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 MnF2 (Materials Project id mp-560902)

       158       67       67        0        0        0  
        67       99       77        0        0        0  
        67       77       99        0        0        0  
         0        0        0       68        0        0  
         0        0        0        0       29        0  
         0        0        0        0        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 86.444 GPaEV = 92.203 GPaGV = 34.867 GPaνV = 0.32223
ReussKR = 84.063 GPaER = 67.582 GPaGR = 24.737 GPaνR = 0.36601
HillKH = 85.253 GPaEH = 80.075 GPaGH = 29.802 GPaνH = 0.34346

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 29 GPa 29 GPa 68 GPa 71.821 GPa 262.18 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 37.143 GPa 127.03 GPa 2.2305 TPa–1 4.8327 TPa–1 11 GPa 68 GPa-0.0659260.70979Value
Anisotropy 3.42 2.1667 6.182Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0002
0.7071
-0.7071
0.0000
-0.0000
1.0000
0.0000
0.7071
-0.7071
0.5498
0.0004
0.8353
Axis
0.0002
-0.7071
-0.7071
-0.0000
1.0000
0.0000
-0.0000
0.7071
0.7071
-0.0005
1.0000
-0.0001
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