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 H6PbCI3N (Materials Project id mp-995214)

        22        9       12        0        0        0  
         9       33       10        0        0        0  
        12       10       23        0        0        0  
         0        0        0        5        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0        5  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 15.556 GPaEV = 18.563 GPaGV = 7.1333 GPaνV = 0.30112
ReussKR = 15.309 GPaER = 16.721 GPaGR = 6.3433 GPaνR = 0.31797
HillKH = 15.433 GPaEH = 17.647 GPaGH = 6.7383 GPaνH = 0.30942

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 10 GPa 10.477 GPa 20.297 GPa 47.226 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 13.553 GPa 27.743 GPa 16.23 TPa–1 26.486 TPa–1 5 GPa 10 GPa0.134220.54932Value
Anisotropy 2.047 1.6319 2 4.0926Anisotropy
Axis -0.8262
0.5634
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.6537
0.0000
0.7568
-0.0000
0.0000
1.0000
0.5498
0.6269
-0.5520
0.4634
0.7332
-0.4978
Axis
0.0000
1.0000
-0.0000
-1.0000
0.0000
-0.0000
-0.7154
0.0122
-0.6986
-0.4979
0.6801
0.5381
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