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 U2CrN3 (Materials Project id mp-10247)

       488      162      122        0        0        0  
       162      445      129        0        0        0  
       122      129      319        0        0        0  
         0        0        0      100        0        0  
         0        0        0        0       80        0  
         0        0        0        0        0       70  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 230.89 GPaEV = 275.64 GPaGV = 105.93 GPaνV = 0.30103
ReussKR = 220.96 GPaER = 253.62 GPaGR = 96.898 GPaνR = 0.3087
HillKH = 225.92 GPaEH = 264.65 GPaGH = 101.42 GPaνH = 0.30477

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
70 GPa 80 GPa 100 GPa 235.64 GPa 306.38 GPa 709.98 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 216.8 GPa 409.03 GPa 1.0922 TPa–1 2.2306 TPa–1 70 GPa 151.66 GPa0.17490.58125Value
Anisotropy 1.887 2.0424 2.167 3.3233Anisotropy
Axis 0.6318
0.5688
0.5266
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0001
-0.0000
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.7261
0.6876
-0.0000
Axis
0.0001
1.0000
0.0000
-0.7071
0.7071
0.0000
-1.0000
0.0000
0.0000
-0.6876
0.7261
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