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 EuIr2 (Materials Project id mp-995)

       218      111      111        0        2       -1  
       111      218      111        1        0       -1  
       111      111      218        1        2       -0  
         0        1        1       70        0        0  
         2        0        2        0       70        0  
        -1       -1       -0        0        0       70  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 146.67 GPaEV = 166.25 GPaGV = 63.4 GPaνV = 0.31108
ReussKR = 146.63 GPaER = 163.7 GPaGR = 62.296 GPaνR = 0.31392
HillKH = 146.65 GPaEH = 164.98 GPaGH = 62.848 GPaνH = 0.3125

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
69.911 GPa 69.973 GPa 69.987 GPa 107.03 GPa 107.08 GPa 440.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 143.02 GPa 182.29 GPa 2.209 TPa–1 2.3623 TPa–1 53.493 GPa 70.083 GPa0.208710.40206Value
Anisotropy 1.275 1.0694 1.31 1.9264Anisotropy
Axis 0.0146
0.9998
-0.0145
0.5724
0.5467
0.6111
0.7071
0.0000
0.7071
0.6301
0.4538
-0.6301
0.7071
0.0002
-0.7071
-0.9780
0.2077
-0.0220
0.7071
-0.0000
-0.7071
-0.0283
0.7071
-0.7066
Axis
-0.7071
-0.0000
-0.7071
-0.0220
-0.2076
-0.9780
-0.7071
0.0003
-0.7071
-0.9996
-0.0198
0.0202
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