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 Te (Materials Project id mp-10654)

        91       32       32       -0       -0        0  
        32       91       32       -0       -0        0  
        32       32       91       -1       -1        0  
        -0       -0       -1        3        0       -0  
        -0       -0       -1        0        3       -0  
         0        0        0       -0       -0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 51.667 GPaEV = 37.509 GPaGV = 13.6 GPaνV = 0.379
ReussKR = 51.592 GPaER = 13.595 GPaGR = 4.6682 GPaνR = 0.45608
HillKH = 51.629 GPaEH = 25.876 GPaGH = 9.1341 GPaνH = 0.41647

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2.9718 GPa 3 GPa 3 GPa 59 GPa 59.024 GPa 155 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 8.6959 GPa 74.33 GPa 4.9383 TPa–1 8.0081 TPa–1 2.9706 GPa 29.519 GPa0.0335270.90467Value
Anisotropy 8.548 1.6216 9.937 26.9830Anisotropy
Axis 0.5682
0.5682
0.5952
1.0000
0.0000
0.0039
0.5059
0.5060
-0.6986
0.4940
0.4940
0.7155
-0.0125
-0.0125
0.9998
0.7004
-0.0132
0.7136
0.7134
0.0031
-0.7007
0.7138
0.0066
-0.7003
Axis
0.7070
0.7070
0.0177
0.7137
0.0135
-0.7003
0.0006
1.0000
0.0051
-0.7004
0.0041
-0.7138
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