Hydrostatic Pressure Derivatives Research Articles

Optical and ultrasonic properties of europium phosphate glasses

To provide an overall picture of the vibrational properties of phosphate glasses containing high concentrations of europium, measurements have been made of their ultrasonic wave velocities and attenuation, optical absorption spectra and laser-induced fluorescence. To examine their valence state, the fluorescence of the glasses has been examined. The spectra do not show any obvious sign of divalent europium ions, only trivalent europium ion fluorescence being observed. Room-temperature absorption spectra of these glasses also provide evidence of only the absorption bands of trivalent europium. The elastic stiffnessesC11 andC44 continue to increase down to low temperatures and the ultrasonic attenuation is characterized by a broad peak, properties which are consistent with thermally activated relaxations of two-level systems. The longitudinal and shear ultrasonic wave velocities decrease under pressure; the hydrostatic pressure derivatives (∂C11/∂P)T, P=0 and (∂C44/∂P)T, P=0 of the elastic stiffness tensor componentsCIJ and (∂B/∂P)T, P=0 of the bulk modulus,B0, are negative. When compressed, the europium phosphate glasses, like their samarium analogues, show the interesting property of becoming easier to squeeze. Measurements, using a pulse superposition technique, of the effect of uniaxial stress on ultrasonic wave velocities have been used to determine the temperature dependences of the third-order elastic stiffness tensor components of (Eu2O3)0.186(P2O5)0.814 and (Eu2O3)0.20(P2O5)0.80 glasses between 77 and 400 K. The uniaxial and hydrostatic pressure dependences of the elastic constants quantify the cubic term in the strain Hamiltonian and the vibrational anharmonicity of the long-wavelength phonons of these glasses. The acoustic mode Gruneisen parameters are negative: application of pressure induces a decrease in the long-wavelength acoustic phonon mode frequencies. As the temperature is reduced the pressure-induced mode softening becomes enhanced. The hydrostatic pressure derivative (∂C11/∂P)T, P=0 is larger than (∂C44/∂P)T, P=0 over the whole temperature range, and the longitudinal acoustic mode Gruneisen parameter ∥γL∥ is larger than that ∥γS∥ of the shear wave: the longitudinal mode softens more with pressure than the shear mode. Murnaghan's equation-of-state is used to determine the compressionV(P)/V0.

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.

Contrasting effects of lanthanum and samarium modifiers on the elastic and non-linear acoustic properties of phosphate glasses

While samarium phosphate (Sm2O3) x (P2O5)(1−x) glasses are known to show pronounced long-wavelength acoustic-mode softening, their lanthanum (La2O3) x (P2O5)(1−x) analogues do not. To investigate experimentally this different influence of lanthanide modifiers, a comparative study has been made of the effects of temperature and pressure on the velocities of ultrasonic waves propagated in binary ((La2O3) x (P2O5)(1−x) and (Sm2O3) x (P2O5)(1−x)) and ternary ((La2O3) x (Sm2O3) y (P2O5)(1−x−y)) phosphate glasses with compositions near to that corresponding to the metaphosphate (R2O3)0.25(P2O5)0.75. For each glass the second-order elastic stiffness tensor componentsC IJ S continue to increase down to 10 K in a manner consistent with ultrasonic interactions with two-level systems. Measurements of the effects of hydrostatic pressure on the ultrasonic wave velocities have been used to determine the hydrostatic pressure derivatives (∂C IJ S /∂P)T,P=0 of the second-order elastic stiffness tensor components and (∂B 0 S /∂P)T,P=0 of the bulk modulusB 0 S at room temperature (293 K). For the ternary glasses (∂C 11 S /∂P)T,P=0, (∂C 44 S /∂P)T,P=0 and (∂B 0 S /∂P)T,P=0 are small but positive; these glasses stiffen under pressure. Replacement of samarium by lanthanum in the ternary glasses negates the acoustic-mode softening. Possible sources of the different effects of lanthanum and samarium modifiers on the non-linear acoustic properties of metaphosphate glasses are discussed.

