The Grüneisen parameter γ of KBr,RbCl and Bi through high pressure phase transitions

High pressure values for the adiabatic pressure derivative of temperature $\text{(}\text{?T}\text{?P}\text{)}{}_{\mathrm{s}}$ have been obtained by measuring the temperature change caused by a small rapid increase in pressure. Values for KBr and RbCl in phases B1 and B2 and for Bi in phases I, II and III are given for T = 295 K. The Grüneisen parameter γ is given by $\text{γ =}\text{B}{}_{\mathrm{s}}\text{(}\text{?T}\text{?P}\text{)}{}_{\mathrm{s}}\text{T}$ where B_s is the adiabatic bulk modulus. Ultrasonic and statk compressibility data are used to estimate the pressure and phase dependence of B_s. Dramatic increases in both γ and (?T/?P)_s are observed as the pressure increases through a phase transition. Values for the logarithmic derivate $\text{q ≡ (? ln}\text{γ}\text{?}\text{ln V}{}_{\mathrm{T}}$ are given.     

The elastic behaviour of the ternary zincblende structure semiconductor CuGe2P3

A single crystal has been grown of CuGe₂P₃, a ternary semiconductor with a zincblende structure in which the copper and germanium atoms are randomly distributed on the cation sites. The second order elastic constants measured by the ultrasonic pulse echo overlap technique (C₁₁ = 13.66, C₁₂ = 6.17, C₄₄ = 6.66 and bulk modulus B = 8.67 in units of 10¹⁰Nm^?2 at 291 K) are closely similar to those of GaP and conform well to Keyes' correlation for zincblende structure crystals. The hydrostatic pressure derivatives of the second order elastic constants ($\text{?C}{}_{11}\text{?P}\text{= 4.40}$, $\text{?C}{}_{12}\text{?P}\text{= 3.9}$, $\text{?C}{}_{44}\text{?P}\text{= 0.93}$ and $\text{?B}\text{?P}\text{= 4.07}$) and the third order elastic constants (C₁₁₁ = ? 8.45, C₁₁₂ = ? 3.49, C₁₂₃ = ? 1.13, C₁₄₄ = ? 2.82, C₁₅₅ = ? 1.44 and C₄₅₆ = ? 0.69 in units of 10¹¹Nm^?2) also resemble those of GaP: even the anharmonicity of the long wavelength acoustic modes of this ternary semiconductor resembles that of its binary “parent” compound. The positive signs of the hydrostatic pressure derivatives and the negative signs of the third order elastic constants show that the acoustic modes at the long wavelength limit stiffen under pressure, an effect which is quantified here by computation of the mode Grüneisen parameters, which are all positive. The harmonic and anharmonic force constants, obtained in the valence force field model, fit well into the pattern shown by related zincblende structure compounds: the ratio ($\text{β}\text{α}$) for bond bending (β) to stretching (α) force constants is greater than 4:1; the dominating anharmonic force constant is γ: most of the anharmonicity is associated with nearest neighbour atoms. Analysis of the temperature dependence of the elastic constants on the basis of a simple anharmonic model again emphasises the similarity between the elastic behaviour of CuGe₂P₃ and GaP. The thermal expansion of CuGe₂P₃ varies almost linearly with temperature between 291 K and 1000 K, the linear coefficient of thermal expansion α being 8.21 ± 0.02 × 10^?6 °C^?1. The similar lattice parameters and elastic behaviour of CuGe₂P₃ and GaP indicate that semiconducting devices made of epitaxial deposits of CuGe₂P₃ on a GaP substrate should prove to be almost strain-free.     

Pressure dependence of elastic behaviour and force constants of GaP

The six third order elastic constants of GaP have been obtained from measurements of the effect of hydrostatic and uniaxial pressures on ultrasonic wave velocities. The valence force field model has been used to obtain the bond-bending and stretching force constants. Confirmatory evidence is added to the hypotheses that zinc blende structure crystals undergo the densification transition under pressure when (1) a modified Born stability criterion that $\text{1}\text{2}\text{(C}{}_{11}\text{? C}{}_{12}\text{)}\text{B}$ equals about 0.2 is reached at the phase transition pressure P_t, and (2) the ratio $\text{β}{}_{\mathrm{t}}\text{α}{}_{\mathrm{t}}$ of the second order bond-bending β_t to bond-stretching α_t, force constants is about 0.1. These findings suggest that a macroscopic shear takes place at the transition     

