Experimental Investigation of Crystal Structure of Zr<sub>0.98</sub>NiGe<sub>2.94</sub> and Phase Equilibria in Zr-Ni-Ge System

Citation

Zhengyang Wang, Weijing Zeng, Hong Zhang, Huashan Liu. Experimental Investigation of Crystal Structure of Zr_0.98NiGe_2.94 and Phase Equilibria in Zr-Ni-Ge System[J]. Journal of Harbin Institute of Technology (New Series), 2023, 30(4): 1-14. DOI: 10.11916/j.issn.1005-9113.22009

Fund

Sponsored by the Major State Basic Research Development Program of China (Grant No. 2014CB6644002)

Corresponding author

Huashan Liu, Ph.D., Professor. E-mail: hsliu@csu.edu.cn

Article history

Received: 2022-03-02

Contents Abstract Full text Figures/Tables PDF

Experimental Investigation of Crystal Structure of Zr_0.98NiGe_2.94 and Phase Equilibria in Zr-Ni-Ge System

Zhengyang Wang^1,2, Weijing Zeng^1,2, Hong Zhang^1,2, Huashan Liu^1,2

1. School of Materials Science and Engineering, Central South University, Changsha 410083, China;
2. Key Lab of Non-Ferrous Metal Materials Science and Engineering, Ministry of Education, Central South University, Changsha 410083, China

Received: 2022-03-02; Available online: 2022-07-07

Sponsored by the Major State Basic Research Development Program of China (Grant No. 2014CB6644002)

Corresponding author: Huashan Liu, Ph.D., Professor. E-mail: hsliu@csu.edu.cn.

Abstract: Based on the results of electron probe microanalysis (EPMA) and X-ray diffraction (XRD), the isothermal sections of Zr-Ni-Ge ternary system at 973 K and 1173 K were constructed through alloy sampling approach. It is worth noting that the crystallographic information of the formerly reported τ₂(Zr_0.98NiGe_2.94) was determined, which belongs to the space group Pbcm (No.57). Besides the formerly reported ternary compounds, τ₁(Zr₆Ni₁₆Ge₇), τ₂(Zr_0.98NiGe_2.94), τ₃(Zr₃Ni₄Ge₄), τ₄(ZrNiGe) and τ₅(Zr₂Ni_0.54Ge_0.46), a new ternary phase named τ₆ with the composition of Zr₃₉Ni₁₈Ge₄₃ was primarily detected in this work. In addition, an invariant reaction Ni₅Ge₃+τ₄↔τ₁+τ₃ between 973 K and 1173 K was deduced.

Keywords: Zr-Ni-Ge system phase diagram isothermal section crystal structure Zr_0.98NiGe_2.94

0 Introduction

Zr-Ni based amorphous metal films are widely applied as functional materials, e.g., hydrogen storage materials and sensor materials, due to their unique hydrogen storage properties and better catalytic property^[1-2]. However, Zr-Ni alloys alone generally have relatively low glass-forming ability, especially as the Ni concentration increases^[3-5], which results in the weakening of corrosion resistance. Therefore, a tertiary element could be added into the Zr-Ni alloys to improve corrosion resistance and glass-forming ability. Ge is such an ideal element for its special metallic and semiconductor properties. The melting point of Ge is lower than that of Zr, Ni and other alloying elements, which can reduce the melting point of the system. For the composition design of amorphous alloy, adding Ge element can not only enlarge the composition range of amorphous alloy, but also effectively improve the corrosion resistance of Zr-Ni alloy^[6]. In order to better understand the existing state of the third element Ge in Zr-Ni alloy and the effect of Ge on the phase formation and stability of Zr-Ni alloy, it is necessary to study the phase equilibrium relationship of Zr-Ni-Ge ternary system. Hence, phase equilibria of the Zr-Ni-Ge ternary alloy system are crucial for further understanding the role of Ge element in Zr-Ni based alloys and are of fundamental importance to composition and heat-treatment design.

The research of boundary binary phase relations in the Zr-Ni-Ge ternary system has been perfected, as shown in Fig. 1. In regard to Zr-Ni binary system, in 1961, Kirkpatrick et al.^[7] first measured the Zr-Ni binary phase diagram in the whole composition range by means of the optical microscope, X-ray diffraction and optical pyrometer. After that, Nash et al.^[8] completely evaluated this system and found 8 stable intermediates: ZrNi₅, Zr₂Ni₇, Zr₈Ni₂₁, ZrNi₃, ZrNi, Zr₇Ni₁₀, Zr₉Ni₁₁ and Zr₂Ni. There are 11 invariant reactions in the Zr-Ni binary system, including 4 eutectic reactions, 4 eutectoid reactions, 2 peritectic reactions and 1 peritectoid reaction. Recently, Kosorukova et al.^[9] re-measured the phase equilibrium relationship of the Zr-Ni binary system, and revised the temperature of each invariant reaction.

