Interplanar Interactions Research Articles

Molecular Calculations of Interplanar Electronic Interactions in a Ybacu2O6+δ Cluster as a Function of the Oxygen Concentration.

ABSTRACTMolecular ab initio SCF calculations on a cluster formed by Y, Cu(2)-O(2)-O(3) plane, Ba-O(1) plane and Cu(1)-O(4) chains are reported. The computations were performed for five different sets of lattice parameters of YBACu2O6+δ Each of these sets correspond to a values of the oxygen stoichiometry. Mulliken population analysis results show a charge transfer to the Cu(2)-O(2)-O(3) plane when the oxygen stoichiometry is increased from six to seven.

Theory of the successive magnetic phase transitions in tetragonal RBa2Cu3O6+xcompounds

A theory based on the analysis of a Landau-type free energy is presented to explain the variety of unusual magnetic phase transitions recently observed in tetragonal RBa2Cu3O6+x compounds with R=Y, Nd. The results show that up to three successive transitions can occur that involve antiferromagnetic orderings of the Cu ions. The number of transitions predicted to occur depends on a delicate interplay among weak inter-planar exchange interactions. Oxygen content is expected to be the principal factor in determining this balance of exchange forces.

Nonequilibrium phonon effects on hot carrier transport and thermal noise in semiconductor heterostructures

Hot carrier steady state and transient transport in bulk semiconductors and heterostructures is analyzed here using a general balance equation formulation with nonequilibrium phonon occupation and an ambient magnetic field of arbitrary strength. Carrier-carrier Coulomb interactions are also incorporated dynamically, and for superlattices both intraplanar and interplanar interactions are included. We have also examined the thermal noise temperature for hot electrons at a nonzero bias.

Theory of Interplanar Interaction in Metals of Close-Packed Structures on Free Electron Model

Interplanar interactions between the hexagonal net planes in close-packed metals are discussed as a function of the electron-atom ratio on the same model that Blandin et al. used. Now the expansions are done to second order, whereas those by Blandin et al. are only to first. The second order asymptotic expansions show that the anomaly in the interplanar interactions at ≈1.140, found by Blandin et al. , disappears. These expansions are applied to evaluate approximate values of the stacking fault energy, γ SF , and the difference Δ U HF in the binding energies between HCP and FCC lattices. Comparisons of these values with those accurately calculated show that the second order expansion is a good approximation. The approximate relation γ SF ≈2 N p Δ U HF holds in =1.0∼1.2, where N p is the density of lattice points on the net plane.

Calculation of Stacking Fault Energy by Use of Long-Range Interionic Potential. II. Asymptotic Expansion for Interplanar Interaction

Following the preceding paper I, the formation energy of an intrinsic stacking fault, γ SF , in an fcc metal is calculated as a function of the electron-atom ratio, ( e / a ), in a range from 0.9 to 4.1 for the interionic potentials of the forms V P cos sin (2 k F r )/(2 k F r ) m with m =3, 4 and 5. In the calculation, the interplanar interactions are asymptotically expanded to the third order. The asymptotic expressions show that the Blandin-Friedel-Saada anomaly at ( e / a )≈1.140 is derived only from the expansion of the first order, and that the anomaly vanishes when we expand the asymptotic expressions to higher orders. Good accuracy in the calculation is confirmed by comparison of the binding energies of fcc and hcp lattices calculated from the interplanar interactions by the use of the Ewald-Fuchs method. Analytic expressions are given for the lattice sums appearing in the calculation of γ SF .

PHONONS IN ALKALI GRAPHITE INTERCALATION COMPOUNDS

The (001)L phonon branches of alkali-graphite intercalation compounds C/sub x/M (x = 8, 24, 36; M = K, Rb, Cs) have been measured by means of inelastic neutron scattering experiments. In all cases the phonon branches show zone folding effects, due to the enlarged unit cell as compared to pristine graphite, along with opening of frequency gaps at the center and boundary of the Brillouin zone. All measured (001)L phonon dispersions are describable by one-dimensional shell models with different masses and force constants to account for the graphite and alkali area-mass densities along the c-axis and their interplanar interactions.

Coherent twin boundaries and interatomic potentials in b.c.c. metals

Abstract The structure of the coherent {112} twin boundary has been computed using interplanar interactions for lithium. Two stable configurations with almost the same energy were found. It is shown that the existence of these two configurations is a consequence of the relatively simple form of the interactions between atomic rows parallel to . This behaviour of atomic forces is common to b.c.c. simple metals. It is further considered whether modifications of these results may be expected when phenomenological potentials, usually used to describe transition metals, are employed.

Spin-wave theory of the nearly two-dimensional ferromagnet (C 3H 7NH 3) 2CuCl 4

A renormalized spin-wave theory is developed for the layer-type ferromagnet (C 3H 7NH 3) 2CuCl 4. In contrast with the case of K 2CuF 4, the main perturbation to the isotropic intralayer exchange interaction leading to three-dimensional long-range order is here the anisotropy in the intraplanar interaction. An analytical expression for the magnetization of the two-dimensional Heisenberg ferromagnet with a weak anisotropy in the intraplanar exchange as well as interplanar interactions has been obtained. It is shown that an excellent agreement between theory and experiment can be obtained using the interaction constants estimated in previous investigations, and further that the spin-wave interactions have a significant effect on the temperature dependence of the magnetization.

Why are the close-packed structures of the noble metals cubic?

