Defects in solids

Type of physical science: Condensed matter physics

Field of study: Solids

Defects in solids control the thermal, electrical, mechanical, plastic, magnetic, and optical properties of the material. The defect interaction, kinetics, and diffusion influence crystal growth.

Overview

Defects in solids can generally be classified as point defects, extended defects, crystal excitations, or transient or incident imperfections.

Point defects are atomistic in nature; the principal types are vacancies (vacant lattice sites), interstitials (extra atoms or ions not in regular lattice positions), and chemical impurities (foreign atoms or ions at substitutional lattice positions or interstitial positions). In addition, electron-level defects resulting from excess electrons or deficient electrons (holes) are related to the color-center and donor or acceptor impurity defects.

Extended defects include linear defects, planar defects, and three-dimensional clusters. Linear defects include dislocation boundaries between slipped and unslipped crystal surface regions, as well as dislocation, vacancy, or interstitial loops. Planar defects may be intrinsic stacking faults, caused by vacancy aggregations; extrinsic stacking faults, caused by interstitial aggregations; crystallographic sheer planes; and Guinier-Preston zones, which are two-dimensional aggregations of impurities and grain boundaries (boundary walls between crystallites having different crystal orientations). Three-dimensional clusters include voids (vacancy clusters) and precipitates (impurity clusters or clusters of alloying atoms).

Crystal excitations are quantized entities. They represent excited states of the entire crystal. They are not localized and are thus imperfections only in the sense that they produce some deviations from perfect symmetry. These entities are phonons, quantized lattice vibrations; magnons, which are quantized spin waves; conduction electrons and holes, which are excited thermally either out of filled bands or out of impurity levels; excitons, which are quantized electron-hole pair excitations; polarons, which are quantized polarization waves; and plasmons, which are quantized plasma waves.

Transient imperfections usually come from sources external to the crystal: energetic charged particles such as electrons, protons, mesons, and ions, or energetic uncharged particles such as neutrons or neutral atoms. Transient imperfections are often the result of experimental tools and techniques; however, photons can be produced internally by electron-hole recombination and other processes, and energetic particles can result naturally as a result of radioactive decay.

Point defects can occur for a number of reasons: thermally, when the material is heated to elevated temperatures; as a result of impurities present in the material; as a result of radiation damage and ion implantation; or with the application of stress. Vacancy defects are further classified as Schottky defects and Frenkel defects, depending on the way they come about: The Schottky defect occurs when an atom or ion is removed from the lattice position completely out of the crystal, thus creating a vacancy. The Frenkel defect is formed when an atom or ion is removed from a lattice position and placed at an interstitial position within the crystal; it is also called a "Frenkel pair," since one vacancy and one corresponding interstitial have been created. In ionic crystals, to keep the charge neutrality of the crystal, the Schottky defect occurs when corresponding cations and anions are missing from their lattice sites, thus creating cation vacancies and anion vacancies in the crystal. Molecular crystals adopt close-packed structures; hence, the volume that is available to accommodate interstitial species is very small. Consequently, the energy required to introduce an interstitial defect is several times greater than that needed to form a vacancy. Hence, the Schottky defect occurs more frequently than the Frenkel defect in molecular crystals, resulting in more vacancy defects than interstitial defects.

In thermal equilibrium, a certain number of vacancies are always present, and their concentration increases as the temperature increases. Vacancies produced as a result of thermal equilibrium processes are called "intrinsic" vacancies; vacancies created by other processes, such as irradiation, deformation, or the addition of impurities, are called athermal (nonequilibrium) or "extrinsic" vacancies. In metals, the concentration of thermal vacancies could be as high as 10^-3 at temperatures close to the melting temperature of the material. In alloys, it may be as high as 0.5 (50 percent) and amorphization may occur where the crystal structure becomes irregular. Such a high concentration of defects may be frozen, or "quenched in," by sudden cooling from elevated temperatures to very low temperatures. The quenching process can be used to prepare amorphous alloys. Another method of preparing amorphous solids is to create highly saturated defect concentrations using high doses of irradiation or ion implantation.

The concentration of nonequilibrium defects in solids can be reduced by annealing the material. Annealing begins with slow heat treatment. There are two annealing processes: isothermal, which fixes the temperature of the material and varies the time of heat treatment; and isochronal, which fixes the time interval for each heat treatment and increases the temperature of the material in steps. After the heat treatment, the samples are cooled very slowly to avoid any quenching effects.