Fig.1 Binary phase diagrams the Zr-Ni-Ge ternary system

As for the Ni-Ge binary system, Ruttewit and Masing ^[10] evaluated the reported experimental information and constructed the phase diagram. Subsequently, Dayer^[11] and Ellner^[12] further improved the phase diagram. Based on the previous experiments, Nash^[13] carried out thermodynamic optimization of the Ni-Ge system for the first time. Later, Ikeda^[14]and Komai^[15] found that the solid solubility of βNi₃Ge phase reduced with the decrease of temperature. Gel'd^[16] and Larsson^[17] conducted experimental studies on the dependable evidence of the εNi₅Ge₃, Ni₁₉Ge₁₂ and Ni₃Ge₂. It was found that the three independent B8-type intermediate phases were eventually non-stoichiometric Ni₅Ge₃ solid solution phase. In view of the above problems, Jin et al.^[18], based on more recent experimental data, re-optimized the Ni-Ge system, which involved seven intermediate compounds, namely, βNi₃Ge, γNi₃Ge, δNi₅Ge₂, Ni₂Ge, Ni₅Ge₃, ε^'Ni₅Ge₃ and NiGe.

The phase equilibrium relationship of the Zr-Ge binary system has been studied by many groups ^[19-24]. Recently, Sha^[24] carried out thermodynamic optimization for the Zr-Ge binary system through First-principle calculation, CALPHAD and experimental methods. As shown in Fig. 1, the Zr-Ge binary system contains five stable intermediate phases Zr₃Ge, Zr₅Ge₃, Zr₅Ge₄, ZrGe and ZrGe₂.

Nevertheless, very little information about phase equilibria and ternary compounds in the Zr-Ni-Ge system was reported besides five ternary intermetallic phases τ₁(Zr₆Ni₁₆Ge₇ ^[25]), τ₂(Zr_0.98NiGe_2.94 ^[26]), τ₃(Zr₃Ni₄Ge₄ ^[26]), τ₄(ZrNiGe ^[27]) and τ₅(Zr₂Ni_0.54Ge_0.46 ^[26]) as listed in Table 1, the detailed crystallographic information about τ₂(Zr_0.98NiGe_2.94) is unknown. The present work focuses on measuring the crystallographic data of τ₂ and phase equilibrium relationship in the Zr-Ni-Ge system at 973 and 1173 K.

Table 1 Crystallographic data of solid phases of Zr-Ni-Ge system

System	Phase	Prototype	Pearson's symbol	Lattice parameters(nm)			Refs.
System	Phase	Prototype	Pearson's symbol	a	b	c	Refs.
Ge	Diamond_A4	C	cF8	0.56512	0.56512	0.56512	[28]
Ni	FCC_A1, (Ni)	Cu	cF4	0.35236	0.35236	0.35236	[29]
αZr	HCP_A3	Mg	hP2	0.32320	0.32320	0.51480	[9]
βZr	BCC_A2	W	cI2	0.36090	0.36090	0.36090	[9]
Ni-Ge	βGeNi₃	AuCu₃	cP4	0.35720	0.35720	0.35720	[30]
	γGeNi₃	NaTl	cF16	0.57436	0.57436	0.57436	[31]
	GeNi₂	InNi₂	hP6	0.39480	0.39480	0.39480	[29]
	δGe₂Ni₅	Pd₅Sb₂	hP84	0.68270	0.68270	1.23950	[12]
	Ge₃Ni₅	InNi₂	hP6	0.39200	0.39200	0.50460	[32]
	Ge₁₂Ni₁₉	Ge₁₂Ni₁₉	mC62	1.16310	0.67150	1.00480	[29]
	Ge₂Ni₃	AsNi	hP4	0.39100	0.39100	0.50360	[29]
	ε'Ge₃Ni₅	Ni₅Ge₃	mC32	1.16820	0.67370	0.62640	[12]
	GeNi	MnP	oP8	0.53810	0.34280	0.58110	[29]
Zr-Ge	Zr₃Ge	Ti₃P	tP32	1.17330	1.17330	0.54740	[19]
	Zr₅Ge₃	Mn₅Si₃	hP16	0.80290	0.80290	0.55940	[19]
	Zr₅Ge₄	Zr₅Si₄	tP36	0.72380	0.72380	1.31540	[19]
	ZrGe	FeB	oP8	0.70680	0.38900	0.53960	[19]
	ZrGe₂	ZrSi₂	oC12	0.38100	1.50720	0.37690	[19]
Zr-Ni	ZrNi₅	AuBe₅	cF24	0.67060	0.67060	0.67060	[9]
	Zr₇Ni₁₀	Zr₇Ni₁₀	oC68	1.23680	0.91560	0.92110	[9]
	Zr₂Ni	CuAl₂	tI12	0.64720	0.64720	0.64720	[9]
	ZrNi₂	Cu₂Mg	cF24	0.69780	0.69780	0.69780	[9]
	Zr₂Ni₇	Zr₂Ni₇	mC36	0.46980	0.82350	1.21930	[9]
	ZrNi₃	Ni₃Sn	hP8	0.53090	0.53090	0.43030	[33]
	Zr₈Ni₂₁	Hf₈Ni₂₁	aP29	0.64720	0.80650	0.85880	[9]
	Zr₉Ni₁₁	Zr₉Pt₁₁	tI40	0.98800	0.66100	0.66100	[9]
	ZrNi	CrB	oC8	0.32680	0.99370	0.41020	[9]
Zr-Ni-Ge	Zr₆Ni₁₆Ge₇(τ₁)	Mn₂₃Th₆	cF116	1.16600	1.16600	1.16600	[25]
	Zr_0.98NiGe_2.94(τ₂)	LaCrSb₃	oP12	1.13150	0.54450	0.53550	This work
	Zr₃Ni₄Ge₄(τ₃)	Gd₃Cu₄Ge₄	oL22	0.64850	1.29800	0.39280	[26]
	ZrNiGe(τ₄)	Co₂Si	oP12	0.65530	0.38830	0.73600	[27]
	Zr₂Ni_0.54Ge_0.46(τ₅)	CuAl₂	tI12	0.66160	0.66160	0.54180	[26]

