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 LiSn (Materials Project id mp-569073)

        58       25       20        0        3        0  
        25       73       21        0        2        0  
        20       21       58        0        1        0  
         0        0        0       18        0        0  
         3        2        1        0       18        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 35.667 GPaEV = 47.971 GPaGV = 18.8 GPaνV = 0.27583
ReussKR = 34.892 GPaER = 47.247 GPaGR = 18.538 GPaνR = 0.27432
HillKH = 35.279 GPaEH = 47.609 GPaGH = 18.669 GPaνH = 0.27508

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17.766 GPa 18 GPa 37.291 GPa 43.634 GPa 108.31 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.154 GPa 59.197 GPa 6.9651 TPa–1 12.449 TPa–1 17 GPa 21.956 GPa0.193080.39511Value
Anisotropy 1.404 1.7874 1.292 2.0464Anisotropy
Axis -0.8511
0.1591
0.5003
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.6415
-0.0000
-0.7671
1.0000
0.0000
-0.0000
0.0715
0.7071
-0.7035
-0.4080
-0.0000
0.9130
-0.5768
0.7905
-0.2060
Axis
-0.0000
1.0000
0.0000
-0.0715
0.7071
0.7035
0.0000
-1.0000
0.0000
-0.7592
-0.6118
-0.2221
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