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 Mg13Ir3 (Materials Project id mp-16860)

        99       39       42        2        0        0  
        39       99       42       -2        0        0  
        42       42       98        0        0        0  
         2       -2        0       27        0        0  
         0        0        0        0       27        2  
         0        0        0        0        2       30  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 60.222 GPa	EV = 73.477 GPa	GV = 28.333 GPa	νV = 0.29665
Reuss	KR = 60.217 GPa	ER = 73.076 GPa	GR = 28.155 GPa	νR = 0.29774
Hill	KH = 60.22 GPa	EH = 73.277 GPa	GH = 28.244 GPa	νH = 0.2972

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
26 GPa	26.759 GPa	31 GPa	55.326 GPa	60.241 GPa	180.67 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	68.333 GPa	78.043 GPa	5.4022 TPa–1	5.6022 TPa–1	26 GPa	31 GPa	0.23483	0.35101	Value
Anisotropy	1.142		1.0370		1.192		1.4948		Anisotropy
Axis	-0.6734 0.3888 -0.6288	0.0000 0.9409 -0.3386	0.0000 0.0000 1.0000	0.9201 0.3917 0.0000	0.3873 0.2236 0.8944	-0.5000 0.8660 -0.0000	0.5000 0.8660 -0.0000	0.5077 0.2928 0.8103	Axis
					-0.5000 0.8660 0.0000	-0.7746 -0.4472 0.4472	-0.7516 0.4340 0.4967	0.7016 0.4054 -0.5861	Second axis

Spatial dependence of Young's modulus

[[99.0, 39.0, 42.0, 2.0, 0.0, 0.0], [39.0, 99.0, 42.0, -2.0, 0.0, 0.0], [42.0, 42.0, 98.0, 0.0, 0.0, 0.0], [2.0, -2.0, 0.0, 27.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 27.0, 2.0], [0.0, 0.0, 0.0, 0.0, 2.0, 30.0]] Mg13Ir3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-16860" target="_blank">mp-16860</a>) young

Spatial dependence of linear compressibility

[[99.0, 39.0, 42.0, 2.0, 0.0, 0.0], [39.0, 99.0, 42.0, -2.0, 0.0, 0.0], [42.0, 42.0, 98.0, 0.0, 0.0, 0.0], [2.0, -2.0, 0.0, 27.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 27.0, 2.0], [0.0, 0.0, 0.0, 0.0, 2.0, 30.0]] Mg13Ir3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-16860" target="_blank">mp-16860</a>) lc

Spatial dependence of shear modulus

[[99.0, 39.0, 42.0, 2.0, 0.0, 0.0], [39.0, 99.0, 42.0, -2.0, 0.0, 0.0], [42.0, 42.0, 98.0, 0.0, 0.0, 0.0], [2.0, -2.0, 0.0, 27.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 27.0, 2.0], [0.0, 0.0, 0.0, 0.0, 2.0, 30.0]] Mg13Ir3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-16860" target="_blank">mp-16860</a>) shear

Spatial dependence of Poisson's ratio

[[99.0, 39.0, 42.0, 2.0, 0.0, 0.0], [39.0, 99.0, 42.0, -2.0, 0.0, 0.0], [42.0, 42.0, 98.0, 0.0, 0.0, 0.0], [2.0, -2.0, 0.0, 27.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 27.0, 2.0], [0.0, 0.0, 0.0, 0.0, 2.0, 30.0]] Mg13Ir3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-16860" target="_blank">mp-16860</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)