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.Version 3.0 of PHONONS
.Copyright (C) 1998-2025 ABINIT group (FB,JB).
ABINIT comes with ABSOLUTELY NO WARRANTY.
It is free software, and you are welcome to redistribute it
under certain conditions (GNU General Public License,
see ~abinit/COPYING or http://www.gnu.org/copyleft/gpl.txt).
ABINIT is a project of the Universite Catholique de Louvain,
Corning Inc. and other collaborators, see
~abinit/doc/developers/contributors.txt .
Please read https://docs.abinit.org/theory/acknowledgments for suggested
acknowledgments of the ABINIT effort.
For more information, see http://www.abinit.org .
.Starting date : 13 Sep 2024.
#############################################################################
######################### ECHO OF INPUT FILE ################################
#############################################################################
======================= Define the unitcell =================================
brav 3 3
natom_unitcell 2
xred_unitcell
0.0000000000 0.0000000000 0.0000000000
-0.2022000000 0.2022000000 0.5000000000
typat_unitcell 1 1
ntypat 1
amu 238.0289000000
======================= Define the supercell ================================
rprimd
21.4400000000 0.0000000000 0.0000000000
0.0000000000 22.1720000000 0.0000000000
0.0000000000 0.0000000000 27.9840000000
multiplicity
4.0000000000 4.0000000000 0.0000000000
-2.0000000000 2.0000000000 0.0000000000
0.0000000000 0.0000000000 3.0000000000
natom 96
typat
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1
temperature 50.0000000000
======================= Define computational details ========================
nstep_max 20
nstep_min 1
rcut 10.7200000000
======================= Optional input variables ============================
use_ideal_positions 1
enunit 3 (Phonon frequencies in THz)
USE IDEAL POSITIONS TO COMPUTE SPECTRUM
-Number of processors 1 1
All quantities are computed from nstep_min= 1
to nstep_max= 20
So, the real number of time steps is nstep= 20
The positions, forces and energies are extracted from the ASCII files: xred.dat, fcart.dat & etot.dat
#############################################################################
########################## Computed quantities ##############################
#############################################################################
acell_unitcell= 5.3600000000 11.0860000000 9.3280000000
rprimd_md= 21.4400000000 0.0000000000 0.0000000000
rprimd_md= 0.0000000000 22.1720000000 0.0000000000
rprimd_md= 0.0000000000 0.0000000000 27.9840000000
bravais= 3 3 1 1 0 -1 1 0 0 0 2
See the sym.dat file
#############################################################################
########################## Q points generation #############################
#############################################################################
Generate the BZ path using the Q points defined by default
See the qpt.dat file
#############################################################################
###### Find the matching between ideal and average positions ###############
#############################################################################
Determine ideal positions and distances...
Compute average positions...
Search the unitcell basis of atoms in the MD trajectory...
Compare ideal and average positions using PBC...
Write the xred_average.xyz file with ideal and average positions...
Compute cartesian coordinates and forces...
#############################################################################
###################### Find the symetry operations ##########################
#################### (connecting the atoms together) ########################
#############################################################################
Search the matrix transformation going from (k) to (i)...
Search the matrix transformation going from (k,l) to (i,j)...
See the Indsym*.dat files (if debug)
#############################################################################
####### FIRST ORDER : find the number of coefficients #######################
#############################################################################
Build the ref1at and Isym1at tables...
Build the Shell1at datatype...
Number of shells= 1
============================================================================
Shell number: 1
For atom 1:
Number of independant coefficients in this shell= 0
Number of interactions in this shell= 0
============================================================================
>>>>>> Total number of coefficients at the first order= 0
#############################################################################
###### SECOND ORDER : find the number of coefficients #######################
#############################################################################
Build the ref2at and Isym2at tables...
Build the Shell2at datatype...
