Trigonal Lattice Research Articles

Dipole fields and electric-field gradients in their dependence on the macroscopic and microscopic crystal parameters for orthorhombic and hexagonal lattices. II

Lorentz factors ( L) at the lattice sites in simple orthorhombic lattices have been calculated by the method of Ewald and Born to a high degree of accuracy (error, either relative or absolute, 10 -11) and their dependence on the structure is discussed in terms of the difference between the actual Lorentz factor and the one belonging to the corresponding one- or two-dimensional structure. It turns out that L along the shortest axis of simple orthorhombic lattices can, even in not extreme cases of axis ratios, be described by a layer or chain picture, but for L corresponding to the middle axis a hybrid view is appropriate. The Lorentz coefficient is evaluated for simple rectangular lattices by applying the Ewald-Born method in two dimensions. Superposition considerations are used to treat the hexagonal and trigonal lattices and to correlate manganese nuclear quadrupole splittings with details of the crystal structure in K 2MgF 4:Mn.

Studies on Ag- Centers in Alkali Halides. I. Nature of Optical Transitions: KCl

A study was made on absorption and emission spectra of Ag - centers in KCl crystals. By inspecting the excitation spectra for emission, two new bands were found at 3.11 and 3.27 eV in addition to the previously known 4.36 eV absorption band. These three bands, named A , B , and C , are ascribed to transitions 1 S 0 → 3 P 1 , 3 P 2 and 1 P 1 respectively. Besides the 2.93 eV emission, another emission band was discovered at 4.08 eV. They are attributed to transitions 3 P 1 and 1 P 1 → 1 S 0 . Energy parameters and electron-lattice coupling constants specifying the configuration-coordinate surfaces were determined from the peak energies, second moments, and Stokes shifts of the observed spectra. Data on the degree of polarization suggest that a trigonal lattice deformation is dominantly realized in each of the relaxed 1 P 1 and 3 P 1 states. The shape of the C band and the ratio of life times for the 1 P 1 and 3 P 1 states are in reasonable agreement with theory.

Magnetic properties of the spinel system Fe 1− xCu xCr 2S 4

FeCr 2Si 4 and CuCr 2S 4 are found to form a series of solid solutions. Measurements of the temperature dependence of the magnetic susceptibility χ and of the saturation magnetization in the Fe 1− x Cu x Cr 2S 4 system reveal a complex transition from a ferrimagnetic spin ordering (FeCr 2S 4) to ferromagnetic interactions (CuC 2S 4). The Curie-Weiss law is only obeyed for small and large x. In the intermediate concentration range, 1 χ vs. T curves do not have any linear portions. The number of Bohr magnetons per molecule also changes nonlinearly with composition. In order to explain the experimental data, it is suggested that some of the chromium ions are in the low-spin state. This low-spin state can be caused by local trigonal lattice distortions around those chromium ions which have on one side next-nearest copper ions and on the other side next-nearest iron ions.

Sign of the Nearest-Neighbor Exchange Interaction and its Derivative in GdAs

The sign of the nearest-neighbor exchange interaction ${J}_{1}$ and its logarithmic derivative $\frac{\ensuremath{\partial}\mathrm{ln}{J}_{1}}{\ensuremath{\partial}r}$ has been determined for the intermetallic type-II antiferromagnet GdAs. The ${\mathrm{As}}^{75}$ nuclear-magnetic-resonance Knight-shift data in the paramagnetic state of GdAs were used to yield a value for the Curie-Weiss temperature $\ensuremath{\theta}\ensuremath{\simeq}\ensuremath{-}35\ifmmode^\circ\else\textdegree\fi{}$K. Combining this value with the N\'eel temperature ${T}_{N}\ensuremath{\simeq}25\ifmmode^\circ\else\textdegree\fi{}$K and using the molecular field theory gives ${J}_{1}=\ensuremath{-}0.08\ifmmode^\circ\else\textdegree\fi{}$K and ${J}_{2}=\ensuremath{-}0.40\ifmmode^\circ\else\textdegree\fi{}$K. The measurement of the sign of $\frac{\ensuremath{\partial}\mathrm{ln}{J}_{1}}{\ensuremath{\partial}r}$ in GdAs was performed using low-temperature x-ray powder-diffraction techniques in order to study the exchange-striction-induced trigonal lattice distortion for $T<{T}_{N}$. The observed trigonal distortion was found to be a compression along the [111] direction of the NaCl-type GdAs crystal structure. From the sign of the trigonal distortion, it is concluded that $\frac{\ensuremath{\partial}\mathrm{ln}{J}_{1}}{\ensuremath{\partial}r}$ is negative. Similar data for GdP suggest that $\frac{\ensuremath{\partial}\mathrm{ln}{J}_{1}}{\ensuremath{\partial}r}$ is also negative for this compound.

