MANY OF THE USEFUL PROPERTIES of iron and steel depend on the crystal structure of the metal. Heating or cooling it may drastically alter its properties because of subtle changes in the crystal structure. Charles F. Walton, a metallurgist and mechanical engineer in Cleveland, has devised a demonstration of how profoundly common steel, a binary (two-element) alloy, changes with heating. His demonstration is simple to do, but it presents several puzzles, not all of which have been solved in detail.

Walton heats and cools a 60-inch length of piano wire (No. 29 steel wire). He suspends the wire horizontally between two post terminals mounted on wood boxes and attaches it to a Variac, which enables him to send electric current through the wire in controlled amounts. The Variac is turned up quickly to about 55 volts in order to supply about 14 amperes to the wire. (Although the current greatly exceeds the Variac's limit, it is kept on for too short a time to damage the device.)

The wire is heated so much by the current that it expands, sags and soon glows red. When the current is turned off, the redness diminishes and the wire contracts. Here the first puzzle arises. For an instant the wire gets red again and sags once more. Thereafter it resumes cooling. For some reason the cooling wire releases energy in a sudden red wink. What is the source of the energy? Why is it not released continuously in the course of cooling?

The second puzzle has to do with the cooling rate of the wire. Walton reheated the wire, turned off the current and wrapped a wet sponge around a section of the red-hot wire for a few seconds The water rapidly cooled that section, but the rest of the wire took a while longer to cool. The rapidly cooled section was so brittle that it snapped easily between Walton's fingers. The point of the broken piece was hard enough to scratch glass. The slowly cooled part of the wire did not snap easily, and a broken point did not scratch glass. How does rapidly cooling a section alter its ductility and hardness?

The third of Walton's puzzles appears in the magnetic properties of the wire. At room temperature the wire is attracted to a small magnet held nearby. When the wire is red-hot, it shows no discernible response to the magnet. Why should the magnetism of a material depend on its temperature? Indeed, what in the cool wire is responsible for the magnetic attraction?

Walton suggests that anyone setting out to repeat his experiment obtain wire of the same size (.075 inch in diameter). A thinner wire oxidizes so much when it is heated that it will serve for only a few experiments. A thicker wire requires too much current to heat. You must be very careful not to touch the wire while the current is flowing. It is lethal! Always turn off or unplug the Variac before you apply the magnet or the wet sponge.

Walton's puzzles can be solved by beginning with iron, the major constituent of steel. Iron is allotropic, meaning that in the solid state it can exist in several different crystalline forms. A crystal is often described in terms of the arrangement of the smallest possible unit of atoms in it. The rest of the crystal is a series of repetitions of the unit cell. The unit cell of iron at room temperature is arrayed with an atom at the center of -a cube formed by eight other atoms at each corner. The formation is called a body-centered cubic structure. Iron with this array of atoms in its crystals is termed alpha iron or ferrite.

Iron usually consists of many independent, crystal regions called grains. Within each grain the unit cells are uniformly oriented, but the orientation of the grains is random. Grains form when hot iron cools and crystals begin to grow at nucleating sites. The crystals continue growing until eventually they come in contact with one another, forming a matrix of grains.

When iron is heated to a temperature of 910 degrees Celsius, its crystals are transformed from the body-centered cubic structure to the face-centered cubic structure, which is characteristic of gamma iron or austenite. The cubic cell has atoms at the corners and at the centers of the faces. Again there are grains, each grain consisting of a crystal at a certain orientation.

The transformation from alpha iron into gamma iron requires energy to rearrange the atoms into the new structure. Another form of iron, delta iron, appears at a temperature much higher than any in Walton's experiment. If iron is heated even more, it melts.

When alpha iron is heated, each addition of energy at first simply raises the temperature. Once the transition point is reached the temperature must remain constant until enough energy is added to transform all the crystals into gamma iron. Only then can heating again raise the temperature.

The converse is also true. When gamma iron cools, its temperature drops until it reaches the transition point. Then heat must be removed until the crystals have reverted to alpha iron. Only then can the temperature begin to drop again.

