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 VRh (Materials Project id mp-1251)

       407      116      172        0        0        0  
       116      407      172        0        0        0  
       172      172      365        0        0        0  
         0        0        0      118        0        0  
         0        0        0        0      118        0  
         0        0        0        0        0       44  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 233.22 GPaEV = 271.47 GPaGV = 103.93 GPaνV = 0.306
ReussKR = 233.15 GPaER = 233.21 GPaGR = 87.455 GPaνR = 0.33329
HillKH = 233.18 GPaEH = 252.54 GPaGH = 95.694 GPaνH = 0.3195

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
44 GPa 118 GPa 118 GPa 188.25 GPa 291 GPa 699.75 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 141.5 GPa 324.76 GPa 1.3589 TPa–1 1.4652 TPa–1 44 GPa 145.5 GPa0.00286570.6765Value
Anisotropy 2.295 1.0782 3.307236.0702Anisotropy
Axis 0.7071
0.7071
0.0000
0.9262
0.0000
-0.3770
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
-0.7071
0.7071
-0.0000
0.5007
0.5002
-0.7065
-0.5603
0.5603
0.6101
Axis
0.0002
1.0000
-0.0000
-0.7071
-0.7071
0.0000
-0.4994
-0.4997
-0.7077
-0.7071
-0.7071
-0.0001
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