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 ZnO (Materials Project id mp-2133)

       188      109       92        0        0        0  
       109      188       92        0        0        0  
        92       92      205        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 129.67 GPaEV = 113.23 GPaGV = 41.8 GPaνV = 0.35446
ReussKR = 129.67 GPaER = 110.65 GPaGR = 40.746 GPaνR = 0.35778
HillKH = 129.67 GPaEH = 111.94 GPaGH = 41.273 GPaνH = 0.35612

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37 GPa 37 GPa 39 GPa 79 GPa 113 GPa 389 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 102.89 GPa 148 GPa 2.5707 TPa–1 2.5707 TPa–1 37 GPa 51.011 GPa0.239410.46653Value
Anisotropy 1.438 1.0000 1.379 1.9486Anisotropy
Axis 0.5636
0.5636
0.6040
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
0.2500
0.9330
0.2588
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
0.7071
0.0000
0.7071
0.7071
-0.0000
Axis
-0.7662
0.6426
-0.0000
0.7071
-0.0005
-0.7071
0.0004
-0.0004
-1.0000
-0.7071
0.7071
-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