Relative stability of f.c.c. and b.c.c. structures for model systems at high temperatures

Summary Free-energy, entropy and volume differences between face-centered and body-centered cubic structures have been evaluated for model rare gas and alkali metal crystals by using the method of overlapping distributions. Stable phases are predicted in agreement with the behaviour of real materials in the regions of validity of classical mechanics and in agreement with the results of previous dynamical-simulation studies of crystal nucleation from the melt and of polymorphic transformations. The existence of a stable b.c.c. phase at high pressure and temperatures is predicted in this way for Lennard-Jones solids, while no high-pressure f.c.c. phase is expected for model Rb and Cs systems. We also show the possibility of making calculations of free-energy barriers to displacive crystalline transformations along a prescribed trajectory in configuration space. Work supported by the U.S. Department of Energy, Istituto per la Ricerca Scientifica e Tecnologica, Trento, and Gruppo Nazionale di Struttura della Materia del C.N.R., Italy.     

Electronically induced lattice instabilities in b.c.c. Zr

Electronically induced lattice instabilities in metals are discussed by means of an accurate determination of the generalized susceptibility function, χ(q), from a KKR band structure and Fermi surface determined for b.c.c. Zr. We describe how the detailed behavior of χ(q) for b.c.c. Zr may be related to the omega phase upon alloying with Nb or upon application of pressure to the b.c.c. lattice.     

h.c.p.-f.c.c. phase transition in solid parahydrogen

The difference of free energies for the h.c.p. and f.c.c. parahydrogen is calculated as a function of molar volume. It is shown that the observed transition in solid parahydrogen¹ can be explained by differences in the structure of the cubic and quartic anharmonic terms.     

Sessile splitting of screw dislocations in b.c.c. metals

The energies of six different sessile splittings of screw dislocation 1/2 [111], which can occur in b.c.c. metals assuming the stacking faults on {110} and {112} planes according to the hard sphere model, are compared. The regions of the values of stacking fault energies on {110} and {112} planes, in which a given splitting is favoured over the other five, are then shown.     

Angular forces in the lattice dynamics of b.c.c. metals

The lattice dynamics of the b.c.c. lattice has been investigated using the central and the angular forces which are in general rotationally invariant. It has been observed that the four force constants are related to three elastic constants only. Dispersion curves for sodium were calculated and were found to be in excellent agreement with experiment.     

The effect of hydrogen on the superconducting and structural properties of b.c.c. Nb-Ru alloys

The superconducting transition temperature (T_c) has been measured before and after the introduction of hydrogen into Nb_(1?x)Ru_x$\text{(0.20?x?0.33)}$. In all cases, the presence of appreciable amounts of this interstitial component led to a sharp increase in the T_c. All the evidence suggests that conversion of the host metal lattice to f.c.c. is necessary for the appearance of the elevated T_c.     

A model for the lattice dynamics of b.c.c. transition metals

Recent ideas proposed by Fielek for the lattice dynamics of f.c.c. noble and transition metals have been extended to b.c.c. transition metals. Phonon dispersion curves, calculated on the basis of this model, for chromium are in fairly good agreement with experimental ones and are far better than those reported so far.     

B.c.c.-f.c.c. allotropy, F-bands,and metallization in xenon and krypton

APW-Xα calculations of a f.c.c.-b.c.c. phase transition in Xe prior to metallization give P ? 950 kbar, contrary to the 820 kbar result of Hama and Matsui; their use of non-touching APW spheres (f.c.c.) may be the crucial difference. Hartree-Fock plus correlation calculations in Kr indicate that f-bands play no role in rare gas crystal metallization.     

Peierls-Nabarro model of planar dislocation cores in b.c.c. crystals

Planar dislocation cores on {110} and {112} planes in b.c.c. crystals are studied using the Peierls-Nabarro model with force laws derived from four different interatomic potentials. A numerical iterative method suitable for solution of the Peierls-Nabarro equation is developed. The cores are represented by a continuous distribution of dislocations. The discussion of the correlation between the force laws and corresponding dislocation densities is based on the properties of the Hilbert transform.     

Mean-square atomic displacements in f.c.c. crystals

The mean-square displacements of volume atoms, surface atoms and atoms near a vacancy are calculated for f.c.c. metals and rare gas solids, using a simple series expansion of the Wallis formula. We employ a model with rotationally invariant bond bending forces, unlike the de Launay model used by Masri and Dobrzynski. For atoms near a vacancy and for rare gas solids this method has been applied for the first time. The calculations are done to the R⁴ term in the expansion. The inclusion of the R⁴ term together with temperature-dependent elastic constants give results which are in better agreement with experiment. For rare gas solids Lindemann ratios calculated by this method agree closely with the values obtained from elaborate computations as well as those deduced from entropy data. The present calculation also supports the view that the melting of solids is initiated at the crystal surfaces and in the neighbourhood of vacancies.     

