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 BeF2 (Materials Project id mp-561543)

        31       -3       -3        0        0        0  
        -3       31       -3        0        0        0  
        -3       -3       31        0        0        0  
         0        0        0       12        0        0  
         0        0        0        0       12        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 8.3333 GPaEV = 26.923 GPaGV = 14 GPaνV = -0.038462
ReussKR = 8.3333 GPaER = 26.425 GPaGR = 13.6 GPaνR = -0.028497
HillKH = 8.3333 GPaEH = 26.675 GPaGH = 13.8 GPaνH = -0.033505

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12 GPa 12 GPa 12 GPa 25 GPa 34 GPa 34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.324 GPa 30.357 GPa 40 TPa–1 40 TPa–1 12 GPa 17 GPa-0.107140.066499Value
Anisotropy 1.248 1.0000 1.417Anisotropy
Axis 0.5774
0.5774
0.5773
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.3536
0.1464
0.9239
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
-0.0000
1.0000
0.7071
-0.0000
-0.7071
Axis
0.1735
0.9848
-0.0000
-0.7071
-0.0002
-0.7071
0.7585
0.6517
0.0000
-0.7071
0.0002
-0.7071
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