Phase equilibria in the Ge-Mn-Ti ternary system at 973 K, 1073 K and 1173 K

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 139–149

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Phase equilibria in the Ge-Mn-Ti ternary system at 973 K, 1073 K and 1173 K

MARK

⁎

Y. Sun, W.J. Zeng, K. Hu, H.S. Liu , G.M. Cai, Z.P. Jin School of Materials Science and Engineering, Central South University, Changsha city, Hunan Province 410083, PR China

A R T I C L E I N F O

A BS T RAC T

Keywords: Ge-Mn-Ti system Isothermal section Rietveld refinement

Phase relationships in the Ge-Mn-Ti ternary system have been studied through alloy samples approach. Assisted with Electron Probe Microanalysis (EPMA) and X-ray diffraction (XRD) techniques, isothermal sections at 973 K, 1073 K and 1173 K of this system were constructed and existence of 2 ternary phases, i.e. GeMnTi and Ge2MnTi, were confirmed. In addition, remarkable ternary solubilities in some binary compounds were detected, e.g. Ge in Mn2Ti and Mn in Ge5Ti6 can be up to 15 at% and 50 at% at 1173 K, respectively. Furthermore, the substitution of Ti by Mn atoms in Ge5Ti6 was confirmed with Rietveld refinement results of solid solutions, Ge5(Mn0.30Ti0.70)6 and Ge5(Mn0.67Ti0.33)6.

1. Introduction Hydrogen is an environmentally friendly energy which has promising prospect for future energy sources, but its storage still remains a challenge [1]. Among those numerous storage methods, metal hydrides are very effective and safe for storing large amounts of hydrogen [2–4]. Mn-Ti based alloys with Laves phase AB2 structure are of technical and commercial interest, performing high hydrogen capacity, easy activation, good hydriding-dehydriding kinetics and excellent cycle property [5–7]. To improve the hydrogen storage properties of the Mn-Ti-based alloys, effects of other transition metals, such as Cr, Zr, V, Mo and W, have been investigated extensively [8–12]. Until now, the influence of Ge on the stability of Mn2Ti based hydrogen storage material have not been reported. The knowledge concerning phase relationships and transformations in the Ge-Mn-Ti system could be a guidance for subsequent study of novel hydrogen storage material. Information of binary Mn-Ti and Ge-Mn systems has been extensively investigated experimentally and through thermodynamic calculation. As for the Mn-Ti system, Murray [13] summarized a variety of experimental phase equilibria firstly, later optimized by Saunders et al. [14] and Chen et al. [15,16]. The assessments by Chen et al. [15,16] are well consistent with the reported experiments and thus are adopted in this work. Gokhale et al. [17] originally published the complete phase diagram of the Ge-Mn system, and the thermodynamic description was reported by Kanibolotskii et al. [18] later. Recently, a satisfactory thermodynamic assessment of the Ge-Mn system has been carried out by Berche et al. [19], mainly adopting the experimental data obtained by Wachtel et al. [20,21], Gupta et al. [22] and Zwicker et al. [23]. ⁎

Dissimilar to the Mn-Ti and Ge-Mn binary systems, the phase diagram of Ge-Ti system is still controversial. In Massalski's compilation [24], the Ge-Ti binary system was evaluated mainly based on the experimental diagram of Rudometkina et al. [25]. Recently, Liu et al. [26] re-assessed this system and only concerned three stable intermediate phases, i.e. Ge3Ti5, Ge5Ti6 and Ge2Ti. Nevertheless, the compound Ge4Ti5 was later reported as a new phase in the Ge-Ti system by Bittner et al. [27]. In addition, the GeTi3 phase, formerly considered to be an unstable phase by Liu et al. [26] and Jain et al. [28], was recently confirmed to be a stable phase by Xie et al. [29]. Phase equilibria of the well accepted boundary binary systems, Mn-Ti [15], Ge-Mn [19] and Ge-Ti [27], are presented in Fig. 1. So far, little information about phase relations in the Ge-Mn-Ti ternary system has been reported. To the best of our knowledge, only three ternary compounds, i.e. GeMnTi, Ge2MnTi, GeMnTi2 and their crystal structure [30] (see Table 1) along with partial phase relationships in the Mn-rich corner at 1173 K [31] were reported. The present work is an experimental study of phase relations in the Ge-Mn-Ti system at 973 K, 1073 K and 1173 K through alloy samples approach. 2. Experimental details More than 50 samples have been prepared. Starting materials of high purity (Ge: 99.99%, Mn: 99.99%, Ti: 99.99%, China New Metal Materials Technology Co., Ltd.) were adopted to prepare the experimental alloys. The weight of each sample was limited to about 6 g. Pre-determined amount of each raw material was weighed by analytical balance, followed by arc-melting on a water-cooled copper plate under purified argon

Corresponding author. E-mail address: [email protected] (H.S. Liu).

http://dx.doi.org/10.1016/j.calphad.2016.12.005 Received 6 October 2016; Received in revised form 7 December 2016; Accepted 19 December 2016 0364-5916/ © 2016 Published by Elsevier Ltd.

