scispace - formally typeset
Search or ask a question

Showing papers on "Debye model published in 1983"


Journal ArticleDOI
TL;DR: In this article, the authors developed a numerical model for calculating thermal accommodation coefficients alpha sub T and trapping functions f sub t for gases incident on solid surfaces, especially designed for astrophysical applications in that it treats economically and with moderate accuracy (+ or - 20%) the dependences of alpha subT and f subT on finite and different surface and gas temperatures for a large number of gas-surface combinations.
Abstract: The paper develops a numerical model for calculating thermal accommodation coefficients alpha sub T and trapping functions f sub t for gases incident on solid surfaces. The method is especially designed for astrophysical applications in that it treats economically and with moderate accuracy (+ or - 20%) the dependences of alpha sub T and f sub t on finite and different surface and gas temperatures for a large number of gas-surface combinations. In particular, the method is applied to the astrophysical combinations of hydrogen and helium gases incident on graphite, silicon, and ice surfaces. Graphs are presented of the dependence of alpha sub T and f sub t on interstellar gas temperatures in the range of 10 to 10,000 K and grain temperatures in the range 10 to 1000 K, assuming the current estimates of the gas-surface physical parameters such as the composition and the Debye temperature of the grain material, the repulsive range of the surface potential, and the gas-grain adsorption energy.

212 citations


Journal ArticleDOI
TL;DR: In this paper, forsterite was measured between 300 and 1,200 K (≃ 1.6 times the Debye temperature) by the Rectangular Parallelepiped Resonance method.
Abstract: Elastic moduli of forsterite were measured between 300 and 1,200 K (≃ 1.6 times the Debye temperature) by the Rectangular Parallelepiped Resonance method. All the moduli decrease regularly with temperature. A summary of the results is as follows: temperature derivatives of elastic moduli, - ∂C ij /∂R in MPa/K whereC si =(C jj +C kk −2·C jk )/4; (i, j, k=1, 2, 3;i ≠j ≠k), and ρ is density in kg/m3. These data permit for the first time the calculation of elastic and thermal properties well into the classical range far above the Debye temperature. We find, for example, that the elastic constants, including the bulk moduls, closely follow standard equations throughout the measured temperature range. This information aids extrapolations up to the melting point. This data, coupled with thermal expansivity data permit the computations of thermal anharmonic parameters of minerals forT>θ.

164 citations


Journal ArticleDOI
TL;DR: Experimental piston-displacement equations of state are given for sodium, potassium, and rubidium to 20 kbar for temperatures from 4 K to just below the melting line in each case.
Abstract: Experimental piston-displacement equations of state are given for sodium, potassium, and rubidium to 20 kbar for temperatures from 4 K to just below the melting line in each case. Except for sodium at high pressures, where the low-temperature bcc-hcp martensitic transition appears to cause problems, these data can be represented by a room-temperature pressure-volume reference function and a thermal pressure which is a function of temperature only. In addition, these three solids appear to obey a reduced equation of state at both 4 K and room temperature, for which $\frac{V}{{V}_{0}}$ is a common function of $\frac{P}{{B}_{0}}$. A modification of the second-order Murnaghan equation which is well behaved at large compressions is used to extrapolate these results to 40 kbar for comparison with higher-pressure, room-temperature results. These data are compared with other high-pressure equation-of-state experiments and are extrapolated to $P=0$ to obtain thermal expansions and isothermal bulk moduli, which in turn are compared with results from other measurements. These comparisons and those with theoretical calculations show, on the whole, satisfactory agreement. The elementary form for the temperature-dependent equation of state is in agreement with a previous suggestion that the Gr\"uneisen parameter is temperature independent and is a linear function of the volume for temperatures greater than the Debye temperature. The 295-K Gr\"uneisen parameters for these solids, as deduced from the high-pressure results, are 1.24 for sodium and potassium and 1.26 for rubidium.

69 citations


Journal ArticleDOI
TL;DR: In this paper, two-level systems (TLSs) are shown to make transitions between levels by phonon-assisted tunneling and flip spins by modulating the spin-orbit interaction.
Abstract: Electron-spin-lattice relaxation times have been measured using adiabatic-passage techniques in doped and undoped $a$-Si: H and $a$-Ge: H. When scaled by the square of the atomic spin-orbit coupling constants, the magnitudes of the relaxation times are found to be surprisingly similar. The temperature dependence of the dangling bonds and band-tail states in all cases shows a nearly quadratic behavior to temperatures far below the Debye temperature. The results are shown to be consistent with relaxation via two-level systems (TLS's). The TLS's make transitions between levels by phonon-assisted tunneling and flip spins by modulating the spin-orbit interaction. Hydrogen evolution studies allow us to vary the TLS distribution and show that the TLS density of states is related to the degree of departure of the network from its thermal-equilibrium value.

