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 PdC (Materials Project id mp-1009533)

       210      158      158        0        0        0  
       158      210      158        0        0        0  
       158      158      210        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 175.33 GPaEV = 64.455 GPaGV = 22.4 GPaνV = 0.43873
ReussKR = 175.33 GPaER = 63.444 GPaGR = 22.034 GPaνR = 0.43969
HillKH = 175.33 GPaEH = 63.95 GPaGH = 22.217 GPaνH = 0.43921

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 20 GPa 20 GPa 52 GPa 52 GPa 526 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 57.802 GPa 74.326 GPa 1.9011 TPa–1 1.9011 TPa–1 20 GPa 26 GPa0.353550.5301Value
Anisotropy 1.286 1.0000 1.3 1.4994Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.0000
-0.7071
0.7071
-0.0002
0.7071
Axis
-0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
-0.0000
-1.0000
-0.0000
0.7071
-0.0005
-0.7071
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