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Questions and Answers
What is the purpose of Miller indices in crystallography?
What information do the angles α, β, and γ provide in crystallography?
Which term refers to the group of three numbers that indicate the orientation of a plane in a crystal?
In Bravais lattices, how many fundamentally different types of unit cells exist?
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What did W.H. Miller devise in 1839 related to crystallography?
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What is the total number of Bravais lattices, including primitives and non-primitives?
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What did Max van Laue predict in 1912 regarding crystals and X-rays?
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Which scientist discovered that X-rays can be regularly reflected by successive atomic planes in a crystal?
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What is the condition for Bragg reflection to occur, as per Bragg's law?
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In X-ray diffraction, when do reflected rays interfere constructively?
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What does the Debye-Scherrer Method involve in X-ray diffraction?
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How does Bragg's law relate to the lattice parameters of a crystal?
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What is a lattice in the context of crystal structure?
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What is a basis in crystallography?
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What is the definition of a unit cell in crystallography?
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Which term refers to the number of atoms per unit cell?
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In crystallography, what do the parameters OX, OY, and OZ refer to?
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What is the Packing fraction formula for a unit cell with a radius $r = 3a/4$?
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Study Notes
Purpose of Miller Indices
- Miller indices provide a shorthand notation for identifying crystallographic planes and directions.
- They consist of three integers that denote the orientation of a plane in a crystal lattice.
Angles in Crystallography
- Angles α, β, and γ represent the interaxial angles between the crystal axes.
- They influence the geometry and symmetry of the crystal structure.
Orientation of a Plane in a Crystal
- The group of three numbers indicating the orientation of a plane in a crystal is called Miller indices.
Types of Unit Cells in Bravais Lattices
- There are 14 fundamentally different types of unit cells in Bravais lattices.
W.H. Miller's Contribution
- In 1839, W.H. Miller devised the system of Miller indices used for describing crystal orientations.
Total Number of Bravais Lattices
- Including both primitive and non-primitive lattices, there are a total of 14 Bravais lattices.
Max von Laue's Prediction
- In 1912, Max von Laue predicted that crystals could diffract X-rays, leading to the study of crystal structures.
Discovery of X-ray Reflection
- William Lawrence Bragg discovered that X-rays could be regularly reflected by successive atomic planes in a crystal.
Condition for Bragg Reflection
- Bragg's law states that constructive interference occurs when the path difference between reflected rays equals an integer multiple of the wavelength.
Constructive Interference in X-ray Diffraction
- Reflected rays interfere constructively when the conditions outlined by Bragg's law are met.
Debye-Scherrer Method
- The Debye-Scherrer Method is a technique used to analyze powdered crystals using X-ray diffraction.
Bragg's Law and Lattice Parameters
- Bragg's law relates the wavelengths of X-rays to the lattice spacing and angles within the crystal structure.
Lattice Definition
- A lattice is a periodic arrangement of points in space that represents the repeating unit of a crystal structure.
Basis in Crystallography
- A basis refers to the group of atoms associated with each lattice point in a crystal.
Definition of a Unit Cell
- A unit cell is the smallest repeating unit of a crystal lattice that reflects the overall symmetry and structure of the crystal.
Number of Atoms per Unit Cell
- The term "formula unit" indicates the number of atoms per unit cell.
Parameters OX, OY, and OZ
- OX, OY, and OZ refer to the coordinates along the respective crystal axes in crystallography.
Packing Fraction Formula
- The packing fraction formula for a unit cell with a radius $r = 3a/4$ calculates the volume occupied by atoms in relation to the volume of the unit cell.
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Description
Explore the concept of space lattice and basis in crystal structures. Learn about Bravais lattice, a hypothetical arrangement of points in space used to describe crystal structures. Understand the significance of basis, a collection of atoms with a fixed arrangement within a lattice.
