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 TiO (Materials Project id mp-2664)

       531       71       71        0        0        0  
        71      531       71        0        0        0  
        71       71      531        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       17  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 224.33 GPa	EV = 266.18 GPa	GV = 102.2 GPa	νV = 0.30224
Reuss	KR = 224.33 GPa	ER = 77.883 GPa	GR = 27.003 GPa	νR = 0.44214
Hill	KH = 224.33 GPa	EH = 176.83 GPa	GH = 64.601 GPa	νH = 0.36863

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
17 GPa	17 GPa	17 GPa	460 GPa	460 GPa	673 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	49.743 GPa	514.25 GPa	1.4859 TPa–1	1.4859 TPa–1	17 GPa	230 GPa	0.014736	0.88979	Value
Anisotropy	10.34		1.0000		13.53		60.3824		Anisotropy
Axis	0.5774 0.5773 -0.5774	0.0000 0.0000 1.0000	0.2241 0.8365 0.5000	0.7934 0.0000 0.6088	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
					-0.1736 0.9848 -0.0000	-0.7071 -0.0002 -0.7071	-0.0000 -1.0000 -0.0000	0.7071 0.0000 -0.7071	Second axis

Spatial dependence of Young's modulus

[[531.0, 71.0, 71.0, 0.0, 0.0, 0.0], [71.0, 531.0, 71.0, 0.0, 0.0, 0.0], [71.0, 71.0, 531.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 17.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 17.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 17.0]] TiO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2664" target="_blank">mp-2664</a>) young

Spatial dependence of linear compressibility

[[531.0, 71.0, 71.0, 0.0, 0.0, 0.0], [71.0, 531.0, 71.0, 0.0, 0.0, 0.0], [71.0, 71.0, 531.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 17.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 17.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 17.0]] TiO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2664" target="_blank">mp-2664</a>) lc

Spatial dependence of shear modulus

[[531.0, 71.0, 71.0, 0.0, 0.0, 0.0], [71.0, 531.0, 71.0, 0.0, 0.0, 0.0], [71.0, 71.0, 531.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 17.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 17.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 17.0]] TiO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2664" target="_blank">mp-2664</a>) shear

Spatial dependence of Poisson's ratio

[[531.0, 71.0, 71.0, 0.0, 0.0, 0.0], [71.0, 531.0, 71.0, 0.0, 0.0, 0.0], [71.0, 71.0, 531.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 17.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 17.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 17.0]] TiO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2664" target="_blank">mp-2664</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)