Temperature Variation Of Elastic Constants Research Articles

Micro-Brillouin Scattering Study on Composition Gradient Li Doped KTa1-xNbxO3 Wafer

The composition gradient Li doped KTa1-xNbxO3 wafer was investigated by micro-Brillouin scattering method. The positional dependence of elastic constants was clearly observed. The origin of positional dependence was discussed by the comparison with the temperature variation of elastic constants of the homogeneous crystal. The difference of elastic constants between high and low defect density regions was also studied.

Ultrasonic Investigation of Elastic Anomalies in Lithium Sodium Sulphate Hexahydrate Single Crystal

An extensive study of the thermal properties of Lithium Sodium Sulphate Hexa hydrate (LSSW) single crystal, with Trigonal structure, has been carried out using ultrasonic Pulse Echo Overlap (PEO) technique, Differential Thermal Analysis (DTA) and Thermo Gravimetric Analysis (TGA). The temperature variation of elastic constants of LiNa3(SO4)2·6H2O single crystal have been reported for the first time. The second order elastic stiffness constants C11, C33, C44, along the various directions in the crystal have been determined in the temperature range 300 - 330 K. The change in velocity with temperature with respect to the room temperature value has been measured using PEO technique. Significant anomalies were observed in C11 and C33 at 316 K. The elastic constant C12 has shown no variation in the temperature range 300 - 319 K. A minor deviation for C44 at 305 K following a parabolic change has been observed. The minor anomalies observed in the elastic constants of LSSW may be due to its dehydration of water of crystallization in the range 304 - 319 K. DTA studies showed an appreciable endothermic change in the range 309 K-369.79 K. TGA curve exhibited a decrease in weight of 1.687 mg in the temperature range 304 K-360 K. The minor anomalies observed in the elastic constants of LSSW may be due to loosing of its water of crystallization in the range 309 - 319 K. On loosing water there will not be any change in chemical structure but there will be physical change associated with loosing of water molecule.

Phonon instability and mechanism of superionic conduction in Li2O

We report studies on the vibrational and elastic behavior of lithium oxide, Li${}_{2}$O, around its superionic transition temperature. Phonon frequencies calculated using the local density approximation and generalized gradient approximation schemes of ab initio density functional theory are in excellent agreement with the reported experimental data. Further, volume dependence of phonon dispersion relation was calculated, which indicated softening of zone boundary transverse acoustic phonon mode along [110] at the volume corresponding to the superionic transition in Li${}_{2}$O. This instability of phonon mode could be a precursor leading to the dynamic disorder of the lithium sublattice. Empirical potential model calculations were carried out to deduce the probable direction of vacancy-assisted lithium movement by constructing a supercell consisting of 12 000 atoms. The energy profile for lithium ion movement was computed at volumes corresponding to ambient and superionic regimes. The energy considerations along various symmetry directions indicated that [001] was the most favorable direction for lithium movement in the fast ion phase. This result corroborated our observation of dynamic instability in the transverse phonon mode along the (110) wave vector. Using molecular dynamics simulations, we studied the temperature variation of elastic constants, which showed a large decrease in C${}_{11}$, consistent with known experimental observation.

Detection of elastic and electric conductivity anomalies in Potassium Sulphamate single crystal

Elastic anomalies in Potassium Sulphamate, (KNH 2SO 3), above room temperature were detected from temperature variation of elastic constants measured by ultrasonic Pulse Echo Overlap technique. Potassium Sulphamate has been reported to be a ferroelectric and piezo electric material. The elastic constants C 11, C 44, C 55 and C 66 have exhibited weak anomalies around 350 K. The DC conductivity measurement along a, b, and c axes also supports this conclusion.

Temperature variation of elastic constants of quartz across the α - β transition

The α − β transition of quartz was successfully observed with using a single sample by means of the rectangular parallelepiped resonance (RPR) method. An oriented rectangular parallelepiped of α-quartz single crystal was prepared and the resonant frequencies of 30–11 vibrational modes were measured from room temperature to 700°C. The softening of quartz crystal was observed as the significant reduction of resonant frequencies near the α–β transition. The present study is the first application of the RPR method to the study of phase transition. The complete set of elastic constants of α- and β-quartz were determined as a function of temperature by the least-squares inversion of the measured frequency data obtained by a single run. This is a merit yielded by the RPR method. It is shown near the α − β transition in both α- and β-quartz that the elastic parameters decrease proportionally to |T−T 0|−n , where T is temperature and T 0 is the transition temperature, 573.0°C for α-quartz and 574.3°C for β-quartz. It was also seen that linear incompressibilities K 1 = (C 11 +C 12 +C 13)/3 and K 3 = (C 33 +2C 13)/3 decrease rapidly toward the transition, whereas, shear moduli C 44, C S1 = (C 11 +C 33 -2C 13)/4 and C S3 = (C 11 -C 12)/2 = C 66 decrease only slightly. The shear modulus C S3 = C 66 increased slightly in α-quartz. The elastic properties of isotropic aggregate of quartz were calculated, and it is shown that the longitudinal wave velocity significantly decreases at the α − β transition, whereas, the shear wave velocity decreases only slightly.

