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 AlMo3 (Materials Project id mp-259)

       435      120      120        0        0        0  
       120      435      120        0        0        0  
       120      120      435        0        0        0  
         0        0        0      102        0        0  
         0        0        0        0      102        0  
         0        0        0        0        0      102  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 225 GPaEV = 314.7 GPaGV = 124.2 GPaνV = 0.26689
ReussKR = 225 GPaER = 302.92 GPaGR = 118.74 GPaνR = 0.27561
HillKH = 225 GPaEH = 308.83 GPaGH = 121.47 GPaνH = 0.27124

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
102 GPa 102 GPa 102 GPa 315 GPa 315 GPa 675 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 265.83 GPa 383.11 GPa 1.4815 TPa–1 1.4815 TPa–1 102 GPa 157.5 GPa0.162460.41108Value
Anisotropy 1.441 1.0000 1.544 2.5303Anisotropy
Axis -0.5774
0.5774
-0.5773
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.4833
0.6289
0.6090
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0001
0.7071
0.7071
-0.0002
0.7071
Axis
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0001
1.0000
0.0000
0.7071
-0.0005
-0.7071
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