M. Cankurtaran

Elastic and non-linear acoustic properties and thermal expansion of cerium metaphosphate glasses

Abstract To test predictions of the soft potential model (SPM) for the thermal and acoustic properties of glasses, the thermal expansion and the ultrasonic wave velocity and attenuation have been measured in cerium metaphosphate glasses with compositions in the vicinity of (Ce 2 O 3 ) 0.25 (P 2 O 5 ) 0.75 . The ultrasonic wave velocities have been determined as functions of temperature and hydrostatic pressure; the results provide the temperature dependences of the adiabatic elastic stiffnesses C 11 and C 44 and related elastic properties, and the hydrostatic-pressure derivatives (∂ C 11 /∂ P ) P =0 and (∂ C 44 /∂ P ) P =0 of the elastic stiffnesses and (∂ B S /∂ P ) P =0 of the bulk modulus. The longitudinal ultrasonic wave velocities increase under pressure. The hydrostatic pressure derivative (∂ B S /∂ P ) P =0 of the bulk modulus B S is positive: when compressed, the cerium metaphosphate glasses show a normal volume elastic response. However, the pressure derivative (∂ C 44 /∂ P ) P =0 of the shear modulus is negative but small, indicating weak softening of shear modes under pressure. The shear wave ultrasonic attenuation is characterised by a broad peak; the calculated relaxation parameters are consistent with phonon-assisted relaxation of two-level systems. The results found for C IJ and (∂ C IJ /∂ P ) P =0 are used to determine the long-wavelength acoustic-mode Gruneisen parameters, which quantify the vibrational anharmonicity and are needed to obtain the acoustic mode contribution to thermal expansion. The temperature dependence of the shear wave ultrasound velocity, after subtraction of the relaxation and anharmonic contributions, follows a linear law as predicted by the SPM for relaxation of soft harmonic oscillators. At low temperatures the excess low-energy vibrational states provide a negative contribution to thermal expansion, which can be understood on the basis of the SPM.

Anisotropic elastic and nonlinear acoustic properties of very dense textured Bi2Sr2CaCu2O8+y

The velocities of longitudinal and shear ultrasonic waves propagated in very dense (95% of theoretical), highly-textured, ceramic Bi2Sr2CaCu2O8+y (Bi2212) have been measured as functions of temperature (between 10 and 290 K) and hydrostatic pressure at 290 K. The main finding is a marked anisotropy of the elastic stiffness constants and their dependences on pressure. The authors have observed an elastic stiffness constant in the a-b plane that is substantially greater than that in the c direction. This observation is consistent with the crystallographic structure of Bi2212. The anomalous elastic effects and thermal hysteresis, observed previously by several groups in various Bi-based superconductors in the range of 19-240 K, have not been found in the present material. These observations suggest that these anomalies are not an inherent property of Bi-based cuprates, but instead may depend on the oxygen content and microstructure of the ceramic material. An analysis of sound velocity in a polycrystalline array of elastically anisotropic crystallites is presented.

Ultrasonic study of the elastic and nonlinear acoustic properties of ceramic aluminum nitride

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of aluminum nitride (AlN) ceramic samples as functions of temperature in the range 100–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Aluminum nitride is an elastically stiff but light ceramic: at 295 K, the longitudinal stiffness (CL), shear stiffness (μ), adiabatic bulk modulus (BS), Youngs modulus (E) and Poissons ratio (σ) are 373 GPa, 130 GPa, 200 GPa, 320 GPa and 0.234, respectively. The temperature dependences of CL and BS show normal behaviour and can be approximated by the conventional model for vibrational anharmonicity. 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 (∂CL/∂P)P=0, (∂μ/∂P)P=0 and (∂BS/∂P)P=0 are 4.7 ± 0.1, 0.22 ± 0.03 and 4.4 ± 0.15, respectively. The adiabatic bulk modulus BS and its hydrostatic-pressure derivative (∂BS/∂P)P=0 are in good agreement with the results of recent high pressure X-ray diffraction measurements and theoretical calculations. The longitudinal (γL), shear (γS), and mean (γel) acoustic-mode Grüneisen parameters of AlN are positive: the zone-centre acoustic phonons stiffen under pressure. The shear γS (=0.006) is much smaller than the longitudinal γL (=1.09) accounting for the low thermal Gr¨neisen parameter γth (=0.65) obtained for this ceramic: since the acoustic Debye temperature ΘD (=980 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic AlN.

