On Fourth-Order Elastic Constants of Degenerately Doped Silicon Resonators

2018 ◽  
Author(s):  
Ville Kaajakari ◽  
Takehiko Kishi ◽  
Toshio Nishimura
Keyword(s):  
Elastic Constants ◽  
Fourth Order ◽  
Doped Silicon ◽  
Silicon Resonators

Elastic anomalies of Hg2X2 compounds

1992 ◽  
Vol 70 (9) ◽  
pp. 745-751
Author(s):  
K. S. Viswanathan ◽  
J. C. Jeeja Ramani
Keyword(s):  
Elastic Constants ◽  
Fourth Order ◽  
Order Parameter ◽  
Zero Point ◽  
Stability Conditions ◽  
Point Energy ◽  
The Third ◽  
Limit Formula ◽  
The Stability ◽  
Elastic Anomalies

The anomalies of the second-, third-, and fourth-order elastic constants are considered for the phase transition of Hg2X2 type of compounds. Expressions are obtained for the equilibrium values of the order parameters in the ferroelastic phase from the stability conditions. The fluctuation in the order parameter is evaluated from the Landau–Khalatnikov equation. An expression is derived for the shift in the zero-point energy in the low-temperature ferroelastic phase and the specific heat anomaly. It is shown that these are proportional to (T − T)2 and (T − Tc), respectively. All the anomalies of the second-order elastic (SOE) constants are obtained from a single general formula, and relations among them are established. The temperature variation of the SOE constants in the limit [Formula: see text] is discussed. Similarly, expressions are derived for the anomalies of the third- and fourth-order elastic constants. In the limit [Formula: see text] it is shown that these constants diverge as [Formula: see text] and [Formula: see text], respectively.

Temperature Dependence of the Elastic Constants of Doped Silicon

2015 ◽  
Vol 24 (3) ◽  
pp. 730-741 ◽  
Author(s):  
Eldwin J. Ng ◽  
Vu A. Hong ◽  
Yushi Yang ◽  
Chae Hyuck Ahn ◽  
Camille L. M. Everhart ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
Elastic Constants ◽  
Doped Silicon

Fourth-order elastic constants and second pressure derivatives of white tin

1991 ◽  
Vol 69 (7) ◽  
pp. 801-807
Author(s):  
R. Ramji Rao ◽  
A. Padmaja
Keyword(s):  
Phase Transformation ◽  
Hydrostatic Pressure ◽  
Elasticity Theory ◽  
Elastic Constants ◽  
Fourth Order ◽  
Finite Strain ◽  
Second Order ◽  
Tetragonal Crystal ◽  
Derivatives Of

The expressions for the 25 fourth-order elastic constants of a body-centered tetragonal crystal are derived with interactions extending to fifth neighbours. The expressions for its effective second-order elastic constants are obtained in terms of its natural second-, third-, and fourth-order elastic constants using the finite strain elasticity theory. The fourth-order elastic constants and the second pressure derivatives of white tin are evaluated using these formulae. All the second pressure derivatives of white tin except that of C11 are positive. The second pressure derivatives C12, C13, and C33 are large suggesting that phase transformation will occur in white tin when subjected to hydrostatic pressure.

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