The transition point between the alpha and the gamma form of iron is similar to the freezing and melting point of water. When ice is heated, its temperature increases until the melting point is reached. The temperature cannot rise further until the ice is fully melted. When water is cooled, it must remain at 11 the freezing point until it fully freezes. Only then can its temperature decrease.

Walton's piano wire consists primarily of alpha iron. When he sends current through it, the collisions of the electrons of the current with the crystal structure of the wire generate heat. Eventually the wire is transformed to gamma iron. Additional heating makes the wire so hot that it soon radiates in the red part of the visible spectrum.

When the current is turned off, the wire cools, dimming the visible emission. At the transition temperature the rearrangement of the face-centered cubic crystals into body-centered cubic crystals releases energy, which momentarily reheats the wire to the point where it again turns red and sags. The glow is brief because the energy is quickly lost through radiation and by convection in the air. The brief wink of red light in Walton's experiment is the energy released by the transition of gamma iron to alpha iron. It is evidence that the atomic arrangement of one crystal form requires more energy than the atomic arrangement of another form.

To solve another of the puzzles in Walton's experiment one must consider the carbon content of steel. There are of course many alloys of steel, but I refer here only to the binary alloy of iron and carbon. The analysis is aided by a phase diagram of the kind shown in the bottom illustration at the left. The ordinate represents the temperature of the alloy, the abscissa the amount of carbon in the iron.

When steel is liquid, carbon can readily dissolve in the iron. Even when the metal is solid, however, carbon may mix with the iron crystals to form what is called a solid solution. The solubility of carbon in such a solution plays an important role in Walton's experiment.

The second phase diagram [see illustration right] identifies a point where the wire is in the gamma-iron state at a temperature of 1,200 degrees C. and the carbon content is .4 percent, that is, there are four parts of carbon to 1,000 parts of solid solution. The carbon is in solution with the gamma iron in the sense that it is dispersed throughout the crystal structure. The carbon atoms can squeeze into the edges of the unit cells. Since the carbon content is small, only a few of the edges contain carbon.

In the diagram the cooling of this steel is represented by a vertical line extending from the initial point down to a line labeled A₃. That line marks the transition from gamma iron to alpha iron. Until the transition point is reached each removal of energy from the iron reduces the temperature but does not change the crystal structure or the solubility of the carbon in that structure. After A₃ has been reached the next removal of energy forces some of the gamma iron (primarily at the grain boundaries) to switch to alpha iron.

Carbon is almost insoluble in alpha iron (its limit of solubility is only .025 percent), so that the solution of gamma iron and carbon becomes more concentrated. In the phase diagram the cooling path follows A₃ downward to the right as the further formation of alpha iron results in a greater concentration of carbon in the remaining gamma iron. Whereas in pure iron the transition between gamma iron and alpha iron takes place at one temperature, the presence of carbon spreads the transition over a range of temperatures.

Eventually the end of A₃ is reached at a temperature of 723 degrees C. This state, called the eutectoid, marks the highest concentration (.8 percent) possible for carbon in gamma iron. Further removal of energy forces the remaining solution to precipitate alternating layers of alpha iron and clusters of iron carbide (Fe3C), commonly known as cementite. The combination of alpha iron and cementite is called pearlite. Since further cooling does not alter the mixture, the steel at room temperature is pearlite.

Heating the steel reverses the process. The steel is pearlite until the eutectoid is reached. Further heating begins to transform the cementite into a solid solution of gamma iron and carbon. Still more heating begins to change the rest of the alpha iron into gamma iron, decreasing the concentration of carbon in the gamma iron. The path on the phase diagram is upward to the left, along the A₃ line. When no alpha iron remains, the path leaves the line and heads upward parallel to the temperature axis. In this period of heating, the crystal structure and the carbon concentration remain constant.

When steel in the gamma-iron state has a carbon concentration less than the .8 percent characteristic of the eutectoid, the steel is said to be hypoeutectoid. Hypereutectoid steel, which has a carbon concentration greater than .8 percent, cools in much the way I have described it except that initially it precipitates iron carbide instead of alpha iron.

Suppose a steel in the gamma-iron state has 1.2 percent carbon. As the steel cools, the concentration of carbon remains constant until a transition point is reached. In the third phase diagram [see illustration at upper left] the relevant line is labeled A_cm.