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Fig. 1. Binary phase diagrams constituting the Ge-Mn-Ti ternary system [15,19,27].

3. Results

atmosphere with titanium as getter material placed in the arc chamber. To ensure a good homogenization, all samples were turned over before each melting and re-melted at least 3 times. The weight losses of the so obtained as-cast button shaped alloys did not exceed 1%. Subsequently, majority of samples were sealed in evacuated quartz capsules and then heat-treated at 973 K for 90 days, 1073 K for 60 days and 1173 K for 40 days. After annealing, alloys were taken out quickly and quenched into water. These samples were ground on abrasive paper, polished with diamond paste and cleaned with alcohol in a standard method. Constituent phases of samples were investigated by electron probe microanalysis (EPMA) (JXA-8800R, JEOL, Japan) equipped with OXFORD INCA 500 wavelength dispersive X-ray spectrometer (WDS). Standard deviations of the measured concentration are ± 0.6 at%. The total mass percent of Ge, Mn and Ti in each phase is in the range of 97–103%, so the effect of reactions between samples and silica capsules could be neglected. Different spots in each sample were examined by EPMA and the data corresponding to a same phase in one sample were averaged as the final phase composition. X-ray diffraction (XRD) was also performed to most of the samples using a Cu Kα radiation on a Rigaku D-max/2550 VB + X-ray diffractometer at 40 kV and 250 mA in continuous mode with a step size of 0.02° at a speed of 8°/min. Highquality powder XRD patterns of two samples within the Ge5Ti6 ternary solid solution, Ge5(Mn0.30Ti0.70)6 and Ge5(Mn0.67Ti0.33)6, were collected at room temperature using a Rigaku D-max/2550 VB + X-ray diffractometer (with Cu Kα radiation) in FT-mode. The scan (2θ) range was from 5° to 100° with a step size of 0.02° and a count time of 2 s per step.

3.1. Phase equilibria at 973 K Phase equilibria of the Ge-Mn-Ti ternary system at 973 K were studied covering almost entire composition range. All samples present a three-phase microstructure or two-phase microstructure and no more than three phases coexisted in annealed alloys, suggesting that a full equilibrium has been reached or nearly reached for the annealed Ge-Mn-Ti alloys at 973 K. The constituent phases in annealed alloys at 973 K are summarized in Table 2. Fig. 2 illustrates the constituent phases in A3 alloy. As seen from Fig. 2a, dark (γMn), gray GeMn3 and white GeMnTi coexist, implying this alloy locates in the three-phase area (γMn) + GeMn3 + GeMnTi. This is confirmed by X-ray diffraction (Fig. 2b). Microstructure of alloy A14 and A15 were respectively presented in Fig. 3a and b. With EPMA-WDS analysis, it is seen that alloy A14 consists of (αTi), (βTi) and GeTi3, while alloy A15 consists of (βTi), GeTi3 and Ge3Ti5, in agreement with its XRD pattern (Fig. 4a). So, it is concluded that these two alloys at 973 K locate in three phase region of (αTi) +(βTi) + GeTi3 and (βTi) + GeTi3 + Ge3Ti5, respectively. This indicates that phase GeTi3 is stable at 973 K, similar to the case in the Ge-Ni-Ti system [29]. As a supplement, Fig. 4b represents the typical XRD pattern of alloy A16 turning out to be in a two-phase region (Ge) + Ge2MnTi, and it is also confirmed by EPMA-WDS as listed in Table 2. Based on experimental results, the isothermal section of the

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Table 1 Crystallographic data of solid phases in the Ge-Mn-Ti system. System

Phase

Prototype

Pearson symbol

Lattice parameters (nm)

Refs.

a

b

c

Ge Mn

Diamond_A4, (Ge)a,b,c (αMn)a,b,c (βMn)a,b,c (γMn)a,b,c (δMn)

C αMn βMn Cu W

cF8 cI58 cP20 cF4 cI2

0.56512 0.89126 0.63152 0.3860 0.3080

– – – – –

– – – – –

[30] [24] [24] [24] [24]

Ti

Hcp_A3, (αTi)a,b Bcc_A2, (βTi)b,c

Mg W

hp2 cI2

0.29503 0.33112

– –

0.46810 –

[30] [30]

Mn-Ti

αMnTia,b,c βMnTic Mn2Tia,b,c Mn3Ti Mn4Ti

FeCr βMnTi Zn2Mg Mn3Ti Co5Mo3Cr2

tP30 tP30 hP12 O** hR53

0.8880 0.8190 0.48333 0.4812 0.11003

– – – – –

0.4542 0.12810 0.79384 0.7895 0.19446

[30] [32] [30] [13] [33]

