Vacancies in binary alloys: II. Equilibrium concentration of vacancies in alloys with long-range order

General formulae are presented for the equilibrium concentration of vacancies in binary alloys having two types of lattice sites. The simple model used takes in account the pair interaction between nearest neighbouring atoms. The formulae derived in this paper yield in special cases identical results as the precedent theories.     

Reaction of different types of attractive dislocations in alloys with long-range order

The strength of junctions is calculated arising from the reaction of attractive superdislocations of the primary glide system with a tree of the forest, and from the reaction of a single glide dislocation with a superdislocation of the secondary glide system. The calculated strength and stability of the junctions are compared with the strength and stability of junctions formed between attractive trees in fcc metals, and superdislocations in an LI₂ superstructure.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 108–113, May, 1976.     

Absence of long-range order with long-range potentials

A particular form of Mermin's inequality is analyzed for repulsive inverse power potentials [V(r)=e ² r ^–m/m] in ad-dimensional space. For long-range potentials (m d) the system is put into a stabilizing background. Long-range order is shown to be excluded ford (m + 2)/2 whenm d, while for short-range potentials (m > d) we recover Mermin's result (d 2). For Coulomb systems (m=d – 2) and the experimentally studied electron surface layer (d = 2,m=1), long-range order cannot be excluded by the present argument.     

Impurity-impurity interactions in dilute alloys

The interaction between impurities of two solute elements in metal hosts leads to a non-random distribution of impurity atoms among the lattice sites. Experimental studies of this distribution provide quantitative information on the energy involved in the formation of an individual impurity-impurity pair. It is shown how this energy can be extracted from PAC and Mössbauer spectra. A review of the experimental results for several metallic matrices is given. The binding energy of the impurity-impurity pairs is discussed in terms of a correlation with the heat of formation for corresponding alloys.     

Configurational energies of different A7B types of the long-range order in Fe-Si alloys

In order to examine the existence of the long-range order of A₇B types in Fe-Si alloys with composition less than 12·5 at.% Si, the configurational energies of several superstructures in b.c.c. alloys with the cubic elementary cell having the lattice parameter 2a are calculated on the basis of a simple model with a pairwise interaction between atoms extending to the third neighbours. From the proposed model it follows that the superstructure of A₇B type suggested byFallot can be expected if the interaction parameter for the third neighboursv ₃>0. On the other hand, the two-phase structure (DO₃ order and pure Fe) will be favoured by the alloy crystal ifv ₃<0.The author is indebted to Dr. F.Kroupa and Dr. A.Gemperle for stimulating discussions.     

The formation of an ultrafine-grained structure in long-range order metals and alloys subjected to phase transformations and irradiation

The generation of an ultrafine-grained structure in long-range order metals and alloys by phase transformations and ion irradiation is studied. It is shown that the structure of pure iridium can be significantly refined under certain regimes of ion irradiation, and a microduplex structure possessing high mechanical properties can be produced in binary and ternary alloys, combining the processes of atomic ordering, aging, and phase recrystallization.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 81–89, August, 2004.     

Atomic displacements in bcc dilute alloys

We present here a systematic investigation of the atomic displacements in bcc transition metal (TM) dilute alloys. We have calculated the atomic displacements in bcc (V, Cr, Fe, Nb, Mo, Ta and W) transition metals (TMs) due to 3d, 4d and 5d TMs at the substitutional site using the Kanzaki lattice static method. Wills and Harrison interatomic potential is used to calculate the atomic force constants, the dynamical matrix and the impurity-induced forces. We have thoroughly investigated the atomic displacements using impurities from 3d, 4d and 5d series in the same host metal and the same impurity in different hosts. We have observed a systematic pattern in the atomic displacements for Cr-, Fe-, Nb-, Mo-, Ta-and W-based dilute alloys. The atomic displacements are found to increase with increase in the number of d electrons for all alloys considered except for V dilute alloys. The 3d impurities are found to be more easily dissolved in the 3d host metals than 4d or 5d TMs whereas 4d and 5d impurities show more solubility in 4d and 5d TMs. In general, the relaxation energy calculation suggests that impurities may be easily solvable in 5d TM hosts when compared to 3d or 4d TMs.      

Magnetoelastic effects in dilute magnetic alloys

Ultrasonic studies of $\text{Cu}$Mn, $\text{Au}$Mn and $\text{Au}$Fe alloys where the concentrations of the transition metal ranges between 1 and 10% show that the longitudinal sound velocity has a marked field dependence at temperatures below the peak in the magnetic susceptibility and a negligible field dependence above it. This suggests that there may be an ordered magnetic state in these alloys.     

Hall effect in dilute magnetic alloys

We review the theory and the experimental results on the Hall effect in noble metals containing magnetic impurities of transition metals. In order to illustrate the various types of observed effects, we focus succesively on selected systems: $\text{Cu}$Mn, with only enhancement of the ordinary Hall effect due to the existance of different spin-up and spin-down currents; $\text{Au}$Fe and $\text{Au}$Cr, with skew scattering by magnetic impurities; $\text{Cu}$MnT ternary alloys (where T is a non-magnetic impurity), with skew scattering effects due to combined spin—orbit scattering by non-magnetic impurities and spin scattering by Mn impurities. The skew scattering in $\text{Au}$Fe and $\text{Au}$Cr can be ascribed to the orbital character of the impurity moments and accounted for in an orbitally degenerate virtual bound state model. However, the anomalous temperature dependence of the skew scattering in Kondo alloys at low temperature is not well understood. We also present some magnetoresistance data in order to describe the links between the Hall effect and the magnetoresistance in magnetic alloys. In particular, we relate the skew scattering and the magnetoresistance anisotropy observed in $\text{Au}$Cr alloys.     

Spin correlation in dilute magnetic alloys

The correlation of a magnetic impurity spin with the spin density of the conduction electrons in a dilute magnetic alloy is calculated non-perturbationally on the basis of the Nagaoka theory. It is shown that there are anomalies due to the Kondo effect in the long range behaviour of this correlation which contradicts the bound state interpretation of the Kondo effect. The most interesting detail is the appearance of a non-oscillating contribution to the correlation.     

Bimodality and long-range order in ideal Bose systems

The cluster expansion for the classical and the quantum canonical partition function are related to the Bell polynomials. This observation is exploited in derivation of a set of recursion relations that render tractable numerical evaluation of quantities such as mean cluster size distributions and pressure isotherms. The exact volume dependences of properties of an ideal Bose gas are calculated under periodic boundary conditions. Numerical calculations with volume-independent cluster integrals show bimodal distributions in the mean cluster weight for two- and three-dimensional ideal Bose gases at sufficiently low temperature and high density. The variation of the size at which the liquid (condensate) peak appears indicates that the liquid clusters are macroscopic in macroscopic systems. The similarity between the Bose-Einstein condensation and the solgel transition in nonlinear chemically polymerizing systems is discussed. When the exact volume dependence of the cluster integrals is taken into account, the mean cluster weight distribution becomes chair shaped rather than bimodal and displays no diagonal long-range order in the canonical ensemble. The Kac density for an ideal Bose gas implies that in the canonical ensemble the Ursell function satisfies a cluster property in the limit in which the coordinates of the particles are widely separated.