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 LiN3 (Materials Project id mp-2659)

        66       19       31        0        6        0  
        19       52       16        0        2        0  
        31       16      105        0       39        0  
         0        0        0        7        0       -6  
         6        2       39        0       27        0  
         0        0        0       -6        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 39.444 GPaEV = 51.472 GPaGV = 20.067 GPaνV = 0.28251
ReussKR = 29.404 GPaER = 25.41 GPaGR = 9.3695 GPaνR = 0.35597
HillKH = 34.424 GPaEH = 38.646 GPaGH = 14.718 GPaνH = 0.31289

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3.5538 GPa 9.8532 GPa 17.446 GPa 38.317 GPa 61.172 GPa 140.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 12.978 GPa 140.72 GPa -1.4122 TPa–1 22.084 TPa–1 3.5538 GPa 34.336 GPa-0.316440.956Value
Anisotropy 10.84 9.662Anisotropy
Axis -0.3661
0.7266
-0.5814
0.4338
0.0000
0.9010
-0.8047
0.0000
-0.5937
-0.5937
-0.0000
0.8047
0.4981
0.0000
0.8671
-0.8935
0.0003
-0.4490
-0.8596
0.4677
0.2058
0.7894
0.0002
0.6139
Axis
-0.0001
1.0000
0.0000
0.4490
-0.0003
-0.8935
-0.0696
-0.5061
0.8596
0.6139
0.0004
-0.7894
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