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 TiZnO3 (Materials Project id mp-14142)

       308      154       99       20       -7        0  
       154      308       99      -20        7        0  
        99       99      241        0        0        0  
        20      -20        0       31        0        7  
        -7        7        0        0       31       20  
         0        0        0        7       20       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 173.44 GPaEV = 164.92 GPaGV = 61.467 GPaνV = 0.34153
ReussKR = 167.41 GPaER = 112.99 GPaGR = 40.717 GPaνR = 0.38751
HillKH = 170.43 GPaEH = 139.35 GPaGH = 51.092 GPaνH = 0.36372

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22.727 GPa 24.088 GPa 85.273 GPa 160.91 GPa 173.14 GPa 529.86 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 66.85 GPa 233.48 GPa 1.5479 TPa–1 2.8777 TPa–1 22.727 GPa 87.337 GPa-0.101750.856Value
Anisotropy 3.493 1.8592 3.843Anisotropy
Axis -0.0856
0.7594
0.6449
0.7907
0.5836
0.1849
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.2926
0.2160
0.9315
0.5123
0.3778
0.7713
0.4673
0.3449
0.8140
-0.0745
0.6604
-0.7472
Axis
-0.5938
0.8046
-0.0000
0.6206
0.4579
-0.6365
-0.5938
0.8046
0.0000
0.0834
-0.7425
-0.6646
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