Number of shells= 11
============================================================================
Shell number: 1
Between atom 1 and 1 the distance is= 0.0000000000
Number of independant coefficients in this shell= 0
Number of interactions in this shell= 1
============================================================================
Shell number: 2
Between atom 1 and 2 the distance is= 5.1747094741
Number of independant coefficients in this shell= 4
Number of interactions in this shell= 2
============================================================================
Shell number: 3
Between atom 1 and 3 the distance is= 9.3280000000
Number of independant coefficients in this shell= 4
Number of interactions in this shell= 2
============================================================================
Shell number: 4
Between atom 1 and 7 the distance is= 6.1568863072
Number of independant coefficients in this shell= 5
Number of interactions in this shell= 4
============================================================================
Shell number: 5
Between atom 1 and 8 the distance is= 9.4623001967
Number of independant coefficients in this shell= 6
Number of interactions in this shell= 4
============================================================================
Shell number: 6
Between atom 1 and 14 the distance is= 9.9988248509
Number of independant coefficients in this shell= 4
Number of interactions in this shell= 2
============================================================================
Shell number: 7
Between atom 1 and 20 the distance is= 6.3114664913
Number of independant coefficients in this shell= 6
Number of interactions in this shell= 4
============================================================================
Shell number: 8
Between atom 1 and 25 the distance is= 5.3600000000
Number of independant coefficients in this shell= 4
Number of interactions in this shell= 2
============================================================================
Shell number: 9
Between atom 1 and 26 the distance is= 7.4503166471
Number of independant coefficients in this shell= 6
Number of interactions in this shell= 4
============================================================================
Shell number: 10
Between atom 1 and 31 the distance is= 9.7655746887
Number of independant coefficients in this shell= 5
Number of interactions in this shell= 4
============================================================================
Shell number: 11
Between atom 1 and 44 the distance is= 9.8637624297
Number of independant coefficients in this shell= 6
Number of interactions in this shell= 4
============================================================================
>>>>>> Total number of coefficients at the second order= 50
#############################################################################
############## Fill the matrices used in the pseudo-inverse #################
#############################################################################
Compute the coefficients (at the 1st order) used in the Moore-Penrose...
------- achieved
Compute the coefficients (at the 2nd order) used in the Moore-Penrose...
------- achieved
#############################################################################
###################### Compute the constraints ##############################
########################## At the 1st order #################################
########################## At the 2nd order #################################
################## Reduce the number of constraints #########################
############### (Solve simultaneously all the orders) #######################
################### And compute the pseudo-inverse ##########################
#############################################################################
