exercise/04: Mixing enthalpy for bcc FeCrx alloy: FM

In this exercise we will practice how to get Mixing enthalpy of bcc \(Fe_{ (1-x) }Cr_x\) alloy with EMTO.

\[H = E_{Fe_{(1-x)}Cr_x} - ( 1-x )E_{Fe_{bcc}} - x E_{Cr_{bcc}}\]

The reference states are chosen as FM Fe and NM Cr, both in bcc structure. [1]
For each \(Fe_{ (1-x) }Cr_x\), we need its equilibrium volume and correspond energy.

alloy setup with CPA in kgrn

create an input files for \(Fe_{50}Cr_{50}\)

we could copy the kgrn input from exercise00 and make some changes.

JOBNAM=fecr_FM
FOR001=../kstr/smx/bcc.tfh, FOR004=../bmdl/mdl/bcc.mdl and IBZ..= 3
MNTA.= 2
AFM..= F
SOFC.= Y
AMIX...= 0.010

Symb   IQ IT ITA NZ  CONC   Sm(s)  S(ws) WS(wst) QTR SPLT Fix
Fe      1  1  1  26  50.00  1.000  1.000  1.000  0.0  2.0  N
Cr      1  1  2  24  50.00  1.000  1.000  1.000  0.0 -1.0  N

Fe
Iz=  26 Norb= 10 Ion=  0 Config= 3d7_4s1
n      1  2  2  2  3  3  3  3  3  4
Kappa -1 -1  1 -2 -1  1 -2  2 -3 -1
Occup  2  2  2  4  2  2  4  4  3  1
Valen  0  0  0  0  0  0  0  1  1  1
Cr
Iz=  24 Norb=  9 Ion=  0 Config= 3d4_4s2
n      1  2  2  2  3  3  3  3  4
Kappa -1 -1  1 -2 -1  1 -2  2 -1
Occup  2  2  2  4  2  2  4  4  2
Valen  0  0  0  0  0  0  0  1  1

Hint

--- /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/04/kgrn/fecr_FM.dat
@@ -1,21 +1,21 @@
 KGRN                                               13 Oct 12
-JOBNAM=cu 
+JOBNAM=fecr_FM
 STRT..=  A MSGL.=  0 EXPAN.= S FCD..=  Y FUNC..= SCA
-FOR001=../kstr/smx/fcc.tfh
-FOR001=../kstr/smx/fcc30.tfh
+FOR001=../kstr/smx/bcc.tfh
+FOR001=../kstr/smx/bcc30.tfh
 DIR002=pot/
 DIR003=pot/
-FOR004=../bmdl/mdl/fcc.mdl
+FOR004=../bmdl/mdl/bcc.mdl
 DIR006=
 DIR009=pot/
 DIR010=chd/
 DIR011=/tmp/
-Self-consistent KKR calculation for fcc Cu
+Self-consistent KKR calculation for bcc FeCrX
 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
+NITER.= 50 NLIN.= 31 NPRN.=  0 NCPA.=  7 NT...=  1 MNTA.=  2
+MODE..= 3D FRC..=  N DOS..=  N OPS..=  N AFM..=  F CRT..=  M
+Lmaxh.=  8 Lmaxt=  4 NFI..= 31 FIXG.=  2 SHF..=  0 SOFC.=  Y
+KMSH...= G IBZ..=  3 NKX..=  0 NKY..= 13 NKZ..=  0 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
@@ -25,15 +25,22 @@
 Setup: 2 + NQ*NS lines
 EFGS...=  0.000 HX....=  0.100 NX...=  5 NZ0..=  6 STMP..= N
 Symb   IQ IT ITA NZ  CONC   Sm(s)  S(ws) WS(wst) QTR SPLT Fix
-Cu      1  1  1  29  1.000  1.000  1.000  1.000  0.0  0.0  N
+Fe      1  1  1  26  50.00  0.000  1.000  1.000  0.0  2.0  N
+Cr      1  1  2  24  50.00  0.000  1.000  1.000  0.0 -1.0  N
 Atom:  4 lines + NT*NTA*6 lines
 IEX...=  4 NP..= 251 NES..= 15 NITER=100 IWAT.=  0 NPRNA=  0
 VMIX.....=  0.300000 RWAT....=  3.500000 RMAX....= 20.000000
 DX.......=  0.030000 DR1.....=  0.002000 TEST....=  1.00E-12
 TESTE....=  1.00E-12 TESTY...=  1.00E-12 TESTV...=  1.00E-12
-Cu
-Iz=  29 Norb= 10 Ion=  0 Config= 3d10_4s1
+Fe
+Iz=  26 Norb= 10 Ion=  0 Config= 3d7_4s1
 n      1  2  2  2  3  3  3  3  3  4
 Kappa -1 -1  1 -2 -1  1 -2  2 -3 -1
-Occup  2  2  2  4  2  2  4  4  6  1
+Occup  2  2  2  4  2  2  4  4  3  1
 Valen  0  0  0  0  0  0  0  1  1  1
+Cr
+Iz=  24 Norb=  9 Ion=  0 Config= 3d4_4s2
+n      1  2  2  2  3  3  3  3  4
+Kappa -1 -1  1 -2 -1  1 -2  2 -1
+Occup  2  2  2  4  2  2  4  4  2
+Valen  0  0  0  0  0  0  0  1  1

kstr, bmdl, shape and kfcd input files

Hint

The input file (kstr/bcc.dat)

