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Chapter 12: Problem 105

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 \(90^{\circ} .\) What kind of primitive lattice have you made?

Short Answer

Expert verified
After applying the transformations of pushing from the top and stretching a face horizontally to the initial cubic lattice, we obtain a primitive lattice with three different side lengths (\(a\), \(b\), and \(c\)) and all angles between them equal to \(90^{\circ}\). This results in an orthorhombic lattice.

Step by step solution

01

Identify the initial lattice type

Initially, we have a primitive cubic lattice. Its side lengths are equal (let's denote them as \(a\)), and the angles between these sides are all \(90^{\circ}\).
02

Transformation 1: Pushing from the top

We push the lattice from the top, straight down. This causes a compression of the lattice along the vertical axis, resulting in a shorter side length along this axis. Let's assume that the new length of this side is \(b\). Since we pushed straight down without any angular deviation, the angles between sides remain \(90^{\circ}\).
03

Transformation 2: Stretching a face to the right

Next, we stretch one of the faces horizontally by pulling it to the right. This transforms one of the remaining side lengths of the lattice. Let's assume that this new side length is \(c\). As mentioned, all angles between sides still remain \(90^{\circ}\).
04

Determine the transformed lattice type

Now, we have a primitive lattice with three different side lengths (\(a\), \(b\), and \(c\)) and all the angles between them equal to \(90^{\circ}\). This defines an orthorhombic lattice. Therefore, after applying the two transformations, the resulting primitive lattice is an orthorhombic lattice.

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Most popular questions from this chapter

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice? $(\mathbf{a}) 1,(\mathbf{b}) 2,(\mathbf{c}) 3,(\mathbf{d}) 4,(\mathbf{e}) 5 .$

Silver chloride (AgCl) adopts the rock salt structure. The density of \(\mathrm{AgCl}\) at \(25^{\circ} \mathrm{C}\) is $5.56 \mathrm{~g} / \mathrm{cm}^{3}$. Calculate the length of an edge of the AgCl unit cell.

Rhodium crystallizes in a face-centered cubic unit cell that has an edge length of \(0.381 \mathrm{nm}\). (a) Calculate the atomic radius of a rhodium atom. (b) Calculate the density of rhodium metal.

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Calculate the volume in \(\AA^{3}\) of each of the following types of cubic unit cells if it is composed of atoms with an atomic radius of \(182 \mathrm{pm}\). (a) primitive (b) face-centered cubic.
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