ISSN 0031-918X, The Physics of Metals and Metallography, 2012, Vol. 113, No. 9, pp. 831–835. © Pleiades Publishing, Ltd., 2012. Original Russian Text © V.I. Bogdanov, V.A. Popov, V.K. Portnoi, A.V. Ruban, 2012, published in Fizika Metallov i Metallovedenie, 2012, Vol. 113, No. 9, pp. 876–880. 831 1. INTRODUCTION The interstitial solid solutions of carbon in nickel were selected as a subject of research due to the obvi- ous interest in Ni–M–C systems (M: Al, Mg, Ga, …) as materials with peculiar physical properties, such as superconductivity (Ni 3 MgC x [1]), and as engineering materials for high-temperature applications [2–5]. In nickel-based solid solutions, the carbon atoms are located in octahedral interstices of the fcc lattice [6, 7]. As a rule, the carbon content in the systems studied differs significantly from the stoichiometric value, and their properties depend substantially on the amount of the dissolved carbon [1, 3, 5, 8]; therefore, to study phase equilibria in carbon solid solutions in nickel-based alloys, it is necessary to have a realistic model of interaction of interstitial atoms located in the interstices of the crystal lattice of metal. The initial concepts of the theory of interstitial solutions [9] are based on the Krivoglaz–Kanzaki– Khachaturyan model of deformational interactions, which are due to high local displacements of metal atoms near the interstitial atoms. It has been assumed in this theory that the determining role in the description of phase equilibria in interstitial solid solutions is played by the deformational interactions. The chemical (atomic) contributions, which describe the energy variations of the solid solution upon the migration of interstitial atoms over inter- stices at fixed positions of metal atoms, have been considered as short-range actions and used as adjust- ing parameters for fitting to existing experimental data [9–13]. A first-principles analysis of ordering phenomena in hcp interstitial solid solutions of oxygen and nitro- gen in titanium, zirconium, and hafnium has dem- onstrated [14] that the chemical contributions to the interaction energy of interstitial atoms are an order of magnitude higher than the contributions from the deformational interaction between the nearest and next-nearest neighbors and that both types of contri- butions are important when taking into account interactions with more distant neighbors. It follows from these results that for studying phase equilibria in interstitial alloys it is, probably, necessary to modify the previous concepts about the predominant role of deformational interactions. This work continues the first-principles investiga- tions of chemical and deformational interactions of interstitial atoms in fcc solid solutions of carbon in nickel (Ni–C). Note that the methods similar to those applied in [14], based on the density-functional theory (DFT) [15], were used in calculations [16, 17] of the heat of solution (ΔH sol ) and of the activation energy for carbon diffusion (E a ) in Ni–C solid solutions. From these calculations, it also follows that it is the octahedral interstices that are energetically more preferable for carbon atoms in nickel. In [11], the energies of defor- mational interactions for Ni–C solid solutions were calculated within the framework of the phenomenolog- ical theory [9]. Chemical and Deformational Interactions in Solid Solution of Carbon in Nickel V. I. Bogdanov a , V. A. Popov a , V. K. Portnoi b , and A. V. Ruban c a Vologda State Technical University, ul. Lenina 15, Vologda, 160000 Russia b Faculty of Chemistry, Moscow State University, Moscow, 119992 Russia c Department of Materials Science and Engineering, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden Received October 19, 2011 Abstract—A first-principles stuy of ordering phenomena in hcp interstitial solid solutions of oxygen and nitrogen in Ti, Zr and Hf has demonstrated that the dominant contributions to the interaction energy of inter- stitial atoms are of chemical nature; thus, it is necessary to modify the previously established concepts about the priority role of deformational interactions in interstitial solutions. We have continued studies of the role of chemical and deformational interactions of interstitial atoms by the example of solid solutions of carbon in nickel. The results obtained also confirm a significant role of chemical interactions between carbon atoms in these solid solutions. The results were compared with the experimental data on the enthalpy of carbon dis- solution in nickel and on the coefficient of solutal expansion of the lattice. Keywords: interstitial phases, first-principles calculations, deformational interactions, chemical interactions DOI: 10.1134/S0031918X1206004X THEORY OF METALS