Showing papers on "Debye model published in 1973"
TL;DR: In this article, the phonon dispersion relations for gold in the high-symmetry directions have been measured at room temperature by the coherent inelastic scattering of neutrons.
Abstract: The complete phonon dispersion relations for gold in the high-symmetry directions have been measured at room temperature by the coherent inelastic scattering of neutrons. It is found that the forces in gold are not homologous with the other noble metals, the frequencies of gold lying appreciably higher than those "scaled" from copper and silver. An analysis of the data in terms of different force-constant models reveals that a general tensor force is required for the first-neighbor interaction, whereas for neighbors beyond the first either general tensor or axially symmetric forces give an excellent fit to the data. The axially symmetric model alone does not adequately describe the data even when forces extending to ninth-nearest neighbors are included in the fit. In addition, simple screened-pseudopoential models were fit to the data and these results also indicate the need for the first-neighbor interaction to be general. Frequency distribution functions and related thermodynamic quantities were calculated from the various force-constant models. The Debye temperature ${\ensuremath{\Theta}}_{C}$ versus temperature curves obtained show an anomaly at low temperatures consistent with the ${\ensuremath{\Theta}}_{C}(T)$ obtained from specific-heat measurements. The relation between this anomaly and the character of the dispersion curves is given.
268 citations
TL;DR: In this article, the adiabatic elastic constants of GaAs (n type carrier density 1.3*1016 cm-3) have been obtained between 2 K and 320 K from measurements of ultrasonic wave velocities by the pulse superposition technique.
Abstract: The adiabatic elastic constants of GaAs (n type carrier density 1.3*1016 cm-3) have been obtained between 2 K and 320 K from measurements of ultrasonic wave velocities by the pulse superposition technique. One aim has been to compare the results with the somewhat scattered data obtained at room temperature by previous workers: particular attention has been paid to estimation of the overall uncertainty in the elastic constants. At 298 K, C11=1.1841+or-0.0037, C12=0.537+or-0.016 and C44=0.5912+or-0.0018 in units of 1012 dynes cm-2. The Debye temperature (346.8 K) computed from the data extrapolated to 0 K is in excellent agreement with that (346.7 K) derived from low temperature specific heat measurements. The temperature dependence of the elastic constants have been fitted by an anharmonic oscillator model. The force constants and effective charge have been calculated on the basis of a rigid-ion model. The Gruneisen parameter, particle displacement and energy-flux vectors and cross-sections of the Young's modulus and wave velocity surfaces have been compiled.
140 citations
TL;DR: The absolute Seebeck coefficient of platinum was determined from 80 to 340 K by direct comparsion to lead as discussed by the authors, which was within 1% of the Sommerfeld value of 2.443×10−8 (V/K)2 from 1.0 to 5.0 ΘD.
Abstract: The absolute Seebeck coefficient of platinum was determined from 80 to 340 K by direct comparsion to lead. Results of this comparison disagree with previous results which have been used for the calculation of absolute values for other materials. The thermal conductivity λ and electrical resistivity ρ of the lead standard were also determined. The electrical resistivity could be described with a modified Gruneisen‐Bloch equation which allows for the effect of thermal expansion on the Debye temperature ΘD. The ratio λρ/T was within 1% of the Sommerfeld value of 2.443×10−8 (V/K)2 from 1.0 to 5.0 ΘD.
104 citations
TL;DR: In this paper, a thermodynamic theory for some types of dielectric and magnetic relaxation phenomena is developed, where a polar and an axial vector field occur as internal thermodynamic degrees of freedom and that these fields influence the polarization and magnetization, respectively.
72 citations
TL;DR: In this paper, a Born-von K\'arm\'an model was fitted to the experimental frequencies of copper and the best fit was obtained using a model with general forces extending to eighth nearest neighbors.
