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 BaTiO3 (Materials Project id mp-2998)

       282      104      104        0        0        0  
       104      282      104        0        0        0  
       104      104      282        0        0        0  
         0        0        0      120        0        0  
         0        0        0        0      120        0  
         0        0        0        0        0      120  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 163.33 GPaEV = 264.68 GPaGV = 107.6 GPaνV = 0.22992
ReussKR = 163.33 GPaER = 260.07 GPaGR = 105.33 GPaνR = 0.23462
HillKH = 163.33 GPaEH = 262.38 GPaGH = 106.46 GPaνH = 0.23226

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
120 GPa 120 GPa 120 GPa 178 GPa 178 GPa 490 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 225.96 GPa 289.18 GPa 2.0408 TPa–1 2.0408 TPa–1 89 GPa 120 GPa0.126150.32227Value
Anisotropy 1.28 1.0000 1.348 2.5548Anisotropy
Axis 0.0000
1.0000
0.0000
0.5774
0.5774
0.5773
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0004
1.0000
0.0003
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