Pressure derivatives of the elastic moduli of a polycrystalline aggregate of hexagonal metal: Calculations using monocrystal elastic‐constant pressure derivatives

1985 ◽  
Vol 57 (11) ◽  
pp. 5095-5097
Author(s):  
R. Ramji Rao ◽  
V. Janardhana
Keyword(s):  
Elastic Constant ◽  
Elastic Moduli ◽  
Constant Pressure ◽  
Polycrystalline Aggregate ◽  
Derivatives Of

Pressure derivatives of elastic moduli of fused quartz to 10 kb

1967 ◽  
Vol 28 (4) ◽  
pp. 635-639 ◽  
Author(s):  
Louis Peselnick ◽  
Robert Meister ◽  
William H. Wilson
Keyword(s):  
Elastic Moduli ◽  
Fused Quartz ◽  
Derivatives Of

scholarly journals Extremely small twist elastic constants in lyotropic nematic liquid crystals

2020 ◽  
Vol 117 (44) ◽  
pp. 27238-27244 ◽  
Author(s):  
Clarissa F. Dietrich ◽  
Peter J. Collings ◽  
Thomas Sottmann ◽  
Per Rudquist ◽  
Frank Giesselmann
Keyword(s):  
Liquid Crystals ◽  
Elastic Constant ◽  
Elastic Constants ◽  
Nematic Phase ◽  
Elastic Moduli ◽  
Building Blocks ◽  
Lyotropic Liquid Crystals ◽  
Order Of Magnitude ◽  
Typical Range ◽  
Special Case

Recent measurements of the elastic constants in lyotropic chromonic liquid crystals (LCLCs) have revealed an anomalously small twist elastic constant compared to the splay and bend constants. Interestingly, measurements of the elastic constants in the micellar lyotropic liquid crystals (LLCs) that are formed by surfactants, by far the most ubiquitous and studied class of LLCs, are extremely rare and report only the ratios of elastic constants and do not include the twist elastic constant. By means of light scattering, this study presents absolute values of the elastic constants and their corresponding viscosities for the nematic phase of a standard LLC composed of disk-shaped micelles. Very different elastic moduli are found. While the splay elastic constant is in the typical range of 1.5 pN as is true in general for thermotropic nematics, the twist elastic constant is found to be one order of magnitude smaller (0.30 pN) and almost two orders of magnitude smaller than the bend elastic constant (21 pN). These results demonstrate that a small twist elastic constant is not restricted to the special case of LCLCs, but is true for LLCs in general. The reason for this extremely small twist elastic constant very likely originates with the flexibility of the assemblies that are the building blocks of both micellar and chromonic lyotropic liquid crystals.

Elastic constants. II

1977 ◽  
Vol 357 (1690) ◽  
pp. 297-307
Keyword(s):  
Energy Density ◽  
Elastic Constant ◽  
Initial Stress ◽  
Elastic Constants ◽  
Interatomic Potential ◽  
Uniform Strain ◽  
Partial Derivatives ◽  
Constant Tensor ◽  
Derivatives Of

In the previous paper of this series we derived expressions for the initial stress and the elastic constant tensor for a crystal in terms of the partial derivatives of the energy density with uniform strain or sublattice displacement. In this paper we shall develop these equations further by considering the most general form of interatomic potential energies.

Phonon dispersion studies in liquid Na–Cs alloy

1991 ◽  
Vol 69 (12) ◽  
pp. 1476-1480 ◽  
Author(s):  
R. V. Gopala Rao ◽  
R. Venkatesh
Keyword(s):  
Effective Potential ◽  
Elastic Moduli ◽  
Phonon Dispersion ◽  
Peak Position ◽  
Collective Excitations ◽  
Longitudinal Phonon ◽  
Second Derivatives ◽  
Pseudopotential Approach ◽  
Total Structure ◽  
Derivatives Of

The Ashcroft empty-core model is used to derive the partial potentials of Na-Cs alloy through a pseudopotential approach. The potential functions are calculated at different concentrations of Cs. From the partial potentials an effective potential is computed. It is in general found that the mixed potential [Formula: see text] lies in between that of the pure metals, namely, [Formula: see text] and [Formula: see text]. The effective potential along with g(r) of the alloy is used to evaluate the longitudinal- and transverse-phonon frequencies in the momentum space through the use of Takeno and Goda's equations. It is found that longitudinal-phonon frequencies ωL(k) show collective excitations even at large values of k while the transverse phonons ωT(k) reach a constant value quickly. Further it is found that the first minimum in the ωL(k) curve appears to coincide with the first peak position in the total structure of the alloy. This is found to be true at all concentrations. Similar observations have been made by other researchers. As a typical illustration the elastic moduli, namely, C11 and C44 are evaluated by different methods for 50 at.% Cs. These methods involve the use of the first and second derivatives of the effective potential. The values calculated show a fair interconsistency proving the veracity of the derived potential function.

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