challenges associated with more traditional melting point measurements made at very high temperatures, such as sample vaporization and reaction with the container. Thermodynamics For a solid to melt, heat is required to raise its temperature to the melting point. However, further heat needs to be supplied for the melting to take place: this is called the heat of fusion, and is an example of latent heat. From a thermodynamics point of view, at the melting point the change in Gibbs free energy (ΔG) of the material is zero, but the enthalpy (H) and the entropy (S) of the material are increasing (ΔH, ΔS > 0). Melting phenomenon happens when the Gibbs free energy of the liquid becomes lower than the solid for that material. At various pressures this happens at a specific temperature. It can also be shown that: Here T, ΔS and ΔH are respectively the temperature at the melting point, change of entropy of melting and the change of enthalpy of melting. The melting point is sensitive to extremely large changes in pressure, but generally this sensitivity is orders of magnitude less than that for the boiling point, because the solid-liquid transition represents only a small change in volume. If, as observed in most cases, a substance is more dense in the solid than in the liquid state, the melting point will increase with increases in pressure. Otherwise the reverse behavior occurs. Notably, this is the case of water, as illustrated graphically to the right, but also of Si, Ge, Ga, Bi. With extremely large changes in pressure, substantial changes to the melting point are observed. For example, the melting point of silicon at ambient pressure (0.1 MPa) is 1415 °C, but at pressures in excess of 10 GPa it decreases to 1000 °C. Melting points are often used to characterize organic and inorganic compounds and to ascertain their purity. The melting point of a pure substance is always higher and has a smaller range than the melting point of an impure substance or, more generally, of mixtures. The higher the quantity of other components, the lower the melting point and the broader will be the melting point range, often referred to as the "pasty range". The temperature at which melting begins for a mixture is known as the solidus while the temperature where melting is complete is called the liquidus. Eutectics are special types of mixtures that