R. G. Leisure

Elastic constants of monocrystal iron from 3to500K

Resonant ultrasound spectroscopy was used to measure the monocrystal elastic constants of iron over a temperature range of 3–500K. All the moduli behave normally as a function of temperature and are well described by the semiempirical Einstein-oscillator model. Values at 300K are bulk modulus=166.2±0.9GPa; shear constant C′=(C11−C12)∕2=48.15±0.9GPa; shear constant C44=115.87±0.17GPa. The Poisson ratio (ν100) is 0.3679±0.0005. Representation surfaces of Young’s and torsion moduli are presented. The Debye temperature (θD) is 476.3K as calculated from 3K measured elastic constants. A thermodynamic Gruneisen parameter γth=1.65 is calculated. The temperature dependence of the internal friction associated with C′ is very different from that associated with C44. Possible reasons for this difference are suggested.

Elastic moduli of polycrystalline LaAlxNi5-x

A hot isostatic pressing technique was used to prepare bulk polycrystalline samples of the hydrogen-absorbing materials LaAlxNi5−x. Ultrasonic methods were used to measure the elastic moduli of these alloys. Small corrections were made for porosity so that values expected for the theoretical density were found. The various moduli decrease somewhat with increasing x; the porosity-corrected bulk and shear moduli are 137.4 GPa and 59.2 GPa, respectively, at x=0 and decrease to 126.6 GPa and 54.1 GPa, respectively, at x=1. Poisson’s ratio is independent of x within experimental error at 0.31, a value typical for metals. Debye temperatures calculated from the porosity-corrected elastic constants ranged from 360 to 365 K, and were in good agreement with those reported from heat capacity measurements. The present measurements on LaAlxNi5−x were combined with earlier heat capacity measurements of the hydrides, LaAlxNi5−xHy, to estimate the elastic moduli of the latter materials. The estimated hydride moduli were ...

Diamond’s elastic stiffnesses from 322 K to 10 K

Using resonant-ultrasound spectroscopy, we measured diamond’s monocrystal elastic-stiffness coefficients C11, C12, and C44, between 322 and 10 K. Changes are small and smooth: The bulk modulus B=(C11+2C12)/3 increases about 1 part in 1000, describable by a quasiharmonic Einstein-oscillator model. Zero-temperature Cij correspond to a 2244-K Debye characteristic temperature. Using a low-temperature form of the Gruneisen–Debye model, we calculated an overall thermodynamic Gruneisen parameter of γ=1.26; using a high-temperature form we calculated 0.71; the lattice specific heat yields γ=1.10.

Elastic properties of tantalum over the temperature range 4–300 K

The elastic properties of tantalum have been investigated over the temperature range 4.2–300 K. The values of the adiabatic elastic constants C11, C44, and CL=(1/2) (C11+C12+2C44) at 4.2 K in units of 1012 dyn/cm2 are, respectively, 2.70, 0.873, and 3.02. The Debye temperature was calculated from the elastic constants and found to have the value of 265 K at low temperature. The elastic constants become temperature independent at low temperatures and approach linear behavior at high temperatures. In contrast to the normal behavior of the elastic constants, nuclear acoustic resonance experiments show anomalous line broadening.

Elastic constants of isotropic cylinders using resonant ultrasound

A method of ultrasonic resonance is used to determine the elastic constants of isotropic cylinders. As applied in this study, this method implies simultaneous application of approximate techniques to solve for the equations of motion of the cylinder and an experimental measurement of the natural frequencies of free vibration. Optimal estimates for the elastic constants are obtained by minimizing the differences between these values. Two separate examples are considered in this study, with promising results.

Elastic moduli of polycrystalline ZrCo as a function of temperature

Abstract The polycrystalline elastic moduli of the intermetallic compound ZrCo have been measured over the temperature range of 3–410 K. The temperature dependence of the moduli resembles that of ordinary metals; the moduli approach zero temperature with zero slope, but decrease monotonically with increasing temperature at higher temperatures. The 296 K values of the bulk, shear, and Young’s moduli are, respectively, 140, 49.2, and 132 GPa. Poisson’s ratio is almost temperature-independent increasing from 0.338 at low temperatures to 0.343 at 410 K. The acoustic contribution to the low temperature specific heat, calculated from the elastic moduli measured at 3 K, is 9.32×10 −5 J/(mol K 4 ). The corresponding Debye temperature is 347 K.

