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 Ge (Materials Project id mp-32)

       104       37       37        0        0        0  
        37      104       37        0        0        0  
        37       37      104        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       56  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 59.333 GPaEV = 111.55 GPaGV = 47 GPaνV = 0.18667
ReussKR = 59.333 GPaER = 106.11 GPaGR = 44.141 GPaνR = 0.20194
HillKH = 59.333 GPaEH = 108.85 GPaGH = 45.571 GPaνH = 0.19425

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56 GPa 56 GPa 56 GPa 67 GPa 67 GPa 178 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 84.582 GPa 127.79 GPa 5.618 TPa–1 5.618 TPa–1 33.5 GPa 56 GPa0.0117930.35157Value
Anisotropy 1.511 1.0000 1.672 29.8129Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.8660
0.0000
0.5000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
-0.7071
0.0002
-0.7071
0.0000
1.0000
0.0000
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