The problem is solved
#############################################################################
#### For each shell, list of coefficients (IFC), number of neighbours... ####
#############################################################################
############# List of (first order) IFC for the reference atom= 1
0.000000 0.000000 0.000000
############# List of (first order) IFC for the reference atom= 2
0.000000 0.000000 0.000000
#############################################################################
#### For each shell, list of coefficients (IFC), number of neighbours... ####
#############################################################################
############# List of (second order) IFC for the reference atom= 1
======== NEW SHELL (ishell= 1): There are 1 atoms on this shell at distance= 0.000000
For jatom= 1 ,with type= 1
0.082792 0.000000 0.000000
0.000000 0.083657 0.000000
0.000000 0.000000 0.077633
The components of the vector are: 0.000000 0.000000 0.000000
Trace= 0.244082
======== NEW SHELL (ishell= 2): There are 2 atoms on this shell at distance= 5.174709
For jatom= 2 ,with type= 2
0.006838 0.000000 0.000000
0.000000 -0.008727 -0.011440
0.000000 -0.011440 -0.008390
The components of the vector are: 0.000000 2.241589 4.664000
Trace= -0.010279
For jatom= 6 ,with type= 2
0.006838 0.000000 0.000000
0.000000 -0.008727 0.011440
0.000000 0.011440 -0.008390
The components of the vector are: 0.000000 2.241589 -4.664000
Trace= -0.010279
======== NEW SHELL (ishell= 8): There are 2 atoms on this shell at distance= 5.360000
For jatom= 25 ,with type= 1
-0.001846 0.001092 0.000000
-0.001092 -0.002274 0.000000
0.000000 0.000000 -0.000312
The components of the vector are: 5.360000 0.000000 0.000000
Trace= -0.004431
For jatom= 73 ,with type= 1
-0.001846 -0.001092 0.000000
0.001092 -0.002274 0.000000
0.000000 0.000000 -0.000312
The components of the vector are: -5.360000 0.000000 0.000000
Trace= -0.004431
======== NEW SHELL (ishell= 4): There are 4 atoms on this shell at distance= 6.156886
For jatom= 7 ,with type= 1
-0.003195 -0.002150 0.000000
-0.002995 -0.009234 0.000000
0.000000 0.000000 -0.001892
The components of the vector are: 2.680000 5.543000 0.000000
Trace= -0.014321
For jatom= 19 ,with type= 1
-0.003195 0.002995 0.000000
0.002150 -0.009234 0.000000
0.000000 0.000000 -0.001892
The components of the vector are: 2.680000 -5.543000 0.000000
Trace= -0.014321
For jatom= 79 ,with type= 1
-0.003195 0.002150 0.000000
0.002995 -0.009234 0.000000
0.000000 0.000000 -0.001892
The components of the vector are: -2.680000 5.543000 0.000000
Trace= -0.014321
For jatom= 91 ,with type= 1
-0.003195 -0.002995 0.000000
-0.002150 -0.009234 0.000000
0.000000 0.000000 -0.001892
The components of the vector are: -2.680000 -5.543000 0.000000
Trace= -0.014321
======== NEW SHELL (ishell= 7): There are 4 atoms on this shell at distance= 6.311466
For jatom= 20 ,with type= 2
-0.002110 0.002834 -0.005115
0.002834 -0.003794 0.006033
-0.005115 0.006033 -0.004132
The components of the vector are: 2.680000 -3.301411 4.664000
Trace= -0.010036
For jatom= 24 ,with type= 2
-0.002110 0.002834 0.005115
0.002834 -0.003794 -0.006033
0.005115 -0.006033 -0.004132
The components of the vector are: 2.680000 -3.301411 -4.664000
Trace= -0.010036
For jatom= 92 ,with type= 2
-0.002110 -0.002834 0.005115
-0.002834 -0.003794 0.006033
0.005115 0.006033 -0.004132
The components of the vector are: -2.680000 -3.301411 4.664000
Trace= -0.010036
For jatom= 96 ,with type= 2
-0.002110 -0.002834 -0.005115
-0.002834 -0.003794 -0.006033
-0.005115 -0.006033 -0.004132
The components of the vector are: -2.680000 -3.301411 -4.664000
Trace= -0.010036
======== NEW SHELL (ishell= 9): There are 4 atoms on this shell at distance= 7.450317
For jatom= 26 ,with type= 2
-0.015420 -0.000554 -0.005144
