Hydrostatic pressure dependences of elastic constants and vibrational anharmonicity of uranium nitride

Measurements of the effect of hydrostatic pressure on ultrasonic wave velocities have been used to determine the pressure derivatives of the elastic stiffness of uranium nitride at room temperature.C ₄₄/P, and hence the Grüneisen parameter for the transverse mode propagating down an 001 axis, is negative; however, this mode softening is not anomalous for rocksalt structure crystals. The Grüneisen gammas of the acoustic modes obtained in the long wavelength limit have a pronounced anisotropy which accrues largely from the presence or absence of contributions to modes of vibration from nearest-neighbour repulsive forces. The compression of uranium nitride calculated from the Murnaghan equation of state is much smaller than those of the alkali halides or IV–VI compounds because this compound is much stiffer.     

Room temperature single crystal elastic constants of boron carbide

Single crystals of the high temperature ceramic boron carbide have been synthesized by the optical floating zone method. Room temperature elastic constants of a carbon-deficient boron carbide single crystal have been measured using the resonant ultrasound spectroscopy technique. Based upon density measurements, the single crystal stoichiometry was specified as B_5.6C. This crystal has room temperature single crystal elastic constants of c ₁₁ = 542.81, c ₃₃ = 534.54, c ₁₃ = 63.51, c ₁₂ = 130.59, and c ₄₄ = 164.79 GPa, respectively. Analysis of Cauchy's relationships, Poisson's ratios, and elastic anisotropic factors for the single crystal elastic constants indicates that it is more strongly anisotropic in elasticity and interatomic bonding than most solids. Room temperature isotropic elastic moduli of boron carbide show that its bulk, shear and Young's moduli are substantially higher than those of most solids, so that boron carbide belongs to the so-called strong solids. Its Poisson's ratio is significantly lower than that of most solids.     

Ultrasonic determination of the temperature and hydrostatic pressure dependences of the elastic properties of ceramic titanium diboride

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of titanium diboride (TiB₂) ceramic samples as functions of temperature in the range 130–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. TiB₂ is an elastically stiff but light ceramic: at 295 K, the longitudinal stiffness (C _L ), shear stiffness (), adiabatic bulk modulus (B ^S ), Young's modulus (E) and Poisson's ratio () are 612 GPa, 252 GPa, 276 GPa, 579 GPa and 0.151, respectively. The adiabatic bulk modulus B ^S is in good agreement with the results of recent theoretical calculations. All elastic moduli increase with decreasing temperature and do not show any pronounced unusual effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Grüneisen parameters. The values determined at 295 K for the hydrostatic-pressure derivatives (C _L /P) _P=0, (/P) _P=0 and (B ^S /P) _P=0 are 7.29 ± 0.1, 2.53 ± 0.1 and 3.91 ± 0.1, respectively. The hydrostatic-pressure derivative (B ^S /P) _P=0 of the bulk modulus of TiB₂ ceramic is found to be larger than that estimated previously from uniaxial shock-wave loading experiments. The longitudinal (_L), shear (_S), and mean (^el) acoustic-mode Grüneisen parameters of TiB₂ are positive: the zone-centre acoustic phonons stiffen under pressure in the usual way. Since the acoustic Debye temperature _D (=1190 K) is very high, the shear modes provide a substantial contribution to the acoustic phonon population at room temperature. Knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic TiB₂.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of hexagonal boron nitride

The second and third order elastic constants and pressure derivatives of second order elastic constants of hexagonal boron nitride have been obtained using the deformation theory. The strain energy derived using the deformation theory is compared with the strain dependent lattice energy obtained from elastic continuum model approximation to get the expressions for second and third order elastic constants. Higher order elastic constants are a measure of anharmonicity of crystal lattice. The six second-order elastic constants and the ten non-vanishing third order elastic constants and six pressure derivatives of hexagonal boron nitride are obtained in the present work and are compared with available experimental values. The second order elastic constant C ₁₁ which corresponds to the elastic stiffness along the basal plane of the crystal is greater than C ₃₃. Since C ₃₃ being the stiffness tensor component along the c-axis of the crystal, this result is expected from a layer-like material like boron nitride (BN). The third order elastic constants of hexagonal BN are generally one order of magnitude greater than the second-order of elastic constants as expected of a crystalline solid. The pressure derivative dC ₃₃/dp obtained in the present study is greater than dC ₁₁/dp which indicates that the compressibility along c-axis is higher than that along ab-plane of hexagonal BN.     