65 citations


Journal ArticleDOI
TL;DR: In this article, the results of the measurement of transverse and longitudinal sound velocities on eigth glass compositions of the GeSb-Se system are reported and their elastic moduli evaluated.
Abstract: The results of the measurement of transverse and longitudinal sound velocities on eigth glass compositions of the GeSbSe system are reported and their elastic moduli evaluated. While the velocities, elastic moduli and Debye temperature show variation with composition for GexSb10Se90−x glasses, they are essentially constant for the glasses with stoichiometric compositions. The dependence of bulk modulus on mean atomic volume has been analysed. Both the mean atomic volume and the type of bonding are found to be effective in determining the composition dependence of bulk modulus.

54 citations


Journal ArticleDOI
TL;DR: In this article, the hyperfine frequency of normal muonium Mu has been measured as a function of temperature in zero magnetic field with an apparatus of high time resolution, and it was shown that the non-monotonic lattice expansion of Si cannot cause the observed effect.
Abstract: The hyperfine frequency ..nu../sub 0/ of normal muonium Mu has been measured as a function of temperature in zero magnetic field with an apparatus of high time resolution. Compared with the usual two-frequency method, the direct measurement of ..nu../sub 0/ typically gives more accurate results by a factor of 10. For Mu in Ge, ..nu../sub 0/ shows a monotonic decrease with increasing temperature which is well described by a Debye model. For Mu in Si, ..nu../sub 0/ exhibits a nonmonotonic temperature variation with a maximum at 80 K. By a measurement with external pressure up to 1.5 kbar it is shown that the nonmonotonic lattice expansion of Si cannot cause the observed effect. Rapid relaxation of the direct transition was observed in Si below 20 K. A similar anomaly of the triplet transition signals in a magnetic field could not be found. A model is presented which assumes diffusion of Mu over slightly different sites and which explains all observed effects consistently.

44 citations


Journal ArticleDOI

38 citations


Journal ArticleDOI
TL;DR: The reliability of estimation of Debye temperature θD evaluated from bulk modul and microhardness is proved for semiconductors with diamond, sphalerite, and chalcopyrite structure as discussed by the authors.
Abstract: The reliability of estimation of Debye temperature θD evaluated from bulk modul and microhardness is proved for semiconductors with diamond, sphalerite, and chalcopyrite structure. The known linear relations available from the literature do not yield a reasonable agreement between experimental and calculated Debye temperatures. As in the case of the Lindemann rule a better approximation is obtained by use of a more general relation θD = a1x + a2. The constants a1 and a2 are calculated for the substances under consideration. Unknown Debye temperatures are calculated. Die Zuverlassigkeit einer Abschatzung der Debyetemperatur θD mittels Kompressions-modul und Mikroharte wird fur Halbleiter mit Diamant-, Sphalerit- und Chalkopyritstruktur untersucht. Die aus der Literatur bekannten linearen Beziehungen ergeben keine vernunftige Ubereinstimmung von experimentellen und berechneten Debyetemperaturen. Wie im Falle der Lindemannregel erhalt man eine bessere Naherung mit der allgemeineren Beziehung θD = a1x + a2. Die Konstanten a1 und a2 werden fur die betrachteten Substanzen bestimmt. Unbekannte Debyetemperaturen werden berechnet.

27 citations


Journal ArticleDOI
TL;DR: In this article, the effect of substitution of one isotope for another in the lithium hydride crystal has been investigated by means of the localized-continuum model introduced in earlier publications in connection with calculations of elastic properties, thermal expansion, and melting phenomena.
Abstract: The effect of substitution of one isotope for another in the lithium hydride crystal has been investigated by means of the localized-continuum model introduced in earlier publications in connection with calculations of elastic properties, thermal expansion, and melting phenomena. Theoretical analysis demonstrates that the observed lattice parameters can be accounted for within the experimental error and the accuracy of the Debye approximation by a combination of the effects of the zero-point displacement and thermal expansion. The contributions of both quantities vary for the different isotopic forms according to different values of the Debye temperature, which in turn varies approximately as the inverse square root of the cation-ion reduced mass. In addition, the analysis elucidates the nature of the quantized thermal oscillators in crystals.

