Shear anisotropy: Tuning high temperature metal hexaborides from soft to extremely hard

doi:10.1016/j.jmst.2017.01.022

Abstract

Abstract:

Easy machining into sharp lending edge, nose tip and complex shape components plays a pivotal role in the application of ultrahigh temperature ceramics in hypersonic vehicles, wherein low and controllable hardness is a necessary parameter to ensure the easy machinability. However, the mechanism that driving the hardness of metal hexaborides is not clear. Here, using a combination of the empirical hardness model for polycrystalline materials and density functional theory investigation, the hardness dependence on shear anisotropic factors of high temperature metal hexaborides has been established. It has come to light that through controlling the shear anisotropic factors the hardness of polycrystalline metal hexaborides can be tailored from soft and ductile to extremely hard and brittle, which is underpinned by the degree of chemical bonding anisotropy, i.e., the difference of B-B bond within the B₆ octahedron and that connecting the B₆ octahedra.

Key words: Microhardness, Electronic structure, Elastic constant, Borides, Structural ceramics

Zhou Yanchun, Dai Fuzhi, Xiang Huimin, Liu Bin, Feng Zhihai. Shear anisotropy: Tuning high temperature metal hexaborides from soft to extremely hard[J]. J. Mater. Sci. Technol., 2017, 33(11): 1371-1377.

Figures/Tables 8

References

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Compound	YB₆	LaB₆	YbB₆	CaB₆	SrB₆	BaB₆
Space group	Pm$\overline{3}$m (No.221)
	Lattice constant
a_exp (?)	4.1016	4.1569	4.1479	4.1514	4.1953	4.2618
a_cal (?)	4.1124	4.1646	4.1361	4.1591	4.2015	4.2660
Atomic coordinate
M	(0,0,0)	(0,0,0)	(0,0,0)	(0,0,0)	(0,0,0)	(0,0,0)
B (z,1/2,1/2), z_exp	0.1988	0.1996	0.2012	0.2019	0.2031	0.2047
B (z,1/2,1/2), z_cal	0.1995	0.2008	0.2015	0.2025	0.2036	0.2055
Bond length
(B-B)_inter-Oct,_exp (?)	1.630	1.659	1.6695	1.676	1.704	1.744
(B-B)_{inter-Oct,cal} (?)	1.6409	1.6733	1.6675	1.6845	1.7106	1.7545
(B-B)_{intra-Oct,exp} (?)	1.746	1.766	1.753	1.752	1.762	1.780
(B-B)_{intra-Oct,cal} (?)	1.7479	1.7631	1.7456	1.7497	1.7613	1.7772
Intra B-B and inter B-B bond length difference
Experimental	0.116	0.107	0.084	0.076	0.058	0.036
Theoretical	0.1070	0.0898	0.0781	0.0652	0.0507	0.0227

Compound	YB₆	LaB₆	YbB₆	CaB₆	SrB₆	BaB₆
Space group	Pm$\overline{3}$m (No.221)
	Lattice constant
a_exp (?)	4.1016	4.1569	4.1479	4.1514	4.1953	4.2618
a_cal (?)	4.1124	4.1646	4.1361	4.1591	4.2015	4.2660
Atomic coordinate
M	(0,0,0)	(0,0,0)	(0,0,0)	(0,0,0)	(0,0,0)	(0,0,0)
B (z,1/2,1/2), z_exp	0.1988	0.1996	0.2012	0.2019	0.2031	0.2047
B (z,1/2,1/2), z_cal	0.1995	0.2008	0.2015	0.2025	0.2036	0.2055
Bond length
(B-B)_inter-Oct,_exp (?)	1.630	1.659	1.6695	1.676	1.704	1.744
(B-B)_{inter-Oct,cal} (?)	1.6409	1.6733	1.6675	1.6845	1.7106	1.7545
(B-B)_{intra-Oct,exp} (?)	1.746	1.766	1.753	1.752	1.762	1.780
(B-B)_{intra-Oct,cal} (?)	1.7479	1.7631	1.7456	1.7497	1.7613	1.7772
Intra B-B and inter B-B bond length difference
Experimental	0.116	0.107	0.084	0.076	0.058	0.036
Theoretical	0.1070	0.0898	0.0781	0.0652	0.0507	0.0227

Compound	YB₆	LaB₆	YbB₆	CaB₆	SrB₆	BaB₆
Elastic constant	YB₆	LaB₆	YbB₆	CaB₆	SrB₆	BaB₆
c₁₁ (GPa)	451	457	422	422	406	381
c₄₄ (GPa)	14	48	37	59	77	108
c₁₂ (GPa)	32	27	6	8	12	25
B (GPa)	172	170	144	146	143	144
G (GPa)	58	92	81	100	114	132
E (GPa)	156	234	205	244	270	303
ν	0.348	0.271	0.263	0.221	0.185	0.149
Cauchy pressure c₁₂-c₄₄	18	-21	-31	-51	-65	-83
Pugh's modulus ratio G/B	0.337	0.541	0.562	0.685	0.797	0.917
Shear anisotropic factor A	0.067	0.223	0.177	0.285	0.391	0.607
Vickers hardness H_v	3.03	10.74	10.33	15.99	21.50	28.43

Compound	YB₆	LaB₆	YbB₆	CaB₆	SrB₆	BaB₆
Elastic constant	YB₆	LaB₆	YbB₆	CaB₆	SrB₆	BaB₆
c₁₁ (GPa)	451	457	422	422	406	381
c₄₄ (GPa)	14	48	37	59	77	108
c₁₂ (GPa)	32	27	6	8	12	25
B (GPa)	172	170	144	146	143	144
G (GPa)	58	92	81	100	114	132
E (GPa)	156	234	205	244	270	303
ν	0.348	0.271	0.263	0.221	0.185	0.149
Cauchy pressure c₁₂-c₄₄	18	-21	-31	-51	-65	-83
Pugh's modulus ratio G/B	0.337	0.541	0.562	0.685	0.797	0.917
Shear anisotropic factor A	0.067	0.223	0.177	0.285	0.391	0.607
Vickers hardness H_v	3.03	10.74	10.33	15.99	21.50	28.43

Compound	YB₆	LaB₆	YbB₆	CaB₆	SrB₆	BaB₆
Theoretical predicted microhardness (GPa)
Macroscopic model	3.03	10.74	10.33	15.99	21.50	28.43
Microscopic model				20.46 [38]	20.93 [38]	21.31 [38]
		29.6 [44]		28.8 [44]	27.9 [44]	30.1 [44]
	26.1	25.7	24.6	24.6	23.6	26.0
Experimental measured microhardness (GPa)
Polycrystalline		12.3 [42]	11.4 [43]
Single crystal		31.5 [42]			33 [47]
Single crystal		19.4 [46]		19.0 [46]	18.5 [46]	18.7 [46]