A Package for calculating elastic tensors of rhombohedral Phases by using second-order derivative with Wien2k Package

Transcription

1 IR ELAST + WIEN2k A Package for calculating elastic tensors of rhombohedral Phases by using second-order derivative with Wien2k Package User s guide, Rhom-elastic_13.1 (Release ) Morteza Jamal Ghods City-Tehran-Iran 1

2 MANDATORY CONDITIONS: In any publication in the scientific literature please reference the program as follows: M. Jamal, Rhom-elastic, (2013). ACKNOWLEDGMENT I gratefully appreciate B.Z. Yanchitsky for fruitful discussions, P. Blaha and S. Jalali Asadabadi for suggestions, and Carol Phillips for editing. For suggestions or bug reports please contact the author by m_jamal57@yahoo.com 2

3 1- Introduction Rhom-elastic is a Package for finding elastic constants of rhombohedral symmetries with Wien2k. This Package calculates elastic constants by second-order derivative ( E (δ) ) of Polynomial fit ( E=E(δ) ) of Energy vs. strains (δ) at zero strain (δ =0). This called energy approach[1]. 2- Background theory (energy approach) Elastic constants are defined by means of a Taylor expansion of the total energy for the system, with respect to a small strain ( ) of the lattice. If we consider the bravais lattice vectors of a rhombohedral crystal structure as a matrix form the distortion of the lattice ( ) is expressed by mul tiplying with a symmetric ( ) distortion matrix i.e. ( ), which is written as, And in Voigt notation ( It is often convenient to change to the Voigt notation in order to reduce the number of indices. The Voigt notation replaces 1, 2, 3, (and ) 4, (and ) 5, (and ) 6 ) 3

4 We express the energy of the strained system by means of a Taylor expansion in the distortion parameters, The linear terms vanish if the strain causes no changes in the volume of the crystal. Otherwise, are related to the strain on the crystal and are elastic constants and is the volume of unstrained rhombohedral system and we use it to evaluate the elastic constants. There are seven ( six) independent elastic constants for a rhombohedral (symmetry group number between 149 and 167) symmetry, called C 11, C 12, C 13, C 14, C 15 ( C 15 =0), C 33, and C 44. Since we have seven independent elastic constants, we need seven different strains to determine these elastic constants. For simplicity in writing the equations used in the rhom-elastic Package, it is convenient to rewrite the above equation as : Which τ represents a linear combination of strain components and C, a linear combination of elastic constants. Therefore the seven distortions used in the rhom-elastic Package are described as following: 1), 2), 3), 4), 4

5 5), 6), 7), 5

6 3- File structure and program flow The following table describes input and output files for each program of the Rhom-elastic Package. Program needs generates R_set_elast_lapw case.struct init.struct runcommand1 runcommand2 pwdname command_init_lapw R_command_run_lapw R_setupc11, R_setupc12 R_setupc13, R_setupc14 R_setupc33,. getcalljobr makestructr init.struct pwdname runcommand1 runcommand2 init.struct.styp RHOM.job auto_init_lapw runcommand1 runcommand2.vper.styp RHOM.job number.strain StypX_Y.struct vol.optimize R_modifyjob_lapw R_calljob_lapw RHOM.job VstVene R_fitdivELC number.strain ELCorder.fit vol.optimize ELC.output.styp ELC.fit VstVene R_ana_elastc_lapw VstVene case.outputeos ELC.fit vol.optimize ELC.ps R_ana_elast_lapw ELC.output ELC-matrix case.output_elastic R_InverseELC ELC-matrix INVELC-matrix MassRho init.struct.rho vol.optimize R_ana_elastorder_lapw ELCorder.fit output-order sgroupcheck_lapw StypX_Y.struct case.struct command_intso_lapw.infso command_initu_lapw.infldau auto_initso_lapw.infso case.inso auto_initu_lapw.infldau case.inorb case.indm/c Bold font is OPTIONAL Italic bold font means it is the user s choice 6