During the annealing process, different types of defects begin migrating at different temperatures and try to leave the material. The migration temperature of a given kind of defect may vary drastically if it is bound or if it interacts with other defects, such as impurities or dislocations. During the migration, mainly in the highly defective solids, defects aggregate to form complexes such as di- and tri-vacancies, and eventually larger complexes such as vacancy loops and three-dimensional clusters such as voids. Similarly, interstitial aggregates form interstitial loops, and impurity aggregates form two-dimensional planar defects called Guinier-Preston zones or three-dimensional clusters called precipitates. Larger clusters become stabilized, and the process of aggregation can in some cases continue to give a superlattice with long-range ordering. In divalently doped alkali halides, for example, this superlattice is called a Suzuki phase.

The second mode of stabilization is the formation of extended planar faults called crystallographic shear planes. During this process, most of the defects are eliminated. The planar faults separate two parts of the crystal. If the fault is caused by the vacancy aggregates, it is called an intrinsic stacking fault; if caused by interstitial aggregation, it is called an extrinsic stacking fault. The internal surfaces of materials are classified as stacking faults, crystallographic shear planes, and grain boundaries. Grain boundaries occur between the crystallites and thus separate regions of the crystal which have different orientations. Impurities and other point defects move from the bulk crystal toward the boundaries; thus, the grain boundaries act as preferential pathways for material transport through solids.

Pure alkali halide crystals are transparent throughout the visible region of the electromagnetic spectrum. They may be colored by the introduction of impurities; by the introduction of excess metal ions by quenching the crystal in alkali metal vapors; by X-ray, gamma-ray, neutron, and electron bombardment; and by electrolysis. A color center is a lattice defect that absorbs visible light. A negative ion vacancy in a perfect periodic ionic crystal lattice has the effect of an isolated positive charge. It attracts and binds an electron. The F-center is the trapped electron center, in which the optical absorption arises from an electric dipole transition to a bound excited state of the center. (The term "F-center" is derived from the German word Farbe, meaning "color.") The energy bands of absorption of these centers are called F-bands and have been identified by electron spin resonances. The F-center may trap another electron, to produce an F'-center, or it may aggregate to F₂-centers and F₃-centers (also called M- and R-centers, respectively). In an F_A-center, one of the nearest neighbors of an F-center has been replaced by a different alkali ion. In alkaline earth oxides, an anion vacancy requires two electrons to produce a neutral defect F-center. An anion vacancy with one trapped electron is called an F⁺-center. Positive holes trapped at cation vacancies are called V-centers. An X₂-center is formed by an X₂-molecular ion (where X is a cation) replacing the two nearest neighbor anions. If an X₂- molecular ion occupies the position of a single anion, it is called an H-center.

Plastic mechanical properties of crystalline solids can be understood in terms of dislocations. Dislocations are linear defects and are present in large numbers, typically 10⁷ cm^-2, even with well-annealed metals. Pure aluminum crystals are elastic (in accordance with Hooke's law) only to a strain of about 10^-5, after which they deform plastically. The experimental values of the elastic limits are much smaller than expected from theory. The movement of dislocations is responsible for slip at very low applied stresses. Although a general dislocation may follow any curved route through a crystal, it is easiest to understand the construction of a dislocation by considering the two simplest types of straight-line dislocations, the edge and screw types. In a pure edge dislocation, one of the planes of atoms terminates, as shown in figure 2a. The last line of atoms in the half plane is the dislocation. The displacement of the lattice or slip distance, called Burger's vector, is perpendicular to the direction of the dislocation. In a screw dislocation, shown in figure 2b, part of the lattice is displaced with respect to the other part, and the displacement (Burger's vector) is parallel to the direction of the dislocation. The boundary between slipped and unslipped parts of the crystal is a screw dislocation.

A dislocation cannot terminate inside a crystal. The dislocation line may, however, be pinned within the crystal--for example, by a large impurity atom--and immobilized. Dislocations multiply during deformation. A common feature of all dislocation sources is the bowing of dislocations. A dislocation segment pinned at each end is called a Frank-Reed source, and it can lead to the generation of a large number of concentric dislocations on a single slip plane. The vacancy type defects associated with dislocations create jogs.

