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 NbPd3 (Materials Project id mp-669692)

       330      122      140        0        0        0  
       122      333      131        0        0        0  
       140      131      316        0        0        0  
         0        0        0       73        0        0  
         0        0        0        0       75        0  
         0        0        0        0        0       60  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 196.11 GPaEV = 212.82 GPaGV = 80.667 GPaνV = 0.31913
ReussKR = 196.1 GPaER = 206.03 GPaGR = 77.754 GPaνR = 0.32489
HillKH = 196.11 GPaEH = 209.43 GPaGH = 79.21 GPaνH = 0.32201

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
60 GPa 73 GPa 75 GPa 179.92 GPa 210.73 GPa 588.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 176.98 GPa 263.43 GPa 1.6684 TPa–1 1.7178 TPa–1 60 GPa 104.64 GPa0.217120.47508Value
Anisotropy 1.488 1.0296 1.744 2.1881Anisotropy
Axis 0.7146
0.6995
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
-0.0001
-0.0000
0.7071
0.7071
-0.0000
0.8320
0.0002
0.5547
-0.7002
0.7139
-0.0000
Axis
0.0001
1.0000
0.0000
-0.7071
0.7071
0.0000
-0.0000
1.0000
-0.0003
-0.7139
-0.7002
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