7 3-1- Short description for input and output files case.struct init.struct pwdname runcommand1/2 Is a Wien2k standard struct file. Is a copy of the case.struct file. Contains the name of the present work directory. Contains the run commands for running. It looks similar to: run_lapw ec p in1new 2 auto_init_lapw A C-shell program which automatically runs the initialization. It looks similar to:.vper.styp RHOM.job #!/bin/csh -f set RM = not if ( $RM == 'not' ) then init_lapw -vxc 13 -ecut -6 -mix 0.2 -numk b else init_lapw -red 0 -vxc 13 -ecut -6 -mix 0.2 -numk b endif Defines the percent of changes for different strains. Defines the type of strain. A C-shell program which calculates the energy for each strain by using the Wien2k Package. It looks similar to: #!/bin/csh -f #STRAIN TYPE IS 1 #Modify this script according to your needs unalias rm set co = 1 set name set bj set file = `pwd` set file = $file:t if (-e VstVene ) then set i=`/bin/ls VstVene* wc ` echo " saving pervious VstVene to VstVene_$i[1]" cp VstVene VstVene_$i[1] rm VstVene endif # # to reuse previous scf runs (without a new scf run) set answscf=y # and use the same "savename". # When you make modifications (RKmax, k-mesh, XC-potentials) choose # answscf=no and a new savename (eg. "_pbe_rk8_1000k"). set answscf=y set savename= 7

8 if (-e cscl.clmsum && \! -z cscl.clmsum) then x dstart -super endif if (-e cscl.clmup && \! -z cscl.clmup ) then x dstart -super -up x dstart -super -dn endif foreach i ( \ ) echo "*******************************" echo $i set name=`echo "$name $i"` echo "*******************************" Styp1_-3.0 \ Styp1_-2.0 \ Styp1_-1.0 \ Styp1 0.0 \ Styp1 1.0 \ Styp1 2.0 \ Styp1 3.0 \ StypX_Y.struct VstVene number.strain case.outputeos A Wien2k struct file for each value of changes and for each strain type where X and Y denote type of strain and value of changes, respectively. The main information file, contains values of changes (strains) and energies for each type of strain, for the calculation of the elastic constant. Contains the number of strains. A Wien2k output of equation of states(eos). For finding the best values of elastic constants, find EOS and then copy the case.outputeos file in the "case" directory within the c11, c12, c13, c14, c15, and directories. Otherwise, it sets the optimized volume from the original struct file i.e. case.struct vol.optimize Contains the optimized volume. ELCorder.fit Contains the elastic constants for different values of order of fit. ELC.output Contains the elastic constants for order of fit =2 ELC.fit Contains the data to plot a curve of energy vs value of changes (strains) for each strain type. ELC-matrix Defines the elastic constant matrix for each symmetry. case.output_elastic Contains the final elastic constant values. INVELC-matrix Defines the inverse of elastic constant matrix. 8

9 .rho.infso.infldau Contains density of mass and atomic volume. Contains information for making the case.inso file for running spin-orbit coupling. Contains information for making the case.inorb and case.indm/c files for LDA+U calculations Flow and short description for programs The Rhom-elastic Package consists of several FORTRAN and SHELL SCRIPTS which are described below. A flowchart of the program is shown in the following diagram. R_set_elast_lapw : Makes an elast-constant directory in the present work directory ( PWD ) and c11, c12, c13, c14, c15, c33, and c44 directories in the elast-constant directory. The R_set_elast_lapw program also copies information of the "PWD" into the c11, c12, c13, c14, c15, c33, and c44 directories and calls "command_init_lapw", R_command_run_lapw, R_setupc11, R_setupc12, R_setupc13, R_setupc14, R_setupc15, R_setupc33, and R_setupc44 programs.. command_init_lapw : Gets information for making "auto_init_lapw". R_command_run_lapw : Gets the run commands for making RHOM.job. R_setupcX (X=11, 12, 13,.) : Gets the type of strain and calls the getcalljobr program. getcalljobr : Calls makestructr program and makes the RHOM.job file. makestructr : Makes the StypX_Y.struct files where X and Y stand for the type of strain and value of changes, respectively and the vol.optimize file. R_modifyjob_lapw : Edits the job files according to the user s needs. R_calljob_lapw : Calls the RHOM.job files for running. 9