Plastic deformation in crystals occurs as a result of slip or twinning caused by the motion of dislocations. In slip, one part of the crystal slides as a unit across an adjacent part, whereas in twinning, the displacement occurs successively on each of many neighboring crystallographic planes. After twinning, the deformed part of the crystal is a mirror image of the undeformed part. The interaction between dislocations reduces their mobility and improves the mechanical strength of solids. Another important consequence of the interactions of dislocations through their long-range elastic strain fields is the formation of low-angle or tilt boundaries. Annealing at higher temperatures will give rise to recrystallization in which larger grains with large-angle grain boundaries form and subsequently grow.

Another type of disorder, known as antistructure, is characterized by combinations of atoms that are occupying the wrong kind of atomic site in a compound. In a compound AB, if the numbers of A and B atoms are equal, the crystal is said to be stoichiometric. In InSb, antistructure does not violate stoichiometry if the number of In atoms occupying Sb positions is equal to the number of Sb atoms occupying In positions. Antistructure is likely to occur only when the two kinds of atoms are comparable in size.

Applications

Important crystal properties are controlled by defects. The electrical properties of semiconductors and the color or luminescence of many crystals depend on the trace amounts of chemical impurities. Impurity atoms have many consequences for the electrical, optical, magnetic, thermal, and mechanical properties of solids. Plasticity, creep, and atomic diffusion are controlled by defects. Defects in solids not only are crucial in determining the properties of solids but also play a central role in the very existence of the solid state--in the processes of crystal formation, crystal growth, and melting.

In alkali and silver halide crystals, associated pairs of vacancies of opposite sign exhibit an electric dipole moment and contribute to the dielectric constant. Vacancy-type defects in solids increase the heat capacity of the material.

In addition to intrinsic defects, much interest has arisen in a number of polymeric materials that are capable of incorporating impurities that generally alter their electrical properties, including electrical conductivity over twelve orders of magnitude. The impurities are doped electrochemically or by diffusion with both anionic and cationic species. Examples of these conducting polymers are polyacetylene, poly(pyrrole tosylate) and poly(pyrrole fluoride). Thiophenes are even more useful, because they are reasonably good electrical conductors to begin with and are more flexible, mechanically strong, and stable.

Electrical conductivity of some crystals is caused by the motion of ions rather than the motion of electrons. These crystals are called ionic conductors. Specific ionic species with large concentrations of ions have a very high mobility and give rise to high ionic conductivities. Fast ionic conduction often is associated with disorder in crystals that are created thermally or as a result of the presence of large concentrations of impurity ions. The fast ionic conductors are useful in fuel cells, advanced battery systems, chemical sensors, and other devices. Many fast ionic conductors at temperatures close to melting points undergo a phase transition that results in available cation sites. One can stabilize such high-temperature phases at low temperatures by adding monovalent cation impurities, such as in MAg₄I₅.

Dislocations play a vital role in determining the strength of a material, in providing non-lattice diffusion pathways, and in crystal growth kinetics. There are four important ways of increasing the yield strength of a material: mechanical blocking of dislocation motion, pinning of dislocations by solute (impurity) atoms, impeding dislocation motion by short-range order, and increasing the dislocation density to cause tangling of dislocations. Mechanical blocking of dislocation motion can be produced by introducing tiny particles of a second phase into a crystal lattice. This process is followed in the hardening of steel, where particles of iron carbide are precipitated into iron, and in the hardening of aluminum, where particles of Al₂Cu are precipitated. In work-hardening or strain-hardening kinds of plastic deformation, the dislocation density is increased. The strain-hardening is limited to temperatures that are sufficiently low to prevent annealing of dislocations. At temperatures at which diffusion can occur, the dislocation climb and annealing tend to decrease the dislocation density. The resulting time-dependent deformation is called creep.

The central problem of strong alloys, however, is not only strength but also ductility, as failure often occurs as a result of fracture. Grain boundaries and dislocations offer relatively little resistance to diffusion of atoms in comparison with diffusion in perfect crystals. Grain boundaries and dislocations act as repositories for many mobile forms of microscopic garbage. Diffusion is greater in plastically deformed materials than in annealed crystals. Diffusion along grain boundaries controls the rates of some precipitation reactions in solids. The precipitation of tin from lead-tin solutions at room temperature proceeds about 10 to the power of 8 times faster than expected from diffusion in an ideal lattice. In some cases, the presence of dislocations may be the controlling factor in crystal growth. The growth rate is enormously faster on dislocation-rich crystal seed than on an ideal crystal. Once a new monolayer of surface is completed, the next monolayer cannot easily be initiated. A screw dislocation threading a surface leaves an atomic step of that surface. If atoms are added from a vapor, the step will advance and facilitate rapid nucleation.