Abstract: Phonon frequencies of copper have been measured at 80 K with a neutron crystal spectrometer at a large number of points---mainly in off-symmetry directions. The frequency distribution is calculated, and also the Debye temperature in the interval 0-300 K. The agreement with calorimetric measurements is very satisfactory. Several Born-von K\'arm\'an models were fitted to the experimental frequencies. The best fit was obtained using a model with general forces extending to eighth nearest neighbors. The conditions for axial symmetry of the interatomic forces are much better fulfilled in copper than, for instance, in aluminum. However, a general force model is preferable also for copper when a good fit in the whole zone is wanted.
68 citations
TL;DR: In this paper, the elastic constants and thermal expansion of single-crystal CdTe have been measured in the temperature range 42-300 K. An anomaly in both parameters is observed, which has hitherto not been reported, and is tentatively attributed to a change in ionicity.
Abstract: The elastic constants and thermal expansion of single-crystal CdTe have been measured in the temperature range 42-300 K. The values of elastic constants obtained at 298 K were C11=538×1010 N m−2, C12=374×1010 N m−2 and C44=2018×1010 N m−2. Their temperature variation is in good agreement with Vekilov and Rusakov's (1971) values and the temperature dependence of the thermal expansion is similar to the other measurements in the literature. An anomaly in both parameters is observed, which has hitherto not been reported, and is tentatively attributed to a change in ionicity. The Debye temperature at 0 K is calculated from the elastic constants and a value of 1627 K obtained.
67 citations
01 Jun 1973
47 citations
TL;DR: The elastic properties of polycrystalline monoclinic Gd2O3 were determined by the sonic-resonance method as mentioned in this paper, where the porosity varied from 0.025 to 0.367 and temperature from room temperature to 1400°C.
Abstract: The elastic properties of polycrystalline monoclinic Gd2O3 were determined by the sonic-resonance method. Volume-fraction porosity varied from 0.025 to 0.367 and temperature from room temperature to 1400°C. The Young's and shear moduli are linear functions of volume-fraction porosity, but the rate of their decrease with increasing porosity is less than that expected. The moduli decreased more rapidly than expected with increasing temperature. The Debye temperature is 362°K. With increasing temperature, the first Grueneisen constant, γ, decreases, whereas the second Grueneisen constant, δ, increases.
46 citations
TL;DR: In this paper, specific heat measurements were performed on small lead particles (22, 37, and 60 \AA{}) and 22 indium particles over the temperature range 1.5-15 K. For all sizes the enhancement of the specific heat due to the increased importance of lowfrequency surface modes and attendant depletion of higher-frequency modes was observed.
Abstract: Specific-heat measurements were performed on small lead particles (22, 37, and 60 \AA{}) and 22 \AA{} indium particles over the temperature range 1.5-15 K. For all sizes the enhancement of the specific heat due to the increased importance of low-frequency surface modes and attendant depletion of higher-frequency modes was observed. Although the magnitude of the observed surface-phonon specific heat agrees reasonably well with theoretical estimates at intermediate temperatures, the observed enhancements apparently are not proportional to the surface area and do not exhibit quadratic temperature dependence. The rapid decreases of the heat capacity at lowest temperature appear to be consistent with the estimates of low-frequency cutoffs in the phonon spectrum caused by quantum size effect. At temperatures around one-tenth of the bulk Debye temperature the surface specific heats exhibit maxima. Differences in the electronic specific heat in the superconducting state between small particles and the bulk were observed. The transition-temperature behavior of lead and indium particles is also discussed.
46 citations
TL;DR: In this paper, sound velocities of hexagonal close-packed H2 and D2 were measured at 4.2 K and at constant volume as a function of X in solid H 2 and D 2, respectively.
