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 LiAlO2 (Materials Project id mp-3427)

       143       63       66        0        0        0  
        63      143       66        0        0        0  
        66       66      167        0        0        0  
         0        0        0       60        0        0  
         0        0        0        0       60        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 93.667 GPaEV = 134.62 GPaGV = 53.4 GPaνV = 0.26047
ReussKR = 93.08 GPaER = 130.99 GPaGR = 51.758 GPaνR = 0.26544
HillKH = 93.373 GPaEH = 132.81 GPaGH = 52.579 GPaνH = 0.26294

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
60 GPa 60 GPa 61 GPa 80 GPa 91.147 GPa 281.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 105.26 GPa 149.37 GPa 2.8805 TPa–1 3.9315 TPa–1 40 GPa 61 GPa0.11540.38371Value
Anisotropy 1.419 1.3649 1.525 3.3249Anisotropy
Axis 1.0000
0.0000
0.0000
0.5419
0.5419
0.6425
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.7071
-0.0000
1.0000
-0.0000
0.0000
-0.7071
0.7071
0.0000
-0.6855
-0.0000
0.7280
Axis
-0.7071
0.7071
0.0000
0.0000
1.0000
-0.0000
-0.7071
-0.7071
-0.0000
-0.0000
-1.0000
-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