Elastic Behaviour of Terbium Metaphosphate Glasses Under High Pressures

The elastic and nonlinear acoustic vibrational properties of terbium metaphosphate glasses (Tb2O3)x(P2O5)1?x with x = 0�226,0�247,0�263 and 0�271 (x is the mole fraction) have been determined from measurements of the effects of temperature, hydrostatic pressure, and uniaxial stress on' ultrasonic wave velocity. At temperatures below about 140 K, the elastic stiffness of' (Tb2O3)x(P2O5)1?x glasses becomes anomalously dependent upon temperature, a behaviour usually associated with interactions between acoustic phonons and two-level systems. Except for the (Tb2O3)0�271(P205)0�729 glass, the hydrostatic pressure derivatives of the elastic stiffness and also of the bulk modulus BS of terbium metaphosphate glasses are small and negative. The third-order elastic stiffness tensor components CIJK of the (Tb2O3)0�247(P2O5)0�753 glass between 77 K and 400 K have also been determined. At room temperature, C112, C123 and C144 are positive while C111, C155 and C456 are negative. Both longitudinal and shear acoustic mode Gr�neisen parameters are small and negative: the application of pressure softens the long-wavelength acoustic phonon mode frequencies. The mode softening is enhanced as the temperature is reduced.

Linear and nonlinear elastic properties of antiferromagnetic γ-manganese-nickel alloys

Abstract The linear and nonlinear elastic properties of single crystals of f.c.c. γ-manganese-nickel alloys with compositions Mn73Ni27, Mn80.5Ni19.5 and Mn84Ni16 have been studied using ultrasonic pulse-echo techniques. The elastic stiffness tensor components of Mn73Ni27 have been determined as a function of temperature and pressure on both sides of the Nee1 temperature. The longitudinal moduli c 11, and c L(= (c 11 + c 22 + 2c 44)/2) and the bulk modulus B S O are larger in the antiferromagnetic than in the paramagnetic state; the reverse is true for the shear stiffness c 44 and c′(= (c 11 - c 12)/2). The hydrostatic pressure derivatives (∂c IJ/∂P) P= 0, of the elastic stiffness tensor components have been measured in both the antiferromagnetic and paramagnetic states of Mn73Ni27. In the antiferromagnetic state (∂c 11/∂P) P=0, and (∂c′/∂P) P=0, increase with temperature, while (∂c 44/∂P) P=0 decreases; in the paramagnetic state (∂c 11/∂P) P = 0 and in consequence (∂B S O/∂P) P=0 are much smaller. Large d...

Ultrasonic study of the temperature and pressure dependences of the elastic properties of a Mn78Pt22-alloy single crystal.

The elastic and nonlinear acoustic properties of monocrystalline ${\mathrm{Mn}}_{78}$${\mathrm{Pt}}_{22}$ alloy have been studied by the ultrasonic pulse-echo-overlap technique. To obtain the three independent elastic-stiffness tensor components ${\mathit{C}}_{\mathit{I}\mathit{J}}$ and the adiabatic bulk modulus ${\mathit{B}}^{\mathit{S}}$ as a function of temperature in the antiferromagnetic D phase, velocity measurements of the three ultrasonic modes, which can be propagated along the [110] direction, have been made between 10 K and room temperature; for the longitudinal mode measurements have been made up to 550 K. At 293 K the elastic stiffnesses are ${\mathit{C}}_{11}$=94.2 GPa, ${\mathit{C}}_{12}$=35.8 GPa, and ${\mathit{C}}_{44}$=84.7 GPa; hence ${\mathit{C}}_{11}$ and in turn ${\mathit{B}}^{\mathit{S}}$=55.2 GPa are comparatively small: the elastic moduli conform with trends with the e/a ratio previously recognized for 3d transition-metal antiferromagnetic Invar alloys. In the temperature range 10--225 K the C' mode exhibits shear-lattice softening that parallels mode softening found in the longitudinal second-order elastic-stiffness tensor component ${\mathit{C}}_{11}$. There is a sharp dip at the N\'eel temperature (515 K) in the velocity of the longitudinal ultrasonic wave propagated along the [110] direction.Measurements of the hydrostatic-pressure dependences of the velocities of ultrasonic modes with a [110] propagation vector have been used to obtain the hydrostatic pressure derivatives (\ensuremath{\partial}${\mathit{C}}_{\mathit{I}\mathit{J}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ of the elastic-stiffness tensor components. At 293 K (\ensuremath{\partial}${\mathit{C}}_{11}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$, (\ensuremath{\partial}${\mathit{C}}_{12}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$, (\ensuremath{\partial}${\mathit{C}}_{44}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$, and (\ensuremath{\partial}${\mathit{B}}^{\mathit{S}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ are 6.2\ifmmode\pm\else\textpm\fi{}0.1, 4.2\ifmmode\pm\else\textpm\fi{}0.3, 4.3\ifmmode\pm\else\textpm\fi{}0.2, and 4.8\ifmmode\pm\else\textpm\fi{}0.2, respectively. To establish the vibrational anharmonicity of the long-wavelength acoustic modes, the results obtained for ${\mathit{C}}_{\mathit{I}\mathit{J}}$ and (\ensuremath{\partial}${\mathit{C}}_{\mathit{I}\mathit{J}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ have been used to calculate the corresponding Gr\"uneisen parameters. In general the elastic and nonlinear acoustic properties show a number of features that resemble those of Invar materials.