Table 1 Crystallographic data of solid phases of Zr-Ni-Ge system

1 Experimental Details

The highly purified zirconium (99.9 wt%), germanium (99.99 wt%) and nickel (99.99 wt%) were used as raw materials. All samples, with a total mass of 6 g, were weighed by using an electronic balance with an accuracy of 0.0001 g.

After being weighed, the raw materials were put into a copper crucible, and then melted in the vacuum non-consumable electric arc furnace. In the melting process, sponge titanium was additionally placed as a getter material. In order to ensure the uniform composition of the alloy, each sample needs to be turned upside and down and melted more than 3 times. After melting, each alloy button was weighed. The mass loss was controlled within 1%.

Each button ingot was wire cut into four parts. After cleaning and removing the oxide layer, each part of the ingot was sealed in a quartz glass tube filled with argon, and then homogenized at 973 K for 100 days and 1173 K for 60 days in a tube furnace, respectively. Then, the tubes containing alloy samples were removed from the furnace and broken immediately so that the alloy was quenched into water at room temperature.

Finally, the constituent phases and their compositions in the annealed samples were investigated by electron probe microanalysis (EPMA) on a JEOL JXA-8800R electron microprobe with an accelerating voltage of 20 kV, a probe current of 1×10^-8 A. Constituent phase of the annealed alloy samples were measured by X-ray diffraction (XRD) (Rigaku D-max/2550 X-ray diffractometer, Cu Kα, 40 kV, 250 mA).

Rietveld refinements were carried out with the programs Jade 6^[34] and Fullprof-suite^[35]. Microstructure characterization using high-resolution transmission electron microscopy (HRTEM) was conducted in a JEM-ARM200 analytic transmission electron microscope working at 200 kV. TEM bright-field (BF) imaging and selected area electron diffraction (SAED) were performed on a JEOL 2010F electron microscope with a field gun at an acceleration voltage of 200 kV.

2 Results and Discussion 2.1 Crystal Structure of Ternary Compound Zr_0.98NiGe_2.94

The phase τ₂ was reported firstly by Lysenko in 1978^[26], and the composition of τ₂ was determined to be Zr₁₁Ni₁₀Ge₂₉. But till now, there has been a lack of detailed crystallographic information on τ₂. Alloy S1 with composition of Zr₁₁Ni₁₀Ge₂₉ was fabricated and annealed at 973 K for 100 days. As shown in Fig. 2, Alloy S1 mainly consists of a gray phase. By EPMA measurement, the gray phase contains 19.34 at.% Zr, 21.01 at.% Ni and 59.65 at.% Ge, which should be τ₂. In addition, a small amount of white phase is determined to be ZrGe₂.