Light scattering study of dispersion and attenuation of hypersound in adamantane

The Brillouin scattering techniques have been used to measure the velocity dispersion of hypersonic acoustic waves in the “high temperature” disordered cubic phase of adamantane. Shear waves, characteristic of the C₄₄ elastic constant, show no significant dispersion. Longitudinal waves propagating in the (001) plane show strong velocity dispersion. The measures have been performed at the same temperature T = 295.7 K. Using a classical single relaxation time model for the dispersion as a function of frequency at temperature T, the L-mode data have been correctly fitted.The importance of the dispersion $\text{(C}{}_{\mathrm{\infty }}\text{? C}{}_{\mathrm{o}}\text{)}\text{C}{}_0$ for the elastic constants is 20% for C₁₁, 51% for C₁₂ #1% for C₄₄ and ?2.8% for $\text{(C}{}_{11}\text{? C}{}_{12}\text{)}\text{2}$. The fitted relaxation time is τ ? 9 × 10^?11 sec.     

Study by brillouin scattering of the C33 constant of thiourea submitted to an electric field

The C₃₃ constant is discontinuous for the lock-in transition at T₁ = 169 K. The variation ΔT₁ of the temperature of transition is a linear function of the applied electric field E and we find $\text{d}\text{T}{}_1\text{d}\text{E}\text{=0.82 deg.cm kV}{}^{\mathrm{?1}}$.Above a mean field E = 10 kV cm^?1 the transition observed for a first heating spreads on several degrees because damages appear in the incommensurate phase and the electric field becomes inhomogeneous.The results obtained at low fields are in very good accordance with the value of $\text{d}\text{T}{}_1\text{d}\text{E}$ calculated from the Clapeyron formula.Taking into account of the incommensurability of the phase above T₁, it can be shown that

$\text{dT}{}_1\text{dE}\text{=}\text{C}\text{2πP}{}_{\mathrm{o}}\text{3}\text{3}\text{?}\text{2}$

The knowledge of the spontaneous polarisation P₀ gives for the Curie constant C = 2.1 × 10³ K in qualitative agreement with the value deduced from measurements of the dielectric constant in the ferroelectric direction.     

Anomalous temperature dependence of third-order elastic constants in NH4Cl and NH4Br near the λ point

Second order elastic constants of NH₄Cl and NH₄Br crystals were measured under hydrostatic and uniaxial pressures near the λ-type phase transitions. Third order elastic constants were calculated from the pressure derivatives of the second order elastic constants. Results show that the temperature dependences of the third order elastic constants of NH₄Cl differ from those of NH₄Br dramatically. In addition, it is found that the coefficients $\text{1}\text{54}\text{(C}{}_{111}\text{+ 6C}{}_{112}\text{+ 2C}{}_{123}\text{)}$ and $\text{(}\text{1}\text{24}\text{√3)(C}{}_{111}\text{? 3C}{}_{112}\text{+ 2C}{}_{123}\text{)}$ of strains in the free energy of NH₄Cl show quite different temperature dependences from those of NH₄Br.     

A Mössbauer study of amorphous Fe40Ni40B20

Amorphous Fe₄₀Ni₄₀B₂₀ (VITROVAC 0040) alloy has been investigated using ⁵⁷Fe Mössbauer Spectroscopy. The Curie temperature T_c is found to be well defined and is 695 ± 1 K. The quadrupole splitting just above T_c is 0.64 mm sec^?1. The crystallization temperature is 698 ± 2 K, close to but definitely above T_c. The average hyperfine field H_eff(T) of the glassy state shows a temperature dependence of $\text{H}{}_{\mathrm{<mtext>eff</mtext>}}\text{(0)[1 ? B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{? C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{? …]}$ indicative of the existence of spin wave excitations. The values of $\text{B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ are found to be 0.40 and 0.06, respectively, for T/T_c ? 0.72. At temperatures close to T_c, H_eff(T) varies as (1 ? T/T_c)^β where β is one of the critical exponents and its value is found to be 0.29 ± 0.02.     