-0.000554 0.000583 0.000440
-0.005144 0.000440 -0.000157
The components of the vector are: 5.360000 2.241589 4.664000
Trace= -0.014994
For jatom= 30 ,with type= 2
-0.015420 -0.000554 0.005144
-0.000554 0.000583 -0.000440
0.005144 -0.000440 -0.000157
The components of the vector are: 5.360000 2.241589 -4.664000
Trace= -0.014994
For jatom= 74 ,with type= 2
-0.015420 0.000554 0.005144
0.000554 0.000583 0.000440
0.005144 0.000440 -0.000157
The components of the vector are: -5.360000 2.241589 4.664000
Trace= -0.014994
For jatom= 78 ,with type= 2
-0.015420 0.000554 -0.005144
0.000554 0.000583 -0.000440
-0.005144 -0.000440 -0.000157
The components of the vector are: -5.360000 2.241589 -4.664000
Trace= -0.014994
======== NEW SHELL (ishell= 3): There are 2 atoms on this shell at distance= 9.328000
For jatom= 3 ,with type= 1
-0.003761 0.000000 0.000000
0.000000 -0.001725 0.000254
0.000000 -0.000254 -0.006740
The components of the vector are: 0.000000 0.000000 9.328000
Trace= -0.012227
For jatom= 5 ,with type= 1
-0.003761 0.000000 0.000000
0.000000 -0.001725 -0.000254
0.000000 0.000254 -0.006740
The components of the vector are: 0.000000 0.000000 -9.328000
Trace= -0.012227
======== NEW SHELL (ishell= 5): There are 4 atoms on this shell at distance= 9.462300
For jatom= 8 ,with type= 2
0.002853 -0.001995 -0.000837
-0.001995 -0.000554 -0.001208
-0.000837 -0.001208 -0.000848
The components of the vector are: 2.680000 7.784589 4.664000
Trace= 0.001451
For jatom= 12 ,with type= 2
0.002853 -0.001995 0.000837
-0.001995 -0.000554 0.001208
0.000837 0.001208 -0.000848
The components of the vector are: 2.680000 7.784589 -4.664000
Trace= 0.001451
For jatom= 80 ,with type= 2
0.002853 0.001995 0.000837
0.001995 -0.000554 -0.001208
0.000837 -0.001208 -0.000848
The components of the vector are: -2.680000 7.784589 4.664000
Trace= 0.001451
For jatom= 84 ,with type= 2
0.002853 0.001995 -0.000837
0.001995 -0.000554 0.001208
-0.000837 0.001208 -0.000848
The components of the vector are: -2.680000 7.784589 -4.664000
Trace= 0.001451
======== NEW SHELL (ishell= 10): There are 4 atoms on this shell at distance= 9.765575
For jatom= 31 ,with type= 1
-0.005283 -0.002105 0.000000
-0.000558 -0.000607 0.000000
0.000000 0.000000 -0.002756
The components of the vector are: 8.040000 5.543000 0.000000
Trace= -0.008645
For jatom= 43 ,with type= 1
-0.005283 0.000558 0.000000
0.002105 -0.000607 0.000000
0.000000 0.000000 -0.002756
The components of the vector are: 8.040000 -5.543000 0.000000
Trace= -0.008645
For jatom= 55 ,with type= 1
-0.005283 0.002105 0.000000
0.000558 -0.000607 0.000000
0.000000 0.000000 -0.002756
The components of the vector are: -8.040000 5.543000 0.000000
Trace= -0.008645
For jatom= 67 ,with type= 1
-0.005283 -0.000558 0.000000
-0.002105 -0.000607 0.000000
0.000000 0.000000 -0.002756
The components of the vector are: -8.040000 -5.543000 0.000000
Trace= -0.008645
======== NEW SHELL (ishell= 11): There are 4 atoms on this shell at distance= 9.863762
For jatom= 44 ,with type= 2
0.001756 -0.000175 -0.001321
-0.000175 0.000118 0.001110
-0.001321 0.001110 -0.002042
The components of the vector are: 8.040000 -3.301411 4.664000
Trace= -0.000168
For jatom= 48 ,with type= 2
0.001756 -0.000175 0.001321
-0.000175 0.000118 -0.001110
0.001321 -0.001110 -0.002042
The components of the vector are: 8.040000 -3.301411 -4.664000
Trace= -0.000168
For jatom= 68 ,with type= 2
0.001756 0.000175 0.001321
0.000175 0.000118 0.001110
0.001321 0.001110 -0.002042
The components of the vector are: -8.040000 -3.301411 4.664000
Trace= -0.000168
For jatom= 72 ,with type= 2
0.001756 0.000175 -0.001321
0.000175 0.000118 -0.001110
-0.001321 -0.001110 -0.002042
The components of the vector are: -8.040000 -3.301411 -4.664000
Trace= -0.000168
======== NEW SHELL (ishell= 6): There are 2 atoms on this shell at distance= 9.998825
