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 BaAl4 (Materials Project id mp-1903)

        87       27       31        0        0        0  
        27       87       31        0        0        0  
        31       31      108        0        0        0  
         0        0        0       36        0        0  
         0        0        0        0       36        0  
         0        0        0        0        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 51.111 GPaEV = 84.823 GPaGV = 34.667 GPaνV = 0.2234
ReussKR = 50.437 GPaER = 84.045 GPaGR = 34.38 GPaνR = 0.22228
HillKH = 50.774 GPaEH = 84.434 GPaGH = 34.524 GPaνH = 0.22284

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36 GPa 36 GPa 37 GPa 60 GPa 67.057 GPa 154.94 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 73.906 GPa 91.174 GPa 5.0048 TPa–1 7.411 TPa–1 30 GPa 37 GPa0.130450.27304Value
Anisotropy 1.234 1.4808 1.233 2.0930Anisotropy
Axis 1.0000
0.0000
0.0000
0.1731
0.1731
0.9696
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
0.3584
0.0001
0.9336
Axis
-0.7071
0.7071
-0.0000
-0.0000
1.0000
-0.0000
-0.7071
0.7071
-0.0000
0.0000
1.0000
-0.0001
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