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 Nb3Au (Materials Project id mp-2752)

       331      110      110        0        0        0  
       110      331      110        0        0        0  
       110      110      331        0        0        0  
         0        0        0       41        0        0  
         0        0        0        0       41        0  
         0        0        0        0        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 183.67 GPaEV = 183.49 GPaGV = 68.8 GPaνV = 0.33349
ReussKR = 183.67 GPaER = 149.48 GPaGR = 54.782 GPaνR = 0.36435
HillKH = 183.67 GPaEH = 166.68 GPaGH = 61.791 GPaνH = 0.34875

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 41 GPa 41 GPa 221 GPa 221 GPa 551 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 114.48 GPa 276.12 GPa 1.8149 TPa–1 1.8149 TPa–1 41 GPa 110.5 GPa0.121140.63546Value
Anisotropy 2.412 1.0000 2.695 5.2455Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.1464
0.3536
0.9239
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
-0.0000
0.7071
-0.0005
-0.7071
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