Abstract: Sound velocity measurements are reported on samples of hexagonal close-packed H2 and D2, believed to be single crystals. In the first part of the experiments, both the longitudinal and transverse velocities (v
1
and v
t
) of crystals grown at a given melting pressureP
M
were measured at 4.2 K. For each mode, the velocities plotted vs.P
M
were found to lie between approximately parallel lines that represented the maximum and minimum observable velocities under the given experimental conditions set by the acoustic cell dimensions. From these extreme velocities v
1max, v
1min, v
tmax, and v
tmin an estimation of the elastic constants was made. Knowledge of these constants in turn permitted the calculation of the velocity surface, the bulk modulus, and the Debye temperature. In spite of the uncertainties in the analysis of the present data, a meaningful comparison could be made with results from other experiments. For both and D
2
, the elastic constants are on the average ∼20% below those derived from neutron scattering data. The transverse velocities, both for H
2
and D
2
, are consistent with those of Bezuglyi and Minyafaev for polycrystalline samples, but the longitudinal velocities are about 10% smaller than those of these authors. The bulk modulus and the Debye temperature from our experiments are compared with those from equation-of-state and calorimetric experiments. In the second part of this research, we have investigated the temperature dependence of the sound velocities at constant volume for both H
2
and D
2
with low concentrationsX of molecules with rotational angular momentumJ=1. From the measurements in H
2
, we are able to calculate the temperature change in the bulk modulus, which is then compared with that calculated from calorimetric data assuming the validity of the Gruneisen equation of state. Good agreement is obtained. In solid D
2
, were were able to deduce the temperature dependence of the adiabatic and isothermal modulusc
33
and make a rough estimation for that ofc
13
. In the third part we present measurements of v
1
and v
t
at 42 K and at constant volume as a function ofX in solid H
2
. It is found that as the orthopara conversion proceeds,v
1
increases andv
t
decreases. From these measurements the bulk modulus change withX is calculated. Comparison with the bulk modulus change calculated from static pressure measurements, assuming electric quadrupole-quadrupole interaction between the (J=1) molecules, shows very good agreement. The calculated dependence of the Debye temperature onX, as obtained from a combination of sound velocity and static measurements, is smaller than that reported from recent neutron scattering results. A short section is then devoted to absorption measurements in solid H
2
, which gave only qualitative results. Finally, in Section 4, we present measurements of the sound velocity in liquid D
2
at saturated vapor pressure as a function of temperature and for both liquid H
2
and D
2
along the melting curve.
45 citations
TL;DR: Inelastic-neutron-scattering measurements of the phonon dispersion relation in thorium at room temperature are reported in this article, where the dispersion curves are dominated by nearest-neighbor interactions but indicate a residual long-range interaction to at least seventh nearest neighbors.
Abstract: Inelastic-neutron-scattering measurements of the phonon dispersion relation in thorium at room temperature are reported The measurements were made along the ($0,0,\ensuremath{\zeta}$), ($0,\ensuremath{\zeta},\ensuremath{\zeta}$), ($\ensuremath{\zeta},\ensuremath{\zeta},\ensuremath{\zeta}$), and ($0,\ensuremath{\zeta},1$) symmetry directions The dispersion curves are dominated by nearest-neighbor interactions but indicate a residual long-range interaction to at least seventh nearest neighbors A seventh-nearest-neighbor force-constant model was fitted to the data and used to obtain a frequency distribution function and the temperature dependence of the Debye temperature The transverse modes along the ($0,\ensuremath{\zeta},\ensuremath{\zeta}$) direction appear to show structure indicative of strong electron-phonon interaction effects
TL;DR: In this article, the elastic properties of tantalum have been investigated over the temperature range 4.2-300 K. The elastic constants become temperature independent at low temperatures and approach linear behavior at high temperatures.
Abstract: The elastic properties of tantalum have been investigated over the temperature range 4.2–300 K. The values of the adiabatic elastic constants C11, C44, and CL=(1/2) (C11+C12+2C44) at 4.2 K in units of 1012 dyn/cm2 are, respectively, 2.70, 0.873, and 3.02. The Debye temperature was calculated from the elastic constants and found to have the value of 265 K at low temperature. The elastic constants become temperature independent at low temperatures and approach linear behavior at high temperatures. In contrast to the normal behavior of the elastic constants, nuclear acoustic resonance experiments show anomalous line broadening.
TL;DR: A relation between the monovacancy formation energy and the Debye temperature for metals was first noticed by Mukherjee (1965) as discussed by the authors, who derived from fundamental considerations.
