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 TcAs3 (Materials Project id mp-972202)

       228      106      115        0        0        0  
       106      228      115        0        0        0  
       115      115      145        0        0        0  
         0        0        0       61        0        0  
         0        0        0        0       61        0  
         0        0        0        0        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 141.44 GPaEV = 132.91 GPaGV = 49.467 GPaνV = 0.34339
ReussKR = 134.02 GPaER = 117.87 GPaGR = 43.547 GPaνR = 0.35342
HillKH = 137.73 GPaEH = 125.41 GPaGH = 46.507 GPaνH = 0.34825

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37 GPa 51.404 GPa 61 GPa 61 GPa 122 GPa 427.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 65.808 GPa 160.83 GPa 1.3649 TPa–1 4.7316 TPa–1 28 GPa 61 GPa0.0514060.70734Value
Anisotropy 2.444 3.4667 2.179 13.7598Anisotropy
Axis 0.0000
0.0000
1.0000
0.8568
0.0000
0.5157
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5001
0.4999
0.7071
0.0000
0.0000
1.0000
-0.4965
0.4963
-0.7122
1.0000
0.0000
-0.0000
Axis
-0.4999
0.5001
-0.7071
0.7660
0.6428
-0.0000
0.5035
-0.5037
-0.7020
-0.0000
0.0002
-1.0000
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