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 PrAl3 (Materials Project id mp-12553)

        90       38       44        0        0        0  
        38       90       44        0        0        0  
        44       44      190        0        0        0  
         0        0        0       65        0        0  
         0        0        0        0       65        0  
         0        0        0        0        0       26  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 69.111 GPa	EV = 115.87 GPa	GV = 47.467 GPa	νV = 0.22057
Reuss	KR = 61.59 GPa	ER = 96.754 GPa	GR = 39.071 GPa	νR = 0.23818
Hill	KH = 65.351 GPa	EH = 106.34 GPa	GH = 43.269 GPa	νH = 0.2288

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
26 GPa	52 GPa	65 GPa	65 GPa	89.48 GPa	228.52 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	70.12 GPa	161.16 GPa	1.9562 TPa–1	7.1401 TPa–1	26 GPa	65 GPa	-0.026502	0.45574	Value
Anisotropy	2.298		3.6500		2.5		∞		Anisotropy
Axis	0.9659 0.2588 0.0000	0.2658 0.0745 0.9611	0.0000 0.0000 1.0000	0.3827 0.9239 0.0000	0.9573 0.2890 0.0000	0.0000 0.0000 1.0000	0.3322 0.6154 -0.7148	0.3069 0.5563 0.7722	Axis
					-0.2890 0.9573 -0.0000	0.7660 0.6428 -0.0000	0.3395 0.6290 0.6993	-0.8756 0.4831 0.0000	Second axis

Spatial dependence of Young's modulus

[[90.0, 38.0, 44.0, 0.0, 0.0, 0.0], [38.0, 90.0, 44.0, 0.0, 0.0, 0.0], [44.0, 44.0, 190.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 65.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 65.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] PrAl3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-12553" target="_blank">mp-12553</a>) young

Spatial dependence of linear compressibility

[[90.0, 38.0, 44.0, 0.0, 0.0, 0.0], [38.0, 90.0, 44.0, 0.0, 0.0, 0.0], [44.0, 44.0, 190.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 65.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 65.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] PrAl3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-12553" target="_blank">mp-12553</a>) lc

Spatial dependence of shear modulus

[[90.0, 38.0, 44.0, 0.0, 0.0, 0.0], [38.0, 90.0, 44.0, 0.0, 0.0, 0.0], [44.0, 44.0, 190.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 65.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 65.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] PrAl3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-12553" target="_blank">mp-12553</a>) shear

Spatial dependence of Poisson's ratio

[[90.0, 38.0, 44.0, 0.0, 0.0, 0.0], [38.0, 90.0, 44.0, 0.0, 0.0, 0.0], [44.0, 44.0, 190.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 65.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 65.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] PrAl3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-12553" target="_blank">mp-12553</a>) poisson

Code version: 2019.01.09 (running on Python 3.7.2)