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 Li3B7O12 (Materials Project id mp-16828)

       105       36       27       -5        2        4  
        36      103       49       10       -4       18  
        27       49      185       18        9       11  
        -5       10       18       71       13       -3  
         2       -4        9       13       34        2  
         4       18       11       -3        2       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 68.556 GPaEV = 108.19 GPaGV = 43.733 GPaνV = 0.23697
ReussKR = 57.075 GPaER = 76.681 GPaGR = 30.045 GPaνR = 0.27608
HillKH = 62.815 GPaEH = 92.551 GPaGH = 36.889 GPaνH = 0.25444

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14.439 GPa 29.778 GPa 64.744 GPa 73.712 GPa 109.56 GPa 225.76 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 35.225 GPa 205.23 GPa 1.6693 TPa–1 12.851 TPa–1 13.822 GPa 74.347 GPa-0.15930.85774Value
Anisotropy 5.826 7.6984 5.379Anisotropy
Axis -0.5454
0.8130
-0.2039
0.1332
0.5018
0.8547
0.7466
0.6443
0.1658
-0.6317
0.7648
-0.1269
0.2160
0.9382
-0.2704
0.3307
0.9404
0.0795
-0.1492
0.4455
-0.8828
0.7809
0.4827
-0.3965
Axis
-0.9762
0.2123
-0.0432
0.1050
0.0470
-0.9934
0.4553
-0.7615
-0.4612
-0.5996
0.7573
-0.2588
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