scholarly journals BRIDGE FUNCTIONS CALCULATED FROM A SECOND-ORDER APPROXIMATION FOR HARD SPHERES AND A LENNARD-JONES FLUID

1996 ◽  
pp. 51 ◽  
Author(s):  
Henderson ◽  
Sokolowski
Keyword(s):  
Hard Spheres ◽  
Order Approximation ◽  
Second Order ◽  
Second Order Approximation ◽  
Lennard Jones

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.

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