Theoretical Strength of Perfect Crystalline Materials
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Report Number: RM-6379-PR
Author(s): Milstein, Frederick
Corporate Author(s): The RAND Corporation
Date of Publication: 1970-12
Contract: F44620-67-C-0045
DoD Task:
Identifier: AD0717698
Abstract:
A mathematical procedure is presented for applying the Born stability criteria to the determination of the mechanical stability of cubic crystals in the presence of applied forces and deformations. The general procedure is suitable for use in conjunction with an electronic computer and is independent of the specific model of interatomic interactions that can be used in numerical calculations. In this report, specific calculations are performed for a body-centered cubic (B.C.C.) crystal lattice with a uniaxial tensile force applied perpendicularly to a face of a unit cell. The atoms in the crystal are assumed to interact through a two-body Morse interatomic potential function appropriate to B.C.C. iron. Two ranges of stability, a B.C.C. phase and body-centered tetragonal (B.C.T.) phase were found to exist: . The B.C.T. phase has a theoretical strength of 0.9 x 1011 dyne/cm2 (1 dyne/cm2 = 1.45 x 10-5 psi) with a corresponding theoretical strain of about 7 percent. These values are fairly close to the values of 1.3 x 1011 dyne/cm2 tensile strength and about 5 percent strain experimentally observed for fine iron whiskers.
Author(s): Milstein, Frederick
Corporate Author(s): The RAND Corporation
Date of Publication: 1970-12
Contract: F44620-67-C-0045
DoD Task:
Identifier: AD0717698
Abstract:
A mathematical procedure is presented for applying the Born stability criteria to the determination of the mechanical stability of cubic crystals in the presence of applied forces and deformations. The general procedure is suitable for use in conjunction with an electronic computer and is independent of the specific model of interatomic interactions that can be used in numerical calculations. In this report, specific calculations are performed for a body-centered cubic (B.C.C.) crystal lattice with a uniaxial tensile force applied perpendicularly to a face of a unit cell. The atoms in the crystal are assumed to interact through a two-body Morse interatomic potential function appropriate to B.C.C. iron. Two ranges of stability, a B.C.C. phase and body-centered tetragonal (B.C.T.) phase were found to exist: . The B.C.T. phase has a theoretical strength of 0.9 x 1011 dyne/cm2 (1 dyne/cm2 = 1.45 x 10-5 psi) with a corresponding theoretical strain of about 7 percent. These values are fairly close to the values of 1.3 x 1011 dyne/cm2 tensile strength and about 5 percent strain experimentally observed for fine iron whiskers.