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 K2Ca(CO3)2 (Materials Project id mp-6494)

       130       46       35       -6        0        0  
        46      130       35        6        0        0  
        35       35       52        0        0        0  
        -6        6        0       15        0        0  
         0        0        0        0       15       -6  
         0        0        0        0       -6       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 60.444 GPaEV = 71.561 GPaGV = 27.467 GPaνV = 0.30268
ReussKR = 47.871 GPaER = 53.41 GPaGR = 20.323 GPaνR = 0.31405
HillKH = 54.158 GPaEH = 62.493 GPaGH = 23.895 GPaνH = 0.30768

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
13.727 GPa 13.972 GPa 34.665 GPa 43.273 GPa 85.028 GPa 193.33 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 35.929 GPa 104.43 GPa 2.5366 TPa–1 15.816 TPa–1 13.727 GPa 43.273 GPa0.0551720.65858Value
Anisotropy 2.907 6.2353 3.152 11.9368Anisotropy
Axis 0.4641
0.2679
0.8443
-0.8597
0.4963
-0.1205
0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
0.0000
0.2076
0.9782
0.8472
0.4891
0.2076
0.6885
0.3975
-0.6066
0.5000
0.8660
-0.0000
Axis
-1.0000
0.0000
0.0000
-0.5000
0.8660
-0.0000
-0.5000
0.8660
0.0000
-0.4402
0.2542
0.8612
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