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 CaTiO3 (Materials Project id mp-5827)

       334       95       95        0        0        0  
        95      334       95        0        0        0  
        95       95      334        0        0        0  
         0        0        0       95        0        0  
         0        0        0        0       95        0  
         0        0        0        0        0       95  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 174.67 GPaEV = 262 GPaGV = 104.8 GPaνV = 0.25
ReussKR = 174.67 GPaER = 259.26 GPaGR = 103.49 GPaνR = 0.25262
HillKH = 174.67 GPaEH = 260.63 GPaGH = 104.14 GPaνH = 0.25131

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
95 GPa 95 GPa 95 GPa 239 GPa 239 GPa 524 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 241.26 GPa 291.93 GPa 1.9084 TPa–1 1.9084 TPa–1 95 GPa 119.5 GPa0.191310.32738Value
Anisotropy 1.21 1.0000 1.258 1.7112Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.2500
0.9330
0.2588
-0.1294
0.9830
-0.1305
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.0000
-0.7071
0.7071
-0.0002
0.7071
Axis
0.1738
0.9848
0.0000
0.7071
-0.0005
-0.7071
-0.0000
-1.0000
-0.0000
0.7071
-0.0005
-0.7071
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