Ichiro Ohno

High temperature elasticity of sodium chloride

Abstract High temperature elasticity of single crystal sodium chloride has been studied by the Rectangular Parallelepiped Resonance (RPR) method up to 770 K (≅ 2.5 times the Debye temperature). The elastic stiffness constants, C 11 and C 44 , decrease linearly with temperature while C 12 is almost independent of temperature and shows a maximum around 500 K. The RPR method is particularly suited to measurements of elasticity at high temperature, since no glues are used to connect the transducers to a specimen, and as a consequence the measured spectrum closely approximates the theoretical spectrum of a specimen suspended freely with no external contact in space. The present elasticity data permits the investigation of the thermodynamic properties of sodium chloride far above the Debye temperature when used together with the previous zero pressure data on thermal expansivity and heat capacity. Anharmonicity affecting the equation of state of sodium chloride is discussed in detail. One result is that the parameters in Deckers equation of state for NaCI are verified. Another result is that the thermal pressure for NaCI linearly increases with temperature, and is independent of volume, for temperatures above the Debye temperature.

Rectangular parallellepiped resonance method for piezoelectric crystals and elastic constants of alpha-quartz

A theory is presented on the free osculations of a rectangular parallelepiped of piezoelectric crystal, by extending the theory of the rectangular parallelepiped resonance (RPR) method to determine elastic constants of crystals, as exemplified by an alpha-quartz specimen. The piezoelectric contribution to resonance frequencies was examined numerically on the specimen, and it was revealed that piezoelectricity causes approximately 5 kHz increase around 1 MHz. The resonance frequencies of the specimen were measured and inverted to elastic constants by least squares inversion. The inversion was by both the previous non-piezoelectric or elastic theory and by the present piezoelectric theory. The use of the non-piezoelectric theory resulted in an overestimate of 2σ or 0.6% in c11 and underestimate of σ or 6% in c12. These are the constants expected to be most affected by piezoelectricity. Errors are less than σ in the other constants. During measurement, it was found that the force applied to hold the specimen caused deviations from free oscillation and experimental errors of 5 kHz. The correction for this force is of some importance in RPR studies of piezoelectric crystals.

Harmonic and anharmonic properties of spinel MgAl2O4

Abstract The resonant sphere technique, RST, was applied to measure the elastic moduli of spinel. Resonant frequencies of 23 modes were measured between 293 and 1167 K. Results are similar to previous measurements by two of the authors (IS and OLA) using a rectangular prism specimen in that resonant frequencies of all modes decrease with temperature, and some modes show discontinuous change of slopes near 904 K. In the present work, inversion calculations of the frequency data to obtain elastic moduli was repeated until the standard error, s, was minimized so that s = 0.16 kHz (0.012%). Elastic moduli and their probable errors in GPa are: C11 = 281.310 ± 0.014, C12 = 155.437 ± 0.013, C44 = 154.587 ± 0.007, and Cs = 62.936 ± 0.003, where density p = 3.5846 g/cm3 at 293 K. The anisotropy factor is A = C44/Cs = 2.46 and is much larger than that of other cubic crystals. Isotropic properties are: bulk moduli, KS = 197.39 ± 0.01 GPa; isothermal bulk modulus, KT = 196.20 GPa; and rigidity modulus, μ = 107.81 GPa (the Hill average). Temperature dependence was clarified for elastic moduli in which one of shear moduli, Cs [= (C11 - C12)/2] shows a distinctive bend at Tc = 904 K. The bend in KS [ = (C11 + 2C12)/3] at Tc is less pronounced because of opposite changes of slopes for C11 and C12 at 904 K. Combining elasticity and thermal expansivity data, we evaluate anharmonic parameters, resulting in the Grüneisen parameter, γ = 1.17, and the Anderson-Grüneisen parameters, δS = 2.98 and δT = 4.72 at T = 300 K; whereas, these are parameters are 1.10, 4.46, and 6.37, respectively, at T = 1200 K. The Grüneisen parameter is about 0.1 lower on the high-temperature side of Tc compared to its value on the lowtemperature side

Pressure dependence of the elasticity of a steel sphere measured by the cavity resonance method

The pressure derivatives of elastic moduli of a steel sphere were measured by the cavity resonance method, a modified resonant sphere technique under gas pressure using a spherical three-layered structure (3LS) consisting of a sample-thin gas layer–cavity container system. The pressure-induced shifts of resonance peaks of both toroidal and spheroidal modes were observed up to 100 MPa (1 kbar) under gas pressure with helium gas. The resultant pressure derivatives of frequencies of toroidal modes yielded a pressure derivative of shear modulus of ∂G/∂P=2.01±0.08. The pressure derivative of the bulk modulus was determined from the data of spheroidal modes, ∂K/∂P=5.0±0.4, by analyzing these data as free oscillations of the 3LS superimposed on the static compression. The results demonstrate the efficiency of the cavity resonance method for measuring pressure derivatives of elastic moduli of solids.

Elasticity measurements on the material analogous to iron in the inner core of the Earth by FT‐ultrasonic spectroscopy

Iron constituting the inner core of the Earth is probably of e‐phase with hexagonal closest packing structure stable only above 10 GPa. The elastic properties of e‐iron can be studied by using analogue materials, solid solutions of iron with ruthenium, which take hcp at relevant condition. Single crystalline ruthenium sample was grown by means of floating zone method and its elastic parameters and internal frictions were determined with an FT (Fourier Transform) ultrasonic spectroscopy introduced successfully to RST (Resonant Sphere Technique). The potentiality of the new method is discussed in relation to the study of physical properties of iron in high pressure phase.

Pressure derivatives of elastic constants of iron by cavity resonance method

Pressure dependence of frequencies of normal modes was measured on a sphere sample of iron(steel) up to 0.1GPa under gas pressure, and pressure derivative of rigidity was obtained, ∂μ/∂P=1.76±0.20. Tentative but reasonable value of pressure derivative of bulk modulus was obtained, ∂K/∂P=5.4±0.5, by assuming the sample‐gas coupling is negligible.

Measurements for pressure and temperature dependencies of elastic moduli by the resonant sphere technique, RST.

The resonant sphere technique, RST, has been developed for measurements of elasticity and anelasticity of small crystal specimens. This method has advantages over other methods, especially in high‐temperature and high‐pressure measurements. New methods of data acquisition have made it convenient to measure resonance frequency at high temperatures (using a buffer rod), making a 1 K temperature interval measurement possible; this opens up many possibilities in the determination of physical properties of solids. Preliminary measurements of resonance frequency were performed by RST up to 100 MPa, which showed interference of vibration modes between the specimen and the pressure medium, even for helium gas as the pressure medium. This interference may become more serious at higher pressures or under liquid pressure. In order to evaluate such effects, the cavity resonance method was developed by Ohno in 1993, with a spherical shell structure with a spherical specimen at the center. This gives clear boundary con...