F. W. de Wette

On the calculation of lattice sums

Synopsis A short and straightforward method for the conversion of slowly converging lattice sums into expressions with good convergence is presented. As an illustration a well-known expression for the Madelung constant is rederived. The method is then applied to two general types of lattice sums, the latter of which has not been treated before.

The internal field in dipole lattices

Synopsis The internal field for Bravais lattices of equal parallel dipoles having monoclinic and higher symmetry is evaluated. The electric field at a lattice point due to all the other dipoles in the lattice is given by a conditionally convergent sum. It is shown that, when considering a slab of dielectric material in a parallel plate condensor, this ‘dipole sum’ should be summed ‘plane-wise’ in order to obtain the correct contribution to the internal field. Rapidly converging expressions for this contribution are derived. For a simple cubic lattice the resulting expression for the internal field reduces, of course, to that of Lorentz.

The electrostatic potential in multipole lattices

Synopsis General expressions for the electrostatic potential in perfect multipole lattices are given as expansions in terms of spherical harmonics. The coefficients occurring in these expansions contain lattice sums of a general type, which have been treated previously. Such expressions are derived for a point charge lattice, a multipole lattice, and finally for a lattice built up from a number of different arbitrary charge distributions.

Surface Thermodynamic Functions for Noble‐Gas Crystals

Surface thermodynamic quantities have been calculated as functions of temperature between 0°K and the melting temperature for the (111), (100), and (110) surfaces of the noble‐gas solids Ne, Ar, Kr, and Xe. The method of calculation differs from the methods used in previous treatments of surface thermodynamic functions in that the atomic vibrations are taken into account, and the vibrational frequencies are properly calculated rather than obtained from a Debye model or an Einstein model. The quantities calculated are the static surface energy, vibrational surface energy, surface entropy, vibrational surface free energy, and surface specific heat. In addition, a surface frequency‐distribution function f8(ω) has been calculated; f8(ω) is positive at low frequencies, because of the presence of surface modes of vibration, and negative at higher frequencies. This behavior of f8(ω) produces a narrow peak in the graph of the surface specific heat as a function of temperature.

Lattice dynamics of the high-Tc superconductor La2−xMxCuO4

Abstract The phonon dispersion curves, the one-phonon density of states and the specific heat of the high-T c superconductor La 2− x M x CuO 4 have been calculated in the framework of a shell model. The zone center frequencies are classified according to their vibrational character and compared with the available IR and Raman data. A slight adjustment of the parameters obtained from the known interaction potentials of oxides with perovskite and rock salt structure yields reasonable agreement with the IR, Raman, specific heat, and inelastic neutron scattering data of the polycrystalline material.

Phonons in Nd2−xCexCuO4

We have measured far infrared reflection and Raman spectra on high quality single crystals and ceramic samples of the Nd2−xCexCuO4 system. The TO and LO frequencies of all infrared-active phonons were determined from a Kramers-Kronig analysis of the infrared reflection spectra. The frequencies of the detected Raman-active phonons are 228 cm−1 (A1g Nd), 328 cm−1 (B1g O2) and 480 cm−1 (Eg 02). A resonantly enhanced peak at 580 cm−1 is observed for Ce-doped samples only with polarization properties like an A1g phonon. We have also performed lattice-dynamical calculations with parameters extracted from those of perovskites and metallic oxides. The frequencies obtained agree well with our experimental findings. We present the eigenvectors of all zone center phonons. Finally, we also detected a feature at 165 cm−1 in the ab-polarized infrared spectra in Nd2CuO4 which might be of magnetic origin.

Surface relaxation and thermal expansion for the (001) face of α-Fe and Cu

Abstract The surface relaxation and the near-surface enhancement of thermal expansion have been calculated for the (001) face of a bcc crystal, α-Fe, and an fcc crystal, Cu. The calculations make use of the anharmonic perturbation formalism of Dobrzynski and Maradudin; the results for certain equal-time vibrational correlation functions which arise in this formalism are also presented. The crystal potential is described in terms of several kinds of short-range empirical interatomic potentials, such as have been used in studies of defects in bulk; in the near-surface region, the effects of surface redistribution of the electron distribution are modelled by the addition of a simple surface Madelung (SSM) force. The effect of the SSM force is to limit severely the usual outward relaxation driven by short-range interatomic potentials. For Fe(001), the five and one-half percent outward static relaxation driven by the short-range potentials acting alone is changed to a one percent inward static relaxation when the SSM force is incorporated; for Cu(001), the comparable change is from a one percent outward relaxation to a one-half percent outward relaxation. On the other hand, the SSM force makes only a small effect on the surface-enhanced thermal expansion coefficients (STEC) for interplanar spacings. The STEC for the outermost spacing is between 2.5. and 3.0 times of that for the bulk at the Debye temperature for both Fe(001) and Cu(001); for the second interplanar spacing, the STEC is smaller than 1.5 times of that of the bulk at the Debye temperature. The ratios of the near-surface mean-square amplitudes (MSA) to those of the bulk at high temperatures are, for Fe(001), about 1.75 for z -components (normal to surface) and 1.55 for x -components (parallel to surface) in the surface layer; for Cu(001), about 1.95 for z -components and 1.30 for x -components. The interplanar correlation functions, while smaller than the MSA on an absolute scale, do show considerable surface-enhancement, particularly for the zz -compoments. For example, the zz -correlation between an atom in the outermost layer and its nearest neighbor in the next layer is nearly twice the comparable bulk correlation above the Debye temperature for both Fe(001) and Cu(001).

Tunneling phonon structures and the calculated phonon density of states for Bi2Sr2CaCu2O8

Abstract The spectral function of the electron–phonon interaction, determined by a tunneling experiment, is compared with a calculated phonon density of states. The agreement between them is considerable. For each peak in α 2 F , atomic displacements of the corresponding phonon modes at particular points in the Brillouin zone are shown. Of these, vibrations of oxygen atoms along a c -axis and low-frequency cation vibrations are noteworthy.

Distribution of surface phonon branches in RbF and RbCl

Abstract Predictions based on a realistic (shell) model are presented for the surface phonon branches of (001) surfaces of RbF and RbCl, RbF being the rocksalt-structure alkali halide having the largest gap between optical and acoustical frequencies in the bulk. The gap structure within the bulk bands is clarified, and new branches of LO and TO surface modes are found. Some caution is urged in the inference of details of surface mode existence based on the surface excess distribution of frequencies.

Effects of atomic polarization in ionic crystals

The effect of higher order atomic polarizations on the cohesive energy of ionic crystals is treated on the basis of a model according to which the crystal consists of polarizable non-overlapping electrostatic charge distributions. By means of methods developed in previous papers, the multipoles induced in the atoms by the crystalline field are calculated in a self-consistent way. A general formula for the effect of these polarizations on the cohesive energy of ionic crystals is derived and numerically evaluated for the crystals of KCl, KI, CsCl and CsI.