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.     

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.     

Logarithmic correction to the specific heat in tris-sarcosine calcium chloride

Specific heat experimental results in the 3x10^?2 ≦ | t | ≦5.5x10^?5 temperature range ($\text{t =}\text{(T?T}{}_{\mathrm{C}}\text{)}\text{T}{}_{\mathrm{C}}$) were fitted by means of the logarithmically corrected Landau theory of uniaxial dipolar ferroelectrics. The non-universal parameters b and t_O as well as the transverse and longitudinal correlation lengths at zero temperature are determined.     

The influence of excess oxygen on the elastic properties of non-stoichiometric SrO crystals

Measurements have been carried out of the elastic constants of SrO in the virgin undoped state and of the changes produced in them by equilibrium doping with oxygen at ? 1200°C and oxygen partial pressure of 0.95 atm. The method used was Papadakis' pulse-echo overlap technique in conjunction with thermogravimetric analysis (T.G.A.) to determine mass and density changes due to oxygen doping.The values obtained for C₁₁, C₁₂ and C₄₄ of the virgin crystal at 23°C are

$\text{C}{}_{11}\text{= 17.60 ± 0.03 × 10}{}^{11}\text{dynes/cm}{}^2$

;

$\text{C}{}_{12}\text{= 4.808 ± 0.007 × 10}{}^{11}\text{dynes/cm}{}^2$

;

$\text{C}{}_{44}\text{= 5.577 ± 0.008 × 10}{}^{11}\text{dynes/cm}{}^2$

.(These values are in very good agreement with those of Son and Bartels [2].)Values for $\text{δC}{}_{11}\text{C}{}_{11}$ and $\text{δC}{}_{44}\text{C}{}_{44}$ were found to be ?1.74% and ?0.86% respectively. Accurate valu $\text{δC}{}_{12}\text{C}{}_{12}$ could not be obtained because of sample size limitations after quenching. However, C₁₂ was shown to definitely increase due to doping.Analysis of the results indicate that the elastic modulus changes can only be attributed to the formation of cation vacancies during doping. Analysis of the T.G.A. behavior indicates that this cation vacancy formation is probably associated with the presence of various tripositive cation and uninegative anion species depending upon the impurity concentrations of the sample. This implied impurity-controlled cation vacancy concentration is consistent with the earlier observed extrinsic nature of cation diffusion in SrO at 1200°C.     

Temperature derivatives at constant volume of the elastic constants of the alkali halides

Values of dC/dT)_V have been computed from experimental dC/dT)_P and dC/dP)_T for the three elastic constants (expressed as $\text{B}{}_{\mathrm{T}}\text{, C}{}_{44}\text{and}\text{(C}{}_{11}\text{?C}{}_{12}\text{)}\text{2)}$ of each of the 16 Li, Na, K, and Rb halides. The dC/dT)_V measure the explicit dependence of C on T, the effect of thermal expansion having been removed. The dC/dT)_V are all small (compared with dC/dT)_P), are all negative, and vary quite systematically and smoothly with anion, with cation and with the three elastic constants. Negative dB_T/dT)_V is accounted for both thermodynamically and by available lattice dynamical calculations. dC/dT)_V for shear constant is expressed in terms of two vibrational mode parameters, whose values can then be estimated from the observed value, and the trend of dC/dT)_V with Debye temperature.     

Critical slowing down of fluctuations in squaric acid (H2C4O4) at the phase transition observed by 13C spin-lattice relaxation

Spin lattice relaxation T₁ of naturally abundant ¹³C nuclei in squaric acid was measured close to the antiferroelectric-paraelectric phase transition temperature T_c = 373 K. A rapid increase in $\text{1}\text{T}{}_1$ is observed close to T_c coming from above, which follows the power law $\text{1}\text{T}{}_1\text{～ ε}{}^{\mathrm{?1.4}}$ where $\text{ε =}\text{(T ? T}{}_{\mathrm{c}}\text{)}\text{T}{}_{\mathrm{c}}$. This behaviour is explained on the basis of the two-dimensional character of the fluctuations.     

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.     

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.     

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.     

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.     

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.     

Elastic-constant measurements in solid argon at the melting point

The velocities of ultrasonic waves have been measured in solidified argon in the pressure range up to 6 kb (600 MPa). Shear wave velocities could be measured to temperatures very close to the melting point, such that both liquid and solid phases coexisted, $\text{(T?T}{}_{\mathrm{<mtext>m</mtext>}}\text{)}\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{<10}{}^{-5}$. The measurements show that neither the shear velocity tends to zero nor its derivative with temperature tends to -8 as T→T_m.     

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.     

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.     

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.     

Elastic constants of LaB6 at room temperature

Measurements have been made of the transit times of pulses of longitudinal and transverse ultrasonic waves propagating in single crystal LaB₆ at room temperature. A unique set of values for the three independent elastic constants has been calculated from the resultant velocities and is; C₁₁ = (45.33 ± 0.11) × 10¹¹dynecm^-2, $\text{C}{}_{12}\text{= (1.82 ± 0.17) × 10}{}^{11}\text{dyne}\text{cm}{}^2$ and C₄₄ = (9.01 ± 0.05) × 10¹¹dyne/cm². The Debye temperature of LaB₆ from these measurements is 773 K, which agrees relatively well with the X-ray Debye temperature, however, differs much from the calorimetric and electrical resistance Debye temperatures.     

Monte Carlo study on dynamical behaviour of spins and spin clusters in the 2D ± J Ising spin-glass

To investigate dynamical (time-dependent) behavior of spins and spin clusters in the two-dimensional ± J Ising spin-glass, we have evaluated the relaxation time τ_i of individual spins by the Monte Carlo simulation. An interesting finding is that, at least in the temperature range $\text{T ? 0.8J}$, most of τ_i are described by $\text{τ}{}_{\mathrm{i}}\text{∝}\text{exp}\text{{}\text{E}{}_{\mathrm{i}}\text{(T ? T}{}_0\text{}}$ with T₀?0.5J (E_i being a constant), which suggests that the system undergoes a glass transition obeying Fulcher's law.     

Softening of acoustic and optical modes in ferroelastic phase in Hg2Br2

The softening of an acoustic and an optical phonons in Hg₂Br₂ has been investigated by means of the light scattering technique.It has been observed that the cube of the frequency of the soft optical phonon varies proportionally with the temperature below T_c.An expression for the relation of the elastic constant C₆₆ to the temperature has been derived from the phenomenological thermodynamic potential function. The observed temperature dependence of the elastic constant and the optical phonon frequency is described when we assume that the order parameter Q varies as $\text{Q ∝ [T ? T}{}_0\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>6</mtext>}}$.     

Hole contribution to the elastic constants of SnTe

Ultrasonic wave velocities have been measured in SnTe single crystals with hole concentrations of 1.0 and 4.5 × 10²⁰/cm³. The shear elastic stiffness constant C₄₄ is sensitive to the hole concentration but $\text{1}\text{2}\text{(C}{}_{11}\text{? C}{}_{12}\text{)}$ is not, a result which is consistent with the valence band pockets being sited at the L points. The non-ellipsoidal, non-parabolic multivalley band model has been used to calculate the hole contribution to the elastic constants. The calculated difference between the shear constant C₄₄ (2.78 × 10¹⁰ dyne cm^-2) for the two crystals is in agreement with that measured experimentally (2.67 × 10¹⁰ dyne cm^-2). The shear deformation potential constant E_u for the SnTe valence band is 7.8 eV at 293°K.