Correct spelling, explanation: there is a Latin-origin suffix -cle which gives the noun meaning to a word. Here, the correct form particle is this suffix with the word part. Pronunciation may mislead to spelling partical, however, it is incorrect.

Definition of particle:
noun, a very small piece, fragment; usually used to describe elements of matter in physics or chemistry
He is a liar! There is no particle of truth in what he is saying.
Particle is a general term and it may concern, for example, atoms.

Incorrect spelling, explanation: partical is a misspelling, because the correct word, particle, uses the Latin suffix -cle. Pronunciation is probably the cause for this mistake, but particle is the only correct form.