L-Fuzzy子格群的若干刻画

在L是完全分配格时，讨论L-Fuzzy子格群的一些特征性质。特别地，借助L—Fuzzy集的几种水平截集给出它的若干刻画。最后给出这些刻画的一个应用。     

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, “weak” or “strong”, interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular ,are found to be robust against these perturbations. Received: 7 October 1997 / Accepted: 19 November 1997     

K_3Dy(PO_4)_2晶体的生长

二磷酸钕钾作为新型的化学计量比激光材料已有报导.由于二磷酸稀土钾盐具有独特的结构性质,即PO_4四面体与LnO_7十面体的相互隔离,使Ln~(3+)-Ln~(3+)之间的相互作用减少,荧光猝灭较小,以及在磷酸盐晶体中有较高的热稳定性,因而引起人们的关注.对K_3Ln(PO_4)_2(Ln:Pr,Nd,Sm,Gd)晶体的生长、结构和光谱已进行了深入的研究,但是Tb-Lu的稀土二磷酸钾盐晶体由于难以生长,至今未见报导.本文参照K_3Nd(PO_4)_2晶体的生长方法,用助熔剂缓冷法从KCl-KF熔体中生长出K_3Dy(PO_4)_2晶体.工艺过程如     

Lattice imperfection studies in polycrystalline materials by x-ray diffraction line-profile analysis

This review concerns our recent investigations with a series of binary fcc Ag- and Cu-base alloys (viz Ag-Ga, Ag-Ge, Ag-Al and Cu-Ga, Cu-Ge) from detailed analyses of x-ray diffraction line profiles, the importance of which has been briefly summarized. The theoretical formulations of the Warren-Averbach’s method of Fourier analysis of peak-shapes along with the methods of peak-shift and peak-asymmetry have been outlined. A preview on the significant studies carried out earlier with Ag- and Cu-base (fcc) binary alloys has been made in short. A detailed analyses on the recorded profiles in the present considerations revealed, in general, quantitative estimates of several microstructural parameters characterising the deformed state of the materials namely, propensity of stacking faults (intrinsic, extrinsic and twin faults), rms microstrains, coherent domain sizes, long-range residual stresses, lattice parameter changes, dislocation density and stacking fault energy. The results indicate a general trend of increase in the concentrations of stacking faults, primarily, of intrinsic character, with increase in solute concentrations; which are solely responsible for the observed peak-shifts as well as domain size broadening. Small asymmetry in the profiles is due to the presence of extrinsic stacking faults, relatively less in magnitude compared to the intrinsic ones while the deformation twin faults are almost absent—an observation with significance. The dislocation density, quite appreciable in magnitude, has been evaluated from the anisotropic values of the coherent domain sizes and rms microstrains. The stacking fault energies of pure Ag and Cu, an important parameter have also been estimated and compared with those obtained from electron microscopy. Annealing experiments with a Ag-5·8% Al alloy, aluminium being a precipitating solute, do not reveal any detectable evidence of solute segregation at the stacking faults. The occurrence of stacking faults in the alloy systems has been correlated with a number of physical factors involving solvent-solute types.     

Normal modes of oscillations of lattices

Polynomial equations are obtained for the solutions of the vibrational frequencies of a simple cubic, primitive orthorhombic and tetragonal Bravais lattices of finite size with particles connected to their nearest neighbours through both central and non-centrarl forces, but with arbitrary forces connecting the surface atoms to the rigid walls. The exact expressions of the different normal modes of oscillations and the amplitudes of vibration of different particles in various modes are obtained by solving three decoupled partial difference equations.     

Quasi-classical approach: Electronic structure of cubic boron nitride crystals

Using the new version of the quasi-classical parameterization based on the screened Coulomb-like atomic potentials the band structure and the unit cell total energy are obtained for boron nitride cubic crystal (c−BN). The calculated density of electron states of the upper valence and lower conduction bands reveals that c−BN is an insulator with band gap of . The quasi-classical estimation of lattice constant is found to be a=3.588 Å.     

Lattice dynamics of beryllium

Phonon frequencies in beryllium along the principal symmetry directions have been determined by means of the slow neutron inelastic scattering technique. The data are analysed in terms of a six-neighbour force constant model and the force constants are evaluated. It is concluded that strong tensor forces are present in beryllium and the importance of this finding to basic theories of lattice dynamics is pointed out.     

Phase transition of hard hexagons on a triangular lattice

Systems of hard hexagons on a triangular lattice are investigated. The orientation of the hexagons is kept fixed, while the size of the hexagons is varied. The existence of a phase transition is proved for all sizes by means of the Peierls'argument. The proof does not imply a phase transition in the continuous limit.Work supported by the U. S. Air Force under Contract No. F 44620-71-C-0013.     

Highly improved lattice field-strength tensor

We derive an -improved lattice version of the continuum field-strength tensor. Discretization errors are reduced via the combination of several clover terms of various sizes, complemented by tadpole improvement. The resulting improved field-strength tensor is used to construct -improved topological charge and action operators. As a test of our improved field-strength tensor, we compare the values attained by these operators as we cool several configurations to self-duality with a previously defined highly improved action and assess the relative scale of the remaining discretization errors. We demonstrate accuracy to better than one part in 10,000.