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The phrase "break down of" is correct and usable in written English.
It is usually used to describe the separation or division of something into smaller parts or components. For example: "The break down of the company's assets was complicated and time consuming."
Exact(39)
General duties include daily cleaning, set up and break down of climbing equipment.
After thermal treatment, dehydration, break down of hemicellulose coupled with elimination of volatile organic compounds results in the disappearance of these absorption bands (Fig. 1a).
This phenomenon could be attributed to break down of glucan, a polysaccharide made of several glucose sub-units to release glucose.
To evaluate the break down of the cartilage, the concentration of proteoglycan of the joints was evaluated.
The diagram below shows the break down of the microcontroller signals to each driver circuit.
Later both sides blamed each other for the break down of the African Union talks.
Similar(21)
Break-down of the silicide network during rolling led to an improved ductility at 20°C.
The story is a minute-by-minute break-down of her match with Talbott.
(Click here to read Ian Burrell's break-down of Ofcom's plans for machine-to-machine communications).
Nitric oxide (NO) derived from iNOS then prevents a break-down of the BBB and non-regulated passage of cells.
In addition, the break-down of biocides can result in metabolites with greater toxicity and longevity than the parent compound.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com