Elastic constants of nematic liquid crystals of uniaxial symmetry

We study, in detail, the influence of molecular interactions on the Frank elastic constants ofuniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. This workis based on a weighted density functional formalism developed by us in a previous paper(Singh et al 1992 Phys. Rev. A 30 583). A brief summary of the status of theoreticaldevelopment for the elastic constants of nematics is presented. Considering a pair potentialhaving both repulsive and attractive parts, numerical calculations are reported for threenematics: MBBA, PAA and 8OCB. For these systems the length-to-width ratiox0 is estimated from the experimentally determined structure of the molecules. The repulsiveinteraction is represented by a repulsion between hard ellipsoids of revolution (HER) andthe attractive potential is represented by the quadrupole and dispersion interactions. Fromthe numerical results we observe that in the density range of nematics the contributions ofthe quadrupole and dispersion interactions are small as compared to the repulsiveHER interaction. The inclusion of attractive interactions reduces the values ofelastic constant ratios. The absolute values of elastic constants are sensitive tothe values of potential parameters. The elastic constants and their ratios are inagreement with the experimental and computer simulation values. The temperaturevariation of elastic constants and their ratios are reported and compared withthe experimental values. It is found that the calculated values are in agreementwith the experimental data. The twist elastic constant has a weak temperaturedependence but a pronounced influence is found on the bend elastic constants.

Ultrasonic measurement of the elastic constants of LiKSO 4 between 300 and 370 K

All five independent elastic constants of LiKSO 4 have been determined from absolute velocity measurements on single crystal samples using ultrasonic pulse echo overlap technique. The constant C 13 is reported for the first time. Measurement of the temperature variation of elastic constants between 300 and 370 K indicates no anomaly near 333 K, ruling out a phase transition occurring in the sample at this temperature reported in an earlier Brillouin scattering work.

Defects and Ion Transport Properties of Yttrium Doped Zirconia

AbstractA comparison of calculated and experimental temperature variation of elastic constants were used to predict types of oxygen—vacancy dopant clusters in yttria stabilised cubic zirconia, which serves as an electrolyte in solid oxide fuelcells. Such clusters were incorporated in supercells set up for molecular dynamics studies, where oxygen transport properties were investigated at concentrations of 9.4 and 24 mol % of yttrium oxide and up to 1600K.

Temperature variation of elastic constants of NaCl.

Isothermal elastic constants ${\mathit{C}}_{11}$, ${\mathit{C}}_{12}$, and ${\mathit{C}}_{44}$ have been evaluated for crystalline NaCl using a realistic potential of the form ${\mathit{AR}}^{\mathrm{\ensuremath{-}}8}$+${\mathit{BR}}^{\mathrm{\ensuremath{-}}6}$\ifmmode\pm\else\textpm\fi{}${\mathit{CR}}^{\mathrm{\ensuremath{-}}1}$ and normal-mode frequencies obtained from local dynamics of two particles allowed to oscillate in a static potential field due to all the rest of the particles assumed at rest in their mean positions. The temperature variation of these principal elastic constants is examined in comparison with the available experimental data, and a reasonable agreement is observed.

Computer Modelling of Elastic Properties of LaF3Using Free Energy Minimisation Techniques

Abstract An effective use of computer simultion methods in the study of solids depends on the derivation of reliable potential models. Hence, the empirically derived interionic potentials of LaF3 were tested by free energy minimisation techniques, within the quasi-harmonic approximation. This was achieved by calculating the temperature variation of elastic constants derived directly from the shell model potentials. These changes agree reasonably well with those calculated from an experimental lattice expansion, below 800 K. However, the departure from linearity and experimental results occur in the range 800–1100 K, which is below the transition temperature to the state of high ionic conductivity. This shows how far the fitted shell model potentials can reliably predict the elastic behaviour of LaF3.

Temperature variations of the elastic constants of CaF2 and SrF2 crystals.

We have investigated the temperature variations of the second-order elastic constants of ${\mathrm{CaF}}_{2}$ and ${\mathrm{SrF}}_{2}$ crystals by means of a three-body-interaction potential model which earlier has successfully described such variations exhibited by the other members of the fluorite family [Phys. Rev. B 39, 13493 (1989)]. Our results, obtained from the three-body-interaction potential model, have shown reasonably good agreement with their experimental neutron-scattering data. On the basis of these successful descriptions, we have concluded that three-body interactions and lattice anharmonicity play an important role in revealing the anomalous behavior and temperature variations of the elastic constants of fluorites.

