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 Li2LaTa2O7 (Materials Project id mp-15901)

       308       83       65        0        0        0  
        83      308       65        0        0        0  
        65       65      107        0        0        0  
         0        0        0       67        0        0  
         0        0        0        0       67        0  
         0        0        0        0        0       63  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 127.67 GPaEV = 184.79 GPaGV = 73.4 GPaνV = 0.25876
ReussKR = 96.774 GPaER = 158.26 GPaGR = 64.47 GPaνR = 0.22743
HillKH = 112.22 GPaEH = 171.66 GPaGH = 68.935 GPaνH = 0.24506

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
63 GPa 67 GPa 67 GPa 79.843 GPa 225 GPa 418.16 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 85.389 GPa 261.46 GPa 1.258 TPa–1 7.8174 TPa–1 47.224 GPa 112.5 GPa0.0536470.50903Value
Anisotropy 3.062 6.2143 2.382 9.4885Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.2549
0.9670
0.0000
0.0000
0.0000
1.0000
0.5001
0.5000
-0.7071
0.7071
0.7071
-0.0000
0.4859
0.4859
0.7265
1.0000
0.0002
0.0000
Axis
-0.5000
-0.5000
-0.7071
-0.7071
0.7071
-0.0000
0.5137
0.5137
-0.6871
0.0000
0.0003
-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