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 Ni (Materials Project id mp-10257)

       320      142      128        0        0        0  
       142      320      128        0        0        0  
       128      128      336        0        0        0  
         0        0        0       55        0        0  
         0        0        0        0       55        0  
         0        0        0        0        0       89  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 196.89 GPaEV = 207.48 GPaGV = 78.333 GPaνV = 0.32436
ReussKR = 196.89 GPaER = 194.94 GPaGR = 73.012 GPaνR = 0.33498
HillKH = 196.89 GPaEH = 201.24 GPaGH = 75.673 GPaνH = 0.32965

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
55 GPa 55 GPa 89 GPa 178 GPa 207.33 GPa 590.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 166.21 GPa 265.07 GPa 1.6821 TPa–1 1.6985 TPa–1 55 GPa 99.564 GPa0.204090.51279Value
Anisotropy 1.595 1.0097 1.81 2.5125Anisotropy
Axis 0.6721
0.2708
0.6891
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.3283
0.6263
-0.7071
-0.6266
0.1205
-0.7700
0.6882
0.0001
-0.7255
Axis
1.0000
0.0002
-0.0000
-0.3282
-0.6263
-0.7071
-0.1888
-0.9820
0.0000
-0.7255
-0.0000
-0.6882
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