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 LiTaO3 (Materials Project id mp-3666)

       223       51       78       -6        0        0  
        51      223       78        6        0        0  
        78       78      257        0        0        0  
        -6        6        0       83        0        0  
         0        0        0        0       83       -6  
         0        0        0        0       -6       86  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 124.11 GPaEV = 204.55 GPaGV = 83.467 GPaνV = 0.22532
ReussKR = 122.37 GPaER = 202.71 GPaGR = 82.814 GPaνR = 0.22391
HillKH = 123.24 GPaEH = 203.63 GPaGH = 83.14 GPaνH = 0.22462

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
78.315 GPa 82.198 GPa 90.685 GPa 154.86 GPa 172.8 GPa 376.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 189.49 GPa 217.18 GPa 2.0258 TPa–1 3.073 TPa–1 78.266 GPa 90.685 GPa0.126930.29982Value
Anisotropy 1.146 1.5169 1.159 2.3620Anisotropy
Axis 0.8207
0.4738
0.3193
0.6118
0.3533
-0.7077
0.0000
0.0000
1.0000
0.9668
0.2557
0.0000
0.0000
0.4824
-0.8760
0.6826
0.3941
0.6154
0.5000
0.8660
0.0000
-0.0000
0.3009
0.9537
Axis
-0.0000
-0.8760
-0.4824
-0.5000
0.8660
-0.0000
-0.8279
0.4780
-0.2934
0.0000
0.9537
-0.3009
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