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 Ba2YTaO6 (Materials Project id mp-12385)

       224       86       78        0        0       -5  
        86      224       78        0        0        5  
        78       78      274        0        0        0  
         0        0        0       64        0        0  
         0        0        0        0       64        0  
        -5        5        0        0        0       94  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 134 GPaEV = 192.6 GPaGV = 76.4 GPaνV = 0.26045
ReussKR = 133.28 GPaER = 187.43 GPaGR = 74.045 GPaνR = 0.26563
HillKH = 133.64 GPaEH = 190.02 GPaGH = 75.223 GPaνH = 0.26303

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
64 GPa 64 GPa 92.892 GPa 139.11 GPa 180.23 GPa 403.77 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 168.37 GPa 234.75 GPa 2.1162 TPa–1 2.6933 TPa–1 64 GPa 94.963 GPa0.15570.40426Value
Anisotropy 1.394 1.2727 1.484 2.5964Anisotropy
Axis -0.0781
0.8191
0.5683
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1094
0.9940
0.0000
0.0000
0.0000
1.0000
-0.0950
0.9955
0.0000
-0.6663
0.5502
0.5033
-0.5351
0.4419
-0.7200
Axis
0.1736
0.9848
-0.0000
-0.9955
-0.0950
-0.0000
-0.6367
-0.7711
0.0000
-0.5552
0.4585
0.6940
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