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 PaAs (Materials Project id mp-15694)

       284       20       20        0        0        0  
        20      284       20        0        0        0  
        20       20      284        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       26  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 108 GPa	EV = 169.43 GPa	GV = 68.4 GPa	νV = 0.23853
Reuss	KR = 108 GPa	ER = 102.76 GPa	GR = 38.304 GPa	νR = 0.34142
Hill	KH = 108 GPa	EH = 137.43 GPa	GH = 53.352 GPa	νH = 0.28792

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
26 GPa	26 GPa	26 GPa	264 GPa	264 GPa	324 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	72.206 GPa	281.37 GPa	3.0864 TPa–1	3.0864 TPa–1	26 GPa	132 GPa	0.020737	0.70554	Value
Anisotropy	3.897		1.0000		5.077		34.0231		Anisotropy
Axis	0.5774 0.5773 -0.5774	0.0000 0.0000 1.0000	0.4830 0.3706 0.7934	0.5000 0.0000 0.8660	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	-0.7071 0.0000 0.7071	0.7071 -0.0000 -0.7071	Axis
					0.1735 0.9848 -0.0000	-0.7071 -0.0002 -0.7071	-0.0000 -1.0000 -0.0000	-0.7071 0.0002 -0.7071	Second axis

Spatial dependence of Young's modulus

[[284.0, 20.0, 20.0, 0.0, 0.0, 0.0], [20.0, 284.0, 20.0, 0.0, 0.0, 0.0], [20.0, 20.0, 284.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 26.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 26.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] PaAs (Materials Project id <a href="https://www.materialsproject.org/materials/mp-15694" target="_blank">mp-15694</a>) young

Spatial dependence of linear compressibility

[[284.0, 20.0, 20.0, 0.0, 0.0, 0.0], [20.0, 284.0, 20.0, 0.0, 0.0, 0.0], [20.0, 20.0, 284.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 26.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 26.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] PaAs (Materials Project id <a href="https://www.materialsproject.org/materials/mp-15694" target="_blank">mp-15694</a>) lc

Spatial dependence of shear modulus

[[284.0, 20.0, 20.0, 0.0, 0.0, 0.0], [20.0, 284.0, 20.0, 0.0, 0.0, 0.0], [20.0, 20.0, 284.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 26.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 26.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] PaAs (Materials Project id <a href="https://www.materialsproject.org/materials/mp-15694" target="_blank">mp-15694</a>) shear

Spatial dependence of Poisson's ratio

[[284.0, 20.0, 20.0, 0.0, 0.0, 0.0], [20.0, 284.0, 20.0, 0.0, 0.0, 0.0], [20.0, 20.0, 284.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 26.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 26.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] PaAs (Materials Project id <a href="https://www.materialsproject.org/materials/mp-15694" target="_blank">mp-15694</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)