It is shown that the method of Blandin, in which the energy difference between various close-packed metallic structures is expressed as the sum of interplanar interactions, is not restricted to non-degenerate second order perturbation theory. If the latter theory is applied to the case of the noble metals, assuming one valence electron per atom, the hexagonal close-packed structure is calculated to be stable, whereas the face-centered cubic structure is found experimentally. The result is not improved, if one includes in the theory the estimated influence of the dependence of the pseudopotential matrix elements on scattering vector and - angle. However, if the interplanar interactions are calculated numerically with the help of degenerate perturbation theory (2 OPW approximation for the one-electron energy levels) results in agreement with the experimental data are obtained. The improvement can be ascribed to the fact that allowance is made for the deformations of the Fermi sphere by the perturbation. The results of degenerate and non-degenerate perturbation theory agree with each other at valence electron concentrations exceeding 1.5 electron per atom, provided that an exponential “smearing” factor is inserted in the formulas of the non-degenerate second order perturbation theory.

Theory of the antiferroelectric transition in copper formate tetrahydrate

The basic dimer model for copper formate tetrahydrate has been extended recently by Ishibashi, Ohya and Takagi (1973) by adding mean-field interactions to account for both interplanar and further-neighbour intraplanar interactions. However, the present use of exact calculations for the basic model gives substantially different values for the interaction strengths when compared with the Bethe approximation for the basic model used by these workers. The calculation is extended to include the electric field and obtain a phase diagram with four phases, all separated by first-order phase lines. Although the dielectric data can be fitted reasonably well with this model, it is impossible to obtain agreement with the experimental latent heat and the discontinuity observed in the specific heat. The calculations support the idea that the transition in Cu(HCOO)2.4H2O is primarily two dimensional, because the ratio of the interplanar to intraplanar interaction is about 10-3.

Neutron scattering investigation of magnetic excitations in CoCl2

Neutron scattering has been used to investigate the energy dispersion relation of spin waves in CoCl2 at temperatures between 4.4 K and 34 K. CoCl2 orders antiferromagnetically at TN=24.9 K with the Co2+ spins lying within ferromagnetic planes which are antiferromagnetically stacked along the hexagonal c axis. The interplanar exchange interactions are much weaker than those within the planes, giving rise to the 'metamagnetic' property of ferromagnetic saturation in relatively weak magnetic fields, and suggesting that above TN there could be correlations between spins appropriate to a two-dimensional ferromagnet. The observed spin waves at low temperature indeed only exhibit strong dispersion within the basal plane and measurement of this dispersion enables an accurate value for the nearest-neighbour exchange constant to be determined.

System Exhibiting a Critical Point of Order Four: Ising Planes with Variable Interplanar Interactions

System Exhibiting a Critical Point of Order Four: Ising Planes with Variable Interplanar Interactions

Behavior of Helical Spin Structures in Applied Magnetic Fields

The problem of the behavior of helical spin structures and the phase transitions they exhibit in applied magnetic fields is studied theoretically. We have obtained a numerical solution valid for the planar helix at $T=0$ \ifmmode^\circ\else\textdegree\fi{}K with an arbitrary number of interplanar exchange interactions, an arbitrary form of in-plane anisotropy, and an external magnetic field applied in the plane. We calculated the phase diagram for the case of two interplanar exchange constants and no anisotropy, and found different behavior in the intermediate field region from that predicted by the previous theory. As a new result, in the case of an in-plane anisotropy, the angle dependence of the transition fields has been obtained.

Numerical Solution of the Behavior of Helical Spin Structures in Applied Magnetic Fields

The behavior of helical spin structures and the phase transitions they exhibit in applied magnetic fields are studied theoretically.1 Approximate solutions have been developed in the cases of high and low fields.2 We have obtained a numerical solution valid for the case of the planar helix with an arbitrary number of interplanar exchange interactions, an arbitrary form of in-plane anisotropy, and an external magnetic field applied in the plane. We calculated the phase diagram for the case of two interplanar exchange constants and no anisotropy in order to compare with the previous theory and found different behavior in the intermediate field region. As a new result in the case of an in-plane anisotropy the angle dependence of the transition fields has been obtained.

Theory of Phonon Dispersion Curves in Silicon Carbide Polytypes

A theory is presented to explain fine-structure-dependent details in the phonon spectra obtained by Raman scattering measurements on silicon carbide polytypes, using the method of interactions between planes or atoms. Doublets of small energy splitting represent discontinuities in the dispersion curves within the large zone and are analogous to the band gaps appearing in nearly free-electron band structures. They give a measure of the range of interplanar interactions and of small energy differences between polytypes. These results are used to comment qualitatively on the relative stability of silicon carbide polytypes. The theory also accounts satisfactorily for the infrared (ir) strengths of the weak modes observed in these structures.

Some Critical Properties of Quantum-Mechanical Heisenberg Ferro-and Antiferromagnets

High-temperature expansions of the staggered susceptibility for the Heisenberg antiferromagnet are analyzed for two-dimensional lattices. The evidence favoring a divergent staggered susceptibility χ̃ is found to be essentially as strong as that presented earlier in support of a divergent susceptibility χ for the two-dimensional Heisenberg ferromagnet. Thus the very recent experimental and theoretical findings which favor a phase transition in various ``planar antiferromagnets'' (or materials with the K2NiF4 structure in which the intraplanar interactions may be as much as 105 times stronger than any interplanar interactions) would appear to be supported by the series expansions. We also consider the question of the dependence of the susceptibility exponent γ[χ∼(T-Tc)−γ] upon spin quantum number S for three-dimensional lattices. The previously proposed behavior must definitely be revised in the light of additional terms in the expansions and the availability of more refined extrapolation procedures. Here we argue (a) that γ(∞)=1.38±0.01 and (b) that γ(S) does not appear to jump, for S finite, to 1.43 (its presumed value for S=½).