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 Li3Sb (Materials Project id mp-2074)

        53       30       30        0        0        0  
        30       53       30        0        0        0  
        30       30       53        0        0        0  
         0        0        0       48        0        0  
         0        0        0        0       48        0  
         0        0        0        0        0       48  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 37.667 GPaEV = 77.34 GPaGV = 33.4 GPaνV = 0.15779
ReussKR = 37.667 GPaER = 53.445 GPaGR = 21.149 GPaνR = 0.26352
HillKH = 37.667 GPaEH = 65.914 GPaGH = 27.275 GPaνH = 0.20834

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 23 GPa 48 GPa 48 GPa 48 GPa 113 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 31.313 GPa 101.07 GPa 8.8496 TPa–1 8.8496 TPa–1 11.5 GPa 48 GPa-0.323790.74932Value
Anisotropy 3.228 1.0000 4.174Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
-0.5773
0.2053
0.7663
0.6088
0.9239
0.0000
0.3827
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.7071
-0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
-1.0000
0.0000
0.0000
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