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.

Non-linear acoustic properties of samarium phosphate glasses

Measurements, using a pulse superposition technique, of the effect of uniaxial stress on ultrasonic wave velocities have been used to determine the temperature dependences of the third order elastic constants (TOEC) of 20 and 25 mol% Sm 2O 3 phosphate glasses between 77 and 293 K. The signs of the TOEC are consistent with the negative values found previously at higher temperatures for the hydrostatic pressure derivatives, ( ϖC 11/ ϖP) T, P=0 and ( ϖC 44/ ϖP) T, P=0 , of the elastic stiffness tensor components and for ( ϖB/ ϖP) T, P=0 of the bulk modulus, B 0. The TOEC data yield negative ultrasonic mode Grüneisen parameters confirming that application of pressure induces a decrease in the long wavelength acoustic phonon mode frequencies. As the temperature is reduced, the pressure-induced mode softening becomes enhanced. The hydrostatic pressure derivative, ( ϖC 11/ ϖP) T, P=0 , is larger than ( ϖC 44/ ϖP) T, P=0 ) over the entire temperature range, and the longitudinal acoustic mode Grüneisen parameter, | γ L|, is larger than that, | γ S|, of the shear wave: the longitudinal mode softens more with pressure than the shear mode. The vibrational anharmonicity of the acoustic modes plays an important part in causing the thermal expansion of 20 mol% Sm 2O 3 phosphate glass to be negative below 120 K. The relative merits of using Murnaghan's, Birch's and polynomial equations of state to determine the compression, V( P)/ V 0, as a function of pressure are assessed for vitreous materials which have a negative value ofthe hydrostatic pressure derivative, ( ϖB/ ϖP) T, P=0 , of the bulk modulus.

Acoustic mode vibrational anharmonicity of hexahelometallate crystals

The vibrational anharmonicity and Grüneisen parameters of hexahelometallate A 2MX 6 single crystals have been determined theoretically by making use of phonon lattice theory. The potential model employed to calculate these properties consists of long range coulomb, three body interactions, short range overlap repulsion effective upto the nearest neighbour ions and phonon-lattice interactions. These antifluorite structure compounds contain large MX 2− 6- ions and as the interionic spacings are much greater than those of the alkaline-earth fluorite structure halides, their elastic constants are correspondingly smaller. The hydrostatic pressure derivatives of the second order elastic constants (SOEC) calculated for K 2SnCl 6, K 2ReCl 6, (NH 4) 2SnCl 6, (NH 4) 2TeCl 6, (NH 4) 2SnBr 6, and (NH 4) 2TeBr 6, are found to be positive and close to the experimental values. The vibrational anharmonicities of the long-wavelength modes are explained in terms of the acoustic mode Grüneisen parameters.

Elastic and nonlinear acoustic properties of the terbium iron garnet Tb3Fe5O12 in relation to those of other garnets.

