Magnetoelastic contribution to the thermal expansion of the rare-earth phosphates TbPO4 and TmPO4

The thermal expansion of the rare-earth phosphates TbPO₄ and TmPO₄ having zircon structure has been investigated experimentally and theoretically. Significant magnetoelastic anomalies of the thermal expansion have been identified and the magnetoelastic contributions have been isolated allowing for corrections to the variation of the phonon contribution along the rare-earth ion series. It is shown that the magnetoelastic contribution to the thermal expansion of terbium and thulium phosphate is well described by the temperature dependence of the quadrupole moments of the rare-earth ions. The fully symmetric magnetoelastic coefficients for Tb³⁺ and Tm³⁺ are determined and a comparison is made of the magnetoelastic anomalies of the thermal expansion and the magnetoelastic coefficients of rare-earth phosphates and vanadates allowing for the differences in the crystal fields of the two isomorphic groups of zircons. Fiz. Tverd. Tela (St. Petersburg) 39, 106–111 (January 1997)     

Estimation of thermal expansion and thermal conductivity coefficients of amorphous dielectrics at high temperatures

Expressions for estimation of the thermal linear expansion coefficients and of the thermal conductivities of amorphous dielectrics above the Debye temperature are obtained. It is shown that for the compounds of the chemical composition corresponding to the rare-earth magnesium hexaaluminates taken as an example these parameters for amorphous compounds are less than for polycrystalline.     

The magnetoelastic contribution to thermal expansion of rare-earth metal scheelites RLiF<Subscript>4</Subscript> (R = Tb-Yb)

The paper presents systematic experimental and theoretical studies of thermal expansion for rare-earth metal scheelites RLiF₄ (R = Tb-Ho, Tm, and Lu). Pronounced thermal expansion anomalies were observed. The magnetoelastic contributions were determined taking into account corrections for changes in the phonon contribution in the RLiF₄ series according to the Debye thermal expansion model. The calculated multipole moments of various orders for various rare-earth metal ions were compared to analyze the applicability of the quadrupole approximation to totally symmetric modes in the scheelite structure. For some ions (Ho and Tm), the magnetoelastic contributions to thermal expansion could not be described by the temperature dependences of their quadrupole moments, that is, multipole moments made considerable contributions. The totally symmetric magnetoelastic coefficients for the scheelite structure were determined from the experimental data on magnetoelastic contributions. These coefficients were compared with those for the zircon structure.     

Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures

A novel theoretical basis for the evaluation of the thermal conductivity and the thermal diffusion ratios of dilute polyatomic gas mixtures is derived within the semi-classical isotropic kinetic theory. New expressions for species diffusion coefficients, thermal diffusion coefficients, and thermal diffusion ratios are also obtained by using an expansion vector based upon the total energy of the molecules. Finally, practical and accurate expressions for the thermal conductivity and the thermal diffusion ratios are derived by using the recent theory of iterative transport algorithms, as developed by the authors. The resulting expressions can be used in either theoretical calculations or computational models of multicomponent flows.     

Intensity of the <Emphasis Type="Italic">f-f</Emphasis> transitions of Nd<Superscript>3+</Superscript>, Er<Superscript>3+</Superscript>, and Tm<Superscript>3+</Superscript> rare-earth ions in calcium niobium gallium garnet crystals

This paper reports on the results of the investigation into the intensities of the f-f transitions of Nd³⁺, Er³⁺, and Tm³⁺ ions in calcium niobium gallium garnet (CNGG) crystals. The values of the oscillator strengths and line strengths obtained for hypersensitive transitions and the intensity parameters Ω _t of the rare-earth ions in the CNGG crystals are compared with the corresponding quantities for crystals of other garnets and some oxide and fluoride crystals. The assumption is made that an increase in the oscillator strengths and line strengths for the hypersensitive transitions and the intensity parameters Ω₂ of the Nd, Er, and Tm ions in the CNGG crystals as compared to those for crystals of other garnets is associated with the specific features revealed in the crystal structure of the calcium niobium gallium garnet, in particular, with the lowering of the symmetry of the positions occupied by rare-earth ions in the crystal structure.     