Average polarization of 12B in 12C(μ, ν)12B(g.s.) reaction: Helicity of the π-decay muon and nature of the weak coupling

The helicity, h^?, of μ^? in π-decay has been determined as positive (h^??+0.90) from the average polarization, P_av≡〈J_B·s_μ〉, of ¹²B produced in the $\text{μ}{}^{\mathrm{?}}\text{+}{}^{12}\text{C}\text{→ν}{}_{\mathrm{\mu }}\text{+}{}^{12}\text{B}$ reaction. We obtain also dynamical information on μ-capture: (i) the weak magnetism form factor, μ=4.5±1.1, and (ii) the sum of the induced pseudoscalar (g_p) and the 2nd class induced tensor (g_T) couplings versus g_A, ($\text{g}{}_{\mathrm{<mtext>P</mtext>}}\text{+g}{}_{\mathrm{<mtext>T</mtext>}}\text{)}\text{g}{}_{\mathrm{<mtext>A</mtext>}}\text{=7.1±2.7}$. The latter result, adopting the “canonical” value of $\text{g}{}_{\mathrm{<mtext>P</mtext>}}\text{g}{}_{\mathrm{<mtext>A</mtext>}}$, leads to $\text{g}{}_{\mathrm{<mtext>T</mtext>}}\text{g}{}_{\mathrm{<mtext>A</mtext>}}\text{=+1±2.7}$ which is compatible with zero and in strong contradiction with the value ?—6 recently advocated by Kubodera, Delorme and Rho.     

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.     

Deuteron optical model calculations including a Tp tensor interaction

Deuteron-nucleus optical model calculations which include two types of tensor spin-orbit interactions are compared. The interactions considered are of the forms $\text{V}{}_{\mathrm{<mtext>T</mtext><mtext>R</mtext>}}\text{(r)T}{}_{\mathrm{r}}\text{and}\text{1}\text{2}\text{[V}{}_{\mathrm{<mtext>T</mtext><mtext>P</mtext>}}\text{(r)T}{}_{\mathrm{p}}\text{+ T}{}_{\mathrm{p}}\text{V}{}_{\mathrm{<mtext>T</mtext><mtext>P</mtext>}}\text{(r)]}$ where the operators T_r and T_p are defined as $\text{T}{}_{\mathrm{r}}\text{ (}\text{s}\text{·}\text{r}\text{?}\text{)}{}^2\text{?}\text{2}\text{3}\text{and}\text{T}{}_{\mathrm{p}}\text{ (}\text{s}\text{·}\text{p}\text{)}{}^2\text{?}\text{2}\text{3}\text{p}{}^2$. Here, $\text{s}\text{,}\text{r}\text{and}\text{p}$ are the deuteron spin, position, and momentum operators, respectively. If a physically reasonable radial dependence V_TP(r) is used, the S-matrix elements (and hence all observables) calculated using a T_p tensor potential are found to be similar to those calculated using a suitably chosen T_r potential, provided that the incident deuteron energy is small compared to the real central potential. At higher deuteron energies, the differences between the effects of T_r and T_p potentials are more pronounced.     

Specific heat and resistivity of GdSb and HoSb above the néel temperature

The specific heat C_P is found to vary as $\text{dR}\text{dT}$ in the critical region above T_N for the antiferromagnets GdSb and HoSb. This correspondence holds despite a dramatic difference between the two systems in the strength of the divergence C_P = A?^?α, $\text{? =}\text{(T ? T}{}_{\mathrm{N}}\text{)}\text{T}{}_{\mathrm{N}}$, where for HoSb we find α = 0.83 ± 0.10 while for GdSb α = 0.20 ± 0.10.     

The microwave spectrum of 2,4-dioxabicyclo[3.1.0]hexan-3-one

The R band (26.5–40 GHz) microwave spectrum of 2,4-dioxabicyclo[3.1.0]hexan-3-one is reported. Rotational constants for the ground vibrational state of the common ¹²C₄¹H₄¹⁶O₃ and ¹³C₁, ¹³C₆ isotopically substituted species (the latter observed in natural abundance) have been evaluated. In addition rotational constants of the V_B = 1 to V_B = 5 quanta associated with the bending vibration of the five membered ring have been determined. A partial r_s structure has been calculated:

$\text{r(}\text{C}{}_1\text{?}\text{C}{}_5\text{) = 1.497± 0.016}\text{A}\text{?}\text{, r(}\text{C}{}_1\text{?}\text{C}{}_6\text{) = r(}\text{C}{}_6\text{?}\text{C}{}_5\text{) = 1.522 ± 0.015}\text{A}\text{?}$

,

$\text{∠}\text{C}{}_6\text{C}{}_1\text{C}{}_5\text{= ∠}\text{C}{}_1\text{C}{}_5\text{C}{}_6\text{= 60°32′ ± 1°36′, ∠}\text{C}{}_1\text{C}{}_6\text{C}{}_5\text{= 58°′ ± 1°47′}$

. With certain assumed molecular information a least squares fit yields the following parameters:

$\text{β = 68.5 ± 0.02°, r(}\text{C}{}_1\text{O}{}_2\text{= 1.408 ± 0.004}\text{A}\text{?}$

,

$\text{∠}\text{C}{}_5\text{C}{}_1\text{O}{}_2\text{= 105.8 ± 0.02°, ∠}\text{C}{}_1\text{O}{}_2\text{C}{}_3\text{= 108.10 ± 0.03°}$

,

$\text{∠}\text{O}{}_2\text{C}{}_3\text{O}{}_4\text{= 112.8 ± 0.02°}$

.     