Elastic behaviour under pressure of high-T c superconductors RBa2Cu3O7-x (R = Y, Gd and Eu)

Abstract The effects of hydrostatic pressure on the velocities of longitudinal and shear ultrasonic waves have been measured in YBa2Cu3O7-x, GdBa2Cu3O7-x and EuBa2Cu7O7-x. Measurements have been made for samples having different porosities to determine the effects of porosity on elastic behaviour under pressure. Results have been analysed on the basis of multiple scattering theory to provide the elastic properties of the non-porous matrix. The effects of hydrostatic pressure on the ultrasonic wave velocities are markedly nonlinear and have been used to obtain combinations of the effective third- and fourth-order elastic constants appropriate to a porous small-grained ceramic material treated as an isotropic body. The hydrostatic pressure derivatives (∂CIJ/∂P)r = o of the isotropic elastic constants and the acoustic mode Gruneisen parameter in the long-wavelength limit are very large, features which can be attributed to the open structure of this defect perovskite, although a valence change of copper could...

Elastic and nonlinear acoustic properties and thermal expansion of rare-earth metaphosphate glasses

Abstract The thermal expansions and the ultrasonic wave velocities and attenuations of (Sm2O3)0.234(P2O5)0.776 and (La2O3)0.222 (P2O5)0.778 and mixed (La2O3)x (Sm2O3)y(P2O5)0.75 (where x + y = 0.25) metaphosphate glasses have been measured as functions of temperature. The change in the ultrasonic wave velocity induced by application of hydrostatic pressure up to 0.16 GPa has also been measured at selected temperatures between room temperature and 375 K. The experimental results provide the temperature dependences of the adiabatic elastic stiffnesses C11 and C44 and related elastic properties and provide the hydrostatic-pressure derivatives (∂C 11/∂P)P=0 and (∂C 44/∂P)p=0 of the elastic stiffnesses and (∂B S/∂P)P=0 of the bulk modulus. The results obtained for C IJ and (∂C IJ/∂P)P=0 are used to determine the long-wavelength acoustic-mode Gruneisen parameters; these quantify the vibrational anharmonicity, which is essential information for developing the acoustic mode contribution to the thermal expansion o...

Ultrasonic study of the temperature and pressure dependences of the elastic properties of fully oxygenated YBa2Cu3O6.94

The effects of temperature and hydrostatic pressure on the velocities of longitudinal and shear ultrasonic waves propagated in ceramic specimens of YBa2Cu3O6.94 have been measured. The ultrasonic wave velocities in this fully oxygenated material increase smoothly with decreasing temperature from 300 K to 10 K; the anomalous elastic effects and thermal hysteresis, observed previously by several groups in various YBa2Cu3O7-x superconductors in the range of 190-240 K, have not been found; this is in accord with the phase relationships expected for a material with this high oxygen concentration. The ultrasonic wave velocities in YBa2Cu3O6.94 increase linearly with pressure. The hydrostatic pressure derivatives ( delta CL/ delta P)p=0 (=20) and ( delta mu / delta P)p=0 (=0.9) of the elastic stiffnesses and ( delta Bs/ delta P)p=0 (=18.8) of the bulk modulus, and the mean long-wavelength acoustic mode Gruneisen parameter gamma el (=2.3) obtained for YBa2Cu3O6.94 are substantially smaller than those found previously for YBa2Cu3O7-x ceramics containing less oxygen. It is concluded that the oxygen content of YBa2Cu3O7-x strongly influences the elastic and nonlinear acoustic properties.

Correlation between anomalous elastic behaviour under pressure and with temperature near 220 K in YBa2Cu3O7-x

The velocities of longitudinal and shear ultrasonic waves propagated in dense (96% of theoretical density) ceramic YBa2Cu3O7-x have been measured as functions of temperature and hydrostatic pressure. The temperature dependences of the elastic stiffnesses and bulk modulus, which have been determined from the velocity data between 10 K and 300 K, show the previously recognized step-like increase at about 200 K on cooling and a similar decrease at about 225 K during warming, with a pronounced hysteresis in the range 190-235 K. The pressure dependences of the velocities of both longitudinal and shear ultrasonic waves show a substantial reduction in slope at a pressure Pc and are practically linear on either side of Pc. The pressure Pc at which the kink occurs decreases linearly on decreasing the temperature from 297 K to 247 K and extrapolates to atmospheric pressure at 220 K, which is within the temperature range where the steep changes in the temperature dependences of the elastic moduli occur. Hence the kink in the elastic properties under pressure at Pc correlates with the steep change observed in the range 190-235 K at atmospheric pressure, which has been attributed previously to a phase transition involving oxygen ordering. The measured pressure and temperature dependences of the anomalies in the ultrasonic wave velocities have been used to locate the ortho-I to mixed (ortho-I and ortho-III) phase boundary in the P-T plane of the phase diagram.