Anomalous pressure dependences of the superconducting transition temperature of dilute alloys of LaSn3 containing light rare earth impurities

The initial depressions of the superconducting transition temperature T _c of LaSn₃ by rare earth (RE) impurities are known to be anomalous. In an attempt to clarify this behavior, we have measured the pressure dependence of the T _c of (LaRE)Sn₃ alloys (RE = Y, Ce, Pr, Nd, Sm, Eu, Gd, and Lu) to pressures up to 25 kbar. The magnitude of the pressure dependence of the T _c of (LaRE)Sn₃ alloys containing RE impurities with partially filled 4f electron shells decreases monotonically with increasing RE atomic number. A general discussion of existing zero- and high-pressure data for various physical properties of (LaRE)Sn₃ alloys demonstrates that the association of large pressure dependences of T _c with the occurrence of unstable impurity 4f shells (the Kondo effect) should be made with caution. The experimental high-pressure results are analyzed in terms of appropriate theoretical models for magnetic and nonmagnetic localized impurity states in superconductors.Supported by the US DOE Contract E(04-3)-34PA227.National Science Foundation Postdoctoral Fellow.     

Anomalies of temperature dependences of the elastic moduli of steels of the austenitic and transition classes

Data on the temperature dependence of the moduli of longitudinal elasticity E of a number of commercial steels of the ferritic, martensitic, austenitic, and transition classes in the temperature interval from room temperature to the temperature of liquid helium are presented. It is shown that for the austenitic and transition classes of steels, the elastic modulus E does not increase, but decreases when the test temperature is lowered within certain temperature ranges. It is suggested that this anomaly is associated with antiferromagnetic ordering in the austenite.Translated from Problemy Prochnosti, No. 1, pp. 20–23, January, 1992.     

Ultrasonic study of the temperature and pressure dependences of the elastic properties of a single-crystal Heusler structure Cu41Mn20Al39 alloy

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic-stiffness tensor components Cu and the adiabatic bulk modulus, BS, of a ferromagnetic Heusler structure Cu41Mn20Al39 at % alloy single crystal as functions of temperature in the range 14–300 K and hydrostatic pressure up to 0.2 GPa at room temperature. At 295 K the elastic stiffnesses are: C11=133 GPa, C44=92 GPa, C (=(C11–C12)/2)=17 GPa, C12=99 GPa, CL(=C11+C44–C)=205 GPa, and BS (=C11–4C/3)=106 GPa. Cu41Mn20Al39 is a comparatively soft material elastically because its elastic properties are influenced strongly by magnetoelastic effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to obtain the hydrostatic-pressure derivatives of the elastic – stiffness tensor components. At 295 K (C11/P)P=0, (C44/P)P=0, (C/P)P=0, (C12/P)P=0, (CL/P)P=0, and (BS/P)P=0 are 5.0±0.1, 3.0±0.1, 1.0±0.2, 3.0±0.3, 7.7±0.4 and 3.7±0.4, respectively. Application of hydrostatic pressure does not induce acoustic-mode softening: the pressure derivatives (CIJ/P)P=0 and (BS/P)P=0 and the acoustic-mode Grüneisen parameters are positive. An interesting feature of the non-linear acoustic behaviour of this alloy is that the value obtained for (C/P)P=0, associated with the softer shear mode propagated along the [1 1 0] direction and polarized along the [1 1 0] direction, is small in comparison with those of the other shear and longitudinal modes. The Grüneisen parameter of this mode, and hence its vibrational anharmonicity, is much larger than those of the other long-wavelength acoustic phonon modes. © 1998 Kluwer Academic Publishers     

Ambiguity of temperature dependences for the elastic characteristics of materials with nickel and germanium as examples

Experimental data are presented for precise measurements of longitudinal ultrasonic wave propagation rate in single-crystal germanium and polycrystalline nickel. With these materials as examples the existence of ambiguity is demonstrated in values of elastic characteristics in successive cycles of thermal exposure, i.e., temperature ranges in which the material does not undergo phase transformation.It is suggested that the ambiguity of mechanical properties of the materials is due to possible variations in the distribution of energy between the lattice framework and the electron subsystem of atoms.Translated from Problemy Prochnosti, No. 10, pp. 54–56, October, 1990.     

