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 Sn4Bi2Se7 (Materials Project id mp-675477)

        64        6        7        0       15        0  
         6      113       11        0       -2        0  
         7       11       67        0       -8        0  
         0        0        0       13        0        1  
        15       -2       -8        0       21        0  
         0        0        0        1        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 32.444 GPaEV = 55.156 GPaGV = 22.667 GPaνV = 0.21667
ReussKR = 29.91 GPaER = 34.613 GPaGR = 13.24 GPaνR = 0.30713
HillKH = 31.177 GPaEH = 45.186 GPaGH = 17.953 GPaνH = 0.25844

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5.8599 GPa 13.14 GPa 14.44 GPa 63.967 GPa 70.013 GPa 116.58 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 19.387 GPa 110.6 GPa 6.8246 TPa–1 16.654 TPa–1 5.8599 GPa 37.177 GPa-0.129710.79639Value
Anisotropy 5.705 2.4404 6.344Anisotropy
Axis 0.7270
0.6517
-0.2163
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
-0.8729
0.0000
0.4880
-0.9903
0.0000
0.1387
0.8861
0.0001
-0.4635
-0.2733
0.2754
0.9217
-0.6383
0.6935
-0.3341
Axis
-0.0000
-1.0000
0.0000
-0.4635
-0.0001
-0.8861
-0.8273
0.4216
-0.3713
-0.7211
-0.6906
-0.0559
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