1 / 10

Statistical Thermodynamics of Defects in Solids

Statistical Thermodynamics of Defects in Solids. May have a perfect crystal at 0 K, but otherwise defects will occur in the structure Important influence on properties Electronic and thermal conduction Mechanical strength Diffusion Colour etc. Exploited in many applications.

kathy
Download Presentation

Statistical Thermodynamics of Defects in Solids

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Statistical Thermodynamics of Defects in Solids • May have a perfect crystal at 0 K, but otherwise defects will occur in the structure • Important influence on properties • Electronic and thermal conduction • Mechanical strength • Diffusion • Colour etc. • Exploited in many applications

  2. Classification • Intrinsic vs extrinsic • Intrinsic - integral to the pure crystal • Extrinsic - foreign atoms. • Dimensionality • Point defects at isolated atomic positions • Extended • Linear, planar, 3D

  3. Thermodynamic equilibrium • Can represent a minimum in the free energy of the crystal • Independent of sample history • Or can be metastable and change with the history of the sample. • We will look at intrinsic, point defects in thermal equilibrium.

  4. Two categories • Schottky • Vacancies in the lattice • For an ionic compound, consist of a combination of cation and anion vacancies, to maintain charge neutrality • Frenkel • Interstitials and vacancies in the lattice • Tend to be cation interstitials due to size

  5. Why do they exist at equilibrium? • Creation of a defect normally costs energy. • But it also increases the entropy of the crystal! • Defects increase in concentration until the free energy is a minimum.

  6. Thus need to be able to understand how the enthalpy and the entropy vary with defect concentration. • If the defects are truly isolated from each other, then the enthalpy should just be proportional to the number of defects • E.g. for ns Schottky pairs

  7. The entropy • Consider a 1:1 ionic crystal with N cation sites, N anion site, ns Schottky cation vacancies and ns anion vacancies. • The vacancies will be able to take up many different possible positions in the crystal so there will be a configurational entropy associated with their distribution

  8. N boxes (lattice sites) with ns identical objects (vacancies) to put in

  9. What is the magnitude of the enthalpy term? • Normally about 60-600 kJ mol-1 • So typical concentrations (ns/N) are:

More Related