On the order of levels in charmonium

We prove a theorem concerning the energies of the 2S and 3D states in a potential $\text{V(r) =}\text{?g}{}^2\text{r}\text{+ V}{}_{\mathrm{<mtext>c</mtext>}}\text{(r)}$, where V_c is a non-singular confining potential. If $\text{(}\text{d}\text{d}\text{r)}{}^3\text{(r}{}^2\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ is positive, then the 3D state lies above the 2S state, provided

$\text{d}\text{d}\text{r}\text{1}\text{r}\text{d}\text{d}\text{r}\text{2V}{}_{\mathrm{<mtext>c</mtext>}}\text{+r}\text{d}\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{d}\text{r}\text{< 0, ?}{}_{\mathrm{r}}\text{>0.}$

For V_c = r^α, this corresponds to 0 < α < 2.     

Anomalies in the elastic constants of antiferromagnetic uranium mononitride

Measured anomalies in the elastic constants of a single crystal of cubic anti-ferromagnetic uranium mononitride are reported. A dip of about 10% occurs in C₁₁ at 6 K below the Néel point $\text{T}{}_{\mathrm{<mtext>N</mtext>}}\text{?53}\text{K}$. Starting at T_N a renormalization in C₄₄ which is proportional to the square of the sublattice ,magnetization also occurs. The results are in general agreement with model calculations of the sound velocity renormalization due to spin-phonon interactions.     

Elastic moduli and mode gammas of GaP: Their relationship to those of other isomorphic crystals and the high pressure structural-electrical transition

The transit times of ultrasonic waves associated with piezoelectrically inactive modes have been measured in sulfur-dope, n-type GaP using hydrostatic pressures up to 5 kbar. The velocities and elastic constants of most modes increase linearly with pressure but $\text{C}{}_{\mathrm{S}}\text{=}\text{1}\text{2}\text{(}\text{C}{}_{11}\text{?}\text{C}{}_{12}\text{)}$ decreases slightly. The behavior of the elastic constants and their associated mode gammas are compared to those of other III–V compounds and of Si and Ge. We suggest that the behavior of C_S is related to the occurrence of the structural-electrical transition which occurs at high pressure. A modified Born criterion for lattice stability developed by Demarest $\text{et}$$\text{al}$. is used to explain this relationship. The contribution of thermal dilatation to the temperature dependence of each elastic constant is deduced. Using it and data from the literature we find that the explicit thermal contribution to each elastic constant is significant and in the case of C₁₂ has an anomalous sign.     

Effects of composition on the upper critical field of V-Ga

Measurements of the temperature dependence of the upper critical field, H_c2(T), for a series of V_100?xGa_x materials are presented for 20.5 ≤ × ≤ 29.6. Fits of the data to conventional theory for a paramagnetically limited, dirty, type II superconductor show: 1) a maximum in T_c and H_c2(0) for x ? 25; 2) a constant ( for x ≤ 25; 3) a slowly increasing value of λ_so with increasing x up to x ～ 25; and 4) good agreement with stoichiometric ordered and thermally disordered V₃Ga. Above $\text{x ? 25}$ broader transitions are observed. For x = 25, T_c = 15.3 K, (, λ_so = 0.3 and H_c2(0) = 23.4 tesla. The effects of inclusion of strong-coupling in the theory are discussed briefly.     

