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 SnP3 (Materials Project id mp-7541)

       101       28       29       14        0        0  
        28      101       29      -14        0        0  
        29       29       43        0        0        0  
        14      -14        0       27        0        0  
         0        0        0        0       27       14  
         0        0        0        0       14       37  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 46.333 GPa	EV = 71.571 GPa	GV = 28.8 GPa	νV = 0.24255
Reuss	KR = 39.04 GPa	ER = 54.595 GPa	GR = 21.546 GPa	νR = 0.26693
Hill	KH = 42.687 GPa	EH = 63.113 GPa	GH = 25.173 GPa	νH = 0.25358

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
17.134 GPa	19.652 GPa	26.578 GPa	46.866 GPa	80.348 GPa	145.42 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	29.961 GPa	105.03 GPa	3.6223 TPa–1	18.37 TPa–1	15.104 GPa	46.617 GPa	0.017172	0.7242	Value
Anisotropy	3.506		5.0714		3.086		42.1741		Anisotropy
Axis	0.0000 0.0000 1.0000	-0.7962 0.4623 0.3904	0.9201 0.3917 0.0000	0.0000 0.0000 1.0000	-0.4822 0.2605 -0.8364	-0.7063 0.4047 -0.5809	-0.5056 0.8628 0.0031	1.0000 0.0002 0.0000	Axis
					0.7253 -0.4168 -0.5480	-0.4966 -0.8680 -0.0009	-0.7398 -0.4317 -0.5161	-0.0001 0.5226 0.8526	Second axis

Spatial dependence of Young's modulus

[[101.0, 28.0, 29.0, 14.0, 0.0, 0.0], [28.0, 101.0, 29.0, -14.0, 0.0, 0.0], [29.0, 29.0, 43.0, 0.0, 0.0, 0.0], [14.0, -14.0, 0.0, 27.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 27.0, 14.0], [0.0, 0.0, 0.0, 0.0, 14.0, 37.0]] SnP3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7541" target="_blank">mp-7541</a>) young

Spatial dependence of linear compressibility

[[101.0, 28.0, 29.0, 14.0, 0.0, 0.0], [28.0, 101.0, 29.0, -14.0, 0.0, 0.0], [29.0, 29.0, 43.0, 0.0, 0.0, 0.0], [14.0, -14.0, 0.0, 27.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 27.0, 14.0], [0.0, 0.0, 0.0, 0.0, 14.0, 37.0]] SnP3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7541" target="_blank">mp-7541</a>) lc

Spatial dependence of shear modulus

[[101.0, 28.0, 29.0, 14.0, 0.0, 0.0], [28.0, 101.0, 29.0, -14.0, 0.0, 0.0], [29.0, 29.0, 43.0, 0.0, 0.0, 0.0], [14.0, -14.0, 0.0, 27.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 27.0, 14.0], [0.0, 0.0, 0.0, 0.0, 14.0, 37.0]] SnP3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7541" target="_blank">mp-7541</a>) shear

Spatial dependence of Poisson's ratio

[[101.0, 28.0, 29.0, 14.0, 0.0, 0.0], [28.0, 101.0, 29.0, -14.0, 0.0, 0.0], [29.0, 29.0, 43.0, 0.0, 0.0, 0.0], [14.0, -14.0, 0.0, 27.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 27.0, 14.0], [0.0, 0.0, 0.0, 0.0, 14.0, 37.0]] SnP3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7541" target="_blank">mp-7541</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)