Abstract
A method is given for the location of certain types of stationary value of a function of many variables under conditions which make it applicable to atomistic modelling of crystal defects, for calculation of migration energies. The method, an adaptation of the conjugate gradients method of function minimization locates equilibrium configurations which have one unstable mode of vibration. It does not depend for its success on constraint of any coordinate of the system or on symmetry in the structure. Like the conjugate gradients minimization method, it requires evaluation of first, but not second, derivatives of the objective function. Examples are given of its application to the Frenkel-Kontorova model of a dislocation, and to the propagation of a crack in a brittle crystal.
Keywords
Saddle pointDislocationConstraint (computer-aided design)MinificationFunction (biology)Point (geometry)Crystallographic defectSaddleSymmetry (geometry)Stationary pointClassical mechanicsStatistical physicsVibrationPhysicsMathematical analysisMathematicsMathematical optimizationGeometryCondensed matter physicsQuantum mechanics
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Publication Info
- Year
- 1974
- Type
- article
- Volume
- 7
- Issue
- 5
- Pages
- 864-870
- Citations
- 74
- Access
- Closed
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Cite This
J. E. Sinclair,
R. Fletcher
(1974).
A new method of saddle-point location for the calculation of defect migration energies.
Journal of Physics C Solid State Physics
, 7
(5)
, 864-870.
https://doi.org/10.1088/0022-3719/7/5/009
Identifiers
- DOI
- 10.1088/0022-3719/7/5/009