Dynamical Jahn-Teller Effect in Alkali Halide Phosphors Containing Heavy Metal Ions

Possible patterns of vibration-induced splitting in the absorption band of localized electrons in solid are investigated within the Condon approximation. The modes of lattice vibrations around the imperfection which give rise to the level splitting of degenerate excited states are classified into active and potentially active modes according as they cause the absorption band to split or not. The result is applied to the analysis of the absorption bands of Tl + - like ions in alkali halides. One can explain the triplet structure of the C band and the doublet structure of the A band with its temperature sensitive asymmetry, by introducing the coupling constant c between the p -electron and the trigonal lattice vibrations as a single adjustable parameter. The dependences of c upon the host alkali halide and on the charge of the impurity ion are explained by a point-charge plus point-dipole model for the neighboring halide ions.

Layer Structures of Magnetic Oxides

In most of the ferromagnetic oxides, the anion lattices are constructed by piling up two dimentional trigonal lattice layers in succession. Metallic ions locate on the proper interstices of these anion layers, forming themselves also several kinds of layers. It has been shown that the crystal lattices of these oxides can be constructed uniquely by assuming 1) the layer structures outlined above, 2) requirement of minimizing the sum of electrostatic energy and interionic repulsive energy and, 3) the numbers of cations locating between two neighbouring anion layers are all the same, e. g. equal to that corresponding to the molecular ratio notwithstanding that there may be several kinds of cation structures as such inter-layer cation arragements. From this consideration, 13 M–O–M configurations are derived as possible configurations acting for the superexchange interaction in magnetic oxides. It is shown that the magnetic lattices also have layer structures.

X-ray analysis of solid solutions

The atomic structure of solid solutions of copper-aluminium, aluminium-magnesium, and copper-nickel has been examined by the X-ray spectrometer. In each case it was found that the solute atom replaces an atom in the lattice of the solvent, the substitution being accompanied by a distortion of the lattice. A saturated solution of aluminium in copper shows that the aluminium expands the copper lattice from 3.60? to 3.65?. The effect of adding nickel to copper was to produce a contraction of the lattice, the contraction being approximately a linear function of the atomic percentage of either constituent. The addition of 8 per cent. magnesium by weight to aluminium causes the average parameter of the aluminium lattice to increase from 4.05? to 4.10?. The addition of 8 per cent. aluminium by weight to magnesium decreases the average parameter of the hexagonal lattice of magnesium from 3.17? to 3.15?, and increases its axial ratio from 1.63 to 1.66. An examination of the eutectic alloy of aluminium and copper showed that this alloy consists of a mixture of two distinct substances with different space lattices. The one substance being Cu Al2 and the other a substance, the space lattice of which could not be distinguished from that of pure aluminium. The intermetallic compound Cu Al2 was found to possess a simple tetragonal lattice of side 4.28? and axial ratio 0.562, the copper atoms being at the corners and the aluminium atoms at the centres of the four small faces. The atomic structure of the compound CuAl resembles that of a solid solution of aluminium in copper, but the distortion is considerably greater. The material was found to have a face centred trigonal lattice of side 3.89? and an angle between the axes of 94.6?, the 111 planes being composed alternately of aluminium and copper atoms.