exercise/03: elastic constance calculation for fcc Cu
In this exercise we will practice how to get elastic constance for fcc copper with EMTO code.
Orthorhombic distortion
\[\begin{split}D_o(\delta_o) + I = \left[\begin{matrix}
1+\delta_o&0&0\\
0&1-\delta_o&0\\
0&0&\frac{1}{(1-\delta_o^2)}\\
\end{matrix}\right]\end{split}\]
leads to energy change
\[\Delta E(\delta_o) = 2Vc'\delta_o^2+O(\delta_o^4)\]
Monoclinic distortion
\[\begin{split}D_m(\delta_m) + I = \left[\begin{matrix}
1&\delta_m&0\\
\delta_m&1&0\\
0&0&\frac{1}{(1-\delta_m^2)}\\
\end{matrix}\right]\end{split}\]
leads to energy change
\[\Delta E(\delta_m) = 2Vc_{44}\delta_m^2+O(\delta_m^4)\]
\[B=\frac{1}{3}(c_{11}+2c_{12})\]
\[c'=\frac{1}{2}(c_{11}-c_{12})\]
Isochoric stain
volume not changed: SWS not changed.
only even order of \(\delta\).
Orthorhombic distortion apply to fcc: face center orthorhombic (fco).
Monoclinic distortion apply to fcc: body center orthorhombic (bco).
Note
All files for this exercise are in the path exercise/03
fco lattice in emto
\(\delta=0.00\)
The input file (kstr/fco0.dat)
1KSTR HP......=N 22 Jan 08
2JOBNAM...=fco0 MSGL.= 0 MODE...=B STORE..=Y HIGH...=Y
3DIR001=smx/
4DIR006=./
5Slope matrices, fco (spdf) DeltaE/V = (C11-C12)*e^2+O[e^4] (e=0.00)
6NL.....= 4 NLH...=11 NLW...= 9 NDER..= 6 ITRANS= 3 NPRN..= 0
7(K*W)^2..= 0.000000 DMAX....= 1.6000 RWATS...= 0.10
8NQ3...= 1 LAT...=11 IPRIM.= 1 NGHBP.=13 NQR2..= 0
9A........= 1.0000000 B.......= 1.0000000 C.......= 1.0000000
10ALPHA....= 90.d0 BETA....= 90.d0 GAMMA...= 90.d0
11QX(.1)...= 0.0000000 QY......= 0.0000000 QZ......= 0.0000000
12a/w(.2)..= 0.70 0.70 0.70 0.70
13LAMDA....= 2.5000 AMAX....= 4.5000 BMAX....= 4.5000
In the output file (kstr/fco0.prn)
PRIMV: Default choice of primitive vectors.
A = 1.000000 B = 1.000000 C = 1.000000
ALPHA = 90.000000 BETA = 90.000000 GAMMA = 90.000000
Primitive vectors for Fco lattice in
units of the lattice spacing a:
( 0.50000, 0.00000, 0.50000 )
( 0.50000, 0.50000, 0.00000 )
( 0.00000, 0.50000, 0.50000 )
Basis vectors: NQ3 = 1
( 0.00000, 0.00000, 0.00000 )
\(\delta=0.05\)
The input file (kstr/fco5.dat)
1KSTR HP......=N 22 Jan 08
2JOBNAM...=fco5 MSGL.= 0 MODE...=B STORE..=Y HIGH...=Y
3DIR001=smx/
4DIR006=./
5Slope matrices, fco (spdf) DeltaE/V = (C11-C12)*e^2+O[e^4] (e=0.05)
6NL.....= 4 NLH...=11 NLW...= 9 NDER..= 6 ITRANS= 3 NPRN..= 0
7(K*W)^2..= 0.000000 DMAX....= 1.6000 RWATS...= 0.10
8NQ3...= 1 LAT...=11 IPRIM.= 1 NGHBP.=13 NQR2..= 0
9A........= 1.0000000 B.......=0.90476190 C.......=0.95476786
10ALPHA....= 90.d0 BETA....= 90.d0 GAMMA...= 90.d0
11QX(.1)...= 0.0000000 QY......= 0.0000000 QZ......= 0.0000000
12a/w(.2)..= 0.70 0.70 0.70 0.70
13LAMDA....= 2.5000 AMAX....= 4.5000 BMAX....= 4.5000
In the output file (kstr/fco5.prn)
PRIMV: Default choice of primitive vectors.