23 citations


Journal ArticleDOI
TL;DR: In this article, the specific heat (Cp) of the amorphous alloys Ni100-xZrx for x = 75, 65, 55 and 35 was measured from 0.8K to 40K and the composition trends of the transition temperature Tc, the enhanced density of states at the Fermi level Nγ(F) and the Debye temperatures θD(0), θ D(T) established.

21 citations


Journal ArticleDOI
TL;DR: The Debye-Waller parameters were determined at room temperature and around 90 K for palladium metal powders with different particle sizes in this paper, where the effective values obtained were divided into the dynamic component Bd, which is due to the thermal vibration of the constituent atoms and are temperature dependent, and the static component Bs, which probably due to static displacement of the atoms and is temperature independent.
Abstract: The Debye—Waller parameters were determined at room temperature and around 90 K for palladium metal powders with different particle sizes The effective values obtained were divided into the dynamic component Bd, which is due to the thermal vibration of the constituent atoms and are temperature dependent, and the static component Bs, which is probably due to the static displacement of the atoms and is temperature independent The Debye temperature θD calculated from the component Bd decreased with the increase in the component Bs, of which the relation was able to extrapolate to the θd-value determined on single crystals at Bs = 0 The decrease in θD was qualitatively explained by using a simple core-shell model, the shell part having as low a θD-value as 140 K

Journal ArticleDOI
TL;DR: In this paper, heat capacity measurements from 5 to 345 K for Mn 3 GaC were conducted and two anomalies were detected: the first at T c = (243 ± 1) K, with height Δ C p,m / R = 2.2 due to para-to-ferromagnetic ordering; the second at T A = (171.83 ± 0.06) K due to ferro-toantiferro-magnetic reordering together with lattice expansion.

Journal ArticleDOI
TL;DR: The behavior of zone-centre acoustic phonons has been investigated in LaF3′ CeF3'' PrF3 and NdF3 over a wide temperature range as discussed by the authors.
Abstract: The behaviour of the zone-centre acoustic phonons has been investigated in LaF3′ CeF3′ PrF3 and NdF3 over a wide temperature range. It is shown that in spite of the trigonal structure of these crystals, their elastic properties can be well described with an approximation to hexagonal symmetry. The values of the elastic coefficients increase with increasing atomic number of the cations. The Debye temperatures were determined at temperatures from 80 to 560K with a typical value of θ D = 385 K at 300 K.

Journal ArticleDOI
TL;DR: The heat capacity of Mn4N has been determined in the range from 5 to 345 K by adiabatic calorimetry and between 335 and 500 K by d.s.c. as mentioned in this paper.

Journal ArticleDOI
TL;DR: In this article, a cooperative peak of 3.8K was found for monoclinic Gd2O3 and the entropy associated with this peak is the full 2R ln 8 expected for the Gd3+ ions.
Abstract: Specific heat measurements on monoclinic Gd2O3 show a cooperative peak at 3.8K. The entropy associated with this peak is the full 2R ln 8 expected for the Gd3+ ions. Measurements on GdAg are affected by the presence of small inclusions of Gd2O3, but it proves possible to allow for these and to deduce values for the electronic specific heat constant gamma which is 11.4+or-1.7 mJ mol.-1 K-2. For LaAg, gamma =9.9+or-0.2 mJ mol.-1 K-2. The lattice heat capacities are analysed in terms of a Debye temperature which is found to vary strongly with temperature; the low-temperature limiting values are 208K and 150K for GdAg and LaAg respectively.

Journal ArticleDOI
TL;DR: In this paper, the lattice vibrations of the two constituent atoms in the III-V semiconductors GaP, GaAs, GaSb, InP, InAs, and InSb have been studied experimentally by neutron diffraction and theoretically by calculations within the framework of various phonon models proposed in the literature for these compounds.
Abstract: The lattice vibrations of the two constituent atoms in the III–V semiconductors GaP, GaAs, GaSb, InP, InAs, and InSb have been studied experimentally by neutron diffraction and theoretically by calculations within the framework of various phonon models proposed in the literature for these compounds. The mean-square amplitudes (measured at 295 K) show a general increase with increasing lattice constant and seem furthermore to reflect the partial ionicity of the compounds. The different phonon models for the lattice dynamics are compared with each other and tested critically against the experimental data. Several models are found to be insufficient. The most satisfactory ones are some shell models. 119Sn Mossbauer impurity atoms have been implanted site-selectively on the two different substitutional lattice sites and their Debye temperatures have been determined. A rigorous result relating Debye temperatures of host and impurity atoms permits a simplified interpretation of the experimental results in terms of “Einstein-Debye force constants”. Both lower and higher force constants are deduced for the impurities as compared with the host atoms. Larger force constants are found on V sites than on the III sites for Sn in the Ga compounds, whereas the opposite holds in the In compounds. Further details can be obtained in an extended version of this paper available from the authors.

