Thermal expansion and kinetic coefficients of crystals

Electrical (ρ) and thermal (W) resistivities and thermal expansion coefficient (β) of Cu, Zn, Al, Pb, Ni, β-brass, Al₂O₃, NaCl, Si, SiO₂(∥), and SiO₂(⊥) were simultaneously measured with standard four-probe, absolute steady-state, and quartz dilatometer techniques. Measurements of Ni and β-brass were performed at temperatures from 300 to 1100 K and measurements of all other samples were made between 90 and 500 K. This temperature range includes the range below and above the Debye temperature (T_D). The total uncertainties of the specific electrical and thermal resistivities and thermal expansion coefficient (TEC) measurements are 0.5%, 3.0%, and (1.5-4.0%), respectively. The universal linear relationship between the electrical and thermal resistivities and βΤ over the wide temperature range was found experimentally. Using the Landau criterion for convection development for ideal phonon and electron gases in the solids, the universal relations, ρ^ph/ρ^*≡βT and W^ph/W^*≡βT (where ρ^ph is the phonon electrical resistivity, is the characteristic electrical resistivity, W^ph is the phonon thermal resistivity, and W^*=k_BG/qc_p is the characteristic thermal resistivity) between relative phonon electrical and phonon thermal resistivities and βΤ were derived. The derived universal relations provide a new method for estimating the kinetic coefficients (electrical and thermal resistivities) from TEC measurements.     

Thermal expansion of anharmonic crystals composed of inert gases

The temperature dependence of the lattice constant and linear expansion coefficient for inert gas crystals are determined using the second-order approximation of Bogolyubov's temperature expansion. It is shown that when the temperature dependence of the Gruneisen constant is taken into account the agreement with experiment is improved over the thermodynamic perturbation theory and the theory based on a multiplicative binary distribution function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 44–47, April, 1976.     

Thermal expansion of cadmium fluoride crystals at high temperatures

The thermal expansion coefficient of cadmium fluoride crystals has been measured over the temperature range of 300 to 1070 K. The data fit well to measurements done by other authors in the range 80–300 K. At temperatures above 1070 K the thermal expansion coefficient shows an anomalous behaviour which has been attributed to the formation of cadmium oxide on the surface of the sample.     

Thermal conductivity and expansion of PbF2 single crystals

In order to check a phenomenon of the negative correlation between ionic and thermal conductivities of solid substances, we studied the thermal conductivity and expansion of cubic PbF₂ single crystals at 50–300 and 5.6–317 K, respectively. We found that lead difluoride had a thermal expansion coefficient α that was equal to (28.5 ± 0.3)10⁻⁶ K⁻¹ at 300 K, and a thermal conductivity coefficient k(T) was equal to 1.40 ± 0.07 W/(m K) at the same temperature. Thus, the thermal conductivity for PbF₂ is the lowest among fluorite-type MF₂ (M = Ca, Sr, Ba, Cd, Pb) thermal conductivities, whereas its fluoride-ion conductivity is the highest one among MF₂ (M = Ca, Sr, Ba, Cd, Pb) ionic conductors.

     

Thermal expansion and elastic properties of the crystals with modulated structure

An experimental study of structure characteristics and elastic properties of the incommensurate crystals is reported.     

Thermal expansion of Sn2P2S6 crystals

We present the results for thermal expansion coefficients of Sn₂P₂S₆ crystals determined both in the crystallographic system and the system based on eigenvectors of thermal expansion tensor. Peculiarities of temperature evolution of the indicative surface of thermal expansion tensor for Sn₂P₂S₆ are discussed, including the region of their ferroelectric phase transition.     

Operator product expansion on a fractal: The short chain expansion for polymer networks

We prove to all orders of renormalized perturbative polymer field theory the existence of a short chain expansion applying to polymer solutions of long and short chains. For a general polymer network with long and short chains we show factorization of its partition sum by a short chain factor and a long chain factor in the short chain limit. This corresponds to an expansion for short distance along the fractal perimeter of the polymer chains connecting the network vertices and is related to a large mass expansion of field theory.

The scaling of the second virial coefficient for bimodal solutions is explained. Our method also applies to the correlations of the multifractal measure of harmonic diffusion onto an absorbing polymer. We give a result for expanding these correlations for short distance along the fractal carrier of the measure.     

Luminescence kinetics of linear polymer molecules with chromophores randomly distributed along the chain

Luminescence kinetics of chromophores randomly attached to an isolated flexible polymer chain is studied. In the static case, when the polymer chain does not change its conformation during the donor excited-state lifetime, analytical equations are derived for the luminescence kinetics of both ideal and nonideal polymer chains. The conditions are formulated when the inhomogeneous broadening should be taken into account. For the dynamic case, the diffusion and hopping mechanisms of the polymer motion are studied.     

