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 UCdO4 (Materials Project id mp-545598)

       211       38       73        0        0        0  
        38      129      101        0        0        0  
        73      101      328        0        0        0  
         0        0        0       25        0        0  
         0        0        0        0       54        0  
         0        0        0        0        0       15  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 121.33 GPa	EV = 130.03 GPa	GV = 49.2 GPa	νV = 0.32139
Reuss	KR = 97.468 GPa	ER = 85.771 GPa	GR = 31.689 GPa	νR = 0.35334
Hill	KH = 109.4 GPa	EH = 108.02 GPa	GH = 40.444 GPa	νH = 0.33543

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
15 GPa	25 GPa	54 GPa	86.255 GPa	176.77 GPa	404.98 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	49.323 GPa	239.56 GPa	0.26868 TPa–1	6.5187 TPa–1	15 GPa	89.431 GPa	0.06739	0.72697	Value
Anisotropy	4.857		24.2622		5.962		10.7876		Anisotropy
Axis	-0.6693 0.7430 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.0000 1.0000 0.0000	1.0000 -0.0002 0.0000	0.7071 -0.0002 0.7071	-0.0000 0.8298 0.5581	0.0000 0.2796 0.9601	Axis
					0.0002 1.0000 0.0000	0.7071 0.0001 -0.7071	-1.0000 -0.0000 -0.0000	-0.0000 0.9601 -0.2796	Second axis

Spatial dependence of Young's modulus

[[211.0, 38.0, 73.0, 0.0, 0.0, 0.0], [38.0, 129.0, 101.0, 0.0, 0.0, 0.0], [73.0, 101.0, 328.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 25.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 54.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 15.0]] UCdO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-545598" target="_blank">mp-545598</a>) young

Spatial dependence of linear compressibility

[[211.0, 38.0, 73.0, 0.0, 0.0, 0.0], [38.0, 129.0, 101.0, 0.0, 0.0, 0.0], [73.0, 101.0, 328.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 25.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 54.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 15.0]] UCdO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-545598" target="_blank">mp-545598</a>) lc

Spatial dependence of shear modulus

[[211.0, 38.0, 73.0, 0.0, 0.0, 0.0], [38.0, 129.0, 101.0, 0.0, 0.0, 0.0], [73.0, 101.0, 328.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 25.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 54.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 15.0]] UCdO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-545598" target="_blank">mp-545598</a>) shear

Spatial dependence of Poisson's ratio

[[211.0, 38.0, 73.0, 0.0, 0.0, 0.0], [38.0, 129.0, 101.0, 0.0, 0.0, 0.0], [73.0, 101.0, 328.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 25.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 54.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 15.0]] UCdO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-545598" target="_blank">mp-545598</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)