Distinguish among and sketch simple cubic, body-centered...

Name: Problem 84, Chapter 13: Chemistry
Uploaded: 2021-08-20T14:17:35-08:00
Duration: 4 min 5 s
Channel: Crystal Wang
Description: Distinguish among and sketch simple cubic, body-centered cubic (bcc), and face-centered cubic (fcc) lattices. Use CsCl, sodium, and nickel as examples of solids existing in simple cubic, bcc, and fcc lattices, respectively.

Distinguish among and sketch simple cubic, body-centered cubic (bcc), and face-centered cubic (fcc) lattices. Use CsCl, sodium, and nickel as examples of solids existing in simple cubic, bcc, and fcc lattices, respectively.

Key Concepts

Face-Centered Cubic (FCC) Lattice

A face-centered cubic lattice features lattice points at each of the cube's corners and at the centers of all six faces. This structure provides a high coordination number and the most efficient sphere packing among the three, often resulting in enhanced stability and distinct material properties.

Simple Cubic Lattice

A simple cubic lattice is the most basic crystal structure where lattice points are located only at the eight corners of a cube. This arrangement results in a low coordination number and relatively inefficient sphere packing.

Body-Centered Cubic (BCC) Lattice

A body-centered cubic lattice has lattice points at each corner of the cube as well as a single lattice point at the center of the cube. This configuration increases the coordination number compared to the simple cubic lattice, leading to a different spatial arrangement and packing efficiency.

Crystal Lattice

A crystal lattice is a three-dimensional, periodic arrangement of atoms, ions, or molecules in a solid. It defines the structure's overall symmetry and plays a crucial role in determining the material’s properties.

Unit Cell

The unit cell is the smallest repeating structural unit of a crystal lattice that, when translated along its axes, can reproduce the entire lattice. It encapsulates the fundamental geometric arrangement and symmetry of the solid.

Transcript

00:01 In this question, we're going to be sketching some of the different lattices.

00:10 So the first one is the unit cell simple cubic lattice.

00:16 So simple cubic lattice is as the name implies, the simplest kind of the unit cell lattice.

00:23 So what we're going to do is we will draw a square.

00:37 And then in this square, we're just going to put atoms in, of the corners so that is going to give us our simple cubic lattice so that's going to be the simplest unit cell that we have now let's look at the bcc the body centered cubic so for the body centered cubic we're just going to basically have the same thing except now there is an out of the middle so that's body center cube then we're going to do face -centric cubic so face so this is the same as a simple cubic.

01:18 Now we're just going to have atoms on each of the faces.

01:23 So they're kind of going to be halfway in between each of the faces.

01:29 Like they're sticking out and half of it's in the cube, half of it's out, basically.

01:36 So that is face centricubricubic.

01:39 So, all right, now let's use the example as given.

01:45 So cesium chloride is going to be in simple cube.

01:50 So remember simple cubic is just with the atoms in the corner.

01:59 All right.

02:00 So then i'm going to just draw the cesium as a smaller atom and chloride as a larger because chloride will be the larger one.

02:08 We're just going to have to show that these are alternating because remember that in an ionic lettuce, atoms will be alternating with each other...

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