For jatom= 14 ,with type= 2
0.000172 0.000000 0.000000
0.000000 -0.002129 0.000399
0.000000 0.000399 0.000278
The components of the vector are: 0.000000 -8.844411 4.664000
Trace= -0.001678
For jatom= 18 ,with type= 2
0.000172 0.000000 0.000000
0.000000 -0.002129 -0.000399
0.000000 -0.000399 0.000278
The components of the vector are: 0.000000 -8.844411 -4.664000
Trace= -0.001678
############# List of (second order) IFC for the reference atom= 2
======== NEW SHELL (ishell= 1): There are 1 atoms on this shell at distance= 0.000000
For jatom= 2 ,with type= 2
0.082792 0.000000 0.000000
0.000000 0.083657 0.000000
0.000000 0.000000 0.077633
The components of the vector are: 0.000000 0.000000 0.000000
Trace= 0.244082
======== NEW SHELL (ishell= 2): There are 2 atoms on this shell at distance= 5.174709
For jatom= 1 ,with type= 1
0.006838 0.000000 0.000000
0.000000 -0.008727 -0.011440
0.000000 -0.011440 -0.008390
The components of the vector are: 0.000000 -2.241589 -4.664000
Trace= -0.010279
For jatom= 3 ,with type= 1
0.006838 0.000000 0.000000
0.000000 -0.008727 0.011440
0.000000 0.011440 -0.008390
The components of the vector are: 0.000000 -2.241589 4.664000
Trace= -0.010279
======== NEW SHELL (ishell= 8): There are 2 atoms on this shell at distance= 5.360000
For jatom= 26 ,with type= 2
-0.001846 -0.001092 0.000000
0.001092 -0.002274 0.000000
0.000000 0.000000 -0.000312
The components of the vector are: 5.360000 0.000000 0.000000
Trace= -0.004431
For jatom= 74 ,with type= 2
-0.001846 0.001092 0.000000
-0.001092 -0.002274 0.000000
0.000000 0.000000 -0.000312
The components of the vector are: -5.360000 0.000000 0.000000
Trace= -0.004431
======== NEW SHELL (ishell= 4): There are 4 atoms on this shell at distance= 6.156886
For jatom= 8 ,with type= 2
-0.003195 -0.002995 0.000000
-0.002150 -0.009234 0.000000
0.000000 0.000000 -0.001892
The components of the vector are: 2.680000 5.543000 0.000000
Trace= -0.014321
For jatom= 20 ,with type= 2
-0.003195 0.002150 0.000000
0.002995 -0.009234 0.000000
0.000000 0.000000 -0.001892
The components of the vector are: 2.680000 -5.543000 0.000000
Trace= -0.014321
For jatom= 80 ,with type= 2
-0.003195 0.002995 0.000000
0.002150 -0.009234 0.000000
0.000000 0.000000 -0.001892
The components of the vector are: -2.680000 5.543000 0.000000
Trace= -0.014321
For jatom= 92 ,with type= 2
-0.003195 -0.002150 0.000000
-0.002995 -0.009234 0.000000
0.000000 0.000000 -0.001892
The components of the vector are: -2.680000 -5.543000 0.000000
Trace= -0.014321
======== NEW SHELL (ishell= 7): There are 4 atoms on this shell at distance= 6.311466
For jatom= 7 ,with type= 1
-0.002110 -0.002834 0.005115
-0.002834 -0.003794 0.006033
0.005115 0.006033 -0.004132
The components of the vector are: 2.680000 3.301411 -4.664000
Trace= -0.010036
For jatom= 9 ,with type= 1
-0.002110 -0.002834 -0.005115
-0.002834 -0.003794 -0.006033
-0.005115 -0.006033 -0.004132
The components of the vector are: 2.680000 3.301411 4.664000
Trace= -0.010036
For jatom= 79 ,with type= 1
-0.002110 0.002834 -0.005115
0.002834 -0.003794 0.006033
-0.005115 0.006033 -0.004132
The components of the vector are: -2.680000 3.301411 -4.664000
Trace= -0.010036
For jatom= 81 ,with type= 1
-0.002110 0.002834 0.005115
0.002834 -0.003794 -0.006033
0.005115 -0.006033 -0.004132
The components of the vector are: -2.680000 3.301411 4.664000
Trace= -0.010036
======== NEW SHELL (ishell= 9): There are 4 atoms on this shell at distance= 7.450317
For jatom= 25 ,with type= 1
-0.015420 0.000554 0.005144
0.000554 0.000583 0.000440
0.005144 0.000440 -0.000157
The components of the vector are: 5.360000 -2.241589 -4.664000
Trace= -0.014994
For jatom= 27 ,with type= 1
-0.015420 0.000554 -0.005144
0.000554 0.000583 -0.000440
-0.005144 -0.000440 -0.000157
The components of the vector are: 5.360000 -2.241589 4.664000
