There are several types of imperfections or defects that can occur in crystal structures including point defects, line defects, interfacial defects, and bulk defects. Point defects include vacancies and interstitials which occur naturally in all crystals. Line defects are imperfections where rows of atoms have a differing structure, such as dislocations. Interfacial defects include grain boundaries and twin boundaries. The number and type of defects can be controlled and affect material properties, both positively and negatively.

1. IMPERFECTIONS IN CRYSTALS BY, MAYUR BAGALE AND SUSHANT MODI.

2. IMPERFECTIONS IN CRYSTALS ISSUES TO ADDRESS... How do defects affect material properties? What types of defects arise in solids? Are defects undesirable?

3. Crystalline Imperfections There is no such thing as a perfect crystal! • Thermodynamically “impossible” • “ defects” lower the energy of a crystal & make it more stable • always have vacancies and impurities, to some extent Defect does not necessarily imply a bad thing • addition of C to Fe to make steel • addition of Cu to Ni to make thermocouple wires • addition of Ge to Si to make thermoelectric materials • addition of Cr to Fe for corrosion resistance • introduction of grain boundaries to strengthen materials …… and so on “ Defect” (in this context) can be either desirable or undesirable. In general, a defect simply refers to a disruption in the crystalline order of an otherwise periodic material.

4. CRYSTALLINE IMPERFECTIONS are frequently classified according to geometry or dimensionality of the defect. Point defects Line defects Interfacial defects Bulk or volume defects

5. Point Defects Atoms in solid possess vibrational energy, some atoms have sufficient energy to break the bonds which hold them in eqbm position. Hence once the atoms are free they give rise to Point Defects . Classes of point defects: Intrinsic defects . Vacancy Interstitial Extrinsic defects Substitution Interstitial

6. Vacancies A lattice position that is vacant because the atom is missing There are naturally occurring vacancies in all crystals The concentrations of vacancies increase with: increasing temperature decreasing activation energy

7. Vacancies -vacant atomic sites in a structure. Vacancy distortion of planes

8. Self-Interstitial If the matrix atom occupies its own interstitial site, the defect is called Self Interstitial. Self-interstitials in metals introduce large distortions in the surrounding lattice. self- interstitial distortion of planes

9. For Ionic Solids, Frenkel and Schottky defects are likely to form. Schottky Defects When cation vacancy is associated with anion vacancy, the defect is called Schottky Defect. Frenkel Defects When an atom leaves its regular site and occupy nearby interstitial site it gives rise to two defects i.e. one vacancy and other self interstitial these two defects are called as Frenkel Defects.

10. DEFECTS IN CERAMIC STRUCTURES 8 • Frenkel Defect -- a cation is out of place. • Shottky Defect -- a paired set of cation and anion vacancies. • Equilibrium concentration of defects Adapted from Fig. 13.20, Callister 5e. (Fig. 13.20 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials , Vol. 1, Structure , John Wiley and Sons, Inc., p. 78.) See Fig. 12.21, Callister 6e .

11. Equilibrium Concentration: Point Defects Boltzmann's constant (1.38 x 10 -23 J/atom-K) (8.62 x 10 -5 eV/atom-K)   N v N  exp  Q v k T       No. of defects No. of potential defect sites. Activation energy Temperature Each lattice site is a potential vacancy site • Equilibrium concentration varies with temperature!

12. Measuring Activation Energy • We can get Q v from an experiment.   N v N = exp  Q v k T       • Measure this... N v N T exponential dependence! defect concentration • Replot it... 1/ T N N v ln - Q v / k slope

13. Line Defects Line defects are imperfections in a crystal structure for which a row of atoms have a local structure that differs from the surrounding crystal. 1. Edge dislocations 2. Screw dislocations

14. Linear Defect ( Dislocations ) Are one-dimensional defects around which atoms are misaligned Edge dislocation: extra half-plane of atoms inserted in a crystal structure Burger vector  to dislocation line Screw dislocation: spiral planar ramp resulting from shear deformation Berger vector  to dislocation line

15. Edge Dislocation

16. Screw Dislocation

17. Interfacial Defects Are boundaries that have two dimensions and normally separate regions of the materials that have different crystal structures. 1. External surface 2. Grain boundary 3. Twin boundary

18. External Surfaces Surface atoms have unsatisfied atomic bonds, and higher surface energies, γ (J/m2 or, erg/cm2) than the bulk atoms. To reduce surface free energy, material tends to minimize its surface areas against the surface tension (e.g. liquid drop).

19. Grain Boundaries Polycrystalline material comprised of many small crystals or grains having different crystallographic orientations. Atomic mismatch occurs within the regions where grains meet. These regions are called grain boundaries. Segregation of impurities occurs at grain boundary. Grains tend to grow in size at the expense of smaller grains to minimize surface energy. This occurs by diffusion, which is accelerated at high temperatures. Dislocations can usually not cross the grain boundary.

20. Twin Boundaries Special type of grain boundaries with twin directions mirrored atomic positions across the boundary. May be produced by shear deformation of BCC/HCP materials ( mechanical twin), or during annealing following deformation ( annealing twin) of FCC materials

21. Bulk or Volume Defects Pores affect optical, thermal, and mechanical properties Cracks affect mechanical properties Foreign inclusions affect electrical, mechanical, optical properties

22. Summary • Point , Line , and Area defects exist in solids . • The number and type of defects can be varied and controlled (e.g., T controls vacancy conc.) • Defects affect material properties (e.g., grain boundaries control crystal slip). • Defects may be desirable or undesirable (e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not.)

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