Abstract: A relation, first noticed by Mukherjee (1965), between the monovacancy formation energy and the Debye temperature for metals has been derived from fundamental considerations.
TL;DR: The elastic constants of single crystals of double hcp allotrope of praseodymium have been measured over the temperature range 4.2-300 K as mentioned in this paper, and it has been shown that the thermal expansion behavior at low temperatures is very highly anisotropic.
Abstract: The elastic constants of single crystals of double hcp allotrope of praseodymium have been measured over the temperature range 4.2–300 K. Maxima are observed near 100 K in the temperature dependences of C11, C33, and (C11 − C12)/2, and minima are observed near 30 K. The maxima correlate with the upper temperature limit of an anomalous contribution which has been reported in the heat capacity. The minima correlate with peculiar behavior which has been observed in other physical phenomena. Inference may be drawn from the elasticity data that the thermal expansion behavior of praseodymium at low temperatures is very highly anisotropic. Comparison of the elastic constants of praseodymium with available data for the other rare earths shows that the praseodymium data fit a general pattern. Evaluation from the elastic constants shows that the Debye temperature of praseodymium remains nearly constant throughout the temperature range of measurement within ± 2 K of 152 K.
TL;DR: In this article, the elastic coefficients of hexagonal erbium single crystals have been determlned by means of an ultrasonic pulse technique at a frequency of 10 MHz, between 4.2 and 300 deg K.
Abstract: The five independent elastic coefficients of hexagonal erbium single crystals have been determlned by means of an ultrasonic pulse technique at a frequency of 10 MHz, between 4.2 and 300 deg K. From the elastic coefficients were calculated the temperature variation of the directional adiabatic compressibilities (parallel and perpendicular to the hexagonal c axis), the limiting Debye temperature, and the anisotropy ratios. The elastic coefficients exhibit typical anomalies at the magnetic ordering transitions known to occur in erbium. The most prominent anomaly ln the elastic properties of erbium was found on the low-temperature side of the transition from the sinusoidal modulation of the antiferromagnetic arrangement into the helical (square-wave) one at 54 deg K. The character of this anomaly suggests the occurrence of a first-order phase change. The adiabatic compressiibilty in the direction parallel to the hexagonal axls displays an unusual 'softening'' effect at low temperatures. The limiting value of the Debye temperature of erbium, extrapolated to 0 deg K, is 190.3 deg K. The present measurements of the single-crystal elastic constants of erbuum and the reported magnetostriction data, enabled the calculation of the magnetoelastic energy contribution DELTA E/sub me/ to the total energy at the magnetic transition from square-wavemore » modulation to the conical ferromagnetic ordering at 19.5 deg K. DELTA E/sub me/ was found to be -1.01 J cm/sup -3/. (auth)« less
TL;DR: A complete set of intensity-energy spectra as a function of electron energy, crystal temperature, and incidence angle have been measured for the specular and the first-order nonspecular beams for the (111) xenon surface as mentioned in this paper.
Abstract: A complete set of intensity-energy spectra as a function of electron energy, crystal temperature, and incidence angle have been measured for the specular and the first-order nonspecular beams for the (111) xenon surface. The xenon single crystals were formed by epitaxial deposition onto a (100) iridium substrate and were of excellent order and purity. The character of the intensity-energy spectra indicated xenon to be a highly kinematic electron scattering material. Hence the formalism for kinematic scattering could be applied with confidence to the analysis of electron scattering in xenon and with specific reference to the surface dependence of the effective Debye temperature and to surface-layer thermal expansion.
TL;DR: In this paper, the thermal conductivity and heat capacity of polyethylene and nylon samples have been measured in the temperature range 0.15-4°K using a Debye ω2 phonon frequency distribution with constant mean free path internal boundary scattering and amorphous structure scattering.
