A simple and accurate theory of short-range order in alloys

Abstract

The authors propose a very simple method of calculating short-range order parameters alpha ij in disordered alloys using a series expansion in powers of a parameter gamma =exp(-1/ xi ) where xi is the dimensionless correlation length of the pair correlation function. In authors' approximation the sum rule alpha ii=1 is satisfied exactly, unlike in previous theories. In the zeroth order their approach leads to the spherical model results. The high accuracy of the theory developed is illustrated by comparing its results with those of Monte Carlo simulation and estimating the pair interactions from diffuse scattering data. In the latter problem pair-interaction potentials are explicitly expressed in terms of experimentally determined quantities.

Topologically correct phase boundaries and transition temperatures for Ising Hamiltonians via self-consistent coarse-grained cluster-lattice models

“…However, from the perspective of DCA where N cell = N c , all values ofΣ are potentially finite. Although the values of Σ ij decrease rapidly with shell distance for the disordered phase 47 (also observed in our work), this is not the case for ordered system. For example, Fig.…”

Interatomic Interactions in F.C.C.-Ni–Fe Alloys

“…There are number of various statistical-thermodynamic theories and approximations for definition of such interactions in alloys. In particular, we would like to indicate on: conventional SCF approximation based on the Krivoglaz-Clapp-Moss (KCM) formula [39][40][41][42], inverse Monte Carlo (IMC) method [43], spherical model (SM) [39,41,42,44,45], Onsager cavity field (OCF) approach [46][47][48], Tahir-Kheli approximation [49], Vaks-Zein-Kamyshenko cluster-field (CF) approach [50][51][52] and cluster variation methods (CVM) [53][54][55][56], Tokar-Masanskii-Grishchenko approach based on the 'gamma' expansion method [57], alpha-expansion (AE), including high-temperature expansion methods (HTM) [58], so-called 'ring' approximation [59], and some approximations developed in works reported in [60][61][62][63]. All above-mentioned approximations can be divided into two groups: (i) reciprocal-space (k-space) representations [39-42, 44-49, 59-63], which have no limitation on the effective radius of interatomic interactions and (ii) direct-space (r-space) representations [43,[50][51][52][53][54][55][56][57][58] having limitations for the interatomic-interaction extent (with using a limited number of the SRO parameters, ( ) α...…”

“…If we consider explicitly a mutual influence of the magnetic and atomic subsystems in the configuration-dependent part of free energy of a disordered alloy (see Eqs. (19)- (22)), the KCM formula (36) stays valid [131], and it is not necessary to overestimate the statistical correlation influence and many-particle force interactions of substitutional atoms in magnetic alloy, at the same time, unreasonably neglecting the apparent magnetism of an alloy [50][51][52]57].…”

“…(15)). Therefore, before explanation of microstructure features and microscopic physical phenomena [1-4, 108-119, [135][136][137] in magnetic alloy at issue, it is necessary to investigate an essential interplay of the atomic and magnetic orders of constituents, and it may be found that there is no need for considering both the substitutional correlation between atoms and their many-particle force interactions [50][51][52]57].…”

Direct and Indirect Methods of the Analysis of Interatomic Interaction and Kinetics of a Relaxation of the Short-Range Order in Close-Packed Substitutional (Interstitial) Solid Solutions

“…При цьому було використано ідею М. О. Кривоглаза [2,8,48,53,[126][127][128] про прийнятність застосування методу термодинамічних флуктуацій для оцінювання параметрів кореляції навіть в рамках сере-дньопольового усереднення [143,314]. З усіх отриманих й відомих на-ближень найвищу чисельну точність результатів дає узагальнена, так звана «сферична» модель [112,125,143,182,201,314]. Однак, навіть в рамках «сферичної» моделі неможливо описати явище температурної залежності положення максимуму фур'є-компонент параметрів близь-кого порядку в оберненому просторі (наприклад, для Cu-Au, Cu-Pd) у випадку незалежності енергії взаємодії атомів в сплаві від температури (тобто у такому сплаві, для якого можна знехтувати внесками у міжато-мну взаємодію ефектів розмірної невідповідності й магнетизму компо-нентів та теплового розширення кристалічної решітки).…”