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

ZHANG Dong; SUN Yihua; YIN Chaochao

doi:10.7498/aps.74.20250713

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–x Fe_xC 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–x Fe_xC 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.

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Authors and contacts

Corresponding author: SUN Yihua, sunny.hust@ctgu.edu.cn ; YIN Chaochao, ycc0125@126.com

Funds: Project supported by the National Key Research and Development Program, China (Grant No. 2023YFB3812200), the Natural Science Foundation Innovation Development Joint Fund of Hubei Province, China (Grant No. 2025AFD412), the Open Fund of the Hubei Key Laboratory of Hydroelectric Mechanical Equipment Design and Maintenance (China Three Gorges University), China (Grant No. 2025KJX07), the Open Fund of the Hubei Key Laboratory of System Science for Metallurgical Industry Processes (Wuhan University of Science and Technology), China (Grant No. Y202301), and the Scientific Research Start Fund of Three Gorges University, China (Grant No. 2023RCKJ0031).

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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

DownLoad: CSV

	a/Å	b/Å	c/Å	$\alpha $/(°)	$\beta $/(°)	γ/(°)	ΔH_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

DownLoad: CSV

碳化物	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	B_H/GPa	G_H/GPa	B_H/G_H	E	$\nu $	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
VC	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

DownLoad: CSV

		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

DownLoad: CSV

碳化物	γ	A_γ /(10^–8)	V	$\delta $/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

DownLoad: CSV

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Vol. 74, Issue 21 - 2025-11-05

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