Textbook Question
Imagine the primitive cubic lattice. Now imagine pushing on top of it, straight down. Next, stretch another face by pulling it to the right. All angles remain 90°. What kind of primitive lattice have you made?
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Ch.12 - Solids and Modern Materials
Chapter 12, Problem 109
For each of the intermetallic compounds shown in Figure 12.17 determine the number of each type of atom in the unit cell. Do your answers correspond to the ratios expected from the empirical formulas: Ni3Al?
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Cell
A unit cell is the smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal. It defines the arrangement of atoms in three-dimensional space and is characterized by its dimensions and the types of atoms it contains. Understanding the unit cell is crucial for determining the composition and properties of crystalline materials.
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01:27
Simple Cubic Unit Cell
Empirical Formula
An empirical formula represents the simplest whole-number ratio of atoms of each element in a compound. For example, the empirical formula Ni3Al indicates that for every three nickel (Ni) atoms, there is one aluminum (Al) atom. This concept is essential for analyzing the composition of intermetallic compounds and verifying if the observed atomic ratios in the unit cell match the expected ratios from the empirical formula.
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02:26Empirical vs Molecular Formula
Face-Centered Cubic (FCC) Structure
The face-centered cubic (FCC) structure is a type of crystal lattice where atoms are located at each corner and the centers of all the cube faces. This arrangement allows for a high packing efficiency and is common in metals. Understanding the FCC structure is important for determining the number of atoms per unit cell and how they relate to the empirical formula of intermetallic compounds like Ni3Al.
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00:51Face Centered Cubic Example
Related Practice
Textbook Question
Pure iron crystallizes in a body-centered cubic structure, shown in the figure. but small amounts of impurities can stabilize a facecentered cubic structure. Which form of iron has a higher density?
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Textbook Question
Introduction of carbon into a metallic lattice generally results
in a harder, less ductile substance with lower electrical
and thermal conductivities. Explain why this might be so.
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Textbook Question
What type of lattice—primitive cubic, body-centered cubic, or face-centered cubic—does each of the following structure types possess: (e) ZnS?
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Textbook Question
Silicon carbide, SiC, has the three-dimensional structure shown in the figure.
(b) Would you expect the bonding in SiC to be predominantly ionic, metallic, or covalent?
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Textbook Question
Energy bands are considered continuous due to the large number of closely spaced energy levels. The range of energy levels in a crystal of copper is approximately 1 * 10–19 J. Assuming equal spacing between levels, the spacing between energy levels may be approximated by dividing the range of energies by the number of atoms in the crystal. (b) Determine the average spacing in J between energy levels in the copper metal in part (a).
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