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 Li3BO3 (Materials Project id mp-27275)

       179       46       37        0      -21        0  
        46      145       50        0        0        0  
        37       50       95        0       -3        0  
         0        0        0       27        0        6  
       -21        0       -3        0       40        0  
         0        0        0        6        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76.111 GPaEV = 112.08 GPaGV = 44.667 GPaνV = 0.25458
ReussKR = 70.242 GPaER = 97.81 GPaGR = 38.571 GPaνR = 0.26792
HillKH = 73.176 GPaEH = 104.96 GPaGH = 41.619 GPaνH = 0.26095

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25.972 GPa 36.415 GPa 62.028 GPa 63.497 GPa 121.53 GPa 237.56 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 72.71 GPa 172.64 GPa 3.1599 TPa–1 7.8965 TPa–1 25.972 GPa 62.197 GPa0.0221480.51181Value
Anisotropy 2.374 2.4990 2.395 23.1083Anisotropy
Axis -0.1242
0.4988
0.8578
0.9663
0.0000
-0.2574
0.9650
-0.0000
-0.2623
0.2623
0.0000
0.9650
-0.1688
0.0000
0.9856
-0.2192
0.9494
0.2251
0.4346
0.6420
0.6317
-0.7669
0.5929
0.2456
Axis
0.0000
1.0000
-0.0000
-0.9718
-0.1921
-0.1366
-0.8810
0.4486
0.1502
-0.1824
-0.5682
0.8024
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