Temperature and pressure dependences of the elastic properties of ceramic boron carbide (B4C)

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic boron carbide (B₄C) as functions of temperature in the range 160–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. B₄C is an elastically stiff but extremely light ceramic: at 295 K, the longitudinal stiffness (C _L), shear stiffness (), adiabatic bulk modulus (B ^S ), Young's modulus (E) and Poisson's ratio () are 498 GPa, 193 GPa, 241 GPa, 457 GPa and 0.184, respectively. In general, the adiabatic bulk modulus B ^S agrees well with both experimental and theoretical values determined previously and is approximately constant over the measured temperature range. Both E and increase with decreasing temperature and do not show any unusual effects. The values determined at 295 K for the hydrostatic-pressure derivatives ( C _L/P) _P=O , (/P) _P=O and (B ^S /P) _P=O are 5.7 ± 0.3, 0.78 ± 0.4 and 4.67 ± 0.3, respectively. The hydrostatic-pressure derivative (B ^S /P) _P=O of the bulk modulus is found to be comparable with that estimated previously from dynamic yield strength measurements. The effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Grü neisen parameters. The longitudinal (_L), shear (_S), and mean (^el) acoustic-mode Grüneisen parameters of B₄C are positive: the zone-centre acoustic phonons stiffen under pressure in the usual way. Knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic B₄C. Since the acoustic Debye temperature _D (=1480 K) is very high, the shear modes provide a substantial contribution to the acoustic phonon population at room temperature.     

A theoretical study of the valence transition in Sm1 − x M x S alloys

We present a theoretical model to explain the valence transitions of Sm in Sm_{1 – x} M _x S alloys, where M is a transition metal (e.g., Y or La). The f-level of Sm is described as a zero-width band with a finite Coulomb repulsion U, hybridized with the d band of the alloy, which is treated in the coherent potential approximation (CPA). The results show a change of the number of 4f electrons as a function of the concentration, which explains the valence transition observed in these alloys.Work supported in part by CNPq and FINEP.     

Low temperature acoustically measured specific heats and elastic constants of four technical polymers

The velocity of longitudinally and transversely polarized 10 MHz sound waves has been measured in four technical polymers (nylon, Teflon, and two epoxy resins) between 4 and 100K. The values of the specific heat divided by T³ calculated from these measurements is considerably less than the values measured calorimetrically below 4 K. This discrepancy is due to the existence of localized modes which make the extrapolation of specific heat measurements in amorphous materials extremely dangerous. Low temperature values of the bulk and shear moduli well as Poisson's ratio are also presented.     

Determination of mass density, dielectric, elastic, and piezoelectric constants of bulk GaN crystal

Mass density, dielectric, elastic, and piezoelectric constants of bulk GaN crystal were determined. Mass density was obtained from the measured ratio of mass to volume of a cuboid. The dielectric constants were determined from the measured capacitances of an interdigital transducer (IDT) deposited on a Z-cut plate and from a parallel plate capacitor fabricated from this plate. The elastic and piezoelectric constants were determined by comparing the measured and calculated SAW velocities and electromechanical coupling coefficients on the Z- and X-cut plates. The following new constants were obtained: mass density p = 5986 kg/m(3); relative dielectric constants (at constant strain S) ε(S)(11)/ε(0) = 8.6 and ε(S)(11)/ε(0) = 10.5, where ε(0) is a dielectric constant of free space; elastic constants (at constant electric field E) C(E)(11) = 349.7, C(E)(12) = 128.1, C(E)(13) = 129.4, C(E)(33) = 430.3, and C(E)(44) = 96.5 GPa; and piezoelectric constants e(33) = 0.84, e(31) = -0.47, and e(15) = -0.41 C/m(2).