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 CuN3 (Materials Project id mp-27954)

       115        4        4        0        0        0  
         4        4        3        0        0        0  
         4        3        4        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        3        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 16.111 GPaEV = 22.477 GPaGV = 8.8667 GPaνV = 0.26748
ReussKR = 3.4977 GPaER = 3.5143 GPaGR = 1.3187 GPaνR = 0.33254
HillKH = 9.8044 GPaEH = 13.023 GPaGH = 5.0927 GPaνH = 0.27862

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 3 GPa 3 GPa 6.7045 GPa 115.3 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 1.741 GPa 110.43 GPa -1.2937 TPa–1 143.6 TPa–1 0.5 GPa 3 GPa-0.462531.127Value
Anisotropy 63.43 6Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.7934
0.6088
0.0003
0.7071
-0.7071
-0.0000
0.0000
1.0000
0.9182
0.0000
-0.3960
0.9322
-0.0004
-0.3619
Axis
0.0002
-0.7071
-0.7071
-1.0000
0.0000
-0.0000
-0.3960
0.0000
-0.9182
0.0003
1.0000
-0.0004
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