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 YbBi2BrO4 (Materials Project id mp-552016)

       134       62       27        0        0        0  
        62      134       27        0        0        0  
        27       27       66        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       50  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 62.889 GPa	EV = 74.355 GPa	GV = 28.533 GPa	νV = 0.30295
Reuss	KR = 52.173 GPa	ER = 47.985 GPa	GR = 17.816 GPa	νR = 0.34671
Hill	KH = 57.531 GPa	EH = 61.293 GPa	GH = 23.174 GPa	νH = 0.32243

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
10 GPa	10 GPa	50 GPa	55.614 GPa	72 GPa	206.39 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	32.531 GPa	126.98 GPa	3.3978 TPa–1	12.371 TPa–1	10 GPa	50 GPa	0.074138	0.67749	Value
Anisotropy	3.903		3.6410		5		9.1383		Anisotropy
Axis	0.6686 -0.0001 0.7437	0.7071 0.7071 0.0000	0.2588 0.9659 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 0.0007 -0.0000	0.4777 0.4777 0.7373	0.5646 0.5645 0.6022	Axis
					-0.7660 0.6428 -0.0000	-0.0007 1.0000 -0.0000	-0.7071 0.7071 -0.0000	0.4257 0.4258 -0.7984	Second axis

Spatial dependence of Young's modulus

[[134.0, 62.0, 27.0, 0.0, 0.0, 0.0], [62.0, 134.0, 27.0, 0.0, 0.0, 0.0], [27.0, 27.0, 66.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 50.0]] YbBi2BrO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-552016" target="_blank">mp-552016</a>) young

Spatial dependence of linear compressibility

[[134.0, 62.0, 27.0, 0.0, 0.0, 0.0], [62.0, 134.0, 27.0, 0.0, 0.0, 0.0], [27.0, 27.0, 66.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 50.0]] YbBi2BrO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-552016" target="_blank">mp-552016</a>) lc

Spatial dependence of shear modulus

[[134.0, 62.0, 27.0, 0.0, 0.0, 0.0], [62.0, 134.0, 27.0, 0.0, 0.0, 0.0], [27.0, 27.0, 66.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 50.0]] YbBi2BrO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-552016" target="_blank">mp-552016</a>) shear

Spatial dependence of Poisson's ratio

[[134.0, 62.0, 27.0, 0.0, 0.0, 0.0], [62.0, 134.0, 27.0, 0.0, 0.0, 0.0], [27.0, 27.0, 66.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 50.0]] YbBi2BrO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-552016" target="_blank">mp-552016</a>) poisson

Code version: 2019.01.09 (running on Python 3.7.2)