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-3953)

       147       57       54       17        0        0  
        57      147       54      -17        0        0  
        54       54       85        0        0        0  
        17      -17        0       32        0        0  
         0        0        0        0       32       17  
         0        0        0        0       17       45  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 78.778 GPaEV = 93.874 GPaGV = 36.067 GPaνV = 0.3014
ReussKR = 72.835 GPaER = 75.853 GPaGR = 28.593 GPaνR = 0.32643
HillKH = 75.807 GPaEH = 84.917 GPaGH = 32.33 GPaνH = 0.3133

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20.3 GPa 23.33 GPa 47.69 GPa 56.7 GPa 98.67 GPa 241.31 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 54.898 GPa 135.33 GPa 2.6938 TPa–1 8.342 TPa–1 20.3 GPa 56.7 GPa0.0221380.72686Value
Anisotropy 2.465 3.0968 2.793 32.8329Anisotropy
Axis -0.6224
0.3594
-0.6953
-0.8031
0.4637
0.3742
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.4910
0.2835
0.8238
0.5000
0.8660
-0.0000
-0.6575
0.3796
0.6509
-0.5000
0.8660
-0.0000
Axis
-0.5000
0.8660
0.0000
-0.7134
0.4119
-0.5669
-0.5000
-0.8660
0.0000
-0.5509
-0.3181
0.7716
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