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 PCl3O (Materials Project id mp-27277)

         4        1        2        0        0        0  
         1        5        2        0        0        0  
         2        2        5        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        2  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 2.6667 GPaEV = 4 GPaGV = 1.6 GPaνV = 0.25
ReussKR = 2.5769 GPaER = 3.6949 GPaGR = 1.465 GPaνR = 0.26103
HillKH = 2.6218 GPaEH = 3.8478 GPaGH = 1.5325 GPaνH = 0.2554

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 2 GPa 2 GPa 2.3126 GPa 3.5684 GPa 8.119 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.9333 GPa 4.8 GPa 74.627 TPa–1 179.1 TPa–1 1 GPa 2 GPa-0.0219290.47424Value
Anisotropy 1.636 2.4000 2Anisotropy
Axis 0.7687
0.0000
-0.6396
-0.0000
0.7817
0.6236
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.6924
0.0000
0.7215
-0.7002
0.7140
0.0001
0.6466
0.0001
0.7629
Axis
1.0000
0.0000
-0.0000
-0.0000
1.0000
-0.0000
-0.7140
-0.7002
0.0001
0.7629
0.0000
-0.6466
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