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 GaP (Materials Project id mp-2490)

       125       52       52        0        0        0  
        52      125       52        0        0        0  
        52       52      125        0        0        0  
         0        0        0       65        0        0  
         0        0        0        0       65        0  
         0        0        0        0        0       65  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76.333 GPaEV = 130.3 GPaGV = 53.6 GPaνV = 0.2155
ReussKR = 76.333 GPaER = 122.17 GPaGR = 49.53 GPaνR = 0.23326
HillKH = 76.333 GPaEH = 126.26 GPaGH = 51.565 GPaνH = 0.22431

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
65 GPa 65 GPa 65 GPa 73 GPa 73 GPa 229 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 94.446 GPa 151.89 GPa 4.3668 TPa–1 4.3668 TPa–1 36.5 GPa 65 GPa0.0141660.41011Value
Anisotropy 1.608 1.0000 1.781 28.9505Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0001
1.0000
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