A = 1.000000 B = 0.904762 C = 0.954768
ALPHA = 90.000000 BETA = 90.000000 GAMMA = 90.000000
Primitive vectors for Fco lattice in
units of the lattice spacing a:
( 0.50000, 0.00000, 0.47738 )
( 0.50000, 0.45238, 0.00000 )
( 0.00000, 0.45238, 0.47738 )
Basis vectors: NQ3 = 1
( 0.00000, 0.00000, 0.00000 )
bco lattice in emto
\(\delta=0.00\)
The input file (kstr/bco0.dat)
1KSTR HP......=N 22 Jan 08
2JOBNAM...=bco0 MSGL.= 0 MODE...=B STORE..=Y HIGH...=Y
3DIR001=smx/
4DIR006=./
5Slope matrices, bco (spdf) DeltaE/V = 2C44e^2+O[e^4] (e=0.00)
6NL.....= 4 NLH...=11 NLW...= 9 NDER..= 6 ITRANS= 3 NPRN..= 0
7(K*W)^2..= 0.000000 DMAX....= 2.4000 RWATS...= 0.10
8NQ3...= 1 LAT...=10 IPRIM.= 1 NGHBP.=13 NQR2..= 0
9A........= 1.0000000 B.......= 1.0000000 C.......=1.41421356
10ALPHA....= 90.d0 BETA....= 90.d0 GAMMA...= 90.d0
11QX(IQ)...= 0.0000000 QY......= 0.0000000 QZ......= 0.0000000
12a/w(IQ)..= 0.70 0.70 0.70 0.70
13LAMDA....= 2.5000 AMAX....= 4.5000 BMAX....= 4.5000
In the output file (kstr/bco0.prn)
PRIMV: Default choice of primitive vectors.
A = 1.000000 B = 1.000000 C = 1.414214
ALPHA = 90.000000 BETA = 90.000000 GAMMA = 90.000000
Primitive vectors for Bco lattice in
units of the lattice spacing a:
( 0.50000, -0.50000, 0.70711 )
( 0.50000, 0.50000, -0.70711 )
( -0.50000, 0.50000, 0.70711 )
Basis vectors: NQ3 = 1
( 0.00000, 0.00000, 0.00000 )
\(\delta=0.05\)
The input file (kstr/bco5.dat)
1KSTR HP......=N 22 Jan 08
2JOBNAM...=bco5 MSGL.= 0 MODE...=B STORE..=Y HIGH...=Y
3DIR001=smx/
4DIR006=./
5Slope matrices, bco (spdf) DeltaE/V = 2C44e^2+O[e^4] (e=0.05)
6NL.....= 4 NLH...=11 NLW...= 9 NDER..= 6 ITRANS= 3 NPRN..= 0
7(K*W)^2..= 0.000000 DMAX....= 2.2000 RWATS...= 0.10
8NQ3...= 1 LAT...=10 IPRIM.= 1 NGHBP.=13 NQR2..= 0
9A........= 1.0000000 B.......=0.90476190 C.......=1.35024566
10ALPHA....= 90.d0 BETA....= 90.d0 GAMMA...= 90.d0
11QX(IQ)...= 0.0000000 QY......= 0.0000000 QZ......= 0.0000000
12a/w(IQ)..= 0.70 0.70 0.70 0.70
13LAMDA....= 2.5000 AMAX....= 4.5000 BMAX....= 4.5000
In the output file (kstr/bco5.prn)
PRIMV: Default choice of primitive vectors.