10 R_ana_elast_lapw : Calls the R_ana_elastc_lapw program for calculating elastic constants then calculates the Voigt, Reuss, and Hill bulk, shear, and the Young modulus as well as the Poisson ratio. After that it calls the R_InverseELC and MassRho programs and calculates sound velocity and Debye temperature then makes two output files in the elastconstant directory with the name case.output_elastic and the INVELC-matrix which is the Elastic compliance constants generated by inverting the elastic constant matrix. At the end it calls R_ana_elastorder_lapw program. R_ana_elastc_lapw : Calls the R_fitdivELC program with appropriate libraries for calculating C11, C12, C13, and. R_InverseELC : Makes the Elastic compliance constants generated by inverting the elastic constant matrix. MassRho : Finds density of mass and atomic volume. R_ana_elastorder_lapw : Checks the sensitivity of the elastic constants to the order of fit. sgroupcheck_lapw : Finds the best value of tol in the sgroup[2] program and copies case.struct_sgroup as case.struct. 10

11 R_set_elast_lapw command_init_lapw generates auto_init_lapw R_command_run_lapw generates commandrun1/2 R_setupcX X=11, 12,. getcalljobr generates RHOM.job makestructr generates StypX_Y.struct sgroupcheck_lapw RHOM.job generates VstVene auto_init_lapw R_ana_elastorder_lapw generates ELCorder.fit R_ana_elast_lapw R_ana_elastc_lapw R_InverseELC MassRho ELASTIC CONSTANTS IS READY generates case.output_elastic and INVELC-matrix Program flow in Rhom-elastic 11 R_fitdivELC calls Libraries generates C 11, C 11 +C 12,. Dash arrow means user must run

12 4 Elastic constants calculation 1. Create a struct file and validate it by running "sgroupcheck_lapw". 2. If Spin-Orbit calculations are required run "command_initso_lapw. 3. If LDA+U calculations are required run "command_initu_lapw" and then "auto_initu_lapw". 4. Run "R_set_elast_lapw.. 5. Now you must adapt the job files according to your needs (you can run "R_modifyjob_lapw" in Terminal ). It is not necessary to do step 5 if you defined the COMMAND RUN commands in step Now you must run the job files (you can run "R_calljob_lapw" ). It will take some time. 7. Run "R_ana_elast_lapw".. This package calculates elastic constants by second-order derivative ( E (δ) ) of Polynomial fit ( E=E(δ) ) of Energy vs. strains ( є) at zero strain (δ =0) so, you must use values of strain around zero and from the viewpoint of fit convergence, we usually expect to see a minimum when we plot Energy vs. strain ( this Package plots it ). It is recommended that the sensitivity of the results is checked to the order of fit. This program shows them. 4-1 Notes about elastic constants calculation After using distortions for the calculation of C44, C14, and the symmetry of the rhombohedral compound changes and usually the number of atoms change. So when you run "command_initso_lapw" or "command_initu_lapw", in the section name of an atom, type "all <name of atom>" ( for example: all Mn). With this command, you use SO or LDA+U calculations for example for all Mn atoms. When you want to rerun job files with modifications in (RKmax, k-mesh, XC-potentials ) call the command_init_lapw and after that choose "answscf=no" in the RHOM.job files and a new "savename" (eg. "_use_pbe_rk8"). 12