Investigation of mixed rare-earth element—alkaline-earth element chromites

Electrical conductivity and the coefficient of thermal expansion of mixed rare-earth element-alkaline-earth element chromites as a function of rare-earth element's ordinal number are investigated. It is shown that the electrical conductivity and the coefficient of thermal expansion are a function of the rare-earth element's ordinal number. Explanations of these dependences are given.     

Variational principles for relativistic transport coefficients

Variational expressions for the transport coefficients of a one-component, relativistic gas are derived from the linearized relativistic Boltzmann equation for both quantum and classical gases. These expressions depend on functions _χ of the energy of the particles comprising the gas in such a way that: a) if _χ differs from a solution of the linearized Boltzmann equation by ε, then the value of the variational expression calculated with this _χ differs from the true value of the corresponding transport coefficient by ε²; and b) the value of the variational expression is always less than this true value. It is shown that values of the transport coefficients obtained by expanding _χ in a particular set of orthogonal polynomials and keeping only the first nontrivial term in the expansion are equivalent to those obtained using the Grad method of moments. It follows therefore that values obtained using this later method represent lower bounds on the true values. We also show that one can obtain simple, closed-form expressions for the various transport coefficients corresponding to an arbitrary number of terms in an expansion of the trial function _χ in the above-mentioned set of orthogonal polynomials. Finally we point out that all of our results can be carried over to the nonrelativistic case by taking the limit c → ∞.     

Nd^3＋：YAlO3晶体折射率温度系数的表示式

建立了Nd~(3+):YAlO_3(Nd:YAP)晶体折射率温度系数的表示式,该式得到的结果与测量值间具有较好的一致性。利用这个式子可以计算0.5398μm～1.0795μm波长范围311K～455K温度范围内Nd:YAP晶体的折射率温度系数。     

Calculation of thermal stresses in profiled single crystals taking into account the temperature dependence of thermal expansion

Approximate expressions for stress tensor components in cylindrical and ribbon crystals are obtained taking into account the temperature dependence of the thermal expansion coefficient. These expressions are used for estimating the effect of the thermal expansion nonlinearity factor on the stress level. It is shown that the stresses emerging in linear temperature fields due to this factor are comparable with critical stresses for defect formation.     

Burning rate of homogeneous energetic materials with thermal expansion and varying thermal properties in the condensed phase

We present a study of the one-dimensional flame structure of combusting solid propellants that focuses on the effects of thermal expansion and variable thermal properties in the condensed phase. A nonlinear heat equation is derived for a burning thermo-elastic solid with temperature-dependent specific heat, thermal expansion, and thermal conductivity coefficients. It is solved for different modelling approximations both analytically and numerically. Explicit expressions are derived for the regression rate of the propellant surface as functions of surface temperature and thermal expansion parameters. A simple one-step reaction model of the gas phase is used to study the full structure of propellent flame and illuminate the influence of temperature-dependent material properties on the regression rate, surface temperature, and flame stand-off distance. Results are displayed for HMX and compared with experimental data and numerical simulation with fair success.     

Pac study of the hyperfine interactions in154Gd3+ in rare-earth-garnets

The attenuation of the anisotropy of the γ-γ angular correlation for a rare-earth ion in magnetic iron and non-magnetic aluminum rare-earth garnets is governed by the static hyperfine electric field gradient (EFG) produced by the surrounding ions and by the static and fluctuating hyperfine magnetic fields produced by the 4f electrons of the ion. The latter effect depends upon the correlation time (τ_c) of the 4f electrons which, in turn, is determined by the interaction of the ionic spin with lattice vibrations and other magnetic ions. In an attempt to determine the significance of spin-spin relaxation on τ_c, perturbed angular correlation (PAC) measurements were performed on the S-state ion¹⁵⁴Gd³⁺ because spin-lattice interactions were expected to be small. The time-integral attenuation coefficients of the 1274/123 keV γ-γ cascade in¹⁵⁴Gd were measured in the temperature region 4.2–650 K for¹⁵⁴Gd³⁺ incorporated in GdAlG, GdIG, YAlG, and YIG. Rotation measurements were also made on the same cascade in the iron garnets at room temperature with an applied magnetic field in the range 0–15 kg. Employing independent measurements and calculated estimates of the static hyperfine magnetic field and EFG, the observed data could be interpreted in terms of reasonable values of τ_c. The correlation times were found to range from about 0.13 ns in YIG to about 1.30 ns in YAlG with GdAlG having a value of approximately 0.71 ns. In the case of GdIG, a self-consistent analysis of the data required a value of the lattice EFG which was larger than that estimated from the nearest neighbor point-ion model. The correlation time in GdIG was then found to be the same as in YIG.     