The effect of hydrostatic pressure on the elastic behaviour of GdBa2Cu3O7-x

The pressure dependences of ultrasonic longitudinal and shear waves have been measured in the high-Tc superconductor GdBa2Cu3O7-x. The effects of porosity have been taken into account by using wave scattering theory in a porous medium. The pressure dependence ( delta B/ delta P)P=0 of the bulk modulus of the nonporous matrix at room temperature has the considerable value of 55. The adiabatic bulk modulus B0s measured ultrasonically at atmospheric pressure is much smaller than that BT(P) determined by X-ray measurements of lattice parameters at high pressure; this discrepancy is due to the large pressure dependence of the bulk modulus. It is suggested that the rather small bulk modulus and its large pressure dependence could be due to a combination of fluctuating copper valence and to the vacant sites in the crystal structure.

Ultrasonic study of the elastic properties of YBa2Cu4O8 and their temperature and pressure dependences

The effects of temperature and hydrostatic pressure have been measured on the velocities of longitudinal and shear 5 MHz ultrasonic waves propagated in ceramic YBa2Cu4O8. The bulk modulus (=58 GPa) of this high-Tc superconductor has the same small magnitude as that of YBa2Cu3O7-x ceramics determined from ultrasonic velocity measurements. With decreasing temperature from 300 K to 12 K the ultrasonic wave velocities increase smoothly but only gradually. Although there is a small increase in gradient near 185 K, the ultrasonic velocities in YBa2Cu4O8 do not show the large step-like changes with pronounced hysteresis in the temperature range 190-235 K, which characterize the elastic behaviour of ceramic YBa2Cu3O7-x. The attenuations of both longitudinal and shear ultrasonic waves in YBa2Cu4O8 do not exhibit relaxation-type peaks. The ultrasonic velocities in YBa2Cu4O8 increase approximately linearly with pressure. The hydrostatic pressure derivatives ( delta CL/ delta P)P=O (=13.9) and ( delta mu / delta P)P=O (=0.6) of the elastic stiffnesses and ( delta Bs/ delta P)P=O (=13.1) of the bulk modulus obtained for YBa2Cu4O8 are much smaller than those found previously for YBa2Cu3O7-x ceramics. The mean acoustic mode Gruneisen parameter gamma el (=1.5) of YBa2Cu4O8 is an order of magnitude smaller than that determined for YBa2Cu3O7-x ceramics from high-pressure ultrasonic studies. The oxygen concentration of YBa2Cu4O8 is stable, in contrast to that of YBa2Cu3O7-x. It is concluded that the differences between the elastic and nonlinear acoustic properties of YBa2Cu4O8 and those of YBa2Cu3O7-x are associated with the absence of oxygen vacancies and therefore of oxygen ordering and migration in YBa2Cu4O8.

High-pressure ultrasonic study of monocrystalline Cr in the antiferromagnetic and paramagnetic phases

Abstract An experimental ultrasonic study has been made of the elastic and nonlinear acoustic behaviour of single-crystal Cr in both the antiferromagnetic (AFM) spin-density wave (SDW) and paramagnetic (PM) phases. The velocities of the ultrasonic waves propagated along the [100] and [110] directions have been measured as a function of hydrostatic pressure up to 0.2 GPa at fixed temperatures in the range from room temperature up to 400 K, which covers the Neel temperature (TN). The results provide complete sets of the elastic-stiffness tensor components and their pressure derivatives as a function of temperature. The longitudinal acoustic-mode Griineisen parameters are positive at room temperature, but they become negative in the range from about 300 K to TN indicating longitudinal-mode softening due to a strong magnetoelastic interaction between the SDW and long-wavelength longitudinal acoustic phonons: the mode softening is much enhanced just below the Nkel point. The Gruneisen gamma γs{N[110]U[110]} co...