Laves phases appears to be on the {011}_BCC plane, which indicates that the habit plane of needle-like precipitates (Fig. 3(b)) in alloy #3 is {011}_BCC plane. Twinning has been widely reported in C15 Laves phases such as NbCr₂,¹⁷⁾ TiCr₂,¹⁴⁾ and HfV₂.²⁰⁾ In this study, twinning was also observed in C15 NbCr₂ Laves phases, as shown in Fig. 5(e), where C15 #3-1&#3-2 share a common (111) twinning plane as a twin pair. Pope and Chu²¹⁾ suggested annealing twins of the type {111}⟨112⟩ formed in C15 HfV₂, while some other researchers have proposed that twinning is generated by a C14/C15 phase transformation.¹⁷⁾

Fig. 5

The results of EBSD analysis of alloy #3 after two-step heat-treatment obtained corresponding to the red box in (a) SEM image. (b) Phase map, IPF maps of (c) BCC phase and (with {011}_BCC plane traces) (d) C15 Laves phases, and PF of (e) C15 #3-1&#3-2 (twin plane is marked by a red circle). Colors for ⟨111⟩ poles correspond to the color in (d).

In the present study, the twinning is more likely to be annealing twins formed during the heat treatment at 1473 K because the C14/C15 transformation temperature is as high as 1860 K for the NbCr₂ Laves phase in the Cr–Nb system. No C14 peaks were observed in the XRD examination for alloys heat-treated at 1473 K, as shown in Fig. 4. Takasugi and Yoshida²²⁾ reported only C15 phases and no C14 phase in the Cr–Mo–Nb ternary system after annealing at 1673 K.

Figure 6 shows pole figures (PFs) of the BCC matrix and C15 #3-1 marked in Fig. 5(d). Two types of ORs between C15 #3-1 and BCC are identified as:   

\begin{equation*} \text{OR 1:}\ (011)_{\text{BCC}} \parallel (11\bar{1})_{\text{C15}}, [0\bar{1}1]_{\text{BCC}} \parallel [\bar{1}10]_{\text{C15}} \end{equation*}

  

\begin{equation*} \text{OR 2:}\ (\bar{4}11)_{\text{BCC}} \parallel (111)_{\text{C15}}, [0\bar{1}1]_{\text{BCC}} \parallel [\bar{1}10]_{\text{C15}}. \end{equation*}

OR 1 between C15 precipitates and the BCC matrix was also reported in the Cr–Hf,²³⁾ Cr–Nb,¹⁷⁾ and Cr–Ti¹⁴⁾ systems. This also explains the preferred growth directions of C15 (see Fig. 5) which has an interfacial boundary along the {011}_BCC plane traces, and which may be caused by the lower interfacial energy. The $(11\bar{1})_{\text{C15}}$ plane in OR 1 is a twinning plane with C15 #3-2; therefore, it is not surprising that OR 1 is found between C15 #3-2 and the BCC matrix. Interestingly, OR 2 is also confirmed between C15 #3-2 and the BCC matrix, as shown in Fig. 7. However, Fig. 8 shows there is only OR 1 between C15 #3-3 and BCC, while OR 2 is not found. The same examination of OR has also been adopted for C15 #3-4, #3-5, and #3-6. The results are summarized in Table 3. C15 #3-5 and C15 #3-6 show the same ORs with the C15 #3-1&#3-2 twin pair, while C15 #3-3 and C15 #3-4 have only OR 1 but no OR 2. All these precipitates always exhibit OR 1, which indicates the principal OR between C15 precipitates and the BCC matrix should be OR 1. However, OR 2 appears occasionally in the twins.

Fig. 6

PFs for (a,c) the BCC matrix and (b,d) C15 #3-1 indicated in Fig. 5(d).

Fig. 7

PFs for (a,c) the BCC matrix and (b,d) C15 #3-2 in Fig. 5(d).

Fig. 8

PFs for (a,c) the BCC matrix and (b,d) C15 #3-3 in Fig. 5(d).

Table 3 OR for grains marked in Fig. 5(d).

Figure 9 shows schematic drawings of the OR between the C15 Laves and BCC phases in the case of the C15 #3-1&#3-2 pair. The angle between the {111}_C15 planes is 70.5°, and the angles between (411)_BCC and (011)_BCC, and between $(\bar{4}11)_{\text{BCC}}$ and (011)_BCC are also 70.5°, as shown by the side views in Fig. 9. Thus, once OR 2 $(\bar{4}11)_{\text{BCC}}$ // (111)_C15 exists in the parent grain, it can also be found in the twinned part of the precipitate. This is the reason why both parts of the twin pairs exhibit both OR 1 and OR 2.