If the sample is cooled further, not all the carbon can remain in solution with the gamma iron. The cooling forces some of the carbon (mainly at the gamma-iron grain boundaries) to precipitate as iron carbide. The concentration of carbon decreases. In the phase diagram the coolingpath follows A_cm toward the eutectoid. There additional cooling results in the formation of pearlite. When the steel reaches room temperature, it has a large amount of iron carbide mixed within the pearlite.

Piano wire in the gamma-iron state contains about .8 percent carbon. After the wire has been heated to red heat it cools fast enough to undercool the temperature of the eutectoid to between 550 and 600 degrees C. Then it suddenly transforms from carbon and gamma iron to pearlite by releasing energy. The wire winks red and sags momentarily. Part of the sag results from thermal expansion as the wire is reheated by the crystal transformation. The rest of the sag derives from the expansion entailed in the rearrangement of the atoms to form pearlite.

The solubility of carbon in iron depends primarily on the space available for carbon among the unit cells of the iron. In the body-centered cubic arrangement of alpha iron a carbon atom can lie on an edge of the cubic cell or at a face center. Since the space available at both locations is less than the size of a carbon atom, the atom must force a corner iron atom out of its proper position. In the illustration at the right two possibilities are shown for the position of a carbon atom on an edge. If the atom forces its way between,.iron atoms A and B by moving B, B moves out of its position toward the right. If instead a carbon atom forces its way between atoms B and C, B might be forced upward. In either case the displacement of B greatly distorts the crystal structure. Carbon is essentially insoluble in alpha iron because little space is available and its presence distorts the crystals.

In gamma iron the carbon is limited to the edges of the crystal cell. Although there are fewer nesting places for the carbon than there are in the alpha iron, the spaces on the edges are slightly larger. The presence of the carbon therefore creates less distortion of the crystal than it does in the alpha iron, allowing more carbon to be in solution.

The primary purpose of having carbon in steel is to strengthen the steel. The iron grains almost always contain dislocations that interrupt the regular pattern of ideal crystals and thereby weaken the grains. Carbon strengthens the grains by anchoring the dislocations in place.

A common type of irregularity is an edge dislocation. Consider a uniform cube of alpha iron with each cell inside the cube bonded to adjacent cells. Make an imaginary slice halfway through the block and force the opposite sides of the slice to slide in opposite directions by an amount equal to the width of one crystal cell. The cube then contains a line of atoms out of alignment with the surrounding cells.

Such an edge dislocation weakens the grain. If a shearing stress is now applied in such a way as to slide the blocks of crystals even more, the vertical line of dislocation is easily moved through the crystal. Normally the bonding between atoms in the cells is strong. The misaligned atoms, however, are poorly held and can be moved with even small shearing forces.

When carbon is mixed into hot iron and then precipitated as cementite as the iron cools, it tends to collect in the space provided by the edge dislocations. It anchors the dislocations, thereby diminishing the chance that an applied stress can move them through the crystals and rupture the grains. When Walton heats piano wire and lets it cool by radiation and air convection, the carbon atoms have time to diffuse through the iron and form cementite at the dislocation sites. The wire is then ductile enough to be bent without breaking.

When Walton heats the wire and cools it rapidly with water on a sponge, he blocks the formation of cementite. This quenching process proceeds so fast that the carbon cannot diffuse. Moreover, only part of the gamma iron has time to transform into alpha iron. Although the transformation is initially rapid, it soon slows. Hence the section of wire quenched with water consists of a small amount of alpha iron and a good deal of gamma iron. Nearly all the carbon atoms are frozen in place. The mixture is a supersaturated solution of carbon because the concentration of carbon in the iron is greater than is normally possible at that temperature.

The formation of this new structure, which is called martensite, requires neither diffusion nor nucleation. It is a spontaneous change in the existing crystal structure of the gamma iron with carbon atoms on a few edges. The iron atoms change from a face-centered cubic structure to a body-centered tetragonal structure. The carbon atoms in the gamma iron are not given enough time to diffuse and are trapped at their locations in the unit cells. They force iron atoms out of their usual places in the body-centered tetragonal structure.

