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 TaGaCo2 (Materials Project id mp-30555)

       272      167      167        0        0        0  
       167      272      167        0        0        0  
       167      167      272        0        0        0  
         0        0        0      119        0        0  
         0        0        0        0      119        0  
         0        0        0        0        0      119  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 202 GPaEV = 240.53 GPaGV = 92.4 GPaνV = 0.30155
ReussKR = 202 GPaER = 209.63 GPaGR = 78.982 GPaνR = 0.32704
HillKH = 202 GPaEH = 225.23 GPaGH = 85.691 GPaνH = 0.31417

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
105 GPa 105 GPa 119 GPa 119 GPa 119 GPa 606 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 144.94 GPa 298.4 GPa 1.6502 TPa–1 1.6502 TPa–1 52.5 GPa 119 GPa-0.00861580.61926Value
Anisotropy 2.059 1.0000 2.267Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.2500
0.9330
0.2588
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-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