Good question! Various lines of evidence (mostly from the seismic waves generated by earthquakes) suggest that the inner core of the Earth is solid. The inner core must also be very hot, as it is “insulated” by the outer core and the mantle that surround it (the outermost layer is the crust, but it’s so think compared to the other layers that it probably doesn’t insulate much). If it’s so hot, then why is it solid? Basically, the pressure is so high that the iron and nickel (and other elements) in the core cannot melt. Generally, increasing pressure increases the melting temperature of a solid “phase” (this is not always true). The pressure at the boundary of the inner core is approximately 330 gigapascals (GPa; Alfè et al., 1999). That’s about 3.3 million times the pressure of the atmosphere at sea level! Under these extremely high-pressure conditions, the core is stable as a solid phase.

A little more detail, if you want it: Chemical components can exist as different physical “phases”. A familiar example is water (H₂O), which can exists as a solid (ice), liquid (water), or vapor (steam) at or near the surface of the Earth. Ice, liquid water, and water vapor are three different “phases” of the same chemical “component”. The field of science that describes or predicts whether a material of a certain composition will be solid, liquid, or vapor is known as thermodynamics. A common tool used in thermodynamics (and geology) is called a pressure-temperature phase diagram, which shows the “phase” that is predicted to be stable at different pressure and temperature conditions.

People have calculated what a phase diagram would look like for iron (which make up most of the core, along with nickel and maybe also carbon) at very high pressures and temperatures. The figure that I have included shows of these phase diagrams calculated by Alfè et al. (1999) based on thermodynamic properties of iron. The curve on the diagram represents the melting curve, where iron should melt (with increasing temperature) or solidify (with decreasing temperature). Notice that at a given temperature (a vertical line on the diagram), a solid phase of iron is stable at high pressures. At 330 Gpa (the pressure at the inner core boundary), the solid iron phase is stable, so the temperature must be to the left of the curve. Keep in mind that we can’t do experiments at such high pressures and temperatures, so it’s hard to determine exactly where this line should be! There’s still a lot that we don’t know about the core of the Earth! Maybe you can help with some of the unanswered questions some day! reference Alfè, D., Gillan, M.J., and Price, G.D. (1999). The melting curve of iron at the pressures of the Earth’s core from ab initio calculations. Letters to Nature, 401, pp. 462–464.

The state of material (solid, liquid, gas, plasma) depends on two factors: temperature and pressure. Although the temperature at the center of the Earth is hot enough to turn rock into vapor or even plasma on the surface, the pressure is high enough to keep it solid despite the heat.

Your question used to confuse me as well. The answer lies on two factors: temperature and pressure.

You are correct that as we go deeper into the earth, the hotter it becomes. Intuitively, that should mean that everything would be melted by the time we reach the inner core. But we also know that pressure increases with depth. At some point the pressure effect 'overrides' the temperature effect. Really high pressure can keep rocks together, therefore keeping them solid. This is what happens in the inner core. It was weird to me when I first learned about this, but it explains why the inner core stays solid despite the high temperature.

I hope I answered your question. Good luck with your studies!

This is a great question! Indeed, the center of the earth is subject to very high temperatures, but it is also subject to very high pressures. In general, materials existing at higher pressures require higher temperatures to melt them! You can see this if you look at a Pressure/Temperature phase diagram for some chemical (e.g. carbon, which comprises graphene and diamonds!). Look for the solid-liquid coexistence curve (the line that separates the solid phase from the liquid phase). If we want to melt a solid, we have to cross that line, but at higher pressures, we would need higher temperatures to melt the solid phase into a liquid one.