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	<updated>2026-10-17T06:42:08Z</updated>
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	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Bragg%27s_Law_and_Diffraction_Geometry&amp;diff=39320</id>
		<title>Bragg&#039;s Law and Diffraction Geometry</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Bragg%27s_Law_and_Diffraction_Geometry&amp;diff=39320"/>
		<updated>2025-04-11T03:19:51Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Create Bragg&amp;#039;s Law and Diffraction Geometry page&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Bragg&#039;s Law is a fundamental equation that describes the conditions under which X-rays are diffracted by the periodic atomic planes within a crystalline solid. It is essential to the interpretation of X-ray diffraction (XRD) data and underpins many techniques used in the structural analysis of materials.&lt;br /&gt;
&lt;br /&gt;
In conjunction with the geometric arrangement of incident and diffracted beams, Bragg’s Law enables the determination of crystallographic information such as interplanar spacing, lattice parameters, and crystal structure.&lt;br /&gt;
&lt;br /&gt;
=== Bragg’s Law ===&lt;br /&gt;
&lt;br /&gt;
Bragg’s Law is given by the equation:&lt;br /&gt;
nλ=2dsin⁡θ&lt;br /&gt;
&lt;br /&gt;
Where:&lt;br /&gt;
* n is the order of reflection (an integer),&lt;br /&gt;
* λ is the wavelength of the incident X-rays,&lt;br /&gt;
* d is the spacing between adjacent crystallographic planes,&lt;br /&gt;
* θ is the angle between the incident beam and the plane of reflection (the Bragg angle).&lt;br /&gt;
&lt;br /&gt;
This relation is derived from the condition for constructive interference of X-rays scattered from adjacent atomic planes. When the path difference between reflected X-ray beams is an integer multiple of the wavelength, the waves interfere constructively, producing an observable diffraction peak.&lt;br /&gt;
&lt;br /&gt;
=== Application in X-ray Diffraction (XRD) ===&lt;br /&gt;
Bragg’s Law is utilized in X-ray diffraction techniques to extract structural information from crystalline materials. When the Bragg condition is met for a specific set of lattice planes, a peak appears in the diffraction pattern. By analyzing these peaks, a wide range of material properties can be assessed.&lt;br /&gt;
==== Common Applications ====&lt;br /&gt;
* Phase Identification: Comparing measured peak positions to known reference patterns allows identification of crystalline phases.&lt;br /&gt;
* Lattice Parameter Determination: Precise measurements of diffraction angles enable calculation of unit cell dimensions.&lt;br /&gt;
* Crystallite Size and Microstrain: Broadening of diffraction peaks can be analyzed using the Scherrer equation and related methods.&lt;br /&gt;
* Texture and Orientation Analysis: Intensity variations reveal preferred crystallographic orientations within polycrystalline samples.&lt;br /&gt;
* Residual Stress Measurement: Shifts in diffraction peak positions can indicate strain in the crystal lattice.&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
[[Category:Theory]]&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39319</id>
		<title>Grain Boundaries</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39319"/>
		<updated>2025-03-09T20:21:05Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: /* Applications */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Structure ==&lt;br /&gt;
&lt;br /&gt;
Grain boundaries are interfaces where crystals of different orientations meet in a polycrystalline material. These boundaries are considered defects in the crystal structure, but they play a crucial role in determining the material&#039;s mechanical, electrical, and thermal properties. The structure and energy of grain boundaries depend on the misorientation between adjacent grains and the boundary plane&#039;s orientation.&lt;br /&gt;
&lt;br /&gt;
=== Low-Angle vs. High-Angle Grain Boundaries ===&lt;br /&gt;
Grain boundaries are broadly classified into two categories based on the misorientation angle between adjacent grains:&lt;br /&gt;
&lt;br /&gt;
# Low-Angle Grain Boundaries: These occur when the misorientation between adjacent grains is less than approximately 15 degrees. The boundary consists of an array of dislocations, which are line defects in the crystal lattice. The energy of low-angle boundaries is relatively low because the lattice distortion is localized around the dislocations.&lt;br /&gt;
# High-Angle Grain Boundaries: These occur when the misorientation exceeds approximately 15 degrees. High-angle boundaries are more complex and disordered, often resembling an amorphous structure. They have higher energy compared to low-angle boundaries and are more chemically active, making them prone to segregation of impurities and diffusion.&lt;br /&gt;
&lt;br /&gt;
=== Tilt Boundary ===&lt;br /&gt;
A tilt boundary is a type of grain boundary where the misorientation between adjacent grains is caused by a rotation about an axis that lies within the plane of the boundary. This results in a series of edge dislocations aligned along the boundary. Tilt boundaries are generally low-energy configurations because the lattice distortion can be accommodated by a wedge of atoms that supports the bending of the crystal lattice.&lt;br /&gt;
