mirror of https://gitlab.com/QEF/q-e.git
35 lines
1.2 KiB
Plaintext
35 lines
1.2 KiB
Plaintext
This is an example in which the Born effective charge for Pb in perovskite
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PbTiO3 is calculated.
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1) make a self-consistent calculation for a cubic structure of PbTiO3 in
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which the Pb atom has been displaced a small distance 0.01*a0 in the z
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axis (a0 is the lattice constant, 7.3699 bohr).
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(input=chg.in, output=chg.out)
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2) make a non-self-consistent calculation to compute the polarization
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(lberry=.true. in the input file 'BP.in'). In the ouput file 'BP.out'
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we find that the polarization (P) multiplied by the volume of the unit
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cell (Omega) is:
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Omega * P = 0.2884752 e.bohr
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while the distance the Pb atom has been displaced from the perfect cubic cell
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structure is
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r - r0 = 0.01 * 7.3699 bohr = 0.073699 bohr.
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Given that the Born effective charge is defined as
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dP
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z* = Omega ----
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dr
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we can use a finite differences approximation to get
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0.2884752 e.bohr
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z* = ------------------ = 3.91 e
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0.073699 bohr
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in good agreement with published results. For example, in Zhong, King-Smith
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and Vanderbilt, PRL 72, 3618 (1994) the value found is 3.90 e.
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