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 DyCu (Materials Project id mp-2334)

       121       57       57        0        0        0  
        57      121       57        0        0        0  
        57       57      121        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0       38  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 78.333 GPa	EV = 92.749 GPa	GV = 35.6 GPa	νV = 0.30266
Reuss	KR = 78.333 GPa	ER = 92.181 GPa	GR = 35.349 GPa	νR = 0.30387
Hill	KH = 78.333 GPa	EH = 92.465 GPa	GH = 35.474 GPa	νH = 0.30327

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
38 GPa	38 GPa	38 GPa	64 GPa	64 GPa	235 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	84.494 GPa	98.132 GPa	4.2553 TPa–1	4.2553 TPa–1	32 GPa	38 GPa	0.24113	0.35748	Value
Anisotropy	1.161		1.0000		1.187		1.4825		Anisotropy
Axis	0.0000 0.0000 1.0000	0.5774 0.5774 0.5773	0.6088 0.0000 0.7934	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	0.0000 0.0000 1.0000	0.7071 -0.0002 0.7071	0.7071 -0.0005 0.7071	Axis
					-0.7071 -0.0002 -0.7071	-0.7660 0.6428 -0.0000	0.7071 -0.0006 -0.7071	0.0004 1.0000 0.0004	Second axis

Spatial dependence of Young's modulus

[[121.0, 57.0, 57.0, 0.0, 0.0, 0.0], [57.0, 121.0, 57.0, 0.0, 0.0, 0.0], [57.0, 57.0, 121.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 38.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 38.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 38.0]] DyCu (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2334" target="_blank">mp-2334</a>) young

Spatial dependence of linear compressibility

[[121.0, 57.0, 57.0, 0.0, 0.0, 0.0], [57.0, 121.0, 57.0, 0.0, 0.0, 0.0], [57.0, 57.0, 121.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 38.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 38.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 38.0]] DyCu (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2334" target="_blank">mp-2334</a>) lc

Spatial dependence of shear modulus

[[121.0, 57.0, 57.0, 0.0, 0.0, 0.0], [57.0, 121.0, 57.0, 0.0, 0.0, 0.0], [57.0, 57.0, 121.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 38.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 38.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 38.0]] DyCu (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2334" target="_blank">mp-2334</a>) shear

Spatial dependence of Poisson's ratio

[[121.0, 57.0, 57.0, 0.0, 0.0, 0.0], [57.0, 121.0, 57.0, 0.0, 0.0, 0.0], [57.0, 57.0, 121.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 38.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 38.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 38.0]] DyCu (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2334" target="_blank">mp-2334</a>) poisson

Code version: 2019.01.09 (running on Python 3.7.2)