&lt;br /&gt;
=== Twist Boundary ===&lt;br /&gt;
A twist boundary is formed when the misorientation between adjacent grains results from a rotation about an axis perpendicular to the boundary plane. This type of boundary is characterized by a network of screw dislocations. Twist boundaries tend to have higher energy compared to tilt boundaries due to the more complex arrangement of dislocations.&lt;br /&gt;
&lt;br /&gt;
== Properties and Effects of Grain Boundaries ==&lt;br /&gt;
Grain boundaries significantly influence the properties of polycrystalline materials. Some key effects include:&lt;br /&gt;
&lt;br /&gt;
# Mechanical Properties: Grain boundaries act as barriers to dislocation motion, which strengthens the material (Hall-Petch effect). However, they can also serve as sites for crack initiation and propagation, reducing toughness.&lt;br /&gt;
# Diffusion and Segregation: Grain boundaries are pathways for rapid diffusion of atoms and impurities due to their disordered structure. This can lead to segregation of solute atoms at the boundaries, affecting the material&#039;s chemical and mechanical properties.&lt;br /&gt;
# Electrical and Thermal Conductivity: Grain boundaries scatter electrons and phonons, reducing electrical and thermal conductivity. This is particularly important in semiconductors and thermoelectric materials.&lt;br /&gt;
# Corrosion and Oxidation: Grain boundaries are often more chemically reactive than the grain interiors, making them susceptible to corrosion and oxidation.&lt;br /&gt;
&lt;br /&gt;
== Grain Boundary Engineering ==&lt;br /&gt;
Grain boundary engineering is a field focused on controlling the structure, distribution, and properties of grain boundaries to optimize material performance. Techniques include:&lt;br /&gt;
&lt;br /&gt;
# Thermomechanical Processing: Controlled rolling, annealing, and other processes are used to manipulate grain size and boundary character.&lt;br /&gt;
# Alloying: Adding specific elements can alter grain boundary energy and segregation behavior.&lt;br /&gt;
# Grain Boundary Characterization: Microscopy and spectroscopy techniques, such as electron backscatter diffraction (EBSD), are used to study grain boundary structure and properties.&lt;br /&gt;
&lt;br /&gt;
== Applications ==&lt;br /&gt;
* Metallurgy: Improving the strength, ductility, and corrosion resistance of metals and alloys.&lt;br /&gt;
* Semiconductors: Enhancing the performance of electronic devices by controlling grain boundary effects.&lt;br /&gt;
* Ceramics: Tailoring the mechanical and thermal properties of ceramic materials.&lt;br /&gt;
* Energy Materials: Optimizing grain boundaries in batteries, fuel cells, and thermoelectric materials for improved efficiency.&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
[[Category:Theory]]&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39318</id>
		<title>Grain Boundaries</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39318"/>
		<updated>2025-03-09T20:20:27Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Add to theory category&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Structure ==&lt;br /&gt;
&lt;br /&gt;
Grain boundaries are interfaces where crystals of different orientations meet in a polycrystalline material. These boundaries are considered defects in the crystal structure, but they play a crucial role in determining the material&#039;s mechanical, electrical, and thermal properties. The structure and energy of grain boundaries depend on the misorientation between adjacent grains and the boundary plane&#039;s orientation.&lt;br /&gt;
&lt;br /&gt;
=== Low-Angle vs. High-Angle Grain Boundaries ===&lt;br /&gt;
Grain boundaries are broadly classified into two categories based on the misorientation angle between adjacent grains:&lt;br /&gt;
&lt;br /&gt;
# Low-Angle Grain Boundaries: These occur when the misorientation between adjacent grains is less than approximately 15 degrees. The boundary consists of an array of dislocations, which are line defects in the crystal lattice. The energy of low-angle boundaries is relatively low because the lattice distortion is localized around the dislocations.&lt;br /&gt;
# High-Angle Grain Boundaries: These occur when the misorientation exceeds approximately 15 degrees. High-angle boundaries are more complex and disordered, often resembling an amorphous structure. They have higher energy compared to low-angle boundaries and are more chemically active, making them prone to segregation of impurities and diffusion.&lt;br /&gt;
&lt;br /&gt;
=== Tilt Boundary ===&lt;br /&gt;
A tilt boundary is a type of grain boundary where the misorientation between adjacent grains is caused by a rotation about an axis that lies within the plane of the boundary. This results in a series of edge dislocations aligned along the boundary. Tilt boundaries are generally low-energy configurations because the lattice distortion can be accommodated by a wedge of atoms that supports the bending of the crystal lattice.&lt;br /&gt;
&lt;br /&gt;
