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The phrase "state of matter" is correct and usable in written English.
It is typically used in scientific contexts to refer to the distinct forms that different phases of matter take on, such as solid, liquid, gas, and plasma.
Example: "Water can exist in three states of matter: solid (ice), liquid (water), and gas (steam)."
Alternatives: "phase of matter" or "form of matter".
Dictionary
state of matter
noun
Any of the different phases of matter whose properties are dependent on the motions and forces of the molecules of which they are composed
synonyms
Exact(56)
Plasma is the fourth state of matter.
"It shows that there is a new state of matter.
In this new state of matter, all the atoms are in the same coherent quantum state.
"It's a very exotic state of matter, and we actually made it in this furnace.
This ionized gas is in a plasma state, the fourth state of matter.
Liquid crystals, David Dunmur and Tim Sluckin explain, are a fourth state of matter.
A Fourth State of Matter What Are the Colors of Alien Life?
We here at CERN found some evidence of a new state of matter.
Some say it is neither liquid nor solid but another state of matter entirely.
The first Bose-Einstein condensate (BEC), as this new state of matter is called, was created in 1995.
Other current research involves the search for a new state of matter called the quark-gluon plasma.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com