Lattice vibrations and local order in substitutional solid solutions. IV

For solid solutions satisfying the Kopp-Neumann rule a relation is derived between the amplitudes of thermal vibrations of atoms of the components in a solid solution. The derived relation enables the separation of these quantities from the measured mean-square amplitudes of the atoms of the solid solution to be made.     

Lattice vibrations and local order in substitutional solid solutions. I

Expressions are derived for the effective mean square amplitudes of the thermal vibrations of atoms and the Debye characteristic temperatures for the case of binary, substitutional, metallic solid solutions. Both solid solutions with random distribution of atoms and also those with a partially ordered distribution of atoms are investigated. The calculations respect the change in the vibrational state of atoms on solid solution formation. The parameterα, characterizing this change, can be determined from X-ray diffraction experiments or from the concentration dependence of the melting temperature and lattice constant. The results are applied to a solid solution of Ag in Al. A comparison with the experimental values measured by M. Simerská (Czech. J. Phys.B 13 (1963), 737) shows good agreement.     

Lattice vibrations and local order in substitutional solid solutions. III

A new expression for the mean vibrational state of the atoms in a solid solution is derived by means of a model of the central atom. In contrast to an expression given earlier which contained recurrent formulas, it is now possible, in a general case, to express the mean vibrational state of the atoms in a solid solution directly for an arbitrary degree of the polynomial expressing the vibrational state of the central atom.     

Elastic lattice distortion in the statistical theory of multicomponent substitutional solid solutions with short-range order

The statistical theory of atomic distributions in multicomponent substitutional solid solutions with short-range order is considered, taking into account the various sizes of atomic components. The effect of elastic lattice distortions on the atomic distribution is estimated, and the dependence of the interatomic distance on alloy composition and amount of short-range order is calculated.     

Complexes of impurity atoms in diluted substitutional solid solutions

The equilibrium concentration of complexes composed of two B atoms is calculated for an A–B diluted substitutional solid solution with a body-centered cubic lattice. The conditions under which the fraction of the complexes becomes significant are determined.     

Theory of ordering of ternary substitutional solid solutions

The theory of the ordering of ternary substitutional solid solutions of the type B(A_m–D_n) with body-centered (bcc) cubic lattices and the type B₃(A_m–D_n) with face-centered cubic lattices (fcc) is investigated by the Gorskii-Bragg-Williams method. The applicability of the results obtained is analyzed.     

The solubility of substitutional atoms in ordered substitutional-intrestitial solid solutions

The solubility of substitutional impurities in ordered bcc A–B–(C) solid solutions has been calculated in a static approximation. The effect of the energy splitting of geometrically equivalent interstitial sites into interstitial sites of two types during ordering was taken into account. The solubility has been determined as a function of temperature, alloy composition, and long-range order parameter.     

Modelling of short-range ordering kinetics in dilute multicomponent substitutional solid solutions

ABSTRACT

Short-range ordering as the formation of couples and pairs between solutes is affected by their formation energies. This is not reflected in the standard regular solution model. Here, we present a new thermodynamic model which accounts for the dependence of the molar Gibbs energy on the concentrations of couples and pairs and their formation energies. The model treats kinetics of couples and pairs formation controlled by diffusion. This new model uses tracer diffusion coefficients of solutes and bond formation energies, which can be taken from ab initio calculations. Insofar, the current concept bridges the gap between ab initio methods and non-equilibrium thermodynamics. The reliability of the model is checked by comparison with kinetic Monte Carlo simulations. The model is applied to an Al-Mg-Si-Cu system. Finally, the configurational entropy for a binary system evaluated with the current model is compared with Bethe’s approximation, which allows estimating of applicability limits of the current model.     

Short-range order in Fe-Rh solid solutions

We have used diffuse scattering of x-rays (DSX) and a model potential to show short-range order exists in iron-rhodium alloys. After the alloy Fe-25 at. % Rh was quenched following annealing at 900°C for 1 h, a clearly visible diffuse maximum (characteristic of short-range order) appeared in the diffraction pattern, in addition to reflections from the α- and γ-phases. For the single-phase, dilute solid solution Fe-2.5 at. % Rh, starting with the effects of static displacements, we have calculated the short-range order parameters (α₁ = −0.02, α₂ = −0.09, α₃ = 0.02, α₄ = 0.05). The elastic constants of Fe-2.5 at. % Rh needed to compute the short-range order parameters from the DSX data were calculated using a model potential. Theoretical calculations of the order energy and the short-range order parameters, performed using a model potential for these alloys, agree with the experimental data. M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 71–77, March, 1998.     

