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 ErNi2 (Materials Project id mp-1939)

       148       89       89        0        0        0  
        89      148       89        0        0        0  
        89       89      148        0        0        0  
         0        0        0       55        0        0  
         0        0        0        0       55        0  
         0        0        0        0        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 108.67 GPaEV = 118.16 GPaGV = 44.8 GPaνV = 0.31877
ReussKR = 108.67 GPaER = 108.95 GPaGR = 40.869 GPaνR = 0.3329
HillKH = 108.67 GPaEH = 113.58 GPaGH = 42.835 GPaνH = 0.3258

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
55 GPa 55 GPa 55 GPa 59 GPa 59 GPa 326 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 81.156 GPa 141.18 GPa 3.0675 TPa–1 3.0675 TPa–1 29.5 GPa 55 GPa0.0831790.55133Value
Anisotropy 1.74 1.0000 1.864 6.6283Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.2500
0.9330
0.2588
0.3794
0.9160
-0.1305
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0003
-0.7071
Axis
-0.7071
-0.0002
-0.7071
0.1736
0.9848
-0.0000
0.7071
-0.0006
-0.7071
0.0002
1.0000
-0.0003
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