=== Twist Boundary ===&lt;br /&gt;
A twist boundary is formed when the misorientation between adjacent grains results from a rotation about an axis perpendicular to the boundary plane. This type of boundary is characterized by a network of screw dislocations. Twist boundaries tend to have higher energy compared to tilt boundaries due to the more complex arrangement of dislocations.&lt;br /&gt;
&lt;br /&gt;
== Properties and Effects of Grain Boundaries ==&lt;br /&gt;
Grain boundaries significantly influence the properties of polycrystalline materials. Some key effects include:&lt;br /&gt;
&lt;br /&gt;
# Mechanical Properties: Grain boundaries act as barriers to dislocation motion, which strengthens the material (Hall-Petch effect). However, they can also serve as sites for crack initiation and propagation, reducing toughness.&lt;br /&gt;
# Diffusion and Segregation: Grain boundaries are pathways for rapid diffusion of atoms and impurities due to their disordered structure. This can lead to segregation of solute atoms at the boundaries, affecting the material&#039;s chemical and mechanical properties.&lt;br /&gt;
# Electrical and Thermal Conductivity: Grain boundaries scatter electrons and phonons, reducing electrical and thermal conductivity. This is particularly important in semiconductors and thermoelectric materials.&lt;br /&gt;
# Corrosion and Oxidation: Grain boundaries are often more chemically reactive than the grain interiors, making them susceptible to corrosion and oxidation.&lt;br /&gt;
&lt;br /&gt;
== Grain Boundary Engineering ==&lt;br /&gt;
Grain boundary engineering is a field focused on controlling the structure, distribution, and properties of grain boundaries to optimize material performance. Techniques include:&lt;br /&gt;
&lt;br /&gt;
# Thermomechanical Processing: Controlled rolling, annealing, and other processes are used to manipulate grain size and boundary character.&lt;br /&gt;
# Alloying: Adding specific elements can alter grain boundary energy and segregation behavior.&lt;br /&gt;
# Grain Boundary Characterization: Microscopy and spectroscopy techniques, such as electron backscatter diffraction (EBSD), are used to study grain boundary structure and properties.&lt;br /&gt;
&lt;br /&gt;
== Applications ==&lt;br /&gt;
Understanding and controlling grain boundaries is critical in various applications, including:&lt;br /&gt;
* Metallurgy: Improving the strength, ductility, and corrosion resistance of metals and alloys.&lt;br /&gt;
* Semiconductors: Enhancing the performance of electronic devices by controlling grain boundary effects.&lt;br /&gt;
* Ceramics: Tailoring the mechanical and thermal properties of ceramic materials.&lt;br /&gt;
* Energy Materials: Optimizing grain boundaries in batteries, fuel cells, and thermoelectric materials for improved efficiency.&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
[[Category:Theory]]&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39317</id>
		<title>Grain Boundaries</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39317"/>
		<updated>2025-03-07T16:48:19Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Fix formatting&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Structure ==&lt;br /&gt;
&lt;br /&gt;
Grain boundaries are interfaces where crystals of different orientations meet in a polycrystalline material. These boundaries are considered defects in the crystal structure, but they play a crucial role in determining the material&#039;s mechanical, electrical, and thermal properties. The structure and energy of grain boundaries depend on the misorientation between adjacent grains and the boundary plane&#039;s orientation.&lt;br /&gt;
&lt;br /&gt;
=== Low-Angle vs. High-Angle Grain Boundaries ===&lt;br /&gt;
Grain boundaries are broadly classified into two categories based on the misorientation angle between adjacent grains:&lt;br /&gt;
&lt;br /&gt;
# Low-Angle Grain Boundaries: These occur when the misorientation between adjacent grains is less than approximately 15 degrees. The boundary consists of an array of dislocations, which are line defects in the crystal lattice. The energy of low-angle boundaries is relatively low because the lattice distortion is localized around the dislocations.&lt;br /&gt;
# High-Angle Grain Boundaries: These occur when the misorientation exceeds approximately 15 degrees. High-angle boundaries are more complex and disordered, often resembling an amorphous structure. They have higher energy compared to low-angle boundaries and are more chemically active, making them prone to segregation of impurities and diffusion.&lt;br /&gt;
&lt;br /&gt;
=== Tilt Boundary ===&lt;br /&gt;
A tilt boundary is a type of grain boundary where the misorientation between adjacent grains is caused by a rotation about an axis that lies within the plane of the boundary. This results in a series of edge dislocations aligned along the boundary. Tilt boundaries are generally low-energy configurations because the lattice distortion can be accommodated by a wedge of atoms that supports the bending of the crystal lattice.&lt;br /&gt;
&lt;br /&gt;
=== Twist Boundary ===&lt;br /&gt;
