FME Modelling course 2011 Tutorial 1 ( )

Transcription

1 FME Modelling course 2011 Tutorial 1 ( ) Brief introduction to LMTO: To obtain the state, φ nlm (r), of an ELECTRON -and hence its charge density ρ(r) = φ nlm (r) 2 - we must solve Schrödinger's equation in the potential from the protons in the nucleus and all other electrons in the atomic shells. For an atom, this potential is spherical, and so it is approximately spherical in a solid, except between the atoms. A Muffin-tin (MT)-potential is spherically symmetric inside non-overlapping spheres surrounding the atoms and constant in between. In the interstitial region, a linear muffin-tin orbital (LMTO) is a spherical harmonics times the appropriate spherical Hankel or Neumann function, regular at infinity and with a fixed wavenumber k 0. In the TB-LMTO program, input is the crystal structure Output s are: the charge- and spin-selfconsistent band structure, the partial densities of states, the Fermi surface, plots of the full charge and spin-densities, the total energy, and the partial pressures. The executables for the TB-LMTO program are: (explained in following sections, for more details, refer to the manual. 1. lminit 2. lmhart 3. lmovl 4. lmes 5. lmctl 6. lmstr 7. lm 8. lmbnd

2 Task 1: Calculating total energy Calculations are done using TB-LMTO program. There are two main input files: (i) The INIT file contains crystal structure details (ii) CTRL file contains basis-set informations and other control parameters to run the calculation. Crystal system: Cubic Space group: Fd-3m (227) Lattice parameter = Å Si = (0 0 0)

3 Part 1: Preparing INIT file: 1. Run lminit 2. Give space group No.; Choice of origin is asked give 1 3. (symmetry operators are written) 4. Units for Lattice parameter is asked; give F 5. Now enter lattice parameter FCC lattice vectors are written 7. Give label/atomic number of atom Type Si 8. Give position As there is only one type of atom, type q to quit. 10. Type ls to check the files generated; There are three files : CTRL, INIT, and CBAK. INIT file has the details that we have supplied. The CTRL file contains more structural information (Point group generators, atoms in inequivalent positions etc). Refer to the file (LMTO_manual.pdf) for more details on tokens used in CTRL file. Part 2: Generating basis-set information: 1. Run lmhart (to find size of atomic spheres (& MT-sphere radii) 2. Mv out hart.out 3. Edit CTRL file; insert the token SCALE SCLWSR=T 4. Run lmovl (to check overlap between Wigner-Seitz spheres) 5. Mv out ovl.out

4 Output of lmovl: Lattice info Symmetry y info Check VOLSPH/VOL ratio Volume of cell and volume of atomic spheres should match. 1. Run lmes to insert interstitial (empty) spheres 2. Mv out es.out. Edit es.out to see empty spheres

5 Output of lmes: Check VOLSPH/VOL ratio 1. Edit the current CTRL file 2. Change VERBOSE=50, to insert more control parameters in CTRL file 3. Edit CTRL. More info on basis-set, parameters are inserted (refer the manual for explanation on tokens) Number of iterations Mixing parameter Convergence criterion Brillouin-zone sampling

6 4. Reduce again VERBOSE= 30 in CTRL file 5. Run lmstr ( to calculate TB real space structure constants) 6. Run lm (self-consistent-field calculation) 7. Mvout lmout First iteration: Check output file: lmout After convergence is reached Note: Total energy in Rydberg units

7 Optimization of k-point set to calculate properties The k-point set for which total energy stabilizes (eg. 145k ) can be selected Task 2: Calculating electronic structure After scf is reached, ed, electronic ec c band Structure can be calculated 1. mkdir band 2. mp CTRL file to band 3. Run lm (to prepare STR & other POT files 4. Run lmbnd 5. Output file BNDS is created 6. Run gnubnd Enter output device: Give 1 (postscript) Give title (of plot, eg. Si bnd) energies t (ev) energies relative to EF t landscape plot t connected by lines t Show E_nus t plot orbital character f enter emin, emax= select energy range First Brillouin i zone of fcc lattice

8 Three new files are created: BNDS.DAT can be visualized in Xmgrace and BNDS.GNU in gnuplot. For that Run gnuplot Load BNDS.GNU & quit A file (bnds.ps) is created; to visualize the file Run gv bnds.ps To oanalyze ay eband-structure: ds u The individual orbitals contributing to the bands can be highlighted. Edit CTRL file: Change FATBAND = T

9 After editing CTRL file: 1. Run lm 2. Run lmbnd 3. Two new files (BNDS & EIGN) are generated 4. Run gnubnd 5. Proceed as earlier until 6. plot orbital character: type t 7. Change coordinate system? Type f 8. Select atom classes: in our case: Si 9. Two Si atoms are there (equivalent) 1 / 10. Each orbital is given a code number ( eg. s = 1; p_y=2; p_z=3, p_x = 4 etc.) 11. For plotting Si-p_x orbital, give 4 / 12. Enter emin, emax (eg: ) 13. Change scale factor scaling of fat bands give values greater than 1.0 (e.g 1.2 /) 14. Edit the resulting BNDS.GNU file make the last line plot into a single line (command shift j in vim editor); save and quit. 15. Run gnuplot load BNDS.GNU as earlier 16. gv bnds.ps Si p x orbital

10 Exercise 1.1: 1. Analyze electronic structure of Si (Direct or indirect band-gap; type of orbitals at valence band maximum and conduction band minimum etc) 2. Plot band structure without inserting empty spheres compare with that of empty spheres Exercise 1.2: 1. Calculate total energy 2. Plot and analyze band structure of GaAs Crystal system: Cubic Space group: F -4 3 m (216) Lattice parameter = Å Volume = Å 3 Ga = (0 0 0) As = ( ) Exercise 1.3: 1. Calculate total energy of Cu in FFC structure 2. Plot and analyze band structure of Cu 3. Assume Cu in BCC structure (space group: Im-3m (no: 229), Alat = same as in FCC 4. Calculate total-energy and find which structure is energetically favorable 5. Compare band structure of BCC-Cu with that of FCC-Cu. Crystal system: Face-centered Cubic Space group: F m -3m (225) Lattice parameter = Å Volume = 47.16Å 3 Cu = (0 0 0) First Brillouin zone of BCC