13 Optionally you can specify more cases by rerunning R_setupcX (X=11, 12, 13, 14, 44, see section 4-3 ). Specify also your old cases. The old results will then be taken automatically into account without recalculation (unless you modify job files i.e: set answscf=no ). For the calculation of the best values of elastic constants, please find EOS and then copy case.outputeos in the "case" directory within the c11, c12, c13, and directories. Otherwise, it sets the optimized volume from the original struct file i.e. case.struct. 4-2 One calculation To calculate C 33 or C 44 calculation of C 44 : the following steps should be performed for example for 1. Make a directory for example c Make a "case" directory in c44 directory. 3. Make a "case.struct" file in the "case" directory and name it "init.struct". Create a "pwdname" file and write in it "case." and save it. 4. Run the command_init_lapw 5. chmod +x auto_init_lapw 6. For SO calculations, run the command_initso_lapw. 7. For LDA+U calculations, run the command_initu_lapw and auto_initu_lapw To avoid step 10, you can run R_command_run_lapw for setting the COMMAND RUN commands for making RHOM.job. 8. Run the R_setupc44 program. 9. chmod +x RHOM.job file. 10. Modify the RHOM.job file. 11. Call RHOM.job 12. Call R_ana_elastc_lapw 4-3 Run with more data points Optionally you can specify more data points, for the calculation of the elastic constants, by rerunning R_setupcX (X=11, 12, 13, ). Specify also your old data points. The old results will then be taken automatically into account without recalculation ( unless you modify the job files i.e: set answscf=no ). Please do the following steps for this goal for example for c Cd to the elast-constant directory. 2. Cd to the c44 directory. 3. cd the case directory. 3-1) To avoid step 6, you can run R_command_run_lapw for setting the COMMAND RUN commands for making the RHOM.job. 13

14 4. Run the R_setupc44 program. 5. If you want to rerun the job files with modifications in (RKmax, k-mesh, XCpotentials ) call command_init_lapw and then choose "answscf=no" in RHOM.job files and a new "savename" (eg. "_use_pbe_rk8"). 6. Modify the RHOM.job file. 7. Call RHOM.job 8. Call R_ana_elastc_lapw 4-4 Elastic constants calculation for Al2O3 Al2O3 compound is a test case for elastic constants calculation. The Al2O3 structure is described in detail in the following: Al2O3 R LATTICE,NONEQUIV.ATOMS: 2167_R-3c MODE OF CALC=RELA unit=bohr ATOM 1: X= Y= Z= MULT= 4 ISPLIT= 4 ATOM 1:X= Y= Z= ATOM 1:X= Y= Z= ATOM 1:X= Y= Z= Al1 NPT= 781 R0= RMT= Z: 13.0 LOCAL ROT MATRIX: ATOM 2: X= Y= Z= MULT= 6 ISPLIT= 8 ATOM 2:X= Y= Z= ATOM 2:X= Y= Z= ATOM 2:X= Y= Z= ATOM 2:X= Y= Z= ATOM 2:X= Y= Z= O 1 NPT= 781 R0= RMT= Z: 8.0 LOCAL ROT MATRIX: NUMBER OF SYMMETRY OPERATIONS Select Xc = PBE-GGA, R_Kmax = 7, L_max = 8, and nkpoint = 600 In the following examples you can find the percents that were used for strains. 14

15 ####################################### # R_ana_elast_lapw analyses Elastic # # constant # # C(2013) by Morteza Jamal # ####################################### ########################################## # R_ana_elastc_lapw analyses Elastic # # constant # # C(2013) by Morteza Jamal # # using case.outputeos # # VstVene # # which have been created by # # RHOM.job # ########################################## =============================================================== Order of fit: 2 C11 is: GPa, RMS: E-04 Order of fit: 3 C11 is: GPa, RMS: E-04 Order of fit: 4 C11 is: GPa, RMS: E-12 ****************************************** Polynomial fit for C11 done A RMS of E-04 was achieved using a polynome of degree : 2 At volume= bohr^3 C11 is: a.u or GPa ****************************************** Analyze done... Do you want a hardcopy? (y/n) *************************************** You can find data in ELC.output file. *************************************** ########################################## # R_ana_elastc_lapw analyses Elastic # # constant # # C(2013) by Morteza Jamal # # using case.outputeos # # VstVene # # which have been created by # # RHOM.job # ########################################## =============================================================== Order of fit: 2 C11+C12 is: GPa, RMS: E-04 Order of fit: 3 C11+C12 is: GPa, RMS: E-05 Order of fit: 4 C11+C12 is: GPa, RMS: E-12 ****************************************** 15

