Elastic constants, ultrasonic technique

The discrepancy between the first determination of the elastic constants and the following ones is not surprising, due to the very indirect way utilised in [33]. The difference between the Brillouin spectroscopy results on the one hand and those obtained with resonance ultrasonic spectroscopy on the other one is mostly due to the difference in C33. Although the authors claim that the most precise measurements of elastic moduli are obtained using ultrasonic techniques, the samples should have a... 

Thompson et al. described a series of ultrasonic techniques used for in-.situ measurements of elastic constants on thick-walled submersible vessels [149]. The elastic constants can provide information about fabrication errors such as wavy fibers and fiber disbonds. Elastic constant measurements can be performed using Rayleigh or Lamb wave modes, or by using angle beam techniques, It was shown that the effect of the ani.sotropy increases... 

Recently, Kinney etal. [2004] used the technique of resonant ultrasound spectroscopy (RUS) tomeasure the elastic constants (Qj) of human dentin from both wet and dry samples. As (%) and Ac (%) calculated from these data are included in both Table 47.5 and Figure 47.4. Their data showed that the samples exhibited transverse isotropic symmetry. However, the Qj for dry dentin implied even higher symmetry. Indeed, the result of using the average value for Q i and Cu = 36.6 GPa and the value for C44 = 14.7 GPa for dry dentin in the calculations suggests that dry human dentin is very nearly elastically isotropic. This isotropic-lifce behavior of the dry dentin may have clinical significance. There is independent experimental evidence to support this calculation of isotropy based on the ultrasonic data. Small angle x-ray diffraction... 

As a result of the above difficulties, alternative techniques were sought and have become established. One approach (sound velocity) involves passing ultrasonic waves through the material and determining their velocities. The other approach (dynamic resonance) uses the natural vibration of the material. The elastic constants are determined from specimen geometry and the resonant frequency. For these last two techniques, experimental accuracies of <0.1% are not uncommon. Both of these latter techniques can also be used on anisotropic materials but the current discussion will emphasize isotropic materials. 

A variety of experimental techniques are available for the investigation of the electron-lattice interaction. For static phenomena such as thermal expansion and magnetostriction one can use dilatometric and X-ray techniques. For dynamic effects such as elastic constant measurements, ultrasonic propagation and phonon dispersion the methods of sound velocity and attenuation measurements, and inelastic neutron or light scattering are available. In addition high-pressure work can give valuable information for some quantities. 

The calculated binding energies in oxides (rows from 11 to 13 of Table 9.1) also agree weU with experimental data. The first-principle simulation correctly predicts the greatest cohesive energy for CaO and similar values for MgO and SrO. Precise measurements of the bulk moduli for oxides is difficult. The reported values are in agreement with elastic constants measured by ultrasonic techniques. 

ULTRASONIC TECHNIQUES FOR DETERMINING ELASTIC CONSTANTS AND ACOUSTIC ABSORPTION... 

It is seen that ultrasonic techniques have two major advantages high accuracy and the ability to determine the complete set of elastic constants for a sample of small size. As a result of these capabilities, all five independent stiffness constants have been obtained for extruded rods of PLC of high draw ratio (2 = 15) and small diameter (0.8 mm). Moreover, it has been possible to study the skin-core structure in injection molded PLC by monitoring the variation in stiffness with position. For blends of a PLC and a thermoplastic or glass fiber-reinforced PLC, successful correlation has been obtained between the modulus data and the orientation of the PLC fibrils or glass fibers. 

No single crystal elastic constant data for cerium were found by the writer This probably reflects the difficulty of obtaining suitable single phase crystals. The most complete and systematic investigation of the polycrystalline elastic properties of cerium was conducted by Rosen (1969a). He used an ultrasonic pulse technique employing a frequency of 10 MHz to measure sound velocities in spectrographically pure (99.9 + %) metal and corrected the acoustic path... 

The only investigation of the elastic constants of thulium known to the writer is that of Rosen (1971) on polycrystalline samples using an ultrasonic pulse technique (10 MHz). Acoustical path lengths were corrected for temperature variations. The temperature dependence of the elastic moduli, compressibility and theta (0) are shown in figs. 8.83 and 8.84. Theta (0) and the moduli, E and G,... 

The cohesion of the solid depends on the interatomic forces. It is usually described by means of phenomenological or semi-phenomenological theoretical models. In the framework of the valence-force-field model, the chemical bonds and their interactions are replaced by springs called force constants. The latter are related to the phenomenological coefficients used in elastic theory of solids, namely the elastic constants Cij. The Cij can be measured by means of Brillouin spectroscopy or ultrasonic techniques. The study of elastic properties is of great interest if some cell strain is involved in a physical phenomena (see Sec. 3 Applications). 

Yet another technique, measuring ultrasonic velocity anisotropies in the vicinity of the NA transition, however, also find anisotropies consistent with crossover behaviour. Sonntag et al [52] studied the divergence of three elastic constants, the bulk compression constant A, the layer compression constant B and the bulk-layer coupling constant C. B and C have critical exponents that are unequal and are in between that of the 3DXY values and anisotropic scaling values. 

Measurements of elastic constants by classical methods and ultrasonic pulse methods are described in [3.23,24], respectively. Elastic constants can also be measured by Brillouin scattering or from inelastic neutron scattering techniques [1.35]. 

Ultrasonic Microhardness. A new microhardness test using ultrasonic vibrations has been developed and offers some advantages over conventional microhardness tests that rely on physical measurement of the remaining indentation size (6). The ultrasonic method uses the DPH diamond indenter under a constant load of 7.8 N (800 gf) or less. The hardness number is derived from a comparison of the natural frequency of the diamond indenter when free or loaded. Knowledge of the modulus of elasticity of the material under test and a smooth surface finish is required. The technique is fast and direct-reading, making it useful for production testing of similarly shaped parts. 

The piezoelectric constant studies are perhaps the most unique of the shock studies in the elastic range. The various investigations on quartz and lithium niobate represent perhaps the most detailed investigation ever conducted on shock-compressed matter. The direct measurement of the piezoelectric polarization at large strain has resulted in perhaps the most precise determinations of the linear constants for quartz and lithium niobate by any technique. The direct nature of the shock measurements is in sharp contrast to the ultrasonic studies in which the piezoelectric constants are determined indirectly as changes in wavespeed for various electrical boundary conditions. 

Yuya et al. [243] extracted the elastic modulus of single electrospun PAN nanofibre dynamically through the natural frequencies of a pair of AFM microcantilevers linked by a nanofibre segment (Fig. 4.24b). The theory of this technique is based on the dynamic relationship between the fibre stiffness (i.e. spring constant) and the resonance frequencies of cantilever vibration mode. On the other hand, Liu et al. [244] used atomic force acoustic microscopy (AFAM) based on ultrasonic frequency oscillations to excite an AFM cantilever when the tip was in contact with a sample. A different approach based on a model of the resonant frequency that is dependent on the bob s free flight was employed to measure the elastic modulus of as-spun nylon 6, 6. A ball was glued to a nanofibre and suspended from a cantilever beam that was attached to a piezoelectric-actuated base [245]. 

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