Ge-Mn

GeMn2c GeMn3a,b,c Ge2Mn5a,b,c Ge3Mn5a,b,c Ge8Mn11a,b

InNi2 InNi3 Ge2Mn5 Si3Mn5 Ge8Mn11

hP6 hP8 hP42 hP16 oP76

0.4171 0.5347 0.7198 0.7184 1.3201

– – – – 1.5878

0.5278 0.4316 1.3076 0.5053 0.5087

[30] [30] [30] [34] [35]

Ge-Ti

GeTi3a Ge3Ti5a,b,c Ge4Ti5a,b,c Ge5Ti6a,b,c Ge2Tia,b,c

PNi3 Si3Mn5 Ge4Sm5 Si5V6 Si2Ti

tI32 hP16 oP36 oI44 oF24

1.0290 0.7537 0.66380 1.6915 0.8588

– – 1.28522 0.7954 0.5032

0.5140 0.5223 0.67698 0.5233 0.8862

[30] [30] [27] [30] [30]

Ge-Mn-Ti

GeMnTia,b,c Ge2MnTia,b GeMnTi2

SiFeTi Si2CrZr TiCuHg2

oI36 oP48 cF16

0.72147 0.9877 0.6076

1.11494 0.8959 –

0.64946 0.7948 –

[30] [30] [36]

a b c

Phase stable at 973 K. Phase stable at 1073 K. Phase stable at 1173 K.

+ Ge5Ti6 + Ge8Mn11, (Ge) + Ge5Ti6 + Ge2MnTi, Ge5Ti6 + Ge2MnTi + Ge2Ti, and Ge3Ti5 + GeMnTi + Ge5Ti6, were not measured directly, they could be reasonably predicted according to the adjacent twophase regions.

Ge-Mn-Ti ternary system at 973 K is constructed as illustrated in Fig. 5. And the dark gray phase fields are apparently the measured three-phase equilibria while the bright gray ones are the tentative three-phase fields. Bold dotted lines are used to represent Ge3Mn5 and Ge8Mn11 phases considering that only a few measured compositions are available to well reflect their composition ranges. As seen in Fig. 5, considerable solubilities appear in Mn2Ti, Ge5Ti6 and Ge3Mn5. Although some relevant three-phase regions, e.g. (αMn) +(βMn) +(γMn), (αMn) + Mn2Ti + GeMnTi, (αMn) +(γMn) + GeMnTi, (Ge)

3.2. Phase equilibria at 1073 K 22 alloys were employed for determining isothermal section of the Ge-Mn-Ti ternary system at 1073 K. Detected equilibrium phases and

Table 2 Constituent phases and their compositions in the Ge-Mn-Ti alloys annealed at 973 K. Alloys’ number & composition (at%)

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16

Ge5Mn75Ti20 Ge15Mn70Ti15 Ge25Mn65Ti10 Ge30Mn65Ti5 Ge5Mn50Ti45 Ge40Mn35Ti25 Ge60Mn36Ti4 Ge46Mn22Ti32 Ge10Mn20Ti70 Ge60Mn15Ti25 Ge35Mn10Ti55 Ge40Mn10Ti50 Ge50Mn10Ti40 Ge2Mn5Ti93 Ge20Mn5Ti75 Ge60Mn20Ti20

Phase equilibria

Phase composition (at%)

Phase 1/Phase 2/Phase 3

Phase 1

(αMn)/Mn2Ti (αMn)/GeMnTi (γMn)/GeMn3/GeMnTi Ge2Mn5/Ge3Mn5 αMnTi/Mn2Ti/Ge3Ti5 Ge5Ti6/GeMnTi (Ge)/Ge8Mn11 Ge5Ti6/Ge2MnTi (βTi)/αMnTi/Ge3Ti5 (Ge)/Ge2Ti/Ge2MnTi Mn2Ti/Ge3Ti5/GeMnTi Ge3Ti5/Ge5Ti6 Ge5Ti6/Ge2Ti (αTi)/(βTi)/GeTi3 (βTi)/GeTi3/Ge3Ti5 (Ge)/Ge2MnTi