16 Polynomial fit for C11+C12 done A RMS of E-04 was achieved using a polynome of degree : 2 At volume= bohr^3 C11+C12 is: a.u or GPa ****************************************** Analyze done... Do you want a hardcopy? (y/n) *************************************** You can find data in ELC.output file. *************************************** ########################################## # R_ana_elastc_lapw analyses Elastic # # constant # # C(2013) by Morteza Jamal # # using case.outputeos # # VstVene # # which have been created by # # RHOM.job # ########################################## =============================================================== Order of fit: 2 C11+C33+2C13 is: GPa, RMS: E-03 Order of fit: 3 C11+C33+2C13 is: GPa, RMS: E-04 Order of fit: 4 C11+C33+2C13 is: GPa, RMS: E-12 ****************************************** Polynomial fit for C11+C33+2C13 done A RMS of E-03 was achieved using a polynome of degree : 2 At volume= bohr^3 C11+C33+2C13 is: a.u or GPa ****************************************** Analyze done... Do you want a hardcopy? (y/n) *************************************** You can find data in ELC.output file. *************************************** ########################################## # R_ana_elastc_lapw analyses Elastic # # constant # # C(2013) by Morteza Jamal # # using case.outputeos # # VstVene # # which have been created by # # RHOM.job # ##########################################

17 =============================================================== Order of fit: 2 C11+4C44+4C14 is: GPa, RMS: E-04 Order of fit: 3 C11+4C44+4C14 is: GPa, RMS: E-04 Order of fit: 4 C11+4C44+4C14 is: GPa, RMS: E-12 ****************************************** Polynomial fit for C11+4C44+4C14 done A RMS of E-04 was achieved using a polynome of degree : 2 At volume= bohr^3 C11+4C44+4C14 is: a.u or GPa ****************************************** Analyze done... Do you want a hardcopy? (y/n) *************************************** You can find data in ELC.output file. *************************************** ########################################## # R_ana_elastc_lapw analyses Elastic # # constant # # C(2013) by Morteza Jamal # # using case.outputeos # # VstVene # # which have been created by # # RHOM.job # ########################################## =============================================================== Order of fit: 2 C33 is: GPa, RMS: E-04 Order of fit: 3 C33 is: GPa, RMS: E-04 Order of fit: 4 C33 is: GPa, RMS: E-12 ****************************************** Polynomial fit for C33 done A RMS of E-04 was achieved using a polynome of degree : 2 At volume= bohr^3 C33 is: a.u or GPa ****************************************** Analyze done... Do you want a hardcopy? (y/n) *************************************** You can find data in ELC.output file. *************************************** 17

18 ########################################## # R_ana_elastc_lapw analyses Elastic # # constant # # C(2013) by Morteza Jamal # # using case.outputeos # # VstVene # # which have been created by # # RHOM.job # ########################################## =============================================================== Order of fit: 2 C44 is: GPa, RMS: E-04 Order of fit: 3 C44 is: GPa, RMS: E-04 Order of fit: 4 C44 is: GPa, RMS: E-12 ****************************************** Polynomial fit for C44 done A RMS of E-04 was achieved using a polynome of degree : 2 At volume= bohr^3 C44 is: a.u or GPa ****************************************** Analyze done... Do you want a hardcopy? (y/n) *************************************** You can find data in ELC.output file. *************************************** Printing final Elastic constant At voulme= bohr^3. ======================================================================= C11 = GPa C11+C12 = GPa C33 = GPa C44 = GPa C11+4C44+4C14 = GPa C15 = 0 GPa C11+C33+2C13 = GPa ======================================================================= LU decomposition successful Inverse Successful You can find Inverse Matrix in INVELC-matrix file Done ======================================================================= Atom name = Al Atomic Mass from Periodic table = (gr/mol) Atomic Mass from Periodic table = *10^(-23) (gr) Atom name = O Atomic Mass from Periodic table = (gr/mol) Atomic Mass from Periodic table = *10^(-23) (gr) Volume in unit of cm^3 = *10^(-24) (cm^3) Mass of Compound : *10^(-23) (gr) Density of Compound : (gr/cm^3) 18

