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 Sb2Te3 (Materials Project id mp-1201)

        63       15       10       -6        0        0  
        15       63       10        6        0        0  
        10       10       14        0        0        0  
        -6        6        0       10        0        0  
         0        0        0        0       10       -6  
         0        0        0        0       -6       24  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 23.333 GPaEV = 38.671 GPaGV = 15.8 GPaνV = 0.22378
ReussKR = 13.515 GPaER = 24.446 GPaGR = 10.198 GPaνR = 0.19854
HillKH = 18.424 GPaEH = 31.572 GPaGH = 12.999 GPaνH = 0.2144

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7.7805 GPa 8.1913 GPa 11.014 GPa 26.22 GPa 49.809 GPa 80.986 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 11.436 GPa 59.594 GPa 4.4843 TPa–1 65.022 TPa–1 7.1556 GPa 26.22 GPa-0.0108160.79148Value
Anisotropy 5.211 14.5000 3.664Anisotropy
Axis 0.0000
0.0000
1.0000
0.8466
0.4888
-0.2107
1.0000
0.0001
0.0000
0.0000
0.0000
1.0000
-0.0001
0.8815
0.4723
0.8122
0.4690
0.3469
-0.7384
0.4263
-0.5224
-0.5000
0.8660
-0.0000
Axis
0.0000
-0.4723
0.8815
-0.5000
0.8660
-0.0000
-0.5000
-0.8660
-0.0000
-0.4664
-0.2693
-0.8426
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