Fig. 9

Schematic diagrams showing the crystallographic OR between the C15 precipitate and BCC phase when the twins hold both OR 1 and OR 2 in alloy #3. (a) Perspective view of the BCC unit cell, (b) perspective view of {111}_C15 tetrahedrons after twinning, (c) side view of BCC indicated in (a), and (d) side view of C15 indicated in (b).

Figure 10 shows orientation maps for alloy #2 annealed at 1473 K for 100 h after homogenization. It should be noted that BCC₁ and BCC₂ have the same crystallographic orientations through the alloy. C15 #2-1&#2-2, C15 #2-3&#2-4, C15 #2-5&#2-6, C15 #2-7&#2-8 and C15 #2-9&#2-10 share a common (111) plane, as shown in Fig. 11. C15 #2-3, #2-4, #2-9, and #2-10 are considered to precipitate as one grain, and then divide into four parts. Each part has twin relationships, but the twin planes are not identical. Therefore, this strongly suggests that the twins are not transformation twins but annealing twins. OR 1 and OR 2 are also found in C15 #2-1 (Fig. 12); however, only OR 2 exists for the counter part of the twin grain, i.e., C15 #2-2 (Fig. 13). (111)_C15 in OR 2 is identified as a twin plane. The twinning plane tends to be involved in OR 2 for alloy #2, while it tends to be involved in OR 1 for alloy #3. For the C15 #2-3&#2-4 pair, OR 3: (011)_BCC // (111)_C15, $[\bar{1}1\bar{1}]_{\text{BCC}}$ // $[01\bar{1}]_{\text{C15}}$ is identified between BCC and C15 #2-3, while neither OR 1 nor OR 2 appear, as shown in Fig. 14, and there is no fixed OR between the BCC matrix and C15 #2-4 (Fig. 15). In this case, C15 #2-3 should be the parent grain and OR 3 should be the principal OR. Bhowmik et al.²⁴⁾ have also found an OR which is similar with OR 3, just the ⟨111⟩_BCC and ⟨110⟩_C15 are within a few degrees of each other in Cr matrix and cubic Cr₂Ta. The same examination is employed to deal with the other twin pairs, and the results are summarized in Table 4. C15 #2-7&#2-8 share the same OR with that found in C15 #2-1&#2-2, while C15 #2-5&#2-6 and C15 #2-9&#2-10 have the same OR as that found in C15 #2-3&#2-4. No OR 3 was identified in alloy #3 in any combination of Laves phase and BCC matrix.

Fig. 10

(a) SEM images and EBSD analysis results of alloy #2 aged at 1473 K for 100 h: (b) phase map and IPF maps of (c) BCC and (d) Laves phase.

Fig. 11

PFs for the grains marked in Fig. 10(d). (Colors for ⟨111⟩ poles correspond to the colors in Fig. 10(d)).

Fig. 12

PFs for (a,c) the BCC matrix and (b,d) C15 #2-1 in Fig. 10(d).

Fig. 13

PFs for (a,c) the BCC matrix and (b,d) C15 #2-2 in Fig. 10(d).

Fig. 14

PFs for (a,c,e) the BCC matrix and (b,d,f) C15 #2-3 in Fig. 10(d).

Fig. 15

PFs for (a,c,e) the BCC matrix and (b,d,f) C15 #2-4 in Fig. 10(d).

Table 4 OR for grains in Fig. 10(d).

Figure 16 shows schematic drawings of the OR between C15 Laves and the BCC matrix phase in the case of the C15 #2-1&#2-2 pair or the C15 #2-7&#2-8 pair, where OR 2 is found in both grains of the twin pairs, while OR 1 appears in only one of the grains of the twin pairs in alloy #2. This strongly suggests that OR 2 governs the precipitation of Laves phase from BCC, i.e., the twin part of the grain is selected to have another OR 2. From this point of view, alloy #2 has two principal ORs, OR 2 and OR 3.

Fig. 16

Schematic diagram showing the crystallographic OR based on OR 1 and OR 2 between the C15 precipitate and BCC matrix phase in alloy #2. (a) Perspective view of the BCC unit cell, (b) perspective view of {111}_C15 tetrahedrons after twinning, (c) side view of BCC indicated in (a), and (d) side view of C15 indicated in (b).