Trace= -0.014994
For jatom= 73 ,with type= 1
-0.015420 -0.000554 -0.005144
-0.000554 0.000583 0.000440
-0.005144 0.000440 -0.000157
The components of the vector are: -5.360000 -2.241589 -4.664000
Trace= -0.014994
For jatom= 75 ,with type= 1
-0.015420 -0.000554 0.005144
-0.000554 0.000583 -0.000440
0.005144 -0.000440 -0.000157
The components of the vector are: -5.360000 -2.241589 4.664000
Trace= -0.014994
======== NEW SHELL (ishell= 3): There are 2 atoms on this shell at distance= 9.328000
For jatom= 4 ,with type= 2
-0.003761 0.000000 0.000000
0.000000 -0.001725 -0.000254
0.000000 0.000254 -0.006740
The components of the vector are: 0.000000 0.000000 9.328000
Trace= -0.012227
For jatom= 6 ,with type= 2
-0.003761 0.000000 0.000000
0.000000 -0.001725 0.000254
0.000000 -0.000254 -0.006740
The components of the vector are: 0.000000 0.000000 -9.328000
Trace= -0.012227
======== NEW SHELL (ishell= 5): There are 4 atoms on this shell at distance= 9.462300
For jatom= 19 ,with type= 1
0.002853 0.001995 0.000837
0.001995 -0.000554 -0.001208
0.000837 -0.001208 -0.000848
The components of the vector are: 2.680000 -7.784589 -4.664000
Trace= 0.001451
For jatom= 21 ,with type= 1
0.002853 0.001995 -0.000837
0.001995 -0.000554 0.001208
-0.000837 0.001208 -0.000848
The components of the vector are: 2.680000 -7.784589 4.664000
Trace= 0.001451
For jatom= 91 ,with type= 1
0.002853 -0.001995 -0.000837
-0.001995 -0.000554 -0.001208
-0.000837 -0.001208 -0.000848
The components of the vector are: -2.680000 -7.784589 -4.664000
Trace= 0.001451
For jatom= 93 ,with type= 1
0.002853 -0.001995 0.000837
-0.001995 -0.000554 0.001208
0.000837 0.001208 -0.000848
The components of the vector are: -2.680000 -7.784589 4.664000
Trace= 0.001451
======== NEW SHELL (ishell= 10): There are 4 atoms on this shell at distance= 9.765575
For jatom= 32 ,with type= 2
-0.005283 -0.000558 0.000000
-0.002105 -0.000607 0.000000
0.000000 0.000000 -0.002756
The components of the vector are: 8.040000 5.543000 0.000000
Trace= -0.008645
For jatom= 44 ,with type= 2
-0.005283 0.002105 0.000000
0.000558 -0.000607 0.000000
0.000000 0.000000 -0.002756
The components of the vector are: 8.040000 -5.543000 0.000000
Trace= -0.008645
For jatom= 56 ,with type= 2
-0.005283 0.000558 0.000000
0.002105 -0.000607 0.000000
0.000000 0.000000 -0.002756
The components of the vector are: -8.040000 5.543000 0.000000
Trace= -0.008645
For jatom= 68 ,with type= 2
-0.005283 -0.002105 0.000000
-0.000558 -0.000607 0.000000
0.000000 0.000000 -0.002756
The components of the vector are: -8.040000 -5.543000 0.000000
Trace= -0.008645
======== NEW SHELL (ishell= 11): There are 4 atoms on this shell at distance= 9.863762
For jatom= 31 ,with type= 1
0.001756 0.000175 0.001321
0.000175 0.000118 0.001110
0.001321 0.001110 -0.002042
The components of the vector are: 8.040000 3.301411 -4.664000
Trace= -0.000168
For jatom= 33 ,with type= 1
0.001756 0.000175 -0.001321
0.000175 0.000118 -0.001110
-0.001321 -0.001110 -0.002042
The components of the vector are: 8.040000 3.301411 4.664000
Trace= -0.000168
For jatom= 55 ,with type= 1
0.001756 -0.000175 -0.001321
-0.000175 0.000118 0.001110
-0.001321 0.001110 -0.002042
The components of the vector are: -8.040000 3.301411 -4.664000
Trace= -0.000168
For jatom= 57 ,with type= 1
0.001756 -0.000175 0.001321
-0.000175 0.000118 -0.001110
0.001321 -0.001110 -0.002042
The components of the vector are: -8.040000 3.301411 4.664000
Trace= -0.000168
======== NEW SHELL (ishell= 6): There are 2 atoms on this shell at distance= 9.998825
For jatom= 13 ,with type= 1
0.000172 0.000000 0.000000
0.000000 -0.002129 0.000399
0.000000 0.000399 0.000278
The components of the vector are: 0.000000 8.844411 -4.664000
Trace= -0.001678
For jatom= 15 ,with type= 1
0.000172 0.000000 0.000000
