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 Au (Materials Project id mp-81)

       144      134      134        0        0        0  
       134      144      134        0        0        0  
       134      134      144        0        0        0  
         0        0        0       29        0        0  
         0        0        0        0       29        0  
         0        0        0        0        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 137.33 GPaEV = 55.583 GPaGV = 19.4 GPaνV = 0.43255
ReussKR = 137.33 GPaER = 29.093 GPaGR = 9.9315 GPaνR = 0.46469
HillKH = 137.33 GPaEH = 42.485 GPaGH = 14.666 GPaνH = 0.44844

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 10 GPa 29 GPa 29 GPa 29 GPa 412 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.82 GPa 81.279 GPa 2.4272 TPa–1 2.4272 TPa–1 5 GPa 29 GPa-0.339321.2463Value
Anisotropy 5.484 1.0000 5.8Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.9992
-0.0001
-0.0393
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
-0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.1736
0.9848
-0.0000
-0.7071
-0.0002
-0.7071
-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