When steel is heat treated, changes occur not only to the crystal structure and grain size but also in the state of the foreign atoms present in the steel. The minimum equilibrium concentration of a foreign atom at which the atom precipitates is defined as solubility limit. The foreign atoms form solid solution when the concentration of the atom is less than the solubility limit, and precipitate as a compound when the solubility limit is exceeded. Solubility limit is determined by the thermodynamic properties of entities which react to each other to form precipitates. When interaction between the entities is affirmative and Gibb's energy of the precipitate formation is negatively large, precipitates are formed even at low concentrations of the entities. The figure shows an iron-carbon phase diagram, which is the most fundamental for steel, showing how the transformation temperature or solubility limit depends upon the carbon content. In the heat treatment of low-carbon steel, the line segment PQ, which represents the solubility limit of carbon in -ferrite, is important. The solubility limit represented by PQ increases as the temperature increases. Therefore, if, on heating, the solubility limit increases and, subsequently, exceeds the carbon concentration of the steel, all the carbides that have been precipitated will decompose and dissolve. Precipitation will occur again when the solubility limit decreases as the steel cools. Equilibrium theories based on thermodynamics deal with the stable crystal structure and the state of foreign atoms. However, structures formed in practice by heat treatment are not determined solely by equilibrium theory. This is illustrated by the fact that the carbon in the steel is precipitated not as graphite (thermodynamically stable phase), but as the metastable cementite phase (Fe3C). For graphite to precipitate, it would be necessary to achieve complete diffusion of the carbon atoms to bring about the change predicted by equilibrium theory. When such diffusion is not achieved, for example in rapid cooling, the change is suspended while in progress. On the other hand, plastic deformation accelerates precipitation by increasing the precipitation sites available and by promoting diffusion. By making use of these phenomena, different structures can be obtained in steel of the same composition by control of the crystal structure and the size and distribution of the precipitated particles. Fine precipitates induce strain in the surrounding crystal lattice of iron, and consequently provide great resistance to dislocation movements and increase the strength, even though they are present in only minute amounts. Hence, elements which cause dissolution and precipitation within the temperature range of heat treatment and hot working are suitable for the formation of fine precipitates. Typical elements like niobium and vanadium result in the formation of carbonitrides. When steels containing these elements are hot rolled, thermo-mechanical control processes are used practically to increase strength by precipitating fine particles and by refining the crystal grains, which is accomplished by controlling the conditions for rolling and cooling. Thus, the structure of such steels can be changed considerably by the heat treatment applied. This makes it possible to produce steel materials with diverse properties, and thus to select the properties suitable for specific applications.