0.000000 -0.002129 -0.000399
0.000000 -0.000399 0.000278
The components of the vector are: 0.000000 8.844411 4.664000
Trace= -0.001678
#############################################################################
############## Compute the phonon spectrum, the DOS, ########################
############## the dynamical matrix and write them ########################
#############################################################################
#############################################################################
################### vibrational Density OF States (vDOS) ####################
#############################################################################
See the vdos.dat and TDEP_PHDOS* files
Write the IFC of TDEP in ifc_out.dat (and ifc_out.nc)
------- achieved
Compute the vDOS
------- achieved
(Please, pay attention to convergency wrt the BZ mesh : the ngqpt2 input variable)
See the dij.dat, omega.dat and eigenvectors files
See also the DDB file
#############################################################################
######################### Elastic constants #################################
################ Bulk and Shear modulus--Sound velocities ###################
#############################################################################
========== Using the formulation proposed by Wallace (using the IFC) =========
Cijkl [in GPa]=
| C11 C12 C13 C14 C15 C16 | 303.664 79.611 57.986 0.000 0.000 0.000
| C21 C22 C23 C24 C25 C26 | 79.611 203.078 68.822 0.000 0.000 0.000
| C31 C32 C33 C34 C35 C36 | 57.986 68.822 228.292 0.000 0.000 0.000
| C41 C42 C43 C44 C45 C46 | = 0.000 0.000 0.000 115.690 0.000 0.000
| C51 C52 C53 C54 C55 C56 | 0.000 0.000 0.000 0.000 156.469 0.000
| C61 C62 C63 C64 C65 C66 | 0.000 0.000 0.000 0.000 0.000 61.594
========== For an Anisotropic Material =======================================
Sijkl [in GPa-1]=
| S11 S12 S13 S14 S15 S16 | 0.004 -0.001 -0.001 0.000 0.000 -0.000
| S21 S22 S23 S24 S25 S26 | -0.001 0.006 -0.001 0.000 0.000 -0.000
| S31 S32 S33 S34 S35 S36 | -0.001 -0.001 0.005 0.000 0.000 -0.000
| S41 S42 S43 S44 S45 S46 | = 0.000 0.000 0.000 0.009 0.000 -0.000
| S51 S52 S53 S54 S55 S56 | 0.000 0.000 0.000 0.000 0.006 -0.000
| S61 S62 S63 S64 S65 S66 | 0.000 0.000 0.000 0.000 0.000 0.016
========== For an Orthotropic Material (see B. M. Lempriere (1968)) ==========
Young modulus E1, E2 and E3 [in GPa]= 267.764 168.970 201.440
Poisson ratio Nu21, Nu31, Nu23, Nu12, Nu13 and Nu32= 0.215 0.114 0.247 0.341 0.151 0.294
Shear modulus G23, G13 and G12 [in GPa]= 115.690 156.469 61.594
Sijkl [in GPa-1]=
| S11 S12 S13 S14 S15 S16 | 0.004 -0.001 -0.001 0.000 0.000 0.000
| S21 S22 S23 S24 S25 S26 | -0.001 0.006 -0.001 0.000 0.000 0.000
| S31 S32 S33 S34 S35 S36 | -0.001 -0.001 0.005 0.000 0.000 0.000
| S41 S42 S43 S44 S45 S46 | = 0.000 0.000 0.000 0.009 0.000 0.000
| S51 S52 S53 S54 S55 S56 | 0.000 0.000 0.000 0.000 0.006 0.000
| S61 S62 S63 S64 S65 S66 | 0.000 0.000 0.000 0.000 0.000 0.016
For density rho [in kg.m-3]=19249.404
========================= Voigt average (constant strain) ===================
ISOTHERMAL modulus [in GPa]: Bulk Kt= 127.541 and Shear G= 101.992
Average of Young modulus E [in GPa]= 241.580 Lame modulus Lambda [in GPa]= 59.547 and Poisson ratio Nu= 0.184
Velocities [in m.s-1]: compressional Vp= 3700.039 shear Vs= 2301.832 and bulk Vphi= 2574.047
Debye velocity [in m.s-1]= 2536.968 and temperature [in K]= 275.825
========================= Reuss average (constant stress) ===================
ISOTHERMAL modulus [in GPa]: Bulk Kt= 124.685 and Shear G= 90.649
Average of Young modulus E [in GPa]= 218.899 Lame modulus Lambda [in GPa]= 64.252 and Poisson ratio Nu= 0.207
Velocities [in m.s-1]: compressional Vp= 3571.593 shear Vs= 2170.070 and bulk Vphi= 2545.061
