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 Na2HgO2 (Materials Project id mp-4961)

        49        1       20        0        0        0  
         1       49       20        0        0        0  
        20       20      129        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       15  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 34.333 GPaEV = 49.822 GPaGV = 19.8 GPaνV = 0.25814
ReussKR = 24.781 GPaER = 38.084 GPaGR = 15.309 GPaνR = 0.24386
HillKH = 29.557 GPaEH = 43.96 GPaGH = 17.554 GPaνH = 0.25212

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 15 GPa 40.918 GPa 48 GPa 138.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 31.092 GPa 113 GPa 1.7699 TPa–1 19.292 TPa–1 11 GPa 26.482 GPa-0.0457690.61498Value
Anisotropy 3.634 10.9000 2.407Anisotropy
Axis 0.5937
0.5937
0.5431
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
1.0000
0.0007
-0.0000
0.5522
0.0001
0.8337
Axis
-0.7880
0.6157
-0.0000
-0.7071
-0.0002
-0.7071
-0.0007
1.0000
-0.0000
0.8337
0.0003
-0.5522
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