Fig.2 BSE (Back-Scattered Electron) image of Alloy S1

Then, the S1 sample was ground into powder to further collect its X-ray diffraction pattern and HRTEM data. The experimental parameters of XRD are as follows: the 2 θ range was 5°-120°, each step was 0.02~, and each step was stopped for 2 s. The crystal structure of phase τ₂ was indexed with the Jade 6 program^[34]. It was found that τ₂ has an orthorhombic unit cell and the lattice parameters are as follows: a=11.315(1) Å, b=5.444(9) Å, c=5.355(5) Å. The reflection conditions are as follows:

1) hkl: no conditions;

2) 0kl: l=2n;

3) h0l: h=2n;

4) hk0: no conditions;

5) h00: h=2n;

6) 0k0: no conditions;

7) 00l: l=2n.

The reflection conditions indicate that the possible space group is Pbcm (No.57) or Pca2₁ (No.29). τ₂ is isostructural with LaCrSb₃ (Pbcm)^[36] by further comparing the powder XRD pattern in the crystallographic characteristics database. So the space group Pbcm (No.57) and crystallographic information of LaCrSb₃ were taken as the starting value when the structure refinement of sample S1 was performed by using the Fullprof-Suite program ^[35]. The formula of τ₂ was refined to be Zr_0.98NiGe_2.94 (19.93 at.% Zr, 20.34 at.% Ni, 59.73 at.% Ge), agreeing well with the measured data, 19.34 at.% Zr, 21.01 at.% Ni and 59.65 at.% Ge. It should be pointed out that, ZrGe₂ was input as the second phase during the refinement. The weight percent of the two phases is calculated by quantitative phase analysis in the Rietveld method, which is solved through the Fullprof-Suite program. The powder XRD pattern of the mixture is the weight superposition of the powder XRD patterns of each component phase, and the weight factor of each phase is related to the weight fraction of the phase in the mixture. Therefore, the weight percent of the two phases can be obtained from the relationship between the weight factor and the weight fraction. By this method, the amount of ZrGe₂ is calculated to be about 8.8wt% in sample S1.

Fig. 3 shows the calculated and experimental patterns of Alloy S1. The refinement details and crystal data are summarized in Tables 2-4. The final reliability R-factors of R_p=7.46% and R_wp=9.69% indicate highly reliable crystal structure refinement. It can be seen that two disordered sites, Zr 4d and Ge1 4d sites, exist in the lattice and the occupation rate of these two sites are approximately 0.98 and 0.94, respectively. In addition, all bond lengths are reasonable with respect to atomic radii. The crystallographic unit cell of Zr_0.98NiGe_2.94 is presented in Fig. 4. Neighbors of the Zr and Ni atoms form a cube (CN=11 and 10), and those of the Ge1, Ge2 and Ge3 atoms build heptahedron (CN=6), enneahedron (CN=7) and hendecahedron (CN=8), respectively.

Fig.3 Experimental and calculated XRD patterns of Alloy S1

Table 2 Crystal data and structure refinement details for the compounds Zr_0.98NiGe_2.94

Table 3 Atomic coordinates and temperature factors for Zr_0.98NiGe_2.94

Table 4 Interatomic distances (δ, Å) and coordination numbers (CN) of the atoms in the crystal structure of Zr_0.98NiGe_2.94

Fig.4 Projection of the crystallographic unit cell of Zr_0.98NiGe_2.94 on ab plane and the coordination polyhedral of the atoms

TEM was employed to further confirm the crystal structure of the Zr_0.98NiGe_2.94. The Zr_0.98NiGe_2.94 powders are smaller than 500 nm, as shown in Fig. 5 (a). The calculated XRD pattern of Zr_0.98NiGe_2.94 phase based on the crystal structure obtained by refinement is illustrated in Fig. 5 (b). Fig. 5 (c) presents the SAED pattern of a representative powder, the lengths of OA, OB, OC are 3.9525, 5.5096 and 3.23721/nm, respectively, corresponding to the (121) (123) (002) crystal planes of Zr_0.98NiGe_2.94 phase. This is along [2 1 0] zone axis of the Zr_0.98NiGe_2.94 phase. Similarly, the SAED pattern in Fig. 5 (d) illustrates the (2 20), (131) and (111) crystal planes along with the [11 2] zone axis of the Zr_0.98NiGe_2.94 phase. Furthermore, HRTEM image illustrates the interplanar crystal spacing of the (002), (121) and (1 21) crystal planes along [2 10] zone axis is 0.2657, 0.2389 and 0.2358 nm (Fig. 5 (e)). All these results are consistent with the crystal structure of the Zr_0.98NiGe_2.94 phase. In brief, based on the EPMA and TEM analysis, phase τ₂ is refined to be Zr_0.98NiGe_2.94 with the space group Pbcm (No.57).

