<trans-title xml:lang="en">Predictions of Phase Stability and Properties of S-group Elements Containing MAX Borides</trans-title>

Yuchen ZHANG; Zhiyao LU; Xiaodong HE; Guangping SONG; Chuncheng ZHU; Yongting ZHENG; Yuelei BAI

doi:10.15541/jim20230188

Journal of Inorganic Materials, Volume. 39, Issue 2, 225(2023)

Predictions of Phase Stability and Properties of S-group Elements Containing MAX Borides

Yuchen ZHANG1... Zhiyao LU1, Xiaodong HE1, Guangping SONG1, Chuncheng ZHU2, Yongting ZHENG1 and Yuelei BAI1,* |Show fewer author(s)

Author Affiliations

¹1. National Key Laboratory of Science and Technology on Advanced Composites in Special Environments/Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China

²2. School of Chemistry and Chemical Engineering, Harbin Normal University, Harbin 150025, China

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Figures & Tables(10)

1. Bulk moduli against mean bond stiffness for M₂AB (M = Zr, Hf; A = S, Se, Te)

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2. Temperature dependence of (a) C_P and (b) α_l of M₂AB (M = Zr, Hf; A = S, Se, Te)

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S1. (a) Side and (b) top views of 211 type MAX phase

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S2. Phonon dispersions (left) and density of states (right) of (a) Zr₂SB, (b) Hf₂SB, (c) Zr₂SeB, (d) Hf₂SeB, (e) Zr₂TeB, and (f) Hf₂TeB along the high symmetry directions

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S3. Pressure dependence of normalized bond length d/d₀ of (a) M-A and (b) M-B bonds in M₂AB (M = Zr, Hf; A = S, Se, Te)

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Table 1. M₂AB (M = Zr, Hf; A = S, Se, Te) of which formation enthalpy ΔH_comp<0

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Table 1. M₂AB (M = Zr, Hf; A = S, Se, Te) of which formation enthalpy ΔH_comp<0

Compound	a/Å	c/Å	V/Å³	Most competing phases	ΔH_comp/(eV·atom^-1)
Zr₂SB	3.521	12.302	132.12	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Exp.^[8]	3.500	12.271	130.19	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Hf₂SB	3.484	12.122	127.40	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Exp.^[8]	3.467	12.105	126.01	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Zr₂SeB	3.573	12.733	140.78	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Exp.^[9]	3.644	12.632	145.27	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Hf₂SeB	3.538	12.544	136.01	0.0185Hf₂₃Se₂₅ + 0.5370Hf₂Se + 0.5HfB₂	-0.0838
Exp.^[9]	3.523	12.478	134.11	0.0185Hf₂₃Se₂₅ + 0.5370Hf₂Se + 0.5HfB₂	-0.0838
Hf₂TeB	3.619	13.239	150.14	0.5Hf₃Te₂ + 0.5HfB₂	-0.0100
Exp.^[10]	3.605	13.127	147.72	0.5Hf₃Te₂ + 0.5HfB₂	-0.0100

Table 1. Formation enthalpy ΔH_comp of M₂AB, M₃AB₂ and M₄AB₃ (M = Zr, Hf; A = S, Se, Te)

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Table 1. Formation enthalpy ΔH_comp of M₂AB, M₃AB₂ and M₄AB₃ (M = Zr, Hf; A = S, Se, Te)

