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 CuBr (Materials Project id mp-22917)

        42       -2       -1        0        0        0  
        -2       42       -1        0        0        0  
        -1       -1        6        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0        2  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 9.1111 GPaEV = 17.594 GPaGV = 7.4667 GPaνV = 0.17816
ReussKR = 4.25 GPaER = 6.921 GPaGR = 2.8167 GPaνR = 0.22859
HillKH = 6.6806 GPaEH = 12.276 GPaGH = 5.1417 GPaνH = 0.19375

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 2 GPa 5.9413 GPa 40.059 GPa 44 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 4.8861 GPa 41.721 GPa 29.412 TPa–1 176.47 TPa–1 2 GPa 22 GPa-0.17530.81679Value
Anisotropy 8.539 6.0000 11Anisotropy
Axis 0.4609
0.4609
0.7584
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
-1.0000
-0.0000
-0.0000
-0.7071
0.7071
0.0000
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.7071
-0.0000
-0.0000
0.0000
1.0000
-0.7071
-0.7071
-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