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 Zr2Fe (Materials Project id mp-1159)

       200       75       75        0        0        0  
        75      178      132        0        0        0  
        75      132      178        0        0        0  
         0        0        0       36        0        0  
         0        0        0        0       24        0  
         0        0        0        0        0       24  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 124.44 GPaEV = 96.167 GPaGV = 35.067 GPaνV = 0.3712
ReussKR = 123.78 GPaER = 82.072 GPaGR = 29.533 GPaνR = 0.38949
HillKH = 124.11 GPaEH = 89.165 GPaGH = 32.3 GPaνH = 0.38026

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24 GPa 24 GPa 36 GPa 46 GPa 135.52 GPa 374.48 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 66.72 GPa 163.71 GPa 2.4631 TPa–1 3.1527 TPa–1 23 GPa 55.621 GPa0.11510.69308Value
Anisotropy 2.454 1.2800 2.418 6.0217Anisotropy
Axis -0.5742
0.8187
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0003
0.7071
0.7071
0.7071
0.5000
-0.5000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
Axis
0.0004
0.7071
-0.7071
-0.7071
0.5000
-0.5000
-1.0000
0.0000
0.0000
-0.0000
1.0000
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