Analysis on Phase Stability and Mechanical Property of Newly-discovered Ternary Layered Boride Cr4AlB4

doi:10.15541/jim20190160

Abstract

Abstract:

As newly-discovered member of the MAB phases, Cr₄AlB₄ has much potential for high-temperature structural applications due to possible formation of a protective oxide scale. By use of “linear optimization procedure” and theoretical model of “bond stiffness” based on first-principle calculations, the phase stability and mechanical behavior of Cr₄AlB₄ were investigated. No imaginary frequencies in phonon dispersion indicate the intrinsic stability. The lower energy as compared with the set of other competing phases also shows the thermodynamic stability. Based on the quantificationally calculated bond stiffness by use of the model of “bond stiffness”, strong covalent bonding is present between Cr and B atoms as well as B and B atoms, while the Cr-Al (625 GPa) and B-Al (574 GPa) bond is relatively weak. It follows that Cr₄AlB₄ can be described as layered structure of strong covalently bonded Cr-B blocks interleaved by Al atomic planes where the bonding is relatively weak, similar to the well-known MAX phases, which demonstrates the similar damage tolerance and fracture toughness of Cr₄AlB₄ with the MAX phases.

Key words: MAB phases, density functional theory, phase stability, mechanical property

CLC Number:

TQ134

QI Xin-Xin, SONG Guang-Ping, YIN Wei-Long, WANG Ming-Fu, HE Xiao-Dong, ZHENG Yong-Ting, WANG Rong-Guo, BAI Yue-Lei. Analysis on Phase Stability and Mechanical Property of Newly-discovered Ternary Layered Boride Cr₄AlB₄[J]. Journal of Inorganic Materials, 2020, 35(1): 53-60.

Figures/Tables 10

References 35

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			Lattice parameters				Internal coordinates					Density /(g·cm^-3)	DOS at E_f/(States·eV^-1· Unit cell^-1)	Bulk modulus /GPa	Pressure derivative
			a/nm	b/nm	c/nm	V/nm³	y_Cr1	y_Cr2	y_Al	y_B1	y_B2	Density /(g·cm^-3)	DOS at E_f/(States·eV^-1· Unit cell^-1)	Bulk modulus /GPa	Pressure derivative
Cr₄AlB₄	LDA		0.28766	1.8578	0.28867	0.15427	-	-	-	-	-	-	-	-	-
	GGA	PBE	0.29312	1.8923	0.29512	0.16370	-	-	-	-	-	-		-	-
		RPBE	0.29334	1.8963	0.29551	0.16439	0.2926	0.5875	0.5	0.3803	0.6720	5.64	7.031	234.16	4.55
		PW91	0.29197	1.8863	0.29435	0.16212	-	-	-	-	-	-	-	-	-
	Exp^[13]		0.29343	1.8891	0.29733	0.16481	0.2936	0.5859	0.5	0.3839	0.6646	-	-	-	-
CrB	Cal^[27]		0.2924	0.7836	0.2911	0.06670	-	-	-	-	-	6.25	-	-	-

			Lattice parameters				Internal coordinates					Density /(g·cm^-3)	DOS at E_f/(States·eV^-1· Unit cell^-1)	Bulk modulus /GPa	Pressure derivative
			a/nm	b/nm	c/nm	V/nm³	y_Cr1	y_Cr2	y_Al	y_B1	y_B2	Density /(g·cm^-3)	DOS at E_f/(States·eV^-1· Unit cell^-1)	Bulk modulus /GPa	Pressure derivative
Cr₄AlB₄	LDA		0.28766	1.8578	0.28867	0.15427	-	-	-	-	-	-	-	-	-
	GGA	PBE	0.29312	1.8923	0.29512	0.16370	-	-	-	-	-	-		-	-
		RPBE	0.29334	1.8963	0.29551	0.16439	0.2926	0.5875	0.5	0.3803	0.6720	5.64	7.031	234.16	4.55
		PW91	0.29197	1.8863	0.29435	0.16212	-	-	-	-	-	-	-	-	-
	Exp^[13]		0.29343	1.8891	0.29733	0.16481	0.2936	0.5859	0.5	0.3839	0.6646	-	-	-	-
CrB	Cal^[27]		0.2924	0.7836	0.2911	0.06670	-	-	-	-	-	6.25	-	-	-

	Cr₄AlB₄		Cr₂AlB₂		CrB
	d/nm	k/GPa	d/nm^[3]	k/GPa^[26]	d/nm	d/nm^[27]	k/GPa
Cr1-Al	0.2662	625	0.26443	617	-	-	-
Cr1-B1	0.2169	885	0.22014	813	0.21712	0.2158	917
Cr1-B2	0.2180	1190	0.21876	1149	0.2212	0.2200	1123
Cr2-B1	0.2224	1074	-	-	-	-	-
Cr2-B2	0.2187	840	-	-	-	-	-
Cr2-B3	0.2288	826	-	-	-	-	-
B1-B2	0.1771	1123	0.17616	1099	0.17841	0.1722	1149
Al-B1	0.2269	574	0.22765	571	-	-	-

	Cr₄AlB₄		Cr₂AlB₂		CrB
	d/nm	k/GPa	d/nm^[3]	k/GPa^[26]	d/nm	d/nm^[27]	k/GPa
Cr1-Al	0.2662	625	0.26443	617	-	-	-
Cr1-B1	0.2169	885	0.22014	813	0.21712	0.2158	917
Cr1-B2	0.2180	1190	0.21876	1149	0.2212	0.2200	1123
Cr2-B1	0.2224	1074	-	-	-	-	-
Cr2-B2	0.2187	840	-	-	-	-	-
Cr2-B3	0.2288	826	-	-	-	-	-
B1-B2	0.1771	1123	0.17616	1099	0.17841	0.1722	1149
Al-B1	0.2269	574	0.22765	571	-	-	-

Included phases	Compound	Most competing phases	ΔH_comp/(eV·atom^-1)
CrB, CrB₂, CrB₄, Cr₂B, Cr₅B₃, Cr₃B₄, Cr₂B₃, Cr₂Al, Cr₅Al₈, Cr₇Al₄₅, AlB₂, AlB₁₂, Cr₂AlB₂, Cr₃AlB₄, Cr₄AlB₆	Cr₄AlB₄	2CrB+Cr₂AlB₂	-0.2207
	Cr₂AlB₂^[26]	2CrB+Al	-0.0461

Analysis on Phase Stability and Mechanical Property of Newly-discovered Ternary Layered Boride Cr₄AlB₄

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Boder charge/e	Cr1	Cr2	Al	B1	B2
CrB	-0.79	-	-	0.78	-
Cr₂AlB₂^[26]	-0.37	-	-1.50	1.12	-
Cr₄AlB₄	-0.39	-0.76	-1.48	1.15	0.74

Compound	c₁₁	c₁₂	c₁₃	c₂₂	c₂₃	c₃₃	c₄₄	c₅₅	c₆₆	G	B	G/B	E	μ	θ_D/K
Cr₄AlB₄	594	112	126	472	120	467	185	176	231	194	245	0.79	460	0.19	923
Cr₂AlB₂^[26]	505	101	111	410	109	437	158	162	209	174	221	0.79	414	0.19	892
MoAlB^[25]	327	143	150	313	128	384	187	156	166	142	207	0.66	347	0.22	675
CrB	495	165	165	581	147	579	220	220	265	219	289	0.78	525	0.2	963
Cr₂AlC^[23]	396	117	156	-	-	382	173	-	-	146.9	225.8	-	357.7	0.236	774

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