Context

Defects in solids are of fundamental interest to scientists in chemistry, physics, metallurgy, and geology. In research, they are essential in the production of catalysts, ceramics, semiconductor components, solid electrolytes, and conducting polymers. The relevance of defects to many areas of science has long been recognized. For example, understanding the role of defects in material properties has tremendous applications in technology. Understanding the influence of energetics, kinetics, and interactions of defects on mechanical properties such as void swelling, microstructure, lattice parameter change, intergranular embrittlement, surface corrosion, and blistering will help to develop new materials for future nuclear-reactor walls. Since phase stability, material properties, and microstructure of defect-rich materials are determined by the point-defect-controlled diffusion processes, direct information on the annealing behavior of defects is quite useful.

Several experimental techniques and methods have been developed to introduce and characterize defects in materials in order to achieve required material characteristics. For example, ion beams have been developed for the fabrication and processing of microelectronic and large-scale integrated circuit devices. Precise control of lateral profiles of impurity is very important in the fabrication of delicate device structures such as LDDs (lightly doped drains) in small MOSFETS (metal oxide semiconductor field effect transistors). In the refinement of the microstructures and production of nonequilibrium structures, rapid solidification, hot isostatic processes are used to achieve high strength-to-weight ratio alloys, such as Al-Be, by fine dispersion of solute atoms above the solubility limit without aggregate. Such alloys have potential applications in aerospace technology.

Principal terms:

ANNEALING: very slow, regulated cooling to relieve strains

COLOR CENTER: a lattice defect that absorbs visible light; mostly found in ionic crystals

DEFORMATION: an alteration in the size or shape of a body that results in disorder in the crystal lattice

DISLOCATION: a line defect in a crystal, the result of a slip along a surface of one or more lattice constants

GAIN BOUNDARY: the boundary between the crystallites having different crystal orientations

IMPURITY: a foreign atom or ion in the host lattice at either a lattice or an interstitial position

INTERSTITIAL: an additional atom or ion situated between the normal sites in a crystal lattice, causing a defect

QUENCHING: rapid cooling of a material from high temperature to low temperature in order to freeze the defects present at high temperature

VACANCY: an irregularity in a crystal lattice that occurs when a site normally occupied by an atom or ion is unoccupied

Bibliography

Blakemore, J. S. SOLID STATE PHYSICS. 3d ed. Cambridge, England: Cambridge University Press, 1985. The section (1.6) on crystalline defects describes various types of defects in crystals, including point defects, dislocations, stoichiometry, and defect densities under thermal equilibrium.

Chadwick, Alan V., and Mario Terenzi, eds. DEFECTS IN SOLIDS: MODERN TECHNIQUES. New York: Plenum Press, 1986. Various experimental techniques for defect studies in solids have been presented with the results. The first chapter gives an introduction to defects in solids. A good book for advanced study.

Harrison, Walter A. SOLID STATE THEORY. New York: McGraw-Hill, 1970. Section 6.4 of chapter 4 describes types of dislocations, dislocation pinning, and Frank-Read sources. The effect of an applied stress on dislocation loops is explained.

Kittel, Charles. INTRODUCTION TO SOLID STATE PHYSICS. 6th ed. New York: John Wiley & Sons, 1986. Chapter 18, on point defects, gives information on vacancies, thermal diffusion in metals, and color centers. Chapter 20, on dislocations, discusses types of dislocations and their effects on the strength of crystals, alloys, and crystal growth.

Levy, Robert A. PRINCIPLES OF SOLID STATE PHYSICS. New York: Academic Press, 1972. Imperfections in solids are covered in chapter 10, which includes discussion of static imperfections, excitation states of crystals, and transient imperfections. Few theoretical aspects of the defect concentration, ionic conductivity, and the strength of crystals are described.

Point defects in a periodic lattice

Dislocations

Radiation: Interactions with Matter

Deformation of Solids

Electrical Properties of Solids

Magnetic Properties of Solids

Optical Properties of Solids

Thermal Properties of Solids