# The Importance of Imperfections by Manuel de Landa

Following is an interesting article of Manuel de Landa excerpted from a series of "columns" he wrote for Domus Magazine a couple of years ago.

It is entitled The Importance of Imperfections and investigates the minor science of metallurgy (to use Deleuzian terminology) as a celebration of material transformation by its main characters: the blacksmiths.

The Importance of Imperfections

In the ancient craft of metallurgy the distinction between being hard and being tough has long been understood. A blacksmith manufacturing a sword in classical times, for example, knew that the edge and body of the weapon had to have distinct properties. The edge, if it is to stay sharp, must be able to preserve its pointy, triangular shape for as long as possible, that is, it must be hard. But the sword’s body, the part that must perform a load-bearing role, must be tough: rather than trying to hold on to a particular form it must be able to change shape, that is, it must yield without breaking under the blows of another sword. If instead of tough the swords’s body was hard it would be brittle and hence incapable of bearing the loads placed on it during hand to hand combat. A similar point applies to metallic armor: it must yield without breaking under the impact of an arrow or other projectile, and the more it yields, the more it allows the arrow to dent it, the more it robs the arrow of its kinetic energy as the latter exhausts itself trying to penetrate it. Hardness and toughness are distinct but complementary properties in metallurgy.

Ancient blacksmiths also knew the kinds of operations or transformations that human beings can apply to metals in order to get these properties. They knew that cold working a piece of metal, by repeatedly hammering it, for example, would yield a hard edge. They also knew that the brittleness that inevitably accompanies hardness could be eliminated by annealing the metal piece, that is, heating it to a high temperature below its melting point, then allowing it to cool down slowly. Annealing restores the ductility, hence the toughness, of a cold worked piece of metal. Yet, despite this ability to successfully match physical operations to desired metallic properties, the actual microscopic mechanisms unleashed by the operations and responsible for the properties remained a mystery. Today we know the main characters in this hidden drama and they turn out to be imperfections.

A piece of metal is typically crystalline. When molten metal undergoes the critical transition to the solid state, crystallization may begin at several points in the liquid simultaneously, with different crystals growing at different angles from each other. When two such growing crystals eventually meet a boundary forms, a layer that may be more or less deformed depending on how different the angles of growth were to begin with. These are two-dimensional defects, surfaces dividing the piece of metal into separate grains. Within these grains another type of imperfection exists, a one dimensional defect called a “dislocation”. Given that crystals are nothing but geometrically packed atoms, and that we can arrange many of these atoms into mathematically perfect arrays, it is tempting to picture a crystal’s internal structure as consisting of rows of atoms placed precisely on top of one another. But here and there we can fi nd extra rows of atoms that disrupt the perfection of the array, introducing a distortion in neighboring rows.

Moreover, these extra rows can, in a sense, move through the crystal. Because the chemical bonds that join metallic atoms together, when broken by the application of a force, can easily reconstitute themselves, the atoms in an extra row can, one at a time, break and become bonded to those in a neighboring row. These atoms will now become part of a non defective row but will leave behind another defect displaced relative to the first. Although strictly speaking this is a process in which one defect disappears as a new one is born next to it, for all practical purposes it all happens as if the original dislocation had actually moved in position. For this reason dislocations are considered mobile line defects, and they exist in more or less numerous populations in most crystalline materials.

The ductility of metals, their ability to yield without breaking, is mostly derived from the fact that the mobility of dislocations allows entire layers of atoms to slide over one another when subjected to a force. For this effect to happen without the assistance of mobile defects all the bonds in a given layer of atoms would have to break and reconstitute simultaneously, a relatively unlikely event. But with dislocations this process can take place by repeatedly breaking only a few bonds at a time. The existence of populations of mobile defects implies that this ability of atom layers to slide can be present throughout a piece of metal. On the other hand, too many dislocations may have the opposite effect: with less room to maneuver defects start getting into each others way, eventually becoming immobilized, caught in complex tangles. This, in turn, reduces the sliding capacity of the non-defective atom layers. In other words, the metal becomes hard.

Hammering (and other types of cold working) produces large numbers of dislocations with limited mobility, and it is thus the appropriate operation to produce the cutting edge of a weapon or tool. But if the load-bearing body is to remain tough it must be annealed, a process that erases many dislocations allowing the surviving ones to break away from their tangles and recover their mobility. Two-dimensional defects, that is, grain boundaries, may also participate in the generation of ductility. Although the movement of dislocations is constrained by these boundaries, impurities accumulating along surface defects may sometimes act as lubricants allowing grains to slide over one another. The key role played by both one and two dimensional defects in the emergence of large-scale metallic properties is the reason why the practice of metallurgists today is aimed in large part at the control of grain and dislocation structure and distribution. Evidently, the descendants of the ancient blacksmiths have become aware of the importance of imperfections.