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 NaCdO2 (Materials Project id mp-754567)

       131       57       44       -3        0        0  
        57      131       44        3        0        0  
        44       44       99        0        0        0  
        -3        3        0       23        0        0  
         0        0        0        0       23       -3  
         0        0        0        0       -3       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 72.333 GPaEV = 81.375 GPaGV = 31 GPaνV = 0.3125
ReussKR = 70.19 GPaER = 76.645 GPaGR = 29.076 GPaνR = 0.31801
HillKH = 71.262 GPaEH = 79.013 GPaGH = 30.038 GPaνH = 0.31521

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22.384 GPa 22.649 GPa 37.616 GPa 67 GPa 74.351 GPa 220 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 62.002 GPa 99.893 GPa 3.7313 TPa–1 6.7843 TPa–1 22.384 GPa 37.616 GPa0.157020.47042Value
Anisotropy 1.611 1.8182 1.68 2.9959Anisotropy
Axis 0.0000
0.6902
-0.7236
0.8618
0.4975
-0.0984
0.9659
0.2589
-0.0000
0.0000
0.0000
1.0000
-0.0000
0.2011
0.9796
0.8483
0.4898
0.2011
0.5166
0.2983
-0.8026
0.0000
0.7177
0.6964
Axis
-1.0000
0.0000
-0.0000
-0.5000
0.8660
-0.0000
-0.5000
0.8660
-0.0000
0.0000
-0.6964
0.7177
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