Differentiation played a critical role in the formation of the solid Earth by separating the planet's materials into layers based on their density. Here's how differentiation contributed to the formation of a solid Earth:

1. Formation of the Core: Earth's early stage was completely or largely molten. As the planet's interior began to cool, heavier elements like iron and nickel sank towards the center due to their higher density. This gravitational settling led to the formation of the Earth's metallic core.

2. Crust Formation: Lighter elements like silicon and oxygen, along with other rock-forming elements, remained towards the outer layers of the Earth. These elements combined to form silicate minerals that solidified into the solid outer layer of the Earth, known as the crust.

3. Mantle and Lithosphere: Beneath the crust, the remaining silicate materials formed the mantle. The mantle is mostly solid but can undergo slow plastic deformation over long periods due to heat and pressure from within the Earth. The rigid outermost part of the mantle, along with the crust, constitutes the lithosphere, which is the solid, stable outer layer of the Earth.

4. Density-Driven Convection: As the Earth continued to cool, differentiation led to density differences within the mantle. The hotter and less dense mantle material near the core rose towards the surface due to convection currents. Meanwhile, the cooler and denser mantle material sank back down. This process of convection helped distribute heat within the Earth and further solidify the mantle and crust.

5. Plate Tectonics: The solid and rigid lithosphere, resulting from differentiation and cooling, became divided into tectonic plates. The movement and interactions of tectonic plates through plate tectonics shape the Earth's surface features like mountain belts, ocean basins, and volcanoes.

In summary, differentiation acted as a fundamental process in the formation of the solid Earth. It led to the separation of Earth's materials according to their density, resulting in the formation of the core, mantle, crust, and lithosphere. Differentiation drove convection currents within the Earth, influenced the distribution of heat, and set the stage for plate tectonics, which continues to shape the Earth's surface today.