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 Ti7Al2O15 (Materials Project id mp-15397)

       323      144      110        0        0        0  
       144      364      120        0        6        0  
       110      120      343        0        7        0  
         0        0        0       79        0        4  
         0        6        7        0       57        0  
         0        0        0        4        0       91  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 197.56 GPaEV = 232.44 GPaGV = 89.133 GPaνV = 0.3039
ReussKR = 196.28 GPaER = 219.54 GPaGR = 83.568 GPaνR = 0.31357
HillKH = 196.92 GPaEH = 226.01 GPaGH = 86.35 GPaνH = 0.3087

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56.713 GPa 77.789 GPa 92.211 GPa 197.82 GPa 238.03 GPa 594.44 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 169.43 GPa 289.26 GPa 1.4212 TPa–1 2.0244 TPa–1 56.647 GPa 115.85 GPa0.149380.50998Value
Anisotropy 1.707 1.4244 2.045 3.4140Anisotropy
Axis -0.7033
-0.0000
0.7109
0.0374
-0.0002
0.9993
0.0000
1.0000
0.0000
-0.7071
0.0000
0.7071
0.0335
0.0009
0.9994
0.0049
0.7071
0.7071
0.5887
-0.0000
-0.8084
-0.7101
-0.0001
-0.7041
Axis
0.9994
-0.0003
-0.0335
-0.0048
0.7071
-0.7071
-0.0000
1.0000
-0.0000
0.7041
0.0000
-0.7101
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