Fig.5 (a) Morphology of the Alloy S1 powders; (b) The calculated XRD patterns of Zr_0.98NiGe_2.94 according to the lattice parameter and interplanar crystal spacing obtained by refinement; (c) SAED pattern of Zr_0.98NiGe_2.94 along the [2 10] zone axis; (d) SAED pattern of Zr_0.98NiGe_2.94 along the [11 2] zone axis; (e) HRTEM image of Zr_0.98NiGe_2.94 along the [2 10] zone axis and its corresponding Fourier transformed pattern

2.2 Phase Equilibria at 973 K

All alloy samples annealed at 973 K contain two or three phases. According to the phase law, after annealing at 973 K, the samples of Zr-Ni-Ge alloy basically reach or are close to an equilibrium state. The constituent phases and their composition in the annealed alloys are summarized in Table 5.

Table 5 Constituent phases in annealed Zr-Ni-Ge alloys at 973 K

Alloy's Number	Nominal Composition (at.%)	Phase equilibria Phase 1/Phase 2/Phase 3	Composition (at.%)
			Phase 1			Phase 2			Phase 3
			Zr	Ge	Ni	Zr	Ge	Ni	Zr	Ge	Ni
A1	Zr₅Ge₈₀Ni₁₅	(Ge)/NiGe/τ₂	0.4	95.9	3.7	0.6	49.5	49.9	18.6	60.1	21.3
A2	Zr₁₅Ge₈₀Ni₅	(Ge)/ZrGe₂/τ₂	0.8	99.1	0.1	32.3	65.6	2.1	19.4	58.4	22.2
A3	Zr₅Ge₉₀Ni₅	(Ge)/τ₂	0.2	99.4	0.4	19.4	59.3	21.3	-	-	-
A4	Zr₂₀Ge₅₀Ni₃₀	NiGe/τ₂/τ₃	0.3	49.3	50.4	20.3	58.1	21.6	28.1	36.6	35.3
A5	Zr₃₀Ge₅₅Ni₁₅	ZrGe₂/τ₂/τ₃	33.4	63.9	2.7	20.2	57.1	22.7	25.9	36.9	37.2
A6	Zr₁₀Ge₄₀Ni₅₀	NiGe/Ni₅Ge₃/τ₃	1.2	49.9	48.9	1.3	34.6	64.1	27.9	36.3	35.8
A7	Zr₂₀Ge₃₀Ni₅₀	Ni₅Ge₃/τ₁/τ₄	1.3	34.5	64.2	20.3	24.8	54.9	32.9	33.8	33.3
A8	Zr₅Ge₃₀Ni₆₅	Ni₅Ge₃/τ₁/Ni₃Ge	0.3	34.6	65.1	18.2	23.9	57.9	-0.6	25.3	75.3
A9	Zr₄₀Ge₃₀Ni₃₀	Zr₇Ni₁₀/Zr₅Ge₃/τ₄	42.4	4.9	52.7	62.2	35.7	2.1	30.8	36.3	32.9
A10	Zr₆₀Ge₁₀Ni₃₀	ZrNi/Zr₂Ni/Zr₅Ge₃	52.2	2.3	45.5	66.6	1.8	31.6	62.1	35.1	2.8
A11	Zr₇₀Ge₂₅Ni₅	Zr₂Ni/Zr₃Ge/Zr₅Ge₃	68.8	3.5	27.7	74.9	24.0	1.1	64.0	34.1	1.9
A12	Zr₈₀Ge₁₀Ni₁₀	(Zr)/Zr₂Ni/Zr₃Ge	99.3	0.6	0.1	67.6	2.2	30.2	75.4	22.7	1.9
A13	Zr₅Ge₁₀Ni₈₅	(Ni)/ZrNi₅/τ₁	0.7	10.9	88.4	18.2	3.9	77.9	19.3	20.5	60.2
A14	Zr₃₅Ge₅₅Ni₁₀	ZrGe₂/Zr₅Ge₄ /τ₆	32.2	66.6	1.2	53.3	46.1	0.6	37.2	44.3	18.5
A15	Zr₄₀Ge₄₀Ni₂₀	Zr₅Ge₄/τ₄/τ₆	54.2	45.1	0.7	32.5	35.2	32.3	38.5	42.3	19.2
A16	Zr₂₅Ge₂₀Ni₅₅	Zr₂Ni₇/τ₄	22.3	6.8	70.9	32.3	31.4	36.3	-	-	-
A17	Zr₃₀Ge₁₀Ni₆₀	ZrNi₃/τ₄/Zr₈Ni₂₁	25.2	2.2	72.6	32.3	31.4	36.3	28.2	1.6	70.2
A18	Zr₁₀Ge₅Ni₈₅	(Ni)/ZrNi₅	1.1	5.6	93.3	17.2	1.7	81.1	-	-	-

Table 5 Constituent phases in annealed Zr-Ni-Ge alloys at 973 K

The microstructure of the alloy A4(Zr₂₀Ge₅₀Ni₃₀) annealed at 973 K is illustrated in Fig. 6 (a). It can be seen that alloy A4(Zr₂₀Ge₅₀Ni₃₀) consists of NiGe, τ₂ and τ₃ with a composition of Zr_27.6Ni_35.0Ge_37.4. Because there are no obvious differences in the color of τ₂ and τ₃, X-ray diffraction was used to verify the existence of τ₂ and τ₃, which can be seen in Fig. 6 (b). It means that the alloy A4(Zr₂₀Ge₅₀Ni₃₀) locates in the three-phase region of NiGe+τ₂+τ₃.