Abstract: The thermal conductivity and heat capacity of polyethylene and nylon samples have been measured in the temperature range 0.15–4°K. A good theoretical fit is obtained for the thermal conductivity above 1°K by using a Debye ω2 phonon frequency distribution with constant mean free path internal boundary scattering and amorphous structure scattering. Below 1°K the experimental results show a lower power dependence on temperature than would be predicted by the above theory. The theory can be modified to fit the low‐temperature data by the addition of a term containing a frequency distribution proportional to ω, corresponding to two‐dimensional vibrations due to the platelike nature of the individual crystallites. At temperatures below 1°K the heat‐capacity data show a lower power dependence on temperature than that predicted by the Debye model. The proposed phonon frequency distribution also provides a satisfactory explanation for this behavior.
TL;DR: In this paper, the critical magnetic field for superconductivity In tungsten from 5.5 to 15 mK using a {gamma}-ray anisotropy thermometer was measured, and the heat capacity between 0.35 and 25 K.
Abstract: We have measured the critical magnetic field for superconductivity In tungsten from 5.5 to 15 mK using a {gamma}-ray anisotropy thermometer, and we have measured the heat capacity between 0.35 and 25 K. Analysis of the data gives H{sub 0} = 1.237 Oe for the 0 K critical field, T{sub c} = 16.0 mK for the critical temperature, {gamma} = 1.008 mJ/mole K{sup 2} for the coefficient of the electronic heat capacity, and {Theta}{sub 0} = 383 K for the 0 K Debye temperature. The measured values of the critical field H{sub c} are consistently higher than those reported by Black, Johnson and Wheatley (BJW) on the CMN temperature scale, but the temperature dependence is similar. This discrepancy and the temperature dependence of H{sub c} suggest that both sets of H{sub c} data are affected by magnetic impurities. Use of the calorimetric {gamma} value permits an improved test of the CMN temperature scale with the very low temperature H{sub c} data obtained by BJW.
TL;DR: In this article, the authors report the properties of amorphous and partly crystalline materials below 4 K in terms of thermal conductivity, specific heat capacity, and velocity of sound in materials useful for the construction of cryogenic apparatus.
TL;DR: In this paper, the adiabatic elastic constants of holmium were determined in the temperature range from 78 to 300 K, using high-purity single crystals, and the constants were obtained from the ultrasonic-wave velocities (20 MHz) measured by the pulse-superposition method.
Abstract: The adiabatic elastic constants of holmium were determined in the temperature range from 78 to 300 K, using high‐purity single crystals. The constants were obtained from the ultrasonic‐wave velocities (20 MHz) measured by the pulse‐superposition method. The values of the constants at room temperature in units of 1011 dyn/cm2 are c33 =8.015, c44=2.592, c11 =7.612, c12=2.600, and c13 =2.072. Using these values, the Debye temperature was computed to be 181 K. The sound velocities tend to vary with temperature in an anomalous fashion near the Neel temperature (TN=131 K). Attenuation and sound‐velocity measurements near TN permit an estimate of the relaxation time for spin fluctuations, which was found to be 3×10−10 sec.
TL;DR: In this article, the elastic properties of InBi have been found to show the characteristics of a layer-like crystal with weak interlayer binding; this finding is illustrated by the linear compressibilities and by a compilation of cross-sections of the wave velocity and Young's modulus surfaces.
01 Jan 1973
TL;DR: In this paper, a simple expression for the Debye characteristic temperature at absolute zero was developed under the assumption that cubic solids show polycrystalline behavior as well as are well represented by Debye's model at near absolute zero.
Abstract: Near absolute zero, a solid can be very well represented by means of Debye's continuum model. The calculation of OO(D), the Debye characteristic temperature at absolute zero, is then given in terms of the elastic constants of the solid. In the past, severa1 theoretical expressions have been developed by Blackman', de Launay, Hopf-Lechner3, Houston, Bhatia and Tauber and by Fedorov. A11 these methods utilize physical properties of the crystal which can be expressed in terms of averages involving its elastic constants. Recently, Konti and Varshni have reviewed and revised the different methods of calculating O0(D), for 24 cubic solids. We have developed a very simple expression to calculate Oo(D) under the assumption that cubic solids show polycrystalline behavior as well as are well represented by Debye's model at absolute zero. The calculated values of Oo(D), for 24 cubic crystals, have been compared
TL;DR: In this article, experimental data for NQR frequency shifts as a function of temperature reveal a dominant T4 dependence at sufficiently low temperature, T ⪝ 20°K, in accord with a recent prediction.
