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 LiBe (Materials Project id mp-1001825)

        30       46       -4        0        1        0  
        46      107       19        0        1        0  
        -4       19      156        0        0        0  
         0        0        0       70        0        1  
         1        1        0        0        2        0  
         0        0        0        1        0       73  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 46.111 GPaEV = 100.95 GPaGV = 44.467 GPaνV = 0.13512
ReussKR = 17.08 GPaER = 16.782 GPaGR = 6.2794 GPaνR = 0.33624
HillKH = 31.595 GPaEH = 60.046 GPaGH = 25.373 GPaνH = 0.18326

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1.9469 GPa 7.6241 GPa 69.697 GPa 73.303 GPa 121.71 GPa 163.72 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 5.3416 GPa 154.47 GPa -22.521 TPa–1 72.422 TPa–1 1.9494 GPa 73.303 GPa-1.2242.3634Value
Anisotropy 28.92 37.6Anisotropy
Axis -0.8022
-0.0000
0.5971
0.0006
0.3879
0.9217
0.0000
1.0000
0.0000
0.9818
-0.0000
-0.1901
-0.0349
0.0004
0.9994
-0.9571
-0.0000
-0.2897
0.0117
0.0000
-0.9999
0.4166
0.8537
0.3126
Axis
0.9994
0.0000
0.0349
0.0000
-1.0000
0.0000
-0.9999
-0.0003
-0.0117
-0.7507
0.1292
0.6479
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