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 HoP (Materials Project id mp-744)

       209       28       28        0        0        0  
        28      209       28        0        0        0  
        28       28      209        0        0        0  
         0        0        0       48        0        0  
         0        0        0        0       48        0  
         0        0        0        0        0       48  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 88.333 GPa	EV = 156.59 GPa	GV = 65 GPa	νV = 0.20455
Reuss	KR = 88.333 GPa	ER = 144.97 GPa	GR = 59.102 GPa	νR = 0.22647
Hill	KH = 88.333 GPa	EH = 150.83 GPa	GH = 62.051 GPa	νH = 0.21541

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
48 GPa	48 GPa	48 GPa	181 GPa	181 GPa	265 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	121.92 GPa	202.38 GPa	3.7736 TPa–1	3.7736 TPa–1	48 GPa	90.5 GPa	0.079025	0.41013	Value
Anisotropy	1.66		1.0000		1.885		5.1899		Anisotropy
Axis	0.5774 0.5774 0.5773	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.7934 0.0000 0.6088	0.0000 0.0000 1.0000	0.7071 -0.0003 0.7071	-0.7071 -0.0000 -0.7071	0.7071 -0.0000 -0.7071	Axis
					0.1735 0.9848 -0.0000	0.7071 -0.0005 -0.7071	0.0000 -1.0000 -0.0000	-0.7071 0.0002 -0.7071	Second axis

Spatial dependence of Young's modulus

[[209.0, 28.0, 28.0, 0.0, 0.0, 0.0], [28.0, 209.0, 28.0, 0.0, 0.0, 0.0], [28.0, 28.0, 209.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 48.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 48.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 48.0]] HoP (Materials Project id <a href="https://www.materialsproject.org/materials/mp-744" target="_blank">mp-744</a>) young

Spatial dependence of linear compressibility

[[209.0, 28.0, 28.0, 0.0, 0.0, 0.0], [28.0, 209.0, 28.0, 0.0, 0.0, 0.0], [28.0, 28.0, 209.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 48.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 48.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 48.0]] HoP (Materials Project id <a href="https://www.materialsproject.org/materials/mp-744" target="_blank">mp-744</a>) lc

Spatial dependence of shear modulus

[[209.0, 28.0, 28.0, 0.0, 0.0, 0.0], [28.0, 209.0, 28.0, 0.0, 0.0, 0.0], [28.0, 28.0, 209.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 48.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 48.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 48.0]] HoP (Materials Project id <a href="https://www.materialsproject.org/materials/mp-744" target="_blank">mp-744</a>) shear

Spatial dependence of Poisson's ratio

[[209.0, 28.0, 28.0, 0.0, 0.0, 0.0], [28.0, 209.0, 28.0, 0.0, 0.0, 0.0], [28.0, 28.0, 209.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 48.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 48.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 48.0]] HoP (Materials Project id <a href="https://www.materialsproject.org/materials/mp-744" target="_blank">mp-744</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)