Estimation of the thermal diffusivity of solids based on ‘instantaneous velocimetry’ using an interferometer

A conceptually new approach is proposed to estimate the thermal diffusivity of optically transparent solids at ambient temperature based on the ‘position-dependent instantaneous velocity’ of isothermal surfaces using a self-reference interferometer. A new analytical model is proposed using the exact solution to relate the instantaneous velocity of isothermal surfaces with the thermal diffusivity of solids. The experiment involves setting up a one-dimensional non-stationary heat flow inside the solid via step-temperature excitation to launch a spectrum of dissimilar ‘moving isothermal surfaces’ at the origin. Moving isothermal surfaces exhibit macroscale ‘rectilinear translatory motion’; the instantaneous velocity of any isothermal surface at any location in the heat-affected region is unique and governed by the thermal diffusivity of the solids. The intensity pattern produced by the self-reference interferometer encodes the moving isothermal surfaces into the corresponding moving intensity points. The instantaneous velocities of the intensity points are measured. For a given thermo-optic coefficient, the corresponding values of the isothermal surfaces are predicted to estimate the thermal diffusivity of the solids using BK7 glass as an example. Another improved method is proposed in which thermal diffusivity is estimated without measuring thermo-optic coefficient and quartz glass is utilized as a specimen. The results obtained using the proposed approaches closely match with the literature value.     

Inverted equations of state for solids under high pressures

In the present communication we have reviewed some inverted type equations of state for solids under high pressures. An inverted equation of state (EOS) gives volume as a function of pressure for a solid under isothermal conditions. We have considered various equations of state proposed by earlier workers which express volume as a function of pressure. Expressions for bulk modulus and its pressure derivatives based on such EOSs are obtained and reported here. It is emphasized here that the high pressure derivative properties are very sensitive to the forms of equations of state representing volume-pressure relationships. We have also studied the thermoelastic properties of solids based on pressure derivatives of bulk modulus. Applications have been extended in the present review article to the solids which are metals as well as non-metals including geophysical minerals present in the lower mantle and core of the Earth.     

Estimates of isothermal bulk moduli for group iva crystals with the zincblende structure

By equating the differential changes in macroscopic work of compression and potential energy for group IVA crystals of the zincblende structure we have obtained an expression for the isothermal bulk modulus as a function of pressure. The model used for the potential energy for these covalent crystals is that of distinct nearest-neighbor bonds with force constants taken directly from the molecular seriesX₂H₆ andXYH₆. We calculate this isothermal bulk modulus in the limit of zero external pressure to be 4070 (4420, 5450, 5600), 1060 (970·8, 988), 960 (712, 724·3, 771·7), 720±50 (?) and 2240 (?) kbar for diamond, Si, Ge, sn (α, gray), and SiC (β, cubic) respectively, with experimental data in parentheses. It would seem that the value for α-Sn lies in the range 400–800 kbar, while that for β-SiC may not differ much from the calculated one. The treatment of a zincblende structure covalent crystal as a giant molecule for purposes of estimating low pressure isothermal bulk moduli is thus fairly satisfactory. For extending the moduli to higher pressures it suffers a serious defect as the (dimensionless) pressure derivative of the isothermal bulk modulus in the limit of zero pressure turns out to be 1·0 for all covalent solids regardless of the number of bound neighboring atoms, compared to e.g. 4·16 and 4·35 for Si and Ge.     

Isothermal equation of state for the skutterudites CoSb3 and LaFe3CoSb12

The thermoelectric materials CoSb₃ and LaFe₃CoSb₁₂ with skutterudite structure were subjected to high pressures using a diamond anvil high-pressure cell up to 20 GPa. Energy-dispersive X-ray diffraction was used to determine the dependence of the lattice parameter on pressure. No major change in the X-ray diffraction spectra was observed for both compounds, constituting evidence that both compounds are stable within this pressure range, despite their relatively open structures. Three distinct isothermal equations of state for solids under high pressure were fitted to the experimental data to determine the bulk modulus for both compounds. The filled skutterudite showed a greater compressibility than the unfilled one, this difference can be understood in terms of the larger lattice parameter of the former.     

Temperature effects on a new equation of state of solids

Recently we have proposed an isothermal equation of state of solids, and applied it to a variety of substances to show that it agrees with the isothermal pressure-volume data quite accurately up to ultrahigh pressures, and that its agreement with data is superior to the existing equations of state. Further, it has been shown that the bulk modulus and its first pressure derivative, extracted by it, are in excellent agreement with experiment. In the present study, temperature effect is added on this new equation of state, following a widely used approach involving the input of zero-pressure bulk moduli parameters and thermal expansion, all evaluated at a single reference temperature. The resultant temperature-dependent equation of state is applied to predict the isotherms over a wide range of temperature, the thermal expansion as a function of temperature, and the temperature dependence of the isothermal bulk modulus and its pressure derivative. These predictions are tested using literature data for four solids: sodium chloride, gold, molybdenum and tungsten. Good agreement is obtained between theory and data. Furthermore, the predictions are compared with those obtained from a similar temperature-dependent equation of state recently proposed, and the superior prediction capability of our model, in the P-V-T space, is demonstrated.     