A = 1.000000 B = 0.904762 C = 1.350246
ALPHA = 90.000000 BETA = 90.000000 GAMMA = 90.000000
Primitive vectors for Bco lattice in
units of the lattice spacing a:
( 0.50000, -0.45238, 0.67512 )
( 0.50000, 0.45238, -0.67512 )
( -0.50000, 0.45238, 0.67512 )
Basis vectors: NQ3 = 1
( 0.00000, 0.00000, 0.00000 )
kgrn inputs
--- /home/runner/work/emto-best-practices/emto-best-practices/content/exercise/solutions/00/kgrn/cu.dat
+++ /home/runner/work/emto-best-practices/emto-best-practices/content/exercise/solutions/03/kgrn/cuf5.dat
@@ -1,25 +1,25 @@
KGRN 13 Oct 12
-JOBNAM=cu
+JOBNAM=cuf5
STRT..= A MSGL.= 0 EXPAN.= S FCD..= Y FUNC..= SCA
-FOR001=../kstr/smx/fcc.tfh
-FOR001=../kstr/smx/fcc30.tfh
+FOR001=../kstr/smx/fco5.tfh
+FOR001=../kstr/smx/fco510.tfh
DIR002=pot/
DIR003=pot/
-FOR004=../bmdl/mdl/fcc.mdl
+FOR004=../bmdl/mdl/fco5.mdl
DIR006=
DIR009=pot/
DIR010=chd/
DIR011=/tmp/
-Self-consistent KKR calculation for fcc Cu
+Self-consistent KKR calculation for fcc Cu, (C11-C12)/2
Band: 10 lines
NITER.= 50 NLIN.= 31 NPRN.= 0 NCPA.= 7 NT...= 1 MNTA.= 1
MODE..= 3D FRC..= N DOS..= N OPS..= N AFM..= P CRT..= M
Lmaxh.= 8 Lmaxt= 4 NFI..= 31 FIXG.= 2 SHF..= 0 SOFC.= N
-KMSH...= G IBZ..= 2 NKX..= 0 NKY..= 13 NKZ..= 0 FBZ..= N
+KMSH...= G IBZ..= 11 NKX..= 27 NKY..= 27 NKZ..= 27 FBZ..= N
KMSH2..= G IBZ2.= 1 NKX2.= 4 NKY2.= 0 NKZ2.= 51
ZMSH...= C NZ1..= 16 NZ2..= 8 NZ3..= 8 NRES.= 4 NZD.=1500
DEPTH..= 1.000 IMAGZ.= 0.020 EPS...= 0.200 ELIM..= -1.000
-AMIX...= 0.100 EFMIX.= 1.000 VMTZ..= 0.000 MMOM..= 0.000
+AMIX...= 0.050 EFMIX.= 1.000 VMTZ..= 0.000 MMOM..= 0.000
TOLE...= 1.d-07 TOLEF.= 1.d-07 TOLCPA= 1.d-06 TFERMI= 500.0 (K)
SWS......=2.686842 NSWS.= 1 DSWS..= 0.05 ALPCPA= 0.6020
Setup: 2 + NQ*NS lines
--- /home/runner/work/emto-best-practices/emto-best-practices/content/exercise/solutions/00/kgrn/cu.dat
+++ /home/runner/work/emto-best-practices/emto-best-practices/content/exercise/solutions/03/kgrn/cuo5.dat
@@ -1,25 +1,25 @@
KGRN 13 Oct 12
-JOBNAM=cu
+JOBNAM=cuo5
STRT..= A MSGL.= 0 EXPAN.= S FCD..= Y FUNC..= SCA
-FOR001=../kstr/smx/fcc.tfh
-FOR001=../kstr/smx/fcc30.tfh
+FOR001=../kstr/smx/bco5.tfh
+FOR001=../kstr/smx/bco510.tfh
DIR002=pot/
DIR003=pot/
-FOR004=../bmdl/mdl/fcc.mdl
+FOR004=../bmdl/mdl/bco5.mdl
DIR006=
DIR009=pot/
DIR010=chd/
DIR011=/tmp/
-Self-consistent KKR calculation for fcc Cu
+Self-consistent KKR calculation for fcc Cu, C44
Band: 10 lines
NITER.= 50 NLIN.= 31 NPRN.= 0 NCPA.= 7 NT...= 1 MNTA.= 1
MODE..= 3D FRC..= N DOS..= N OPS..= N AFM..= P CRT..= M
Lmaxh.= 8 Lmaxt= 4 NFI..= 31 FIXG.= 2 SHF..= 0 SOFC.= N
