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add explanation for lambda tensor
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samwaseda committed Aug 4, 2024
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12 changes: 12 additions & 0 deletions elaston/linear_elasticity/linear_elasticity.py
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Expand Up @@ -63,6 +63,18 @@
job.run()
dipole_tensor = -job.structure.get_volume()*job['output/generic/pressures'][-1]
```
Instead of working with atomistic calculations, the dipole tensor can be calculated by the
lambda tensor, which is defined as:
.. math:
\\lambda_{ij} = \\frac{1]{V} \\frac{\\partial \\varepsilon_{ij}}{\\partial c}
where :math:`c` is the concentration of the defect, :math:`V` is the volume
and :math:`\\varepsilon` is the strain field. Then the dipole tensor is given by:
.. math:
P_{ij} = VC_{ijkl}\\lambda_{kl}
"""


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