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-755175)

       440      122       64        0       -6        0  
       122      440       64        0        6        0  
        64       64      345        0        0        0  
         0        0        0       87        0        6  
        -6        6        0        0       87        0  
         0        0        0        6        0      159  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 191.67 GPaEV = 321.27 GPaGV = 131.6 GPaνV = 0.22063
ReussKR = 186.44 GPaER = 295.32 GPaGR = 119.47 GPaνR = 0.236
HillKH = 189.06 GPaEH = 308.35 GPaGH = 125.53 GPaνH = 0.22817

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
86.503 GPa 86.689 GPa 159.5 GPa 312.21 GPa 318.31 GPa 594.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 237.84 GPa 400.44 GPa 1.5132 TPa–1 2.3371 TPa–1 86.503 GPa 160.97 GPa0.0848480.41957Value
Anisotropy 1.684 1.5445 1.861 4.9449Anisotropy
Axis 0.6873
-0.0000
0.7264
0.4996
0.8654
0.0372
-0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
-0.0825
-0.0000
0.9966
-0.6925
-0.0012
0.7214
0.2444
0.4232
0.8725
0.7173
0.0001
-0.6967
Axis
-0.0000
1.0000
0.0000
-0.7214
-0.0010
-0.6925
-0.8660
0.5000
-0.0000
-0.6967
-0.0001
-0.7173
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