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 VPd3 (Materials Project id mp-873)

       231      164      138        0        0        0  
       164      231      138        0        0        0  
       138      138      256        0        0        0  
         0        0        0      107        0        0  
         0        0        0        0      107        0  
         0        0        0        0        0      118  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 177.56 GPaEV = 219.76 GPaGV = 84.933 GPaνV = 0.29372
ReussKR = 177.55 GPaER = 180.06 GPaGR = 67.642 GPaνR = 0.33098
HillKH = 177.56 GPaEH = 200.19 GPaGH = 76.288 GPaνH = 0.31208

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
67 GPa 107 GPa 107 GPa 118 GPa 118.33 GPa 532.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 105.34 GPa 274.72 GPa 1.8721 TPa–1 1.8879 TPa–1 33.5 GPa 118 GPa-0.0986180.73982Value
Anisotropy 2.608 1.0085 3.522Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5892
0.5892
-0.5529
0.1283
0.9917
-0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
1.0000
-0.0000
0.0000
0.6975
-0.0000
-0.7165
0.0000
0.7440
-0.6682
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
0.0000
-0.7165
0.0002
-0.6975
-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