Anharmonic Constant
Material properties that describe the first-order deviation from linear elastic behavior under mechanical stress characterize the non-linear stiffness of solid structures. These third order elastic moduli determine the dependence of acoustic wave velocities on the applied stress state in the material. They are used to predict the behavior of sensors and structural components subjected to high dynamic loads or pre-stress conditions.
Characterization Method
Evaluating these coefficients requires precise measurement of the change in ultrasonic wave velocity as a function of applied uniaxial or hydrostatic stress. In a typical characterization procedure, the third order elastic moduli are calculated from the slope of the velocity-pressure curve. This method demands high-resolution time-of-flight measurements to resolve the fractional velocity changes, which are typically in the range of parts per million.
Device Engineering
Sensor designers use these parameters to model frequency shifts in resonant devices and to optimize temperature compensation strategies. For instance, the stress-dependent behavior governed by the third order elastic moduli can be harnessed to design pressure sensors with high sensitivity. Conversely, in high-stability frequency standards, these effects must be minimized by selecting specific crystal cuts where the stress sensitivity is zero.
Reference Condition
The measurements are conducted at a controlled temperature because the elastic constants themselves vary with thermal changes. This precaution ensures that the extracted coefficients represent the pure mechanical response of the lattice without thermal interference.
