Mode softening and the elastic constants of CeSn3

The transverse and longitudinal acoustic velocities have been measured in the [100] and [111] directions of CeSn₃ as a function of temperature for 4.2 ≤ T ≤ 290 K. The elastic constants c₄₄ and $\text{1}\text{2}\text{(c}{}_{11}\text{?c}{}_{12}\text{)}$ increase smoothly with decreasing temperature and become temperature independent below 10 K but the bulk modulus has a 2% decrease at 135 K which is indicative of an electronically driven mode softening.     

The pressure dependence of elastic moduli of NiF2 to 10 kbar

At room temperature, the pressure dependence of the elastic stiffness moduli of NiF₂ have been measured by pulse superposition method to 10 kbar. The observed strong decreasing behavior in the modulus $\text{C}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{1}\text{2}\text{(C}{}_{11}\text{? C}{}_{12}\text{)}$ is discussed.     

The thermodynamics of elastic deformation—I: Equation of state for solids

The isobaric and isothermal volume derivatives of In B, In μ and In μ' are investigated, where B, μ and μ' are the isothermal bulk modulus and the two shear moduli, respectively, of a cubic crystal. In the case of the bulk modulus, the temperature independence of αB (where α is the volume thermal expansion) for a large number of materials, ensures that the derivatives are constant and approximately equal, while for the shear moduli, evidence is advanced that the isothermal derivatives are constant along an isotherm, but not along an isobar except at high temperatures near the melting point. The relationships satisfied by the bulk modulus enable the explicit temperature and pressure dependence of the molar volume, V, thermal expansion, and bulk modulus to be determined. The most adequate representation of the volume dependence of the Grüneisen parameter, γ, appears to be that γ/V is independent of volume between the Debye and melting temperatures.     

Elastic properties of one dimensional compounds

We have investigated the elastic properties of several one-dimensional compounds using a vibrating reed technique. A model calculation shows that a vanishing Young's modulus will occur for elastic one-dimensionality. TTF-TCNQ exhibits a small modulus which decreases with increasing temperature extrapolating to zero at T ≈ 500–700K. The uniaxial stress dependence of the metal-insulator transition temperature is calculated to be $\text{¦}\text{d}\text{T}{}_{\mathrm{c}}\text{/}\text{d}\text{σ¦ ～ (10 ± 5)}\text{K/bar}$. KCP shows a much higher modulus and a phase transformation at ～ 35 K.     

Elastic anharmonicity of InP: Its relationship to the high pressure transition

Ultrasonic wave transit times have been measured in n-type InP at room temperature using hydrostatic pressures up to 4 kbar. Linear pressure dependences are found for the elastic stiffness moduli implying that at the high pressure structural-electrical transition the shear-to-bulk modulus ratio $\text{(C}{}_{11}\text{?C}{}_{12}\text{)}\text{2B}$ has a (fractional) value which fits the modified Born criterion for stability developed by Demarest $\text{et al}$. The anharmonic force constants and some of the third order elastic constants are found to be smaller the higher the transition pressure for indium III-V compounds.     

Attenuation of longitudinal ultrasonic wave near the diffuse phase transition in CdF2

The attenuation of a longitudinal ultrasonic wave propagating in the [111] direction in CdF₂ is studied as function of temperature from 300K to 1030K. An ultrasonic attenuation peak has been observed for the first time near 983K. This peak is used to define the diffuse transition temperature (T_c = 983K) in CdF₂ which is well below its melting temperature of 1372K. The Arrhenius activation energy of anion motion above T_c was obtained from the temperature dependence of the attenuation and the theory of the dynamics of the coupled crystalline-cage-charged-liquid fluctuations. The elastic constant, $\text{C}{}_{11}\text{+2}\text{C}{}_{12}\text{+4}\text{C}{}_{44}\text{)}\text{3}$, measured simulataneously with the ultrasonic attenuation displays a large decrease near 983K in addition to the nearly linear decrease in the elastic constant with temperature.     