Compound	Included phase	a/Å	c/Å	V/Å³	Most competing phases	ΔH_comp/(eV·atom^-1)
Zr₂SB	Zr, S, B, Zr₂S, Zr₃S₄, Zr₉S₂, ZrS, ZrS₂, ZrS₃, ZrB₂, B₂S₃, BS₂	3.521	12.302	132.12	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Exp.^[8]		3.500	12.271	130.19	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Zr₃SB₂					0.0833Zr₉S₂+ 0.5833ZrB₂ + 0.8333Zr₂SB	0.0919
Zr₄SB₃					0.1667Zr₉S₂+ 1.1667ZrB₂ + 0.6667Zr₂SB	0.1588
Hf₂SB	Hf, S, B, Hf₂S, HfS, HfS₂, HfS₃, HfB₂, B₂S₃, BS₂	3.484	12.122	127.40	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Exp.^[8]		3.467	12.105	126.01	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Hf₃SB₂					0.5Hf + 0.5HfB₂+ Hf₂SB	0.0807
Hf₄SB₃					Hf + HfB₂+ Hf₂SB	0.1422
Zr₂SeB	Zr, Se, B, Zr₂Se, Zr₂Se₃, ZrSe, ZrSe₂, ZrSe₃, ZrB₂, BSe₂	3.573	12.733	140.78	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Exp.^[9]		3.644	12.632	145.27	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Zr₃SeB₂					0.5Zr + 0.5ZrB₂+ Zr₂SeB	0.1649
Zr₄SeB₃					Zr + ZrB₂+ Zr₂SeB	0.1559
Hf₂SeB	Hf, Se, B, Hf₂Se, Hf₂Se₃, HfSe₂, HfSe₃, Hf₂₃Se₂₅, HfB₂, BSe₂	3.538	12.544	136.01	0.0185Hf₂₃Se₂₅+0.5370Hf₂Se + 0.5HfB₂	-0.0838
Exp.^[9]		3.523	12.478	134.11	0.0185Hf₂₃Se₂₅+0.5370Hf₂Se + 0.5HfB₂	-0.0838
Hf₃SeB₂					0.5Hf + 0.5HfB₂+ Hf₂SeB	0.0836
Hf₄SeB₃					Hf + HfB₂+ Hf₂SeB	0.1457
Zr₂TeB	Zr, Te, B, Zr₂Te₃, Zr₃Te, Zr₅Te₄, ZrTe, ZrTe₂, ZrTe₃, ZrTe₅, ZrB₂	3.650	13.415	154.77	0.2143Zr₅Te₄+ 0.1429Zr₃Te + 0.5ZrB₂	0.0305
Zr₃TeB₂					0.1429Zr₅Te₄+ 0.4286Zr₃Te + ZrB₂	0.1321
Zr₄TeB₃					0.0174Zr₅Te₄+ 0.7143Zr₃Te + 1.5ZrB₂	0.1960
Hf₂TeB	Hf, Te, B, Hf₃Te₂,Hf₅Te₄, HfTe₂, HfTe₅, HfB₂	3.619	13.239	150.14	0.5Hf₃Te₂+ 0.5HfB₂	-0.0100
Exp.^[10]		3.605	13.127	147.72	0.5Hf₃Te₂+ 0.5HfB₂	-0.0100
Hf₃TeB₂					0.5Hf + 0.5HfB₂+ Hf₂TeB	0.0994
Hf₄TeB₃					Hf + HfB₂+ Hf₂TeB	0.1613

Table 2. Heat capacity at constant pressure and the average linear thermal expansion coefficient of M₂AB (M = Zr, Hf; A = S, Se, Te) in the temperature range of 300-1300 K

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Table 2. Heat capacity at constant pressure and the average linear thermal expansion coefficient of M₂AB (M = Zr, Hf; A = S, Se, Te) in the temperature range of 300-1300 K

Compound	Curve fitting equation (300-1300 K)	TEC (300-1300 K)/ K^-1
Zr₂SB	C_P= 0.83×10^-2T + 96.9 - 1.28×10⁶T^-2	10.97×10^-6K^-1
Hf₂SB	C_P = 0.74×10^-2T + 96.6 - 1.25×10⁶T^-2	9.66×10^-6K^-1
Zr₂SeB	C_P = 0.82×10^-2T + 96.7 - 1.06×10⁶T^-2	11.11×10^-6K^-1
Hf₂SeB	C_P = 1.28×10^-2T + 94.4 - 0.89×10⁶T^-2	10.17×10^-6K^-1
Zr₂TeB	C_P = 1.07×10^-2T + 94.7 - 0.84×10⁶T^-2	12.63×10^-6K^-1
Hf₂TeB	C_P = 0.83×10^-2T + 96.1 - 0.87×10⁶T^-2	10.07×10^-6K^-1

Table 2. Second-order elastic constants and engineering elastic moduli of M₂AB (M = Zr, Hf; A = S, Se, Te) and several typical MAX phases

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Table 2. Second-order elastic constants and engineering elastic moduli of M₂AB (M = Zr, Hf; A = S, Se, Te) and several typical MAX phases

Compound	c₁₁/GPa	c₁₂/GPa	c₁₃/GPa	c₃₃/GPa	c₄₄/GPa	G/GPa	B/GPa	E/GPa	μ	G/B	Ref.
Zr₂SB	264	76	91	298	135	108	148	262	0.206	0.730	This work
Hf₂SB	296	74	97	318	147	122	160	292	0.196	0.763	This work
Zr₂SeB	252	64	83	277	125	105	137	250	0.197	0.766	This work
Hf₂SeB	275	66	90	292	134	113	148	270	0.195	0.764	This work
Zr₂TeB	198	67	78	225	104	79	118	194	0.226	0.669	This work
Hf₂TeB	225	61	88	257	119	93	130	225	0.211	0.715	This work
Ti₃SiC₂	366	94	100	352	153	142	187	339	0.192	0.759	[16]
Ti₃GeC₂	357	94	97	333	143	142	182	340	0.196	0.780	[16]
Hf₂InC	309	81	80	273	98	105	152	256	0.21	0.691	[37]
Hf₂SnC	251	71	107	238	101	87	145	218	0.25	0.600	[37]