This distortion of the crystals creates regions of high stress in the martensite. The distortion is also responsible for the hardness of the martensite because it locks dislocations in place within the grains. That is why the martensite Walton creates by quenching the wire while it is hot is hard enough to scratch glass. It is also brittle because of the numerous sites of high stress in the grains. If the wire is bent, it breaks because of the internal stress.

The carbon in martensite is not permanently trapped, but it diffuses so slowly through the iron crystal that it can be regarded as permanently fixed. If the temperature of the martensite is increased, the rate of diffusion increases, allowing the carbon to collect into tiny amounts of cementite. With enough temperature and time the steel regains more of the properties of pearlite.

The third puzzle raised by Walton's work involves the magnetization of the steel wire. Iron is said to be ferromagnetic. One property of such a material is that it has regions called domains, each domain contributing a magnetic field to its surroundings. The material as a whole may seem to be nonmagnetic because normally the magnetic fields from all the domains cancel.

The domains in piano wire cancel in this way until a magnet is brought close to the wire. The field of the magnet realigns the domains so that they give the wire a net magnetic field. The realignment is primarily due to changes in the size of the domains. Any domain with a magnetic field approximately parallel to the magnet's field grows larger at the expense of adjacent domains that are in other orientations.

The result of the growth of domains is an attraction between the wire and the magnet. When piano wire is at room temperature, the attraction is strong enough to move the wire. At a temperature characteristic of gamma iron the attraction is absent.

When the wire is heated, the increase in temperature leads to greater agitation of the atoms and molecules. The agitation begins to disrupt the organization of the magnetic field of a domain The hotter the substance becomes, the weaker each domain's magnetic field becomes. Eventually the organization of the domains disappears entirely. This event takes place at what is called the Curie temperature after Pierre Curie, who in 1894 found that iron loses its ferromagnetism when it is heated above 768 degrees C.

The ultimate source of the magnetic field in a ferromagnetic substance such as iron is still not understood. Apparently when an iron atom joins a crystal, it partially ionizes (loses one electron or more) as the electrons in its outer orbit become loosely bound because of the proximity of other iron ions. Although the electrons are not entirely free, they are mobile enough to hop between ions.

Every electron has a magnetic field. Although the origin of this field is not understood, the field is as characteristic of an electron as the electric charge is. As the electrons hop between ion sites in an iron crystal they influence one another through what is called an exchange interaction. The individual magnetic fields of the semifree electrons line up in the same direction. An electron with its magnetic field aligned in some other direction would require mare energy. Thus the organization of fields from the electrons in a domain that gives the domain a net magnetic field comes from a minimizing of the energy associated with the exchange interaction.

As the temperature increases, the thermal agitation destroys the cooperative behavior of the electrons until, above the Curie temperature, the domain structure is spoiled. At the Curie temperature the semifree electrons still have individual magnetic fields, but there is no overall organization of fields. If a magnet is brought near iron that is hotter than the Curie temperature, the iron is only weakly attracted to the magnet. The magnetic field of the magnet can orient some of the fields of individual electrons, but the alignment is fleeting because of the thermal agitation.

The loss of magnetism can be followed in a phase diagram. Consider the pearlite of a low-carbon steel. When it is heated to the eutectoid and begins to reform into gamma iron and carbon, the transformed iron loses its ferromagnetism. As the heating path-continues upward along A₃ the remaining alpha iron maintains its magnetism until the material reaches the Curie temperature. Thereafter none of the iron (including the alpha iron) is ferromagnetic.

Much more can be said about the effect of temperature on the crystal structure of steel. By employing etching processes and photographing specimens through a microscope you can study the precipitation of iron carbide from steels. When the steel contains more carbon than the forms I have discussed, new formations appear. I leave their cause and structure for you to look into.

Bibliography

STRUCTURE AND PROPERTIES OF ALLOYS. Robert M. Brick, Robert B. Gordon and Arthur Phillips. McGraw-Hill Book Company, 1965.

MAGNETISM IN SOLIDS. D. H. Martin. The MIT Press, 1967.

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