Orientation dependence of screw dislocation motion in b.c.c. transition metals

A tight-binding type electronic theory is used to calculate the Peierls stress of the screw dislocation in b.c.c. transition metals. The repulsive core-core interaction energies are simulated by Born-Mayer type potentials as well as the modified Born-Mayer potentials. It is shown that there are essential differences in the orientation dependence of the screw dislocation motion among the transition metals, in agreement with experiments.     

Binding energy of a hydrogen impurity in an f.c.c. lattice

Hydrogen impurities in f.c.c. lattices, Pd metal for example, can occupy two interstitial sites, with tetrahedral or octahedral symmetries. Using the Husimi cactus to represent the f.c.c. lattice and two clusters to describe the two different interstices, we calculate the densities of states and the occupation numbers at the impurity site and on its nearest neighbours. The binding energies are calculated and plotted against the hopping integral between the hydrogen and its neighbours (t_a). We found that the octahedral site is the stable one for values of t_a from 0 to 1.5 eV.     

Interatomic forces in the b.c.c. transition metals

Using information obtained from X-ray scattering data, a model for the charge density in the transition metals is constructed. In this model the charge density is given by the sum of the charges situated at the ionic and bond centre sites. Within this framework, expressions for the second order elastic constants and the phonon frequencies in the cubic transition metals are obtained. These quantities have been calculated with and without the bond charge contributions for iron. The comparison with the experimental results shows that the introduction of bond charges, and hence angularity in the force-fields, in iron leads to distinctly better agreement with experiment. From a study of the elastic constants of the other b.c.c. transition metals some observations as to the nature of the angular force fields are made.     

Hall effect studies in ytterbium through the f.c.c.-h.c.p. transformation

The Hall coefficient (R_H) of polycrystalline Yb showing the f.c.c.-h.c.p. transformation has been determined at 20 koe in the range 1.8–420°K. Both the structural and the associated magnetic transformation would separately be expected to modify R_H, but the evidence suggests that the observed behaviour through the transition arises primarily from the effects of the change in structure. A more detailed interpretation is presently not possible, however, because of the lack of knowledge of the band structure of h.c.p. Yb.     

On the equivalence of angular force for lattice dynamics of b.c.c. metals

All angular force models developed for the study of lattice dynamics of b.c.c. metals are bound to give identical results. The recent model of Rani and Gupta is not an exception from this rule.     

Optical properties and electronic structure of simple cubic and f.c.c. T1I

T1I-layers with simple cubic and f.c.c. structure have been prepared by evaporation of CsI and RbI. The optical absorption spectra of these layers have been measured for the first time and are shown to be very similar to those of simple cubic and f.c.c. T1C1 and T1Br, respectively. Relativistic band-structure calculations explain the optical spectra as well as these similarities.     

A re-examination of the induction (crystal field) energy contribution to the relative stabilities of the f.c.c. and h.c.p. rare-gas crystal structures

A new calculation of the induction (crystal field) energy of the f.c.c. and h.c.p. structures of the rare-gas crystals of neon and argon gives an energy in favour of f.c.c. which is more than sufficient to counter the summed pair-potential which favours h.c.p. Predicted values of (E _f.c.c. - E _h.c.p.)/E _f.c.c. for neon and argon are 0·9 × 10^-3 and 1·3 × 10^-3 respectively. These values are similar to those that have been obtained for a modified dispersion energy and it is concluded that they should be added to these dispersion energies. Calculations on solid helium show a negligible difference in the induction energy for the two close-packed structures.     

The anisotropy of conductivity of n-type germanium in strong d.c. fields

The electric conductivity ofn-type germanium at large d.c. field intensities has been measured in three directions of symmetry of the cubic lattice. From these data the repopulation of valleys of the conduction band has been determined. Measurements were done with three materials of different purity. The variation of repopulation between these materials can be explained qualitatively by the influence of Coulomb scattering at ionized impurities. The data are compared with those ofNathan and theoretical data ofFranz andReik et al. The relations of these data to those of the current component perpendicular to the field direction (Sasaki et al.) are also given.     

Strengthening at nanoscaled coherent twin boundary in f.c.c. metals

This paper analyses slip transfer at the boundary of nanoscaled growth twins in face-centred cubic (f.c.c.) metals for strengthening mechanism. The required stress for slip transfer, i.e. inter-twin flow stress, is obtained in a simple expression in terms of stacking fault energy and/or twin boundary (TB) energy, constriction energy and activation volume. For nanotwinned Al, Cu and Ni, inter-twin flow stress versus twin thickness remarkably shows Hall–Petch relationship. The Hall–Petch slope is rationalized for various reactions of screw and non-screw dislocations at the TB. Additionally, strengthening at the boundary of nanoscaled deformation twins in f.c.c. metals is analysed by evaluating required twinning stress. At small nanograin size, the prediction of deformation twin growth stress shows inverse grain-size effect on twinning, in agreement with recent experimental finding.