钢中多组分V1–xFexC碳化物结构和物性的第一性原理研究*

张东; 孙宜华; 尹朝朝

doi:10.7498/aps.74.20250713

摘要
钒碳化物通常作为金属材料的增强相, 其弹性和延展-脆性特性对于力学性能至关重要. 本研究基于特殊准随机结构(SQS)方法和第一性原理计算系统探讨了多组分V_1–xFe_xC系碳化物的稳定性、电子结构、机械性能和热性质随元素Fe含量变化的规律. 研究结果表明, 5种组分(V_0.125Fe_0.875C, V_0.25Fe_0.75C, V_0.5Fe_0.5C, V_0.75Fe_0.25C和V_0.875Fe_0.125C)随着元素Fe含量的减小稳定性提高, V_1–xFe_xC系碳化物键合类型以共价键、金属键和离子键的混合特征为主. 相较于V_1–xFe_xC系其他碳化物, V_0.875Fe_0.125C由于具有高的共价键强度, 因此表现出高的弹性模量和硬度, 元素Fe的掺杂引入显著影响V_1–xFe_xC碳化物的晶格振动模式和电子结构, V_0.875Fe_0.125C碳化物较高的德拜温度, 同样印证了其高温下优异的机械强度. 此外, 热导率的计算不仅指导V_1–xFexC系碳化物的实验选择, 同时为开发高性能耐高温涂层提供重要的理论支持.

关键词:
钢 /

V_1–xFe_xC碳化物 /

第一性原理计算 /

特殊准随机结构 /

物理性质
Abstract
Vanadium carbides commonly serve as strengthening phases in metallic materials, where their elastic and ductile-brittle characteristics are critical for mechanical performance. This work systematically investigates the structural stability, electronic properties, mechanical behaviors, and thermal characteristics of multi-component V_1–xFexC carbides by using first-principles calculations, aiming to elucidate the influence of Fe content on their physical properties and provide a theoretical basis for the design and application of carbides in high-performance steels. The calculations are performed using the Vienna ab initio simulation package (VASP) based on density functional theory (DFT). Special quasirandom structures (SQS) are employed to construct five carbide models with varying Fe/V ratios (from V_0.125Fe_0.875C to V_0.875Fe_0.125C). Key parameters including formation enthalpy, electronic density of states, elastic constants, Debye temperature, and thermal conductivity are computed. The results indicate that as the Fe content decreases, the formation enthalpy shifts from positive to negative, reflecting a significant improvement in thermodynamic stability. Electronic structure analyses reveal metallic behavior of all compositions, with stronger covalent bonding in V-C than that in Fe–C. The V_0.875Fe_0.125C carbide exhibits the highest elastic modulus (C₁₁ = 615.80 GPa) and Vickers hardness (21.06 GPa), which is attributed to its strong covalent interactions, though it also shows increased brittleness. The Debye temperature rises with the decrease of Fe content, further confirming superior mechanical strength at elevated temperatures. Calculations of the thermal conductivity for V_0.875Fe_0.125C yield values of 9.427 W·m^－¹·K^－¹ at 300 K and 2.357 W·m^－¹·K^－¹ at 1300 K. Its minimum lattice thermal conductivity (2.001 W·m^－¹·K^－¹) is comparable to that of typical thermal barrier coating materials, demonstrating high potential for high-temperature thermal insulation. This study reveals the structure-property relationships in V_1–xFexC carbides on an atomic scale, indicating that low-Fe compositions are advantageous for high-temperature and high-strength applications. These findings provide important theoretical support for the development of novel heat-resistant coatings and high-strength steels.

Keywords:
steel /

V_1–xFe_xC carbides /

first-principles calculations /

SQS /

physical properties
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施引文献

图 1 试样钢微观组织以及定性表征元素分布　(a)微观组织形貌; (b)高角环形暗场像; (c) HRTEM-EDS能谱面扫和(d)线扫图

Fig. 1. Microstructure of sample steel and distribution of qualitatively characterised elements: (a) Microstructural morphology; (b) high-angle annular dark-field image; (c) HRTEM-EDS energy spectrum area scan and (d) line scan image.