Thermal Expansion Coefficients of Thin Crystal Films

The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green＇s function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.     

Effect of phonon decay processes on the formation of a phonon nonequilibrium signal in crystals with two two-level subsystems

The effect of phonon decay on the characteristic propagation time and shape of a phonon nonequilibrium signal in disordered crystals, including crystals containing inelastic phonon scattering centers, is studied theoretically. Attention is focused on slow processes, which are typical of yttrium-aluminum garnet solid solutions and erbium-doped aluminates. It is shown that the temperature dependence of the arrival time of a phonon nonequilibrium signal in these systems can be governed, to a considerable extent, by phonon-phonon interactions. The results of the theoretical studies are compared with experimental data on the propagation of weakly nonequilibrium thermal phonons in solid solutions of rare-earth yttrium-aluminum garnets and aluminates.     

高掺镁LiNbO3晶体折射率温度系数的表示式

推导了掺５ｍｏｌ％ＭｇＯ的ＬｉＮｂＯ３晶体折射率温度系数的表示式。利用这些表示式可以计算２９３～４２８Ｋ温度和０．５３９８μｍ～１．３４１４μｍ波长范围内的折射率温度系度，结果表明：计算值和实验值的最大相对偏差是１２％，用具有最大相对偏差的折射率温度系数的计算值，计算１．０７９５μｍ波长的非临界相位匹配温度，其值为３８２．４Ｋ，它与实验值仅差６Ｋ。因此，本文得到的表示式，对于采用这种晶体，设计在上     

Non-linear population processes of Er3+ laser levels in chromium-doped garnet crystals

In garnets doped with chromium and rare-earth ions, the processes of energy transfer, including upconversion, were investigated. Their influence on laser properties is established.     

Non-linear population processes of Er3+ laser levels in chromium-doped garnet crystals

In garnets doped with chromium and rare-earth ions, the processes of energy transfer, including upconversion, were investigated. Their influence on laser properties is established.     

带有任意自旋粒子衰变产物的角分布

本文研究了具有任意自旋的粒子衰变为一个自旋为零,另一个自旋为1/2的粒子的角分布。给出了球谐函数展开式系数的表式。发现偶次球谐函数项的系数是和引起衰变的相互作用哈密顿量具体形式无关的。但是在球谐函数展开式的奇次项的系数却和一个参变数α有关,而α的值却反映了宇称守恒的相互作用和宇称不守恒的相互作用之间干涉作用的大小。我们给出了这些系数的极大值,发现凡是偶次项系数的极大值是随着衰变粒子自旋的增加而增加的,而奇次项系数的极大值却随着衰变粒子自旋的增加而减小。本文还给出了衰变着的粒子的密度矩阵作为展开式的系数的函数的表式。当这些展开式系数已经知道以后,用这些函数就能决定衰变前的粒子的极化状态,决定宇称守恒相互作用和宇称不守恒相互作用之间的干涉的程度。     

用电子散斑干涉法测量材料热膨胀系数

 利用双光束电子散斑干涉法（ESPI）对试件受热变形进行了实时观测，针对一次实验过程中得到的图片较多（300～500幅）的特点，在图像处理时摒弃了以往的手动识别等位移线的办法，用MATLAB语言编写了批处理程序，能够在采集的大量散斑图片中自动快速准确地标定等位移线，得到相应的位移和应变，并结合实时测量的温度值，获得了45钢和LY12铝合金在不同温升率下的热膨胀系数及其随温度的变化。实验结果表明，在涉及的温升率范围内，温升率的改变对材料热膨胀系数的影响不明显，材料的热膨胀系数随温度的升高略有上升。