CaF2 Structure Research Articles

Hund's basic potential from direct summation

The Coulomb potential at points inside NaCl and CsCl structures was calculated previously by a method of direct summation. This method consists, simply, of adding all the Coulomb potentials, at the point of consideration, due to the point charges of the ions in a piece of the crystal. The shape of the piece of crystal should be determined correctly. Although this method succeeded when applied to NaCl and CsCl structures, it failed when applied to ZnS, CaF2, and Cu2O structures; the reason is that the last three structures lack a certain type of symmetry. However, a hypothetical structure H was constructed such that this method succeeded when applied to it. Moreover, Hund's basic potential can be expressed in terms of the potentials of H and CsCl by a simple relation derived from Hund's identity. Thus, Hund's basic potential was computed at a grid of points of intervals a/16 and tabulated. The potential inside all structures having the cubic Bravais lattices as components can, therefore, be computed easily from this table.

Electric Fields Produced in Cubic Crystals by Point Defects.

Charged point defects in crystals polarize the surrounding ions. These induced dipoles contribute to the electric field in the crystal. In this paper, lattice sums for the calculation of this contribution are given for the NaCl, CsCl, CaF2, and ZnS structures. Various positions for the defect are chosen, and the field evaluated near lattice sites in the vicinity of the defect, with radial (with respect to the defect) displacements of ± 20 percent of the cation-anion distance allowed away from each lattice site. The lattice sums are expressed in power series, including terms up to cubic in the displacements, and the coefficients tabulated.

Study of Erbium Thin Film Oxidation in the Electron Microscope

AbstractThis paper describes the formation of suspect ErO single crystals during erbium evaporation onto NaCl in ultrahigh vacuum (10−8 Torr); and a unique twinning phenomenon in these f.c.c. NaCl‐type crystals (a = 5.12 Å) is observed by electron microscopy. The oxidation of thin erbium foils (650 Å thickness) directly within the electron microscope by double condenser beam heating of selected areas and the sequential recrystallization and growth of the completely oxidized erbium (Er2O3) are investigated. It is shown that the Er2O3 films have a b.c.c. structural characteristic with the unit cell defined by a vacancy defect CaF2 structure composition possessing the T5 (I213) space group for a = 10.55 Å. Er oxidation in the electron microscope at a background pressure of roughly 10−4 Torr appeared to be logarithmic, and presumably lattice diffusion controlled.

High‐Temperature X‐Ray Diffraction Investigation of the Uranium‐Carbon System

The system UC‐UC2 was investigated at temperatures to 2200°C. utilizing high‐temperature X‐ray diffraction techniques. UC2, which has the CaC2 structure, was shown to transform to the CaF2 structure at 1820°C. Mean coefficients of expansion of UC, U2C3, and UC2 were determined. The decomposition of U2C3 to cubic UC2 and to UC saturated metastably with carbon was observed. Solubilities of UC in UC2 and UC2 in UC were determined near 1800°C. by a method based on lattice‐parameter measurements. The formation of, and existence conditions for, U2C3 were confirmed. It was observed that UC2 tends to decompose toward UC at the extreme temperatures, probably by loss of carbon to CO.