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 Ac2O3 (Materials Project id mp-11107)

       180      108       71       26        0        0  
       108      180       71      -26        0        0  
        71       71      113        0        0        0  
        26      -26        0       50        0        0  
         0        0        0        0       50       26  
         0        0        0        0       26       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 108.11 GPaEV = 111.71 GPaGV = 42.067 GPaνV = 0.32778
ReussKR = 97.661 GPaER = 75.389 GPaGR = 27.487 GPaνR = 0.37134
HillKH = 102.89 GPaEH = 93.766 GPaGH = 34.777 GPaνH = 0.34811

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16.074 GPa 22.62 GPa 67.315 GPa 69.926 GPa 99.38 GPa 333.69 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 48.047 GPa 173.29 GPa 1.8698 TPa–1 6.4999 TPa–1 16.074 GPa 69.926 GPa-0.0521370.90016Value
Anisotropy 3.607 3.4762 4.35Anisotropy
Axis 0.0000
0.8744
0.4852
-0.0000
0.8573
-0.5149
-0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
1.0000
0.0003
0.0002
0.5268
0.3041
-0.7937
0.4819
0.2783
0.8308
-1.0000
-0.0000
0.0000
Axis
-0.0001
0.7937
-0.6083
-0.5000
0.8660
0.0000
-0.5000
0.8660
-0.0000
-0.0000
-0.8444
-0.5357
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