The lattice misfit of the C15 precipitate and BCC matrix strongly affects the selection of the OR between the two phases. The lattice misfit (δ) between two planes of matrix (α) and precipitate (P) can be estimated with the planar disregistry proposed by Bramfitt²⁵⁾ as:   

\begin{equation} \delta_{(hkl)_{P}}^{(hkl)_{\alpha}} = \sum_{i = 1}^{3}\frac{|(d_{[uvw]_{\alpha}^{i}}\cos\theta) - d_{[uvw]_{P}^{i}}|}{3d_{[uvw]_{P}^{i}}} \times 100, \end{equation} (1)

where (hkl)_i are the low-index planes of the BCC matrix and C15 precipitate. [uvw]_i are the low-index directions in (hkl)_i. $\text{d}_{[\text{uvw}]_{\text{i}}}$ are the interatomic spacing along [uvw]_i. θ is the angle between the [uvw]_α and [uvw]_P. Presuming that the thermal expansion has a linear relationship for any phases with temperature in the range from room temperature to 1473 K, the lattice constants of the BCC matrix and C15 NbCr₂ at 1473 K are calculated based on the room temperature lattice constants obtained from the present XRD results. The lattice parameters are a_BCC = 0.2960 nm, a_C15 = 0.6979 nm for alloy #3; $\text{a}_{\text{BCC}_{1}} = 0.2965$ nm, $\text{a}_{\text{BCC}_{2}} = 0.3132$ nm, a_C15 = 0.6986 nm for alloy #2; a_BCC = 0.3151 nm, a_C15 = 0.6983 nm for alloy #1 at room temperature. The planar disregistry was then deduced using the lattice constants at 1473 K. The coefficients of thermal expansion for Cr, Mo, and Nb are 11 × 10⁻⁶/K, 5.5 × 10⁻⁶/K, and 8 × 10⁻⁶/K, respectively.²⁶⁾ Considering the high solid solution and different composition of each BCC phase, 10 × 10⁻⁶/K was employed as the thermal expansion coefficient for approximation. It was confirmed that the lattice constants of BCC₁ and BCC₂ in alloy #2 are very close to the results of Goldschmidt and Brand.²⁷⁾ The atoms of the three matched BCC/C15 interfaces are illustrated in Fig. 17. The interatomic distances and planar disregistry calculated from the lattice constants for alloy #3 are listed in Table 5 as an example. In the same manner, the lattice misfit for the other alloys was determined, as presented in Table 6.

Fig. 17

Atomic matching at three BCC/C15 interfaces.

Table 5 Planar disregistry calculations between C15 NbCr₂ and the BCC matrix phase for alloy #3.

Table 6 Lattice misfit δ, between C15 NbCr₂ and the BCC matrix.

The δ value increases with the lattice constant of the BCC matrix, i.e., with a decrease in the Cr content, which slightly decreases at first for OR 1 and OR 2. OR 1 and OR 2 are more favorable for alloy #3 due to the small δ values. Relatively larger δ values are presented for alloy #1, in which case no precipitation is found in the grain interior. For alloy #2, the Cr-rich BCC₁ matches well with C15 in the form of OR 1 and OR 2 after decomposition to BCC₁ and BCC₂. OR 3 also exists in alloy #2 but not in alloy #3 although the δ values are almost the same for these two alloys (#3 and #2-BCC₁). One possible explanation is that the phase boundaries between BCC₁ and BCC₂ in alloy #2 may facilitate the formation of C15 NbCr₂ in OR 3 due to fast diffusion. The change in elastic constants with the composition of the BCC matrix may have some effect on the selection of OR through the interfacial elastic energy. The δ values for OR 1 and OR 2 are 8.75% for alloy #1, where no fixed OR exists. OR 3 with a δ value of 8.78% is not found in alloy #3. Bramfitt suggested that the δ of 12% is the upper limit value for the formation of a matching interface in supercooled liquid iron.²⁵⁾ It appears the limit value is around 8%, which is much smaller than the 12% in the present system.

4. Conclusions

Based on the isothermal sections of the Cr–Mo–Nb ternary phase diagram at 1473 K confirmed by the present study, the precipitation behavior of C15 NbCr₂ Laves phase in various alloys at 1473 K was investigated using SEM, XRD, and EBSD. The results are summarized as follows:

1. (1)    The C15 NbCr₂ Laves precipitation behavior is quite different in the three alloys of #1, #2, and #3. After two-step heat treatment, gray precipitates appear at the grain boundaries and cellular structures are formed in alloy #1, while precipitates appear not only at the grain boundaries but also in the grain interior of alloy #3. Alloy #2 is a three-phase alloy that consists of a fine lamellar structure of two BCC phases with relatively larger Laves precipitates.
2. (2)    OR 1 and OR 2 with low lattice misfit are both observed between the BCC matrix phase and C15 precipitates in alloys #3 and #2. OR 3 with a relatively larger δ value is also found in alloy #2, which may be a result of the presence of phase boundaries of BCC₁ and BCC₂ formed after BCC decomposition. The limit value appears to be 8% for the formation of a matching interface between the BCC matrix and Laves precipitates.

Acknowledgments

This work was supported by JST ALCA Grant Number JPMJAL1407, Japan. A part of this work was conducted at the Laboratory of Nano-Micro Materials Analysis, Hokkaido University, supported by the “Nanotechnology Platform” Program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. One of the authors (S. M.) thanks Prof. Y. Mishima for his suggestion of this study.

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