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 K3BP2 (Materials Project id mp-9664)

        20       12       19        0       -0        0  
        12       30       11        0        2        0  
        19       11       32        0       -4        0  
         0        0        0        8        0        5  
        -0        2       -4        0       17        0  
         0        0        0        5        0        8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 18.444 GPaEV = 23.812 GPaGV = 9.2667 GPaνV = 0.28483
ReussKR = 17.46 GPaER = 14.372 GPaGR = 5.2727 GPaνR = 0.36282
HillKH = 17.952 GPaEH = 19.215 GPaGH = 7.2697 GPaνH = 0.32161

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 5.2323 GPa 13 GPa 14.806 GPa 23.035 GPa 55.927 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.3739 GPa 42.015 GPa 3.7362 TPa–1 35.822 TPa–1 2.7687 GPa 16.824 GPa-0.0563890.94835Value
Anisotropy 5.698 9.5880 6.076Anisotropy
Axis 0.9992
0.0000
-0.0394
-0.5963
0.0000
0.8028
0.0187
-0.0001
0.9998
0.9998
-0.0000
-0.0187
0.6680
-0.0000
-0.7441
0.9473
0.3014
-0.1086
0.6643
-0.0000
-0.7475
-0.0156
0.0000
0.9999
Axis
-0.7441
0.0002
-0.6680
0.0239
0.2716
0.9621
-0.7475
0.0001
-0.6643
0.9999
0.0001
0.0156
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