A twist boundary is formed when the misorientation between adjacent grains results from a rotation about an axis perpendicular to the boundary plane. This type of boundary is characterized by a network of screw dislocations. Twist boundaries tend to have higher energy compared to tilt boundaries due to the more complex arrangement of dislocations.&lt;br /&gt;
&lt;br /&gt;
== Properties and Effects of Grain Boundaries ==&lt;br /&gt;
Grain boundaries significantly influence the properties of polycrystalline materials. Some key effects include:&lt;br /&gt;
&lt;br /&gt;
# Mechanical Properties: Grain boundaries act as barriers to dislocation motion, which strengthens the material (Hall-Petch effect). However, they can also serve as sites for crack initiation and propagation, reducing toughness.&lt;br /&gt;
# Diffusion and Segregation: Grain boundaries are pathways for rapid diffusion of atoms and impurities due to their disordered structure. This can lead to segregation of solute atoms at the boundaries, affecting the material&#039;s chemical and mechanical properties.&lt;br /&gt;
# Electrical and Thermal Conductivity: Grain boundaries scatter electrons and phonons, reducing electrical and thermal conductivity. This is particularly important in semiconductors and thermoelectric materials.&lt;br /&gt;
# Corrosion and Oxidation: Grain boundaries are often more chemically reactive than the grain interiors, making them susceptible to corrosion and oxidation.&lt;br /&gt;
&lt;br /&gt;
== Grain Boundary Engineering ==&lt;br /&gt;
Grain boundary engineering is a field focused on controlling the structure, distribution, and properties of grain boundaries to optimize material performance. Techniques include:&lt;br /&gt;
&lt;br /&gt;
# Thermomechanical Processing: Controlled rolling, annealing, and other processes are used to manipulate grain size and boundary character.&lt;br /&gt;
# Alloying: Adding specific elements can alter grain boundary energy and segregation behavior.&lt;br /&gt;
# Grain Boundary Characterization: Microscopy and spectroscopy techniques, such as electron backscatter diffraction (EBSD), are used to study grain boundary structure and properties.&lt;br /&gt;
&lt;br /&gt;
== Applications ==&lt;br /&gt;
Understanding and controlling grain boundaries is critical in various applications, including:&lt;br /&gt;
* Metallurgy: Improving the strength, ductility, and corrosion resistance of metals and alloys.&lt;br /&gt;
* Semiconductors: Enhancing the performance of electronic devices by controlling grain boundary effects.&lt;br /&gt;
* Ceramics: Tailoring the mechanical and thermal properties of ceramic materials.&lt;br /&gt;
* Energy Materials: Optimizing grain boundaries in batteries, fuel cells, and thermoelectric materials for improved efficiency.&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39316</id>
		<title>Grain Boundaries</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39316"/>
		<updated>2025-03-07T16:46:14Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Update article&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Structure ==&lt;br /&gt;
&lt;br /&gt;
Grain boundaries are interfaces where crystals of different orientations meet in a polycrystalline material. These boundaries are considered defects in the crystal structure, but they play a crucial role in determining the material&#039;s mechanical, electrical, and thermal properties. The structure and energy of grain boundaries depend on the misorientation between adjacent grains and the boundary plane&#039;s orientation.&lt;br /&gt;
&lt;br /&gt;
=== Low-Angle vs. High-Angle Grain Boundaries ===&lt;br /&gt;
Grain boundaries are broadly classified into two categories based on the misorientation angle between adjacent grains:&lt;br /&gt;
&lt;br /&gt;
1. Low-Angle Grain Boundaries: These occur when the misorientation between adjacent grains is less than approximately 15 degrees. The boundary consists of an array of dislocations, which are line defects in the crystal lattice. The energy of low-angle boundaries is relatively low because the lattice distortion is localized around the dislocations.&lt;br /&gt;
&lt;br /&gt;
2. High-Angle Grain Boundaries: These occur when the misorientation exceeds approximately 15 degrees. High-angle boundaries are more complex and disordered, often resembling an amorphous structure. They have higher energy compared to low-angle boundaries and are more chemically active, making them prone to segregation of impurities and diffusion.&lt;br /&gt;
&lt;br /&gt;
=== Tilt Boundary ===&lt;br /&gt;
A tilt boundary is a type of grain boundary where the misorientation between adjacent grains is caused by a rotation about an axis that lies within the plane of the boundary. This results in a series of edge dislocations aligned along the boundary. Tilt boundaries are generally low-energy configurations because the lattice distortion can be accommodated by a wedge of atoms that supports the bending of the crystal lattice.&lt;br /&gt;
&lt;br /&gt;
=== Twist Boundary ===&lt;br /&gt;
A twist boundary is formed when the misorientation between adjacent grains results from a rotation about an axis perpendicular to the boundary plane. This type of boundary is characterized by a network of screw dislocations. Twist boundaries tend to have higher energy compared to tilt boundaries due to the more complex arrangement of dislocations.&lt;br /&gt;
