My chemistry teacher told us that graphite or diamond had an atomicity of infinity. However, the definition of molecule in my testbook is

A molecule is the smallest part of an element or compound which can exist on its own under ordinary condition.

It doesn't make sense to me because if a molecule has an atomicity of infinity, it it is not a discrete compound anymore. It contradicts the definition of molecule.

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    $\begingroup$ That's why graphite and diamond are not made of molecules. $\endgroup$ – Ivan Neretin Oct 11 '19 at 13:32
  • $\begingroup$ but my notes from my teacher actually classify them as molecules $\endgroup$ – Learning Mathematics Oct 11 '19 at 13:39
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    $\begingroup$ Then I disagree with your teacher quite strongly. $\endgroup$ – Ivan Neretin Oct 11 '19 at 14:02
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    $\begingroup$ I don't see what one gains, and in which context, by speaking about infinite atomicity in non molecular solids. Atomicity presumes molecularity. And atomicity is taken as 1 for carbon allotrops except fullerenes. Which also point to the relative usefulness of the term. Speaking about biatomic, triatomic, ... seems more immediate. Also the definition of molecule in the book is wrong. It doesn't always work. You might find cases in which it fails. "Part of a substance" might be already better. .. $\endgroup$ – Alchimista Oct 11 '19 at 15:27
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    $\begingroup$ @Jan No. Then again, what is the point of talking about molecules in this case? $\endgroup$ – Ivan Neretin Oct 11 '19 at 18:23

Introducing the idea of "infinite atomicity" can be useful to highlight the importance of particle size on the properties of metallic or network covalent solids. As the surface to volume ratio of discrete particles becomes sufficiently large, properties of crystalline solids such as melting point, absorption wavelength and reactivity begin to diverge significantly from the limiting values observed for larger crystals. A pronounced change often occurs as the nanoparticle regime is entered, at ~$\pu{ 0.1 \mu m}$, which corresponds to ~$\pu{10^8 atoms/particle}$ or so, well short of infinity, but converging to that limit (presumably heading closer to infinite atomicity will bring you into the regime where gravitational forces become very important, but I am guessing your teacher did not mean this).

But to answer your question, I found the wikipedia useful. On network solids, it states that

In a network solid there are no individual molecules, and the entire crystal or amorphous solid may be considered a macromolecule.

On atomicity it provides the following comment:

All metals and some other elements, such as carbon, do not have a simple structure but consist of a very large and indefinite number of atoms bonded together. Their atomicity cannot be determined and is usually considered as 1.

  • $\begingroup$ Is it true that there are $\pu{10^8 atoms}$ in $0.1\mu m$? I think the diameter of a single atom is about $1\mu m$. Or am I missing something? $\endgroup$ – Learning Mathematics Oct 12 '19 at 3:57
  • $\begingroup$ You can calculate the number of atoms in a sphere 0.1 microns in diameter, starting from the density of a solid, say gold. $\endgroup$ – Buck Thorn Oct 12 '19 at 7:50
  • $\begingroup$ @LearningMathematics You are missing a factor of at least 1,000 (or even 10,000) in your measurement of atomic size. Atomic radii are usually fractions of 1nm. $\endgroup$ – matt_black Oct 13 '19 at 12:48

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