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 AlAs (Materials Project id mp-8881)

       125       44       32        0        0        0  
        44      125       32        0        0        0  
        32       32      143        0        0        0  
         0        0        0       32        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 67.667 GPaEV = 100.25 GPaGV = 40 GPaνV = 0.25309
ReussKR = 67.642 GPaER = 97.039 GPaGR = 38.48 GPaνR = 0.2609
HillKH = 67.654 GPaEH = 98.648 GPaGH = 39.24 GPaνH = 0.25698

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 32 GPa 41 GPa 81 GPa 108.91 GPa 203.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 87.57 GPa 130.88 GPa 4.7471 TPa–1 5.0183 TPa–1 32 GPa 50.342 GPa0.176470.38015Value
Anisotropy 1.495 1.0571 1.573 2.1542Anisotropy
Axis 0.7603
0.0000
-0.6496
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.5000
0.5000
0.7071
-0.3326
0.3326
0.8825
-0.4767
0.4767
0.7386
Axis
1.0000
0.0000
-0.0000
0.5000
0.5000
-0.7071
-0.7071
-0.7071
-0.0000
-0.5222
0.5223
-0.6742
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