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 ZnGeO3 (Materials Project id mp-1016930)

       293      146      146        0        0        0  
       146      293      146        0        0        0  
       146      146      293        0        0        0  
         0        0        0      100        0        0  
         0        0        0        0      100        0  
         0        0        0        0        0      100  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 195 GPaEV = 232.65 GPaGV = 89.4 GPaνV = 0.30116
ReussKR = 195 GPaER = 228.11 GPaGR = 87.396 GPaνR = 0.30503
HillKH = 195 GPaEH = 230.38 GPaGH = 88.398 GPaνH = 0.30309

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
100 GPa 100 GPa 100 GPa 147 GPa 147 GPa 585 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 195.89 GPa 256.2 GPa 1.7094 TPa–1 1.7094 TPa–1 73.5 GPa 100 GPa0.189460.40389Value
Anisotropy 1.308 1.0000 1.361 2.1318Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.3536
0.8536
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0004
-0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
-0.8660
0.0000
-0.7071
0.0002
-0.7071
0.0003
1.0000
-0.0003
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