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Morse function description of anharmonicity in pressure‐volume relations of cubic metals
Author(s) -
Milstein F.
Publication year - 1971
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220480226
Subject(s) - anharmonicity , morse code , morse potential , moduli , cubic crystal system , function (biology) , morse theory , interatomic potential , lattice (music) , thermodynamics , materials science , representation (politics) , bulk modulus , volume (thermodynamics) , condensed matter physics , physics , atomic physics , quantum mechanics , mathematical analysis , mathematics , molecular dynamics , evolutionary biology , politics , political science , acoustics , law , electrical engineering , biology , engineering
The Morse function, Φ( r ) = D (e −2α ( r −r 0 ) − 2e −α( r − r 0 ) ), is often used to represent interatomic interactions in investigations of a wide variety of physical phenomena. In view of the wide‐spread use of this function, it is of interest to investigate quantitatively the extent to which experimentally determined anharmonic behavior is exhibited by solids with Morse function interatomic interactions. Numerical values of the Morse parameters D , α, and r 0 are determined for a number of cubic metals from experimental values of the lattice constant and the elastic moduli C 11 and C 12 . Morse parameters are then used to compute theoretical pressure‐volume ( P ‐ V ) behavior, and comparisons are made with P ‐ V data determined from shock‐wave measurements. Prior studies by other authors have indicated that the Morse function representation of anharmonic effects in metals is satisfactory; however, the present study shows that this representation, in general, becomes fairly poor for pressures which are large enough to produce considerable non‐linearity in the experimentally determined P ‐ V behavior.