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 Mg2P2O7 (Materials Project id mp-5427)

       223       54       74        0       15        0  
        54      206       91        0       21        0  
        74       91      200        0       12        0  
         0        0        0       95        0       14  
        15       21       12        0       66        0  
         0        0        0       14        0       37  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 118.56 GPa	EV = 169 GPa	GV = 66.933 GPa	νV = 0.26242
Reuss	KR = 114.44 GPa	ER = 148.82 GPa	GR = 57.987 GPa	νR = 0.28325
Hill	KH = 116.5 GPa	EH = 158.97 GPa	GH = 62.46 GPa	νH = 0.27257

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
33.798 GPa	62.408 GPa	98.202 GPa	109.42 GPa	164.72 GPa	358.45 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	97.967 GPa	227.67 GPa	1.7 TPa–1	3.8957 TPa–1	33.798 GPa	98.202 GPa	0.0049744	0.63395	Value
Anisotropy	2.324		2.2915		2.906		127.4416		Anisotropy
Axis	-0.6681 0.7189 0.1921	0.1759 0.7230 0.6681	-0.6350 0.0000 -0.7725	0.7725 -0.0000 -0.6350	-0.9748 0.0000 0.2230	-0.2230 0.0000 -0.9748	-0.2957 0.5300 0.7947	-0.6825 0.4859 -0.5459	Axis
					-0.0000 -1.0000 0.0000	-0.0000 -1.0000 -0.0000	-0.5661 0.5729 -0.5927	-0.6864 -0.6826 0.2506	Second axis

Spatial dependence of Young's modulus

[[223.0, 54.0, 74.0, 0.0, 15.0, 0.0], [54.0, 206.0, 91.0, 0.0, 21.0, 0.0], [74.0, 91.0, 200.0, 0.0, 12.0, 0.0], [0.0, 0.0, 0.0, 95.0, 0.0, 14.0], [15.0, 21.0, 12.0, 0.0, 66.0, 0.0], [0.0, 0.0, 0.0, 14.0, 0.0, 37.0]] Mg2P2O7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-5427" target="_blank">mp-5427</a>) young

Spatial dependence of linear compressibility

[[223.0, 54.0, 74.0, 0.0, 15.0, 0.0], [54.0, 206.0, 91.0, 0.0, 21.0, 0.0], [74.0, 91.0, 200.0, 0.0, 12.0, 0.0], [0.0, 0.0, 0.0, 95.0, 0.0, 14.0], [15.0, 21.0, 12.0, 0.0, 66.0, 0.0], [0.0, 0.0, 0.0, 14.0, 0.0, 37.0]] Mg2P2O7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-5427" target="_blank">mp-5427</a>) lc

Spatial dependence of shear modulus

[[223.0, 54.0, 74.0, 0.0, 15.0, 0.0], [54.0, 206.0, 91.0, 0.0, 21.0, 0.0], [74.0, 91.0, 200.0, 0.0, 12.0, 0.0], [0.0, 0.0, 0.0, 95.0, 0.0, 14.0], [15.0, 21.0, 12.0, 0.0, 66.0, 0.0], [0.0, 0.0, 0.0, 14.0, 0.0, 37.0]] Mg2P2O7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-5427" target="_blank">mp-5427</a>) shear

Spatial dependence of Poisson's ratio

[[223.0, 54.0, 74.0, 0.0, 15.0, 0.0], [54.0, 206.0, 91.0, 0.0, 21.0, 0.0], [74.0, 91.0, 200.0, 0.0, 12.0, 0.0], [0.0, 0.0, 0.0, 95.0, 0.0, 14.0], [15.0, 21.0, 12.0, 0.0, 66.0, 0.0], [0.0, 0.0, 0.0, 14.0, 0.0, 37.0]] Mg2P2O7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-5427" target="_blank">mp-5427</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)