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-105)

        66       15       36        0       24        0  
        15       71       45        0      -19        0  
        36       45       79        0       -2        0  
         0        0        0       28        0       -7  
        24      -19       -2        0       43        0  
         0        0        0       -7        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 45.333 GPaEV = 59.895 GPaGV = 23.4 GPaνV = 0.2798
ReussKR = 41.181 GPaER = 29.292 GPaGR = 10.602 GPaνR = 0.38145
HillKH = 43.257 GPaEH = 45.095 GPaGH = 17.001 GPaνH = 0.32625

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3.9616 GPa 17.004 GPa 23.725 GPa 30.038 GPa 79.236 GPa 139.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 13.529 GPa 120.8 GPa 0.50784 TPa–1 13.907 TPa–1 3.9616 GPa 46.272 GPa-0.392291.1356Value
Anisotropy 8.929 27.3855 11.68Anisotropy
Axis -0.6764
0.7199
-0.1555
-0.7946
0.0000
-0.6071
0.1224
-0.0000
0.9925
0.9925
-0.0000
-0.1225
0.9601
-0.0001
0.2796
-0.8334
0.5502
0.0517
0.4370
0.6041
-0.6664
-0.3819
0.3987
-0.8338
Axis
0.0001
1.0000
-0.0000
-0.3155
-0.3969
-0.8619
-0.5221
-0.4329
-0.7348
-0.7289
-0.6846
0.0065
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