Unit Cells of Crystal Lattices
Liquid metals nucleate crystals on cooling (Fig 11-1). The atoms joining the crystals form a packing arrangement in space that is characteristic of that metal or alloy at equilibrium. The smallest division of the crystalline metal that defines the unique packing is called the unit cell. When the unit cell is repeated in space, the repeating atomic positions form the crystal lattice structure of a crystalline solid (Fig 11-2). The atoms at the corners of the unit cell are shared among the adjacent eight-unit cells, as shown for the body-centered unit cell. Therefore, one-eighth of the corner atom is associated with the cell; there are eight corner atoms, so they each contribute one atom to the unit cell. The body-centered atom is totally inside the unit cell and is not shared, so it contributes the second atom to the unit cell mass. Using the lattice parameters to calculate the volume of the cubic cell, the density of the metal can be calculated by dividing the mass of atoms in the unit cell by its volume. The lattice parameters for metals and alloys range between 2 Å and 10 Å for the different unit cells formed.
It has been observed that the position of the neighboring atoms surrounding every atom of a crystal lattice is identical in a pure crystalline metal. When the property of identical periodic points in space was explored mathematically, it was discovered that there are 14 ways to arrange points in space, called space lattices (Fig 11-3). A pure metal crystal lattice is similar to one of the space lattices except that each mathematic point is the site of an atom. Complex crystal lattices like amalgam alloy and enamel have the points of their space lattices replaced by the different atoms of the material or by groups of atoms. The unit cell of each crystalline material, no matter how complex, corresponds with one of these 14 space lattice unit cells (see Table 11-1).
Nucleation and Polycrystalline Grain Structure
As the melt of metal is cooled, clusters of atoms come together from the liquid to form solid crystal nuclei. These nuclei will be stable and grow into crystallites or grains if the energy of the system is favorable, ie, lowered by the process. The energy is lowered by an atom bonding to the solid nuclei, thereby giving up its liquid-state kinetic energy of motion. However, when an atom bonds to the nuclei, the energy can also be raised by the creation of more interfacial surface energy as a result of the increased surface area of the nuclei in contact with the liquid. The energy of the system is favorable for stable nuclei and growth when more energy is lost by bonding than is gained by increasing the interfacial surface area.
Nucleation can occur by two processes. The first, called homogeneous nucleation, is enhanced by rapid cooling, or supercooling, of the nuclei. The result is that more energy is lost when an atom of the liquid bonds to the solid. With rapid cooling (quenching in water), more nuclei are formed per unit volume. These nuclei grow together to form the irregular polycrystalline grains or crystallites that fit together like a three-dimensional puzzle to form the bulk of the metal shape (Figs 11-4 and 11-5). The more nuclei that are formed by rapid cooling, the smaller the grain size or crystallite dimensions. Another means of decreasing the grain size (grain refining) is by adding to the melt a foreign solid particle or surface to which the atoms are attracted, such as a very fine high-melting metal or oxide powder. This process of seeding the nuclei is called heterogeneous nucleation.
Grain size and properties
Decreasing the grain size can have a number of beneficial effects on the cast alloy structure of a crown or removable partial denture. The finer grain size can raise the yield stress, increase the ductility (percent elongation), and raise the ultimate strength. The change in these properties according to changes in grain size is related to the processes of plastic deformation and fracture and how the boundaries between grains relate to these processes. The size of metal grains in different metals may range from less than 1,000 Å to more than 1 cm. Grains contain large numbers of unit cells—even grains that are only 1,000 Å across. The lattices of the grains are formed in random directions when they grow from the melt. A boundary is formed where the grains grow into contact, because the atoms in one grain’s crystal lattice are not in position to mesh with the repeating atoms in the crystal lattices of adjacent grains. These grain boundaries are several atom layers thick that are distorted from normal atomic positions to bridge the mismatch in the lattice orientations of adjacent grains.
Only metals with simple body-centered or face-centered cubic unit cells have enough densely packed planes of atoms in their lattices to allow plastic deformation at yield stress. These lattice types permit shearing of the densely packed planes of atoms like cards of a microscopic deck sliding over each other. However, the lattice of adjacent grain can be viewed as a second microscopic card deck at a different angle. To get the metal to deform, it is necessary to force the cards of one deck into other decks at an angle. But the more grains per unit volume, the more difficult it is to get the planes (cards) to slide because the dislocated slipping planes run against the grain boundaries sooner. Thus, a greater resistance to slippage is created by more grain boundaries, and higher yield stress results.
On the other hand, a material will fracture because a crack opens up on a grain boundary. This situation is more likely to occur in large-grain metals, when the planes cannot be slipped into the adjacent grains. Many smaller grains in various orientations can divide the plastic strain among the grains more easily, with more of them oriented for slipping. Large grains must each accommodate a larger strain and will have fewer planes properly oriented to slip. The result is lower ductility and lower ultimate strength for large-grain metals, which open cracks more readily at grain boundaries because the plastic deformation cannot be accommodated. For these reasons, grain-refined or micrograin alloys produced by heterogeneous nucleation are advantageous for developing fixed partial denture alloys with higher yield stress, better ductility, and improved ultimate strength.
Most pure metals are miscible when melted together. When two metals form a solution in the liquid state so their atoms mix randomly on the atomic scale, they are said to form an alloy. As the alloy liquid freezes, the atoms may remain randomly distributed on the unit-cell lattice sites in each crystal grain. This random distribution in the solid alloy is called a solid solution