Pressure derivatives of the elastic moduli of strontium,barium and lead nitrate

The pressure derivatives of the elastic moduli of Sr(NO₃)₂, Ba(NO₃)₂ and Pb(NO₃)₂ single crystal, have been measured by the ultrasonic pulse superposition method. The results for Sr(NO₃)₂ and Pb(NO₃)₂ are similar in magnitude and character, while the ones for Ba(NO₃)₂ differ strongly, $\text{?c}{}_{11}\text{?P}$ and $\text{?c}{}_{12}\text{?P}$ even From the measured pressure derivatives, the mode Grüneisen gammas and the Grüneisen constant as a function of temperature have been determined, and the latter is correlated with the experimental values, deduced from thermal expansion. The explicit temperature dependence of the elastic moduli is calculated, and found to be always negative, increasing in absolute value from Sr(NO₃)₂ to Pb(NO₃)₂.     

Pressure effect on the Curie temperature of rare-earth and transition metal compounds

A simple formula for the pressure dependence of the Curie temperature $\text{d}\text{T}{}_{\mathrm{c}}\text{d}\text{P}$ is derived in the s-d model for heavy rare-earth and transition metal (Fe, Co, and Ni) compounds. A qualitative agreement between the calculated and experimental results for $\text{d}\text{T}{}_{\mathrm{c}}\text{d}\text{P}$ is obtained for various intermetallic compounds.     

Softening of surface phonons in the (100) plane of Nb3Sn

The propagation of the surface acoustic mode in the (001) plane is investigated as a function of the temperature dependent elastic moduli of Nb₃Sn in the cubic phase. For the [100] and [110]-directions a softening of the surface mode velocity ν_s is found to follow the softening of the velocity ν_T2 of the bulk shear mode T₂A. It is shown that for the [100]-direction the ratio $\text{(}\text{ν}{}_{\mathrm{s}}\text{ν}{}_{\mathrm{T2}}\text{)}$ tends to ?2 at the structural phase transition. The question is discussed of whether the softening of the surface mode can be observed with Brillouin scattering from opaque surfaces.     

Elastic constants of single crystals of the three phases of In---Pb alloys

In a study of the elastic behaviour of the InPb alloys, the elastic stiffness tensor components of crystals of each of the three phases (fct, $\text{c}\text{a}\text{> 1}$; fct, $\text{c}\text{a}\text{> 1}$; fcc) have been obtained as a function of temperature from pulse superposition measurements of ultrasonic wave velocities. Comparison of the elastic stiffness constants obtained for a fct ($\text{c}\text{a}\text{> 1}$) 5 atm.% Pb alloy with those of In itself and those of InTl and InCd alloys, establishes for this phase that alloying with Pb, as with TI and Cd, enhances the softening of the acoustic [110] phonon mode, polarization [1$\text{1}$0] near the Brillouin zone centre. The elastic properties of a 17 atm.% Pb crystal, which is in the fct ($\text{c}\text{a}\text{> 1}$) phase, are quite different from those shown by In alloys in the fct ($\text{c}\text{a}\text{> 1}$ phase; in particular the response to a shear stress is remarkably isotropie: there is no phonon mode softening in this alloy. Neither is there softening of this mode (which corresponds at the zone centre to the shear stiffness $\text{1}\text{2}$(C₁₁;C₁₂)) in crystals of the fee phase — in complete contrast to the dominating influence of the softening of $\text{1}\text{2}$(C₁₁;C₁₂) in the InTl and InCd fee alloys. In fact for a fcc In-75 atm.% Pb alloy the anistropy ratio for shear $\text{2C}{}_{44}\text{(C}{}_{11}\text{C}{}_{12}\text{)}$ is close to unity. The transitions between the three phases of the InPb alloys are markedly first order and acoustic mode softening has a much smaller influence on the elastic behaviour of the fct ($\text{c}\text{a}\text{< 1}$) and fcc InPb alloys than it has on the fct ($\text{c}\text{a}\text{< 1}$) InPb, InCd and InTl alloys.     