19 ======================================================================= C11 = GPa C12 = GPa C13 = GPa C33 = GPa C44 = GPa C14 = GPa C15 = 0 GPa Prediction VOIGT Bulk modulus by using elastic constant values Prediction REUSS Bulk modulus by using elastic constant values Prediction HILL Bulk modulus by using elastic constant values = (GPa) = (GPa) = (GPa) Prediction VOIGT Shear modulus by using elastic constant values = (GPa) Prediction REUSS Shear modulus by using elastic constant values = (GPa) Prediction HILL Shear modulus by using elastic constant values = (GPa) Prediction VOIGT Young modulus by using elastic constant values = (GPa) Prediction REUSS Young modulus by using elastic constant values = (GPa) Prediction HILL Young modulus by using elastic constant values = (GPa) Prediction VOIGT Poisson's coefficient by using elastic constant values =.223 Prediction REUSS Poisson's coefficient by using elastic constant values =.226 Prediction HILL Poisson's coefficient by using elastic constant values =.224 ======================================================================= By using HILL data Transverse elastic wave velocity = (m/s) Longitudinal elastic wave velocity = (m/s) The average wave velocity = (m/s) Debye Temperature = (K) ======================================================================= Press enter key to continue... ################################################ # R_ana_elastorder_lapw checks the sensitivity # # of elastic constants to the order of fit # # by using ELCorder.fit file # # C(2013) by Morteza Jamal # # # ################################################ CHECK THE SENSITIVITY OF YOUR RESULT TO THE ORDER OF FIT Press enter key to continue... Order of fit for calculations were 4,4,4,4, 4, and 4 We select minimum value for ORDER OF FIT i.e. 4 Press enter key to continue... ######## ORDER OF FIT IS : 2, At volume = (bohr^3) ######## (c11) = (GPa) (c11+c12) = (GPa) (c33) = (GPa) (c44) = (GPa) (c11+c33+2c13) = (GPa) (c11+4c44+4c14)= (GPa) (c15)= 0 (GPa) 19

20 c11 = (GPa) c12 = (GPa) c13 = (GPa) c33 = (GPa) c14 = (GPa) c44 = (GPa) c15 = 0 (GPa) ======================================================================= Prediction VOIGT Bulk modulus by using elastic constant values = (GPa) Prediction REUSS Bulk modulus by using elastic constant values = (GPa) Prediction HILL Bulk modulus by using elastic constant values = (GPa) Prediction VOIGT Shear modulus by using elastic constant values = (GPa) Prediction REUSS Shear modulus by using elastic constant values = (GPa) Prediction HILL Shear modulus by using elastic constant values = (GPa) Prediction VOIGT Young modulus by using elastic constant values = (GPa) Prediction REUSS Young modulus by using elastic constant values = (GPa) Prediction HILL Young modulus by using elastic constant values = (GPa) Prediction VOIGT Poisson's coefficient by using elastic constant values =.223 Prediction REUSS Poisson's coefficient by using elastic constant values =.226 Prediction HILL Poisson's coefficient by using elastic constant values =.224 ======================================================================= ######## ORDER OF FIT IS : 3, At volume = (bohr^3) ######## (c11) = (GPa) (c11+c12) = (GPa) (c33) = (GPa) (c44) = (GPa) (c11+c33+2c13) = (GPa) (c11+4c44+4c14)= (GPa) (c15)= 0 (GPa) c11 = (GPa) c12 = (GPa) c13 = (GPa) c33 = (GPa) c14 = (GPa) c44 = (GPa) c15 = 0 (GPa) ======================================================================= Prediction VOIGT Bulk modulus by using elastic constant values = (GPa) Prediction REUSS Bulk modulus by using elastic constant values = (GPa) Prediction HILL Bulk modulus by using elastic constant values = (GPa) Prediction VOIGT Shear modulus by using elastic constant values = (GPa) Prediction REUSS Shear modulus by using elastic constant values = (GPa) Prediction HILL Shear modulus by using elastic constant values = (GPa) Prediction VOIGT Young modulus by using elastic constant values = (GPa) Prediction REUSS Young modulus by using elastic constant values = (GPa) Prediction HILL Young modulus by using elastic constant values = (GPa) Prediction VOIGT Poisson's coefficient by using elastic constant values =.223 Prediction REUSS Poisson's coefficient by using elastic constant values =.226 Prediction HILL Poisson's coefficient by using elastic constant values =

