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-1007760)

       127       32       17        0        0        0  
        32      127       17        0        0        0  
        17       17      147        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       48  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 59.222 GPaEV = 111 GPaGV = 46.733 GPaνV = 0.18761
ReussKR = 59.208 GPaER = 107.39 GPaGR = 44.832 GPaνR = 0.1977
HillKH = 59.215 GPaEH = 109.2 GPaGH = 45.783 GPaνH = 0.19264

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37 GPa 37 GPa 48 GPa 95 GPa 128.22 GPa 177.78 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 97.028 GPa 143.36 GPa 5.4837 TPa–1 5.703 TPa–1 37 GPa 59.173 GPa0.106920.32099Value
Anisotropy 1.478 1.0400 1.599 3.0022Anisotropy
Axis 0.7583
-0.0001
0.6519
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1305
0.9914
0.0000
-0.0000
-0.0000
1.0000
0.5000
0.5000
0.7071
0.0000
0.0000
1.0000
0.4826
0.4828
0.7308
Axis
-0.7648
0.6443
0.0000
0.5000
0.5000
-0.7071
-0.7660
0.6428
0.0000
0.5169
0.5165
-0.6826
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