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 CsAuO (Materials Project id mp-9986)

        38       12       12        0        0        0  
        12       39       16        0        0        0  
        12       16       39        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0        5        0  
         0        0        0        0        0        5  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 21.778 GPaEV = 24.347 GPaGV = 9.2667 GPaνV = 0.31367
ReussKR = 21.711 GPaER = 20.629 GPaGR = 7.6878 GPaνR = 0.34164
HillKH = 21.744 GPaEH = 22.507 GPaGH = 8.4773 GPaνH = 0.32749

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 11 GPa 23 GPa 27.52 GPa 65.48 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 15.966 GPa 32.764 GPa 14.428 TPa–1 17.203 TPa–1 5 GPa 13.137 GPa0.138840.60339Value
Anisotropy 2.052 1.1923 2.627 4.3460Anisotropy
Axis 0.6992
0.5056
0.5055
1.0000
0.0000
0.0000
0.0000
0.5000
0.8660
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.7904
-0.0000
0.6126
-0.7147
0.6994
0.0000
Axis
1.0000
0.0000
-0.0000
-0.7071
0.7071
0.0000
0.0000
1.0000
0.0000
-0.6994
-0.7147
-0.0000
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