The use of acoustic axes in deciding between the Voigt and Laval-Raman theories of the elastic properties of crystals

A method is derived for finding the crystal directions that are acoustic axes, independently of the values of the elastic constants and of the assumption of the validity of Voigt's theory of the elastic properties of crystals. If, on the other hand, the Laval-Raman theory is satisfactory for the given crystal, the found directions lose the properties of acoustic axes. Measurement of the phase velocity of elastic waves in the found directions makes it possible to decide for each crystal whether these directions are really acoustic axes and thus to determine which of the two theories is valid.     

Theories of elastic properties and elastic waves of equal phase velocities in crystals

A survey is made of pairs of heteronormal planar elastic waves, which can propagate in an unlimited crystal medium and have equal theoretical values of the phase velocity, using Voigt elastic moduli. Such pairs are chosen for which it is possible that the theoretical equality of velocities will be disturbed when using another theory of the elastic properties of crystals with generally different tensors of material constants (for example Kuvshinskij J. V., Aero E. L.: Fiz. tv. tela5 (1963), 2591). In such a case, a comparison of the measured velocities of a suitable pair of waves can help to decide between the two theories. Pairs of waves are found for 12 non-piezoelectric crystal classes. Among such pairs it is easy to find pairs of waves of the same properties for piezoelectric crystal classes.     

Statistical theory of the elastic constants of nematic liquid crystals

A statistical mechanical theory of the Frank elastic constants is formulated. The free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients. The Frank constants are expressed in terms of the direct correlation function c(1, 2) and the orientational single particle distribution function. For the example of Onsager spherocylinders three constants K ₁, K ₂ and K ₃ are calculated. The results of these calculations are similar to those given by Priest and by Straley.     

The static and elastic properties of mixed diatomic crystals

An interionic potential model has been proposed to study the static and elastic properties of mixed diatomic crystals. The interaction system of this potential consists of the long-range Coulomb and three-body interaction and the short-range overlap repulsion. This potential has been used to calculate the cohesive energy, phase-transition pressure and volume, third-order elastic constants and pressure derivatives of the effective second-order elastic constants for NaCl-NaBr mixed crystals. These results agree reasonably well with the available experimental results on the host crystals and allow us to draw some meaningful conclusions for the mixed alkali halide crystals.     

Cohesive and anharmonic elastic properties of mixed fluorite crystals

Summary The cohesive and anharmonic elastic properties of four mixed fluorite crystals (Ca _x Sr_1−x F₂, Sr _x Ba_1−x F₂ Ba _x Ca_1−x F₂ and Cd _x Pb_1−x F₂) have been investigated by means of a three-body potential (TBP) model which consists of the long-range Coulomb and three-body interactions and the short-range van der Waals attraction and overlap repulsion effective up to the second-neighbour ions. Due to the lack of measured data on cohesive energy, third-order elastic constants and pressure derivatives of the secondorder elastic constants of mixed fluorites, the accuracy of the present results has been tested by comparing them with the so-called experimental results generated by the application of Vegard’s law to their corresponding experimental values for the host fluorites.

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Riassunto Sono state ricercate le proprietà elastiche coesive e anarmoniche di quattro cristalli misti di fluorite (Ca _x Sr_1∮x F₂, Sr _x Ba_1−x F₂, Ba _x Ca_1−x F₂ e Cd _x Pb_1−x F₂) per mezzo di un modello del potenziale a tre corpi (TBP) che consiste di interazioni di Coulomb a lungo raggio e a tre corpi, di attrazione di van der Waals a corto raggio e di repulsione di sovrapposizione efficace fino agli ioni del secondo vicino. A causa della mancanza di dati misurati sull’energia coesiva, di costanti elastiche di terz’ordine e di derivate di pressione delle costanti elastiche di secondo ordine, l’accuratezza dei risultati attuali è stata provocata confrontandoli con i cosidetti risultati sperimentali generati dalla applicazione della legge di Vegard ai loro valori sperimentali corrispondenti per i fluoriti ospiti.

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Резюме С помощью трех-частичной потенциальной модели исследуются когезионные и ангармоничные упрыгие свойства четырех смешанных кристаллов флюорита (Ca _x Sr_1−x F₂, Sr _x Ba_1−x F₂, Ba _x Ca_1−x F₂ и Cd _x Pb_1−x F₂). Используемая модель состои т из длиннодейтсвующего кулоновского и трех-частичного веаимодействий и короткодействующего притяжения Ван дер Ваальса и перекрывающегося отталкивания, эффективного вплоть до вторых соседних ионов. Из-за недостатка зкспериментальных данных для когезионной энергии упругих постоянных третьего порядка и производных по давлехию упрутих постоянных второго поядка для смешанных флюоритов, проверяется точность полученных результатов посредством сравнения их с так называемыми экспериментальными результатами, образованными с помощью применения закона Вегарда к соответствующим экспериментальным величинам для первичных кристаллов флюоритов.

     

Cohesive and elastic properties of alkaline earth chalcogenide crystals

In the present study an analysis of the cohesive and elastic properties has been performed in fourteen alkali chalcogenide crystals using the composite potential forms based on the Drude oscillator model. The short-range overlap repulsion has been considered up to the second nearest neighbour interactions. The van der Waals coefficients have been estimated from the Kirkwood-Muller formulae. Cohesive energies, bulk-modulus and its pressure derivatives calculated for the entire family of crystals under study are found to present a good agreement with available experimental data, better than those obtained by previous workers using the traditional Born potential model.On leave from theDepartment of Physics, G. B. Pant University, Pantnagar-263 145, India.Authors are thankful to Mr. Saleh O. Harraga for the computational help.     

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.     

