Tutorial =============== Metal-organic framework MIL-53(Al) [3D material] ----------------------------------------------------- The stiffness matrix (coefficients in GPa) is input (Cij.dat) .. math:: \mathbf{C_{ij}} = \begin{pmatrix} \ C_{11} & \ C_{12} & \ C_{13} & \ C_{14} & \ C_{15} & \ C_{16} \\ \ C_{21} & \ C_{22} & \ C_{23} & \ C_{24} & \ C_{25} & \ C_{26} \\ \ C_{31} & \ C_{32} & \ C_{33} & \ C_{34} & \ C_{35} & \ C_{36} \\ \ C_{41} & \ C_{42} & \ C_{43} & \ C_{44} & \ C_{45} & \ C_{46} \\ \ C_{51} & \ C_{52} & \ C_{53} & \ C_{54} & \ C_{55} & \ C_{56} \\ \ C_{61} & \ C_{62} & \ C_{63} & \ C_{64} & \ C_{65} & \ C_{66} \\ \end{pmatrix}= \begin{pmatrix} \ 90.85 & \ 20.41 & \ 54.28 & \ 0 & \ 0 & \ 0 \\ \ 20.41 & \ 65.56 & \ 12.36 & \ 0 & \ 0 & \ 0 \\ \ 54.28 & \ 12.36 & \ 33.33 & \ 0 & \ 0 & \ 0 \\ \ 0 & \ 0 & \ 0 & \ 7.24 & \ 0 & \ 0 \\ \ 0 & \ 0 & \ 0 & \ 0 & \ 39.52 & \ 0 \\ \ 0 & \ 0 & \ 0 & \ 0 & \ 0 & \ 8.27 \\ \end{pmatrix}. :: Run: ElaTools.x :: > Select system dimension: ======================= 3D => 3 2D => 2 ======================== 3 The compound is a 3D system, so we have to choose the number 3. :: > Select using output code: ============================================================ IRelast-----------------------( wein2k )-=> 1 Elast-------------------------( wein2k )-=> 2 AELAS-------------------------( VASP )-=> 3 ElaStic-----------------------( QE,Wien2k,Exciting )-=> 4 Using Cij Tensor in Cij.dat---( Other codes )-=> 5 Using EC Databank-------------( MP )-=> 6 ============================================================ 5 We use Cij.dat file. So we choose the number 5: Initial output data: :: ######################################################################### Cij: 90.850000 20.410000 54.280000 0.000000 0.000000 0.000000 20.410000 65.560000 12.360000 0.000000 0.000000 0.000000 54.280000 12.360000 33.330000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 7.240000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 39.520000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 8.270000 Sij: 0.4081110 -0.0018805 -0.6639371 0.0000000 0.0000000 0.0000000 -0.0018805 0.0164084 -0.0030224 0.0000000 0.0000000 0.0000000 -0.6639371 -0.0030224 1.1123872 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.1381216 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0253036 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.1209190 ######################################################################### ========================================================== Elastic properties | Voigt Reuss Average ========================================================== = Bulk modulus (GPa) | 40.427 5.019 22.723 = = Shear modulus (GPa) | 17.852 1.550 9.701 = = Young modulus (GPa) | 46.684 4.217 25.450 = = P-wave modulus(GPa) | 64.2293 7.0864 35.6579 = = Poisson ratio | 0.3075 0.4811 0.3943 = <--( Ductile regime ) = Pugh ratio | 2.2645 3.2379 2.3423 = <--( Brittle regime ) ========================================================== > Universal anisotropy index (AU) : 59.6328 > Log-Euclidean anisotropy parameter (AL): 13.1795 > Chung-Buessem Anisotropy Index (Ac) : 0.8402 > Cauchy pressure(GPa) (Pc) : 83.6100 <--( Metallic-like bonding ) ---------------------------------------------------------- This data is stored in the **DATA.out** file. We need another input to continue the `EAlTools.x`, :: > Select the (m k l) index for 2D cut: 1 1 0 We select (1 1 0) palne Then, the other output data listed in **DATA.out** file are as follows: :: ==================================================> Youngs Modulus Max(GPa) Min(GPa) 94.71 0.90 ------------------------------------------ Theta Phi Theta Phi 2.23 6.28 3.14 0.00 ------------------------------------------ x y z x y z 0.79 -0.00 -0.61 0.00 0.00 -1.00 ================================================== ==================================================> Linear Compressibiliy Max(TPa-1) Min(TPa-1) 445.428 -257.707 ------------------------------------------ Theta Phi Theta Phi 3.14 0.00 1.57 6.28 ------------------------------------------ x y z x y z 0.00 0.00 -1.00 1.00 -0.00 0.00 ================================================== ==================================================> Shear Modulus Max(GPa) Min(GPa) 39.52 0.35 ------------------------------------------ Theta Phi Theta Phi 3.14 0.00 2.36 6.28 ------------------------------------------ x y z x y z 0.00 