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 NaO3 (Materials Project id mp-22464)

        70       -3       12        0        0        0  
        -3       35        6        0        0        0  
        12        6       48        0        0        0  
         0        0        0        7        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       13  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 20.333 GPaEV = 38.775 GPaGV = 16.4 GPaνV = 0.18217
ReussKR = 18.364 GPaER = 31.882 GPaGR = 13.167 GPaνR = 0.21065
HillKH = 19.349 GPaEH = 35.348 GPaGH = 14.784 GPaνH = 0.19552

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 13 GPa 16 GPa 31.126 GPa 46.592 GPa 75.282 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 21.399 GPa 66.409 GPa 13.025 TPa–1 27.259 TPa–1 7 GPa 24.656 GPa-0.131390.53549Value
Anisotropy 3.103 2.0928 3.522Anisotropy
Axis 0.0000
0.7368
0.6761
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.0003
-0.0000
1.0000
0.7071
0.7071
0.0000
1.0000
0.0006
-0.0000
0.0002
0.6712
-0.7412
Axis
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0001
-0.0006
1.0000
0.0000
0.0001
-0.7412
-0.6712
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