The steel products we encounter everyday are polycrystalline materials consisting of many grains of steel. Iron atoms arrange themselves regularly in one crystal, and the direction of the arrangement of atoms differs among grains. The diameter of an iron atom is 0.25 nanometers, while that of a grain is usually 10 to 20m. Iron atoms arrange themselves in one of two stable crystal structures called the body-centered cubic structure and the face-centered cubic structure. The body-centered cubic structure of iron, which is called ferrite, is stable at (i) a temperature of 1,665K (1,392) or above and (ii) at 1,184K (911) or below, the crystal forms being referred to as iron and a iron, respectively. The face-centered cubic structure, which is called austenite, is stable in a temperature range everywhere between the above-mentioned two temperature ranges, and the iron of this structure in this temperature range is called iron. The phenomenon by which a crystal structure changes to another due to a change in temperature is referred to as a phase transformation. The temperature at which this phenomenon occurs is called the transformation temperature. The transformation temperature depends upon both the nature and the amount of the alloying elements. There are portions in actual grains where the regularity of the positions of the iron atoms is lost, these portions being called lattice defects. Particularly important lattice defects are (i) "vacancies", which are point-like defects in which an iron atom is missing at a lattice point, and (ii) "dislocations", which are linear defects. Vacancies play an important role in the diffusion of atoms, and plastic deformation occurs when dislocations move. Foreign atoms, with a size different from that of iron atoms, are present in a steel grain. These atoms exist in two different forms, i.e., as a "solid solution", in which they are present in the lattice structure of iron as shown in the figure, and as a "precipitate", in which they form another crystal structure and are present within the grain or at the grain boundaries. Solid solutions are divided into interstitial solid solutions and substitutional solid solutions. In the former type, carbon, nitrogen, and other atoms much smaller than iron atoms are located in the space between iron atoms. In the latter type, atoms larger in size (aluminum, titanium), atoms that have almost the same size (nickel, chromium), or atoms smaller in size (silicon, phosphorous) than iron atoms, take the place of some of the iron atoms. A polycrystal is composed of many grains with different orientations. Although a polycrystal usually has no orientation as a whole, it can assume a texture that has many grains with specific orientations under some working and heat-treatment conditions. A grain boundary has excess energy; therefore, when it becomes possible for atoms to move, a change occurs in such a manner that the area of the grain boundary decreases; that is, grain growth occurs. The smaller the grain size, the higher the strength and toughness. In other words, the smaller, the grain size, the better. It is therefore necessary to reduce the size of grains. Grains can be newly generated by the two mechanisms of transformation and recrystallization. Transformation was discussed above. Recrystallization is the phenomenon in which, when a material is heated after being worked beyond its critical strain, the strain energy accumulated by working is released by diffusion which rearranges the position of the atoms, and new grains are formed. Thus, grain refinement is achieved by utilizing these mechanisms.