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 CaCO3 (Materials Project id mp-556235)

       112       70       60        0      -15        0  
        70      149       41        0        9        0  
        60       41      103        0      -21        0  
         0        0        0       21        0        5  
       -15        9      -21        0       39        0  
         0        0        0        5        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 78.444 GPaEV = 93.37 GPaGV = 35.867 GPaνV = 0.30162
ReussKR = 71.826 GPaER = 75.327 GPaGR = 28.421 GPaνR = 0.32521
HillKH = 75.135 GPaEH = 84.396 GPaGH = 32.144 GPaνH = 0.31279

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20.28 GPa 27.398 GPa 42.233 GPa 55.72 GPa 93.783 GPa 239.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.775 GPa 134.89 GPa 2.4499 TPa–1 8.6977 TPa–1 20.321 GPa 56.661 GPa0.026090.72122Value
Anisotropy 2.508 3.5502 2.788 27.6432Anisotropy
Axis -0.9284
-0.0000
-0.3715
0.5768
0.8068
0.1280
0.0000
1.0000
0.0000
0.4784
-0.0000
0.8781
0.6004
0.5028
0.6219
0.7614
0.5124
-0.3971
0.3995
0.0002
-0.9167
-0.7716
0.5006
0.3925
Axis
-0.7810
0.5357
0.3209
-0.1174
0.7114
0.6929
-0.0001
1.0000
0.0002
0.0637
-0.5531
0.8307
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