Dear Noorudin Reshi

As for "magic numbers" there is a good paper https://www.researchgate.net/profile/Alexander_Schmidt7/publication/225876498_Concept_of_magic_number_clusters_as_a_new_approach_to_the_interpretation_of_unusual_kinetics_of_the_Heck_reaction_with_aryl_bromides/links/0046353361f888daf4000000/Concept-of-magic-number-clusters-as-a-new-approach-to-the-interpretation-of-unusual-kinetics-of-the-Heck-reaction-with-aryl-bromides.pdf

At the same time the crystal structure of Ruthenium is hexagonal close-packed (hcp) but in the above-mentioned paper presented the equations for number of atoms for cubic lattices.

Maybe it will be better to calculate the surface of nanoparticle and divide it on the surface of atom (π*r{Covalent radius}2).

With kind regards,

Liliya

Dear Noorudin Reshi , crystalline packaging and crystal shape can be related, but often it is not the case. Imagine you have a cubic salt crystal and a needle like crystal of the same salt, both with the same volume, both are fcc by their atomic arrangement, but clearly they have different shapes and their surfaces are also different, therefore, the number of surface atoms will be different in each case.

Often, crystal faces have different energy, and some grow at lower pace that other, so you can see truncated vertices and edges, or face defects... while the crystallyne arrangement is keeped.

The platonic solids are just regular polyhedrons, and yes, your nanoparticles can take these shapes, while have different packaging. So hcp is not a type of platonic solid (but a crystal with hcp structure can grows as a platonic solid).

It happens that particles (atoms, molecules, oranges...) have a trend to arrange in one of these shapes, due to energy reasons. They try to minimise energy.

So you need to know your nanoparticle crystalline structure, the nanoparticle shape and orientation of the crystalline structure respect to the shape to calculate the number of atoms by surface. You also need the size of the Ru atoms and the nanoparticle dimensions.

If you apporoximate the shape of your nanoparticle by a sphere, its surface changes with the square of the nanoparticle radius, and the number of surface atoms follows a similar change.

Nanoparticles are different in size. Therefore, the effects that Manuel Gómez writes about will be covered by a size error. Determine the average diameter, area. Take the atom size from the reference data and determine its amount on the surface. The magic number associated with stability are best determined by numerical experiment.

Manuel Gómez Yuri Mirgorod

Thank you both for your valuable insight.

So if I calculate the total number of atoms using

volume of particle/volume of atom (assuming both spheres).

How do I find the nearest magic number (hcp Ru) to calculate the percentage of atoms at the surface. Is a table available (total atoms vs surface atoms) for hcp solids just like it is known for platonic systems. Of course, assuming that the particles are spherical.

Thank you.

Noorudin Reshi

A numerical experiment involves a theoretical calculation using a theory (from first principles) on a computer of such a magic number so that the gain in energy of system is maximum. It is possible that you will find such articles for other nanoparticles.

Yuri Mirgorod Thank you. It was a useful discussion with you.

You can use this aricle to calculate the number of Nps

http://sustainable-nano.com/2016/07/28/how-many-atoms-are-in-a-nanoparticle/

Dear Noorudin Reshi

As for "magic numbers" there is a good paper https://www.researchgate.net/profile/Alexander_Schmidt7/publication/225876498_Concept_of_magic_number_clusters_as_a_new_approach_to_the_interpretation_of_unusual_kinetics_of_the_Heck_reaction_with_aryl_bromides/links/0046353361f888daf4000000/Concept-of-magic-number-clusters-as-a-new-approach-to-the-interpretation-of-unusual-kinetics-of-the-Heck-reaction-with-aryl-bromides.pdf

At the same time the crystal structure of Ruthenium is hexagonal close-packed (hcp) but in the above-mentioned paper presented the equations for number of atoms for cubic lattices.

Maybe it will be better to calculate the surface of nanoparticle and divide it on the surface of atom (π*r{Covalent radius}2).

With kind regards,

Liliya