Temperature and pressure dependence of the elastic property of GeS2 glass

The sound velocities in GeS₂ glass have been measured by means of ultrasonic interferometry as a function of temperature or pressure up to 1.8 kbar. The bulk modulus K_s = 117.6 kbar and shear modulus G = 60.60 kbar were obtained for GeS₂ glass at 15°C and 1 atm. The temperature derivatives of both sound velocities and elastic moduli are negative :

$\text{(}\text{?ν}{}_1\text{?T}\text{)}$

_p =

$\text{?1.54 × 10}{}^{\mathrm{?4}}\text{km}\text{sec}$

°C,

$\text{(}\text{?ν}{}_1\text{?T}\text{)}$

_p =

$\text{?1.27× 10}{}^{\mathrm{?4}}\text{km}\text{sec}$

°C and

$\text{(}\text{?K}{}_{\mathrm{s}}\text{?T}\text{)}$

_p =

$\text{?1.27 × 10}{}^{\mathrm{?2}}\text{kbar}\text{°C}$

,

$\text{(}\text{?G}\text{?T}\text{)}$

_p = ?1.23 × 10^?2 kbar/°C,

$\text{(}\text{?Y}\text{?T}\text{)}$

_p = ?2.93 × 10^?2 their pressure derivatives are positive:

$\text{(}\text{?ν}{}_1\text{?P}\text{)}$

_T = 4.43× 10^?2km/kbar,

$\text{(}\text{?ν}{}_1\text{?P}\text{)}$

_T =

$\text{0.633 × 10}{}^{\mathrm{?2}}\text{km}\text{kbar}$

and (?K_s?P0)_T=6.81,

$\text{(}\text{?G}\text{?P)}{}_{\mathrm{T}}$

= 1.03, (?Y?T_T= 3.57. The Grüneisen parameter, γ_th= 0.298, and the second Grüneisen parameter, δ_s = 3.27, have also been calculated from these data. The elastic behavior of GeS₂ glass has proved to be normal despite the structural similarity among the tetrahedrally coordinated SiO₂, GeO₂ and GeS₂ glasses.     

Influence of self-fields on the Vlasov equilibrium and stability properties of relativistic electron beam-plasma systems

The influence of self-fields on the equilibrium and stability properties of relativistic beam-plasma systems is studied within the framework of the Vlasov-Maxwell equations. The analysis is carried out in linear geometry, where the relativistic electron beam propagates through a background plasma (assumed nonrelativistic) along a uniform guide field $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, It is assumed that $\text{ν}\text{γ}{}_0\text{? 1}$ for the beam electrons (ν is Budker's parameter, and γ₀mc² is the electron energy), but no a priori assumption is made that the beam density is small (or large) in comparison with the plasma density, or that conditions of charge neutrality or current neutrality prevail in equilibrium. It is shown that the equilibrium self-electric and self-magnetic fields, $\text{E}{}_{\mathrm{r}}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{r}}$ and $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$, can have a large effect on equilibrium and stability behavior. Equilibrium properties are calculated for beam (j = b) and plasma (j = e, i) distribution functions of the form f_b⁰(H, P_θ, P_z) = F(H ? ω_rbP_θ) × δ(P_z ? P₀)(j = b), and $\text{f}{}_{\mathrm{j}}{}^0\text{(H, P}{}_{\mathrm{\theta }}\text{, P}{}_{\mathrm{z}}\text{) = f}{}_{\mathrm{j}}{}^0\text{(H ? ω}{}_{\mathrm{rj}}\text{P}{}_{\mathrm{\theta }}\text{? V}{}_{\mathrm{j}}\text{P}{}_{\mathrm{z}}\text{?}\text{m}{}_{\mathrm{i}}\text{V}{}_{\mathrm{j}}{}^2\text{2}\text{)}$ (j = e, i), where H is the energy, P_θ is the canonical angular momentum, P_z is the axial canonical momentum, and ω_rj (the angular velocity of mean rotation for j = b, e, i), V_j (the mean axial velocity for j = e, i), and P₀ are constants. The linearized Vlasov-Maxwell equations are then used to investigate stability properties in circumstances where the equilibrium densities of the various components (j = b, e, i) are approximately constant. The corresponding electrostatic dispersion relation and ordinary-mode electromagnetic dispersion relation are derived (including self-field effects) for body-wave perturbations localized to the beam interior (r <R_b). These dispersion relations are analyzed in the limit of a cold beam and cold plasma background, to illustrate the basic effect that lack of charge neutrality and/or current neutrality can have on the two-stream and filamentation instabilities. It is shown that relative rotation (induced by self-fields) between the various components (j = b, e, i) can (a) result in modified two-stream instability for propagation nearly perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, and (b) significantly extend the band of unstable k_z-values for axial two-stream instability. Moreover, in circumstances where the beam-plasma system is charge-neutralized but not current-neutralized, it is shown that the azimuthal self-magnetic field $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$ has a stabilizing influence on the filamentation instability for ordinary-mode propagation perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$.