新型三元层状硼化物Cr4AlB4的物相稳定性和力学行为分析

doi:10.15541/jim20190160

无机材料学报 ›› 2020, Vol. 35 ›› Issue (1): 53-60.DOI: 10.15541/jim20190160

所属专题： MAX相和MXene材料；计算材料论文精选(2020)

新型三元层状硼化物Cr₄AlB₄的物相稳定性和力学行为分析

齐欣欣¹,宋广平¹,尹维龙¹,王明福²,赫晓东¹,郑永挺¹,王荣国¹,柏跃磊¹()

^1. 哈尔滨工业大学特种环境复合材料技术国家级重点实验室, 哈尔滨 150080
^2. 北京动力机械研究所, 北京 100074

收稿日期:2019-04-17 修回日期:2019-05-14 出版日期:2020-01-20 网络出版日期:2019-07-23
作者简介:齐欣欣(1995-), 博士研究生. E-mail:16S118138@stu.hit.edu.cn
基金资助:
国家自然科学基金(51972080);黑龙江省自然科学基金重点项目(ZD2017011);中国博士后科学基金(2017T100230)

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

QI Xin-Xin¹,SONG Guang-Ping¹,YIN Wei-Long¹,WANG Ming-Fu²,HE Xiao-Dong¹,ZHENG Yong-Ting¹,WANG Rong-Guo¹,BAI Yue-Lei¹()

^1. National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, China
^2. Beijing Power Machinery Research Institute, Beijing 100074, China

Received:2019-04-17 Revised:2019-05-14 Published:2020-01-20 Online:2019-07-23
About author:QI Xin-Xin(1995-), PhD Candidate. E-mail:16S118138@stu.hit.edu.cn
Supported by:
National Natural Science Foundation of China(51972080);Natural Science Foundation of Heilongjiang Province of China(ZD2017011);China Postdoctoral Science Foundation(2017T100230)

摘要/Abstract

摘要：

Cr₄AlB₄是一种近期发现的三元层状硼化物MAB相陶瓷。该材料可形成具有保护性的氧化膜, 在高温结构材料领域有巨大应用潜力。本工作采用基于第一性原理的“线性优化法”和“键刚度”理论模型分别研究了Cr₄AlB₄的物相稳定性和力学行为。声子谱中没有虚频出现, 表明Cr₄AlB₄具有本征稳定性。而与其它Cr-Al-B系内的竞争相相比, Cr₄AlB₄具有最低的能量, 表明其在热力学上也是稳定的。采用“键刚度”模型对化学键刚度的定量计算显示, Cr₄AlB₄中Cr和B以及B和B原子之间形成了强共价键, 而Cr和Al原子则形成相对较弱的Cr-Al(625 GPa)和 B-Al(574 GPa)键。Cr₄AlB₄可以看成是由强共价键紧密连接在一起的Cr-B结构单元, 被弱Cr(B)-Al键分割而成的层状结构, 与MAX相结构类似。Cr₄AlB₄具有类似于MAX相的高损伤容限和断裂韧性。

关键词: MAB相, 密度泛函理论, 物相稳定性, 力学性能

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

中图分类号:

TQ134

齐欣欣, 宋广平, 尹维龙, 王明福, 赫晓东, 郑永挺, 王荣国, 柏跃磊. 新型三元层状硼化物Cr₄AlB₄的物相稳定性和力学行为分析[J]. 无机材料学报, 2020, 35(1): 53-60.

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.

图/表 10

表1 Cr4AlB4及CrB晶格参数及基本属性

Table 1 Lattice parameters and some basic property of Cr4AlB4 and CrB

			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	-	-	-

图1 Cr4AlB4(a)和CrB(b)的晶体结构 Cr4AlB4 can be regarded as CrB with Al monolayer inserted along the b axis

Fig. 1 Crystal structure of Cr4AlB4 (a) and CrB (b)

表2 Cr4AlB4、Cr2AlB2以及二元硼化物CrB的键长和键刚度

Table 2 Bond length and bond stiffness in Cr4AlB4, and Cr2AlB2 as well as binary borides CrB

	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	-	-	-

图2 Cr4AlB4沿高对称点方向的声子色散曲线(a)和态密度(b)

Fig. 2 Phonon dispersions (a) and density of state (b) of Cr4AlB4 along the high symmetry directions

表3 Cr4AlB4的形成焓ΔHcomp, ΔHcomp< 0的相以粗体表示

Table 3 Formation enthalpy ΔHcomp for Cr4AlB4, phases with ΔHcomp < 0 are in bold

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

图3 压力对Cr4AlB4的归一化体积V/V0及归一化晶格常数a/a0, b/b0和c/c0 (a)和归一化键长d/d0 (b)的影响

Fig. 3 Pressure dependence of the normalized cell volume V/V0 as well as the normalized lattice parameters a/a0, b/b0 and c/c0 of Cr4AlB4 (a) and the normalized bond length d/d0 in Cr4AlB4 (b)

图4 Cr4AlB4 (a)和CrB (b)的态密度及分波态密度

Fig. 4 Total and partial density of states of Cr4AlB4 (a) and CrB (b)

图5 Cr4AlB4在(001) (a)、(100) (b)和(101) (c)平面上的差分电荷密度

Fig. 5 Electron density difference maps on (001) (a), (100) (b) and (101) (c) planes of Cr4AlB4

表4 Cr4AlB4, Cr2AlB2 和 CrB的贝德电荷分析

Table 4 Bader charge analysis of Cr4AlB4, Cr2AlB2 and CrB

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

表5 Cr4AlB4的二阶弹性常数(cij/GPa)、体积模量(B/GPa)、剪切模量(G/GPa)、杨氏模量(E/GPa)、泊松比(μ)和德拜温度(θD/K)

Table 5 The calculated second-order elastic constants (cij/GPa), shear moduli (G/GPa), bulk moduli (B/GPa), Young’s moduli (E/GPa), Poisson ratio (μ), and Debye temperature (θD/K) of Cr4AlB4

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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新型三元层状硼化物Cr₄AlB₄的物相稳定性和力学行为分析

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

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