0.00 -1.00 0.71 -0.00 -0.71 ================================================== ==================================================> Bulk Modulus Max(GPa) Min(GPa) 3647.02 -95238.29 ------------------------------------------ Theta Phi Theta Phi 1.85 2.01 0.93 6.13 ------------------------------------------ x y z x y z -0.41 0.87 -0.28 0.79 -0.13 0.60 ================================================== ==================================================> Poissons Ratio Max Min 2.977 -2.400 ------------------------------------------ Theta Phi Theta Phi 1.57 4.21 1.92 4.71 ------------------------------------------ x y z x y z -0.48 -0.88 0.00 -0.00 -0.94 -0.34 ================================================== ==================================================> Pugh Ratio Max Min 3.22 -10.18 ------------------------------------------ Theta Phi Theta Phi 3.14 0.00 1.57 6.28 ------------------------------------------ x y z x y z 0.00 0.00 -1.00 1.00 -0.00 0.00 ================================================== ==================================================> Sound Transverse high Longitudinal Transverse low 49.82 33.33 0.35 ================================================== > NOTE :The above information is stored in 'DATA.out' file. #==================================# .. note:: Sound and Pugh Ratio are being tested! In the following: :: > Do you want to plot data? (Y/N): If you select **N**, the name.dat files will be saved in the **DataFile** folder. If you select **Y**, the ploting process is activated and Figures are saved in the **PicFils** folder. We select `Y`: **Some temporary Figs.:** .. image:: Images/5.png :width: 250 .. image:: Images/3.png :width: 250 .. image:: Images/4.png :width: 250 .. image:: Images/6.png :width: 350 .. image:: Images/7.png :width: 350 It is better to use **dat2wrl_lapw**, **dat2gnu_lapw** and **dat2agr_lapw** to draw more advanced 2d and 3D Figs.. For example, 3D representation of Linear Compressibiliy and Poissons Ratio by :: $ dat2wrl_lapw com $ dat2wrl_lapw poi outpot files: Poissons.wrl and Compressibiliy.wrl, And using View3dscene , we will see it. .. image:: Images/8.png :width: 300 .. image:: Images/9.png :width: 300 2D representation of Poisson’s ratio and Linear Compressibiliy in the (1 1 0 ) plane, :: $ dat2gnu_lapw poi > Using: go to gnuplot, call 'poissons.gpi' '0.2' '0.6' (or other scale) $ dat2gnu_lapw com > Using: go to gnuplot, call 'compressibiliy.gpi' '25' '120' (or other scale) **Resalt:** poissons.ps and compressibiliy.ps .. image:: Images/10.png :width: 350 .. image:: Images/11.png :width: 350 Gallium Thiophosphate-GaPS4 [2D material] ------------------------------------------ The stiffness matrix (coefficients in N/m) is input (Cij-2D.dat) .. math:: \mathbf{C_{ij}} = \begin{pmatrix} \ C_{11} & \ C_{12} & \ C_{16} \\ \ C_{12} & \ C_{22} & \ C_{26} \\ \ C_{61} & \ C_{62} & \ C_{66} \\ \end{pmatrix}= \begin{pmatrix} \ 4.45 & \ 3.63 & \ 0.00 \\ \ 3.63 & \ 19.22 & \ 0.00 \\ \ 0.00 & \ 0.00 & \ 4.71 \\ \end{pmatrix}. :: Run: EalTools.x :: > Select system dimension: ======================= 3D => 3 2D => 2 ======================== 2 The compound is a 2D system, so we have to choose the number 2. :: > Select using output code: ================================================== Using Cij Tensor in Cij.dat (other codes) => 3 ================================================== 3 We use Cij-2D.dat file. So we choose the number 3: Initial output data: :: ######################################## Cij: 4.450000 3.630000 0.000000 3.630000 19.220000 0.000000 0.000000 0.000000 4.710000 Sij: 0.265645 -0.050171 0.000000 -0.050171 0.061505 0.000000 0.000000 0.000000 0.212314 ######################################## ================================================ Elastic properties ================================================ = Young modulus [Ex] (N/m) 3.764 = = Young modulus [Ey] (N/m) 16.259 = = Shaer modulus [Gxy] (N/m) 4.710 = = Shaer modulus [Gv] (N/m) 4.406 = = Shaer modulus [Gr] (N/m) 3.126 = = Area modulus [Kv] (N/m) 7.732 = = Area modulus [Kr] (N/m) 4.409 = = Poisson ratio [vxy] 0.189 = = Poisson ratio [vyx] 0.816 = ================================================================== = Elastic anisotropy index (A_SU): 0.579 = = Ranganathan Elastic anisotropy index (A_SU): 1.573 = = Kube Elastic anisotropy index (A_SU): 0.322 = ================================================================== > Preparing