ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of Al2O3 (Materials Project id mp-7048)

       251      116      152        0       -1        0  
       116      387       61        0        2        0  
       152       61      387        0       22        0  
         0        0        0       62        0        5  
        -1        2       22        0      119        0  
         0        0        0        5        0      128  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 187 GPaEV = 272.12 GPaGV = 108.2 GPaνV = 0.25747
ReussKR = 184.2 GPaER = 238.98 GPaGR = 93.079 GPaνR = 0.28377
HillKH = 185.6 GPaEH = 255.7 GPaGH = 100.64 GPaνH = 0.27038

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
61.623 GPa 112.04 GPa 128.38 GPa 139.23 GPa 328.43 GPa 564.3 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 167.32 GPa 360.28 GPa 1.3912 TPa–1 2.3833 TPa–1 61.623 GPa 165.27 GPa-0.0292340.62177Value
Anisotropy 2.153 1.7131 2.682Anisotropy
Axis 0.9982
0.0000
0.0598
0.4683
0.0000
0.8836
0.1366
-0.0000
0.9906
-0.9906
-0.0000
0.1366
-0.0751
0.0000
0.9972
0.1834
0.7071
0.6829
-0.0146
-0.0000
0.9999
-0.0434
0.0007
0.9991
Axis
0.0000
1.0000
-0.0000
-0.1833
0.7071
-0.6829
0.0000
-1.0000
-0.0000
0.9991
0.0001
0.0434
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane