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-561412)

        90       52       52        0       -0        0  
        52      142       57        0       16        0  
        52       57      142        0      -16        0  
         0        0        0       41        0       16  
        -0       16      -16        0       25        0  
         0        0        0       16        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 77.333 GPaEV = 85.289 GPaGV = 32.4 GPaνV = 0.31619
ReussKR = 73.111 GPaER = 65.379 GPaGR = 24.197 GPaνR = 0.35096
HillKH = 75.222 GPaEH = 75.436 GPaGH = 28.299 GPaνH = 0.33286

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15.111 GPa 17.423 GPa 50.889 GPa 52.967 GPa 92.577 GPa 236.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.477 GPa 125.17 GPa 3.0395 TPa–1 7.5988 TPa–1 15.111 GPa 51.721 GPa-0.0639220.81149Value
Anisotropy 2.947 2.5000 3.423Anisotropy
Axis 0.6346
0.6677
-0.3893
0.3128
0.0000
-0.9498
-0.0000
0.9239
-0.3827
1.0000
0.0000
0.0000
-0.8507
-0.0000
0.5257
0.5134
0.7388
-0.4367
-0.6718
-0.0000
0.7407
0.0026
0.4992
0.8665
Axis
0.0000
-1.0000
0.0000
-0.0113
0.5146
0.8573
0.0000
-1.0000
0.0000
-0.6976
-0.6199
0.3592
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