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 Ta (Materials Project id mp-569794)

       302      148      148        0        0        0  
       148      290      140        0        0        0  
       148      140      290        0        0        0  
         0        0        0       67        0        0  
         0        0        0        0       44        0  
         0        0        0        0        0       44  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 194.89 GPaEV = 165.05 GPaGV = 60.733 GPaνV = 0.35885
ReussKR = 194.69 GPaER = 156.47 GPaGR = 57.272 GPaνR = 0.36605
HillKH = 194.79 GPaEH = 160.78 GPaGH = 59.003 GPaνH = 0.36244

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
44 GPa 44 GPa 67 GPa 147.13 GPa 150 GPa 584.87 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 134.24 GPa 200.12 GPa 1.5572 TPa–1 1.7896 TPa–1 44 GPa 75 GPa0.224160.54754Value
Anisotropy 1.491 1.1493 1.705 2.4426Anisotropy
Axis 0.6872
0.5137
0.5137
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.9660
0.2587
0.0000
0.0000
1.0000
0.0002
0.7071
-0.7071
-0.6788
-0.0000
0.7343
0.7113
-0.0002
0.7028
Axis
1.0000
0.0000
-0.0000
0.0002
-0.7071
-0.7071
0.0000
-1.0000
-0.0000
0.7028
-0.0006
-0.7113
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