The melting temperature of a bulk material is independent of its size. However, when the dimensions of a material decrease towards the atomic scale, the melting temperature changes with the dimensions of the material. The decrease in melting temperature can be of the order of ten to several hundred degrees for nanoscale metals.     The model calculates the fusion conditions based on two competing order parameters using Landau potentials. One order parameter represents a solid nanoparticle, while the other represents the liquid phase. Each of the order parameters is a function of the radius of the particles. When using a nucleus-shell configuration, the lowering of the melting point of the nanoparticles is dominated by the two outermost atomic layers, but the atoms inside the nucleus remain their mass. Melting points are often used to characterize organic and inorganic crystalline compounds and determine their purity. Pure substances melt at an acute, precisely defined temperature (very small temperature range of 0.5 to 1°C), while impure and contaminated substances usually have a large melting range. The temperature at which all the material of a contaminated substance is melted is usually lower than that of a pure substance.
This behaviour is called melting point lowering and can be used to obtain qualitative information about the purity of a substance. The melting point is a characteristic property of solid crystalline substances. This is the temperature at which the solid phase turns into the liquid phase. This phenomenon occurs when the substance is heated. During the melting process, all the energy supplied to the substance is consumed as melting heat and the temperature remains constant (see diagram below). During the phase transition, the two physical phases of the material coexist. The liquid nucleation and growth (LNG) model treats nanoparticle fusion as a surface-initiated process.  The surface initially melts and the liquid-solid interface moves rapidly through the entire nanoparticle. LNG defines fusion conditions through Gibbs-Duhem relationships, resulting in a fusion temperature function that depends on the interfacial energies between the solid and liquid phases, the volumes and surfaces of each phase, and the size of the nanoparticle.
Model calculations show that the liquid phase forms at lower temperatures for smaller nanoparticles. Once the liquid phase is formed, the free energy conditions change rapidly, favoring fusion. Equation 6 gives the fusion conditions of a spherical nanoparticle according to the LNG model.  A melting point is a characteristic physical property of a substance. Therefore, melting point analysis is one of the simplest and most useful techniques for identifying a chemical. Melting point determination begins at a preset temperature close to the predicted melting point. Up to the starting temperature, the heating medium is quickly preheated. At the starting temperature, the capillaries are inserted into the oven and the temperature begins to rise with the set heating ramp speed. Common formula for calculating the starting temperature: Starting temperature = expected MP – (5 min * heating rate) Melting point determination begins at a preset temperature close to the expected melting point. The solid red line represents the temperature of the sample (see figure below). At the beginning of the melting process, the temperature of the sample and that of the furnace are identical; The oven and sample temperatures are thermally balanced beforehand. The temperature of the sample increases in proportion to the temperature of the oven.
We must bear in mind that the temperature of the sample increases with a short delay caused by the time it takes to transfer heat from the furnace to the sample. During heating, the oven temperature is always higher than the sample temperature. At some point, the heat of the oven melts the sample in the capillary. The temperature of the sample remains constant until the entire sample is melted. We identify different temperature values of the TA and TC furnace, which are defined by the respective steps of the melting process: collapse point and clear point. The temperature of the sample in the capillary increases significantly once the sample is completely melted. It rises parallel to the temperature of the furnace and has a delay similar to that of the beginning. Due to the dependence on the rate of heat gain, melting point measurements are only comparable if they are made at the same speeds.
Melting point lowering is the phenomenon of reducing the melting point of a contaminated and impure material compared to pure material. The reason for this is that impurities weaken the strengths of the lattice in a solid crystalline sample. In summary, less energy is needed to break the forces of attraction and destroy the crystal structure. Melting point measurement is usually carried out in thin glass capillary tubes with an internal diameter of 1 mm and a wall thickness of 0.1 to 0.2 mm. A finely ground sample is placed in the capillary tube up to a level of 2 to 3 mm and placed in a heated carrier (liquid bath or metal block) in the immediate vicinity of a high-precision thermometer. The temperature in the heating bracket is increased to a fixed rate programmable by the user. The melting process is visually inspected to determine the melting point of the sample. Advanced instruments such as METTLER TOLEDO`s Melting Point Excellence instruments enable automated melting point and melting zone detection and visual inspection by video camera. The hair method is required in many local pharmacopoeias as a standard technique for melting point determination. Proper sample preparation is crucial for highly accurate melting point measurements. The shape of nanoparticles affects the melting point of a nanoparticle. Facets, edges, and deviations from a perfect sphere change the extent of the melting point lowering. These shape changes affect the surface-to-volume ratio, affecting the cohesive energetic and thermal properties of a nanostructure. Equation 7 gives a shape-corrected general formula for the theoretical melting point of a nanoparticle based on its size and shape.  In general, the smaller the melting temperature range, the higher the purity of the sample.