Fig.6 (a) BSE image and (b)XRD pattern of Alloy A4 annealed at 973 K for 90 days

Fig. 7 shows BSE images of alloy A7(Zr₂₀Ge₃₀Ni₅₀) and alloy A13(Zr₅Ge₁₀Ni₈₅). The existence of the three-phased equilibria τ₁+τ₄+Ni₅Ge₃ and τ₁+(Ni)+ ZrNi₅ could be identified in alloys A7(Zr₂₀Ge₃₀Ni₅₀) and A13(Zr₅Ge₁₀Ni₈₅), respectively.

Fig.7 BSE images

Fig. 8 (a) presents the microstructure of alloy A14(Zr₃₅Ge₅₅Ni₁₀), and it can be seen that alloy A14(Zr₃₅Ge₅₅Ni₁₀) contains ZrGe₂, ZrGe, and a new unknown phase with a composition of Zr_37.2Ni_18.5Ge_44.3. After excluding the diffraction peaks of the ZrGe₂ and ZrGe phase, some characteristic peaks remained unidentified, as shown in Fig. 8 (b). These peaks must belong to the unknown phase, which is named τ₆ hereafter. τ₆ was also detected in alloy A15 (Zr₄₀Ge₄₀Ni₂₀). But we failed to prepare a single-phase sample to further collect the X-ray patterns of τ₆. The related study of the crystal structure of the phase τ₆ will be investigated in future work.

Fig.8 Constituent phases in alloy A14 annealed at 973 K for 90 days

According to the present experimental data, combined with the information of relevant binary systems in the literature, 15 three-phase regions have been measured in the isothermal section of the Zr-Ni-Ge ternary system. In addition, according to the phase law and the measured equilibria phase relations, 11 unmeasured three-phase regions can be extrapolated, as shown in Fig. 9. It should be noted that a new ternary compound τ₆ was found.

Fig.9 Isothermal section of Zr-Ni-Ge system at 973 K

2.3 Phase Equilibria at 1173 K

About twenty alloy samples were prepared to determine phase equilibria at 1173 K. The constituent phases and their compositions in the annealed alloys are summarized in Table 6.