Phase 2

Phase 3

Ge

Mn

Ti

Ge

Mn

Ti

Ge

Mn

Ti

0.6 3.8 13.8 26.0 2.0 40.7 99.2 44.6 1.0 99.2 15.8 39.8 44.8 1.2 1.3 99.4

85.1 91.0 85.7 73.7 49.0 32.2 0.8 23.6 17.9 0.5 55.2 3.6 13.8 0.5 11.3 0.4

14.3 5.2 0.5 0.3 49.0 27.1 0.0 31.8 81.1 0.3 29.0 56.6 41.4 98.3 87.4 0.2

2.6 26.4 23.0 30.9 6.0 32.8 42.2 49.0 1.1 66.2 37.1 44.5 65.7 0.7 23.6 49.7

63.8 43.0 76.5 57.7 57.0 34.7 52.6 26.5 47.7 0.5 3.5 11.0 0.3 6.2 0.1 25.4

33.6 30.6 0.5 11.4 37.0 32.5 5.2 24.5 51.2 33.3 59.4 44.5 34.0 93.1 76.3 24.9

– – 30.7 – 31.6 – – – 34.0 50.0 32.5 – – 22.9 34.8 –

– – 38.1 – 4.6 – – – 2.2 25.3 30.9 – – 0.1 0.7 –

– – 31.2 – 63.8 – – – 63.8 24.7 36.6 – – 77.0 64.5 –

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Fig. 2. Alloy A3 annealed at 973 K for 90 days: (a) backscattered electron image (BSE); (b) XRD pattern.

Fig. 3. Backscattered electron images (BSE) of ternary alloys annealed at 973 K for 90 days: (a) alloy A14; (b) alloy A15.

Fig. 4. X-ray diffraction patterns (XRD) of ternary alloys annealed at 973 K for 90 days: (a) alloy A15; (b) alloy A16.

structure, which turns out to be (Ge) + Ge8Mn11 derived from EPMA. It is known from Ge-Mn binary phase diagram [19] that a small liquid region appears at 1073 K, from which these eutectic structures are likely to form during rapid cooling. During subsequent cooling after annealing, the primary Ge8Mn11 forms from Liquid in alloy B7, followed by formation of the eutectic structure through the reaction Liquid → (Ge) + Ge8Mn11. Similarly, solidification path of liquid in B11

corresponding constituents in different annealed samples are listed in Table 3. BSE image of alloy B10 annealed at 1073 K is illustrated in Fig. 6a, which consists of three phases, i.e. dark (βTi), gray αMnTi and white Ge3Ti5, suggesting it locates in the three-phase area (βTi) +αMnTi + Ge3Ti5, in agreement with XRD pattern shown in Fig. 6b. Apparently, B7 and B11 alloys (Fig. 7) possess typical eutectic 142

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after annealing is: Liquid → (Ge) and Liquid → (Ge) + Ge8Mn11. To summarize, actual phase equilibria in B7 (Fig. 7a) and B11 (Fig. 7b) alloys at 1073 K should be Ge8Mn11 + Liquid and (Ge) + Ge5Ti6 + Liquid, respectively. In addition, Fig. 8a presents the BSE image of alloy B15, where only dark (βTi) and white Ge3Ti5 were detected, agreeing with the XRD pattern (Fig. 8b). The gray GeTi3 ever occurring at 973 K in A15 of the same nominal composition disappeared in B15 alloy. This phenomenon makes it clear that GeTi3 is really unstable at 1073 K, in consistence with former report in Ge-Ni-Ti system [29]. According to EPMA and XRD results as listed in Table 3, the isothermal section at 1073 K is established (see Fig. 9). It is evident that eight three-phase regions were completely determined, including (γMn) + GeMn3 + GeMnTi, αMnTi + Mn2Ti + Ge3Ti5, Ge5Ti6 + GeMnTi + Ge3Mn5, Mn2Ti + Ge3Ti5 + GeMnTi, (βTi) +αMnTi + Ge3Ti5, (Ge) + Ge5Ti6 + Liquid, Ge3Ti5 + GeMnTi + Ge5Ti6, and (Ge) + Ge2Ti + Ge2MnTi. 3.3. Phase equilibria at 1173 K Fig. 5. Isothermal section of the Ge-Mn-Ti ternary system at 973 K.

In order to determine the isothermal section of the Ge-Mn-Ti ternary system at 1173 K, more than 25 alloys were prepared and

Table 3 Constituent phases and their compositions in the Ge-Mn-Ti alloys annealed at 1073 K. Alloys’ number & composition (at%)

B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15

Ge5Mn75Ti20 Ge15Mn70Ti15 Ge25Mn65Ti10 Ge30Mn65Ti5 Ge5Mn50Ti45 Ge35Mn50Ti15 Ge45Mn50Ti5 Ge20Mn35Ti45 Ge30Mn35Ti35 Ge25Mn10Ti65 Ge50Mn35Ti15 Ge40Mn20Ti40 Ge60Mn15Ti25 Ge50Mn10Ti40 Ge20Mn5Ti75

Phase equilibria

Phase composition (at%)