Design and development of a controlled pressure/temperature set‐up for in situ studies of solid–gas processes and reactions in a synchrotron X‐ray powder diffraction station

A novel set‐up has been designed and used for synchrotron radiation X‐ray high‐resolution powder diffraction (SR‐HRPD) in transmission geometry (spinning capillary) for in situ solid–gas reactions and processes in an isobaric and isothermal environment. The pressure and temperature of the sample are controlled from 10^?3 to 1000 mbar and from 80 to 1000 K, respectively. To test the capacities of this novel experimental set‐up, structure deformation in the porous material zeolitic imidazole framework (ZIF‐8) by gas adsorption at cryogenic temperature has been studied under isothermal and isobaric conditions. Direct structure deformations by the adsorption of Ar and N₂ gases have been observed in situ, demonstrating that this set‐up is perfectly suitable for direct structural analysis under in operando conditions. The presented results prove the feasibility of this novel experimental station for the characterization in real time of solid–gas reactions and other solid–gas processes by SR‐HRPD.     

Assembling of hydrogenated aluminum clusters

The electronic and atomic structure of Al₁₃H has been studied using Density Functional Theory. Al₁₃H has closed electronic shells. This makes the cluster very stable and suggests that it could be a candidate to form cluster assembled solids. The interaction between two Al₁₃H clusters was analyzed and we found that the two units preserve their identities in the dimer. A cubic-like solid phase assembled from Al₁₃H units was then modeled. In that solid the clusters retain much of their identity. Molecular dynamics runs show that the structure of the assembled solid is stable at least up to 150 K. A favorable relative orientation of the clusters with respect to their neighbors is critical for the stability of that solid. Received 21 November 2000     

应用于碱卤化物固体的通用状态方程

提出一种能精确考虑固体结合能的通用状态方程,并且在高压和膨胀区域都具有正确的行为,不会出现物理上不正确的振荡现象.将新方程与文献中的典型方程应用于15种碱金属卤化物和一种碱土金属氧化物,结果表明新方程在给出正确结合能数据的同时,能够很好地拟合实验压缩数据.由Vinet方程和Morse方程定出的参数随数据范围变化很明显,新方程定出的参数随数据范围变化不明显.新方程的通用性优于Vinet方程和Morse方程. 关键词： 固体 通用状态方程 结合能 碱金属卤化物     

Electron inelastic mean free paths in solids: A theoretical approach

In the present paper, the inelastic mean free path (IMFP) of incident electrons is calculated as a function of energy for silicon (Si), oxides of silicon (SiO2 ), SiO, and Al2O3 in bulk form by employing atomic/molecular inelastic cross sections derived by using a semi-empirical quantum mechanical method developed earlier. A general agreement of the present results is found with most of the available data. It is of great importance that we have been able to estimate the minimum IMFP, which corresponds to the peak of inelastic interactions of incident electrons in each solid investigated. New results are presented for SiO, for which no comparison is available. The present work is important in view of the lack of experimental data on the IMFP in solids.     

Synthesis and photoluminescence characteristics of AlN nanocrystalline solids

A new condensed form of AlN nanocrystalline solids was obtained directly from reactions of metal Al and (NH₄Cl+NH₄I) in liquid ammonia at 550 °C, without the subsequent consolidation process as in the conventional method. The synthesized product is a transparent bulk solid, while the constituted nanocrystals have an average size of about 18 nm and possess the same wurtzite structure as bulk AlN. (NH₄Cl+NH₄I), which plays a role of a catalyst in the present synthetic route, is indispensable. The photoluminescence spectrum of the AlN nanocrystalline solids shows a broad blue band centered at 400 nm. Received: 20 June 2000 / Accepted: 22 June 2000 / Published online: 9 August 2000     

High pressure phase transitions in organic solids I:α → β transition in resorcinol

An experimental program has been started to study polymorphic phase transitions under pressure in organic solids using the Be gasketing technique developed by us. This allows us to obtain x-ray diffraction patterns of low symmetry organic solids with high resolution, employing CuK _α radiation. The first organic solid studied is α-resorcinol. At 0.5 GPa, it transforms to its high temperature and denser modification, β-resorcinol. The transformation mechanism is discussed with the help of molecular packing calculations.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

Study of the form of nuclear magnetic resonance lines in solids with internal mobility by the “moment” method

A new approach is proposed for study of the form of nuclear magnetic resources (NMR) lines in solids with internal mobility of the magnetic nuclei. The NMR spectra are represented in the form of an infinite continued fraction, summation of which permits obtaining the line form to any desired accuracy. The proposed method is used to study diffusion mobility of fluorine ions in PbF₂.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 15–20, November, 1989.The authors express their deep gratitude to V. M. Buznik and V. A. Vopilov for providing the NMR spectra and to R. Ya. Zakirov for synthesizing the specimen.     

