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 Li15Si4 (Materials Project id mp-569849)

        47       21       21        0        0        0  
        21       47       21        0        0        0  
        21       21       47        0        0        0  
         0        0        0       30        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 29.667 GPaEV = 55.209 GPaGV = 23.2 GPaνV = 0.18984
ReussKR = 29.667 GPaER = 48.383 GPaGR = 19.697 GPaνR = 0.22819
HillKH = 29.667 GPaEH = 51.85 GPaGH = 21.448 GPaνH = 0.20871

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 26 GPa 30 GPa 30 GPa 30 GPa 89 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 34.029 GPa 67.311 GPa 11.236 TPa–1 11.236 TPa–1 13 GPa 30 GPa-0.0985590.49085Value
Anisotropy 1.978 1.0000 2.308Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.7934
0.0000
0.6088
0.3316
0.8001
0.4998
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0003
-0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0002
1.0000
-0.0003
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