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图 2 V_1–xFe_xC碳化物晶体结构　(a) VC; (b) V_0.125Fe_0.875C; (c) V_0.25Fe_0.75C; (d) V_0.5Fe_0.5C; (e) V_0.75Fe_0.25C; (f) V_0.875Fe_0.125C

Fig. 2. Crystal structure of V_1–xFe_xC carbides: (a) VC; (b) V_0.125Fe_0.875C; (c) V_0.25Fe_0.75C; (d) V_0.5Fe_0.5C; (e) V_0.75Fe_0.25C; (f) V_0.875Fe_0.125C

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图 3 V_1–xFe_xC碳化物的TDOS和PDOS　(a) V_0.125Fe_0.875C; (b) V_0.25Fe_0.75C; (c) V_0.5Fe_0.5C; (d) V_0.75Fe_0.25C; (e) V_0.875Fe_0.125C

Fig. 3. TDOS and PDOS of V_1–xFe_xC carbides (a) V_0.125Fe_0.875C; (b) V_0.25Fe_0.75C; (c) V_0.5Fe_0.5C; (d) V_0.75Fe_0.25C and (e) V_0.875Fe_0.125C

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图 4 V_1–xFe_xC碳化物的声速(纵波v_l、剪切波v_s和平均声速v_m )以及德拜温度($ \theta_{\text{D}} $)

Fig. 4. Calculated sound velocities (long wave v_l, shear wave v_s, and average sound velocity v_m), and Debye temperature ($ \theta_{\text{D}} $) of V_1–xFe_xC carbides.

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表 1 X射线能谱分析下的碳化物元素含量

Table 1. Elemental content of carbides after energy-dispersive X-ray spectroscopy.

元素	原子百分比/%	质量分数/%
C	4.47	1.04
Fe	60.96	66.11
V	27.35	27.06
Cr	1.16	1.17
Mn	2.29	2.44
Other elements	3.77	2.18

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表 2 V_1–xFe_xC碳化物结构晶胞参数、形成焓(ΔH_f)、金属性(f_m)和Bader电荷

Table 2. Calculated structural cell parameters, formation energy (ΔH_f), metallicness (f_m) and Bader charge of V_1–xFe_xC carbides

	a/Å	b/Å	c/Å	α/(°)	β/(°)	γ/(°)	$ {{\Delta}{H}}_{\text{f}} $/( meV·atom^–1)	f_m	Bader
V_0.125Fe_0.875C	8.061	8.065	8.063	90.08	89.99	89.95	0.443	0.548	0.840
V_0.25Fe_0.75C	8.106	8.107	8.107	90.00	90.00	90.01	0.321	0.622	0.914
V_0.5Fe_0.5C	8.203	8.188	8.195	90.00	90.00	90.00	0.042	0.844	1.052
V_0.75Fe_0.25C	8.262	8.261	8.258	89.92	90.08	89.99	–0.230	0.971	1.146
V_0.875Fe_0.125C	8.287	8.287	8.288	89.93	90.00	89.97	–0.439	1.19	1.213

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表 3 V_1–xFe_xC碳化物的弹性常数C_ij、体积模量B_H、剪切模量G_H、杨氏模量E、泊松比ν、普格模量比B_H/G_H、硬度H_V、断裂韧性K_IC以及脆性指数$ {{M}}_{{x}} $

Table 3. Calculated elastic constants C_ij, bulk modulus B_H, shear modulus G_H, Young's modulus E, Poisson's ratio ν, Pugh modulus ratio B_H/G_H, hardness H_V, fracture toughness K_IC, and brittleness index $ {{M}}_{{x}} $ of V_1–xFe_xC carbides.

