Solidification

• Solid


  State of matter characterized by resistance to deformation and changes of volume, with high values of Young's modulus and shear modulus
• Solid (microscopic scale)


  • Atoms/molecules are packed closely together
  • Constituent elements have fixed positions relative to each other
• Crystal structure


  Unique arrangement of atoms in a crystal, composed of a unit cell that is periodically repeated in 3 dimensions
• Lattice parameters


  Spacing between unit cells in various directions
• Amorphous solid


  Solid with no long-range order of atomic positions
• Liquid


  Fluid state of matter with loose particles that can freely form a distinct surface
• Solidification of metals


  1. Nucleation: Formation of stable nuclei

  2. Growth of nuclei: Formation of grain structure
• Nucleation


  • Two main mechanisms: Homogenous and heterogeneous
• Homogenous nucleation


  Metal itself provides atoms to form nuclei when significantly undercooled
• Embryo


  Cluster of atoms below critical size
• Nucleus


  Cluster of atoms greater than critical size
• Volume free energy (ΔGv)


  Energy released by liquid to solid transformation
• Surface energy (ΔGs)


  Energy required to form new solid surface
• As undercooling (ΔT) increases


  Critical nucleus size decreases
• Heterogeneous nucleation


  Nucleation occurs on surfaces of structural materials like insoluble impurities
• Nucleating agents


  Lower the free energy required to form stable nucleus and critical size
• Growth of crystals and formation of grain structure

  1. Nuclei grow into crystals in different orientations

  2. Crystal boundaries form when crystals join at complete solidification
• Homogenous nucleation


  First and simplest case, where the metal itself will provide atoms to form nuclei
• Embryo


  Cluster of atoms below critical size
• Nucleus


  Cluster of atoms that are greater than critical size
• Formation of stable nuclei

  1. Homogenous nucleation

  2. Heterogeneous nucleation
• Homogenous nucleation


  • Metal, when significantly undercooled, has several slow moving atoms which bond each other to form nuclei
• Volume free energy (ΔGv)


  Released by liquid to solid transformation
• Surface energy (ΔGs)


  Required to form new solid surface
• Critical radius (r*)


  When r=r*, d(ΔGT)/dr = 0
• As undercooling (ΔT) increases


  Critical nucleus size decreases
• Undercooling (ΔT)


  Difference between the equilibrium freezing temperature and the actual temperature of the liquid

  
• As the extent of undercooling increases, the thermodynamic driving force for the formation of a solid phase from the liquid overtakes the resistance to create a solid-liquid interface