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 BiIO (Materials Project id mp-22987)

        87       31        3        0        0        0  
        31       87        3        0        0        0  
         3        3        6        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0       35  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 28.222 GPa	EV = 43.163 GPa	GV = 17.333 GPa	νV = 0.2451
Reuss	KR = 5.8475 GPa	ER = 9.406 GPa	GR = 3.8177 GPa	νR = 0.23191
Hill	KH = 17.035 GPa	EH = 26.287 GPa	GH = 10.576 GPa	νH = 0.24281

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
2 GPa	2 GPa	5.8395 GPa	35 GPa	56 GPa	118.16 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	5.2865 GPa	87.027 GPa	4.3478 TPa–1	162.32 TPa–1	2 GPa	35 GPa	0.025424	0.58489	Value
Anisotropy	16.46		37.3333		17.5		23.0057		Anisotropy
Axis	0.4931 0.0000 0.8700	0.7071 0.7071 0.0000	1.0000 0.0000 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 0.0007 0.0000	0.0000 0.0000 1.0000	-0.6572 0.6573 0.3688	Axis
					1.0000 0.0000 -0.0000	-0.0007 1.0000 0.0000	0.1736 0.9848 -0.0000	-0.2608 0.2608 -0.9295	Second axis

Spatial dependence of Young's modulus

[[87.0, 31.0, 3.0, 0.0, 0.0, 0.0], [31.0, 87.0, 3.0, 0.0, 0.0, 0.0], [3.0, 3.0, 6.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 2.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 2.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 35.0]] BiIO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-22987" target="_blank">mp-22987</a>) young

Spatial dependence of linear compressibility

[[87.0, 31.0, 3.0, 0.0, 0.0, 0.0], [31.0, 87.0, 3.0, 0.0, 0.0, 0.0], [3.0, 3.0, 6.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 2.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 2.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 35.0]] BiIO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-22987" target="_blank">mp-22987</a>) lc

Spatial dependence of shear modulus

[[87.0, 31.0, 3.0, 0.0, 0.0, 0.0], [31.0, 87.0, 3.0, 0.0, 0.0, 0.0], [3.0, 3.0, 6.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 2.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 2.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 35.0]] BiIO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-22987" target="_blank">mp-22987</a>) shear

Spatial dependence of Poisson's ratio

[[87.0, 31.0, 3.0, 0.0, 0.0, 0.0], [31.0, 87.0, 3.0, 0.0, 0.0, 0.0], [3.0, 3.0, 6.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 2.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 2.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 35.0]] BiIO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-22987" target="_blank">mp-22987</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)