ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-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 scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 90.667 GPa	EV = 136 GPa	GV = 54.4 GPa	νV = 0.25
Reuss	KR = 90.667 GPa	ER = 73.747 GPa	GR = 27.025 GPa	νR = 0.36444
Hill	KH = 90.667 GPa	EH = 106.24 GPa	GH = 40.712 GPa	νH = 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 modulus		Linear compressibility		Shear modulus		Poisson's ratio
	Emin	Emax	βmin	βmax	Gmin	Gmax	νmin	νmax
Value	50.648 GPa	233.45 GPa	3.6765 TPa–1	3.6765 TPa–1	18 GPa	109 GPa	0.019117	0.74935	Value
Anisotropy	4.609		1.0000		6.056		39.1975		Anisotropy
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

[[236.0, 18.0, 18.0, -0.0, -0.0, 0.0], [18.0, 236.0, 18.0, 0.0, 0.0, -0.0], [18.0, 18.0, 236.0, -0.0, 0.0, -0.0], [-0.0, 0.0, -0.0, 18.0, -0.0, 0.0], [-0.0, 0.0, 0.0, -0.0, 18.0, -0.0], [0.0, -0.0, -0.0, 0.0, -0.0, 18.0]] ScF3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-559092" target="_blank">mp-559092</a>) young

Spatial dependence of linear compressibility

[[236.0, 18.0, 18.0, -0.0, -0.0, 0.0], [18.0, 236.0, 18.0, 0.0, 0.0, -0.0], [18.0, 18.0, 236.0, -0.0, 0.0, -0.0], [-0.0, 0.0, -0.0, 18.0, -0.0, 0.0], [-0.0, 0.0, 0.0, -0.0, 18.0, -0.0], [0.0, -0.0, -0.0, 0.0, -0.0, 18.0]] ScF3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-559092" target="_blank">mp-559092</a>) lc

Spatial dependence of shear modulus

[[236.0, 18.0, 18.0, -0.0, -0.0, 0.0], [18.0, 236.0, 18.0, 0.0, 0.0, -0.0], [18.0, 18.0, 236.0, -0.0, 0.0, -0.0], [-0.0, 0.0, -0.0, 18.0, -0.0, 0.0], [-0.0, 0.0, 0.0, -0.0, 18.0, -0.0], [0.0, -0.0, -0.0, 0.0, -0.0, 18.0]] ScF3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-559092" target="_blank">mp-559092</a>) shear

Spatial dependence of Poisson's ratio

[[236.0, 18.0, 18.0, -0.0, -0.0, 0.0], [18.0, 236.0, 18.0, 0.0, 0.0, -0.0], [18.0, 18.0, 236.0, -0.0, 0.0, -0.0], [-0.0, 0.0, -0.0, 18.0, -0.0, 0.0], [-0.0, 0.0, 0.0, -0.0, 18.0, -0.0], [0.0, -0.0, -0.0, 0.0, -0.0, 18.0]] ScF3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-559092" target="_blank">mp-559092</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)