Cr5Si3B and Hf5Si3B: New MAB phases with anisotropic electrical, mechanical properties and damage tolerance

doi:10.1016/j.jmst.2017.12.014

Abstract

Abstract:

Through a combination of electronic structure, chemical bonding and mechanical property investigations, anisotropic electrical and mechanical properties, and damage tolerant ability of MAB phases Cr₅Si₃B and Hf₅Si₃B are predicted. The anisotropic electrical conductivity is due to the anisotropic distribution of Cr in Cr₅Si₃B and Hf in Hf₅Si₃B, which mainly contribute to the electrical conductivity. The anisotropic mechanical properties are underpinned by the anisotropic chemical bonding within the crystal structures of Cr₅Si₃B and Hf₅Si₃B. The high stiffness is determined by the strong covalent-ionic Cr1-B-Cr1 and Cr1-Si bonds in Cr₅Si₃B and the ionic-covalent Hf1-B-Hf1 and Si-B bonds in Hf₅Si₃B; while the low shear deformation resistance is attributed to the presence of metallic Cr-Cr, Hf-Hf and Si-Si bond. Based on the low Pugh’s ratio, Cr₅Si₃B and Hf₅Si₃B are predicted tolerant to damage. The possible cleavage plane is (0001) and the possible slip systems are ＜1 $\bar{1}$00＞|{11 2ˉ0} and ＜11 $\bar{2}$0＞|{0001} for both Cr₅Si₃B and Hf₅Si₃B.

Key words: MAB phases, Cr₅Si₃B and Hf₅Si₃B, First-principles calculations, Mechanical properties, Chemical bonding

Yanchun Zhou, Huimin Xiang, Fu-Zhi Dai, Zhihai Feng. Cr₅Si₃B and Hf₅Si₃B: New MAB phases with anisotropic electrical, mechanical properties and damage tolerance[J]. J. Mater. Sci. Technol., 2018, 34(8): 1441-1448.

Figures/Tables 11

Fig. 1. Crystal structure of Cr5Si3B (a), distribution of BCr16 octahedra viewed along [0001] direction (b), zigzag Cr1BCr1BCr1 bond chains on (1 $\bar{1}$00) plane interleaved by Si layers (c).

Table 1 Experimental and geometry optimized lattice parameters of Cr5Si3B and Hf5Si3B.

Compound	Cr₅Si₃B [38]	Hf₅Si₃B [39]
Space group	P6₃/mcm (No.193)
Z formula units	2
Density (g/cm³)	5.78	11.01
Lattice constants (?)	Experimental
	a = 7.06	a = 7.8557
	c = 4.73	c = 5.5262
	Theoretical
	a = 7.0306	a = 7.9270
	c = 4.7326	c = 5.5212
Atomic positions	Experimental
	B 2b (0, 0, 0)	B 2b (0, 0, 0)
	Si 6g (0.62, 0, 1/4)	Si 6g (0.6108, 0, 1/4)
	Cr1 6g (0.27, 0, 1/4)	Hf1 6g (0.2467, 0, 1/4)
	Cr2 4d (1/3, 2/3, 0)	Hf2 4d (1/3, 2/3, 0)
	Theoretical
	B 2b (0, 0, 0)	B 2b (0, 0, 0)
	Si 6g (0.6004, 0, 1/4)	Si 6g (0.6025, 0, 1/4)
	Cr1 6g (0.2435, 0, 1/4)	Hf1 6g (0.2473, 0, 1/4)
	Cr2 4d (1/3, 2/3, 0)	Hf2 4d (1/3, 2/3, 0)

Table 2 Second order elastic constants cij of single crystalline Cr5Si3B, Hf5Si3B, Cr2AlC and Ti3SiC2 (GPa).

Compound	c₁₁	c₃₃	c₄₄	c₁₂	c₁₃	c₆₆
Cr₅Si₃B	418	346	148	131	142	143
Hf₅Si₃B	332	298	110	102	88	115
Cr₂AlC	385	360	154	94	118	132
Ti₃SiC₂	354	344	165	91	103	131

Table 3 Computed bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s ratio v, anisotropic Young’s modulus Ex, Ez (GPa), and anisotropic Poisson’s ratios vxy, vxz and vzx of Cr5Si3B, Hf5Si3B, Cr2AlC and Ti3SiC2.

Compound	B	G	E	v	E_x	E_z	v_xy	v_xz	v_zx	G/B
Cr₅Si₃B	223	138	343	0.243	344	272	0.203	0.328	0.260	0.619
Hf₅Si₃B	168	112	275	0.227	287	262	0.249	0.222	0.203	0.666
Cr₂AlC	188	143	346	0.210	337	301	0.158	0.279	0.249	0.718
Ti₃SiC₂	183	141	337	0.193	312	296	0.187	0.244	0.232	0.770

Fig. 2. Overall surface contours of Young’s modulus of Cr5Si3B (a) and Hf5Si3B (b), and planar projections of directional dependent Young’s modulus on (0001) and (01 $\bar{1}$0) planes of Cr5Si3B (c) and Hf5Si3B (d).

Fig. 3. Projection of shear modulus on (0001) and (11 $\bar{2}$0) shear planes of Cr5Si3B (a) and Hf5Si3B (b).

Fig. 4. Band structure of Cr5Si3B (a) and Hf5Si3B (b).

Fig. 5. Total density of states (TDOS) and projected density of states (PDOS) of Cr5Si3B (a) and Hf5Si3B (b).

Fig. 6. Electron density difference maps on (1 $\bar{1}$00) plane (a), (0004) plane (b) and (11 $\bar{2}$0) plane (c) of Cr5Si3B.

Fig. 7. Electron density difference maps on (1 $\bar{1}$00) plane (a), (0004) plane (b) and (11 $\bar{2}$0) plane (c) of Hf5Si3B.

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Cr₅Si₃B and Hf₅Si₃B: New MAB phases with anisotropic electrical, mechanical properties and damage tolerance

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