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It is common to find accounts of Democritus explaining his thought experiment to demonstrate the existence of atoms by taking a piece of rock/shell/cheese, and breaking it in smaller and smaller bits until no more division is possible. I recall the cheese version, and searching recently, found many instances of the shell version.
What is the main source of the story?
Our main reference on Democritus is Diogenes Laërtius, and I could not find the story there.
It would be nice if people stopped ascribing to the source what they think is a neat illustration of the source's idea, especially when it does not really make sense. Not much cogent on Democritus's natural philosophy survives, and what there is is in retellings of Aristotle, Diogenes Laertius and Simplicius. Neither of them tells anything close to the shell story. The obvious flavor borrowed from Zeno's Dichotomy (in some narrations the shell is first split in half, then a half is itself split in half, and so on) suggests how it might have been invented.
The more cautious academic accounts forego the shell and simply state that Leucippus and Democritus developed atomism in response to Zeno's (and Parmenides's) arguments. Even that is somewhat controversial, but most modern scholars accept it (see SEP, Atomism before Leucippus?) based on Aristotle's passages in De Generatione et Corruptione I, 8 and in Physics A3, 187, a1-3, see English translation. The rest is an interpolation with a rock/shell/cheese "experiment" added for vividness and "scientificity". Perhaps, following the lead of Lucretius, who already popularized arguments for atomism for the general audience in De Rerum Natura, but more competently.
The relevant passages are discussed in detail in Furley's Two Studies in the Greek Atomists, chapter 6. The closest Aristotle comes to linking atomists to Dichotomy is a passage from Physics:
"Some gave in to both of these [sc. Eleatic] arguments - to the argument that all is one if "what is" means one, by saying that not-being exists, and to the argument from Dichotomy, by positing atomic magnitudes." [Furley's translation]
Alas, ancient commentators of this passage thought that "some" refers to Plato and Xenocrates, so even this is controversial. And if Leucippus or Democritus sought to answer Zeno the "experiment" with "indivisible" shell powder is just silly, Zeno's argument does not depend on how far things can be physically split, as Furley himself remarks.
In De Generatione et Corruptione Democritus is at least mentioned by name around an argument "which appears to prove that there are indivisible magnitudes". The argument is theoretical and involves potentially (i.e. conceptually, not physically) dividing "a stick or something else... at whatever point", which makes more sense, see Aristotle's Diagnosis of Atomism by Hasper for another reconstruction. Although this is the closest we have to "Democritus's exposition", the prominence of Aristotle's own potentiality in it makes some scholars dispute even this attribution. Here is Aristotle's summary of the conclusion:
"Neither, then, may one dividing in successive stages bring about an infinite process of breaking, nor is it possible for the magnitudes to be divided at every point (κατά πάν σημεϊον) at the same time (for it is not possible), but [only] up to a limit (άλλα μέχρι του). It is necessary, therefore, that there are invisible atomic magnitudes in it." [Hasper's translation]
Although Zeno is not mentioned, Luria observed that the argument Aristotle retells seems to parallel one of his lesser known arguments reported by Simplicius. As for Lucretius, he does talk of physical splitting in De Rerum Natura I.746-752. But there is still no shell, and he does not suggest that the powder particles we see are the atoms. Even his is not an "experiment" but only an analogy:
"Next, because they assume that there is no end to the cutting up of bodies, and that no stop is made in their breaking, and indeed that there is no minimum at all in things; though we see that there exists in everything that last extremity which is seen to be the minimum with respect to our senses, so that you may infer from this that of those things which you cannot see the last extremity is the minimum".
