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 LiHO (Materials Project id mp-625998)

        99       28       35        0       -1        0  
        28       99       35        0       -0        0  
        35       35       56        0       -0        0  
         0        0        0       12        0       -0  
        -1       -0       -0        0       12        0  
         0        0        0       -0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 50 GPaEV = 55.724 GPaGV = 21.2 GPaνV = 0.31425
ReussKR = 47.087 GPaER = 45.726 GPaGR = 17.085 GPaνR = 0.33815
HillKH = 48.544 GPaEH = 50.756 GPaGH = 19.143 GPaνH = 0.32574

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11.983 GPa 12 GPa 30 GPa 30.594 GPa 71.008 GPa 152.41 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 34.187 GPa 76.638 GPa 4.5041 TPa–1 12.228 TPa–1 11.972 GPa 35.511 GPa0.0793710.59577Value
Anisotropy 2.242 2.7149 2.966 7.5061Anisotropy
Axis -0.3669
0.3401
0.8659
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0243
-0.0001
0.9997
0.0303
-0.0004
0.9995
0.7069
0.7071
-0.0150
-0.9999
-0.0000
-0.0138
0.9377
0.0002
0.3475
Axis
0.9991
-0.0311
-0.0303
-0.7070
0.7071
0.0150
0.0000
-1.0000
-0.0000
0.3475
0.0003
-0.9377
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