The Eδ′ and triplet‐state centers in x‐irradiated high‐purity amorphous SiO2

High‐purity silicas synthesized by the chemical‐vapor‐deposited soot remelting method were studied by electron‐spin‐resonance techniques after being irradiated by x rays at 77 K or higher temperatures. The spectra of the Eδ′ center including its 29Si hyperfine splitting, and the triplet‐state center, were measured using two different detection modes. The effects of x‐ray dose, thermal annealing, hydrogen treatment, and impurities were examined; the Eδ′ and the triplet‐state centers have a similar dependence on all these parameters, indicating that they share a common precursor. These centers are found only in low OH, oxygen‐deficient samples. There appears to be no correlation with chlorine impurities. The measured intensity of the Eδ′ center’s 29Si hyperfine signal indicates that approximately four Si atoms are involved. A model for this center and the triplet‐state center is proposed.

Low-temperature elastic and piezoelectric constants of paratellurite (α-TeO2)

We report paratellurite’s 300-10-K elastic constants Cij, six constants reflecting tetragonal symmetry (P422 point group). The quantity e142∕k11, where e14 denotes the sole independent piezoelectric constant and k11 denotes a dielectric constant, was determined over the same temperature range. All the principal Cij show approximately regular temperature-change behavior: increasing with decreasing temperature, the increases being 2%–10%. One derived elastic constant, C′=(C11−C12)∕2, a shear constant, shows strongly anomalous temperature behavior, decreasing continuously during cooling to 10K, the total decrease being 5%. The quantity e142∕k11 was essentially independent of temperature. Obtained by resonant-ultrasound spectroscopy, our results differ from previous studies, none of which went to 10K, a temperature region of much practical interest for this material. From the near-zero-temperature elastic constants, we derive a Debye temperature of 235K. The slope dC′∕dT yields a negative Gruneisen parameter ...

Elastic moduli of a Ti-Zr-Ni i-phase quasicrystal as a function of temperature

The elastic constants of an icosahedral-phase (i-phase) quasicrystal of Ti39.5Zr39.5Ni21 were measured over the temperature range 3–292 K using the technique of resonant ultrasound spectroscopy. Common elastic quantities were derived over this temperature range. Values at 290 K are: bulk modulus = 116.8 GPa; shear modulus = 37.0 GPa; Youngs modulus = 100.5 GPa; Poissons ratio = 0.356. The internal friction was also studied. A Debye temperature of 316.7 K was computed from the low-temperature elastic moduli. The present values for the elastic moduli and Poissons ratio compare well with ultrasonically-derived values reported earlier for an i-phase Ti41.5Zr41.5Ni17 quasicrystal, but do not agree with recently reported results for i-phase forms of Ti40Zr40Ni20 and Ti52.8Zr26.2Ni21 obtained by pressure-volume measurements and conventional mechanical testing.

Elastic properties of intermetallic AB2 and AB5 hydrogen-absorbing compounds

Abstract The elastic properties of AB 2 and AB 5 hydrogen-absorbing intermetallic compounds are reviewed. The relevance of these properties to hydrogen absorption is discussed briefly. In many cases the temperature dependence of the elastic constants of the AB 2 compounds is anomalous in that the moduli do not decrease monotonically with increasing temperature. This unusual behavior appears to be associated with electronic structure effects in a number of cases. The absorption of hydrogen by polycrystalline TaV 2 has a profound effect on the aggregate shear modulus, changing both the magnitude and temperature dependence significantly. This effect of hydrogen on the mechanical properties appears to occur via effects on the electronic structure. Few measurements of elastic properties have been reported for hydrogen-absorbing AB 5 intermetallic compounds. The LaAl x Ni 5− x system has been investigated by means of measurements on polycrystals prepared by hot isostatic pressing. The moduli decrease about 8% as x increases from 0 to 1.