Table 3. Bond length, bond stiffness and k_min/k_max in M₂AB (M = Zr, Hf; A = S, Se, Te)

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Table 3. Bond length, bond stiffness and k_min/k_max in M₂AB (M = Zr, Hf; A = S, Se, Te)

Compound	M−A bond		M−B bond		k_min/k_max	H_micro/GPa	H_macro/GPa
Compound	d/nm	k/GPa	d/nm	k/GPa	k_min/k_max	H_micro/GPa	H_macro/GPa
Zr₂SB	0.26997	458.93	0.24124	612.75	0.7490	21.29	18.40
Exp.^[8]	0.26844		0.24032			9-12^[12]
Hf₂SB	0.26800	472.37	0.23722	652.32	0.7241	24.74		21.20
Exp.^[8]	0.26643		0.23688
Zr₂SeB	0.28062	442.87	0.24282	560.54	0.7901	21.09		19.30
Exp.^[9]	0.28071		0.24729
Hf₂SeB	0.27869	455.17	0.23899	595.24	0.7647	22.97		20.17
Exp.^[9]	0.27735		0.23789
Zr₂TeB	0.29743	432.53	0.24526	487.09	0.8880	14.45		13.12
Hf₂TeB	0.29604	439.17	0.24156	517.33	0.8489	17.90		16.16

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Yuchen ZHANG, Zhiyao LU, Xiaodong HE, Guangping SONG, Chuncheng ZHU, Yongting ZHENG, Yuelei BAI. Predictions of Phase Stability and Properties of S-group Elements Containing MAX Borides[J]. Journal of Inorganic Materials, 2023, 39(2): 225

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Paper Information

Category:

Received: Apr. 14, 2023

Accepted: --

Published Online: Jul. 8, 2024

The Author Email: BAI Yuelei (baiyl@hit.edu.cn)

DOI:10.15541/jim20230188

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. M2AB (M = Zr, Hf; A = S, Se, Te) of which formation enthalpy ΔHcomp<0

Table 1. M2AB (M = Zr, Hf; A = S, Se, Te) of which formation enthalpy ΔHcomp<0

Table 1. Formation enthalpy ΔHcomp of M2AB, M3AB2 and M4AB3 (M = Zr, Hf; A = S, Se, Te)

Table 1. Formation enthalpy ΔHcomp of M2AB, M3AB2 and M4AB3 (M = Zr, Hf; A = S, Se, Te)

Table 2. Heat capacity at constant pressure and the average linear thermal expansion coefficient of M2AB (M = Zr, Hf; A = S, Se, Te) in the temperature range of 300-1300 K

Table 2. Heat capacity at constant pressure and the average linear thermal expansion coefficient of M2AB (M = Zr, Hf; A = S, Se, Te) in the temperature range of 300-1300 K

Table 2. Second-order elastic constants and engineering elastic moduli of M2AB (M = Zr, Hf; A = S, Se, Te) and several typical MAX phases

Table 2. Second-order elastic constants and engineering elastic moduli of M2AB (M = Zr, Hf; A = S, Se, Te) and several typical MAX phases

Table 3. Bond length, bond stiffness and kmin/kmax in M2AB (M = Zr, Hf; A = S, Se, Te)

Table 3. Bond length, bond stiffness and kmin/kmax in M2AB (M = Zr, Hf; A = S, Se, Te)

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Table 1. M₂AB (M = Zr, Hf; A = S, Se, Te) of which formation enthalpy ΔH_comp<0

Table 1. M₂AB (M = Zr, Hf; A = S, Se, Te) of which formation enthalpy ΔH_comp<0

Table 1. Formation enthalpy ΔH_comp of M₂AB, M₃AB₂ and M₄AB₃ (M = Zr, Hf; A = S, Se, Te)

Table 1. Formation enthalpy ΔH_comp of M₂AB, M₃AB₂ and M₄AB₃ (M = Zr, Hf; A = S, Se, Te)

Table 2. Heat capacity at constant pressure and the average linear thermal expansion coefficient of M₂AB (M = Zr, Hf; A = S, Se, Te) in the temperature range of 300-1300 K

Table 2. Heat capacity at constant pressure and the average linear thermal expansion coefficient of M₂AB (M = Zr, Hf; A = S, Se, Te) in the temperature range of 300-1300 K

Table 2. Second-order elastic constants and engineering elastic moduli of M₂AB (M = Zr, Hf; A = S, Se, Te) and several typical MAX phases

Table 2. Second-order elastic constants and engineering elastic moduli of M₂AB (M = Zr, Hf; A = S, Se, Te) and several typical MAX phases

Table 3. Bond length, bond stiffness and k_min/k_max in M₂AB (M = Zr, Hf; A = S, Se, Te)

Table 3. Bond length, bond stiffness and k_min/k_max in M₂AB (M = Zr, Hf; A = S, Se, Te)