Phase 1/Phase 2/Phase 3

Phase 1

(αMn)/Mn2Ti (αMn)/GeMnTi (γMn)/GeMn3/GeMnTi Ge2Mn5/Ge3Mn5 αMnTi/Mn2Ti/Ge3Ti5 Ge5Ti6/GeMnTi/Ge3Mn5 Ge8Mn11/Liquid Mn2Ti/Ge3Ti5 Mn2Ti/Ge3Ti5/GeMnTi (βTi)/αMnTi/Ge3Ti5 (Ge)/Ge5Ti6/Liquid Ge3Ti5/GeMnTi/Ge5Ti6 (Ge)/Ge2Ti/Ge2MnTi Ge5Ti6/Ge2Ti (βTi)/Ge3Ti5

Phase 2

Phase 3

Ge

Mn

Ti

Ge

Mn

Ti

Ge

Mn

Ti

1.5 8.6 13.3 27.6 1.8 38.8 41.0 10.2 14.8 1.3 98.0 37.8 98.2 45.4 1.1

88.8 85.5 85.5 71.8 44.7 36.2 51.1 56.8 54.3 21.0 1.8 6.9 0.8 10.1 10.7

9.7 5.9 1.2 0.6 53.5 25.0 7.9 33.0 30.9 77.7 0.2 55.3 1.0 44.5 88.2

8.7 30.7 23.3 32.5 2.8 32.0 – 35.0 36.0 0.9 44.6 33.0 66.9 65.0 35.7

62.1 38.9 72.9 57.4 55.8 44.5 – 3.0 6.0 45.0 36.7 33.8 1.6 0.2 0.4

29.2 30.4 3.8 10.1 41.4 23.5 – 62.0 58.0 54.1 18.7 33.2 31.5 34.8 63.9

– – 35.0 – 30.5 35.4 – – 32.5 35.6 – 43.4 51.7 – –

– – 25.6 – 8.1 56.6 – – 34.2 1.0 – 17.6 20.9 – –

– – 39.4 – 61.4 8.0 – – 33.3 63.4 – 39.0 27.4 – –

Fig. 6. Alloy B10 annealed at 1073 K for 60 days: (a) backscattered electron image (BSE); (b) XRD pattern.

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Fig. 7. Backscattered electron images (BSE) of ternary alloys annealed at 1073 K for 60 days: (a) alloy B7; (b) alloy B11.

Fig. 8. Alloy B15 annealed at 1073 K for 60 days: (a) backscattered electron image (BSE); (b) XRD pattern.

1173 K. In the C4 alloy, two-phase (αMn) +(βMn) microstructure was observed (Fig. 11a). And gray (αMn), dark (γMn) and white GeMnTi were detected in alloy C5 (Fig. 11b), in agreement with phase relationships in the Mn-rich portion of Ge-Mn-Ti at 1173 K [31]. Phase equilibrium of (βTi) +αMnTi + Ge3Ti5 occurs in C11 alloy (see Fig. 11c). As seen from Fig. 11d, it is known C13 locates in the three-phase area Ge5Ti6 + Ge2Ti + Liquid. Accordingly, the isothermal section at 1173 K of the Ge-Mn-Ti system is constructed in Fig. 12. Clearly, the liquid region at 1173 K in the Ge-Mn binary system is larger than that at 1073 K [19], resulting in change of phase equilibria in the Ge-rich corner. 17 three-phase regions and 34 two-phase regions were identified. Among which, (αMn) +(βMn) +(γMn), (αMn) + Mn2Ti + GeMnTi, (γMn) + GeMn3 + GeMnTi, Ge3Mn5 + Ge5Ti6 + GeMnTi, Ge3Ti5 + GeMnTi + Ge5Ti6, (Ge) + Ge2Ti + Liquid, were reasonably deduced in light of their adjacent two-phase regions. 4. Discussion 4.1. Solubility of Mn in Ge5Ti6

Fig. 9. Isothermal section of the Ge-Mn-Ti ternary system at 1073 K.

analyzed. Phases in equilibrium of some representative samples are summarized in Table 4. The microstructure of alloy C3 in BSE is shown in Fig. 10a. By employing EPMA-WDS, it is evident that alloy C3 contained 3 phases, i.e. dark βMnTi, gray Mn2Ti and white Ge3Ti5, consistent with result of XRD shown in Fig. 10b. Fig. 11 illustrates the BSE images of other samples annealed at

In order to demonstrate huge solubility of Mn in Ge5Ti6 intermetallic phase, 2 additional alloys C17 (Ge45.4Mn16.4Ti38.2) and C18 (Ge44.8Mn34.5Ti20.7) of solid solution Ge5(MnxTi1-x)6 were successfully synthesized. And their high-quality powder XRD patterns were also obtained which turn out to be similar to that of prototype Ge5Ti6 except that the peak position moving towards right as content of Mn increased. 144

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Table 4 Constituent phases and their compositions in the Ge-Mn-Ti alloys annealed at 1173 K. Alloys’ number & composition (at%)

