Crystal Structures

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Last updated 4:53 AM on 10/15/26
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13 Terms

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Why is it important to understand crystal structure? (3 reasons)

  1. Big influences on the property of the material

    1. Think graphite vs diamond

  2. When growing semiconductors on top of each other, crystal structures have to match

  3. Macroscopic structure of crystal mirrors the atomic structure


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What determines density of a material? And for what type of material is that most important?

  1. Element Type

    1. Directly related to the weight/mass of each element

    2. Matters more in metals

  2. Atomic Arrangement

    1. Crystal structure

    2. Matters more in ceramics

  3. % of Open Space

    1. Matters more in polymers

      1. Van der Waals force between chains and rather empty


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Why do crystal structures exhibit close packing?

  • All solids desire atomic packing arrangement that minimizes the total energy of the system

  • If wasted area is smaller, there is less energy


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Packing Density Equation

  • The percentage of space occupied by the atoms

  • (total space - empty space) / total space


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Close Packing for 3-layers (2)

  • Hexagonal Close Packed (HCP)

  • Face Centered Cubic (FCC)


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Hexagonal Close Packed (HCP)

Same A B A pattern repeating

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Face Centered Cubic (FCC)

Different A B C pattern repeating

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Coordination Number (CN)

  • The number of nearest neighbor atoms surrounding a given atom

  • Close-packed system will maximize coordination number ALWAYS


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SRO: Short Range Order

  • CN is a form of this

  • Most things are SRO

  • Ex. Glass


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LRO: Long Range Order

  • Occurs in crystalline materials

  • Requires that each the SRO units repeat their arrangement in 3-dimensional space

  • Ex. Quartz


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Symmetry (3 types)

Symmetry is when an object/pattern remains unchanged when a “geometric transformation” is applied to it

  1. Mirror

  2. Rotation

    1. if rotated by 360⁰ / n, structure overlaps with itself

      1. Structure has a n-fold symmetry

  3. Translation


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Why do we use symmetry to describe crystals?

We can analyze a small portion of a unit cell to understand the whole structure

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What are the banned rotations for n-fold symmetry?

  • 1-fold: 360⁰

  • 2-fold: 180⁰

  • 3-fold: 120⁰

  • 4-fold: 90⁰

  • 6-fold: 60⁰