Journal ArticleDOI
TL;DR: In this paper, a method was developed for discussion of the brownian movement of a rotator in a periodic potential to calculate the transient behaviour when the linear approximation of the Debye theory is discarded.

Journal ArticleDOI
TL;DR: In this article, the same authors used a simple MO-model to find three dopedependent charge states of substitutional iodine and attributed them to I++, I0, I1 and Io.
Abstract: Laser annealed129mTc-implanted silicon has been investigated using129I Mossbauer spectroscopy. At least three dopedependent charge states of substitutional iodine are found. For heavily doped p-type Si a single line component S1, with isomer shift S=0.96(4) mm/s w. r. t. Cu129I and an effective Debye temperature ϕ′=196(3) K is observed. This component is attributed to I++. For compensated Si a single line component, S2, assigned to I+, with S=2.39 (4) mm/s and ϕ′=170 (3) K is found. For n-type Si, a component S3, characterized at 4.2 K by S=2.15 (4) mm/s and a quadrupole splitting eQVzz/h=452 (8) MHz (n≃0)is observed. At higher temperatures S3 shows quadrupole relaxation and its recoilless fraction becomes strongly anisotropic. This behaviour is explained on the basis of a transition from a static to a dynamic Jahn-Teller distortion. Component S3 has been attributed to I0. In the spectra of compensated and n-type Si a less well-defined component Q, with parameters resembling those of S3 but showing no quadrupole relaxation, is observed. This component has tentatively also been assigned to Io. The results can be understood qualitatively on the basis of a simple MO-model.

Journal ArticleDOI
Akihisa Inoue, Naoki Toyota, T. Fukase, T. Masumoto, Y. Takahashi1 
TL;DR: In this paper, superconducting amorphous alloys with high strength and good ductility have been found in rapidly quenched alloys of the Zr-Nb-Si system.
Abstract: Superconducting amorphous alloys with high strength and good ductility have been found in rapidly quenched alloys of the Zr-Nb-Si system. These alloys were produced in a continuous ribbon form of 1 to 2 mm width and 0.02 to 0.03 mm thickness using a modified single roller quenching apparatus. The amorphous alloys were formed over the whole composition range between zirconium and niobium, but the silicon content was limited to the relatively narrow range between about 12 and 24 at%. All the amorphous alloys showed a superconducting transition whose temperature, Tc, increased from 2.31 to 4.20 K with increasing niobium content or with decreasing silicon content. The upper critical magnetic field, Hc2, and the critical current density, Jc, for Zr15Nb70Si15 alloy were of the order of 4.5 Tesla(T) and 5.5×106 A m−2 at 1.5 K in the absence of applied field. The upper critical field gradient at Tc, \((dH_{c2} /dT)_{T_c } \), and the electrical resistivity at 4.2 K, ρn, decreased from 2.89 to 2.10 T K−1 and from 2.70 to 1.80μΩm, respectively, with the amount of niobium. The Debye temperature, θD, the electron-phonon coupling constant, λ, and the bare density of electronic states at the Fermi level, N(Ef) were calculated from the experimentally measured values of ρn, \((dH_{c2} /dT)_{T_c } \), Young's modulus and density by using the strong-coupling theories. From the comparison of Tc with their calculated parameters, it was found that λ is the most dominant parameter for Tc. The GL parameter, κ, and the GL coherence length, ξGL(0), were estimated to be 70 to 100 and about 7.6 nm, respectively, from the experimental values of \((dH_{c2} /dT)_{T_c } \) and ρn by using the GLAG theory and hence it is concluded that the present amorphous alloys are an extremely “dirty” type-II superconductor having a very weak flux pinning force.