The Debye temperature and Grüneisen parameter of the CaLa<Subscript>2</Subscript>S<Subscript>4</Subscript>-La<Subscript>2</Subscript>S<Subscript>3</Subscript> system

The thermal expansion coefficient of solid solutions in the CaLa₂S₄-La₂S₃ system at a temperature of 300 K is investigated experimentally. The Debye temperature, the Grüneisen parameter, and the isothermal compressibility coefficient of solid solutions in the system under investigation are determined from the experimental thermal expansion coefficient. It is demonstrated that, upon substitution of calcium ions for cation vacancies in La₂S₃, the Debye temperature decreases, the isothermal compressibility coefficient increases, and the Grüneisen parameter remains constant for all compositions in the CaLa₂S₄-La₂S₃ system. A correlation between the ionic radii of Ca²⁺ and La³⁺, the concentration of cation vacancies, and the rigidity of the lattice, on the one hand, and the Debye temperature, the Grüneisen parameter, and the isothermal compressibility coefficient, on the other, is revealed for the studied samples.     

Analysis of thermoelastic constants of solids and minerals at high temperatures

In the present communication, the thermoelastic constants of ionic solids NaCl and KCl and the minerals MgO, CaO and Mg₂SiO₄ are analyzed using the tabulated data compiled by Anderson and Isaak. It is found that there exists a precise linear relationship between the thermoelastic constant and the thermal pressure. The proposed empirical relationship provides a method to estimate the thermoelastic properties out side the experimental data range.     

A novel pressure–velocity formulation and solution method for fluid–structure interaction problems

In the standard approach for simulating fluid–structure interaction problems the solution of the set of equations for solids provides the three displacement components while the solution of equations for fluids provides the three velocity components and pressure. In the present paper a novel reformulation of the elastodynamic equations for Hookean solids is proposed so that they contain the same unknowns as the Navier–Stokes equations, namely velocities and pressure. A separate equation for pressure correction is derived from the constitutive equation of the solid material. The system of equations for both media is discretised using the same method (finite volume on collocated grids) and the same iterative technique (SIMPLE algorithm) is employed for the pressure–velocity coupling. With this approach, the continuity of the velocity field at the interface is automatically satisfied. A special pressure correction procedure that enforces the compatibility of stresses at the interface is also developed. The new method is employed for the prediction of pressure wave propagation in an elastic tube. Computations were carried out with different meshes and time steps and compared with available analytic solutions as well as with numerical results obtained using the Flügge equations that describe the deformation of thin shells. For all cases examined the method showed very good performance.     

Five-parameter equation of solids considering thermal effect which correctly incorporates cohesive energy

A five-parameter equation of state (EOS) is proposed, which correctly incorporates the cohesive energy data without physically incorrect oscillations in both extreme high pressure and expansion regions. Based on a modified Einstein model, the thermal effect is included in the proposed EOS complying with the zero-pressure condition. With this thermal EOS applied to five solids (Ar, Al, Au, Cu and Li), some important thermodynamic properties as isotherm, isochore, thermal expansion coefficient, volume modulus, heat capacity and Hugoniot are calculated for each selected solid with good agreement with experimental data, which confirms the validity of the present work     

A model of melting of rare gases within bubbles of crystalline metal matrix

Abstract

On the basis of experimental results obtained in the present and some other works a model of melting of rare gas solids within bubbles formed in a crystalline metal matrix as a result of ion implantation is proposed. Rare gas solid is supposed to melt on heating at the expense of the bubble volume expansion by emission of a dislocation loop. On this basis the melting temperature can be estimated as one which is enough to provide for a pressure inside a bubble sufficient for the initiation of the dislocation loop punching. Values of melting temperatures obtained in this way are in good agreement with available experimental data.     

Static and thermophysical properties of chalcogenide crystals with NaCl structure

In the present communication an analysis of interionic potentials in fourteen chalcogenide crystals has been performed. This interionic potential has been used to predict the values of cohesive energy, isothermal bulk modulus and the pressure derivatives of bulk modulus in the solids under study. The many body interaction (MBI) effects have been taken into account within the framework of Hafemeister Zarht potential. Instead of using BM potential the Hafemeister-Zarht (HZ) type short range overlap potential has been considered between nearest as well as between next nearest neighbour ions. The short-range interactions, effective up to second neighbours are treated by considering the hardness parameter as an ionic property. The hardness parameter ρ_ij is evaluated using the data on overlap integrals. The results achieved in the present study are generally in good agreement with available experimental data. Values of cohesive energy, bulk modulus and its pressure derivatives calculated by previous investigators have also been shown for the sake of comparison.     

Thermodynamic and magnetic properties of LaSn3

Thermal expansion coefficient between 77 and 900K, isothermal compressibility in the 0–80 Kbar pressure range, magnetic susceptibility between 77 and 1300 K and heat capacity at constant pressure in the 20–300 K temperature range were determined for the LaSn₃ compound. From the experimental data, the specific heat at constant volume was calculated and the thermal dependence of the Debye's parameter θ_D was obtained. The electron contribution to the heat capacity was also determined from the high temperature data. The magnetic properties confirm that there is no evidence of the existence of a magnetic moment localized on La atoms, in contrast with a previous report and in agreement with the general assumptions. A little anomaly found in the expansion coefficient, in the isothermal compressibility and in the specific heat is discussed in terms of a lattice order-disorder phenomenon.