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 ErNi5 (Materials Project id mp-853)

       233      106       85        0        0       -3  
       106      233       85        0        0       -3  
        85       85      298        0        0       -2  
         0        0        0       68        0        0  
         0        0        0        0       68        0  
        -3       -3       -2        0        0       64  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 146.22 GPaEV = 186.73 GPaGV = 72.533 GPaνV = 0.28717
ReussKR = 145.38 GPaER = 182.05 GPaGR = 70.489 GPaνR = 0.2913
HillKH = 145.8 GPaEH = 184.39 GPaGH = 71.511 GPaνH = 0.28923

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
63.934 GPa 68 GPa 68 GPa 127 GPa 196.57 GPa 440.5 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 169.83 GPa 255.37 GPa 1.9527 TPa–1 2.6088 TPa–1 63.5 GPa 87.64 GPa0.167710.39763Value
Anisotropy 1.504 1.3360 1.38 2.3710Anisotropy
Axis 0.6318
0.6318
0.4490
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
-0.7071
0.7071
-0.0000
-0.5000
0.5000
0.7071
0.7071
0.7071
-0.0000
-0.7071
0.7071
0.0000
Axis
-0.7071
-0.7071
0.0000
0.5000
-0.5000
0.7071
0.0004
-0.0004
-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