Table 6 Constituent phases in annealed Zr-Ni-Ge alloys at 1173 K

Alloy's Number	Nominal Composition (at.%)	Phase equilibria Phase 1/Phase 2/Phase 3	Composition (at.%)
			Phase 1			Phase 2			Phase 3
			Zr	Ge	Ni	Zr	Ge	Ni	Zr	Ge	Ni
B1	Zr₂₅Ge₆₀Ni₁₅	ZrGe₂/τ₃/Liquid	31.7	66.5	1.8	27.1	36.2	36.7	-	-	-
B2	Zr₄₅Ge₅₅Ni₁₀	ZrGe₂/ZrGe/τ₆	32.8	65.8	1.4	50.3	49.6	0.1	39.3	43.1	17.6
B3	Zr₁₀Ge₄₀Ni₅₀	Ni₅Ge₃/τ₃/Liquid	0.3	34.9	65.4	27.7	35.5	36.8	-	-	-
B4	Zr₄₀Ge₄₀Ni₂₀	Zr₅Ge₄/τ₄/τ₆	53.9	45.7	0.4	32.5	35.1	32.4	39.2	43.4	17.4
B5	Zr₂₀Ge₃₀Ni₅₀	Ni₅Ge₃/τ₁/τ₃	0.5	35.3	64.2	18.5	27.2	54.3	32.2	33.7	34.1
B6	Zr₅Ge₃₀Ni₆₅	Ni₅Ge₃/τ₁/Ni₃Ge	1.2	33.4	65.4	16.2	25.1	58.7	0.1	25.1	74.8
B7	Zr₄₀Ge₃₀Ni₃₀	Zr₇Ni₁₀/τ₄/Zr₅Ge₃	43.0	4.5	52.5	33.2	34.0	32.8	61.3	36.8	1.9
B8	Zr₁₀Ge₁₀Ni₈₀	τ₁/ZrNi₅/(Ni)	20.0	21.7	58.3	16.4	5.8	77.8	1.0	10.3	88.7
B9	Zr₈₀Ge₁₀Ni₁₀	(Zr)/Zr₂Ni/Zr₃Ge	99.6	0.3	0.1	68.0	1.3	30.7	76.4	22.3	1.3
B10	Zr₁₀Ge₅Ni₈₅	(Ni)/ZrNi₅	2.0	8.1	89.9	16.8	3.3	79.9	-	-	-
B11	Zr₃₀Ge₁₀Ni₆₀	Zr₈Ni₂₁/τ₄/ZrNi₃	28.8	1.6	69.6	32.2	32.1	35.7	24.2	1.3	74.5
B12	Zr₃₅Ge₅₅Ni₁₀	ZrGe₂/τ₃/τ₆	31.0	66.8	2.2	32.5	37.1	30.4	39.1	42.1	18.8
B11	Zr₅₀Ge₁₀Ni₄₀	Zr₅Ge₃/Zr₇Ni₁₀/ZrNi	62.1	36.3	1.6	41.9	3.4	54.7	49.6	49.8	0.6
B14	Zr₅₀Ge₂Ni₄₈	ZrNi/Zr₂Ni	50.7	2.1	47.2	66.4	1.3	32.3	-	-	-
B15	Zr₂₅Ge₂₀Ni₅₅	Zr₂Ni₇/τ₄	21.7	5.7	72.6	32.1	32.0	35.9	-	-	-
B16	Zr₂₀Ge₁₀Ni₇₀	Zr₂Ni₇/τ₁	19.1	6.2	74.7	21.2	20.5	58.3	-	-	-
B17	Zr₅₅Ge₃₀Ni₁₅	Zr₇Ni₁₀/Zr₅Ge₃	41.7	3.6	54.7	60.3	36.4	2.3	-	-	-
B18	Zr₆₀Ge₂₅Ni₁₅	ZrNi/Zr₅Ge₃	50.2	0.6	49.2	64.4	34.2	1.4	-	-	-
B19	Zr₆₀Ge₂₀Ni₂₀	ZrNi/τ₅/Zr₅Ge₃	51.5	1.9	46.6	62.4	21.2	16.4	64.1	32.1	2.8
B20	Zr₇₀Ge₂₅Ni₅	Zr₂Ni/Zr₃Ge/Zr₅Ge₃	66.2	3.4	30.4	75.2	24.5	0.3	63.8	34.8	1.4
B21	Zr₇₀Ge₂₀Ni₁₀	Zr₃Ge/τ₅	75.5	23.9	0.6	64.2	19.0	16.8	-	-	-
B22	Zr₃₀Ge₃₀Ni₄₀	τ₁/τ₄	18.4	23.2	58.4	31.6	33.4	35.0	-	-	-

Table 6 Constituent phases in annealed Zr-Ni-Ge alloys at 1173 K

The microstructure of alloy B4(Zr₄₀Ge₄₀Ni₂₀) is presented in Fig. 10 (a). Through EPMA and XRD (Fig. 10 (b)), the white Zr₅Ge₄ and dark τ₄ with a composition of Zr_32.5Ni_32.4Ge_35.1 could be easily observed. Similar to 973 K, an unknown phase with the composition of Zr_39.2Ni_17.4Ge_43.4 similar to that of τ₆ was detected. In the XRD pattern of alloy B4(Zr₄₀Ge₄₀Ni₂₀)(Fig. 10 (b)), besides the characteristic peaks of τ₄ and Zr₅Ge₄, there are also some characteristic peaks that cannot be identified with the Jade program. These unknown residual diffraction peaks belong to the new phase τ₆.

Fig.10 (a) BSE image and (b)XRD pattern of Alloy B4 annealed at 1173 K for 60 days

BSE image of alloy B7(Zr₄₀Ge₃₀Ni₃₀) is given in Fig. 11 (a), which consists of dark phase τ₄ with a composition of Zr_33.2Ni_32.8Ge_34.0, gray Zr₇Ni₁₀ and white Zr₃Ge₂. This alloy locates in the three-phase region of Zr₇Ni₁₀+Zr₃Ge₂+τ₄. The ternary phase τ₄ is consistent with that detected by Yarmolyuk ^[27].

