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 Eu(MnP)2 (Materials Project id mp-21474)

       153       64       56       20        0        0  
        64      153       56      -20        0        0  
        56       56      170        0        0        0  
        20      -20        0       70        0        0  
         0        0        0        0       70       20  
         0        0        0        0       20       45  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 92 GPa	EV = 141.73 GPa	GV = 57 GPa	νV = 0.24324
Reuss	KR = 91.946 GPa	ER = 124.85 GPa	GR = 49.01 GPa	νR = 0.27369
Hill	KH = 91.973 GPa	EH = 133.39 GPa	GH = 53.005 GPa	νH = 0.25828

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
33.915 GPa	49.663 GPa	81.085 GPa	109.34 GPa	110.89 GPa	276.11 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	93.497 GPa	187.35 GPa	3.4294 TPa–1	3.7233 TPa–1	33.622 GPa	80.997 GPa	0.062652	0.52137	Value
Anisotropy	2.004		1.0857		2.409		8.3217		Anisotropy
Axis	0.0000 0.9349 0.3550	0.6673 0.3868 0.6365	0.0000 0.0000 1.0000	0.9668 0.2557 -0.0000	0.7538 0.4477 0.4809	-0.4177 0.2402 -0.8763	-0.0000 0.8823 -0.4707	1.0000 0.0004 -0.0000	Axis
					-0.5190 0.8546 0.0179	-0.4989 -0.8667 0.0002	0.0000 0.4707 0.8823	-0.0004 0.8506 0.5258	Second axis

Spatial dependence of Young's modulus

[[153.0, 64.0, 56.0, 20.0, 0.0, 0.0], [64.0, 153.0, 56.0, -20.0, 0.0, 0.0], [56.0, 56.0, 170.0, 0.0, 0.0, 0.0], [20.0, -20.0, 0.0, 70.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 70.0, 20.0], [0.0, 0.0, 0.0, 0.0, 20.0, 45.0]] Eu(MnP)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-21474" target="_blank">mp-21474</a>) young

Spatial dependence of linear compressibility

[[153.0, 64.0, 56.0, 20.0, 0.0, 0.0], [64.0, 153.0, 56.0, -20.0, 0.0, 0.0], [56.0, 56.0, 170.0, 0.0, 0.0, 0.0], [20.0, -20.0, 0.0, 70.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 70.0, 20.0], [0.0, 0.0, 0.0, 0.0, 20.0, 45.0]] Eu(MnP)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-21474" target="_blank">mp-21474</a>) lc

Spatial dependence of shear modulus

[[153.0, 64.0, 56.0, 20.0, 0.0, 0.0], [64.0, 153.0, 56.0, -20.0, 0.0, 0.0], [56.0, 56.0, 170.0, 0.0, 0.0, 0.0], [20.0, -20.0, 0.0, 70.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 70.0, 20.0], [0.0, 0.0, 0.0, 0.0, 20.0, 45.0]] Eu(MnP)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-21474" target="_blank">mp-21474</a>) shear

Spatial dependence of Poisson's ratio

[[153.0, 64.0, 56.0, 20.0, 0.0, 0.0], [64.0, 153.0, 56.0, -20.0, 0.0, 0.0], [56.0, 56.0, 170.0, 0.0, 0.0, 0.0], [20.0, -20.0, 0.0, 70.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 70.0, 20.0], [0.0, 0.0, 0.0, 0.0, 20.0, 45.0]] Eu(MnP)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-21474" target="_blank">mp-21474</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)