Structure Chemistry

7/28/2019 Structure Chemistry

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Crystal Structures

Types of crystal structures

Face centered cubic (FCC)

Body centered cubic (BCC)Hexagonal close packed (HCP)

Close Packed Structures

Different Packing of HCP and FCC

Crystallographic Directions and Planes

cubic systems


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Face Centered Cubic (FCC)

Atoms are arranged at the corners andcenter of each cube face of the cell.

Atoms are assumed to touch along facediagonals


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The lattice parameter, a, is related to theradius of the atom in the cell through:

Coordination number: the number ofnearest neighbors to any atom. For FCCsystems, the coordination number is 12.

22Ra =


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Atomic Packing Factor: the ratio of atomicsphere volume to unit cell volume,

assuming a hard sphere model.FCC systems have an APF of 0.74, the

maximum packing for a system in which allspheres have equal diameter.


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Body Centered Cubic

Atoms are arranged at the corners of thecube with another atom at the cube

center.


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Body Centered Cubic

Since atoms are assumed to touch alongthe cube diagonal in BCC, the lattice

parameter is related to atomic radiusthrough:

3

4R

a =


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Body Centered Cubic

Coordination number for BCC is 8. Eachcenter atom is surrounded by the eight

corner atoms.The lower coordination number also

results in a slightly lower APF for BCC

structures. BCC has an APF of 0.68,rather than 0.74 in FCC


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Hexagonal Close Packed

Cell of an HCP lattice is visualized as a topand bottom plane of 7 atoms, forming a

regular hexagon around a central atom.In between these planes is a half-hexagonof 3 atoms.


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Hexagonal Close Packed

There are two lattice parameters in HCP,aand c, representing the basal and height

parameters respectively. In the idealcase, the c/aratio is 1.633, however,deviations do occur.

Coordination number and APF for HCP areexactly the same as those for FCC: 12 and0.74 respectively.

This is because they are both consideredclose acked structures.


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Even though FCC and HCP are closepacked structures, they are quite different

in the manner of stacking their closepacked planes.

Close packed stacking in HCP takes placealong the cdirection ( the (0001) plane). FCCclose packed planes are along the (111).

First plane is visualized as an atomsurrounded by 6 nearest neighbors in both

HCP and FCC.


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The second plane in both HCP and FCC issituated in the holes above the first plane ofatoms.

Two possible placements for the third planeof atoms

Third plane is placed directly above the first plane

of atoms ABA stacking -- HCP structure

Third plane is placed above the holes of the firstplane not covered by the second plane

ABC stacking -- FCC structure


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Crystallographic Directions

Cubic systems

directions are named based upon the

projection of a vector from the origin of thecrystal to another point in the cell.

Conventionally, a right hand Cartesian

coordinate system is used.The chosen origin is arbitrary, but is always

selected for the easiest solution to theproblem.


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Crystallographic Directions

Points within the lattice are written in theform h,k,l, where the three indices

correspond to the fraction of the latticeparameters in the x,y,z direction.


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Miller Indices

Procedure for writing directions in MillerIndices

Determine the coordinates of the two pointsin the direction. (Simplified if one of thepoints is the origin).

Subtract the coordinates of the second pointfrom those of the first.

Clear fractions to give lowest integer valuesfor all coordinates


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Miller Indices

Indices are written in square bracketswithout commas (ex: [hkl])

Negative values are written with a bar overthe integer.

Ex: if h


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Miller Indices

Crystallographic Planes

Identify the coordinate intercepts of the

planethe coordinates at which the plane intercepts the

x, y and z axes.

If a plane is parallel to an axis, its intercept is

taken as .If a plane passes through the origin, choose an

equivalent plane, or move the origin

Take the reciprocal of the intercepts


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Miller Indices

Clear fractions due to the reciprocal, but donot reduce to lowest integer values.

Planes are written in parentheses, with barsover the negative indices.

Ex: (hkl) or if h


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Miller Indices

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Structure Chemistry