Topik 3 - Crystal Structure - Ilmu Bahan

8/11/2019 Topik 3 - Crystal Structure - Ilmu Bahan

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Dr.Ir.Asep Handaya Saputra, MEng.

Lecture Note: Material Science (source: virginia univ)

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Crystal Structures

3rd Topics


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Fundamental Concepts

Atoms self-organize in crystals, most of the time. Thecrystalline lattice, is a periodic array of the atoms. Whenthe solid is not crystalline, it is called amorphous.Examples of crystalline solids are metals, diamond andother precious stones, ice, graphite. Examples ofamorphous solids are glass, amorphous carbon (a-C),amorphous Si, most plastics

To discuss crystalline structures it is useful to consideratoms as being hard spheres, with well-defined radii. In

this scheme, the shortest distance between two likeatoms is one diameter.


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Unit Cells

The unit cell is the smallest structure thatrepeats itself by translation through the crystal.

We construct these symmetrical units with thehard spheres.

The most common types of unit cells are the

faced-centered cubic (FCC), the body-centeredcubic (BCC) and the hexagonal close-packed(HCP).

Other types exist, particularly among minerals.The simple cube (SC) is often used for didacticalpurpose, no material has this structure.


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Metallic Crystal Structures

Important properties of the unit cells areThe type of atoms and their radii R.cell dimensions (side a in cubic cells, side of base a and height cin HCP) in terms of R.

n, number of atoms per unit cell. For an atom that is shared withm adjacent unit cells, we only count a fraction of the atom, 1/m.

CN, the coordination number, which is the number of closestneighbors to which an atom is bonded.

APF, the atomic packing factor, which is the fraction of the

volume of the cell actually occupied by the hard spheres.APF =Sum of atomic volumes/Volume of cell.


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Metallic Crystal StructuresUnit Cell n CN a/R APF

SC 1 6 2 0.52

BCC 2 8 4 3 0.68

FCC 4 12 2 2 0.74

HCP 6 12 0.74


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Simple Cubic CrystalIn the Simple Cubic (SC) unit

cell there is one lattice point ateach of the eight corners of a

cube.

Unit cells in which there arelattice points only at the eight

corners are called primitive.


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Simple Cubic Crystal

An example of a simple cubic crystal is CsCl.

Each ion resides on a separate,

interpenetrating Simple Cubic lattice.The cation is in the center of the anion unit

cell and visa versa, so the two lattices have

the same unit cell dimensions.


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Face Centered CubicIn the Face Centered Cubic(FCC) unit cell there is one hostatom at each corner and onehost atom in each face.

Since each corner atom

contributes one eighth of itsvolume to the cell interior, andeach face atom contributes onehalf of its volume to the cell

interior (and there are six faces),then n = 1/8.8 + 1/2.6 = 4


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Face Centered CubicIn a NaCl crystal, each ion resides on a

separate, interpenetrating FCC lattice, andthe two lattices have the same unit cell

dimensions.


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Hexagonal Closest Packing

(HCP)


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Density Computations

The density of a solid is that of the unit

cell, obtained by dividing the mass of theatoms (n atoms x Matom) and dividing by Vcthe volume of the cell (a3 in the case of a

cube). If the mass of the atom is given in

amu (A), then we have to divide it by the

Avogadro number to get Matom. Thus, theformula for the density is:


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Polymorphism and AllotropySome materials may exist in more than

one crystal structure, this is calledpolymorphism.

If the material is an elemental solid, it iscalled allotropy. An example of allotropy is

carbon, which can exist as diamond,

graphite, and amorphous carbon.


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Crystalline MaterialsSingle Crystals

Crystals can be single crystals where the wholesolid is one crystal. Then it has a regulargeometric structure with flat faces.

Polycrystalline Materials

A solid can be composed of many crystallinegrains, not aligned with each other. It is calledpolycrystalline. The grains can be more or less

aligned with respect to each other. Where theymeet is called a grain boundary.


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Crystals Growth

Topik 3 - Crystal Structure - Ilmu Bahan

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