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 Ge3(BiO3)4 (Materials Project id mp-23560)

       109       22       22        0        0        0  
        22      109       22        0        0        0  
        22       22      109        0        0        0  
         0        0        0       39        0        0  
         0        0        0        0       39        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 51 GPaEV = 96.632 GPaGV = 40.8 GPaνV = 0.18421
ReussKR = 51 GPaER = 96.414 GPaGR = 40.683 GPaνR = 0.18492
HillKH = 51 GPaEH = 96.523 GPaGH = 40.742 GPaνH = 0.18457

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 39 GPa 39 GPa 87 GPa 87 GPa 153 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 93.234 GPa 101.61 GPa 6.5359 TPa–1 6.5359 TPa–1 39 GPa 43.5 GPa0.157340.22046Value
Anisotropy 1.09 1.0000 1.115 1.4012Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9914
0.0000
-0.1305
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0000
-0.7071
0.7071
-0.0002
0.7071
Axis
0.9397
0.3420
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
1.0000
-0.0000
0.7071
-0.0006
-0.7071
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