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-32570)

       270      153      149        0      -15        0  
       153      301      148        0       -1        0  
       149      148      305        0      -15        0  
         0        0        0      158        0       -9  
       -15       -1      -15        0      148        0  
         0        0        0       -9        0      147  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 197.33 GPaEV = 297.25 GPaGV = 119 GPaνV = 0.24895
ReussKR = 196.04 GPaER = 262.88 GPaGR = 102.97 GPaνR = 0.27651
HillKH = 196.68 GPaEH = 280.24 GPaGH = 110.98 GPaνH = 0.26253

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
125.24 GPa 141.95 GPa 143.85 GPa 161.77 GPa 163.05 GPa 593.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 167.62 GPa 382.57 GPa 1.51 TPa–1 2.0518 TPa–1 65.256 GPa 163.05 GPa-0.056930.59333Value
Anisotropy 2.282 1.3588 2.499Anisotropy
Axis 0.9990
0.0000
0.0454
-0.5672
0.5569
0.6067
-0.3687
0.0000
0.9295
-0.9295
-0.0000
-0.3687
0.7053
0.7071
0.0510
-0.4891
-0.0000
0.8722
-0.0423
0.7062
0.7067
0.0370
0.7184
-0.6946
Axis
-0.7053
0.7071
-0.0509
0.0000
-1.0000
-0.0000
-0.0348
-0.7080
0.7054
-0.9986
0.0010
-0.0522
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