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 Sm(CoP)2 (Materials Project id mp-573563)

       256       41       64        0        0        0  
        41      256       64        0        0        0  
        64       64      156        0        0        0  
         0        0        0      111        0        0  
         0        0        0        0      111        0  
         0        0        0        0        0      101  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 111.78 GPa	EV = 227.27 GPa	GV = 97.867 GPa	νV = 0.16113
Reuss	KR = 108.05 GPa	ER = 213.58 GPa	GR = 91.231 GPa	νR = 0.17054
Hill	KH = 109.91 GPa	EH = 220.44 GPa	GH = 94.549 GPa	νH = 0.16573

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
101 GPa	111 GPa	111 GPa	111.77 GPa	215 GPa	341.23 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	128.42 GPa	249.74 GPa	2.4122 TPa–1	4.431 TPa–1	63.843 GPa	111 GPa	0.0032073	0.38393	Value
Anisotropy	1.945		1.8370		1.739		119.7046		Anisotropy
Axis	0.0000 0.0000 1.0000	0.8733 0.0000 -0.4872	1.0000 0.0000 0.0000	0.0000 0.0000 1.0000	-0.5001 0.4998 0.7071	0.0000 0.0000 1.0000	0.4996 0.4996 -0.7077	1.0000 0.0002 0.0000	Axis
					-0.4999 0.5002 -0.7071	-0.9397 0.3420 0.0000	0.5004 0.5004 0.7065	-0.0000 0.0002 -1.0000	Second axis

Spatial dependence of Young's modulus

[[256.0, 41.0, 64.0, 0.0, 0.0, 0.0], [41.0, 256.0, 64.0, 0.0, 0.0, 0.0], [64.0, 64.0, 156.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 111.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 111.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 101.0]] Sm(CoP)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-573563" target="_blank">mp-573563</a>) young

Spatial dependence of linear compressibility

[[256.0, 41.0, 64.0, 0.0, 0.0, 0.0], [41.0, 256.0, 64.0, 0.0, 0.0, 0.0], [64.0, 64.0, 156.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 111.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 111.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 101.0]] Sm(CoP)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-573563" target="_blank">mp-573563</a>) lc

Spatial dependence of shear modulus

[[256.0, 41.0, 64.0, 0.0, 0.0, 0.0], [41.0, 256.0, 64.0, 0.0, 0.0, 0.0], [64.0, 64.0, 156.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 111.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 111.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 101.0]] Sm(CoP)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-573563" target="_blank">mp-573563</a>) shear

Spatial dependence of Poisson's ratio

[[256.0, 41.0, 64.0, 0.0, 0.0, 0.0], [41.0, 256.0, 64.0, 0.0, 0.0, 0.0], [64.0, 64.0, 156.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 111.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 111.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 101.0]] Sm(CoP)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-573563" target="_blank">mp-573563</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)