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![Impurity problem
n Green’s function of the host
n Consider the scattering when one host atom is
replaced by an impurity.
€
˜G = g0 1− thost g0[ ]
−1
€
G = ˜G 1− (timpurity − thost ) ˜G[ ]
−1](https://image.slidesharecdn.com/akaikkr-handson-2-140815051743-phpapp02/85/5-CCMS-AkaiKKR-2-AkaiKKR-23-320.jpg)
![CPA
n Coherent t-matrix satisfy the following relation.
€
˜G = g0 1− ˜tg0[ ]
−1
GA(B)
= ˜G 1− (tA(B) − ˜t) ˜G[ ]
−1
cGA
+ (1− c)GB
= ˜G
c× + (1-c)× =](https://image.slidesharecdn.com/akaikkr-handson-2-140815051743-phpapp02/85/5-CCMS-AkaiKKR-2-AkaiKKR-25-320.jpg)
Uploaded byComputational Materials Science Initiative
第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 2. AkaiKKRの実習
This document contains input parameters for performing a band structure calculation using the KKR method on bcc iron. Key parameters include: - The structure is body centered cubic (bcc) iron with a lattice constant of 5.27 bohr - Non-relativistic and magnetic calculations will be performed - Band energies will be calculated along high symmetry points in the Brillouin zone
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第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 2. AkaiKKRの実習
- 1.
- 2. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile
- 3. #----------------------Fe------------------------------------ go data/fe #------------------------------------------------------------ # brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , #------------------------------------------------------------ # edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd #------------------------------------------------------------ # outtyp bzqlty maxitr pmix update 4 50 0.023 #------------------------------------------------------------ # ntyp 1 #------------------------------------------------------------ # type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 #------------------------------------------------------------ # natm 1 #------------------------------------------------------------ # atmicx atmtyp 0 0 0 Fe #------------------------------------------------------------ Inputfile
- 4. go data/fe bcc 5.27 , , , , , , 0.001 1.0 nrl mjw mag 2nd update 4 50 0.023 1 Fe 1 1 0.0 2 26 100 1 0 0 0 Fe Inputfile
- 5. go data/fe bcc 5.27,,,,,,0.001 1.0 nrl mjw mag 2nd update 4 50 0.023 1 Fe 1 1 0.0 2 26 100 1 0 0 0 Fe Inputfile
- 6. It actually is system standard input. Therefore, input directly to the prompt (actually a null character) would be enough. > specx (or ./specx, run specx, etc.) go data/fe bcc 5.27,,,,,, 0.001 1.0 nrl mjw mag 2nd update 4 50 0.023 1 Fe 1 1 0.0 2 26 100 1 0 0 0 Fe (calculation start) ... Ctl-d > Inputfile
- 7. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile go : Perform a band structure calculation dos : Calculate a density of states
- 8. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile fcc, bcc, hcp, sc, bct, st, etc. See the manual for details.
- 9.
- 10. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile Atomic unit Length : 1 bohr = 0.529 Å Energy : 1 Ry = 13.6 eV
- 11. core state valence state DOS E energycontour C ewidth edelt Im E Re E Atomic unit Length : 1 bohr = 0.529 Å Energy : 1 Ry = 13.6 eV
- 12. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile nrl : non-relativistic sra : relativistic
- 13. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile mjw, vbh, vwn, gga91, etc.
- 14. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile mag : magnetic nmag : non-magnetic
- 15. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile init : make new potential data 2nd : use the latest data 1st : use the second latest data
- 16. c----------------------Fe------------------------------------ go data/fe c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma bcc 5.27 , , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Fe 1 1 0.0 2 26 100 c------------------------------------------------------------ c natm 1 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Fe c------------------------------------------------------------ Inputfile update : save the potential data quit : do not save the data
- 17. Optimize the latticeconstant -2522.8185 -2522.8180 -2522.8175 -2522.8170 -2522.8165 -2522.8160 totalenergy(Ry) 5.405.355.305.255.20 lattice constant (bohr)
- 18. Optimize the latticeconstant -2522.8185 -2522.8180 -2522.8175 -2522.8170 -2522.8165 -2522.8160 totalenergy(Ry) 5.405.355.305.255.20 lattice constant (bohr) a=5.334 -2522.8185 -2522.8180 -2522.8175 -2522.8170 -2522.8165 -2522.8160 totalenergy(Ry) 5.405.355.305.255.20 lattice constant (bohr)
- 19.
