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 Zr3Pd4 (Materials Project id mp-12712)

       181      130      117       -2       -6        0  
       130      181      117        2        6        0  
       117      117      215        0        0        0  
        -2        2        0       27        0        6  
        -6        6        0        0       27       -2  
         0        0        0        6       -2       25  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 145 GPa	EV = 84.194 GPa	GV = 30 GPa	νV = 0.40323
Reuss	KR = 144.64 GPa	ER = 76.374 GPa	GR = 27.045 GPa	νR = 0.412
Hill	KH = 144.82 GPa	EH = 80.296 GPa	GH = 28.522 GPa	νH = 0.40759

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
19.597 GPa	24.033 GPa	32.403 GPa	53.967 GPa	90.715 GPa	435.28 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	57.163 GPa	126.97 GPa	1.95 TPa–1	2.4818 TPa–1	19.609 GPa	39.604 GPa	0.14452	0.66933	Value
Anisotropy	2.221		1.2727		2.02		4.6315		Anisotropy
Axis	-0.5105 0.6914 0.5112	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	-0.1302 0.9915 -0.0000	0.7559 0.0778 -0.6501	-0.5769 -0.0588 0.8147	0.8060 0.5918 0.0030	0.8049 0.5934 0.0027	Axis
					-0.1007 0.9949 0.0020	-0.8105 -0.0830 -0.5798	-0.2255 0.3118 -0.9230	-0.5485 0.7423 0.3848	Second axis

Spatial dependence of Young's modulus

[[181.0, 130.0, 117.0, -2.0, -6.0, 0.0], [130.0, 181.0, 117.0, 2.0, 6.0, 0.0], [117.0, 117.0, 215.0, 0.0, 0.0, 0.0], [-2.0, 2.0, 0.0, 27.0, 0.0, 6.0], [-6.0, 6.0, 0.0, 0.0, 27.0, -2.0], [0.0, 0.0, 0.0, 6.0, -2.0, 25.0]] Zr3Pd4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-12712" target="_blank">mp-12712</a>) young

Spatial dependence of linear compressibility

[[181.0, 130.0, 117.0, -2.0, -6.0, 0.0], [130.0, 181.0, 117.0, 2.0, 6.0, 0.0], [117.0, 117.0, 215.0, 0.0, 0.0, 0.0], [-2.0, 2.0, 0.0, 27.0, 0.0, 6.0], [-6.0, 6.0, 0.0, 0.0, 27.0, -2.0], [0.0, 0.0, 0.0, 6.0, -2.0, 25.0]] Zr3Pd4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-12712" target="_blank">mp-12712</a>) lc

Spatial dependence of shear modulus

[[181.0, 130.0, 117.0, -2.0, -6.0, 0.0], [130.0, 181.0, 117.0, 2.0, 6.0, 0.0], [117.0, 117.0, 215.0, 0.0, 0.0, 0.0], [-2.0, 2.0, 0.0, 27.0, 0.0, 6.0], [-6.0, 6.0, 0.0, 0.0, 27.0, -2.0], [0.0, 0.0, 0.0, 6.0, -2.0, 25.0]] Zr3Pd4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-12712" target="_blank">mp-12712</a>) shear

Spatial dependence of Poisson's ratio

[[181.0, 130.0, 117.0, -2.0, -6.0, 0.0], [130.0, 181.0, 117.0, 2.0, 6.0, 0.0], [117.0, 117.0, 215.0, 0.0, 0.0, 0.0], [-2.0, 2.0, 0.0, 27.0, 0.0, 6.0], [-6.0, 6.0, 0.0, 0.0, 27.0, -2.0], [0.0, 0.0, 0.0, 6.0, -2.0, 25.0]] Zr3Pd4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-12712" target="_blank">mp-12712</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)