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 CaPHO4 (Materials Project id mp-24390)

       123       47       31       -2       -2        8  
        47      140       46        9        1        0  
        31       46      138        5       -2       -6  
        -2        9        5       41       -2        2  
        -2        1       -2       -2       28        1  
         8        0       -6        2        1       35  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 72.111 GPa	EV = 99.703 GPa	GV = 39.267 GPa	νV = 0.26956
Reuss	KR = 71.094 GPa	ER = 94.149 GPa	GR = 36.798 GPa	νR = 0.27929
Hill	KH = 71.603 GPa	EH = 96.934 GPa	GH = 38.032 GPa	νH = 0.27437

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
27.066 GPa	32.955 GPa	40.928 GPa	83.705 GPa	102.38 GPa	217.97 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	73.444 GPa	123.89 GPa	3.5465 TPa–1	5.6579 TPa–1	26.616 GPa	53.174 GPa	0.093223	0.46166	Value
Anisotropy	1.687		1.5953		1.998		4.9522		Anisotropy
Axis	0.7437 0.0083 0.6684	-0.0047 0.8844 0.4667	0.0362 0.9149 0.4020	-0.8904 0.2122 -0.4028	-0.1441 0.3904 -0.9093	0.6871 0.1583 -0.7092	0.0497 -0.1520 0.9871	0.5518 0.8321 0.0556	Axis
					-0.9564 -0.2910 0.0266	-0.6244 -0.3704 -0.6877	-0.7974 -0.6011 -0.0524	-0.8330 0.5469 0.0832	Second axis

Spatial dependence of Young's modulus

[[123.0, 47.0, 31.0, -2.0, -2.0, 8.0], [47.0, 140.0, 46.0, 9.0, 1.0, 0.0], [31.0, 46.0, 138.0, 5.0, -2.0, -6.0], [-2.0, 9.0, 5.0, 41.0, -2.0, 2.0], [-2.0, 1.0, -2.0, -2.0, 28.0, 1.0], [8.0, 0.0, -6.0, 2.0, 1.0, 35.0]] CaPHO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-24390" target="_blank">mp-24390</a>) young

Spatial dependence of linear compressibility

[[123.0, 47.0, 31.0, -2.0, -2.0, 8.0], [47.0, 140.0, 46.0, 9.0, 1.0, 0.0], [31.0, 46.0, 138.0, 5.0, -2.0, -6.0], [-2.0, 9.0, 5.0, 41.0, -2.0, 2.0], [-2.0, 1.0, -2.0, -2.0, 28.0, 1.0], [8.0, 0.0, -6.0, 2.0, 1.0, 35.0]] CaPHO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-24390" target="_blank">mp-24390</a>) lc

Spatial dependence of shear modulus

[[123.0, 47.0, 31.0, -2.0, -2.0, 8.0], [47.0, 140.0, 46.0, 9.0, 1.0, 0.0], [31.0, 46.0, 138.0, 5.0, -2.0, -6.0], [-2.0, 9.0, 5.0, 41.0, -2.0, 2.0], [-2.0, 1.0, -2.0, -2.0, 28.0, 1.0], [8.0, 0.0, -6.0, 2.0, 1.0, 35.0]] CaPHO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-24390" target="_blank">mp-24390</a>) shear

Spatial dependence of Poisson's ratio

[[123.0, 47.0, 31.0, -2.0, -2.0, 8.0], [47.0, 140.0, 46.0, 9.0, 1.0, 0.0], [31.0, 46.0, 138.0, 5.0, -2.0, -6.0], [-2.0, 9.0, 5.0, 41.0, -2.0, 2.0], [-2.0, 1.0, -2.0, -2.0, 28.0, 1.0], [8.0, 0.0, -6.0, 2.0, 1.0, 35.0]] CaPHO4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-24390" target="_blank">mp-24390</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)