KSTR      HP......=N                               22 Jan 08
JOBNAM...=bcc        MSGL.=  1 MODE...=B STORE..=Y HIGH...=Y
DIR001=smx/
DIR006=
Slope matrices, bcc (spdf), (kappa*w)^2= 0.0
NL.....= 4 NLH...=11 NLW...= 9 NDER..= 6 ITRANS= 3 NPRN..= 0
(K*W)^2..=  0.000000 DMAX....=    2.2000 RWATS...=      0.10
NQ3...=  1 LAT...= 3 IPRIM.= 0 NGHBP.=13 NQR2..= 0
A........= 1.0000000 B.......= 1.0000000 C.......= 1.0000000
BSX......= 0.5000000 BSY.....= 0.5000000 BSZ.....=-0.5000000
BSX......= 0.5000000 BSY.....=-0.5000000 BSZ.....= 0.5000000
BSX......=-0.5000000 BSY.....= 0.5000000 BSZ.....= 0.5000000
QX.......= 0.0000000 QY......= 0.0000000 QZ......= 0.0000000
a/w......= 0.70 0.70 0.70 0.70
LAMDA....=    2.5000 AMAX....=    4.5000 BMAX....=    4.5000

The input file (bmdl/bcc.dat)

BMDL      HP......=N                               22 Jan 08
JOBNAM...=bcc        MSGL.=  1 NPRN.=  0
DIR001=mdl/
DIR006=
Madelung potential for bcc bulk 
NL.....= 7
LAMDA....=      2.50 AMAX....=      4.50 BMAX....=      4.50
NQ....=  1 LAT...= 3 IPRIM.= 1 NQR2..= 0
A........=     1.000 B.......=     1.000 C.......=     1.000
ALFA.....=      90.0 BETA....=      90.0 GAMMA...=      90.0
QX(1)....=       0.0 QY(1)...=       0.0 QZ(1)...=       0.0

run all calculations

tree
  .
├── bmdl
│   ├── bcc.dat
│   └── mdl
├── kfcd
│   └── fecr_FM.dat
├── kgrn
│   ├── chd
│   ├── fecr_FM.dat
│   └── pot
├── kstr
│   ├── bcc.dat
│   └── smx
└── shape
    ├── bcc.dat
    └── shp

11 directories, 5 files

check NOS from kgrn/fecr_FM.prn

grep -H NOS *.prn
fecr_FM.prn: KKRFCD: NOS(Ef) =      7.000025 ELT =      7.000000
fecr_FM.prn: KKRFCD: NOS(Ef) =      7.000025 ELT =      7.000000

Hint

increase NCPA to make sure cpa loop converged

sed -i 's/NCPA.=  7/NCPA.= 17/' fecr_FM.dat

create input files with different volumes for each \(Fe_{(1-x)}Cr_x\)

#! /bin/bash
# generate kgrn and kfcd input files based on kgrn/fecr_FM.dat
for i in `seq 0 2 10`  `seq 30 20 90` 100
do
  cr=$(printf "%03d" $i)
  fe=$(printf "%03d" $((100-i)))
  folder=FM/FeCr$cr
  mkdir -p $folder/{kgrn,kfcd}

  ln -s $(pwd)/kstr  $folder/kstr
  ln -s $(pwd)/bmdl  $folder/bmdl
  ln -s $(pwd)/shape $folder/shape

  for sws in `seq 2.59 0.02 2.69`
  do
        # -e "s/NCPA.=.../NCPA.= 17/"  \
        # -e "s/NKY..=.../NKY..= 21/" \
    sed -e "s/JOBNAM=.*/JOBNAM=fecr-$sws/" \
        -e "28 s/ 50.00/$fe.00/"  \
        -e "29 s/ 50.00/$cr.00/"  \
        -e "s/SWS......=......../SWS......=${sws}0000/" \
        kgrn/fecr_FM.dat > $folder/kgrn/fecr-$sws.dat

    sed -e "s/JOBNAM...=.*/JOBNAM...=fecr-$sws/" \
        kfcd/fecr_FM.dat > $folder/kfcd/fecr-$sws.dat
  done
done

get equilibrium state for each concentration.
```
Eos.sh FeCr* > eos
cat eos
```