The elastic behavior as a function of temperature, pressure, and magnetic field of the ferrimagnetic rare-earth garnet ${\mathrm{Tb}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$, in which all the cation sites are occupied by magnetic ions, has been examined experimentally using the ultrasonic pulse overlap technique. The effects on the ultrasonic wave velocities of a magnetic field applied in a fourfold direction have been measured; that for the [001] polarized shear wave propagated in the [110] direction (and thus for the shear modulus ${\mathit{C}}_{44}$) is found to be much larger than for the other ultrasonic modes. Elastic constant determinations made on both sides of the N\'eel temperature ${\mathit{T}}_{\mathit{N}}$ (550\ifmmode\pm\else\textpm\fi{}10) K indicate that the magnetic contributions to the elastic stiffnesses are small, being only \ensuremath{\Delta}${\mathit{C}}_{11}$/${\mathit{C}}_{11}$\ensuremath{\sim}1.0%, \ensuremath{\Delta}${\mathit{C}}_{44}$/${\mathit{C}}_{44}$\ensuremath{\sim}1.3%, \ensuremath{\Delta}${\mathit{C}}_{\mathit{L}}$/${\mathit{C}}_{\mathit{L}}$ [where ${\mathit{C}}_{\mathit{L}}$=(${\mathit{C}}_{11}$+${\mathit{C}}_{12}$+2${\mathit{C}}_{44}$)/2] \ensuremath{\sim}1.0%.The hydrostatic pressure derivatives of the components of the elastic stiffness tensor constants have been measured at room temperature as (\ensuremath{\partial}${\mathit{C}}_{11}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$=7.96, (\ensuremath{\partial}${\mathit{C}}_{44}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$=1.1, (\ensuremath{\partial}C'/\ensuremath{\partial}P${)}_{\mathit{P}=0}$=1.55 [where C'=(${\mathit{C}}_{11}$-${\mathit{C}}_{12}$)/2] and that of the bulk modulus (\ensuremath{\partial}${\mathit{B}}^{\mathit{S}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$=5.8. These hydrostatic pressure derivative results have been used to determine the vibrational anharmonicity of the long-wavelength acoustic phonons in terms of the acoustic mode Gr\uneisen parameters. The mean acoustic mode Gr\uneisen parameter ${\ensuremath{\gamma}}^{\mathrm{el}}$ (=1.36) for ${\mathrm{Tb}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$ is substantially greater, probably due to a magnetic contribution, than those of the other previously investigated garnets ${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ (${\ensuremath{\gamma}}^{\mathrm{el}}$=0.727) and ${\mathrm{Y}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$ (${\ensuremath{\gamma}}^{\mathrm{el}}$=0.885). To provide a basis for comparison of the elastic behavior of terbium iron garnet with those of other garnets, the elastic stiffness tensor components, their hydrostatic pressure derivatives and associated lattice dynamical properties, including the thermodynamic ${\ensuremath{\gamma}}^{\mathrm{th}}$ and mean long-wavelength acoustic ${\ensuremath{\gamma}}^{\mathrm{el}}$ Gr\uneisen parameters and their hydrostatic pressure derivatives, have been calculated for a substantial number of garnet crystals on the basis of the atomistic Born model of solids in which a potential model represents the interionic interactions in the crystal.

Temperature dependence of the acoustic-mode vibrational anharmonicity of quartz from 243 to 393 K.

Measurements made of the effects of hydrostatic pressure on ultrasonic wave velocities have been used to obtain the hydrostatic-pressure derivatives of the six independent second-order elastic constants (SOEC's) and the bulk modulus of very-high-purity quartz crystals in the temperature range 243-393 K. The results, which quantify the nonlinear properties of quartz, show that (∂C IJ /∂P) T,P=0 depend markedly upon temperature (contrary to their previous usage in technological applications as temperature-independent quantities)

Ultrasonic determination of the elastic moduli and their temperature and pressure dependences in YBa2Cu3O7-x/Ag (15 vol.%) composite

