Tutorial¶
Metal-organic framework MIL-53(Al) [3D material]¶
The stiffness matrix (coefficients in GPa) is input (Cij.dat)
\[\begin{split}\mathbf{C_{ij}} =
\begin{pmatrix}
\ C_{11} & \ C_{12} & \ C_{13} & \ C_{14} & \ C_{15} & \ C_{16} \\
\ C_{21} & \ C_{22} & \ C_{23} & \ C_{24} & \ C_{25} & \ C_{26} \\
\ C_{31} & \ C_{32} & \ C_{33} & \ C_{34} & \ C_{35} & \ C_{36} \\
\ C_{41} & \ C_{42} & \ C_{43} & \ C_{44} & \ C_{45} & \ C_{46} \\
\ C_{51} & \ C_{52} & \ C_{53} & \ C_{54} & \ C_{55} & \ C_{56} \\
\ C_{61} & \ C_{62} & \ C_{63} & \ C_{64} & \ C_{65} & \ C_{66} \\
\end{pmatrix}= \begin{pmatrix}
\ 90.85 & \ 20.41 & \ 54.28 & \ 0 & \ 0 & \ 0 \\
\ 20.41 & \ 65.56 & \ 12.36 & \ 0 & \ 0 & \ 0 \\
\ 54.28 & \ 12.36 & \ 33.33 & \ 0 & \ 0 & \ 0 \\
\ 0 & \ 0 & \ 0 & \ 7.24 & \ 0 & \ 0 \\
\ 0 & \ 0 & \ 0 & \ 0 & \ 39.52 & \ 0 \\
\ 0 & \ 0 & \ 0 & \ 0 & \ 0 & \ 8.27 \\
\end{pmatrix}.\end{split}\]
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.:
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.
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
Gallium Thiophosphate-GaPS4 [2D material]¶
The stiffness matrix (coefficients in N/m) is input (Cij-2D.dat)
\[\begin{split}\mathbf{C_{ij}} =
\begin{pmatrix}
\ C_{11} & \ C_{12} & \ C_{16} \\
\ C_{12} & \ C_{22} & \ C_{26} \\
\ C_{61} & \ C_{62} & \ C_{66} \\
\end{pmatrix}= \begin{pmatrix}
\ 4.45 & \ 3.63 & \ 0.00 \\
\ 3.63 & \ 19.22 & \ 0.00 \\
\ 0.00 & \ 0.00 & \ 4.71 \\
\end{pmatrix}.\end{split}\]
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.
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.
Gallium arsenide [3D material]¶
The stiffness matrix (coefficients in GPa) is input (Cij.dat)
\[\begin{split}\mathbf{C_{ij}} =
\begin{pmatrix}
\ C_{11} & \ C_{12} & \ C_{13} & \ C_{14} & \ C_{15} & \ C_{16} \\
\ C_{21} & \ C_{22} & \ C_{23} & \ C_{24} & \ C_{25} & \ C_{26} \\
\ C_{31} & \ C_{32} & \ C_{33} & \ C_{34} & \ C_{35} & \ C_{36} \\
\ C_{41} & \ C_{42} & \ C_{43} & \ C_{44} & \ C_{45} & \ C_{46} \\
\ C_{51} & \ C_{52} & \ C_{53} & \ C_{54} & \ C_{55} & \ C_{56} \\
\ C_{61} & \ C_{62} & \ C_{63} & \ C_{64} & \ C_{65} & \ C_{66} \\
\end{pmatrix}= \begin{pmatrix}
\ 118.8 & \ 3.80 & \ 13.80 & \ 0 & \ 0 & \ 0 \\
\ 3.80 & \ 118.8 & \ 3.80 & \ 0 & \ 0 & \ 0 \\
\ 3.80 & \ 3.80 & \ 118.8 & \ 0 & \ 0 & \ 0 \\
\ 0 & \ 0 & \ 0 & \ 59.40 & \ 0 & \ 0 \\
\ 0 & \ 0 & \ 0 & \ 0 & \ 59.40 & \ 0 \\
\ 0 & \ 0 & \ 0 & \ 0 & \ 0 & \ 59.40 \\
\end{pmatrix}.\end{split}\]
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
