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 CaAu2 (Materials Project id mp-443)

        78       37       37        0        0        0  
        37      109       98        0        0        0  
        37       98      108        0        0        0  
         0        0        0       14        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 71 GPaEV = 47.23 GPaGV = 17 GPaνV = 0.38913
ReussKR = 62.325 GPaER = 33.006 GPaGR = 11.69 GPaνR = 0.41174
HillKH = 66.662 GPaEH = 40.154 GPaGH = 14.345 GPaνH = 0.39961

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10.498 GPa 14 GPa 14 GPa 16 GPa 59.389 GPa 225.11 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 19.677 GPa 64.739 GPa 2.9212 TPa–1 9.9106 TPa–1 5.2493 GPa 23.949 GPa0.0162390.88944Value
Anisotropy 3.29 3.3927 4.562 54.7725Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.0001
0.7071
0.7071
-0.7071
0.5022
0.4977
0.6852
-0.0001
0.7283
0.0001
1.0000
0.0000
Axis
0.0001
0.7071
-0.7071
-0.7071
-0.5023
-0.4977
0.7283
-0.0004
-0.6852
0.0009
0.0000
-1.0000
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