Effect of interstitial carbon distribution and nickel substitution on the tetragonality of martensite: A first-principles study

Abstract

International audienceBy using first principles calculations, the effects of carbon distribution and of 25 at.% of nickel substitution on the tetragonality of ferrous martensite have been investigated. Different carbon concentrations have been considered (0≤xc ≤ 12.5 at.%). All calculations were based on the Projector Augmented Wave (PAW) method of the Density Functional Theory (DFT). The Special Quasirandom Structure (SQS) method has been used to model the disordered structures of the Fe16C2X and (Fe,Ni)16C2X systems. Our calculations demonstrate that the lattice parameters a and c vary linearly with carbon concentration, up to the high value of xc = 12.5 at.% (for X = 1). The nickel substitution enhances the expansion of parameter c of the Fe16C2X system up to 37%. This trend is correlated with the shear moduli calculated for bcc-iron and the disordered Fe25 at.%Ni structure. The mixing energies of the Fe16C2X and (Fe,Ni)16C2X systems indicate that the unmixing of martensite by spinodal decomposition is favoured by the nickel substitution. It is shown that carbon-carbon interactions are mostly repulsive until the distance of two bcc-iron lattice parameters

Temperature hysteresis of the order-disorder transition in carbon-supersaturated α-Fe

“…Density-functional theory (DFT) calculations show that the elasticity coefficients of Fe-C martensite are almost composition independent up to high carbon concentrations (11 at. %) [16], and that the lattice parameters are linear functions of the carbon content [17]. These findings justify the use of the linear elasticity theory of point defects in the context of this paper.…”

“…The lattice expansion concentration coefficients δ a and δ c are related to Vegard's law and can be measured from experimental data [20,21], computed by molecular dynamics [19], or computed ab initio [17] (see Table I). The agreement of DFT values [17] with experiment is very good for δ c . Although the relative error for δ a is large, the absolute error (0.07) is in the range of the uncertainty of the method.…”

Stress-controlled carbon diffusion channeling in bct-iron: A mean-field theory

“…-The material parameters (dipole tensor, stiffness tensor) are composition-and temperature-independent in the range of (a) 0-10 at.% C and 0-1000 K. This hypothesis of homogeneous elasticity is correct within an accuracy of about 10% [25,26); -Hillert's [22) assumption that the strain induced by the popu lation of carbon atoms is uniform in the crystal (the mean-field approximation). This was confirmed by previous studies [27,28].…”

“…Calcula tions were performed according to the computational details described in Ref. [26]. The defect elastic dipole tensors P 0 and p T were calculated with the residual stress method [30].…”

“…In the case of tetragonal deformation, Eq. 15gives the anisotropy ratio (26) We will restrict our analysis to the case of uniaxial expansion/ contraction. With the uniaxial strain e = (0, 0, i: 0 ), the deviatoric strain is E = i: 0 .…”