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 KRbO (Materials Project id mp-755480)

        42       20       32        0        0        0  
        20       42       32        0        0        0  
        32       32       76        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        4        0  
         0        0        0        0        0        6  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 36.444 GPa	EV = 22.016 GPa	GV = 7.8667 GPa	νV = 0.39932
Reuss	KR = 30.977 GPa	ER = 16.789 GPa	GR = 5.9548 GPa	νR = 0.40967
Hill	KH = 33.711 GPa	EH = 19.406 GPa	GH = 6.9107 GPa	νH = 0.40406

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
4 GPa	4 GPa	6 GPa	22 GPa	23.207 GPa	114.79 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	12.802 GPa	42.968 GPa	-0.75075 TPa–1	16.517 TPa–1	4 GPa	11.864 GPa	0.13854	0.75608	Value
Anisotropy	3.356		∞		2.966		5.4574		Anisotropy
Axis	0.5529 0.5528 0.6235	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 0.0000 0.0000	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	-0.7866 0.0000 0.6175	0.6097 0.0001 -0.7926	Axis
					1.0000 0.0000 -0.0000	-0.7071 -0.0002 -0.7071	0.0000 -1.0000 0.0000	-0.7926 -0.0003 -0.6097	Second axis

Spatial dependence of Young's modulus

[[42.0, 20.0, 32.0, 0.0, 0.0, 0.0], [20.0, 42.0, 32.0, 0.0, 0.0, 0.0], [32.0, 32.0, 76.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 4.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 4.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 6.0]] KRbO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-755480" target="_blank">mp-755480</a>) young

Spatial dependence of linear compressibility

[[42.0, 20.0, 32.0, 0.0, 0.0, 0.0], [20.0, 42.0, 32.0, 0.0, 0.0, 0.0], [32.0, 32.0, 76.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 4.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 4.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 6.0]] KRbO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-755480" target="_blank">mp-755480</a>) lc

Spatial dependence of shear modulus

[[42.0, 20.0, 32.0, 0.0, 0.0, 0.0], [20.0, 42.0, 32.0, 0.0, 0.0, 0.0], [32.0, 32.0, 76.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 4.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 4.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 6.0]] KRbO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-755480" target="_blank">mp-755480</a>) shear

Spatial dependence of Poisson's ratio

[[42.0, 20.0, 32.0, 0.0, 0.0, 0.0], [20.0, 42.0, 32.0, 0.0, 0.0, 0.0], [32.0, 32.0, 76.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 4.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 4.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 6.0]] KRbO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-755480" target="_blank">mp-755480</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)