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 ZnPd3 (Materials Project id mp-971909)

       175      164      111        0        0        0  
       164      175      111        0        0        0  
       111      111      237        0        0        0  
         0        0        0       18        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 151 GPaEV = 62.397 GPaGV = 21.8 GPaνV = 0.43113
ReussKR = 150.95 GPaER = 30.807 GPaGR = 10.507 GPaνR = 0.46599
HillKH = 150.98 GPaEH = 46.792 GPaGH = 16.154 GPaνH = 0.44834

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6 GPa 11 GPa 18 GPa 18 GPa 122.95 GPa 453.05 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 21.016 GPa 164.31 GPa 2.1005 TPa–1 2.2621 TPa–1 5.5 GPa 18.565 GPa0.0416740.91058Value
Anisotropy 7.818 1.0769 3.375 21.8499Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
0.5000
0.5000
0.7071
0.9644
0.0002
0.2645
0.0000
1.0000
-0.0000
Axis
-0.7071
0.7071
0.0000
0.5000
0.5000
-0.7071
0.2645
0.0001
-0.9644
-1.0000
0.0000
-0.0000
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