On the accuracy of various statistical methods for describing ordering phase transitions in BCC alloys

The accuracy of various statistical methods for describing B2-or D0₃-type (CuZn or Fe₃Al) ordering phase transitions characteristic of BCC alloys is examined. The temperature-concentration phase diagrams were calculated for several models of alloys discussed in the literature with the use of three methods, namely, the mean-field and pair cluster approximations and the tetrahedron cluster field method developed in this work. The calculation results were compared with each other and with Monte Carlo calculations. The accuracy of various methods was found to sharply depend on the type of interactions in the system, primarily, on the presence of strong competing interactions and short-range correlations that hinder ordering. In the absence of such correlations, in particular, in Fe-Al type alloys with extended interactions, the use of the pair cluster approximation allows the results obtained in the mean-field approximation to be substantially refined without any noticeable complication of calculations. At the same time, for systems with short-range and competing interactions, the use of this approximation could drastically distort the form of phase diagrams, whereas the tetrahedron cluster field method allows the phase diagrams of these systems to be calculated fairly accurately for temperatures and concentrations of interest to physics.     

Electronic topological transitions and phase stability in the fcc Al-Zn alloys

We report on a detailed investigation of the phase equilibria and the Fermi surface in the Al-Zn system. Our calculation are based on the density functional theory and we use the linear muffin-tin orbital method and the Green's function technique. The calculated free energies of alloy formation exhibit the existence of a miscibility gap between the alloys containing approximately 10 and 55 at.% of Zn, in agreement with the phase diagram of the Al-Zn system. Seven electronic topological transitions (ETT) were found in Al-Zn system within the stability range of the fcc solid solution. A relation between these ETT and the phase stability of the fcc Al-Zn solid solutions is established. We show that extremum points on the concentration dependencies of the thermodynamic properties of Al-Zn alloys can be explained by band-filling effects. Received 6 February 2002 Published online 19 November 2002     

Random cluster models for icosahedral phase alloys

We present results on computer generated random cluster models for icosahedral phase alloys. By the application of physically motivated constraints on the local atomic cluster configurations, the model achieves long range translational order comparable to, or greater than, that found in simple icosahedral alloys such asi-AlMnSi andi-AlLiCu. The parallel and perpendicular space structures are explored in some detail including a comparison with experimental powder diffraction patterns and an examination of the phason fluctuations. The latter are shown to decrease markedly with increased constraint on the local environment, but the remaining phason strain would seem finally not to vanish with increasing model size. Our model is compared with other cluster models for quasicrystalline materials and is shown to possess a density and connectivity very close to those of Elser's (best) model and those predicted by Henley for a canonical tiling. The relation of this model to recently discovered icosahedral phase alloys with resolution limited diffraction peak widths, which are essentially free of phason strain, is also discussed.     

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Within the four-loop ε expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is supported by the estimate of critical dimensionality N _c ^C =1.445(20) obtained from six loops via the exact relation N _c ^C =1/2N _c ^R established for the complex and real hypercubic models.     

The theory of atomic and magnetic ordering in ternary alloys with fcc lattice

We consider the theory of the mutual influence of atomic and spin ordering phenomena in ternary alloys of transition elements with fcc lattice. The case of quasibinary alloys B₃A-B₃D is considered in detail. Concentration dependences of the critical temperature of the order-disorder phase transition are considered for cases of atomic and magnetic ordering.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 48–57, December, 1970.     