data. please wait... ==================================================> Youngs Modulus Maximum value of Youngs Modulus = 3.4599 Phi= 99.0000 degree MINimum value of Youngs Modulus = 0.7992 Phi= 0.0000 degree ================================================== ==================================================> Poissons Ratio Maximum value of Poissons Ratio = 0.6860 Phi= 90.0000 degree Minimum value of Poissons Ratio = -0.0391 Phi= 46.8000 degree ==================================================> In the following: :: > Do you want to prepare the data for ploting? (Y/N): If you select **N**, the name.dat files will be saved in the **DataFile** folder. If you select **Y**, the ploting process is activated and Figures are saved in the **PicFils** folder. We select `Y`: resalts Figs.: **2D_sys_Poissons.ps** and **2D_sys_Young.ps**. .. image:: Images/12.png :width: 350 .. image:: Images/13.png :width: 350 Using :: $ dat2gnu_lapw D2 > Using: go to gnuplot, call '2Dpoissons.gpi' '0.2' '0.6' (or other scale) > Using: go to gnuplot, call '2Dyoung.gpi' '50' '100' (or other scale) , you can also draw better charts. .. image:: Images/14.png :width: 350 .. image:: Images/15.png :width: 350 Gallium arsenide [3D material] ------------------------------- The stiffness matrix (coefficients in GPa) is input (Cij.dat) .. math:: \mathbf{C_{ij}} = \begin{pmatrix} \ C_{11} & \ C_{12} & \ C_{13} & \ C_{14} & \ C_{15} & \ C_{16} \\ \ C_{21} & \ C_{22} & \ C_{23} & \ C_{24} & \ C_{25} & \ C_{26} \\ \ C_{31} & \ C_{32} & \ C_{33} & \ C_{34} & \ C_{35} & \ C_{36} \\ \ C_{41} & \ C_{42} & \ C_{43} & \ C_{44} & \ C_{45} & \ C_{46} \\ \ C_{51} & \ C_{52} & \ C_{53} & \ C_{54} & \ C_{55} & \ C_{56} \\ \ C_{61} & \ C_{62} & \ C_{63} & \ C_{64} & \ C_{65} & \ C_{66} \\ \end{pmatrix}= \begin{pmatrix} \ 118.8 & \ 3.80 & \ 13.80 & \ 0 & \ 0 & \ 0 \\ \ 3.80 & \ 118.8 & \ 3.80 & \ 0 & \ 0 & \ 0 \\ \ 3.80 & \ 3.80 & \ 118.8 & \ 0 & \ 0 & \ 0 \\ \ 0 & \ 0 & \ 0 & \ 59.40 & \ 0 & \ 0 \\ \ 0 & \ 0 & \ 0 & \ 0 & \ 59.40 & \ 0 \\ \ 0 & \ 0 & \ 0 & \ 0 & \ 0 & \ 59.40 \\ \end{pmatrix}. :: Run: EalTools.x :: > Select system dimension: ======================= 3D => 3 2D => 2 ======================== 3 The compound is a 3D system, so we have to choose the number 3. :: > Select using output code: ============================================================ IRelast-----------------------( wein2k )-=> 1 Elast-------------------------( wein2k )-=> 2 AELAS-------------------------( VASP )-=> 3 ElaStic-----------------------( QE,Wien2k,Exciting )-=> 4 Using Cij Tensor in Cij.dat---( Other codes )-=> 5 Using EC Databank-------------( MP )-=> 6 ============================================================ 5 We use Cij.dat file. So we choose the number 5. :: > Want to calculate phase and group velocities? (Y/n) Y At this point we are going to calculate the phase and group velocities (add in >v.1.5 ), So, select Y. :: Density of Compound (kg/m^3): note: If you don't know, enter 0 Density of GaAs compound is 5307.0 kg/m^3. But if you do not know it, **dens_lapw** will calculate it for you. Just enter 0. we enter 5307.0,therefore :: > Density of Compound = 5307.00000000000 ######################################################################### Cij: 118.800000 53.800000 53.800000 0.000000 0.000000 0.000000 53.800000 118.800000 53.800000 0.000000 0.000000 0.000000 53.800000 53.800000 118.800000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 59.400000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 59.400000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 59.400000 Sij: 0.0117287 -0.0036559 -0.0036559 0.0000000 0.0000000 0.0000000 -0.0036559 0.0117287 -0.0036559 0.0000000 0.0000000 0.0000000 -0.0036559 -0.0036559 0.0117287 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0168350 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0168350 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0168350 ######################################################################### ========================================================== Elastic properties | Voigt Reuss Average ========================================================== = Bulk modulus (GPa)| 75.467 75.467 75.467 = = Shear modulus (GPa)| 48.640 44.626 46.633 = = Young modulus (GPa)| 120.114 111.833 115.974 = = P-wave modulus(GPa)| 140.3200 134.9672 137.6436 = = Poisson ratio | 