First-principles calculations of the mechanical and electronic properties of Fe–W–C ternary compounds YangZhen Liu a , YeHua Jiang a , Rong Zhou a , Jing Feng b,⇑ a Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, PR China b School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA article info Article history: Received 8 August 2013 Received in revised form 13 September 2013 Accepted 16 September 2013 Available online 10 October 2013 Keywords: Mechanical properties Anisotropy Electronic properties Density functional theory abstract The mechanical and electronic properties of Fe–W–C (Fe 2 W 2 C, Fe 3 W 3 C, Fe 6 W 6 C and Fe 21 W 2 C 6 ) ternary compounds were investigated by first-principles calculations. The cohesive energy and formation enthalpy of these compounds show that they are thermodynamically stable. The elastic constants were calculated by using stress–strain method and the Voigt–Reuss–Hill approximation was applied to esti- mate the mechanical moduli. The calculated bulk modulus values of Fe 2 W 2 C, Fe 3 W 3 C, Fe 6 W 6 C and Fe 21- W 2 C 6 are 324.9 GPa, 326.0 GPa, 326.1 GPa and 336.1 GPa, respectively, which are larger than Fe 3 C and Cr 7 C 3 . The surface constructions of Young’s moduli were plotted to indicate the mechanical anisotropy. Using a theoretical method based on the works of Tian, the hardness of the crystal is estimated. Moreover, the chemical bonding in these carbides were evaluated by calculating the density of states and Mulliken analysis. The results indicate that all the bonding behaviors in Fe–W–C ternary compounds are the com- binations of metallic and covalent bonds. Published by Elsevier B.V. 1. Introduction The transition metal carbides have attracted extensively study owing to its outstanding physical and chemical properties such as extreme hardness, high melting point, interesting catalytic behavior and high thermal conductivity. The crystalline and nano-sized WC-based alloys and composites comprising other transition metals (M are d metals) have got to significant attention, which are fit for extensive technological applications: for example, the properties of the interlayer for widely studied the WC–M com- posite (infiltration casting process [1], electro slag melting and casting process [2]) as well as the Metal-based WC composite coat- ing (SHS-centrifugal cladding W–C–Fe cement coating [3], laser clad layers of W–C–Co alloy powders [4]). One of the most impor- tant carbides is Fe–W–C multiple carbides, which belong to the most promising engineering materials with a wide range of indus- trial applications. Recently, due to their important applications as a protection coating or as a wear resistance phase in the cast irons, several papers have reported the ground state properties of Fe–W–C ternary compounds either by theoretical calculations or by empirical methods. For example, Mercado and co-workers [5] have synthesized of the single phase of Fe 6 W 6 C by mechanical alloying, and the Vickers microhardness (H v ) measurement for Fe 6 W 6 C show that they are hard phases with H v  15.6 GPa. Tsuchida et al. [6] have fabricated Fe 3 W 3 C, Fe 3 Mo 3 C and Fe 6 W 6 C compounds assisted by mechanical activation. Taylor and Sachs [7] have predicted the stability of these eta carbides and elucidated the crystal structure of many carbides occurring in alloy steels, they pointed out that the sequence of the stability in these car- bides: Fe 3 W 3 C > Co 3 W 3 C > Ni 3 W 3 C. Suetin et al. [8] have used the full-potential linearized augmented plane waves (FLAPW) method within the generalized gradient approximation (GGA) to investi- gate the structural, electronic, magnetic properties and stability for a family of related eta carbides M 3 W 3 C and M 6 W 6 C (M = Fe and Co), they concluded that among the examined eta carbides are thermodynamically stable but all of them are less stable than the hexagonal mono-carbide WC, and the most thermodynami- cally stable material should be Fe 6 W 6 C, and the most unstable is Co 3 W 3 C. In addition, magnetism of Fe 3 W 3 C and Fe 6 W 6 C mainly originate from spin polarization of the Fe 3d states, whereas in- duced magnetization on the tungsten and carbon atoms is quite small. Ilyasov et al. [9] have reported the structure of electron en- ergy band of Fe 3 W 3 C by local coherent potential method using the cluster version of MT approximation. Li et al. [10] have studied the stability and mechanical properties of eta M 3 W 3 C (M = Fe, Co and Ni) compounds, they calculated the bulk modulus values are 371.2, 351.7 and 331.2 GPa for Fe 3 W 3 C, Co 3 W 3 C and Ni 3 W 3 C, respectively. Moreover, they also found that the mechanical prop- erties of Fe 3 W 3 C is better than other two eta carbides, and all eta carbides show obvious mechanical advantages and chemical sta- bilities when comparing with Cr 7 C 3 , Fe 2 B and Fe 3 C. To our best 0927-0256/$ - see front matter Published by Elsevier B.V. http://dx.doi.org/10.1016/j.commatsci.2013.09.040 ⇑ Corresponding author. Tel.: +1 617 496 4295; fax: +1 857 259 2445. E-mail address: jfeng@seas.harvard.edu (J. Feng). Computational Materials Science 82 (2014) 26–32 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci