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 Ba5Al5Pb (Materials Project id mp-568809)

        51       11       20        0        0        0  
        11       51       20        0        0        0  
        20       20       55        0        0        0  
         0        0        0       16        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28.778 GPaEV = 43.583 GPaGV = 17.467 GPaνV = 0.24759
ReussKR = 28.37 GPaER = 42.869 GPaGR = 17.173 GPaνR = 0.24815
HillKH = 28.574 GPaEH = 43.226 GPaGH = 17.32 GPaνH = 0.24787

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 16 GPa 20 GPa 30 GPa 40 GPa 87 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.097 GPa 43.41 GPa 8.4291 TPa–1 13.41 TPa–1 16 GPa 20 GPa0.0852390.33265Value
Anisotropy 1.031 1.5909 1.25 3.9026Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0001
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.6863
0.7273
0.0000
0.6381
0.7699
-0.0000
-0.9513
0.2497
-0.1808
Axis
1.0000
0.0000
-0.0000
-0.7273
-0.6863
0.0000
-0.7699
0.6381
-0.0000
0.1749
-0.0459
-0.9835
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