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 TaCo2 (Materials Project id mp-1799)

       383      174      174        0        0        0  
       174      383      174        0        0        0  
       174      174      383        0        0        0  
         0        0        0      131        0        0  
         0        0        0        0      131        0  
         0        0        0        0        0      131  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 243.67 GPaEV = 310.12 GPaGV = 120.4 GPaνV = 0.28788
ReussKR = 243.67 GPaER = 306.88 GPaGR = 118.94 GPaνR = 0.2901
HillKH = 243.67 GPaEH = 308.5 GPaGH = 119.67 GPaνH = 0.28899

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
131 GPa 131 GPa 131 GPa 209 GPa 209 GPa 731 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 274.29 GPa 333.27 GPa 1.368 TPa–1 1.368 TPa–1 104.5 GPa 131 GPa0.207140.3602Value
Anisotropy 1.215 1.0000 1.254 1.7389Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
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
0.7660
0.6428
-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