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# Crystal Systems

## Substances in which the particles arrangement is orderly, repeating, three-dimensional

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Crystal Systems

Credit: Courtesy of the National Cancer Institute
Source: http://commons.wikimedia.org/wiki/File:Photodynamic_therapy.jpg
License: CC BY-NC 3.0

#### What are the different uses of lasers?

The development of modern lasers has opened many doors to both research and applications. A laser beam was used to measure the distance from the Earth to the moon. Lasers are important components of CD players. As the image above illustrates, lasers can provide precise focusing of beams to selectively destroy cancer cells in patients. The ability of a laser to focus precisely is due to high-quality crystals that help give rise to the laser beam. A variety of techniques are used to manufacture pure crystals for use in lasers.

### Crystalline Solids

The majority of solids are crystalline in nature. A crystal is a substance in which the particles are arranged in an orderly, repeating, three-dimensional pattern. Particles of a solid crystal may be ions, atoms, or molecules, depending on the type of substance. The three-dimensional arrangement of a solid crystal is referred to as the crystal lattice. Different arrangements of the particles within a crystal cause them to adopt several different shapes.

### Crystal Systems

Crystals are classified into general categories based on their shapes. A crystal is defined by its faces, which intersect with one another at specific angles, which are characteristic of the given substance. The seven crystal systems are shown below, along with an example of each. The edge lengths of a crystal are represented by the letters a\begin{align*}a\end{align*}, b\begin{align*}b\end{align*}, and c\begin{align*}c\end{align*}. The angles at which the faces intersect are represented by the Greek letters α\begin{align*}\alpha\end{align*}, β\begin{align*}\beta\end{align*}, and γ\begin{align*}\gamma \end{align*}. Each of the seven crystal systems differs in terms of the angles between the faces and in the number of edges of equal length on each face.

 Crystal System Diagram Example Cubic a=b=c;α=β=γ=90∘\begin{align*}a = b = c; \; \alpha = \beta = \gamma = 90^\circ\end{align*} [Figure2] Credit: CK-12 Foundation - Christopher Auyeung License: CC BY-NC 3.0 [Figure3] Credit: User:Teravolt/Wkipedia Source: http://en.wikipedia.org/wiki/File:Pyrite_Cubes.JPG License: CC BY-NC 3.0 Pyrite Tetragonal a=b≠c;α=β=γ=90∘\begin{align*}a = b \ne c; \; \alpha = \beta = \gamma = 90^\circ\end{align*} [Figure4] Credit: CK-12 Foundation - Christopher Auyeung License: CC BY-NC 3.0 [Figure5] Credit: Courtesy of the "Minerals in Your World Project" by the US Geological Survey and the Mineral Information Institute Source: http://commons.wikimedia.org/wiki/File:WulfeniteUSGOV.jpg License: CC BY-NC 3.0 Wulfenite Orthorhombic a≠b≠c;α=β=γ=90∘\begin{align*}a \ne b \ne c; \; \alpha = \beta = \gamma = 90^\circ\end{align*} [Figure6] Credit: CK-12 Foundation - Christopher Auyeung License: CC BY-NC 3.0 [Figure7] Credit: Christoph Radtke Source: http://commons.wikimedia.org/wiki/File:Aragonite_-_crystal_ball.jpg License: CC BY-NC 3.0 Aragonite Monoclinic a≠b≠c;α≠90∘=β=γ\begin{align*}a \ne b \ne c; \; \alpha \ne 90^\circ = \beta = \gamma\end{align*} [Figure8] Credit: CK-12 Foundation - Christopher Auyeung License: CC BY-NC 3.0 [Figure9] Credit: Stephanie Clifford (Flickr: sdixclifford) Source: http://www.flickr.com/photos/30486689@N08/3561497998/ License: CC BY-NC 3.0 Azurite Rhombohedral a=b=c;α=β=γ≠90∘\begin{align*}a = b = c; \; \alpha = \beta = \gamma \ne 90^\circ\end{align*} [Figure10] Credit: CK-12 Foundation - Christopher Auyeung License: CC BY-NC 3.0 [Figure11] Credit: Mike Beauregard (Flickr: subarcticmike) Source: http://www.flickr.com/photos/31856336@N03/3108675089/ License: CC BY-NC 3.0 Calcite Triclinic a≠b≠c;α≠β≠γ≠90∘\begin{align*}a \ne b \ne c; \; \alpha \ne \beta \ne \gamma \ne 90^\circ\end{align*} [Figure12] Credit: CK-12 Foundation - Christopher Auyeung License: CC BY-NC 3.0 [Figure13] Credit: Courtesy of the "Minerals in Your World Project" by the US Geological Survey and the Mineral Information Institute Source: http://commons.wikimedia.org/wiki/File:Feldspar%28Microcline%29USGOV.jpg License: CC BY-NC 3.0 Microcline Hexagonal a=b≠c;α=β=90∘,γ=120∘\begin{align*}a = b \ne c; \; \alpha = \beta = 90^\circ, \; \gamma = 120^\circ\end{align*} [Figure14] Credit: CK-12 Foundation - Christopher Auyeung License: CC BY-NC 3.0 [Figure15] Credit: Parent Gery Source: http://commons.wikimedia.org/wiki/File:H%C3%A9liodore_2_%28Russie%29_.jpg License: CC BY-NC 3.0 Beryl

### Summary

• A crystal is a substance in which the particles are arranged in an orderly, repeating, three-dimensional pattern.
• The crystal lattice is the three-dimensional arrangement of a solid crystal.

### Review

1. What is a crystal?
2. List the seven crystal systems.

### Notes/Highlights Having trouble? Report an issue.

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1. [1]^ Credit: Courtesy of the National Cancer Institute; Source: http://commons.wikimedia.org/wiki/File:Photodynamic_therapy.jpg; License: CC BY-NC 3.0
2. [2]^ Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0
3. [3]^ Credit: User:Teravolt/Wkipedia; Source: http://en.wikipedia.org/wiki/File:Pyrite_Cubes.JPG; License: CC BY-NC 3.0
4. [4]^ Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0
5. [5]^ Credit: Courtesy of the "Minerals in Your World Project" by the US Geological Survey and the Mineral Information Institute; Source: http://commons.wikimedia.org/wiki/File:WulfeniteUSGOV.jpg; License: CC BY-NC 3.0
6. [6]^ Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0
7. [7]^ Credit: Christoph Radtke; Source: http://commons.wikimedia.org/wiki/File:Aragonite_-_crystal_ball.jpg; License: CC BY-NC 3.0
8. [8]^ Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0
9. [9]^ Credit: Stephanie Clifford (Flickr: sdixclifford); Source: http://www.flickr.com/photos/30486689@N08/3561497998/; License: CC BY-NC 3.0
10. [10]^ Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0
11. [11]^ Credit: Mike Beauregard (Flickr: subarcticmike); Source: http://www.flickr.com/photos/31856336@N03/3108675089/; License: CC BY-NC 3.0
12. [12]^ Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0
13. [13]^ Credit: Courtesy of the "Minerals in Your World Project" by the US Geological Survey and the Mineral Information Institute; Source: http://commons.wikimedia.org/wiki/File:Feldspar%28Microcline%29USGOV.jpg; License: CC BY-NC 3.0
14. [14]^ Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0
15. [15]^ Credit: Parent Gery; Source: http://commons.wikimedia.org/wiki/File:H%C3%A9liodore_2_%28Russie%29_.jpg; License: CC BY-NC 3.0

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