碳化物	C₁₁/ GPa	C₁₂/ GPa	C₄₄/ GPa	B_H/ GPa	G_H/ GPa	B_H/G_H	E	v	H_V/ GPa	K_IC/(MPa·m^1/2)	M_x/μm^–1/2
VC	668.78	138.75	200.00	315.43	223.89	1.41	543.15	0.345	28.73	3.83
	648.24 ^[24]	156.88 ^[24]	209.99 ^[24]	318^[9]	213^[9]	1.49^[9]	521^[9]	0.356^[9]	25.8^[9]
V_0.125Fe_0.875C	552.84	165.68	75.32	294.40	110.79	2.657	442.11	0.333	8.49	2.564	3.310
V_0.25Fe_0.75C	553.84	155.42	86.486	288.10	121.67	2.368	319.96	0.315	10.34	2.665	3.878
V_0.5Fe_0.5C	563.87	152.52	113.41	289.61	144.23	2.008	371.09	0.286	14.06	2.925	4.808
V_0.75Fe_0.25C	584.01	148.76	149.97	293.96	174.39	1.686	436.80	0.252	19.63	3.254	6.034
V_0.875Fe_0.125C	615.80	154.92	162.02	308.46	186.60	1.650	465.87	0.248	21.06	3.450	6.104

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表 4 V_1–xFe_xC碳化物沿[100], [110]和[111]方向的声速(m/s)

Table 4. The calculated sound velocities (m/s) along [100], [110], and [111] directions of V_1–xFe_xC carbides.

		V_0.125Fe_0.875C	V_0.25Fe_0.75C	V_0.5Fe_0.5C	V_0.75Fe_0.25C	V_0.875Fe_0.125C
[100]	[100]v_l	9003.42	9126.02	9446.38	9820.16	10182.71
	[010]v_s1	3323.25	3606.30	4236.44	4976.31	5223.03
	[001]v_s2	3323.25	3606.30	4236.44	4976.31	5223.03
[110]	[110]v_l	7982.57	8144.52	8639.03	9233.81	9600.33
	$[1{\bar 1}0] $v_s1	5327.68	5473.24	5705.14	5994.67	6229.07
	[001]v_s2	3323.25	3606.30	4236.44	4976.31	5223.03
[111]	[111]v_l	7611.92	7789.92	8352.592	9029.91	9398.19
	$ [11{\bar 2}] $v_s1	4754.38	4930.12	5261.33	5675.55	5912.77
	$[11{\bar 2}] $v_s2	4754.38	4930.12	5261.33	5675.55	5912.77

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表 5 V_1–xFe_xC碳化物的格林艾森参数γ, A_γ, δ, M_av, 晶格热导率k_ph以及最小晶格热导率k_min

Table 5. Calculated Grüneisen parameter γ, A_γ, δ, M_av, lattice thermal conductivity k_ph, and minimum lattice thermal conductivity k_min of V_1–xFe_xC carbides.

碳化物	γ	A_γ(10^–8)	V	δ/Å	M_av/ (kg·mol^–1)	n	k_ph(300)/ (W·m^–1·K^–1)	k_ph(1300)/ (W·m^–¹·K^–1)	k_min/ (W·m^–1·K^–1)
V_0.125Fe_0.875C	1.996	3.039	524.18	2.016	22.413	64	2.139	0.535	1.536
V_0.25Fe_0.75C	1.869	3.075	532.81	2.027	22.208	64	2.873	0.718	1.609
V_0.5Fe_0.5C	1.692	3.132	550.38	2.049	21.800	64	4.729	1.182	1.752
V_0.75Fe_0.25C	1.511	3.199	563.61	2.065	21.392	64	8.183	2.046	1.929
V_0.875Fe_0.125C	1.492	3.206	569.15	2.072	21.188	64	9.427	2.357	2.001

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钢中多组分V_1–xFe_xC碳化物结构和物性的第一性原理研究*

First-principles study on structures and physical properties of multicomponent V_1–x FeₓC carbides in steel*

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钢中多组分V1–xFexC碳化物结构和物性的第一性原理研究*

First-principles study on structures and physical properties of multicomponent V1–x FeₓC carbides in steel*

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钢中多组分V_1–xFe_xC碳化物结构和物性的第一性原理研究*

First-principles study on structures and physical properties of multicomponent V_1–x FeₓC carbides in steel*