Diffuse X‐ray scattering study of the temperature variation of elastic constants in indium arsenide

AbstractThe elastic constants of indium arsenide have been determined in the temperature range from 80 to 750 K on n‐type samples with a carrier concentration of about 8 · 1017 cm−3 by Wooster's method from the measurements of the thermal X‐ray diffuse scattering intensities. An average decrease in the elastic constants with increasing temperature over the above mentioned temperature range is found to be about 8%.

Low-temperature elastic-constant anomalies in Fe-Cr-Ni-Mn alloys

By measuring velocities of longitudinal and shear waves we determined accurately the temperature variation of elastic constants — Young modulus, shear modulus, bulk modulus, Poisson ratio — of a polycrystalline austenitic steel: Fe-5Cr-26Mn. Versus temperature, near 335 K, this alloy exhibits an anomalous elastic-constant transition. In similar alloys, a magnetic-susceptibility cusp occurs at the transition temperature, T c,. The bulk modulus shows a maximum at a higher temperature. Below T c, the Poisson ratio behaves anomalously, increasing with decreasing temperature.

Elasticity and Orientational Order in Sometrans-p-n-Alkoxy-α-methyl Cyanophenyl Cinnamates

Abstract The splay (k 11), twist (k 22) and bend (k 33) elastic constants determined by the Freedericksz method and the orientational order parameters (s) derived from optical measurements in the nematic phase of six homologues of trans-p-n-alkoxy-α-methyl cyanophenyl cinnamates (n OMCPC) are reported. The data close to the nematic-isotropic transition point (T NI) are compared with T NI and the heats of transition (ΔH). The temperature-variation of elastic constants is discussed in terms of existing theories. The pretransitional increase in the twist and bend constants near the nematic-smectic A transition point (T NA ) of 10 OMCPC has also been analysed.

Temperature variation of elastic constants of pyrope-almandine garnets.

Elastic constants of three natural pyrope-almandine garnets (Fe/(Mg+Fe)=0.18, 0.48 and 0.58) were measured by an RPR method in the temperature range between -190° and 80°C. The temperature derivative of bulk modulus ∂Ks/∂T does not depend much on the composition, but those of shear constants ∂C44/∂T and∂Cs/∂T [Cs=(C11-C12)/2] increase considerably with increase in the Fe-content. The temperature derivatives of the elastic constants (kbar/deg) of pyrope and almandine at room temperature are determined by extrapolation: From the measured elastic parameters of garnet, the material of the high velocity layer (Vp=8.6km/s and Vs=4.9km/s) in the oceanic lithosphere is interpreted as eclogite or garnet peridotite constituted dominantly of garnet.

Temperature variation of elastic constants of single-crystal forsterite between -190.DEG. and 400.DEG.C.

Elastic constants of forsterite Mg2SiO4 were measured by the rectangular parallelepiped resonance (RPR) method at temperatures between -190° and 400°C. Elastic constant Cij(Mbar) and their temperature derivatives ∂Cij/∂T (kbar/deg) are:The adiabatic bulk modulus Ks=1.292Mbar (25°C) and its temperature derivatives ∂Ks/∂T=-0.160kbar/deg (20°-400°C) are obtained by the Voigt-Reuss-Hill scheme.In the temperature range from 100 to 1000K, the Gruneisen constant calculated from the measured bulk modulus is virtually constant at 1.1±0.1, while the Gruneisen-Anderson parameter δs, defined as -(∂ In Ks/∂T)/α(α: the coefficient of volume thermal expansion), decreases with increase of temperature, but tends to approach a constant value of 4.0±0.1 above 500K.

Temperature Variation of the Elastic Constants of Cubic Elements. I. Copper

The ultrasonic pulse technique has been used in conjunction with a specially devised cryogenic technique to measure the velocities of 10-Mc/sec acoustic waves in copper single crystals in the range from 4.2\ifmmode^\circ\else\textdegree\fi{}K to 300\ifmmode^\circ\else\textdegree\fi{}K. The values and the temperature variations of the elastic constants have been determined. The room temperature elastic constants were found to agree well with those of other experimental works. Fuchs' theoretical ${c}_{44}$ at 0\ifmmode^\circ\else\textdegree\fi{}K is 10 percent larger than our observed value but his theoretical ${c}_{11}$, ${c}_{12}$, $K$ and (${c}_{11}\ensuremath{-}{c}_{12}$) agree well with the observations. The isotropy, $\frac{({c}_{11}\ensuremath{-}{c}_{12})}{2{c}_{44}}$, was observed to remain practically constant from 4.2\ifmmode^\circ\else\textdegree\fi{}K to 180\ifmmode^\circ\else\textdegree\fi{}K, then to diminish gradually at higher temperatures. Some general features of the temperature variations of elastic constants are discussed.