　　扩散一及二定律及其在各种条件下的解反映了原子扩散的宏观规律，这些规律为解决许多与扩散有关的实际问题奠定了基础。在扩散定律中，扩散系数是衡量原子扩散能力的非常重要的参数，到目前为止它还是一个未知数。为了求出扩散系数，首先要建立扩散系数与扩散的其他宏观量和微观量之间的联系，这是扩散理论的重要内容。事实上，宏观扩散现象是微观中大量原子的无规则跳动的统计结果。从原子的微观跳动出发，研究扩散的原子理论、扩散的微观机制以及微观理论与宏观现象之间的联系是本节的主要内容。

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History and Bibliography of Diffusion1.1 Pioneers and Landmarks of DiffusionReferences1.2 Bibliography of Solid-State DiffusionPart I Fundamentals of DiffusionContinuum Theory of Diffusion2.1 Fick's Laws in Isotropic Media2.1.1 Fick's First Law2.1.2 Equation of Continuity2.1.3 Fick's Second Law - the 'Diffusion Equation'2.2 Diffusion Equation in Various Coordinates2.3 Fick's Laws in Anisotropic MediaReferencesSolutions of the Diffusion Equation3.1 Steady-State Diffusion3.2 Non-Steady-State Diffusion in one Dimension3.2.1 Thin-Film Solution3.2.2 Extended Initial Distributionand Constant Surface Concentration3.2.3 Method of Laplace Transformation3.2.4 Diffusion in a Plane Sheet - Separation of Variables3.2.5 Radial Diffusion in a Cylinder3.2.6 Radial Diffusion in a Sphere3.3 Point Source in one, two, and three DimensionsReferences4 Random Walk Theory and Atomic Jump Process4.1 Random Walk and Diffusion4.1.1 A Simplified Model4.1.2 Einstein-Smoluchowski Relation4.1.3 Random Walk on a Lattice4.1.4 Correlation Factor4.2 Atomic Jump ProcessReferencesPoint Defects in Crystals5.1 Pure Metals5.1.1 Vacancies5.1.2 Divacancies5.1.3 Determination of Vacancy Properties5.1.4 Self-Interstitials5.2 Substitutional Binary Alloys.5.2.1 Vacancies in Dilute Alloys5.2.2 Vacancies in Concentrated Alloys5.3 Ionic Compounds5.3.1 Frenkel Disorder5.3.2 Schottky Disorder5.4 Intermetallics5.5 SemiconductorsReferences6 Diffusion Mechanisms6.1 Interstitial Mechanism6.2 Collective Mechanisms6.3 Vacancy Mechanism6.4 Divacancy Mechanism6.5 Interstitialcy Mechanism6.6 Interstitial-substitutional Exchange MechanismsReferencesCorrelation in Solid-State Diffusion7.1 Interstitial Mechanism7.2 Interstitialcy Mechanism7.3 Vacancy Mechanism of Self-diffusion7.3.1 A 'Rule of Thumb'7.3.2 Vacancy-tracer Encounters7.3.3 Spatial and Temporal Correlation7.3.4 Calculation of Correlation Factors7.4 Correlation Factors of Self-diffusion7.5 Vacancy-mediated Solute Diffusion7.5.1 Face-Centered Cubic Solvents7.5.2 Body-Centered Cubic Solvents7.5.3 Diamond Structure Solvents7.6 Concluding RemarksReferences……PartⅡ Experimental MethodsPartⅢ Diffusion in Metallic MaterialsPartⅣ Diffusion in Semiconductors PartⅤ Diffusion and Conduction in Ionic MaterialsPartⅥ Diffusion in GlassesPartⅦ Diffusion along High-Diffusivity Paths and in NanomaterialsIndex

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　　6.2 Collective Mechanisms　　Solute atoms similar in size to the host atoms usually form substitutionalsolid solutions. The diffusion of substitutional solutes and of solvent atomsthemselves requires a mechanism different from interstitial diffusion. In the1930s it was suggested that self- and substitutional solute diffusion in metalsoccurs by a direct exchange of neighbouring atoms (Fig. 6.3)， in whichtwo atoms move simultaneously. In a close-packed lattice this mechanismrequires large distortions to squeeze the atoms through. This entails a highactivation barrier and makes this process energetically unfavourable. Theoret-ical calculations of the activation enthalpy for self-diffusion of Cu performedby HUNTINGTON ET AL. in the 1940s [1， 2]， which were confirmed later bymore sophisticated theoretical approaches， led to the conclusion that directexchange at least in close-packed structures was not a likely mechanism.　　The so-called ring mechanism of diffusion was proposed for crystallinesolids by the American metallurgist JEFFRIES [3] already in the 1920s andadvocated by ZENER in the 1950s [4]. The ring mechanism corresponds toa rotation of 3 (or more) atoms as a group by one atom distance. The requiredlattice distortions are not as great as in a direct exchange. Ring versions ofatomic exchanges have lower activation energies but increase the amount ofcollective atomic motion， which makes this more complex mechanism unlikelyfor most crystalline substances.　　Direct exchange and ring mechanisms have in common that lattice de-fects are not involved. The observation of the so-called KirkendaU effect inalloys by KIRKENDALL AND COWORKERS [5， 6] during the 1940s had an im-portant impact on the field (see also Chaps. 1 and 10). The Kirkendall effectshowed that the self-diffusivities of atoms in a substitutional binary alloy dif-fuse at different rates. Neither the direct exchange nor the ring mechanismcan explain this observation. As a consequence， the ideas of direct or ringexchanges were abandoned in the diffusion literature.　　……