Abstract: Analyses of experimental data for NQR frequency shifts as a function of temperature reveal a dominant T4 dependence at sufficiently low temperature, T ⪝ 20°K, in accord with a recent prediction. The results indicate the necessity of adding a Debye term to the usual Bayer expression. The coefficient of the Debye term is shown to vary with TD−5; preliminary results indicate that values of the Debye temperature TD may be obtained from low temperature NQR data.
TL;DR: In this paper, the elastic properties, adiabatic compressibility and Debye temperature of twinned and non-twinned U3Si were determined by means of an ultrasonic pulse technique between liquid helium temperature and the ambient.
Abstract: The elastic properties, adiabatic compressibility and Debye temperature of twinned and non-twinned U3Si were determined by means of an ultrasonic pulse technique between liquid helium temperature and the ambient. The twinned and non-twinned face-centred tetragonal U3Si specimens were prepared employing appropriate heat-treatment regimes. The presence of twins in the U3Si lattice yields a modulus defect of about 18·5%, the Young's modulus of the twinned U3Si having the lower absolute value. At about 85°K the twinned structure displays a prominent minimum in its elastic properties, suggesting a first-order phase transformation. In contrast, the non-twinned U3Si exhibits a maximum in this temperature range. Experimental results are discussed in terms of the effect of twins on the lattice stability of the tetragonal structure of U2Si.
TL;DR: In this article, low temperature specific heat measurements on (TTF) (TCNQ) are reported, and the Debye temperature is 89.5 K. No term linear in temperature is observed, and comparison with other data indicates the low temperature phase is that of a small band gap non-magnetic semiconductor.
TL;DR: In this paper, the elastic constants and their temperature derivatives for As-Se glasses have been determined by means of ultrasonic interferometry technique, and the results are summarized as follows:
Abstract: The elastic constants and their temperature derivatives for As-Se glasses have been determined by means of ultrasonic interferometry technique. The data obtained for wave velocities, bulk modules, shear modulus, Young's modulus, Poisson's ratio, their temperature derivatives, Debye temperature and Gruneisen parameters are listed in Table 2. The data of variation of the elastic constants with composition in the system As-Se are shown in Fig. 2-6, Fig. 10 and Fig. 12.The results are summarized as follows:1) The values of isotropic wave velocities υp and υs at room temperature are υp=1.8km/sec and υs=0.92km/sec for Se glass, υp=2.2km/sec and υs=1.2km/sec for As2Se3 glass. It is found that the value for As-Se glass is lower than that for oxide glasses.2) The elastic constants increase with increasing the As content up to its maximum at about 40 atomic percent As and then decrease. The maximum in the curve seems to be interpreted as evidence of structural grouping tn the glass corresponding to the compound As2Se3.3) The bulk modulus-volume relationship shown in Fig. 8 reveals that the bulk modulus varies approximately as the inverse fourth power of volume.4) Temperature derivative of the isotropic longitudinal wave velocity is negative for As-Se glass and B2O3 glass whereas it is positive for other oxide glasses, that is, SiO2, GeO2 glasses.5) The Debye temperature θD determined from equation (8) is θD=103°K for Se glass and θD=130°K for As2Se3 glass. The Gruneisen parameter δs calculated from the measured thermal data is estimated to be 5-8.
TL;DR: In this article, the mean-square vibrational amplitudes of lead and tellurium atoms in PbTe are derived from both dependences of the integrated intensities on sin θ/λ and on temperature, and the results are discussed in relation to previous works tending to substantiate the Brooks-Yu theory on the temperature dependence of the energy band gap.
