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 ScF3 (Materials Project id mp-559092)

       236       18       18       -0       -0        0  
        18      236       18        0        0       -0  
        18       18      236       -0        0       -0  
        -0        0       -0       18       -0        0  
        -0        0        0       -0       18       -0  
         0       -0       -0        0       -0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 90.667 GPaEV = 136 GPaGV = 54.4 GPaνV = 0.25
ReussKR = 90.667 GPaER = 73.747 GPaGR = 27.025 GPaνR = 0.36444
HillKH = 90.667 GPaEH = 106.24 GPaGH = 40.712 GPaνH = 0.30471

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 18 GPa 18 GPa 218 GPa 218 GPa 272 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 50.648 GPa 233.45 GPa 3.6765 TPa–1 3.6765 TPa–1 18 GPa 109 GPa0.0191170.74935Value
Anisotropy 4.609 1.0000 6.056 39.1975Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.3827
0.0000
0.9239
0.3706
0.4830
0.7934
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
-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