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 PrCo2 (Materials Project id mp-2085)

       140      108      108        6        5       -5  
       108      140      108        5        6       -5  
       108      108      140        5        5       -6  
         6        5        5       22        0        0  
         5        6        5        0       22        0  
        -5       -5       -6        0        0       22  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 118.67 GPa	EV = 55.732 GPa	GV = 19.6 GPa	νV = 0.42173
Reuss	KR = 114.79 GPa	ER = 54.01 GPa	GR = 18.996 GPa	νR = 0.42158
Hill	KH = 116.73 GPa	EH = 54.871 GPa	GH = 19.298 GPa	νH = 0.42165

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
21.235 GPa	21.901 GPa	21.901 GPa	32.099 GPa	32.099 GPa	356.76 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	45.791 GPa	63.634 GPa	1.8479 TPa–1	5.0158 TPa–1	15.918 GPa	22.082 GPa	0.28932	0.59222	Value
Anisotropy	1.39		2.7143		1.387		2.0469		Anisotropy
Axis	-0.0160 -0.0160 0.9997	-0.5893 0.5527 0.5893	0.7071 0.0000 0.7071	0.5774 0.5773 -0.5774	0.0000 0.7071 0.7071	0.7071 0.0000 0.7071	0.7005 0.7004 -0.1371	-0.7071 0.0000 -0.7071	Axis
					-0.1155 0.7024 -0.7024	0.0817 0.9933 -0.0817	-0.7071 0.7071 0.0000	0.0689 -0.9952 -0.0690	Second axis

Spatial dependence of Young's modulus

[[140.0, 108.0, 108.0, 6.0, 5.0, -5.0], [108.0, 140.0, 108.0, 5.0, 6.0, -5.0], [108.0, 108.0, 140.0, 5.0, 5.0, -6.0], [6.0, 5.0, 5.0, 22.0, 0.0, 0.0], [5.0, 6.0, 5.0, 0.0, 22.0, 0.0], [-5.0, -5.0, -6.0, 0.0, 0.0, 22.0]] PrCo2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2085" target="_blank">mp-2085</a>) young

Spatial dependence of linear compressibility

[[140.0, 108.0, 108.0, 6.0, 5.0, -5.0], [108.0, 140.0, 108.0, 5.0, 6.0, -5.0], [108.0, 108.0, 140.0, 5.0, 5.0, -6.0], [6.0, 5.0, 5.0, 22.0, 0.0, 0.0], [5.0, 6.0, 5.0, 0.0, 22.0, 0.0], [-5.0, -5.0, -6.0, 0.0, 0.0, 22.0]] PrCo2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2085" target="_blank">mp-2085</a>) lc

Spatial dependence of shear modulus

[[140.0, 108.0, 108.0, 6.0, 5.0, -5.0], [108.0, 140.0, 108.0, 5.0, 6.0, -5.0], [108.0, 108.0, 140.0, 5.0, 5.0, -6.0], [6.0, 5.0, 5.0, 22.0, 0.0, 0.0], [5.0, 6.0, 5.0, 0.0, 22.0, 0.0], [-5.0, -5.0, -6.0, 0.0, 0.0, 22.0]] PrCo2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2085" target="_blank">mp-2085</a>) shear

Spatial dependence of Poisson's ratio

[[140.0, 108.0, 108.0, 6.0, 5.0, -5.0], [108.0, 140.0, 108.0, 5.0, 6.0, -5.0], [108.0, 108.0, 140.0, 5.0, 5.0, -6.0], [6.0, 5.0, 5.0, 22.0, 0.0, 0.0], [5.0, 6.0, 5.0, 0.0, 22.0, 0.0], [-5.0, -5.0, -6.0, 0.0, 0.0, 22.0]] PrCo2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2085" target="_blank">mp-2085</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)