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 TaBe12 (Materials Project id mp-567842)

       261       59       59        0        0        0  
        59      377       -7        0        0        0  
        59       -7      377        0        0        0  
         0        0        0      127        0        0  
         0        0        0        0      149        0  
         0        0        0        0        0      149  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 137.44 GPaEV = 322.26 GPaGV = 145.27 GPaνV = 0.10922
ReussKR = 136.6 GPaER = 313.09 GPaGR = 140.02 GPaνR = 0.11799
HillKH = 137.02 GPaEH = 317.69 GPaGH = 142.65 GPaνH = 0.11357

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
127 GPa 149 GPa 149 GPa 215.84 GPa 384 GPa 415.16 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 242.18 GPa 362.85 GPa 2.2543 TPa–1 2.8122 TPa–1 112.73 GPa 192 GPa-0.0559230.2387Value
Anisotropy 1.498 1.2475 1.703Anisotropy
Axis 1.0000
0.0000
0.0000
0.2024
-0.0000
0.9793
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.5000
0.5000
0.0001
0.7071
-0.7071
-0.0002
0.0001
1.0000
0.0000
0.0000
1.0000
Axis
-0.7071
0.5000
0.5000
0.0002
-0.7071
-0.7071
0.0000
-1.0000
0.0001
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