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 Al2O3 (Materials Project id mp-1143)

       452      150      107       20        0        0  
       150      452      107      -20        0        0  
       107      107      454        0        0        0  
        20      -20        0      132        0        0  
         0        0        0        0      132       20  
         0        0        0        0       20      151  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 231.78 GPaEV = 368.66 GPaGV = 149.27 GPaνV = 0.2349
ReussKR = 231.43 GPaER = 359.43 GPaGR = 144.79 GPaνR = 0.24116
HillKH = 231.61 GPaEH = 364.05 GPaGH = 147.03 GPaνH = 0.23802

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
119.36 GPa 127.42 GPa 163.64 GPa 306.58 GPa 359.55 GPa 696.45 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 305.45 GPa 415.96 GPa 1.3857 TPa–1 1.5495 TPa–1 119.36 GPa 174.7 GPa0.109370.35318Value
Anisotropy 1.362 1.1182 1.464 3.2292Anisotropy
Axis -0.6898
0.3982
-0.6047
0.0000
0.0000
1.0000
0.3818
0.9242
-0.0000
0.0000
0.0000
1.0000
0.4627
0.2672
0.8453
0.0000
0.6135
-0.7897
-0.0000
0.4994
-0.8664
1.0000
0.0000
0.0000
Axis
-0.5000
0.8660
0.0000
-0.0000
0.7897
0.6135
-1.0000
-0.0000
-0.0000
-0.0000
0.8862
0.4633
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