&lt;br /&gt;
== Properties and Effects of Grain Boundaries ==&lt;br /&gt;
Grain boundaries significantly influence the properties of polycrystalline materials. Some key effects include:&lt;br /&gt;
&lt;br /&gt;
1. Mechanical Properties: Grain boundaries act as barriers to dislocation motion, which strengthens the material (Hall-Petch effect). However, they can also serve as sites for crack initiation and propagation, reducing toughness.&lt;br /&gt;
&lt;br /&gt;
2. Diffusion and Segregation: Grain boundaries are pathways for rapid diffusion of atoms and impurities due to their disordered structure. This can lead to segregation of solute atoms at the boundaries, affecting the material&#039;s chemical and mechanical properties.&lt;br /&gt;
&lt;br /&gt;
3. Electrical and Thermal Conductivity: Grain boundaries scatter electrons and phonons, reducing electrical and thermal conductivity. This is particularly important in semiconductors and thermoelectric materials.&lt;br /&gt;
&lt;br /&gt;
4. Corrosion and Oxidation: Grain boundaries are often more chemically reactive than the grain interiors, making them susceptible to corrosion and oxidation.&lt;br /&gt;
&lt;br /&gt;
== Grain Boundary Engineering ==&lt;br /&gt;
Grain boundary engineering is a field focused on controlling the structure, distribution, and properties of grain boundaries to optimize material performance. Techniques include:&lt;br /&gt;
&lt;br /&gt;
1. Thermomechanical Processing: Controlled rolling, annealing, and other processes are used to manipulate grain size and boundary character.&lt;br /&gt;
2. Alloying: Adding specific elements can alter grain boundary energy and segregation behavior.&lt;br /&gt;
3. Grain Boundary Characterization: Microscopy and spectroscopy techniques, such as electron backscatter diffraction (EBSD), are used to study grain boundary structure and properties.&lt;br /&gt;
&lt;br /&gt;
== Applications ==&lt;br /&gt;
Understanding and controlling grain boundaries is critical in various applications, including:&lt;br /&gt;
- Metallurgy: Improving the strength, ductility, and corrosion resistance of metals and alloys.&lt;br /&gt;
- Semiconductors: Enhancing the performance of electronic devices by controlling grain boundary effects.&lt;br /&gt;
- Ceramics: Tailoring the mechanical and thermal properties of ceramic materials.&lt;br /&gt;
- Energy Materials: Optimizing grain boundaries in batteries, fuel cells, and thermoelectric materials for improved efficiency.&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39314</id>
		<title>Grain Boundaries</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Grain_Boundaries&amp;diff=39314"/>
		<updated>2025-02-10T18:16:50Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Create and start work on Grain Boundaries page&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Grain boundaries are an interface between two different grains in a polycrystalline material. They are defects in the crystal structure that can significantly change the material&#039;s properties.&lt;br /&gt;
&lt;br /&gt;
== Structure ==&lt;br /&gt;
Generally, there are two different categories of grain boundaries: low-angle and high-angle. Low-angle boundaries occur when there is a misorientation of grains of generally less than 15 degrees. High-angle boundaries generally occur when the misorientation is greater than 15 degrees. These misorientations are different from the low-angle boundaries since the dislocations of the boundary are too small. These boundaries generally are more unstable than low-angle boundaries.&lt;br /&gt;
&lt;br /&gt;
=== Tilt Boundary ===&lt;br /&gt;
Tilt boundaries are formed when the misorientation is caused by the defect plane rotating about an axis parallel to the boundary plane. These boundaries are generally low energy, since the bending of the lattice can be supported by a wedge of supporting atoms. &lt;br /&gt;
&lt;br /&gt;
=== Twist Boundary ===&lt;br /&gt;
Twist boundaries occur when the rotation is perpendicular to the boundary plane.&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Band_Theory&amp;diff=39313</id>
		<title>Band Theory</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Band_Theory&amp;diff=39313"/>
		<updated>2025-01-27T22:49:33Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Add to theory category&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Band theory can help characterize different insulators, semi-conductors, and conductors. It provides a way to visualize how electrons behave in a material and why certain materials have specific electrical and thermal properties.&lt;br /&gt;
&lt;br /&gt;
== Principles ==&lt;br /&gt;
Electrons around an atom are organized into orbitals according to their discrete energy levels. These energy levels are quantized, and orbitals are filled starting from the lowest to the highest. However, in solid materials, these energy levels overlap causing energy bands to form. The spacing and size of these bands depend on the nature of the material and its atomic structure. Since there are effectively an infinite energy levels in an atom, there are an infinite number of potential bands. Among these, two important bands surrounding a band gap are given specific names:&lt;br /&gt;
