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 NaHg (Materials Project id mp-255)

        23       17        9        0        0        0  
        17       26       11        0        0        0  
         9       11       30        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        7        0  
         0        0        0        0        0        9  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 17 GPaEV = 18 GPaGV = 6.8 GPaνV = 0.32353
ReussKR = 16.805 GPaER = 15.454 GPaGR = 5.7377 GPaνR = 0.34673
HillKH = 16.902 GPaEH = 16.737 GPaGH = 6.2689 GPaνH = 0.33496

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
4 GPa 7 GPa 7.3965 GPa 9 GPa 20.492 GPa 51.111 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 11.209 GPa 25.071 GPa 12.65 TPa–1 25.946 TPa–1 3.7067 GPa 9.9059 GPa0.071320.67488Value
Anisotropy 2.237 2.0510 2.672 9.4626Anisotropy
Axis 0.0000
0.8266
-0.5628
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0001
-0.5113
0.4885
-0.7071
1.0000
-0.0003
-0.0001
0.0000
1.0000
0.0000
Axis
-0.7071
-0.7071
-0.0000
0.5112
-0.4885
-0.7072
-0.0001
-0.0003
-1.0000
-1.0000
0.0000
-0.0000
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