How deep (kilometers) would an oceanic trench on planet Earth have to be in order for the water to become a solid because of the pressure from the water column? For simplicity, maybe assume chemically pure water, and a constant temperature of 300 kelvin of the entire body of water. An answer with realistic amounts of salt and with temperatures at each depth corresponding to the ambient lithospheric temperature would be welcome too, of course.
It can be assumed that the trench is so narrow that the change in global sea level is negligible.
I considered asking the same question for an air-filled well, in contact with the atmosphere, but I realized that the critical temperature for air is only 133 kelvin, so there would be no depth at which a phase transition would occur.