Journal ArticleDOI
TL;DR: The complex [Fe2S2(S2-o-xylyl)2- in DMF, DMSO or a 1:1 DMF/DMSO mixture, a model for the chromophore in the 2Fe-2S proteins (ferredoxins), has been reduced and studied by conventional EPR over a temperature range and the variable Lorentzian contribution was related to spin-lattice relaxation times.

Journal ArticleDOI
TL;DR: In this article, the differential cross sections for atom scattering by surfaces with one-Rayleigh-phonon exchange are calculated using a Debye model for the solid and an exponential potential for the atom surface interaction.

Journal ArticleDOI
TL;DR: In this article, the formation and migration energies of vacancies in crystals under hydrostatic strain are considered in model fee and bcc crystals using the technique of computer simulation, and the effect of the vacancy migration energy of a neighbouring vacancy is also considered in the model crystals.

Journal ArticleDOI
TL;DR: In this paper, a single line component is observed with an isomer shift of 0.15 (5) mm/s with respect to SnTe and an effective Debye temperature of 207 (3) K.
Abstract: Laser annealed Te-implanted silicon has been investigated using119Sn and125Te Mossbauer spectroscopy. The119Sn Mossbauer spectra consist of a single lorentzian, known to be due to substitutional Sn atoms in Si, independent of the type of doping of the silicon. The results on125Te revcal at least two different components. In heavily doped n-type Si a single line component is observed with an isomer shift of 0.15 (5) mm/s with respect to SnTe and an effective Debye temperature of 207 (3) K. Heavy p-doping leads to another single line component with an isomer shift of −0.13 (5) mm/s and an effective Debye temperature of 232 (3) K. These components are ascribed to the neutral and doubly positive charge state of substitutional Te atoms, respectively.

Journal ArticleDOI
TL;DR: In this paper, the quadrupole splitting δEQ at the Fe-site and its dependence on temperature in Fe85−XCrXB15 and Fe80−XMoXB20 amorphous alloys were investigated.
Abstract: The57Fe-Mossbauer spectroscopy has been used in order to study the quadrupole splitting δEQ at the Fe-site and its dependence on temperature in Fe85−XCrXB15 and Fe80−XMoXB20 amorphous alloys. In all investigated compositions the local symmetry was lower than cubic with room temperature values of δEQ in the range of 0.4–0.5 mm/s. In all cases relatively broad distributions of δEQ and therefore of the EFG have been obtained. The EFG of the investigated compounds changes reversibly with temperature up to about 650 K according to the relation δEQ (T)=δEQ (O)·(1-BTV3/2) as in the case of crystalline noncubic metals. Assuming that the same dependence of B on the Debye temperature θ as in crystalline non-cubic metals holds for amorphous alloys, values of θ have been obtained in good agreement with those determined from the temperature dependence of the Mossbauer f-factor.

Journal ArticleDOI
TL;DR: In this paper, the specific heat properties of PbTiO 3 were investigated on four samples: amorphous ribbon, powder, powder and porcelain pellet, and they showed strong Schottky behavior below 4 K with nearly identical (two level) energy separations.
Abstract: Specific heat data are reported, 1.7–30 K, on four samples of PbTiO 3 : amorphous ribbon (∼20 vm thick); crystallized ribbon (∼1 µm grain size); crystalline powder (∼1 µm grain size); and ceramic pellet (∼2 µm grain size). Both the amorphous and crystallized ribbon samples display strong Schottky behavior below 4 K with nearly identical (two level) energy separations \({\cong}78\) mK. PbO loss from the thin ribbons is postulated to explain these effects. Below 3 K, the powder and pellet samples display a glasslike linear term in the specific heat, and the coefficients of these terms (1.4×10 -5 J cm -3 K -2 ) are the same magnitude as those found in glasses. All crystalline forms of PbTiO 3 display maxima in C / T 3 at 15 K, and these maxima are accurately represented by single Einstein terms with frequencies 47–52 cm -1 . Amorphous PbTiO 3 displays a C / T 3 maximum at 10 K, as does vitreous SiO 2 . A Debye temperature for crystalline PbTiO 3 of 337 K is reported; the effective Debye temperature for amorp...