&lt;br /&gt;
# Valence band: The valence band is the highest band that is fully occupied by electrons at 0 degrees kelvin. This band is composed of the valence orbitals of the atom.&lt;br /&gt;
# Conduction band: The conduction band is the lowest unoccupied band above the valence band. Electrons in this band are free to move and contribute to electrical conductivity. &lt;br /&gt;
&lt;br /&gt;
The band gap is the separation of the bands. The properties of this gap determine whether a material behaves as an insulator, semi-conductor, or conductor.&lt;br /&gt;
&lt;br /&gt;
# Insulator: An insulator&#039;s band gap is relatively &amp;quot;large&amp;quot;, and is typically greater than 4eV. The large gap prevents electrons from gaining enough energy to &amp;quot;jump&amp;quot; to the conduction band from the valence band, making the material a poor conductor.&lt;br /&gt;
&lt;br /&gt;
# Semi-conductor: A semi-conductor&#039;s band gap is &amp;quot;small&amp;quot;, ranging from 0.1eV to 4eV. This gap allows electrons that gain sufficient energy (thermally or optically) to jump to the conduction band and allowing conductivity. Semi-conductors can be doped to shift the band gap up or down.&lt;br /&gt;
&lt;br /&gt;
# Conductors: Conductors have no significant band gap and electrons can freely move between the valence and conduction band.&lt;br /&gt;
&lt;br /&gt;
== Band Theory and Material Properties ==&lt;br /&gt;
In addition to electrical conductivity, the behavior of electrons within bands also determines a material&#039;s properties such as its thermal conductivity and optical properties.&lt;br /&gt;
&lt;br /&gt;
# Thermal Conductivity: Free electrons within conductors contribute to heat transfer.&lt;br /&gt;
&lt;br /&gt;
# Optical Properties: The absorption and emission of light in semiconductors are tied to transitions between valence and electron bands. For example: materials with large energy band gaps that are insulators (such as glass) appear transparent, since the minimum energy required for the photoelectric effect is great, and absorbed light is simply remitted.&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
[[Category:Theory]]&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Band_Theory&amp;diff=39312</id>
		<title>Band Theory</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Band_Theory&amp;diff=39312"/>
		<updated>2025-01-27T22:45:52Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Refine and add additional section&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Band theory can help characterize different insulators, semi-conductors, and conductors. It provides a way to visualize how electrons behave in a material and why certain materials have specific electrical and thermal properties.&lt;br /&gt;
&lt;br /&gt;
== Principles ==&lt;br /&gt;
Electrons around an atom are organized into orbitals according to their discrete energy levels. These energy levels are quantized, and orbitals are filled starting from the lowest to the highest. However, in solid materials, these energy levels overlap causing energy bands to form. The spacing and size of these bands depend on the nature of the material and its atomic structure. Since there are effectively an infinite energy levels in an atom, there are an infinite number of potential bands. Among these, two important bands surrounding a band gap are given specific names:&lt;br /&gt;
&lt;br /&gt;
# Valence band: The valence band is the highest band that is fully occupied by electrons at 0 degrees kelvin. This band is composed of the valence orbitals of the atom.&lt;br /&gt;
# Conduction band: The conduction band is the lowest unoccupied band above the valence band. Electrons in this band are free to move and contribute to electrical conductivity. &lt;br /&gt;
&lt;br /&gt;
The band gap is the separation of the bands. The properties of this gap determine whether a material behaves as an insulator, semi-conductor, or conductor.&lt;br /&gt;
&lt;br /&gt;
# Insulator: An insulator&#039;s band gap is relatively &amp;quot;large&amp;quot;, and is typically greater than 4eV. The large gap prevents electrons from gaining enough energy to &amp;quot;jump&amp;quot; to the conduction band from the valence band, making the material a poor conductor.&lt;br /&gt;
&lt;br /&gt;
# Semi-conductor: A semi-conductor&#039;s band gap is &amp;quot;small&amp;quot;, ranging from 0.1eV to 4eV. This gap allows electrons that gain sufficient energy (thermally or optically) to jump to the conduction band and allowing conductivity. Semi-conductors can be doped to shift the band gap up or down.&lt;br /&gt;
&lt;br /&gt;
# Conductors: Conductors have no significant band gap and electrons can freely move between the valence and conduction band.&lt;br /&gt;
&lt;br /&gt;
== Band Theory and Material Properties ==&lt;br /&gt;
In addition to electrical conductivity, the behavior of electrons within bands also determines a material&#039;s properties such as its thermal conductivity and optical properties.&lt;br /&gt;
