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 FePd (Materials Project id mp-2831)

       293       62      125        0        0        0  
        62      293      125        0        0        0  
       125      125      254        0        0        0  
         0        0        0       99        0        0  
         0        0        0        0       99        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 162.67 GPaEV = 211.49 GPaGV = 82.4 GPaνV = 0.28331
ReussKR = 162.31 GPaER = 182.91 GPaGR = 69.695 GPaνR = 0.31219
HillKH = 162.49 GPaEH = 197.35 GPaGH = 76.048 GPaνH = 0.29757

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 99 GPa 99 GPa 120.65 GPa 231 GPa 488.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 114.49 GPa 257.15 GPa 1.7821 TPa–1 2.1894 TPa–1 38 GPa 115.5 GPa-0.0201680.63771Value
Anisotropy 2.246 1.2286 3.039Anisotropy
Axis 0.7071
0.7071
0.0000
0.8306
0.0000
0.5568
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
-0.7071
0.7071
-0.0000
0.4985
0.4985
-0.7092
-0.5247
0.5247
-0.6704
Axis
0.0002
1.0000
-0.0000
-0.7071
-0.7071
0.0000
0.5015
0.5015
0.7050
-0.7071
-0.7071
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