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 CrNi2 (Materials Project id mp-784631)

       325      176      194        0        0        0  
       176      429       84        0        0        0  
       194       84      394        0        0        0  
         0        0        0       65        0        0  
         0        0        0        0      155        0  
         0        0        0        0        0      165  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 228.44 GPaEV = 313.43 GPaGV = 123.27 GPaνV = 0.27133
ReussKR = 228.26 GPaER = 266.37 GPaGR = 102.02 GPaνR = 0.30551
HillKH = 228.35 GPaEH = 290.21 GPaGH = 112.64 GPaνH = 0.28819

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
65 GPa 132.9 GPa 155 GPa 165 GPa 329.55 GPa 685.54 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 177.76 GPa 401.34 GPa 1.3482 TPa–1 1.5603 TPa–1 65 GPa 163.83 GPa-0.0549920.6311Value
Anisotropy 2.258 1.1574 2.52Anisotropy
Axis 0.0000
0.6837
0.7298
0.5452
0.8383
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.2172
0.7071
0.6729
0.7074
0.5240
-0.4744
0.0000
0.0000
1.0000
Axis
-0.0000
1.0000
0.0000
-0.2171
0.7071
-0.6729
-0.7069
0.5218
-0.4776
1.0000
0.0000
-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