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 TaSbRu (Materials Project id mp-31454)

       266      130      130        0        0        0  
       130      266      130        0        0        0  
       130      130      266        0        0        0  
         0        0        0       72        0        0  
         0        0        0        0       72        0  
         0        0        0        0        0       72  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 175.33 GPaEV = 186.27 GPaGV = 70.4 GPaνV = 0.32294
ReussKR = 175.33 GPaER = 186.14 GPaGR = 70.345 GPaνR = 0.32306
HillKH = 175.33 GPaEH = 186.21 GPaGH = 70.372 GPaνH = 0.323

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
72 GPa 72 GPa 72 GPa 136 GPa 136 GPa 526 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 180.65 GPa 189.99 GPa 1.9011 TPa–1 1.9011 TPa–1 68 GPa 72 GPa0.302550.34086Value
Anisotropy 1.052 1.0000 1.059 1.1266Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.8660
0.0000
0.5000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.7071
-0.0000
-0.7071
Axis
0.7071
-0.0005
-0.7071
0.4962
0.8682
-0.0000
0.7071
-0.0006
-0.7071
-0.0000
-1.0000
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