21 ======================================================================= ######## ORDER OF FIT IS : 4, At volume = (bohr^3) ######## (c11) = (GPa) (c11+c12) = (GPa) (c33) = (GPa) (c44) = (GPa) (c11+c33+2c13) = (GPa) (c11+4c44+4c14)= (GPa) (c15)= 0 (GPa) c11 = (GPa) c12 = (GPa) c13 = (GPa) c33 = (GPa) c14 = (GPa) c44 = (GPa) c15 = 0 (GPa) ======================================================================= Prediction VOIGT Bulk modulus by using elastic constant values = (GPa) Prediction REUSS Bulk modulus by using elastic constant values = (GPa) Prediction HILL Bulk modulus by using elastic constant values = (GPa) Prediction VOIGT Shear modulus by using elastic constant values = (GPa) Prediction REUSS Shear modulus by using elastic constant values = (GPa) Prediction HILL Shear modulus by using elastic constant values = (GPa) Prediction VOIGT Young modulus by using elastic constant values = (GPa) Prediction REUSS Young modulus by using elastic constant values = (GPa) Prediction HILL Young modulus by using elastic constant values = (GPa) Prediction VOIGT Poisson's coefficient by using elastic constant values =.188 Prediction REUSS Poisson's coefficient by using elastic constant values =.201 Prediction HILL Poisson's coefficient by using elastic constant values =.195 ======================================================================= You can find these data in the output-order file. c11 = (GPa) c12 = (GPa) c13 = (GPa) c33 = (GPa) c14 = -2.4 (GPa) c44 = (GPa) c15 = 0.0 (GPa) 21

22 Al2O3(unrelax) Al2O3 (relax) Exp 3 Method FPLAPW FPLAPW Exchange PBE PBE C C C C C C C C66= (C11-C12)/2 22

23 5 Installation of the Rhom-elastic package The Rhom-elastic package comes as a compressed tar file namely Rhom-elastic.tar.gz. To install the package firstly copy the file to a directory of your choice. Now, uncompress and expand it as: tar zxvf Rhom-elastic.tar.gz cd Rhom-elastic Run buildrirelast_lapw This program helps you to create the "Makefile" and then compile Rhom-elastic. By default, the Makefile expects the lapack_lapw and blas_lapw to be in the location../src_lib. This should be changed to the correct location by modifying the FOPT parameter as shown below. This Program helps you to define Fortran compiler, Fortran options, and Library options if you have installed WIEN2k. As you can see here this program defines Fortran compiler, Fortran options, and Library options as automatically. Otherwise you can define compiler and linker options as well as the path of mkl library depending on the your selected system. /home/mylib/mkl/lib/em64t is the path of my mkl library. To make Makefile by the lapack_lapw and blas_lapw libraries in the location../src_lib and gfortran use the following options: Fortran compiler: gfortran Fortran options: -ffree-form Library options (Lapack and BLAS): $(FOPT) L/home/physicsprogram/SRC_lib lpthread static llapack_lapw lblas_lapw the location../src_lib should be changed to the correct location by modifying the FOPT parameter as shown above. PS: To install with -ffree-form, you should compile the lapack_lapw and blas_lapw libraries with -ffree-form options. Otherwise it might was caused error. 23

24 If you view the OPTIONS file of the WIEN2k package you can use the FOPT, LDFLAGS, and R_LIBS of it for compiling. After defining the Fortran compiler, Fortran options, and Library options press Enter key. 24

25 25

26 The Environment Variable ELASTR_PATH is then defined and added to the end of the.bashrc file. Thus you will be able to call Rhom-elastic s programs for any location. 26

27 If you view the.bashrc file you can see Now, logout from your Linux system and then login. 27

28 6 References [1] R. Stadler, W. Wolf, R. Podloucky, G. Kresse, J. Furthmller, J. Hafner, Phys. Rev. B 54 (1996) [2] B. Z. Yanchitsky, A. N. Timoshevskii, Determination of the space group and unit cell for a periodic solid, Comp. Phys. Comm. 139 (2001) [3] C. J. Smithells, E. A. Brandes, F. R. Institute., Smithells metals reference book, Vol. 8, Butterworth-Heinemann,