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 Ta2H (Materials Project id mp-24082)

       316      167      156        0        0        0  
       167      326      147        0        0        0  
       156      147      258        0        0        0  
         0        0        0       76        0        0  
         0        0        0        0       79        0  
         0        0        0        0        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 204.44 GPaEV = 183.32 GPaGV = 67.867 GPaνV = 0.35056
ReussKR = 201 GPaER = 172.59 GPaGR = 63.598 GPaνR = 0.35689
HillKH = 202.72 GPaEH = 177.96 GPaGH = 65.732 GPaνH = 0.35369

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 76 GPa 79 GPa 127.41 GPa 156.42 GPa 616.17 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 129.57 GPa 214.72 GPa 1.306 TPa–1 2.3143 TPa–1 41 GPa 79 GPa0.125080.59814Value
Anisotropy 1.657 1.7720 1.927 4.7819Anisotropy
Axis 0.7204
0.6935
-0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0001
0.0000
0.0000
0.0000
1.0000
-0.5045
0.5204
-0.6889
-0.6082
0.6479
0.4586
Axis
0.0001
1.0000
0.0000
-1.0000
0.0000
0.0000
0.4901
-0.4843
-0.7247
-0.7144
-0.6986
0.0396
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