Debye velocity [in m.s-1]= 2397.635 and temperature [in K]= 260.676
============================== Hill average =================================
ISOTHERMAL modulus [in GPa]: Bulk Kt= 126.113 and Shear G= 96.321
Average of Young modulus E [in GPa]= 230.324 Lame modulus Lambda [in GPa]= 61.899 and Poisson ratio Nu= 0.196
Velocities [in m.s-1]: compressional Vp= 3636.383 shear Vs= 2236.921 and bulk Vphi= 2559.595
Debye velocity [in m.s-1]= 2468.365 and temperature [in K]= 268.366
========================= Elastic anisotropy =================================
Elastic anisotropy index : A_U= 5*G_V/G_R + K_V/K_R - 6 = 0.649
Bulk anisotropy ratio : A_B= (B_V-B_R)/(B_V+B_R) = 0.011
Shear anisotropy ratio : A_G= (G_V-G_R)/(G_V+G_R) = 0.059
#############################################################################
######################### Energies, errors,... #############################
#############################################################################
Thermodynamic quantities and convergence parameters of THE MODEL,
as a function of the step number (energies in eV/atom and forces in Ha/bohr) :
<U_TDEP> = U_0 + U_1 + U_2
with U_0 = < U_MD - sum_i Phi1 ui - 1/2 sum_ij Phi2 ui uj >
and U_1 = < sum_i Phi1 ui >
and U_2 = < 1/2 sum_ij Phi2 ui uj >
Delta_U = < U_MD - U_TDEP >
Delta_U2= (< (U_MD - U_TDEP)^2 >)**0.5
Delta_F2= (< (F_MD - F_TDEP)^2 >)**0.5
Sigma = (< (F_MD - F_TDEP)^2 >/<F_MD**2>)**0.5
<U_MD> U_0 U_1 U_2 Delta_U Delta_U2 Delta_F2 Sigma
-1416.77141 -1416.77867 0.00000 0.00726 -0.00000 0.00652 0.00163 0.44423
NOTE : in the harmonic and classical limit (T>>T_Debye), U_2=3/2*kB*T= 0.00646
See the etotMDvsTDEP.dat & fcartMDvsTDEP.dat files
#############################################################################
################# Thermodynamic quantities: Free energy,...##################
#############################################################################
See the thermo.dat file
#############################################################################
######################### CALCULATION COMPLETED #############################
#############################################################################
Suggested references for the acknowledgment of ABINIT usage.
The users of ABINIT have little formal obligations with respect to the ABINIT group
(those specified in the GNU General Public License, http://www.gnu.org/copyleft/gpl.txt).
However, it is common practice in the scientific literature,
to acknowledge the efforts of people that have made the research possible.
In this spirit, please find below suggested citations of work written by ABINIT developers,
corresponding to implementations inside of ABINIT that you have used in the present run.
Note also that it will be of great value to readers of publications presenting these results,
to read papers enabling them to understand the theoretical formalism and details
of the ABINIT implementation.
For information on why they are suggested, see also https://docs.abinit.org/theory/acknowledgments.
[1] a-TDEP: Temperature Dependent Effective Potential for Abinit
-- Lattice dynamic properties including anharmonicity
F. Bottin, J. Bieder and J. Bouchet, Comput. Phys. Comm. 254, 107301 (2020).
Strong suggestion to cite this paper in your publications.
[2] Thermal evolution of vibrational properties of alpha-U
J. Bouchet and F. Bottin, Phys. Rev. B 92, 174108 (2015).
Strong suggestion to cite this paper in your publications.
[3] Lattice dynamics of anharmonic solids from first principles
O. Hellman, I.A. Abrikosov and S.I. Simak, Phys. Rev. B 84, 180301(R) (2011).
[4] Temperature dependent effective potential method for accurate free energy calculations of solids
O. Hellman, P. Steneteg, I.A. Abrikosov and S.I. Simak, Phys. Rev. B 87, 104111 (2013).
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