&lt;br /&gt;
# Thermal Conductivity: Free electrons within conductors contribute to heat transfer.&lt;br /&gt;
&lt;br /&gt;
# Optical Properties: The absorption and emission of light in semiconductors are tied to transitions between valence and electron bands. For example: materials with large energy band gaps that are insulators (such as glass) appear transparent, since the minimum energy required for the photoelectric effect is great, and absorbed light is simply remitted.&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Band_Theory&amp;diff=39311</id>
		<title>Band Theory</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Band_Theory&amp;diff=39311"/>
		<updated>2025-01-09T21:17:07Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Create Band Theory page&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:Page-under-construction.png|400px|thumb|left]]&lt;br /&gt;
&lt;br /&gt;
Band theory can help characterize different insulators, semi-conductors, and conductors. It provides a way to visualize how electrons behave in a material and why certain materials have specific electrical and thermal properties.&lt;br /&gt;
&lt;br /&gt;
== Principles ==&lt;br /&gt;
Electrons around an atom are organized into orbitals according to their discrete energy levels. These energy levels are quantized and orbitals are filled starting from the lowest. However, in solid materials, these energy levels overlap causing energy bands to form. How far apart and how large these bands are depend on the nature of the material and its atomic structure. Since there are infinite energy levels in an atom, there are an infinite number of bands. Two certain bands surrounding gap between bands are given names:&lt;br /&gt;
&lt;br /&gt;
# Valence band: The valence band is the closest band above the band gap. This band is composed of the valence orbitals of the atom.&lt;br /&gt;
# Conduction band: Conversely, the conduction is the closest band below the band gap. &lt;br /&gt;
&lt;br /&gt;
In insulators, the band gap between the valence and conduction bands is &amp;quot;large&amp;quot; and the bands do not overlap the Fermi level. In metals, the Fermi level overlaps at least one band. However, in semi-conductors, the Fermi level is contained within a band gap. While band gaps in insulators may contain the Fermi level, in semi-conductors, the gap between bands is &amp;quot;small&amp;quot;.&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Plasma_Sputtering&amp;diff=39302</id>
		<title>Plasma Sputtering</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Plasma_Sputtering&amp;diff=39302"/>
		<updated>2024-11-16T22:11:24Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Add short principles and applications sections&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:Page-under-construction.png|400px|thumb|left]]&lt;br /&gt;
{|class=&amp;quot;infobox&amp;quot;&lt;br /&gt;
!style=&amp;quot;font-size:135%;text-align:center;&amp;quot; | Cressington 108 Sputter Coater [https://sites.gatech.edu/mse-mill/sop/sputter-coater/ [SOP&amp;lt;nowiki&amp;gt;]&amp;lt;/nowiki&amp;gt;]&lt;br /&gt;
|-&lt;br /&gt;
|[[File:SputterCoater-052621.png|center|300px]]&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Available Targets&#039;&#039;&#039;: Gold&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
A simple and easy-to-use sputter coater for making samples surface’s more conductive for SEM imagery. A vacuum pump is attached to the sputter coater to achieve vacuum conditions and argon is used as the inert chamber gas. A full calibration has not yet been done on the sputter coater, but the thickness of samples is often changed by varying the time of the sputter.&lt;br /&gt;
&lt;br /&gt;
== Principle ==&lt;br /&gt;
Sputter coating a sample involves introducing argon gas into the chamber which is then ionized. Argon ions then impact the target (in this case, gold), causing them to eject and deposit onto the sample, resulting in a thin, uniform metallic layer.&lt;br /&gt;
&lt;br /&gt;
== Applications ==&lt;br /&gt;
Gold sputter coating is often used in sample preparation for SEM imaging. Non-conductive samples can build up charge in the SEM which prevents proper imaging of the sample. A gold surface coating provides a path for the electrons to ground. However, parts that are coated in gold can be harder to perform EDS on.&lt;br /&gt;
[[Category:Equipment|char]]&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
	<entry>
		<id>https://millwiki.mse.gatech.edu/index.php?title=Optical_Microscopy&amp;diff=39299</id>
		<title>Optical Microscopy</title>
		<link rel="alternate" type="text/html" href="https://millwiki.mse.gatech.edu/index.php?title=Optical_Microscopy&amp;diff=39299"/>
		<updated>2024-11-07T23:11:45Z</updated>

		<summary type="html">&lt;p&gt;Cpeterson70: Add information about optical microscopy&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[File:Page-under-construction.png|400px|thumb|left]]&lt;br /&gt;
{| class=&amp;quot;infobox&amp;quot;&lt;br /&gt;
!style=&amp;quot;font-size:135%;text-align:center;&amp;quot;| Leica DVM6 Digital Microscope [https://sites.gatech.edu/mse-mill/sop/digital-microscope/ [SOP&amp;lt;nowiki&amp;gt;]&amp;lt;/nowiki&amp;gt;]&lt;br /&gt;