- 20. c----------------------Co------------------------------------ go data/co c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma hcp 4.74 , 1.6215 , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Co 1 1 0.0 2 27 100 c------------------------------------------------------------ c natm 2 c------------------------------------------------------------ c atmicx atmtyp 0a 0b 0c Co 1/3a 2/3b 1/2c Co c------------------------------------------------------------ Inputfile(Co)
- 21. c----------------------Co------------------------------------ go data/co c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma hcp 4.74 , 1.6215 , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Co 1 1 0.0 2 27 100 c------------------------------------------------------------ c natm 2 c------------------------------------------------------------ c atmicx atmtyp 0x 0y 0z Co 1/2x 0.86602y 1/2z Co c------------------------------------------------------------ Inputfile(Co)
- 22. c----------------------Co------------------------------------ go data/co c------------------------------------------------------------ c brvtyp a c/a b/a alpha beta gamma hcp 4.74 , 1.6215 , , , , , c------------------------------------------------------------ c edelt ewidth reltyp sdftyp magtyp record 0.001 1.0 nrl mjw mag 2nd c------------------------------------------------------------ c outtyp bzqlty maxitr pmix update 4 50 0.023 c------------------------------------------------------------ c ntyp 1 c------------------------------------------------------------ c type ncmp rmt field mxl anclr conc Co 1 1 0.0 2 27 100 c------------------------------------------------------------ c natm 2 c------------------------------------------------------------ c atmicx atmtyp 0 0 0 Co 0.5 0.86602 0.81075 Co c------------------------------------------------------------ Inputfile(Co)
- 23. Impurity problem n Green’sfunction of the host n Consider the scattering when one host atom is replaced by an impurity. € ˜G = g0 1− thost g0[ ] −1 € G = ˜G 1− (timpurity − thost ) ˜G[ ] −1
- 24. CPA (coherent potentialapproximation) n Consider the t-matrix of the imaginary atom which describes configuration average of a substitutional random alloy (coherent t-matrix). tA tB t ~
- 25. CPA n Coherent t-matrixsatisfy the following relation. € ˜G = g0 1− ˜tg0[ ] −1 GA(B) = ˜G 1− (tA(B) − ˜t) ˜G[ ] −1 cGA + (1− c)GB = ˜G c× + (1-c)× =
- 26. NiFe alloy (fcc) n Replace Ni atoms by Fe atoms. Ni Fe
- 27. NiFe alloy (fcc) Fe0%Fe20% Fe40% Fe60% Fe80% Fe100%
- 28. Theor. Exp. Slater-Pauling curve n Alloysof transition metals, such as Fe, Co and Ni. n The magnetic moments are on the common curve. n Calculation reproduces the experimentally observed behaviors including the branches. H. Akai, Hyperfine Interactions 68 (1991) 3 H.P.J. Wijn, Magnetic Properties of Metals (1991)
- 29. Transition metal impuritiesin Fe n 3d n 4d n 5d n local moment (parallel or antiparallel ?) Sc Ti V Cr Mn Fe Co Ni Cu Zn 21 22 23 24 25 26 27 28 29 30 Y Zr Nb Mo Tc Ru Rh Pd Ag Cd 39 40 41 42 43 44 45 46 47 48 Lu Hf Ta W Re Os Ir Pt Au Hg 71 72 73 74 75 76 77 78 79 80
- 30. Transition metal impuritiesin Fe H. Akai et al, Prog. Theor. Phys. Suppl. 101 (1990) 11.
- 31. Transition metal impuritiesin Fe Fe V Ni < <
- 32. Curie temperature offerromagnets n Ferromagnetic state n The magnetic moments align to the same direction.
- 33. Curie temperature offerromagnets n Paramagnetic state n The directions of the moments are random. n Atoms with up and down moments align randomly. (local moment disorder)
- 34. copy copy fmg n fe.fmg ../data/fe 1 ../data/fe_lmd 1 -1 data/fe potential data for spin up potential data for spin down Potential data file of bcc Fe data/fe_lmd potential data for spin up potential data for spin down New potential data file potential data for spin up potential data for spin down copy copy
- 35. Curie temperature ofFe € TC = 2 3 ELMD − EFerro( )/kBMean field approximation Experimental value： ~ 1000 K Ferromagnetic LMD 1 Ry = 13.6 eV, kB = 8.617 * 10-5 (eV/K)
- 36. Reference etc. n Reference n 計算機ナノマテリアルデザイン入門（笠井秀明・赤井久 純・吉田博編 大阪大学出版会） n W.Kohn and N. Rostoker, Phys. Rev. 94 (1954) 1111. n F.S. Ham and B. Segall, Phys. Rev. 124 (1961) 1786. n H. Akai, J. Phys. Soc. Japan 51 (1982) 468. n H. Akai, J. Phys.: Cond. Matter 1 (1989) 8045. n KKR package http://kkr.phys.sci.osaka-u.ac.jp/