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 Li3P7 (Materials Project id mp-28336)

        36       16       19        0        0        0  
        16       34       17        0        0        0  
        19       17       47        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       11  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 24.556 GPaEV = 30.809 GPaGV = 11.933 GPaνV = 0.29089
ReussKR = 23.921 GPaER = 29.775 GPaGR = 11.518 GPaνR = 0.29254
HillKH = 24.238 GPaEH = 30.292 GPaGH = 11.726 GPaνH = 0.2917

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 16 GPa 18.92 GPa 23.494 GPa 74.586 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.909 GPa 38.118 GPa 8.6264 TPa–1 17.916 TPa–1 9.478 GPa 16 GPa0.149930.40956Value
Anisotropy 1.53 2.0769 1.688 2.7318Anisotropy
Axis 0.0000
1.0000
0.0000
0.5666
0.0000
0.8240
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0000
0.0000
0.0000
1.0000
0.7291
-0.0003
0.6845
-0.6900
0.0000
-0.7238
Axis
-0.7071
-0.7071
-0.0000
-1.0000
0.0000
0.0000
0.6845
-0.0006
-0.7291
-0.0000
-1.0000
-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