|-&lt;br /&gt;
|[[File:LeicaOptical-052621.png|center|300px]]&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Objectives&#039;&#039;&#039; (diagonal FOV, in mm):&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&#039;&#039;&#039;- PlanAPO FOV 43.75&#039;&#039;&#039;&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- Max. magnification: 190x&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- Max. resolution: 415 lp/mm (2.4 μm)&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- Working distance (WD): 60 mm &lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&#039;&#039;&#039;- PlanAPO FOV 12.55&#039;&#039;&#039;&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- Max. magnification: 675x&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- Max. resolution: 1073 lp/mm (0.93 μm)&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- WD: 33 mm&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&#039;&#039;&#039;- PlanAPO FOV 3.60&#039;&#039;&#039;&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- Max. magnification: 2350x &lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- Max. resolution: 2366 lp/mm (0.42 μm)&lt;br /&gt;
|-&lt;br /&gt;
|&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;- WD: 5 mm&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Lens tilt range&#039;&#039;&#039;: ±60°&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Stage XY range&#039;&#039;&#039;: 70 mm x 50 mm&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Stage rotation range&#039;&#039;&#039;: ±180°&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Stage max load&#039;&#039;&#039;: 2 kg&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Illumination sources&#039;&#039;&#039;: 4-quadrant ring light, coaxial light&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Capabilities&#039;&#039;&#039;: XY Image stitching, Z-stack stitching&lt;br /&gt;
|-&lt;br /&gt;
|-&lt;br /&gt;
! style=&amp;quot;font-size:135%;text-align:center;&amp;quot; |AmScope Optical Stereomicroscope [https://sites.gatech.edu/mse-mill/sop/stereomicroscope/ [SOP&amp;lt;nowiki&amp;gt;]&amp;lt;/nowiki&amp;gt;]&lt;br /&gt;
|-&lt;br /&gt;
|[[File:StereoOptical-052621.png|center|300px]]&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Camera&#039;&#039;&#039;: DCM300&lt;br /&gt;
|-&lt;br /&gt;
|-&lt;br /&gt;
! style=&amp;quot;font-size:135%;text-align:center;&amp;quot; |Leica DMi8-M Inverted Microscope [https://sites.gatech.edu/mse-mill/sop/inverted-microscope/ [SOP&amp;lt;nowiki&amp;gt;]&amp;lt;/nowiki&amp;gt;]&lt;br /&gt;
|-&lt;br /&gt;
|[[File:InvertedMicroscope-062621.png|center|300px]]&lt;br /&gt;
|-&lt;br /&gt;
|&#039;&#039;&#039;Camera&#039;&#039;&#039;: Leica DMC2900&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Optical microscopy involves the use of visible light and a series of lenses to image samples at high magnifications and resolutions. Optical microscope can vary in functionality, design, and objectives used. &lt;br /&gt;
&lt;br /&gt;
==Principle==&lt;br /&gt;
Optical microscopy uses the interaction between visible light and the surface of the sample to create an image. A series of lenses can allow for the imaging of surface details normally invisible to the human eye.&lt;br /&gt;
&lt;br /&gt;
==Limitations==&lt;br /&gt;
Optical microscopes are often limited by light itself. Since optical microscopes observe visual light which has wavelengths from approximately 380 to 780 nanometers, a variety of limitations arrise.&lt;br /&gt;
&lt;br /&gt;
===Resolution===&lt;br /&gt;
The resolution of optical microscopes is limited by the diffraction limit of light, preventing them from imaging beyond a certain scale. In order to image at a lower scale, [[Scanning Electron Microscope (SEM)|scanning electron microscopy]] must be used.&lt;br /&gt;
&lt;br /&gt;
===Depth of Field===&lt;br /&gt;
Optical microscopes have limited depth of field due to the lenses used. This necessitates re-focusing on different heights of samples at higher magnifications. However, this limited depth of field can be used as an advantage, as described in [[#Focus/Z Stacking|Focus/Z Stacking]]. On the Leica DVM6, different objectives with different FOVs can be used to migate this issue, however there will still be issues depth of field issues at high magnifications.&lt;br /&gt;
&lt;br /&gt;
==Advantages and Useful Properties==&lt;br /&gt;
Although there are limitations while using optical microscopy, some properties of light can be taken advantage of.&lt;br /&gt;
&lt;br /&gt;
===Focus/Z Stacking===&lt;br /&gt;
Using the Leica DVM6 and it&#039;s software Leica LAS X, images of a sample can be taken at different focus heights in order to create a 3D reconstruction of the sample&#039;s surface. This 3D reconstruction can be used to measure different depths of surface features or distances between different locations on the surface. Additionally, this reconstruction can be exported as a 3D mesh for use outside the software.&lt;br /&gt;
&lt;br /&gt;
[[Category:Equipment|char]]&lt;/div&gt;</summary>
		<author><name>Cpeterson70</name></author>
	</entry>
</feed>