The effects of temperature and hydrostatic pressure have been measured on the velocities of longitudinal and shear ultrasonic waves propagated in ceramic specimens of a composite comprising YBa2Cu3O7-x together with 15 vol.% metallic silver. At room temperature and atmospheric pressure the bulk modulus B0 of the composite is 1.8 times larger than that of the pure YBa2Cu3O7-x ceramic of similar porosity. The ultrasonic wave velocities increase smoothly with decreasing temperature from 300 to 10 K and do not show the anomalous step-like changes including the hysteresis effects in the temperature range 190-235 K, which characterize the elastic behaviour of pure YBa2Cu3O7-x ceramic. The ultrasonic attenuation shows peaks resembling those observed in YBa2Cu3O7-x itself, which result from low-activation-energy anelastic relaxation processes. The effects of hydrostatic pressure on the velocities of ultrasonic waves propagated in the composite and hence the hydrostatic pressure derivatives ( delta CL/ delta P)P=0 and ( delta mu / delta P)P=0 of the elastic stiffnesses and ( delta B/ delta P)P=0 of the bulk modulus are substantially smaller than those found previously for pure YBa2Cu3O7-x ceramics.

Acoustic-mode vibrational anharmonicity related to the anomalous thermal expansion of Invar iron alloys.

Measurements of the temperature dependences of the hydrostatic-pressure derivatives of the velocities of ultrasonic waves propagated in single crystals of the Invars ${\mathrm{Fe}}_{72}$${\mathrm{Pt}}_{28}$ and ${\mathrm{Fe}}_{72}$${\mathrm{Pt}}_{25}$${\mathrm{Ni}}_{3}$ verify that the negative thermal expansion in the ferromagnetic phase of these alloys is directly associated with longitudinal-acoustic-mode softening. In the paramagnetic phase of ${\mathrm{Fe}}_{72}$${\mathrm{Pt}}_{28}$, the hydrostatic-pressure derivatives of each of the elastic-tensor components and the bulk modulus B are positive, showing normal behavior in the sense that the long-wavelength acoustic-phonon frequencies increase under pressure. However, below the Curie temperature ${\mathit{T}}_{\mathit{C}}$ the velocities of longitudinal untrasonic waves propagated along the [100] and [110] directions in ${\mathrm{Fe}}_{72}$${\mathrm{Pt}}_{28}$ and ${\mathrm{Fe}}_{72}$${\mathrm{Pt}}_{25}$${\mathrm{Ni}}_{3}$ decrease strongly with pressure; thus (\ensuremath{\partial}${\mathit{C}}_{11}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$, (\ensuremath{\partial}${\mathit{C}}_{\mathit{L}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$, and (\ensuremath{\partial}${\mathit{B}}^{\mathit{S}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ are negative due to the magnetoelastic interaction. These Invar alloys show the extraordinary property of becoming easier to compress as the pressure is increased. The negative signs of (\ensuremath{\partial}${\mathit{C}}_{11}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ and (\ensuremath{\partial}${\mathit{C}}_{\mathit{L}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ give rise to negative values for all the longitudinal- and quasilongitudinal-acoustic-mode Gr\"uneisen parameters in the ferromagnetic phase.This experimental observation is in accord with a recent prediction of negative longitudinal-acoustic-mode Gr\"uneisen parameters stemming from itinerant-electron-magnetism theory. For ${\mathrm{Fe}}_{72}$${\mathrm{Pt}}_{28}$ the hydrostatic-pressure derivative (\ensuremath{\partial}${\mathit{C}}_{11}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ is negative, attains its maximum value just above room temperature, and becomes much smaller as the temperature is lowered, matching, and accounting for, the behavior of the thermal expansion, which is negative in the temperature range between about 260 K and the Curie temperature. In the case of the archetypal Invar alloy ${\mathrm{Fe}}_{65}$${\mathrm{Ni}}_{35}$, the hydrostatic-pressure derivatives of the elastic-stiffness-tensor components are positive, but (\ensuremath{\partial}${\mathit{C}}_{11}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ and (\ensuremath{\partial}${\mathit{C}}_{\mathit{L}}$/\ensuremath{\partial}P${)}_{\mathit{P}=0}$ are small in the ferromagnetic phase, consistent with its small but positive thermal expansion. It is concluded that longitudinal-acoustic-mode softening due to the magnetoelastic interaction is the source of the Invar behavior of each of these iron alloys. In addition, measurements of the temperature dependences of the ultrasonic wave velocities establish that the fcc-bct martensitic phase transition in Fe-Ni and Fe-Pt alloys is driven by a soft shear zone-center acoustic phonon with propagation vector 〈110〉 and polarization vector 〈11\ifmmode\bar\else\textasciimacron\fi{}0〉.