Journal ArticleDOI
TL;DR: In this paper, Mossbauer spectroscopy was employed to verify the existence and investigate the properties of local disorder in the "ordered" state of the superionic conductor Rb${\mathrm{Ag}}_{4}$${\mathm{I}}_{5}.
Abstract: M\"ossbauer spectroscopy in $^{129}\mathrm{I}$ was employed to verify the existence and investigate the properties of local disorder in the "ordered" state of the superionic conductor Rb${\mathrm{Ag}}_{4}$${\mathrm{I}}_{5}$. Studies were conducted in the temperature range of 4-180 K covering the low-temperature $\ensuremath{\gamma}$ phase ($Tl122$ K) and part of the high-conductivity, disordered $\ensuremath{\beta}$ phase. The absorption spectra at all temperatures were analyzed with two iodine sites, characterized by their quadrupole splitting and isomer-shift values and a third site with a nonsplit single line. It was found that the electric field gradient (efg) at the $^{129}\mathrm{I}$ nucleus, produced by the neighboring Ag ions, has a continuous linear temperature dependence down to 4.2 K. The hyperfine constants and the Debye-Waller factor showed no discontinuity at ${T}_{c}$. The anomalous existence of the single line has been attributed to a fast fluctuating efg due to local hopping of the Ag ions. This dynamic disorder is present even at low temperatures where (8-10)% of Ag ions are locally hopping, and its occurrence increases drastically at $Tg{T}_{c}$. A nonharmonic Debye-Waller factor was observed from which a linear temperature-dependent Debye temperature could be derived.

Journal ArticleDOI
TL;DR: In this article, the heat capacity and Debye temperature of the lattice vibrational spectrum have been calculated as a function of temperature using measurements of the density of states of the L 2 spectrum.
Abstract: The heat capacities of SrF2 and BaF2 have been measured from 1.7K to 40K. Values of 381.7+or-1.0K (SrF2) and 286.6+or-1K (BaF2) obtained for the limiting Debye temperature, theta 0c, agree with values, theta 0el, calculated from elastic stiffness moduli. The heat capacity and Debye temperature, theta (T), for both compounds are calculated as a function of temperature using measurements of the density of states of the lattice vibrational spectrum. Good agreement is obtained with theta c(T) deduced from the heat capacity measurements, showing that variations in theta c(T) may be completely accounted for by lattice dispersion.

Journal ArticleDOI
TL;DR: In this paper, the first five members of the C vi Lyman series emitted from a laser-produced plasma plume at an electron density near 1.3 m/s.
Abstract: Blue shifts of \ensuremath{\sim}85-60 m\AA{} have been observed for the first five members of the C vi Lyman series emitted from a laser-produced plasma plume at an electron density near ${10}^{21}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. These shifts are much larger than density-dependent effects associated with electron collisions and inhomogeneities in ion-produced electric microfields and opposite to plasma polarization shifts according to the linearized Debye model. A nonlinear Debye-type model is consistent with the measurements.

Journal ArticleDOI
TL;DR: In this paper, the integrated Bragg intensities from V, Nb and Ta single crystals as a function of hydrogen (D) concentration and temperature have been carried out, and two different methods were applied: (i) the usual angular dispersive method using MoKα1 characteristic radiation; and (ii) the energy dispersion method using the white spectrum of the Mo tube and an intrinsic Ge detector.

Journal ArticleDOI
TL;DR: In this paper, the physical meaning of the deformation electron-charge-density maps for V/sub 3/Si, V/ sub 3/Ge, and Cr/sub 2/Si was analyzed.
Abstract: The starting point of the present article is a careful analysis of the physical meaning of the three deformation electron-charge-density maps for V/sub 3/Si, V/sub 3/Ge, and Cr/sub 3/Si (previously presented by J.-L. Staudenmann et al., Phys. Rev. B 24, 6446 (1981)). Based on the significant differences exhibited in these maps, it was shown that one can organize all the Debye temperatures at 0 K from specific-heat measurements into five collections which were called Debye classes. The findings here presented are not limited to A15 alloys alone, but rather can be applied to any other family of compounds that satisfies the free-atom superposition principle and the small-amplitude vibration hypothesis. It is shown that deformation electron charge densities depend only weakly upon structure and that they are mainly related to physical properties. Furthermore, the use of deformation electron-charge density as a criterion in setting the starting point for the three main Debye classes is justified a posteriori. We point out that when one takes into account the consequences of the dielectric function, the static or bonding electron charge density can only be extracted with great difficulty from any experimental data. This certainly complicates any comparison between experimental and computed electron chargemore » densities. It is shown that the deformation and total electron charge densities are the only well-defined inverse fourier transforms. If the vibration amplitude of the valence-electron orbitals are non-negligible, the valence-electron charge density, in contrast to the deformation and total electron charge densities, has no simple interpretation.« less