Combinations of Fourth‐Order Elastic Constants of Fused Quartz

1970 ◽  
Vol 41 (12) ◽  
pp. 4913-4917 ◽  
Author(s):  
B. E. Powell ◽  
M. J. Skove
Keyword(s):  
Elastic Constants ◽  
Fourth Order ◽  
Fused Quartz

scholarly journals Elastic constants of fused quartz. Change of young's modulus with temperature

1929 ◽  
Vol 122 (789) ◽  
pp. 274-282 ◽  
Keyword(s):  
Shear Modulus ◽  
Elastic Constants ◽  
Torsional Oscillation ◽  
Elastic Solids ◽  
Continuous Increase ◽  
Rate Of Increase ◽  
Fused Quartz ◽  
Torsional Pendulum ◽  
The Mean ◽  
Good Agreement

When fused quartz is heated, its elastic constants for stretch shear and bulk change all increase, a sharp distinction in behaviour from that of most other elastic solids. An elastically-stretched fibre becomes shorter upon heating, and a strained torsion member reduces its twist for a given twisting effort; and so forth. The changes of shear modulus with temperature have been studied in detail (22 to 98° C.) by Threlfall and later by Horton to about 1000° C., who used methods of experiment based upon the changes in period upon heating, of a torsional pendulum having fused quartz as the elastic member. The results of Horton's experiments showed a continuous increase in modulus up to about 880° C. beyond which temperature the modulus rapidly diminished. At 880° C. the modulus was 5·9 per cent, greater than at 15° C. and the mean rate of increase up to 500° C. was 0·85 × 10 -4 per degree Centigrade. The increase is more rapid at lower temperatures, thus, in the interval 20 to 100° C. mean rate of increase per degree Centigrade was found by Horton to be 1·25 × 10 -4 , which is in good agreement with the earlier determinations made by Threlfall. At still lower temperatures, and using the same method of torsional oscillation, Guye and Einhorn-Bodzechowski showed that the mean temperature coefficient in the interval —194° C. to 0° C. is 1·46 × 10 -4 per degree Centigrade, and that there is no major discontinuity in behaviour in this range.

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.

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.

On the determination of the fourth‐order elastic constants

1977 ◽  
Vol 48 (9) ◽  
pp. 3752-3755 ◽  
Author(s):  
Xanthippi Markenscoff
Keyword(s):  
Elastic Constants ◽  
Fourth Order
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