The concentration dependence of the ferroelectric transition temperature of the solid solution of TSCC and TSCB

The concentration dependence of the ferroelectric transition temperature T_c of single crystals of the solid solution tris-sarcosine calcium chloride_1?x bromide_x is studied experimentally by measurement of the static dielectric constant ?_b and described by the empirical relation $\text{T}{}_{\mathrm{c}}\text{(X) = T}{}_{\mathrm{c}}\text{(0) [1?(X/X}{}_{\mathrm{c}}\text{)]}\text{1}\text{2}$. The Ising model with transverse field and the model of coupled anharmonic oscillators are used to explain the concentration dependence of the transition temperature T_c.     

Elastic constant pressure derivatives and stability of the bcc phase of InTl alloys

Hydrostatic-pressure derivatives of the elastic stiffness constants have been measured ultrasonically in a bcc InTl alloy of composition near the eutectoid. The shear modulus $\text{1}\text{2}\text{(C}{}_{11}\text{?C}{}_{12}\text{)}$ is small, but does not soften under pressure: the eutectoid reaction is not directly associated with a mode softening shear instability. Anharmonic contributions to the excess vibrational entropy from the q 〈110〉, e 〈1$\text{1}$0〉 modes which stabilize the bcc structure are small compared with the harmonic contributions.     

Antiproton-proton total elastic cross sections in the T and U regions (0.69−2.43 GeV/c)

Antiproton-proton total elastic cross sections at 21 incident momenta in the range 0.69 to 2.43 GeV/c have been deduced by combining p?p elastic differential cross sections over a c.m. angular range $\text{?0.95 ?}\text{cos}\text{θ}{}^1\text{? 0.93}$ with forward elastic cross sections derived from recent real-part measurements and p?p total cross sections. Two bumps are observed, at $\text{M}{}_1\text{? 2.155}$ and $\text{M}{}_2\text{? 2.345}\text{GeV}\text{/c}{}^2$, having widths of Г₁ ～ 0.135 and $\text{Г}{}_2\text{～ 0.135}\text{GeV}\text{/c}{}^2$. Corresponding structures in other p?p reaction channels are discussed.     

Surface energy of liquid metals at the melting temperature related to bulk liquid structure

The product σχ_Tm of surface energy σ and isothermal compressibility σχ_Tm for liquid metals at the melting temperature T_m yields a length l ranging from about 0.2 to 0.5 Å over the entire range of liquid metals. The variation of l, which has been related brfore to the thickness of the liquid-vapour interface, is shown to be accurately represented by , where the constant c is determined empirically, K_B and N being the Boltzmann factor and Avogadro's number respectively, and S_Tm(0) the bulk liquid structure factor in the long wavelength limit at the melting temperature. A microscopic interpretation of l is proposed.     

Third and fourth order elastic constants of fluoperovskites CsCdF3, TlCdF3, RbCdF3, RbCaF3

The hydrostatic dependence of the second order elastic constants of several fluoperovskites has been measured and studied from a macroscopic point of view and through a force field analysis. The first part of this paper is devoted to the experimental determination of some combinations of the third and fourth order elastic constants. The second part analyses the pressure dependence of the second order elastic constants from a macroscopic point of view. The large values of the second order anharmonicity coefficients $\text{b}{}_{\mathrm{ij}}\text{=}\text{1}\text{2}\text{(}\text{?}{}^2\text{C}{}_{\mathrm{ij}}\text{?P}{}^2\text{)}{}_0\text{C}{}^{\mathrm{(0)}}{}_{\mathrm{ij}}$ are connected to the occurrence of a phase transition in some compounds, whereas the first order coefficients $\text{(}\text{?C}{}_{\mathrm{ij}}\text{?P}\text{)}{}_0$ have an order of magnitude which agrees with a quasiharmonic hypothesis. The third part is devoted to the microscopic interpretation of the third order elastic constants. A rigid ion model is used with either classical Born Mayer potentials or a modification of these potentials with an axial term (Cowley and Rousseau's models).     

