conduction is possible. If the lower band is only partially full, the electrons can move in an applied field, and the solid is a metal such as the alkali metals. If the equilibrium position is as shown at B, where the bands overlap, there is again free movement of electrons in an applied field and the metallic state (such as the alkaline earth metals). The description of the transition metals is more complex but based on the same principles. If the equilibrium state of the solid is at a point just before the bands overlap, electrons can be transferred across the gap by thermal energy at sufficiently high temperature, and the solid is an intrinsic semiconductor with conductivity increasing with temperature. The band theory is also useful for describing some, although not all, properties of insulators. In typical ionic crystals such as the alkali halides or magnesium oxide, where each ion has a closed ionic shell, the excited states can be more efficiently described by valence bond theory. Valence crystals (typically diamond, silicon, germanium) have strongly directed tetrahedral bonds and may be thought of as one large molecule. Molecular solids with relatively weak binding forces between molecules have narrow energy bands. There has been very little systematic treatment of these to date, but the advent of the crystalline polymer has encouraged interest
Effect of Imperfections I n addition to the gross properties of perfect crystals, many of the important properties of solids are greatly affected by the presence of impurities and structural imperfections ( 3 ) . These may be either point or line impurities. The point impurities include lattice vacancies, interstitial atoms, and foreign atoms in the lattice (for many purposes it is also useful to classify lattice vibrations as a type of imperfection). Diffusion of atoms or ions in the lattice is governed by the possibility of lattice vacancies or interstitial atoms. These imperfections as well as foreign atoms provide energy levels between the valence bond and the
conduction band. These energy levels may act as sources of electrons for the conduction band or sinks for valence bond electrons, giving use to the extrinsic semiconductor. These levels also provide traps for electrons excited by cathode rays, light, or electricity. The later decay of these electrons to the ground state with emission of energy as light provides the phenomenon of phosphorescence, which is of increasing practical importance. Another significant type of imperfection is the dislocation. Pure edge and pure screw dislocations can be described in terms of displaced planes of atoms. Actual dislocations are combinations of these. The physical strength of crystals is largely determined by the amount and character of dislocations present and, primarily, by their ability to move freely through the crystal. Atomic diffusion, and particularly crystal growth rates, are greatly affected by the motion of dislocations. The theory of solid surfaces is not yet so far advanced, but significant progress is being made which will be of particular interest to engineers. Among the many useful solids where modern solid-state theory has made important contributions are: new alloys and stronger metals, semiconductors, photoconductors, phosphors, ferroelectrics, ferrites, garnets, new magnetic materials, plastics for dielectrics and other applications, catalysts, electrodes, and glasses.
Addition of impurities of a given type and concentration to give a specified useful property. The impurity-activated semiconductors for transistor use come to mind immediately. Phosphors are having increasing applications. Electroluminescence may provide a more efficient and flexible lighting system. Impurities also can modify electrical and magnetic properties in useful ways, as well as corrosion resistance. Increase of strength of a material. Changing the crystal size and impurity content, and particularly changing the concentration and nature of dislocations, can drastically modify the strength and ductility of materials. Methods for effecting these changes are largely in the laboratory stage, but it is inevitable that they will be applied in the not too distant future. Development of a specified surface on a solid for specific applications. Advances in catalytic development depend on a better understanding of the solid state, and, in particular, the defect solid state. Many of the notions developed in transitor research are finding application in catalysis. The theory of solid surfaces is in its infancy, but it contains perhaps the most extensive engineering possibilities of any area of solid-state physics. In addition to applications in catalysis, the development of special surfaces for electrodes is important. Theoretical aspects of preparation of amorphous solids such as glasses and plastics are due to receive increasing attention. The preparation under extreme conditions of temperature and pressure is particularly promising.
literature Cited Special Problems of Solid State ’ Problems of the solid state which seem open to attack by chemical engineers include : Creation of new solids with predictable properties. The synthesesof diamond and of cubic boron nitride are recent spectacular examples. The creation of crystalline polymers and of isotactic or syndiotactic polymers is a second example. Many new materials for electrical applications, such as ferroelectrics, come under this classification, as do many special corrosion-resistant materials such as phosphides and silicides.
(1) Coulson, C. A , , “Valence,” Oxford Univ. Press, Oxford, 1952. (2) Seitz, F., “Modern Theory of Solids,” McGraw-Hill, New York, 1940. (3) Shockley, W., others. “Imperfections in Nearly Perfect Crystals,” esp. pp. 3-94, Wley, New York, 1952. RECEIVED for review December 30, 1957 ACCEPTED March 24 1958 Division of Industrial and Engineering Chemistry, .4CS, Symposium on Molecular Physics in Chemical Engineering, Cleveland, Ohio, January 1958.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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Vapor Pressure and Viscosity of Solutions in the Calcium Oxide-Phosphoric OxideWater System at 25’ C. In the article “Vapor Pressure and Viscosity of Solutions in the Calcium Oxide-Phosphoric Oxide-Water System at 25” C. [E. 0. Huffman, J. D. Fleming, A. J. Smith, IXD. ENG.CHEM., CHEM.ENG. DATASERIES3, No. 1, 17 (1958)] on page 18 in the second paragraph under Results, the figure for uncertainty in the density should be 0.0004 gram per ml.
