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Should I replace 'breaking' with 'decomposing'? 'Heavy fractions' or 'heavier fractions' - which is correct? Can you check the rest of the sentence?Thank you.

This is achieved by cracking-processes of the atmospheric residue and heavy vacuum residue, in which the temperature, pressure and catalysts lead to breaking of big molecules (heavier/heavy fractions) into (lighter/light fractions).
Comments  
I wouldn't substitute the word 'decomposing' for 'breaking', it is fine. However if you use 'breaking down' it gives a more apt description of what is happening in the process.

In the refinery process stream there is a 'fractionating tower' which 'breaks' the heavier fractions into lighter 'fractions'. So the word 'breaking' is very appropriate in this context.

So for your example I would word it this way.....

This is achieved by introducing the atmospheric residue and heavy vacuum residues to a cracking process. In this stage of the process the temperature, pressure and catalysts applied on the heavier fractions lead to the breaking down of the larger molecules into lighter fractions.
Thank you Squeaky.