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Dipolar Fluctuation Model with tensorial force constants

The general expression for the dynamical matrix for the dipolar fluctuation model (DFM) is [6]:

\begin{displaymath}
D(\vec{q}) = P(\vec{q}) - T^{\dagger}(\vec{q})[K + S(\vec{q})]^{-1} T(\vec{q})
\end{displaymath}

where $P(\vec{q}),T(\vec{q}),S(\vec{q})$ are Fourier transform of tensorial interaction matrices between couples of sites. The DFM is activated by setting the variable USE_DFM in the input file for dispersionDeb.py :
USE_DFM=1

Then one has to fill in the entries for Tens_P, Tens_S, Tens_T. Tensor K is scaled to $1$ by rescaling S and T [6]. The following is an example for hcp Cobalt :

# XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 
# Tensorial Interactions between 'Co_G0' and 'Co_G0' 
# Shell N0 going from 0.996332 to 0.996332  like Co1 in 0 and Co0 in 1 0 1 
# Shell N1 going from 1.000000 to 1.000000  like Co1 in 0 and Co1 in -1 1 0 
# Shell N2 going from 1.411622 to 1.411622  like Co1 in 0 and Co0 in -1 1 0 
# Shell N3 going from 1.624000 to 1.624000  like Co1 in 0 and Co1 in 0 0 1 
# Shell N4 going from 1.729936 to 1.729936  like Co1 in 0 and Co0 in 0 2 1 
# Shell N5 going from 1.732051 to 1.732051  like Co1 in 0 and Co1 in -2 1 0 
# Shell N6 going from 1.907191 to 1.907191  like Co1 in 0 and Co1 in 0 1 -1 
# Shell N7 going from 2.000000 to 2.000000  like Co1 in 0 and Co1 in 0 2 0 

hcp_a=2.51
hcp_c=1.624*hcp_a

(a1,b1,g1,d1,
 a2,e2,b2,g2, 
 a3,b3,g3,d3)= [0]*12

(a1,b1,g1, 
 a2,b2,g2,e2,
 a3,b3,g3)=                  (    11925.5, 
                                  -1267.4,
                                  36831.4,
                                  -1819.8,
                                  40089.8,
                                   2171.9,
                                   1502.5,
                                    779.8,
                                    455.2,
                                  -3507.4)

Tens_P['Co_G0']['Co_G0']=[  [Numeric.array([     hcp_a/math.sqrt(3.0) ,
                                                     0, hcp_c/2.0  ]    ),
                           Numeric.array([[a1,0 ,d1],
                                  [0 ,b1,0 ],
                                  [d1,0 ,g1]])
                          ], 
                          [Numeric.array([  0 , hcp_a , 0 ]    ),
                           Numeric.array([[a2  ,e2 ,0],
                                  [-e2 ,b2 ,0 ],
                                  [ 0  ,0 ,g2 ]])  
                          ], 
                          [Numeric.array([  -2*hcp_a/math.sqrt(3.0) , 
                                                    0, hcp_c/2.0 ]    ),
                           Numeric.array([[a3  ,0  ,d3],
                                  [0   ,b3 ,0 ],
                                  [d3  ,0  ,g3 ]])  
                           ]
                        ]

one can see that the general form of Tens_P is given, for each shell, by a typical site-to-site vector and the corresponding tensor. The other tensors for the other interaction of the same shell are found by similitude transforming according to the simmetry group of the crystal. Tens_S and Tens_T are specified in analogous way.



Alessandro Mirone 2003-11-17