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Outline of the Lecture. Crystal StructuresUnit CellMetallic Crystal StructuresCrystal Systems (Directions and Planes)Atomic ArrangementsLinear and Planar Atomic DensitiesNoncrystalline Materials. Crystal Structures. Material classification can be made based on the regularity or irregularity

Structures of Metals and Ceramics

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**1. **Structures of Metals and Ceramics Callister, 2000
5th Edition

**2. **Outline of the Lecture Crystal Structures
Unit Cell
Metallic Crystal Structures
Crystal Systems (Directions and Planes)
Atomic Arrangements
Linear and Planar Atomic Densities
Noncrystalline Materials

**3. **Crystal Structures Material classification can be made based on the regularity or
irregularity of atom or ion arrangement with respect to each other.
Materials

**4. **Crystal Structures The crytalline structure of the materials range from simple to more complex and there are many different types of structures.
The atoms or ions are thought as solid spheres with their sizes defined. This is called atomic hard sphere model. All atoms are identical in this model.
Smallest repeating group is called UNIT CELL. Unit cells can be imagined as the building block of the crystal structure. Unit cells in general are paralelepipeds or prisms having three sets of parallel faces, one is drawn within the aggregate of spheres.

**5. **Metallic Crystal Structure Atomic bonding is metallic, which is nondirectional. Therefore there are no restrictions as to the number and position of nearest neighbor atoms. For metals each sphere in crystal structure represents the ion core. There are three simple crystalline structure in metallic materials.
Face centered cubic crystal structure (FCC)
Body centered cubic crytal structure (BCC)
Hexagonal Close-Packed Crystal Structure (HCP)

**6. **Face Centered Cubic Crystal Structure (FCC):

**7. **

**8. **Coordination number: number of nearest neighbor or touching atoms.
For FCC: it is 12 atoms.
Atomic packing factor (APF)=
APF=0.74 for FCC. (see the example problem in textbook)
Metals generally have high APF to maximize the shielding provided by
electron cloud.

**9. **Body Centered Cubic Crystal Structure (BCC):

**10. **Hexagonal Close-Packed Crystal Structure (HCP):

**11. **Theoretical density (mass/ volume) can then be calculated using the
crystal structure of metallic solid material.

**12. **Ceramic Crystal Structures Ceramics crytal structures are more complex since they are composed of different elements. Moreover the bonding in ceramics may range from purely ionic (nondirectional) to totally covalent (directional). We learned the calculation of % ionic character of a covalent bond using the electronegativities and here are some examples for different materials:

**13. **Stable ceramic crystal is when those anions surrounding a cation are all in contact with that cation.

**15. **AX-Type Crystal Structures: For ceramics having equal numbers of cations and anions (A=cation, X=anion). Coordination number for both is 6. For example; NaCl, MgO, MnS, FeO.
Cesium Chloride structure: Coordination number for cation and anion is 8.
Zinc blende structure: ZnS, ZnTe, SiC. Coordination number is 4. The bonding is covalent in this type structure.
AmXp-Type Crystal Structures: CaF2, UO2, PuO2, ThO2.
AmBnXp Type Crystal Structures: BaTiO3

**16. **It is also possible to calculate the theoretical density of ceramic material from the unit cell data.

**17. **Carbon: C can exist in various polymorphic (a material having more than one crystal structure; such as Fe:BCC structure at room T, FCC structure at 9120C, it is also called allotropy for elemental solids) forms as well as amorphous state. Diamond and graphite are two different polymorphic forms of C.

**18. **Crystal Systems The unit cell geometry: x,y,z coordinate system is established with its origin at one of the unit cell corners and axes coincide with the edges of the paralelepiped extending from that corner, the origin.

**19. **There are seven different possible combinations of the lattice parameters respresenting a unique crystal system.

**21. **It is often necessary to specify a particular crystallographic plane of atoms or direction. Labeling using indices helps us to define ceratin planes and directions. The basis for the estimation of index values is the unit cell.
Crystallographic Directions
The direction is a line between two points or a vector as shown below:

**22. **Steps for defining a direction in a crystal system:
A vector is positioned such that it passes through the origin of the coordinate system. Then you can move the vector if you keep the parallelism.
The length of the vector projection on each of the three axes is determined in terms of the unit cell dimensions (a, b, c).
The three numbers are multiplied or divided by a common factor to reduce them to the smallest integer values.
Three indices are enclosed in square brackets as [uvw]
Remember to count for positive and negative coordinates based on the origin. When there is a negative index value, then show that by a bar over it, as

**23. **Examples

**25. ** In cubic crystals, all directions showed by the indices of

**26. **The three a1, a2, and a3 axes are placed withina single plane (basal plane) and at 120° angles to one another. The z axis is perpendicular to the selected basal plane.
There will be four indices to define the direction as [uvtw]:
The first three indices are the projections of a1, a2, and a3 axes. Then convert from three-index system to four-index system as follows:

**28. **Crystallographic Planes Except hexagonal crystal system, crytallographic planes are specified using three Miller indices (hkl). Any two planes parallel to each other are equivalent and have same indices.
The determination of the h,k, and l index numbers are as follows:
If the plane passes through the selected origin, then construct a new parallel plane or change the originto a corner of another unit cell.
Plane intersects or parallels each of the axes: the length of each axis is determined by using lattice parameters; a,b, and c.
Take the reciprocals of the lattice parameters. Therefore a plane that parallels an axis has a ZERO index. (1/infinity=zero)
You may then change these three numbers to the set of smallest integers using a common factor.
Report the indices as (hkl).
An intercept on the negative side of the origin is indicated by a bar over that index.

**30. **For cubic crystals: Planes and directions having the same indices are perpendicular to one another.

**32. **We are interested in specification fo planes because atomic arrangement depends on the crystal structure.

**33. **A family of planes is formed by all those planes that are crystallographically equivalent, {100}, {111}.
{111} =

**34. **Linear and Planar Atomic Densities Linear and planar atomic densities are one and two dimensional analogs of atomic packing factor. Linear density shows directional equivalency, i.e., equivalent directions have identical linear densities. Planar density shows planar equivalency. The following examples illustrate the determination of the linear and planar densities.

**36. **Crystalline and Noncrystalline Materials Single Crystals: When the periodic and repeated arrangement of atoms extends throughout the entirety of the specimen without interruption, the result is a single crystal. Single crystals may exist in nature but they may also be produced artificially.

**37. **37 Polycrystalline Materials: are the materials made of a collection of small crystals or grains.
A typical solidification of a polycrystalline specimen:

**38. **Anisotropy: Some of the physical properties of single crystals may depend on the crystallograhic direction. For axample: the elastic modulus, electrical conductivity of a single crystal may be different in [100] and [111] directions. This directionality of properties is termed anisotropy. This difference is usually due to variance of atomic or ionic spacings in different directions. The extend and magnitude of anisotropy are related with the symmetry of the crystal structure. The degree of anisotropy increases as the symmetry decreases.
Isotropy: Properties are independent of the crystallographic direction.
Determination of Crystal Structures: X-Ray Diffraction (XRD)
Reading assignment for students.
Noncrystalline Solids: lack a systematic and regular arrangement of atoms over relatively large atomic distances.