Interaction of interstitial carbon atoms in austenite

Abstract

~TRODUCTIONThe scientific school of G. V. Kurdyumov has investigated the problem of martensite transformations from a very wide viewpoint. One direction of the research is the study of interatomic interactions and their effect on the structure of the phases and the thermodynamics of the phase transformations [I]. This direction has been developed by A. G. . He has created a theory of strain (elastic, due to deformation of the crystal lattice around the dissolved atoms) interaction within the framework of the model of a discrete crystal lattice. By now the energy of paired strain interaction has been computed for many metals with b.c.c. [4][5][6][7][8][9][10][11][12], f.c.c. [8-10, 13, 14], and hexagonal [15] lattices. The elastic (strain) interaction of carbon and nitrogen atoms in ferrite was considered in [2,4]. The energy of elastic (strain) interaction of carbon and nitrogen atoms in austenite was computed in [16] using a simplified form of the dynamic matrix of the f.c.c, crystal lattice of ),-Fe and only some of the available experimental data on the phonon spectrum.Information on the interaction between carbon atoms in austenite is traditionally obtained from the concentration dependence of the thermodynamic activity of carbon a c measured at various temperatures [17][18][19][20][21]. There are reliable experimental data on the activity of carbon [22 -28]. However, they have been analyzed within the framework of the model of carbon-carbon atomic interaction in the first or first two coordination spheres. At the same time, it is well known that elastic (strain) interaction in interstitial solid solutions is long-range [2, 3] and the interaction distance substantially exceeds two coordination spheres. Despite the limitations of the model of paired interatomic interaction it is useful for solving many problems, in particular, for analyzing thermodynamic properties and phase transformations. As has been mentioned above, there are virtually no realiable published data on the strain (elastic) interaction of carbon and nitrogen atoms in austenite, although such information is i Moscow State Academy of Instrumentation and Information Science, Moscow, Russia.very important for understanding the behavior of austenite and phase transformations in steels. In this connection, we posed the problem 2 of computing the energy of C -C interaction more accurately and using the model of long-range strain interaction to describe the thermodynamic activity of carbon in austenite. ELASTIC (STRAIN) INTERACTION OF INTERSTITIAL ATOMSIn order to compute the energy of paired strain interaction of interstitial carbon atoms at octahedral interstices of the f.c.c, crystal lattice of iron we used the method of lattice statics as formulated by A. G. Khachaturyan [2, 3]. The distortions created in the crystal lattice by interstitial atoms are described by the concentration coefficient of expansion of the crystal lattice U 0 :where c is the atomic fraction of interstitial atoms, a is the period of the crystal lattice of austenite, and a 0 i...

Semi-Empirical Parameterization of Interatomic Interactions and Kinetics of the Atomic Ordering in Ni-Fe-C Permalloys and Elinvars

“…I. [2][3][4] [24,25] despite the differences of temperatures (and compositions). (It is usually assumed that the interatomic-interaction energies weakly depend on temperature.…”

“…I.2) and H-H interactions differ from data in Refs [28] and [30], respectively. As mentioned in [24,25], it is possibly connected with the simplified form of the dynamical matrix ||Ã ij (k)|| used in Refs [21,28,30]. Another cause of difference consists in 'rough' estimation [21,28,30] using the assumption of i-i interatomic interaction in α-Ni and γ-Fe within only six coordination interstitial shells.…”

“…]), the long-range strain-induced i-i interaction must be supplemented with additional short-range ('electrochemical') repulsion inside of the nearest co-ordination shells. As postulated in Refs [17,[24][25][26][27]32], a screened electrostatic (Coulomb) interaction of charged interstitials may be the possible origin of this repulsion. But in general, the 'direct' ('electrochemical') interaction of point defects inside of the crystal arises because of both an interaction of electrical charges, which form these defects, on conditions of their screening by the free charge carriers and the effect of the Pauli exclusion principle for the formation of the state distribution of the identical particles [1,3].Approaches, which do not include both effects due to the lattice displacements and the intrinsic 'electrochemical' interactions on the equal footing, will be discarded.The theory of 'direct' interactions of solute atoms is still not perfectly developed, and it is so far impossible to estimate microscopically the respective energies for many alloys.…”

“…For instance, in case of interstitialsubstitutional alloys based on cubic metals, the parameters of i-s-pairwise interaction appeared to be essential for analysis of Mössbauer spectra [3,4,29], tetragonality [19], and residual electrical resistivity under tempering [18] or diffraction patterns [21, 29-31 etc. ].On the other hand, in cases of α-Ni and γ-Fe, energies of strain-induced i-i interactions have also been calculated [17,21,22,24,25,[28][29][30][31], but for all of them, the different simplified forms of the dynamic matrix of f.c.c. host crystal (with a limited extent and unpaired components of ion-ion interactions) were used [16,37,38].…”

“…Defects and Diffusion in Ceramics X distributed points [16,17,22,24,25] or over only some 'special' points of the 'principal' value ( [21,28]; see bibliography in Ref. [3]) within the irreducible wedge in the first Brillouin zone ('1/48 BZ') of the f.c.c.…”