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 Ho2O3 (Materials Project id mp-812)

       219      108      108        0        0        0  
       108      219      108        0        0        0  
       108      108      219        0        0        0  
         0        0        0       73        0        0  
         0        0        0        0       73        0  
         0        0        0        0        0       73  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 145 GPa	EV = 171.92 GPa	GV = 66 GPa	νV = 0.3024
Reuss	KR = 145 GPa	ER = 169.25 GPa	GR = 64.824 GPa	νR = 0.30546
Hill	KH = 145 GPa	EH = 170.58 GPa	GH = 65.412 GPa	νH = 0.30393

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
73 GPa	73 GPa	73 GPa	111 GPa	111 GPa	435 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	147.66 GPa	187.53 GPa	2.2989 TPa–1	2.2989 TPa–1	55.5 GPa	73 GPa	0.20323	0.39293	Value
Anisotropy	1.27		1.0000		1.315		1.9334		Anisotropy
Axis	0.0000 0.0000 1.0000	0.5774 0.5774 0.5773	0.0000 0.0000 1.0000	-0.1206 0.9160 0.3827	0.7071 0.0001 -0.7071	0.0000 0.0000 1.0000	0.7071 -0.0000 -0.7071	0.7071 -0.0004 -0.7071	Axis
					-0.7071 -0.0002 -0.7071	0.5000 0.8660 -0.0000	-0.7071 0.0002 -0.7071	0.0002 1.0000 -0.0003	Second axis

Spatial dependence of Young's modulus

[[219.0, 108.0, 108.0, 0.0, 0.0, 0.0], [108.0, 219.0, 108.0, 0.0, 0.0, 0.0], [108.0, 108.0, 219.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 73.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 73.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 73.0]] Ho2O3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-812" target="_blank">mp-812</a>) young

Spatial dependence of linear compressibility

[[219.0, 108.0, 108.0, 0.0, 0.0, 0.0], [108.0, 219.0, 108.0, 0.0, 0.0, 0.0], [108.0, 108.0, 219.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 73.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 73.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 73.0]] Ho2O3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-812" target="_blank">mp-812</a>) lc

Spatial dependence of shear modulus

[[219.0, 108.0, 108.0, 0.0, 0.0, 0.0], [108.0, 219.0, 108.0, 0.0, 0.0, 0.0], [108.0, 108.0, 219.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 73.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 73.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 73.0]] Ho2O3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-812" target="_blank">mp-812</a>) shear

Spatial dependence of Poisson's ratio

[[219.0, 108.0, 108.0, 0.0, 0.0, 0.0], [108.0, 219.0, 108.0, 0.0, 0.0, 0.0], [108.0, 108.0, 219.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 73.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 73.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 73.0]] Ho2O3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-812" target="_blank">mp-812</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)