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-5986)

       259      106       76        0        0        0  
       106      259       76        0        0        0  
        76       76       85        0        0        0  
         0        0        0       81        0        0  
         0        0        0        0       81        0  
         0        0        0        0        0      116  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 124.33 GPaEV = 194.76 GPaGV = 78.6 GPaνV = 0.23893
ReussKR = 84.299 GPaER = 143.59 GPaGR = 59.036 GPaνR = 0.21611
HillKH = 104.32 GPaEH = 169.24 GPaGH = 68.818 GPaνH = 0.22961

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48.501 GPa 81 GPa 81 GPa 116 GPa 153 GPa 401.5 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.351 GPa 243.48 GPa 0.46218 TPa–1 10.938 TPa–1 31.25 GPa 116 GPa-0.146570.89975Value
Anisotropy 4.564 23.6667 3.712Anisotropy
Axis 0.0000
0.0000
1.0000
0.6665
0.6665
0.3339
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
1.0000
-0.0003
-0.0000
0.7371
0.0001
-0.6758
0.7071
0.7071
-0.0000
Axis
-0.7071
-0.0002
-0.7071
0.0003
1.0000
0.0000
-0.6758
-0.0000
-0.7371
-0.0000
-0.0000
-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