0.2347 0.2530 0.2439 = <--( Brittle regime ) = Pugh ratio | 1.5515 1.6911 1.6183 = <--( Brittle regime ) ========================================================== > Universal anisotropy index (AU) : 0.4498 > Log-Euclidean anisotropy parameter (AL): 0.4436 > Chung-Buessem Anisotropy Index (Ac) : 0.0430 > Cauchy pressure(GPa) (Pc) : 59.4000 <--( Metallic-like bonding) ---------------------------------------------------------- > Output for ( 1.0, 0.0, 0.0) plane =================================================> Youngs Modulus Max(GPa) Min(GPa) Anisotropy 141.02 85.26 1.65 ------------------------------------------ Theta Phi Theta Phi 126.0 316.8 180.0 0.0 ------------------------------------------ x y z x y z 0.59 -0.55 -0.59 0.00 0.00 -1.00 ================================================== ==================================================> Linear Compressibiliy Max(TPa-1) Min(TPa-1) Anisotropy 4.417 4.417 1.000 ------------------------------------------ Theta Phi Theta Phi 147.6 198.0 102.6 97.2 ------------------------------------------ x y z x y z -0.51 -0.17 -0.84 -0.12 0.97 -0.22 ================================================== ==================================================> Shear Modulus Max(GPa) Min(GPa) Anisotropy 59.40 32.50 1.83 ------------------------------------------ Theta Phi Theta Phi 180.0 0.0 135.0 360.0 ------------------------------------------ x y z x y z 0.00 0.00 -1.00 0.71 -0.00 -0.71 ================================================== ==================================================> Bulk Modulus Max(GPa/100) Min(GPa/100) Anisotropy 2.26 2.26 1.00 ------------------------------------------ Theta Phi Theta Phi 102.6 97.2 147.6 198.0 ------------------------------------------ x y z x y z -0.12 0.97 -0.22 -0.51 -0.17 -0.84 ================================================== ==================================================> Phase P-Mode Max(km/s) Min(km/s) Anisotropy 5.40 4.73 1.14 ------------------------------------------ Theta Phi Theta Phi 54.0 223.2 180.0 0.0 ------------------------------------------ x y z x y z 0.55 0.08 -0.83 -0.80 0.00 -0.60 ================================================== ==================================================> Phase Fast-Mode Max(km/s) Min(km/s) Anisotropy 3.35 3.35 1.00 ------------------------------------------ Theta Phi Theta Phi 124.2 360.0 180.0 0.0 ------------------------------------------ x y z x y z 0.28 -0.95 0.11 -0.80 0.00 -0.60 ================================================== ==================================================> Phase Slow-Mode Max(km/s) Min(km/s) Anisotropy 3.35 0.00 Inf ------------------------------------------ Theta Phi Theta Phi 180.0 0.0 180.0 0.0 ------------------------------------------ x y z x y z -0.80 0.00 -0.60 -0.80 0.00 -0.60 ================================================== ==================================================> Group P-Mode Max(km/s) Min(km/s) Anisotropy 5.40 4.73 1.14 ------------------------------------------ Theta Phi Theta Phi 54.0 316.8 180.0 0.0 ------------------------------------------ x y z x y z 0.49 -0.27 -0.83 -0.80 0.00 -0.60 ================================================== ==================================================> Group Fast-Mode Max(km/s) Min(km/s) Anisotropy 3.37 3.35 1.01 ------------------------------------------ Theta Phi Theta Phi 79.2 133.2 180.0 0.0 ------------------------------------------ x y z x y z -0.19 -0.58 -0.79 -0.80 0.00 -0.60 ================================================== ==================================================> Group Slow-Mode Max(km/s) Min(km/s) Anisotropy 3.35 3.35 1.00 ------------------------------------------ Theta Phi Theta Phi 180.0 0.0 180.0 0.0 ------------------------------------------ x y z x y z -0.80 0.00 -0.60 -0.80 0.00 -0.60 ================================================== ==================================================> Poisson's Ratio Max Min Anisotropy 0.443 0.021 21.21 ------------------------------------------ Theta Phi Theta Phi 135.0 360.0 135.0 360.0 ------------------------------------------ x y z x y z 0.71 -0.00 -0.71 0.71 -0.00 -0.71 ================================================== :: Finally, for example, we use the following command to visualize a 2D heat map of Poisson's Ratio (Figure ‍‍‍‍poissons_smap.png is the result.): :: dat2gnu_lapw hmpoi .. image:: Images/poissons_smap.png :width: 800