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 Sb2Te (Materials Project id mp-6997)

        77       21       21      -15        0        0  
        21       77       21       15        0        0  
        21       21       34        0        0        0  
       -15       15        0       27        0        0  
         0        0        0        0       27      -15  
         0        0        0        0      -15       28  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 34.889 GPaEV = 60.018 GPaGV = 24.733 GPaνV = 0.21329
ReussKR = 29.878 GPaER = 43.056 GPaGR = 17.088 GPaνR = 0.25982
HillKH = 32.383 GPaEH = 51.621 GPaGH = 20.911 GPaνH = 0.23432

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12.492 GPa 15.805 GPa 22.342 GPa 42.508 GPa 67.195 GPa 109.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 25 GPa 92.33 GPa 5.3061 TPa–1 22.857 TPa–1 12.002 GPa 42.508 GPa-0.00197320.73136Value
Anisotropy 3.693 4.3077 3.542Anisotropy
Axis 0.0000
0.0000
1.0000
0.7753
0.4476
-0.4456
-0.9697
0.2441
0.0000
0.0000
0.0000
1.0000
0.0000
0.8424
0.5389
-0.6225
0.3594
0.6952
-0.6702
0.3869
-0.6333
-0.5000
0.8660
-0.0000
Axis
-0.0000
0.5389
-0.8424
-0.5000
-0.8660
0.0000
-0.5000
-0.8660
-0.0000
-0.5497
-0.3174
-0.7728
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