Temperature dependences of the third-order elastic constants and acoustic mode vibrational anharmonicity of vitreous silica

Measurements of the effect of uniaxial stress on ultrasonic wave velocities have been used to determine the temperature dependences of the third-order elastic stiffness tensor components (TOEC) of vitreous silica between 77 and 293 K. In the absence of such data previous practice has been to assume that these TOEC are independent of temperature; however a significant temperature dependence has been observed. With the exception of the smallest C 456 , each of the TOEC is anomalously positive: a feature consistent with the well established aberrant negative values for the hydrostatic pressure derivatives (∂ C ij /α P ) P =0 of the second-order elastic stiffness tensor components (which reveal softening of the long-wave-length acoustic modes under pressure). The TOEC increase as the temperature is reduced showing that the pressure-induced acoustic mode softening becomes enhanced at lower temperatures. The largest TOEC is C 111 which is 46.7 × 10 10 Pa at 293 K and increases to 99.1 × 10 10 Pa at 77 K. The hydrostatic pressure derivatives of the second-order stiffnesses have been calculated from the TOEC; (∂ C 11 /∂ P ) p =0 is much larger than (∂ C 44 /∂ P ) P =0 over the whole temperature range: the longitudinal acoustic mode softens more with pressure than the shear mode. This effect is emphasised by the finding that the acoustic mode Gruneisen parameters are negative with |γ L | > |γ S |. As the temperature is reduced the longitudinal acoustic mode Gruneisen parameter, γ L , increases in magnitude considerably, reaching a value of −5.5 at 77 K. The mean acoustic mode Gruneisen parameter, γ el , increases to a larger negative value (−3.1 at 77 K) than previously suspected on the basis of the assumption of temperature-independent third-order elastic constants: the discrepancy between the low-temperature limits of the thermal, γ th L , and mean acoustic mode, γ el L , Gruneisen parameters is not quite so large as had been thought. The vibrational anharmonicity of the acoustic modes plays an important part in causing the thermal expansion of vitreous silica to be negative at low temperatures.

Direct type II–indirect type I conversion of InP/GaAs/InP strained quantum wells induced by hydrostatic pressure

Photoluminescence from thin strained layers of GaAs grown on InP has been studied under hydrostatic pressure. The structures are type II at atmospheric pressure. At higher pressures the structures change to type I with the lowest conduction band edge in the strained GaAs layer being the X minimum. This transformation is characterized by a drastic change in the pressure derivative of the emission energy and a rapid disappearance of the photoluminescence intensity at slightly higher pressures. A hydrostatic pressure derivative of less than one meV/kbar is measured for the valence band offset.

Ultrasonic evidence of low bulk modulus and large vibrational anharmonicity in the bismuth cuprate high Tc superconductors

The velocities of longitudinal and shear ultrasonic waves propagated in ceramic specimens of single phase Bi(Pb)2223, Bi(Pb)2212 and lead-free Bi2212 have been measured as a function of hydrostatic pressure. The elastic stiffnesses of these bismuth cuprates are unusually small and their hydrostatic pressure derivatives ( delta CL/ delta P)P=0 and ( delta B/ delta P)P=0 at room temperature are large. The ceramic microstructure comprises loosely stacked, thin platelets; the substantial effects of porosity on the elastic properties have been approximated using wave scattering theory in a porous medium. The bismuth cuprates investigated show the common characteristic of high Tc mixed oxides based on copper that the bulk modulus B0 measured ultrasonically is much smaller than the BT(P) determined at very high pressures from X-ray measurements of lattice parameters in a diamond cell. This can be resolved by taking the contribution to the high pressure bulk modulus BT(P) of the pressure derivative ( delta B/ delta P)P=0 into account. In these materials the anharmonicity of the longitudinal acoustic modes in the long wavelength limit is large, probably as a result of the combination of (i) weak interlayer binding forces due to the lone pairs sited between the pairs of widely spaced BiO layers and (ii) intermediate valence effects.

