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 Zr2Fe3Si (Materials Project id mp-16336)

       325      104       88        0        0       -0  
       104      325       88        0        0        0  
        88       88      282        0        0        0  
         0        0        0       73        0        0  
         0        0        0        0       73        0  
        -0        0        0        0        0      110  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 165.78 GPaEV = 238.59 GPaGV = 94.667 GPaνV = 0.26014
ReussKR = 164.57 GPaER = 230.43 GPaGR = 90.964 GPaνR = 0.26663
HillKH = 165.17 GPaEH = 234.52 GPaGH = 92.815 GPaνH = 0.26336

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
73 GPa 73 GPa 110 GPa 210.97 GPa 221 GPa 500.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 202.49 GPa 277.85 GPa 1.839 TPa–1 2.3983 TPa–1 73 GPa 110.5 GPa0.176720.39165Value
Anisotropy 1.372 1.3041 1.514 2.2162Anisotropy
Axis -0.4730
0.4730
0.7433
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
0.6221
0.0001
0.7829
0.7311
-0.0002
0.6823
Axis
1.0000
0.0000
-0.0000
-0.7071
0.7071
-0.0000
-0.0002
1.0000
0.0000
0.6823
-0.0007
-0.7311
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