Fig.11 Constituent phases in Alloy B7 annealed at 1173 K for 60 days

Fig. 12 (a) presents the microstructure of alloy B9(Zr₈₀Ge₁₀Ni₁₀), where phases Zr₂Ni, Zr₃Ge and (Zr) can be easily identified based on EPMA, which indicated that a three-phase equilibrium Zr₂Ni+Zr₃Ge+(Zr) exists in the alloy B9(Zr₈₀Ge₁₀Ni₁₀). From Fig. 12 (b), it can be seen that alloy B1(Zr₂₅Ge₆₀Ni₁₅) contains the light gray phase ZrGe₂, dark gray phase τ₃ and a typical eutectic structure between ZrGe₂ and τ₃. Because the phases in the eutectic structure are minute, EPMA cannot accurately measure their composition. But referring to the Ni-Ge binary phase diagram and considering the alloy compositions, the alloy B1(Zr₂₅Ge₆₀Ni₁₅) should involve a liquid phase at 1173 K and the liquid phase will solidify into a eutectic structure during water quenching. Therefore, in alloy B1(Zr₂₅Ge₆₀Ni₁₅), the liquid should coexist with ZrGe₂ and τ₃ at 1173 K. So, the real phase equilibrium might be ZrGe₂+τ₃+Liquid of alloy B1(Zr₂₅Ge₆₀Ni₁₅) at 1173 K. In this work, the composition of the liquid is estimated by averaging the measured solidified liquid product.

Fig.12 BSE images

According to the results of EPMA and X-ray diffraction (shown in Fig. 13), alloy B19(Zr₆₀Ge₂₀Ni₂₀) locates in the Zr₅Ge₃+ZrNi+τ₅ three-phase region at 1173 K. Similarly, according to Fig. 14, alloy B22 (Zr₃₀Ge₃₀Ni₄₀) locates in the two-phase region τ₁+τ₄.

Fig.13 Constituent phases in Alloy B19 annealed at 1173 K for 60 days

Fig.14 (a)BSE image and (b)XRD pattern of Alloy B22 annealed at 1173 K for 60 days

Based on the experimental results, combined with the phase equilibria at 973 K, the isothermal section of Zr-Ni-Ge system at 1173 K has been determined. Interestingly, τ₂ phase disappears at 1173 K. This isothermal section consists of 26 three-phase regions, including 12 measured three-phase regions and 14 estimated three-phase regions, as shown in Fig. 15.

Fig.15 Isothermal section of the Zr-Ni-Ge system at 1173 K

2.4 Comparison of Phase Equilibria at 973 K and 1173 K

Phase equilibria in the Zr-Ni-Ge ternary system at 973 and 1173 K were compared here. Based on Figs. 9 and 15, some distinct differences between these two isothermal sections are presented.

Firstly, when the temperature increases from 973 K to 1173 K, the liquid phase and τ₅ appear but τ₂ disappears, and the phase relations among (Ge), ZrGe₂, τ₂, NiGe and τ₅ have been changed. It can be seen that phase equilibria (Ge)+τ₂, ZrGe₂+τ₂, (Ge)+ZrGe₂+τ₂, NiGe+Ni₅Ge₃+τ₃, Zr₅Ge₃+Zr₂Ni+ZrNi and Zr₅Ge₃+ Zr₂Ni+Zr₃Ge at 973 K change to (Ge)+ZrGe₂, ZrGe₂+Liquid, (Ge)+ZrGe₂+Liquid, Ni₅Ge₃+τ₃+Liquid, Zr₅Ge₃+ZrNi+τ₅, Zr₅Ge₃+ Zr₃Ge+τ₅, Zr₂Ni+Zr₃Ge+τ₅ and Zr₂Ni+ZrNi+τ₅ at 1173 K.

Secondly, phase relations among Ni₅Ge₃, τ₁, τ₃ and τ₄ change obviously, i.e., the three-phase equilibria Ni₅Ge₃+τ₃+τ₄ and Ni₅Ge₃+τ₁+τ₄ at 973 K transform into Ni₅Ge₃+τ₁+τ₃ and τ₁+τ₃+τ₄ at 1173 K. In light of phase rule, it is inferred that an invariant reaction Ni₅Ge₃+τ₄↔τ₁+τ₃ happen at a temperature between 973 and 1173 K.

3 Conclusions

Phase equilibria relation of the Zr-Ni-Ge system at 973 K and 1173 K have been constructed in this work. Crystal structure τ₂ was determined, which belongs to space group Pbcm (No.57) with cell parameters a=11.315(1) Å, b=5.444(9) Å and c=5.355(1) Å. Besides the existing five ternary compounds, Zr₆Ni₁₆Ge₇(τ₁), Zr_0.98NiGe_2.94(τ₂), Zr₃Ni₄Ge₄(τ₃), ZrNiGe(τ₄) and Zr₂Ni_0.54Ge_0.46(τ₅), a new ternary phase τ₆ with a composition of Zr₃₉Ni₁₈Ge₄₃ was detected. In addition, one four-phase reaction Ni₅Ge₃+τ₄↔τ₁+τ₃ was deduced, which occurred at 973-1173 K.

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