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18

Ge5Mn75Ti20 Ge25Mn65Ti10 Ge5Mn50Ti45 Ge7Mn90Ti3 Ge20Mn60Ti20 Ge15Mn50Ti35 Ge45Mn50Ti5 Ge40Mn35Ti25 Ge50Mn35Ti15 Ge55Mn25Ti20 Ge10Mn20Ti70 Ge40Mn20Ti40 Ge60Mn15Ti25 Ge35Mn10Ti55 Ge55Mn5Ti40 Ge20Mn5Ti75 Ge45.4Mn16.4Ti38.2 Ge44.8Mn34.5Ti20.7

Phase equilibria

Phase composition (at%)

Phase 1/Phase 2/Phase 3

Phase 1

(αMn)/Mn2Ti GeMn3/GeMnTi βMnTi/Mn2Ti/Ge3Ti5 (αMn)/(βMn) (αMn)/(γMn)/GeMnTi Mn2Ti/Ge3Ti5 Ge3Mn5/Ge5Ti6/Liquid Ge5Ti6/GeMnTi Ge5Ti6/Liquid Ge5Ti6/Liquid (βTi)/αMnTi/Ge3Ti5 Ge3Ti5/Ge5Ti6 Ge5Ti6/Ge2Ti/Liquid Mn2Ti/Ge3Ti5/GeMnTi Ge5Ti6/Ge2Ti (βTi)/Ge3Ti5 Ge5(Mn0.30Ti0.70)6 Ge5(Mn0.67Ti0.33)6

Phase 2

Phase 3

Ge

Mn

Ti

Ge

Mn

Ti

Ge

Mn

Ti

1.8 23.9 1.4 6.1 9.0 12.0 37.6 41.5 42.5 44.2 1.5 37.9 44.4 15.3 44.2 2.4 45.0 43.9

87.9 72.0 45.8 87.5 84.0 56.0 56.5 36.2 38.5 29.2 23.1 14.0 20.6 52.9 5.4 15.4 18.6 31.7

10.3 4.1 52.8 6.4 7.0 32.0 5.9 22.3 19.0 26.6 75.4 48.1 35.0 31.8 50.4 82.2 36.4 24.4

8.2 32.6 0.6 4.0 13.1 35.2 41.2 32.7 – – 0.8 41.7 66.1 36.4 66.0 36.6 – –

63.4 38.5 57.6 94.0 84.8 4.3 50.7 40.9 – – 48.2 20.8 0.3 2.7 0.2 0.6 – –

28.4 28.9 41.8 2.0 2.1 60.5 8.1 26.4 – – 51.0 37.5 33.6 60.9 33.8 62.8 – –

– – 32.3 – 32.8 – – – – – 34.4 – – 33.2 – – – –

– – 3.1 – 34.8 – – – – – 2.3 – – 31.5 – – – –

– – 64.6 – 32.4 – – – – – 63.3 – – 35.3 – – – –

Fig. 10. Alloy C3 annealed at 1173 K for 40 days: (a) backscattered electron image (BSE); (b) XRD pattern.

compound of Ge5(MnxTi1-x)6. Further considering atom radius r(Ge) < r(Mn) < r(Ti), since the replacement of small Mn atoms for large Ti atoms, the lattice parameter is also supposed to decrease with increase of Mn content. The final results of the Rietveld refinement also prove this conclusion, as shown in Table 5.

Taking the structure of Ge5Ti6 as the preliminary crystal structure model, we refined the crystal structure of Ge5(MnxTi1-x)6 (x=0.30, 0.67) compounds from the XRD data by the Rietveld refinement method using the program DBWS9807 [37,38]. Table 5 is the list of some detail information of Rietveld refinement and crystal data of Ge5(MnxTi1-x)6 solid solution. The minor impurities Ge3Ti5 (when x=0.30) or Ge8Mn11 (when x=0.67) were refined. And the percentages of impurities from the two-phase Rietveld refinements in the samples are 10.02 at% (Ge3Ti5) and 14.53 at% (Ge8Mn11), respectively. The actual composition of C18 may slightly deviate toward two phase region of Ge5Ti6 + Liquid, and the impurity of Ge8Mn11 was introduced from the subsequent solidification process after annealing at 1173 K. Fig. 13 shows the observed and calculated powder XRD patterns of C17 (Ge5(Mn0.30Ti0.70)6) and C18 (Ge5(Mn0.67Ti0.33)6) compound along with their residuals. And Table 6 is the list of positional parameters and final refined atomic occupancies, which were obtained by Rietveld refinement, in the crystal structure of Ge5(MnxTi1-x)6 solid solution. It is concluded that Mn partially replace Ti3 when x=0.30. As for x=0.67, Mn can completely replace Ti2 and partially replace Ti1 and Ti3 in the

