It’s because of the immense pressure. The core has two layers, the Outer Core which is liquid, and the Inner Core, which is solid.
Whether materials are liquid, solid or gas depends on temperature and pressure. Things solidify if they’re cool enough, but also if you compress them enough (with some specific exceptions, like water).
Right now the solid inner core is growing at the expense of the liquid outer core, because it’s cooling down AND under enough pressure to drive it that way.
As for the superionic thing, I’m not entirely sure, but a quick read says it has something to do with hydrogen diffused in iron under the conditions of the inner core causing the iron-hydrogen alloy to get liquid-like properties, meaning that a part of the inner core that should be solid behaves like a liquid instead, and interacts with the earth’s magnetic field.
Iron and nickel would be liquid at that temperatures *in atmospheric pressure*, i.e. if it was on the surface of the Earth.
However, with thousands of kilometres of rock (some of it molten) on top of it, it is under a lot of pressure, and under these circumstances the same materials are not liquid any more.
The inner core of the Earth is under extreme pressure from gravity pulling together the material. In fact, the pressure at the core is around 3.6 million times the pressure we experience from the atmosphere at sea level.
As the pressure increases, so do the melting and boiling points of materials. It turns out that iron melts at about 7600k or 13000f at that high of a pressure. You can see this in usage when using a pressure cooker or pressure canning, where the increased pressure raises the boiling point of water, allowing the food to get to a higher temperature.
Similarly, reducing the pressure reduces the meting and boiling point. This is why cooking times increase at high elevation: water boils at a lower temperature, slowing cooking. If you went up to 63,000 feet or 19,000 meters, you’d find water boiling off your tongue – at those elevations, the pressure is low enough that water boils below human body temperature*.
* You’d also have to bring oxygen with you, given that you’d be way above the zone where there is enough oxygen to breathe.
The short answer is “pressure”, and the long answer is “there’s literally nowhere for the freedom of flow that characterizes fluids to manifest”. You have all of these hot atoms, and hot atoms really, really want to get moving and do dynamic things, but you’re squeezing them so hard that they can’t move, despite their best efforts. And when atoms can’t really flow past each other, we call that a solid.
Substances under pressure can stay a solid at higher temperature. For example, look at this phase diagram for water and see that it is possible for water to stay frozen as ice at 100 degrees C (and higher) if the pressure is very high.
https://commons.wikimedia.org/wiki/File:Phase_diagram_of_water_simplified.svg
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