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 HoTe (Materials Project id mp-919)

       159       17       17        0        0        0  
        17      159       17        0        0        0  
        17       17      159        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        4        0  
         0        0        0        0        0        4  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 64.333 GPaEV = 79.684 GPaGV = 30.8 GPaνV = 0.29357
ReussKR = 64.333 GPaER = 18.655 GPaGR = 6.4253 GPaνR = 0.45167
HillKH = 64.333 GPaEH = 50.927 GPaGH = 18.613 GPaνH = 0.36807

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
4 GPa 4 GPa 4 GPa 142 GPa 142 GPa 193 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 11.756 GPa 155.72 GPa 5.1813 TPa–1 5.1813 TPa–1 4 GPa 71 GPa0.00948460.91129Value
Anisotropy 13.25 1.0000 17.75 96.0809Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.3827
0.0000
0.9239
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
-0.0000
-0.7071
0.0002
-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