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 AlAsO4 (Materials Project id mp-7849)

        57      -10       19        0        0       -0  
       -10       57       19        0        0        0  
        19       19       51        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       19        0  
        -0        0        0        0        0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 24.556 GPaEV = 47.805 GPaGV = 20.333 GPaνV = 0.17553
ReussKR = 22.945 GPaER = 42.703 GPaGR = 17.945 GPaνR = 0.18982
HillKH = 23.75 GPaEH = 45.26 GPaGH = 19.139 GPaνH = 0.18239

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 19 GPa 19 GPa 22.056 GPa 67 GPa 75.944 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 34.349 GPa 50.439 GPa 5.3731 TPa–1 19.104 TPa–1 12.522 GPa 33.5 GPa-0.34210.5Value
Anisotropy 1.468 3.5556 2.675Anisotropy
Axis -0.7071
0.7071
0.0000
0.7932
-0.0000
0.6090
0.0000
0.0000
1.0000
0.9239
0.3827
0.0000
-0.5001
0.4999
-0.7071
0.7071
0.7071
0.0000
1.0000
0.0007
-0.0000
1.0000
0.0003
0.0000
Axis
0.4998
-0.5001
-0.7071
-0.7071
0.7071
0.0000
-0.0007
1.0000
-0.0000
0.0000
0.0001
-1.0000
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