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 Nd3Tl (Materials Project id mp-1533)

        57       35       35        0        0        0  
        35       57       35        0        0        0  
        35       35       57        0        0        0  
         0        0        0       13        0        0  
         0        0        0        0       13        0  
         0        0        0        0        0       13  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 42.333 GPa	EV = 33.392 GPa	GV = 12.2 GPa	νV = 0.36853
Reuss	KR = 42.333 GPa	ER = 33.189 GPa	GR = 12.119 GPa	νR = 0.36933
Hill	KH = 42.333 GPa	EH = 33.291 GPa	GH = 12.159 GPa	νH = 0.36893

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
13 GPa	13 GPa	13 GPa	22 GPa	22 GPa	127 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	30.37 GPa	35.379 GPa	7.874 TPa–1	7.874 TPa–1	11 GPa	13 GPa	0.30683	0.42563	Value
Anisotropy	1.165		1.0000		1.182		1.3872		Anisotropy
Axis	0.0000 0.0000 1.0000	0.5774 0.5774 0.5773	0.2500 0.9330 0.2588	0.8660 0.0000 0.5000	0.7071 -0.0003 0.7071	-0.0000 0.0000 1.0000	0.7071 -0.0002 0.7071	0.7071 0.0004 -0.7071	Axis
					0.7071 -0.0005 -0.7071	-0.5000 0.8660 -0.0000	0.7071 -0.0006 -0.7071	-0.0003 1.0000 0.0003	Second axis

Spatial dependence of Young's modulus

[[57.0, 35.0, 35.0, 0.0, 0.0, 0.0], [35.0, 57.0, 35.0, 0.0, 0.0, 0.0], [35.0, 35.0, 57.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 13.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 13.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 13.0]] Nd3Tl (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1533" target="_blank">mp-1533</a>) young

Spatial dependence of linear compressibility

[[57.0, 35.0, 35.0, 0.0, 0.0, 0.0], [35.0, 57.0, 35.0, 0.0, 0.0, 0.0], [35.0, 35.0, 57.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 13.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 13.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 13.0]] Nd3Tl (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1533" target="_blank">mp-1533</a>) lc

Spatial dependence of shear modulus

[[57.0, 35.0, 35.0, 0.0, 0.0, 0.0], [35.0, 57.0, 35.0, 0.0, 0.0, 0.0], [35.0, 35.0, 57.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 13.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 13.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 13.0]] Nd3Tl (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1533" target="_blank">mp-1533</a>) shear

Spatial dependence of Poisson's ratio

[[57.0, 35.0, 35.0, 0.0, 0.0, 0.0], [35.0, 57.0, 35.0, 0.0, 0.0, 0.0], [35.0, 35.0, 57.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 13.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 13.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 13.0]] Nd3Tl (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1533" target="_blank">mp-1533</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)