4.2. Comparison of phase relations at 973 K, 1073 K and 1173 K Concerning EPMA and XRD results of samples at 973 K, 1073 K and 1173 K, GeMnTi2 mentioned in literature [36] was not found. Furthermore, as shown in Fig. 9, the composition of GeMnTi2 (marked by ③) exactly falls on a tie-line of Mn2Ti and Ge3Ti5 (constituent phases of B8). Therefore, in light of lever rule, GeMnTi2 can not exist stably at 1073 K. Similar case also happens at 973 K and 1173 K. That is to say, the ternary compound GeMnTi2 does not exist stably at the experimental temperatures. A brief comparison of phase relations at 973 K, 1073 K and 1173 K is carried out in this part. As seen in Figs. 5 and 9, GeTi3 is stable at 973 K while disappear at 1073 K. This leads to a change of phase fields, i.e. 2 145

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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 139–149

Fig. 11. Backscattered electron images (BSE) of ternary alloys annealed at 1173 K for 40 days: (a) alloy C4; (b) alloy C5; (c) alloy C11; (d) alloy C13.

be manifested. Firstly, due to the peritectoid reaction (βTi) + Ge3Ti5 → (αTi) at 1167 K, the three-phase region (αTi) +(βTi) + Ge3Ti5 at 1073 K no longer appear at 1173 K. Secondly, there may be a transitional invariant reaction between 1073 K and 1173 K, Liquid + Ge3Mn5 → Ge5Ti6 + Ge8Mn11, which leads to 2 three-phase regions Ge3Mn5 + Ge8Mn11 + Ge5Ti6 and Ge5Ti6 + Ge8Mn11 + Liquid at 1073 K change into three-phase region Ge3Mn5 + Ge5Ti6 + Liquid at 1173 K. Thirdly, it is interesting that Ge2MnTi phase exists at 1073 K and disappears at 1173 K. According to the lever rule, a peritectoid type invariant reaction (Ge) + Ge5Ti6 + Ge2Ti → Ge2MnTi is proposed here. This reaction can be reproduced with thermodynamic assessment as shown in Fig. 14. The preliminary thermodynamic data of the related phases in Ge-rich corner are summarized in Appendix A. In addition, Ge2MnTi phase was not detected by EPMA in some related as-cast alloys, e.g. Ge41Mn27Ti32 and Ge60Mn15Ti25 (presented in Appendix B), with relevant constituents listed in Appendix C, suggesting Ge2MnTi be formed through a solid-state reaction. 5. Conclusion Phase equilibria of the ternary Ge-Mn-Ti system at 973 K, 1073 K and 1173 K have been experimentally determined. The ternary GeMnTi phase stably exists at 973 K, 1073 K and 1173 K, the Ge2MnTi ternary compound is found at 973 K and 1073 K but not at 1173 K. The GeMnTi2 phase mentioned in literature [36] is unstable at the experimental temperatures. As for binary intermetallics, Ge can substitute for about 15 at% Mn in Mn2Ti. Additionally, typical Rietveld refinement results of Ge5(Mn0.30Ti0.70)6 and Ge5(Mn0.67Ti0.33)6 confirm the substitution of Ti by Mn atoms in Ge5(MnxTi1-x)6 solid solution.

Fig. 12. Isothermal section of the Ge-Mn-Ti ternary system at 1173 K (stars in blue and red color corresponding to C17 and C18 alloys respectively). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

three-phase regions (αTi) +(βTi) + GeTi3 and (βTi) + GeTi3 + Ge3Ti5 at 973 K change into three-phase region (αTi) +(βTi) + Ge3Ti5 at 1073 K, because of the peritectoid reaction (αTi) + Ge3Ti5 → GeTi3 [29]. When Fig. 9 is compared with Fig. 12, three obvious differences can 146

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Table 5 Details of Rietveld refinement and crystal data for Ge5(MnxTi1-x)6 (x=0, 0.30, 0.67). Formula

x=0 Ge5Ti6[30]

x=0.30 Ge5 (Mn0.30Ti0.70)6

x=0.67 Ge5 (Mn0.67Ti0.33)6

Sample

Single-crystal

Radiation type Refined profile range (°2θ) Step size (°2θ) Symmetry Space group Z Impurities (at%) Rp Rwp RF RB a (nm) b (nm) c (nm) Volume (nm3) Caculated density (g/cm−3)

Cu Kα –

Multi-crystal powder Cu Kα 5–100

Multi-crystal powder Cu Kα 5–100

– Orthorhombic Ibam (No.72) 4 – – – – – 1.6915 0.7954 0.5233 0.70406 6.14

0.020 Orthorhombic Ibam (No.72) 4 Ge3Ti5 (10.02%) 6.63 9.27 2.95 4.57 1.66113(2) 0.786852(8) 0.515612(5) 0.673936 6.524

0.020 Orthorhombic Ibam (No.72) 4 Ge8Mn11 (14.53%) 9.04 12.24 5.24 7.44 1.624282(4) 0.769850(2) 0.510821(1) 0.638756 7.05

Fig. 13. Observed, calculated and residual powder XRD patterns: (a) Ge5(Mn0.30Ti0.70)6; (b) Ge5(Mn0.67Ti0.33)6.

