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 Ta2CS2 (Materials Project id mp-559976)

       251       46        4       -3        0        0  
        46      251        4        3        0        0  
         4        4        9        0        0        0  
        -3        3        0        1        0        0  
         0        0        0        0        1       -3  
         0        0        0        0       -3      103  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 68.778 GPaEV = 123.58 GPaGV = 51.467 GPaνV = 0.20054
ReussKR = 8.8328 GPaER = 5.8633 GPaGR = 2.1101 GPaνR = 0.38936
HillKH = 38.805 GPaEH = 65.332 GPaGH = 26.788 GPaνH = 0.2194

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
0.9118 GPa0.91184 GPa 8.8889 GPa 103.09 GPa 205.09 GPa 297.11 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.1982 GPa 242.04 GPa 1.8932 TPa–1 109.43 TPa–1 0.91151 GPa 103.09 GPa-1.54730.9069Value
Anisotropy 75.68 57.8000 113.1Anisotropy
Axis 0.0000
0.6734
-0.7392
0.8632
0.5046
-0.0147
1.0000
0.0001
0.0000
0.0000
0.0000
1.0000
-0.0255
-0.0145
0.9996
0.0000
0.9996
-0.0294
0.5004
0.8658
-0.0000
-0.0000
0.9596
0.2814
Axis
-0.4696
0.8829
0.0009
-1.0000
0.0000
0.0000
-0.6228
0.3599
-0.6947
-0.0000
-0.2814
0.9596
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