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 BaAl2B2O7 (Materials Project id mp-9844)

       187       62       61        6        0        0  
        62      187       61       -6        0        0  
        61       61      111        0        0        0  
         6       -6        0       15        0        0  
         0        0        0        0       15        6  
         0        0        0        0        6       62  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 94.778 GPaEV = 101.65 GPaGV = 38.467 GPaνV = 0.32125
ReussKR = 88.974 GPaER = 68.498 GPaGR = 24.968 GPaνR = 0.37169
HillKH = 91.876 GPaEH = 85.333 GPaGH = 31.718 GPaνH = 0.3452

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14.246 GPa 14.349 GPa 62.754 GPa 69.533 GPa 125.65 GPa 290.47 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 44.766 GPa 149.57 GPa 2.4756 TPa–1 6.2881 TPa–1 14.252 GPa 63.237 GPa0.0235230.75022Value
Anisotropy 3.341 2.5400 4.437 31.8934Anisotropy
Axis -0.5986
0.3464
-0.7223
0.0000
0.9978
-0.0664
0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
-0.1072
0.0617
0.9923
0.7071
0.7017
-0.0875
-0.7020
0.4030
0.5872
0.0000
0.7887
-0.6148
Axis
0.5014
0.8652
0.0003
-0.7071
0.7017
-0.0875
-0.4979
-0.8673
0.0000
-0.0000
-0.6148
-0.7887
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