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#! /usr/bin/env python |
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|
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from __future__ import division,print_function |
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|
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__doc__ = """Luttinger and Tisza Field values |
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|
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Computes the sums for the field values (and also the energy constants |
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for the low energy lattices) from the paper by Luttinger and Tisza |
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paper: |
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|
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J. M. Luttinger and L. Tisza, "Theory of Dipole Interaction in |
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Crystals," Phys. Rev. 70, 954-964 (1946) doi: 10.1103/PhysRev.70.954 |
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|
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Also note the errata: Phys. Rev. 72 257 (1947) doi: 10.1103/PhysRev.72.257 |
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|
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This script can obtain a much higher degree of accuracy than the |
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original paper (simply by going to many more terms). Using the option |
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-c 350 appears to converge the energy constants to approximately 1 |
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part in 10^9 (but takes a long time). |
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|
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Usage: fieldValues |
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|
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Options: |
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|
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-h, --help show this help |
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-c use the specified cutoff in inverse space |
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|
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Example: |
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fieldValues -c 100 |
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""" |
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|
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__author__ = "Dan Gezelter (gezelter@nd.edu) and Kathie Newman (newman@nd.edu)" |
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__version__ = "$Rev: 1917 $" |
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__date__ = "$LastChangedDate: 2013-07-31 08:58:35 -0400 (Wed, 31 Jul 2013) $" |
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__copyright__ = "Copyright (c) 2013 by the University of Notre Dame" |
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__license__ = "OpenMD" |
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|
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import sys |
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import getopt |
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import string |
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import math as m |
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|
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def usage(): |
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print(__doc__) |
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|
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|
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def doSums(r_c): |
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|
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sum1=0 # Sz( 0, 1/2, 1/2) |
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sum2=0 # Sz(1/2, 0, 0) |
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sum3=0 # Sz( 0, 1/4, 1/4) |
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sum4=0 # Sy(1/4, 1/4, 1/4) |
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sum5=0 # Sy( 0, 1/4, 1/4) |
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sum6=0 # Sy(1/2, 1/4, 1/4) |
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|
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x = -r_c-1 |
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|
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while x <= r_c: |
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x = x + 1 |
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dx = x |
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dx2 = 1/2 - x |
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dx4 = 1/4 - x |
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|
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y = -r_c-1 |
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while y <= r_c: |
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y = y + 1 |
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dy = y |
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dy2 = 1/2 - y |
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dy4 = 1/4 - y |
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|
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z = -r_c-1 |
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while z <= r_c: |
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z = z + 1 |
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dz = z |
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dz2 = 1/2 - z |
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dz4 = 1/4 - z |
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|
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r = m.sqrt( dx*dx + dy*dy + dz*dz) |
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r1 =m.sqrt( dx*dx + dy2*dy2 + dz2*dz2) |
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r2 =m.sqrt( dx2*dx2 + dy*dy + dz*dz) |
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r3 =m.sqrt( dx*dx + dy4*dy4 + dz4*dz4) |
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r4 =m.sqrt( dx4*dx4 + dy4*dy4 + dz4*dz4) |
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r5 =r3 |
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r6 =m.sqrt( dx2*dx2 + dy4*dy4 + dz4*dz4) |
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|
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if r <= r_c: |
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r15 = pow(r1,5) |
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r25 = pow(r2,5) |
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r35 = pow(r3,5) |
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r45 = pow(r4,5) |
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r55 = pow(r5,5) |
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r65 = pow(r6,5) |
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|
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term1 = (2 * dz2 * dz2 - dx*dx - dy2*dy2)/r15 |
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term2 = (2 * dz*dz - dx2*dx2 - dy*dy)/r25 |
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term3 = (2 * dz4*dz4 - dx*dx - dy4*dy4)/r35 |
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term4 = 3 * dy4 * dz4 / r45 |
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term5 = 3 * dy4 * dz4 / r55 |
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term6 = 3 * dy4 * dz4 / r65 |
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|
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sum1 += term1 |
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sum2 += term2 |
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sum3 += term3 |
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sum4 += term4 |
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sum5 += term5 |
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sum6 += term6 |
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|
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f2 = -(sum1 - sum2) / 2 |
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f3 = -(sum1 - sum2) / 4 |
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f4 = -(sum1 - sum2) / 4 |
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f5 = -(sum1 + sum2) / 2 |
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f6 = (sum1 + sum2) / 4 |
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f7 = (sum1 + sum2) / 4 |
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g = sum4 |
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h1 = sum1 |
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h2 = sum3 - sum1 |
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h3 = (sum5+sum6)/2 |
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h4 = (sum5-sum6)/2 |
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|
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print ("Raw Sums:") |
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print ("Sz( 0, 1/2, 1/2) = ", sum1) |
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print ("Sz(1/2, 0, 0) = ", sum2) |
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print ("Sz( 0, 1/4, 1/4) = ", sum3) |
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print ("Sy(1/4, 1/4, 1/4) = ", sum4) |
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print ("Sy( 0, 1/4, 1/4) = ", sum5) |
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print ("Sy(1/2, 1/4, 1/4) = ", sum6) |
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print ("") |
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print ("Field Values:") |
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print ("f2 = ", f2) |
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print ("f3 = ", f3) |
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print ("f4 = ", f4) |
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print ("f5 = ", f5) |
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print ("f6 = ", f6) |
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print ("f7 = ", f7) |
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print (" g = ", g) |
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print ("h1 = ", h1) |
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print ("h2 = ", h2) |
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print ("h3 = ", h3) |
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print ("h4 = ", h4) |
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print ("") |
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print ("Energy Constants for selected lattices:") |
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print ("A_sc_001 :", -f5 / 2 ) |
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print ("A_bcc_001 :", 0 ) |
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print ("A_bcc_111 :", -g / 6 ) |
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print ("A_bcc_min :", -(g+f6) / 4) |
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print ("A_fcc_001 :", h1 / 2) |
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print ("A_fcc_011 :", -h1 / 4) |
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print ("B_sc_001 :", -f5 / 2) |
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print ("B_bcc_001 :", -f5 / 4) |
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print ("B_bcc_111 :", -g / 6 ) |
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print ("B_fcc_001 :", -h1 / 4) |
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print ("B_fcc_011 :", -h4 / 8) |
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|
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|
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def main(argv): |
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|
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r_c = 100 |
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try: |
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opts, args = getopt.getopt(argv, "hc:", ["help","r_c="]) |
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except getopt.GetoptError: |
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usage() |
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sys.exit(2) |
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for opt, arg in opts: |
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if opt in ("-h", "--help"): |
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usage() |
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sys.exit() |
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elif opt in ("-c", "--r_c"): |
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r_c = int(arg) |
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|
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doSums(r_c) |
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|
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if __name__ == "__main__": |
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if len(sys.argv) == 1: |
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usage() |
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sys.exit() |
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main(sys.argv[1:]) |
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|