-KMSH...= G IBZ..= 2 NKX..= 0 NKY..= 13 NKZ..= 0 FBZ..= N
+KMSH...= G IBZ..= 10 NKX..= 27 NKY..= 27 NKZ..= 37 FBZ..= N
KMSH2..= G IBZ2.= 1 NKX2.= 4 NKY2.= 0 NKZ2.= 51
ZMSH...= C NZ1..= 16 NZ2..= 8 NZ3..= 8 NRES.= 4 NZD.=1500
DEPTH..= 1.000 IMAGZ.= 0.020 EPS...= 0.200 ELIM..= -1.000
-AMIX...= 0.100 EFMIX.= 1.000 VMTZ..= 0.000 MMOM..= 0.000
+AMIX...= 0.050 EFMIX.= 1.000 VMTZ..= 0.000 MMOM..= 0.000
TOLE...= 1.d-07 TOLEF.= 1.d-07 TOLCPA= 1.d-06 TFERMI= 500.0 (K)
SWS......=2.686842 NSWS.= 1 DSWS..= 0.05 ALPCPA= 0.6020
Setup: 2 + NQ*NS lines
kfcd inputs
--- /home/runner/work/emto-best-practices/emto-best-practices/content/exercise/solutions/00/kfcd/cu.dat
+++ /home/runner/work/emto-best-practices/emto-best-practices/content/exercise/solutions/03/kfcd/cuf5.dat
@@ -1,6 +1,6 @@
-KFCD MSGL..= 1 22 Jan 08
-JOBNAM...=cu
-STRNAM...=fcc
+KFCD MSGL..= 0 22 Jan 08
+JOBNAM...=cuf5
+STRNAM...=fco5
DIR001=../kstr/smx/
DIR002=../kgrn/chd/
DIR003=../shape/shp/
--- /home/runner/work/emto-best-practices/emto-best-practices/content/exercise/solutions/00/kfcd/cu.dat
+++ /home/runner/work/emto-best-practices/emto-best-practices/content/exercise/solutions/03/kfcd/cuo5.dat
@@ -1,6 +1,6 @@
-KFCD MSGL..= 1 22 Jan 08
-JOBNAM...=cu
-STRNAM...=fcc
+KFCD MSGL..= 0 22 Jan 08
+JOBNAM...=cuo5
+STRNAM...=bco5
DIR001=../kstr/smx/
DIR002=../kgrn/chd/
DIR003=../shape/shp/
run the exercise03
submit all kstr, bmdl and shape jobs to the queue, use following sbatch script.
cd kstr
sbatch -A naiss2024-22-241 -c 1 -a 1-12 -t 10:00 ../../emto.sbatch
cd kstr
sbatch -A xxxx -c 1 -a 1-12 -p lrd_all_serial -t 10:00 ../../emto.sbatch
submit all kgrn jobs to the queue, use following sbatch script.
cd kgrn
sbatch -A naiss2024-22-241 -c 8 -a 1-12 -t 10:00 ../../emto.sbatch
cd kgrn
sbatch -A xxxx -c 8 -a 1-12 -p lrd_all_serial -t 10:00 ../../emto.sbatch
check if the kgrn jobs are finished correctly.
Hint
cd kgrn grep -L "finished" *.prn
submit all kfcd jobs to the queue, use following sbatch script.
cd kfcd
sbatch -A naiss2024-22-241 -c 1 -a 1-12 -t 10:00 ../../emto.sbatch
cd kfcd
sbatch -A xxxx -c 1 -a 1-12 -p lrd_all_serial -t 10:00 ../../emto.sbatch
extract the results
In kfcd folder
grep TOT-PBE cuo?.prn | awk '{if(NR==1)e0=$5;printf "%s %.6f %.6f\n" $1,NR*NR*0.0001,$5-e0}'
fit \(\delta_o^2\) vs. \(\Delta E\) with the 2nd and 3th column to get \(c'\).
grep TOT-PBE cuf?.prn | awk '{if(NR==1)e0=$5;printf "%s %.6f %.6f\n" $1,NR*NR*0.0001,$5-e0}'
fit \(\delta_m^2\) vs. \(\Delta E\) with the 2nd and 3th column to get \(c_{44}\).