Influence of the surface on the elastic properties of liquid crystals

A statistical approach including direct correlation functions is applied to study the influence of the surface confining the nematic liquid phase on the Franck elastic coefficients. Specific calculations are made for a model system composed of ellipsoidal molecules interacting by means of the Gay-Berne potential near the interacting surface. Fiz. Tverd. Tela (St. Petersburg) 40, 1356–1359 (July 1998)     

Ferroelastic crystals and their nonlinear elastic properties observed in frequency range from gigahertz to milihertz

The experiments reported in this article have been performed to unify the results of earlier and recent determinations of parameters describing the elastic properties of Rb₄LiH₃(SO₄)₄, LiCsSO₄ (LCS) and KH₂PO₄ crystals measured by different experimental methods. The above crystals undergo a second-order phase transition, incommensurate phase transition (PT) and a first-order but close to second-order phase transition, respectively. To investigate the elastic properties of the crystals in the frequency range from 10^?1 to 10¹⁰ Hz, five experimental methods were applied: dynamic mechanical analysis, piezoelectric resonance, composite oscillator bar, ultrasonic wave propagation and Brillouin light scattering. The results of the experiments allowed identification of the processes contributing to the elastic response of the crystals investigated. Moreover, for the LCS crystal a model of the incommensurate PT was presented.     

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non-linear optical coefficients, often one to two orders of magnitude higher than those of the well-known inorganic non-linear optical materials. Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique usingN, N-dimethyl formamide as the solvent. All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique. The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness, Young’s modulus and linear compressibility surfaces along symmetry planes. The volume compressibility, bulk modulus and relevant Poisson’s ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.     

Propagation properties of elastic waves in semi-infinite phononic crystals and related waveguides

The transmission and reflection coefficients of two-dimensional semi-infinite solid-solid phononic crystal systems and fluid-fluid phononic waveguide structures have been investigated. The numerical results show that the transmission spectra for longitudinally and transversally polarized incident waves are different, and the spectra of the transmission and reflection coefficients of the semi-infinite system agree well with the band structure. The numerical results show that when a guided wave incident, localized modes are excited, and different polarities have different coupling efficiencies with the incident guided wave. At the same time, far from the cutoff frequency, the guided wave couples out of semi-infinite waveguide highly efficiently.     

Self-consistent theory of second order elastic constants for nonionic anharmonic crystals

Elastic constants of strongly anharmonic nonionic dielectric crystals are studied within the pseudoharmonic approximation by means of two-time Green functions. The relation between the method of homogeneous deformation by Leibfried and Ludwig and that of long waves is investigated. These considerations lead to a generalization of the method of homogeneous deformation for the case of strongly anharmonic crystals. A comparison between the results of the two methods shows that the pseudoharmonic approximation satisfies the exact elastic sum rule. On leave from the Institute of Theoretical Physics University of Wrocław, Wrocław, Poland.     

Topological aspect of disclinations in two-dimensional crystals

By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given.     

The influence of excess oxygen on the elastic properties of non-stoichiometric SrO crystals

Measurements have been carried out of the elastic constants of SrO in the virgin undoped state and of the changes produced in them by equilibrium doping with oxygen at ? 1200°C and oxygen partial pressure of 0.95 atm. The method used was Papadakis' pulse-echo overlap technique in conjunction with thermogravimetric analysis (T.G.A.) to determine mass and density changes due to oxygen doping.The values obtained for C₁₁, C₁₂ and C₄₄ of the virgin crystal at 23°C are

$\text{C}{}_{11}\text{= 17.60 ± 0.03 × 10}{}^{11}\text{dynes/cm}{}^2$

;

$\text{C}{}_{12}\text{= 4.808 ± 0.007 × 10}{}^{11}\text{dynes/cm}{}^2$

;

$\text{C}{}_{44}\text{= 5.577 ± 0.008 × 10}{}^{11}\text{dynes/cm}{}^2$

.(These values are in very good agreement with those of Son and Bartels [2].)Values for $\text{δC}{}_{11}\text{C}{}_{11}$ and $\text{δC}{}_{44}\text{C}{}_{44}$ were found to be ?1.74% and ?0.86% respectively. Accurate valu $\text{δC}{}_{12}\text{C}{}_{12}$ could not be obtained because of sample size limitations after quenching. However, C₁₂ was shown to definitely increase due to doping.Analysis of the results indicate that the elastic modulus changes can only be attributed to the formation of cation vacancies during doping. Analysis of the T.G.A. behavior indicates that this cation vacancy formation is probably associated with the presence of various tripositive cation and uninegative anion species depending upon the impurity concentrations of the sample. This implied impurity-controlled cation vacancy concentration is consistent with the earlier observed extrinsic nature of cation diffusion in SrO at 1200°C.     

Self-consistent theory of the surface thermodynamic properties of strongly anharmonic crystals

The nonlinear integral equations of the asymmetric self-consistent field method are applied to a semiinfinite, strongly anharmonic crystal bounded by a gaseous phase. These equations are used to obtain the self-consistent potential for crystal atoms close to the surface, and through this potential, the surface free energy is obtained. The nonlinear integral equation is reduced to a set of transcendental equations and a method is given for the solving the latter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 80–84, March, 1984.     

Acoustooptical and elastic properties of laminated KY(MoO4)2 crystals

Data on acoustic (absorption and velocity of sound), optical (refractive index and optical absorption coefficient), and photoelastic (coefficients of acoustooptical quality and photoelastic constants) properties of KY(MoO₄)₂ crystals are obtained. It is shown that, not only does the anisotropy of binding forces lead to a significant anisotropy of acoustic and photoelastic properties, but it also determines anomalously high elastic nonlinearity in the direction of the Y-axis perpendicular to cleavage planes.