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 CaSb2 (Materials Project id mp-7493)

        48       30       26        0        8        0  
        30       65       29        0       11        0  
        26       29       45        0        2        0  
         0        0        0       31        0       -2  
         8       11        2        0       16        0  
         0        0        0       -2        0       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 36.444 GPaEV = 48.27 GPaGV = 18.867 GPaνV = 0.27925
ReussKR = 32.803 GPaER = 39.214 GPaGR = 15.073 GPaνR = 0.30076
HillKH = 34.624 GPaEH = 43.761 GPaGH = 16.97 GPaνH = 0.28935

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11.685 GPa 22.243 GPa 22.528 GPa 27.723 GPa 31.472 GPa 112.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.442 GPa 62.038 GPa 5.7329 TPa–1 18.126 TPa–1 8.6779 GPa 31.472 GPa-0.178540.71003Value
Anisotropy 2.538 3.1617 3.627Anisotropy
Axis 0.2364
-0.0000
0.9717
-0.4944
0.7285
-0.4741
0.6620
0.0000
0.7495
0.7495
0.0000
-0.6620
0.8576
0.0002
0.5143
-0.2298
0.0000
0.9732
0.5811
0.7194
-0.3805
0.5666
0.8073
-0.1653
Axis
0.5143
0.0000
-0.8576
-0.0000
-1.0000
0.0000
-0.6196
0.6942
0.3662
-0.3901
0.0861
-0.9167
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