Abstract: X-ray diffraction experiments on single crystals and powder specimens are performed in order to obtain the values of the mean-square vibrational amplitudes of lead and tellurium atoms in PbTe. From both dependences of the integrated intensities on sin θ/λ and on temperature, the values 〈u〉 =(2.33 ± 0.15) × 10−18 cm2 and 〈u = (2.09 ± 0.14) × 10−18 cm2 are derived. The X-ray Debye temperature is found to be θM = (107 ± 3) °K. The analysis of the experimental data is given in detail. The results are discussed in relation to previous works tending to substantiate the Brooks-Yu theory on the temperature dependence of the energy band gap.
On a effectue des experiences de diffraction de rayons-X sur des monocristaux ainsi que sur des poudres afin d'obtenir les valeurs des amplitudes vibrationelles quadratiques moyennes des atoms de plomb et de tellure dans le PbTe. En tenant en consideration les dependences des intensites integrees de sin θ/λ aussi bien que de la temperature, on obtient les valeurs 〈u〉 = (2,33 ± 0,15) × 10−18 cm2 et 〈u = (2,09 ± 0,14) × cm2. La temperature de Debye par les rayons-X est θM = (107 ± 3) °K. On donne une analyse des donees experimentales; les resultats sont discutees en tenant compte des travaux precedents, ou on visait a confirmer la theorie de Brooks-Yu sur la dependance de la temperature de la bande d'energie interdite.
TL;DR: In this paper, the change of the specific heat caused from the strain fields of dislocations has been evaluated on the basis of the higher order elasticity theory, and the variations of the lattice vibrational frequencies due to strains were calculated using the quasi-harmonic approximation, and usual and the higher-order mode Gruneisen parameters were expressed as functions of the second-, third-, and fourth-order elastic constants.
Abstract: The change of the lattice specific heat caused from the strain fields of dislocations has been evaluated on the basis of the higher order elasticity theory. The variations of the lattice vibrational frequencies due to strains were calculated using the quasi-harmonic approximation, and the usual and the higher order mode Gruneisen parameters were expressed as functions of the second-, third-, and fourth-order elastic constants. The displacement fields of an edge and a screw dislocation were also calculated with taking into account the elastic anisotropy of the crystal. These results were combined with the Debye theory of specific heat to obtain the expression for the specific heat change from dislocations. Numerical evaluation has been done for the case of copper, and it was found that the specific heat was increased several per cent at liquid helium temperature by dislocations with density of 10 12 cm -2 and the effect was larger for edge dislocations.
TL;DR: In this article, the deformable-shell model has been used to calculate the phonon dispersion relation in both the symmetry and the off-symmetry directions, and the variation of the Debye temperature from the frequency spectra for the following five ionic crystals, NaCl, NaBr, KI, KCl, and KBr.
Abstract: The deformable-shell model developed by Basu and Sengupta and later substantiated by a potential form by Sarkar and Sengupta has found wide application in describing the different static properties of ionic crystals of both NaCl and CsCl structures. But so far a complete calculation of dynamical properties of ionic crystals has been reported for only one crystal. Further, from a critical comparison of the different lattice-dynamical models which effectively introduce many-body interactions between the ions, we have found that there are certain differences between them, some of which are quite fundamental in nature. Moreover, of the current phenomenological models, the deformable-shell model alone is capable of reasonably treating both the static and the dynamic properties of the crystals. Hence it is important to know the results of the calculation according to different models. In this work we present the lattice-dynamic calculation on the following five crystals, NaCl, NaBr, KI, KCl, and KBr according to the deformable-shell model. In order to obtain the parameters, the well-known macroscopic quantities have been used and no least-square-fitting procedure has been adoped. The parameters obtained from the theory have been used to calculate the phonon dispersion relation in both the symmetry and the off-symmetry directions (where experimental results are available) and the variation of the Debye temperature from the frequency spectra for these crystals. We have consistently used the polarizable negative-ion model for all of them. The results thus obtained agree well with experiment. Other theoretical-model results are also discussed in detail.