scholarly journals Mechanomagnetics in Elastic Crystals: Insights from [Cu(acac) 2 ]

2019 ◽  
Vol 58 (42) ◽  
pp. 15082-15088 ◽  
Author(s):  
Elise P. Kenny ◽  
Anthony C. Jacko ◽  
Ben J. Powell
Keyword(s):  
Elastic Crystals

scholarly journals Atomic resolution of structural changes in elastic crystals of copper(II) acetylacetonate

2017 ◽  
Vol 10 (1) ◽  
pp. 65-69 ◽  
Author(s):  
Anna Worthy ◽  
Arnaud Grosjean ◽  
Michael C. Pfrunder ◽  
Yanan Xu ◽  
Cheng Yan ◽  
...  
Keyword(s):  
Structural Changes ◽  
Atomic Resolution ◽  
Elastic Crystals

scholarly journals On the theory of finite deformations of elastic crystals

1942 ◽  
Vol 180 (982) ◽  
pp. 285-304 ◽  
Keyword(s):  
Order Approximation ◽  
Finite Deformations ◽  
Second Order ◽  
Order Effects ◽  
Zero Temperature ◽  
Cubic Crystals ◽  
Special Values ◽  
Lennard Jones ◽  
Second Order Effects ◽  
Elastic Crystals

The general theory of finite deformation of cubic crystals at zero temperature is developed to a second-order approximation, and the cases of (1) a uniform hydrostatic pressure, (2) a tension in the direction of one of the axes, (3) a shear along the (0, 1, 0) planes, and (4) a shear along the (0, 1, 1) planes of the lattice, are worked out in detail. A number of ‘second-order effects’ (deviations from Hooke’s law) are predicted which in case (1) have been observed and measured by Bridgman, and in the remaining cases certainly can be detected and measured by suitable experimental arrangements. Assuming the particular force law between the particles of the lattice which was first introduced by Mie and Grüneisen, and later used in the investigations of Lennard-Jones and of Born and his collaborators, and using some of the results of the latter authors, the constants governing the above-mentioned second-order effects are expressed in terms of the constants governing the force law, and calculated numerically for a number of special values of these constants. Thus by comparing the calculated values of these constants with the results of measurements at low temperature the unknown force law could probably be determined.

A uniqueness proof for the Wulff Theorem

1991 ◽  
Vol 119 (1-2) ◽  
pp. 125-136 ◽  
Author(s):  
Irene Fonseca ◽  
Stefan Müller
Keyword(s):  
Measure Theory ◽  
Isoperimetric Problem ◽  
Geometric Measure Theory ◽  
Minkowski Inequality ◽  
Main Ingredient ◽  
Anisotropic Surface ◽  
Finite Perimeter ◽  
Uniqueness Proof ◽  
Elastic Crystals ◽  
Anisotropic Surface Energy

SynopsisThe Wulff problem is a generalisation of the isoperimetric problem and is relevant for the equilibrium of (small) elastic crystals. It consists in minimising the (generally anisotropic) surface energy among sets of given volume. A solution of this problem is given by a geometric construction due to Wulff. In the class of sets of finite perimeter this was first shown by J. E. Taylor who, using methods of geometric measure theory, also proved uniqueness. Here a more analytic uniqueness proof is presented. The main ingredient is a sharpened version of the Brunn–Minkowski inequality.

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