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 Zr2Al (Materials Project id mp-2557)

       176       88       54        0        0        0  
        88      176       54        0        0        0  
        54       54      186        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       44  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 103.33 GPaEV = 137.97 GPaGV = 54 GPaνV = 0.27747
ReussKR = 103.03 GPaER = 134.32 GPaGR = 52.358 GPaνR = 0.28271
HillKH = 103.18 GPaEH = 136.15 GPaGH = 53.179 GPaνH = 0.28008

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
44 GPa 56 GPa 56 GPa 88 GPa 139.25 GPa 310.75 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 127.7 GPa 163.91 GPa 3.0505 TPa–1 3.6051 TPa–1 44 GPa 60.872 GPa0.159360.45111Value
Anisotropy 1.284 1.1818 1.383 2.8308Anisotropy
Axis 0.9239
0.3827
0.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
0.6034
0.3687
0.7071
1.0000
0.0003
0.0000
0.9453
0.3263
-0.0000
Axis
0.0002
1.0000
-0.0000
0.6034
0.3687
-0.7071
0.0000
0.0001
-1.0000
-0.3263
0.9453
-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