The elastic behaviour under hydrostatic pressure of poly(methyl methacrylate) and its fully deuterated form

Measurements have been made of the effects of hydrostatic pressure on the velocities of longitudinal and shear ultrasonic waves propagated in a commercial poly(methyl methacrylate) (PMMA) and a fully deuterated PMMA. The experimental results provide a comparison of the bulk and shear moduli and their hydrostatic pressure derivatives for the two polymers. The vibrational anharmonicity of the long wavelength acoustic modes is more pronounced in the deuterated than in the commercial PMMA. ∂B/∂P is 32% larger in the deuterated form than in the undeuterated polymer, a finding which may be understood by including the isotopic mass difference in a simple vibrational model.

Vibrational anharmonicity of vitreous samarium phosphate

When subjected to hydrostatic pressure, samarium phosphate glasses become easier to squeeze, an extraordinary effect attributable to fluctuating valence of the samarium ions. To examine how the vibrational anharmonicity varies with temperature in these glasses, the hydrostatic pressure derivatives of the ultrasonic wave velocities have been measured for a 20 mol% Sm 2O 3-P 2O 5 glass between 250 and 450 K and the thermal expansion from 85 to 275 K. Below room temperature, the pressure derivatives ( ∂C 11 S / ∂P) T, P=0 and ( ∂B S / ∂P) T, P=0 of the longitudinal elastic stiffness tensor component C 11 S and the bulk modulus B S become much more negative: longitudinal acoustic mode softening becomes more pronounced with decreasing temperature. This can be attributed to enhancement of the proportion of the 3+ valence state of intermediate valence (2+ to 3+) samarium ions with increasing pressure and/or decreasing temperature. The thermal expansion is small and below 110 K becomes negative; at low temperatures the contributions from the long wavelength acoustic modes, which the measured negative hydrostatic pressure derivatives of the elastic constants show have negative Grüneisen parameters, dominate due to the increased relative proportion of phonons in these low energy, small wavevector states.

Elastic and anelastic properties of rare earth phosphate glasses

The behaviour of the ultrasonic attenuation between 10 K and 400 K in Sm 2O 3P 2O 5 glasses is characterized by the presence of very broad peaks, due to thermally activated relaxations of structural defects, typical of amorphous materials. A study of these anomalies reveals that the addition of Sm 2O 3 to P 2O 5 has little influence on the mean activation energy of the relaxation process, but does cause a decrease in the number of relaxing particles. The effect of temperature on the anomalous negative hydrostatic pressure derivatives of the elastic moduli of samarium phosphate glass is also examined experimentally. Reduction of the temperature below 300 K causes ϖC 11/ ϖP and ϖB/ϖP to increase steeply to more negative values: both longitudinal and shear Gruneisen parameters, which are negative, become much larger. It is suggested that application of pressure drives the samarium ion f → d transition and that the ion size collapse couples to the acoustic modes, strongly enhancing acoustic mode softening.

The elastic behaviour of natural single crystals of the high-spin compound MnS2

The hydrostatic pressure and temperature dependences of velocities of ultrasonic modes propagated in natural single crystals of MnS2 have been measured. The elastic stiffness tensor components and the bulk modulus of this high-spin pyrite structure compound are much smaller than those of the low-spin isostructural crystal FeS2. This is consistent with MnS2 having substantially weaker attractive binding forces than those in FeS2 as would be expected from its larger lattice parameter due in turn to the high-spin configuration of the manganese 3d electrons. The temperature dependences of the elastic stiffnesses measured between 4.2 K and 293 K show that the crystal softens elastically near the Neel temperature but other than this the elastic properties are very similar in the antiferromagnetic and paramagnetic phases. The hydrostatic pressure derivatives of the elastic stiffness tensor components are all positive at room temperature: there is no acoustic mode softening under pressure. The results are used to describe the anharmonicity of the long wavelength acoustic modes in terms of mode Gruneisen parameters in the elastic continuum approximation. The mean long wavelength acoustic mode Gruneisen parameter gamma el (=2.4) is much larger than the thermal Gruneisen parameter gamma th (=0.98) which implies that the mode Gruneisen gammas for optic modes must on average be much smaller than those for the long wavelength acoustic phonons.