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 LiBeB (Materials Project id mp-1018783)

        49        6       10        0       -5        0  
         6      265       12        0       10        0  
        10       12      278        0        3        0  
         0        0        0      145        0       -1  
        -5       10        3        0       29        0  
         0        0        0       -1        0       28  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 72 GPaEV = 171.92 GPaGV = 78 GPaνV = 0.10204
ReussKR = 39.162 GPaER = 93.233 GPaGR = 42.255 GPaνR = 0.10321
HillKH = 55.581 GPaEH = 132.58 GPaGH = 60.128 GPaνH = 0.10245

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
27.209 GPa 27.991 GPa 49.784 GPa 145.01 GPa 258.07 GPa 285.94 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 44.891 GPa 285.31 GPa 2.6718 TPa–1 19.735 TPa–1 26.735 GPa 145.01 GPa-0.0999260.42854Value
Anisotropy 6.356 7.3865 5.424Anisotropy
Axis -0.9621
0.0000
-0.2727
0.0210
0.6140
0.7890
-0.0596
-0.0000
0.9982
0.9982
-0.0000
0.0597
-0.9827
-0.0000
0.1854
-0.0085
-0.0000
1.0000
0.0000
1.0000
0.0000
-0.3165
0.0000
0.9486
Axis
-0.1854
-0.0001
-0.9827
0.0000
-1.0000
-0.0000
-0.5879
-0.0000
0.8090
-0.9486
0.0000
-0.3165
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