Acoustic phonon mode softening in InCd alloy single crystals

To examine the effect of alloying In with Cd on the lattice stability, the elastic constants of single crystals of the tetragonal In 3.42 at.% Cd alloy have been determined. The shear modulus $\text{1}\text{2}\text{(C}{}_{11}\text{? C}{}_{12}\text{)}$ is even less in the alloy than in In and decreases rapidly as temperature rises. It is concluded that the [110], q6[$\text{1}\text{1}\text{0}$] acoustic phonon mode is soft near the zone centre and softens even further as the phase boundary demarking the incipient diffusionless phase transition is approached.     

The law of corresponding states for metals

Using the similarity of the effective potentials seen by ions in metals a reduced phonon equation of state is derived. It is shown that the melting point T_m(0) and the atomic volume Ω₀ at T = 0 K and at p = 0 are suitable macroscopic parameters for scaling ? and σ characterizing the interatomic potentials of metals having similar structures. The temperature and pressure dependence of thermodynamical quantities reduced with the above parameters are discussed and the results are compared with the experiment. It is shown that the pressure dependence of the reduced thermodynamic quantities can be described by the pressure dependence of the scaling parameters T_m(p) and Ω₀(p).The general form of the reduced equation of state (containing the electronic contributions as well) obtained gives that the reduced pressure is a universal function of the following reduced variables: the volume, temperature, de Broglie wavelength, Gibbs free energy of electrons $\text{3}\text{5}\text{zE}{}_{\mathrm{fo}}\text{?}$ (E_fo is the Fermi energy at T = 0 K) and depe of the valence z as well. It is shown that $\text{E}{}_{\mathrm{fo}}\text{?}$ is a function of $\text{Ω}{}_{\mathrm{o}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ and $\text{(}\text{E}{}_{\mathrm{fo}}\text{/?}\text{)Ω}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is approximately constant within the same sub-group of the periodic table.     

Pressure dependence of shear elastic mode near structural transition in the band Jahn-teller model

The temperature dependence of the pressure derivative of the shear elastic constant $\text{dC}{}_{\mathrm{<mtext>S</mtext>}}\text{dp}$ for degenerate electronic system is worked out in the band Jahn Teller model and is shown to follow C_S linearly as the temperature decreases and approaches the transition temperature T_M. The constant of proportionality gives useful informations on the characteristics of the band Jahn-Teller transition. This analysis can explain well the recently observed experimental results on Nb₃Sn.     

Transport properties of a Van der Waals fluid near the critical point

The behaviour of the transport coefficients of a Van der Waals fluid is studied in the one-phase region along the critical isochore of the liquid-vapour phase transition. When $\text{?=}\text{(T?T}{}_{\mathrm{c}}\text{)}\text{T}{}_{\mathrm{c}}\text{→0}$ the strongest singularity is found in the case of the bulk viscosity (??^?2). The divergence of the heat conductivity is shown to be weaker than $\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$. The shear viscosity tends to a finite limit. The coefficients of the asymptotic laws are explicitly given. All the results are established in the region where the Ornstein-Zernike theory applies.     

Superconducting critical current of sputtered Nb-Ge films

The temperature dependence of the superconducting critical current density J_c(T) in zero applied field from 4.2 K to T_c has been measured for 15 films of Nb-Ge with varying composition, deposition conditions, and radiation damage. The results show (i) the enhanced superconductivity observed in stoichiometric Nb₃Ge as well as nonstoichiometric films is “bulk like” rather than filamentary, (ii) a simple correlation of the form which is reasonably independent of how the T_c has been achieved, and (iii) some additional evidence that the enhanced T_c of the films is not due to their chemical composition alone.