Lattice vibrations of AsxP1−xIn solid solutions

On the basis of investigations of reflection spectra from As_xP_1?xIn solid solutions, new data have been obtained on the character of the vibrational spectrum for compositions in which x is, 0, 0·2, 0·3, 0·4, 0·5, 0·6, 0·8, 0·9 and 1. The variation of the frequencies and oscillator strengths that characterize As and P atom vibrations has been determined as a function of composition. From the comparison of calculated with experimental reflection spectra, the dispersion of the real part (∈₁) and the imaginary part (∈₂) of the dielectric constants of the substance as well as |∈| have been estimated. The values of the nonlocal and local parts of the effective ion charge of InAs and InP were also determined.     

Strengthening effect of short-range order esf ternary face-centered cubic substitutional solutions

The increase produced by short-range order in the resistance to the movement of dislocations _sro in ternary f. c. c. substitutional solid solutions was studied. A general expression for _sro was derived taking into account the correlation on the first three coordination spheres and the change in the entropy associated with the passage of dislocations. The expressions obtained were used for qualitative calculation of the concentration dependence of _sro for several ternary systems.     

Thermodynamics of fe-based ternary solid solutions containing nitrogen and a substitutional solute

Simple two-energy level models for ternary solid solutions containing a substitutional (u) solute and an interstitial solute (i) can be used to extract from thermodynamic data and energy needed to insert an i-atom into an interstitial site whose nearest neighbor shell of lattice atoms contains only one U-atom. However, such models are only valid, even in the high-temperature limit, when the U-concentration is small. It has been shown that such models can be extended so as to include all interstitial site types and that the energy parameters extracted from solutions dilute in the U-component may be used to predict the solubility of the i-component up to U-contentrations of more than 10 at.%.     

Thermal vibrations of atoms in equilibrium Al-Ag solid solutions

An expression is derived for the effective mean square amplitude of thermal vibrations of atoms in a crystal lattice for the case of a binary, substitutional, metallic solid solution. All the possible configurations in the first coordination shell are respected. The dependence of on the Ag content is measured at 525°C for an equilibrium solid solution of Ag in Al from X-ray data. The results show that the values of increase for both the Al and Ag atoms as unequal neighbours are added to the first coordination shell. The relation between the force constant and is also derived. By using this relation for our measurements it was shown that the force constants decrease in both Al and Ag atoms as the number of nearest neighbours of different kinds increases; it thus follows that the bonding forces between different kinds of atoms are smaller than between atoms of the same kind. We therefore suppose that this describes the tendency of the equilibrium solid solution to form local regions with increased concentration of identical atoms.In conclusion the author thanks Ing. J. Laek C. Sc. for very carefully carrying out the chemical analysis of the Al-Ag alloys and J. Bedná for exact measurements of the density in order to determine the homogeneity of the alloys. She also thanks Z. iký for help in the X-ray diffraction measurements.     

Structure and properties of Ti1 − x CrxSe2 substitutional solid solutions

Titanium diselenide TiSe₂ is doped for the first time with an acceptor impurity through substitution of Cr³⁺ ions for Ti⁴⁺ ions in the host lattice. The structure and electrical resistivity of the TiSe₂-based solid solutions are investigated in the vicinity of the compensation point, and the influence of the compensation point on the stability of the charge-density-wave state is analyzed. It is demonstrated that disorder in the guest sublattice does not lead to Anderson localization of charge carriers.     

Volume effects in the thermodynamics of binary substitutional solid solutions at high temperatures

Recent measurements of the variation with temperature and composition of the elastic properties of Fe-based solid solution containing the substitutional solutes Mn, Ni and Cr have enabled calculations to be made of the effect of the composition-dependent variation of the specific volume of the lattice upon the partial thermodynamic functions of the solute species. The calculations show that, in contrast to the case of binary interstitial solid solutions, the effects are of the same order, or less, as the normal uncertainty in the experimental determination of the partial thermodynamic functions of solid solutions at high temperatures (1273 K).     

Effect of pretreatment on microdeformation development in hcf polycrystals of substitutional solid solutions

The effect of small plastic deformation and subsequent free-state aging even under a load on microplastic deformation development in hcp polycrystals of substitutional solid solutions is investigated on Cu-Al and Cu-Ni alloys. It is established that in the temperature interval 77–300°K the effect of deformation pretreatment on subsequent microdeformation development is independent of the temperature at which it occurs, but is determined only by the temperature of secondary deformation. At the same time a clear correlation is observed between the change in the macroscopic elasticity limit and the shape of the microdeformation curve. If the macroscopic elasticity limit (σ″)after deformation pretreatment is larger than the friction strain (σ _F), the stress-strain diagram is a second-order parabola, as in the case of annealed alloys. If the macroscopic elasticity limit after deformation pretreatment equals the friction strain, the shape of the curveσ=f (?) changes considerably. A stage of plastic deformation, on which the linear dependence ofσ on ?_P is conserved, is observed on the stress-strain curves after the range of elastic deformation. The mechanism of microplastic deformation development in predeformed alloys is treated by the statistical theory of microdeformation of polycrystals.