Упругие свойства и ангармонизм твердых тел

The squares of the velocities of the longitudinal and transverse acoustic waves separately are practically not associated with anharmonicity, and their ratio (vL2 / vS2) turns out to be a linear function of the Grüneisen parameter γ - the measure of anharmonicity. The obtained dependence of (vL2 / vS2) on γ is in satisfactory agreement with the experimental data. The relationship between the quantity (vL2 / vS2) and anharmonicity is explained through its dependence on the ratio of the tangential and normal stiffness of the interatomic bond λ, which is a single-valued function of the Grüneisen parameter λ (γ). The relationship between Poisson's ratio μ and Grüneisen parameter γ, established by Belomestnykh and Tesleva, can be substantiated within the framework of Pineda's theory. Attention is drawn to the nature of the Leont'ev formula, derived directly from the definition of the Grüneisen parameter by averaging the frequency of normal lattice vibration modes. The connection between Grüneisen, Leontiev and Belomestnykh-Tesleva relations is considered. The possibility of a correlation between the harmonic and anharmonic characteristics of solids is discussed.

Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids

A catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971. These arrangements naturally generalize finite Coxeter arrangements and also the weak order through the poset of regions. The weak order is known to be a congruence normal lattice, and congruence normality of lattices of regions of simplicial arrangements can be determined using polyhedral cones called shards. In this article, we update Grünbaum’s catalogue by providing normals realizing all known simplicial arrangements with up to 37 lines and key invariants. Then we add structure to this catalogue by determining which arrangements always/sometimes/never lead to congruence normal lattices of regions. To this end, we use oriented matroids to recast shards as covectors to determine congruence normality of large hyperplane arrangements. We also show that lattices of regions coming from finite Weyl groupoids of any rank are always congruence normal.

Elastic Properties of Taurine Single Crystals Studied by Brillouin Spectroscopy

The inelastic interaction between the incident photons and acoustic phonons in the taurine single crystal was investigated by using Brillouin spectroscopy. Three acoustic phonons propagating along the crystallographic b-axis were investigated over a temperature range of −185 to 175 °C. The temperature dependences of the sound velocity, the acoustic absorption coefficient, and the elastic constants were determined for the first time. The elastic behaviors could be explained based on normal lattice anharmonicity. No evidence for the structural phase transition was observed, consistent with previous structural studies. The birefringence in the ac-plane indirectly estimated from the split longitudinal acoustic modes was consistent with one theoretical calculation by using the extrapolation of the measured dielectric functions in the infrared range.

Influence of magnesium concentration on the optical properties of ytterbium and holmium co-doped lithium niobate crystal

In this paper, a series of Yb (0.5[Formula: see text]mol.%):Ho (0.5[Formula: see text]mol.%):LiNbO3 crystals doped with various concentration of Mg[Formula: see text] (1, 3, 5 and 7[Formula: see text]mol.%) were grown by the Czochralski technique. The ability of optical damage resistance of Mg:Yb:Ho:LiNbO3 crystals increases with increasing the Mg[Formula: see text] doping concentration. The optical homogeneity of Mg:Yb:Ho:LiNbO3 crystals doped with different concentration of Mg[Formula: see text] was detected using the birefringence gradient method. The results demonstrated that the optical homogeneity is getting better with the increase of the Mg[Formula: see text] doping concentration. The studies on the infrared transmission spectra indicated that Mg[Formula: see text] ions first replaces anti-site Nb[Formula: see text] in the form of Mg[Formula: see text] defect, once the concentration of Mg[Formula: see text] reaches or exceeds the threshold concentration, it begins to substitute Li-site and Nb-site of normal lattice and form defect of Mg[Formula: see text][Formula: see text]3Mg[Formula: see text]. Therefore, the change of Mg[Formula: see text] doping concentration is the fundamental reason leading to a violet shift of the OH[Formula: see text] absorption peak.

Crystal Plasticity Analysis of Scale Effect on Tensile Properties of Ferrite/Cementite Fine Lamellar Structure under Lattice Strain

Tensile properties of ferrite lamella in pearlite under lattice strain are examined by a strain gradient crystal plasticity analysis. Tensile direction is made to be parallel to the lamella. Obtained results of macroscopic stress-strain relation of the lamella show significant increase of yield stress and strain hardening rate with the reduction of the lamella thickness and further increase of the yield stress with positive normal lattice strain parallel to the tensile direction in the ferrite layer. Whereas normal lattice strain perpendicular to the tensile direction contributes little to the tensile properties.

Remarks on annihilators preserving congruence relations

In this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices. We shall give some new characterizations, and a topological interpretation of the notion of annihilator preserving congruences introduced in [JANOWITZ, M. F.: Annihilator preserving congruence relations of lattices, Algebra Universalis 5 (1975), 391–394]. As an application of these results, we shall prove that the quotient of a quasicomplemented lattice by means of a AP-congruence is a quasicomplemented lattice. Similarly, we will prove that the quotient of a normal latttice by means of a AP-congruence is also a normal lattice.

Effect of Electric Field Treatment on Vacancy of Inconel 718 Superalloy at 1073 K

Effect of electric field treatment with different intensities on vacancy of Inconel 718 aged at 1073 K was investigated. The positron annihilation lifetime (PAL) and corresponding concentration of vacancies were measured by positron annihilation technique. It was found that atomic vibration at lattice site can be promoted by an external electric field performed on Inconel 718 superalloy during aged at elevated temperature. Some atoms owing the higher vacancy formation energy or larger radius will jump out from the normal lattice sites and form defects, which is leading to the increase of PAL of monovacancy. Under continuous effect on electric field, monovacancies will transform to three-dimensional vacancies of lower energy and vacancy clusters. Moreover, the vacancy concentration of Inconel 718 superalloy can be improved evidently by electric field treatment, and the average PAL of vacancies can be up to 6.3% when the electric field intensity is up to 8 kV/cm, which is very useful for controlling the microstructures evolution and properties of the superalloy, such as solute redistribution and precipitations.