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 Li3Sb (Materials Project id mp-7955)

        73       15        1        0        0        0  
        15       73        1        0        0        0  
         1        1       71        0        0        0  
         0        0        0       16        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 27.889 GPaEV = 58.689 GPaGV = 25.533 GPaνV = 0.14927
ReussKR = 27.637 GPaER = 53.369 GPaGR = 22.649 GPaνR = 0.17816
HillKH = 27.763 GPaEH = 56.059 GPaGH = 24.091 GPaνH = 0.16347

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 16 GPa 29 GPa 58 GPa 70.883 GPa 88.117 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 44.163 GPa 70.977 GPa 11.207 TPa–1 13.769 TPa–1 16 GPa 34.827 GPa0.0113640.3801Value
Anisotropy 1.607 1.2286 2.177 33.4491Anisotropy
Axis 0.7094
0.0005
0.7049
0.0000
0.0000
1.0000
0.8660
0.5000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1699
0.6864
-0.7071
0.0000
0.0000
1.0000
0.3367
0.6202
-0.7085
Axis
1.0000
0.0000
-0.0000
0.1700
-0.6864
-0.7071
0.1736
0.9848
-0.0000
0.3381
0.6226
0.7057
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