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 Na4CoO3 (Materials Project id mp-18762)

        75       37       26        0        2        0  
        37       87       30        0       -2        0  
        26       30       72        0        1        0  
         0        0        0       16        0        2  
         2       -2        1        0       15        0  
         0        0        0        2        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 46.667 GPaEV = 52.04 GPaGV = 19.8 GPaνV = 0.31414
ReussKR = 45.854 GPaER = 49.638 GPaGR = 18.808 GPaνR = 0.31958
HillKH = 46.26 GPaEH = 50.841 GPaGH = 19.304 GPaνH = 0.31683

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14.697 GPa 15.298 GPa 21.702 GPa 43.762 GPa 49.297 GPa 141.24 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 38.614 GPa 63.434 GPa 5.0825 TPa–1 9.1517 TPa–1 14.771 GPa 24.52 GPa0.163630.46513Value
Anisotropy 1.643 1.8006 1.66 2.8426Anisotropy
Axis -0.7371
0.0000
0.6758
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
-0.3187
-0.0000
0.9479
-0.0349
0.0004
0.9994
-0.1081
0.7071
-0.6988
0.5838
-0.0000
0.8119
0.6765
-0.0001
0.7364
Axis
0.9994
0.0006
0.0349
-0.1081
-0.7071
-0.6988
0.0000
1.0000
0.0000
0.7364
-0.0002
-0.6765
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