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 AsRh2 (Materials Project id mp-2302)

       371      162      162        0        0        0  
       162      371      162        0        0        0  
       162      162      371        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       57        0  
         0        0        0        0        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 231.67 GPaEV = 205.53 GPaGV = 76 GPaνV = 0.35214
ReussKR = 231.67 GPaER = 189.96 GPaGR = 69.667 GPaνR = 0.36334
HillKH = 231.67 GPaEH = 197.77 GPaGH = 72.833 GPaνH = 0.35772

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57 GPa 57 GPa 57 GPa 209 GPa 209 GPa 695 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 158.04 GPa 272.52 GPa 1.4388 TPa–1 1.4388 TPa–1 57 GPa 104.5 GPa0.196940.54898Value
Anisotropy 1.724 1.0000 1.833 2.7876Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3536
0.1464
0.9239
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-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