Luminescence kinetics of linear polymer molecules with chromophores regularly distributed along the chain

An analytical expression for luminescence kinetics of a polymer chain in the static regime is obtained for the case when the rotational motion of monomers, leading to the formation of excimers (traps of excitations), is frozen. The conditions are found when the inhomogeneous broadening of the chromophore spectra and the conformation motion of the polymer chain should be taken into account.     

Thermal expansion measurements for estimating vacancy concentration in X-ray irradiated KCl single crystals

A sensitive capacitance technique is used for measuring changes in length (Δl) of KCl single crystals with temperature in the region 30–300°C. These measurements have been taken on KCl in (i) as-cleaved (ii) X-ray irradiated (iii) quenched and X-ray irradiated conditions (X-ray irradiation was always done at room temperature (≈ 30°C). The linear coefficient of thermal expansion (α) of the as-cleaved sample is 40.8 × 10^-6°C^-1. Variation of Δl with temperature in X-ray irradiated crystal shows two regions: (a) 30–180°C where α is 48.1 × 10^-6°C^-1, (b) 180–300°C where α is 40.4 × 10^-6°C^-1. Similar behaviour is exhibited by quenched and later X-ray irradiated KCl the first region is up to 140°C, beyond which the second region takes over. From these data, concentration of vacancies in X-ray irradiated KCl at room temperature is calculated to be 3.4 × 10¹⁷ cm^-3 which is in fairly good agreement with the value obtained from F-band absorption measurements on the sample. An attempt has been made to understand these results.     

共轭高分子链中电荷迁移的热效应

从理论上研究了共轭高聚物链中在电场作用下极化子运动的热效应.基于SSH模型以及通过绝热动力学演化的方法,模拟了共轭高聚物链中极化子在电场作用下从链左端向右端运动的过程.晶格受到的热扰动作用假设为通过局域的晶格范围内原子位移的随机涨落来实现.结果发现,晶格中的局域热涨落对于运动中的极化子而言等效于一个势垒.势垒高度由高分子中受到热扰动的区域的范围大小以及该区域与其周围环境的温差来决定.当分子中存在热吸收不均匀的现象时,链内极化子迁移率在低电场范围内随电场的变化遵循对数曲线变化规律.     

Thermal expansion in YbGaGe

Thermal expansion and magnetic susceptibility measurements as a function of temperature are reported for YbGaGe. Despite the fact that this material has been claimed to show zero thermal expansion over a wide temperature range, we observe thermal expansion typical of metals and Pauli paramagnetic behavior, which perhaps indicates strong sample dependence in this system.     

Fourier expansion of the Hamiltonian of crystals

The number of independent constants in the Fourier expansion of the matrix of the Hamiltonian of crystals can be diminished if the orthogonality of the states corresponding to different complex bands of the crystal is used in addition to taking account of the spatial symmetry, the symmetry relative to time inversion, and the fact that the matrix is Hermitian. Bands with the space group O⁷ (Si, Ge, cubic SiO₂) are examined as an illustration.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 101–105, July, 1981.In conclusion, the author is grateful to I. V. Abarenkov for useful discussions.     

Vacancy mobility in polymer crystals

A molecular-dynamics model of the behavior of a vacancy in the chain of an equilibrium polymer crystal (the “collective atom” approximation for polyethylene) is developed for the first time. It is shown that a defect of this type in a polymer crystal has a soliton mobility, as opposed to vacancies in crystals of low-molecular substances. Zh. éksp. Teor. Fiz. 115, 1063–1069 (March 1999)     

Liquid crystals of disc-like molecules

Thermotropic mesomorphism has been observed in pure compounds consisting of simple disc-like molecules, viz., benzene-hexa-n-alkanoates. Thermodynamic, optical and x-ray studies indicate that the mesophase is a highly ordered lamellar type of liquid crystal. Based on the x-ray data, a structure is proposed in which the discs are stacked one on top of the other in columns that constitute a hexagonal arrangement, but the spacing between the discs in each column is irregular. Thus the structure has translational periodicity in two dimensions and liquid-like disorder in the third.     

Electron correlations in crystals and molecules

An expression for the Green’s function of a disordered crystal is obtained with allowance for the electron-electron interaction. The electron states of the system are described in the framework of a multiband tight-binding model. The possibility of using the proposed approach for describing the energy spectrum of molecules is demonstrated in the limit of an infinitely large primitive cell of the crystal. The energy spectrum and effective charges of atoms of a tricyanobutadienecarbazole molecule are calculated.     

Thermal expansion of InBi

Linear thermal expansion of InBi single crystal has been measured between ?186 and 100°C. Lattice constant a shows a normal behaviour over the measured temperature range. Lattice constant c, however, contracts monotonically with increasing temperature in this range.