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 ErCu (Materials Project id mp-1955)

       126       56       56        0        0        0  
        56      126       56        0        0        0  
        56       56      126        0        0        0  
         0        0        0       41        0        0  
         0        0        0        0       41        0  
         0        0        0        0        0       41  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 79.333 GPa	EV = 99.64 GPa	GV = 38.6 GPa	νV = 0.29067
Reuss	KR = 79.333 GPa	ER = 99.126 GPa	GR = 38.369 GPa	νR = 0.29175
Hill	KH = 79.333 GPa	EH = 99.383 GPa	GH = 38.484 GPa	νH = 0.29121

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
41 GPa	41 GPa	41 GPa	70 GPa	70 GPa	238 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	91.538 GPa	104.92 GPa	4.2017 TPa–1	4.2017 TPa–1	35 GPa	41 GPa	0.23444	0.34025	Value
Anisotropy	1.146		1.0000		1.171		1.4513		Anisotropy
Axis	0.0000 1.0000 0.0000	-0.5774 0.5774 -0.5773	0.9914 0.0000 0.1305	0.0000 0.0000 1.0000	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0002 0.7071	0.7071 -0.0005 0.7071	Axis
					0.7071 -0.0005 -0.7071	-0.9397 -0.3420 0.0000	0.7071 -0.0006 -0.7071	0.0003 1.0000 0.0004	Second axis

Spatial dependence of Young's modulus

[[126.0, 56.0, 56.0, 0.0, 0.0, 0.0], [56.0, 126.0, 56.0, 0.0, 0.0, 0.0], [56.0, 56.0, 126.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 41.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 41.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 41.0]] ErCu (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1955" target="_blank">mp-1955</a>) young

Spatial dependence of linear compressibility

[[126.0, 56.0, 56.0, 0.0, 0.0, 0.0], [56.0, 126.0, 56.0, 0.0, 0.0, 0.0], [56.0, 56.0, 126.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 41.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 41.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 41.0]] ErCu (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1955" target="_blank">mp-1955</a>) lc

Spatial dependence of shear modulus

[[126.0, 56.0, 56.0, 0.0, 0.0, 0.0], [56.0, 126.0, 56.0, 0.0, 0.0, 0.0], [56.0, 56.0, 126.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 41.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 41.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 41.0]] ErCu (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1955" target="_blank">mp-1955</a>) shear

Spatial dependence of Poisson's ratio

[[126.0, 56.0, 56.0, 0.0, 0.0, 0.0], [56.0, 126.0, 56.0, 0.0, 0.0, 0.0], [56.0, 56.0, 126.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 41.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 41.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 41.0]] ErCu (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1955" target="_blank">mp-1955</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)