Investigation of a magnetic phase transition in fcc iron-nickel alloys

A magnetic phase transition in carbon-doped (0.1 and 0.7 at. %) Fe₇₀Ni₃₀ Invar alloys was investigated by the method of depolarization of a transmitted neutron beam and by small-angle scattering of polarized neutrons. It is shown that for both alloys, two characteristic length scales of magnetic correlations coexist above T _c. Small-angle scattering by critical correlations with radius R _c is described well by the Ornstein-Zernike (OZ) expression. The longer-scale (second) correlations, whose size can be estimated from depolarization data, are not described by the OZ expression, and hypothetically can be modeled by a squared OZ expression, which in coordinate space corresponds to the relation 〈M(r)M(0)〉∝exp(−r/R _d), where R _d is the correlation length of the second scale. The temperature dependence of the correlation radius R _c was obtained: R _c ∝ ((T−T _c)/Tc)^−ν , where ν≈2/3 is the critical exponent for ferromagnets, over a wide temperature range up to T _c ^exp , at which the correlation radius becomes constant and equals its maximum value R _c(T _c)=R _c ^max . The maximum correlation radius established (R _c ^max =140 Å and 230 Å for the first and second alloys, respectively) characterizes the length-scale of the fluctuation for which the appearance of critical correlations first results in the formation of a ferromagnetic phase, and the phenomenon itself exhibits a “disruption” of the second-order phase transition at T=T _c ^exp , as a result of which a first-order transition arises. Temperature hysteresis was also detected in the measured polarization of the transmitted beam and intensity of small-angle neutron scattering in the alloy above T _c, confirming the character of this magnetic transition as a first-order transition close to a second-order transition. Zh. éksp. Teor. Fiz. 112, 2134–2155 (December 1997)     

The Fermi model in describing phase transitions initiated by pressure variation

Having analyzed the pressure dependence of volume V(σ), we demonstrate that the mechanism of the phase transition in HfO₂ corresponds to the Fermi model. This indicates that at σ = 10 GPa, the ground state of Hf ions changes. Within the Fermi model, the stiffness moduli in the phases stable at σ < 10 GPa and σ > 10 GPa are calculated. It is shown that the results obtained are in better agreement with the well-known experiment than the results obtained in the framework of the quantum chemistry model (ab initio calculations) and the Birch-Murnaghan equation of state.     

Transformation strains in martensitic phase transitions of Co alloys

The thermally induced fcc → dhcp martensitic phase transformation was investigated in two different CoFe alloys (Co-5.75 and 6.0at.% Fe). Analysis by transmission electron microscopy methods yields that in both alloys the transformation proceeds by the movement of transformation dislocations (partials) that are correlated on an atomic scale; partials on adjacent close packed planes interact and combine to a paired partial. Two different and competitive modes of the transformation were observed. In Co-6.0 at. % Fe all the paired partials have the same Shockley partial Burgers vector adding up their long-range strain fields (transformation mode A). Contrary to this, in Co-5.75 at.%Fe paired partials of different Burgers vectors are compensating their long-range strain fields on an atomic scale (transformation mode B). The mode of the transformation seems to depend on both the parameters of the material and the experimental conditions.     

Photoacoustic characterization of phase transitions in amorphous metal alloys

Received: 24 February 1997     

Application of epidemic models to phase transitions

The Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) models describe the spread of epidemics in a society. In the typical case, the ratio of the susceptible individuals fall from a value S ₀ close to 1 to a final value S_f , while the ratio of recovered individuals rise from 0 to R_f?=?1???S_f . The sharp passage from the level zero to the level R_f allows also the modeling of phase transitions by the number of “recovered” individuals R(t) of the SIR or SEIR model. In this article, we model the sol–gel transition for polyacrylamide–sodium alginate (SA) composite with different concentrations of SA as SIR and SEIR dynamical systems by solving the corresponding differential equations numerically and we show that the phase transitions of “classical” and “percolation” types are represented, respectively, by the SEIR and SIR models.     

First-order phase transitions in large entropy lattice models

We show the existence of a first-order phase transition in thev-dimensional Potts model forv≧2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature. Also the existence of a first-order transition in thev-dimensional Potts gauge model,v≧3, is obtained if the underlying gauge group is finite but large.     

Ferroelastic phase transitions induced by the orbital and rotation ordering in perovskites

The phases formed in cubic crystals upon ferrodistortion and antiferrodistortion orientational ordering of anion polyhedra distorted as a result of the Jahn-Teller effect are established in terms of the statistical model in the mean-field approximation. For the four-sublattice three-minimum model, there are four types of ordered phases, and one of them is the intrinsic ferroelastic (ferrodistortion) phase. The conditions providing the appearance of ordering of a particular type are determined. The effect of orbital ordering on the rotational structural distortions is discussed. The conditions of the formation of ordered phases (D _4h ⁵ , D _4h ¹⁸ ) that are most frequently encountered in perovskites are found within the eight-sublattice three-minimum model. It turns out that, under certain conditions, these phases can coexist in the same crystal and transform into each other. The variants of their mutual transformations are considered.