phase transition - What happens to water level when ice XII melts?

There exists this famous idea that if all floating icebergs melt, water level will stay the same (because the water replaced by ice is the volume of the melted ice). Now,

1. Is this always so, if you allow more exotic forms of ice (take e.g. ice XII with density 1.29) ?


2. Is this always so on/in earth ?

EDIT:

I was looking a possibility that you would have water as a liquid that contains pieces of water as a solid. No land is assumed to exist here. "Ice" is always floating or sunken(if possible).

To reformulate, can Ice be sunken in water in any circumstance (pressure, temperature)?

EDIT 2:

Wikipedia: "Ice VII has a density of about 1.65 g cm-3 (at 2.5 GPa and 25°C)".

And water as an incompressible liquid has a density of 1 g cm-3. This means that ice VII is at the bottom of the "lake" and will expand when it melts. Is this true? And are there environments in earth where this (or similar) can happen?

Answer

It's certainly possible for ice to sink in water under the right conditions. The diagram this section of Wikipedia's ice page will show you the conditions under which the various types of ice can form. Most of the "exotic" ones such as XII will form only at pressures greater than around 200MPa. These high-pressure forms are all denser than water, so they would sink to the bottom. This means that they would displace less liquid than their weight, so melting them would result in an increase of the surface level.

Earth's oceans aren't deep enough for these types of ice to form. The pressure at the bottom of the Mariana trench is about 100MPa. Since pressure increases linearly with depth, the oceans would need to be around twice as deep in order for this to happen.

However, there is a solid form of water that does sink in Earth's oceans. This is methane clathrate, which is a crystalline solid consisting of methane molecules surrounded by water ones. It can form at pressures found in the ocean, and there's rather a lot of it in sediments below the sea floor. Although methane clathrates are denser than water, I don't know what the effect on the sea level would be if they melted. This is because when it melts the methane is released as gas and bubbles to the surface, and I don't know whether the volume increase due to the melting is bigger or smaller than the volume decrease due to the methane escaping into the atmosphere. (If large quantities of clathrate did melt then the direct effect on sea level would be the least of our worries, because methane is a very powerful greenhouse gas and there's an awful lot more of it locked up in clathrates than we currently release industrially. This could actually happen.)