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 Zr3Tl (Materials Project id mp-977585)

       175       94       94        0        0        0  
        94      175       94        0        0        0  
        94       94      175        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       78  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 121 GPa	EV = 161.05 GPa	GV = 63 GPa	νV = 0.27817
Reuss	KR = 121 GPa	ER = 147.61 GPa	GR = 56.919 GPa	νR = 0.29668
Hill	KH = 121 GPa	EH = 154.38 GPa	GH = 59.959 GPa	νH = 0.28736

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
78 GPa	78 GPa	78 GPa	81 GPa	81 GPa	363 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	109.3 GPa	192.61 GPa	2.7548 TPa–1	2.7548 TPa–1	40.5 GPa	78 GPa	0.037088	0.51722	Value
Anisotropy	1.762		1.0000		1.926		13.9458		Anisotropy
Axis	0.0000 0.0000 1.0000	0.5774 0.5774 0.5773	0.9239 0.0000 0.3827	0.3794 0.9160 -0.1305	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0000 -0.7071	0.7071 -0.0000 0.7071	Axis
					0.7071 -0.0005 -0.7071	-0.7660 0.6428 -0.0000	-0.7071 0.0002 -0.7071	-0.0000 1.0000 0.0000	Second axis

Spatial dependence of Young's modulus

[[175.0, 94.0, 94.0, 0.0, 0.0, 0.0], [94.0, 175.0, 94.0, 0.0, 0.0, 0.0], [94.0, 94.0, 175.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 78.0]] Zr3Tl (Materials Project id <a href="https://www.materialsproject.org/materials/mp-977585" target="_blank">mp-977585</a>) young

Spatial dependence of linear compressibility

[[175.0, 94.0, 94.0, 0.0, 0.0, 0.0], [94.0, 175.0, 94.0, 0.0, 0.0, 0.0], [94.0, 94.0, 175.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 78.0]] Zr3Tl (Materials Project id <a href="https://www.materialsproject.org/materials/mp-977585" target="_blank">mp-977585</a>) lc

Spatial dependence of shear modulus

[[175.0, 94.0, 94.0, 0.0, 0.0, 0.0], [94.0, 175.0, 94.0, 0.0, 0.0, 0.0], [94.0, 94.0, 175.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 78.0]] Zr3Tl (Materials Project id <a href="https://www.materialsproject.org/materials/mp-977585" target="_blank">mp-977585</a>) shear

Spatial dependence of Poisson's ratio

[[175.0, 94.0, 94.0, 0.0, 0.0, 0.0], [94.0, 175.0, 94.0, 0.0, 0.0, 0.0], [94.0, 94.0, 175.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 78.0]] Zr3Tl (Materials Project id <a href="https://www.materialsproject.org/materials/mp-977585" target="_blank">mp-977585</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)