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 Ba3NaN (Materials Project id mp-8868)

        16       10        2        0        0        0  
        10       16        2        0        0        0  
         2        2       44        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 11.556 GPaEV = 13.414 GPaGV = 5.1333 GPaνV = 0.30653
ReussKR = 10.717 GPaER = 5.2025 GPaGR = 1.833 GPaνR = 0.41909
HillKH = 11.136 GPaEH = 9.463 GPaGH = 3.4832 GPaνH = 0.35838

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 3 GPa 6 GPa 25.566 GPa 44.434 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.5418 GPa 43.692 GPa 19.366 TPa–1 36.972 TPa–1 1 GPa 7.7455 GPa0.0769230.80391Value
Anisotropy 12.34 1.9091 7.745 10.4508Anisotropy
Axis 0.1585
0.7216
-0.6739
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.5291
0.4691
-0.7071
0.0000
0.0000
1.0000
0.5220
0.1990
0.8294
Axis
1.0000
0.0000
-0.0000
-0.5291
-0.4692
-0.7071
0.1736
0.9848
-0.0000
0.7749
0.2956
-0.5587
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