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 ZnF2 (Materials Project id mp-7709)

       147       74       81        0        0        0  
        74      131       80        0        0        0  
        81       80      117        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 96.111 GPaEV = 87.058 GPaGV = 32.267 GPaνV = 0.34903
ReussKR = 95.484 GPaER = 82.292 GPaGR = 30.335 GPaνR = 0.35636
HillKH = 95.797 GPaEH = 84.68 GPaGH = 31.301 GPaνH = 0.35267

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
29 GPa 37 GPa 40.837 GPa 42 GPa 65.391 GPa 288.77 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 55.956 GPa 100.52 GPa 2.6688 TPa–1 4.3106 TPa–1 21.449 GPa 42 GPa0.168130.54202Value
Anisotropy 1.796 1.6152 1.958 3.2238Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.7677
0.6408
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0000
0.7071
-0.7071
0.0000
-0.0000
-1.0000
0.3569
0.5956
0.7196
0.0000
1.0000
0.0000
Axis
-0.0000
-0.7071
-0.7071
-0.0000
-1.0000
0.0000
-0.3534
-0.6270
0.6943
-0.0002
0.0000
-1.0000
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