Fig. 14. Simulation results of the (Ge) + Ge5Ti6 + Ge2Ti → Ge2MnTi process: (a) before invariant reaction (1089 K); (b) on invariant reaction (1088 K); (c) after invariant reaction (1073 K).

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Table 6 Atomic coordinates and isotropic displacement parameters for Ge5(MnxTi1-x)6 (x=0.30, 0.67). x=0.30 (C17)

Atom

Site

x

y

z

Occ

x=0.67 (C18)

Atom

Site

x

y

z

Occ

Ge5(Mn0.30Ti0.70)6

Ti1 Ti2 Mn1 Ti3 Ge1 Ge2 Ge3

8j 8j 8f 8f 8j 8j 4a

0.1423(2) 0.4353(2) 0.3065(2) 0.3065(2) 0.2878(1) 0.0690(1) 0

0.1111(4) 0.2416(4) 0 0 0.2990(2) 0.4065(2) 0

0 0 0.25 0.25 0 0 0.25

1 1 0.84(4) 0.16(4) 1 1 1

Ge5(Mn0.67Ti0.33)6

Mn1 Ti1 Mn2 Mn3 Ti3 Ge1 Ge2 Ge3

8j 8j 8j 8f 8f 8j 8j 4a

0.1432(2) 0.1432(2) 0.4372(2) 0.3053(2) 0.3053(2) 0.2881(1) 0.0682(1) 0

0.1107(4) 0.1107(4) 0.2461(4) 0 0 0.2969(3) 0.4082(3) 0

0 0 0 0.25 0.25 0 0 0.25

0.18(5) 0.82(5) 1 0.83(6) 0.17(6) 1 1 1

Basic Research Development Program of China (Grant No. 2014CB6644002) and the Project of Innovation-driven Plan in Central South University (No. 2015CX004).

Acknowledgment This work was financially supported by the National Natural Science Foundation of China (Grant No. 51171210), the Major State

Appendix A Preliminary thermodynamic data of the related phase in Ge-rich corner.

Phase

Thermodynamic parameters (J/mol)

Ref.

Liquid: (Ge, Mn, Ti, Ge3Mn5)

°L(Mn, Ti)=－36297.4＋23.0723×T L(Mn, Ti)=＋14523.3－8.74355×T °L(Ge, Mn)=－9918－7.46×T °L(Ge, Ge3Mn5)=＋24858－19.82×T °L(Mn, Ge3Mn5)=－32870＋30.53×T 1 L(Mn, Ge3Mn5)=－21877＋21.87×T °L(Ge, Ti)=－211359＋3.34×T 1 L(Ge, Ti)=＋43026－11.77×T 2 L(Ge, Ti)=＋43031

[15] [15] [19] [19] [19] [19] [26] [26] [26] [26]

1

Ge2Ti: (Ti)1(Ge)2 Ge5Ti6: (Mn, Ti)6(Ge)5

diam G(Ti: Ge)=－163400＋GTihcp ＋2×GGe G(Ti: Ge)=－1094342＋1673.39×T－286.83×T×ln(T)－0.008314×T2＋1495482×T−1 diam cbcc ＋5×GGe G(Mn: Ge)=－172342＋6×GMn °L(Mn, Ti: Ge)=－110342＋9×T

Ge2MnTi: (Mn)1(Ti)1(Ge)2

diam cbcc G(Mn: Ti:Ge)=－215120＋12×T＋GMn ＋GTihcp ＋2×GGe

Appendix B Backscattered electron images (BSE) of as-cast alloys in nominal compositions of: (a) Ge41Mn27Ti32; (b) Ge60Mn15Ti25.

.

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[26] This work This work This work

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Appendix C Constituent phases and their compositions in two as-cast alloys, i.e. Ge41Mn27Ti32 and Ge60Mn15Ti25.

Nominal composition (at%)

Ge41Mn27Ti32

Phase

Ge3Ti5 Ge5Ti6 Ge8Mn11 (Ge)

Phase composition (at%) Ge

Mn

Ti

38.5 45.2 42.0 92.7

6.9 32.6 57.9 6.9

54.6 22.2 0.1 0.4

Nominal composition (at%)

Ge60Mn15Ti25

Phase

Ge3Ti5 Ge5Ti6 Ge8Mn11 (Ge)

Phase composition (at%) Ge

Mn

Ti

37.7 44.9 46.1 98.5

4.2 5.6 53.2 1.2

58.1 49.5 0.7 0.3

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