Sketch an fcc lattice unit cell (lattice constant =5 Å) with a monoatomic basis, and calculate t

Sketch an fcc lattice unit cell (lattice constant =5 Å) with...

Key Concepts

Face-Centered Cubic (FCC) Lattice

The FCC lattice is a common crystalline structure in which atoms are located at each of the eight corners of a cube and at the centers of each of the six faces. This arrangement maximizes packing efficiency and symmetry, leading to important implications for the material's mechanical and thermal properties.

Unit Cell

A unit cell is the smallest repeating structural element that fully encompasses the symmetry and arrangement of atoms within a crystal lattice. In the context of an FCC lattice, the unit cell includes portions of atoms from the corners and the face centers, which together contribute to the full atomic count per cell.

Lattice Constant

The lattice constant is the physical dimension of the edges of the unit cell in a crystal lattice. It defines the scale of the structure and is critical when calculating distances between atoms, planar spacings, and densities in crystallography.

Planar Density Calculation

Planar density refers to the number of atoms per unit area on a specific crystallographic plane. For the (110) plane in an FCC lattice, determining the atomic density involves identifying the effective number of atoms in the plane and dividing by the projected area, which is influenced by the geometry of the lattice and the lattice constant.

Atomic Density per Unit Volume

Atomic density per unit volume represents the number of atoms within a given volume of the crystal, often derived from the unit cell's dimensions and the total number of atoms it contains. In an FCC structure, this density is calculated by knowing the total atom count in the unit cell and the cell’s volume, which is a function of the lattice constant.

Interstitial Defects

Interstitial defects are imperfections in a crystal structure where extra atoms occupy positions in the lattice that are normally unoccupied, often in the interstices between the regularly arranged atoms. These defects can significantly alter the physical and chemical properties of the material, affecting diffusion and mechanical strength.

Transcript

00:02 Okay, so this question actually asks us to calculate the density, giving the information on the unit cell.

00:14 So it says the x has a body -centered cubic lattice.

00:19 So this is the first piece of information.

00:22 It's a cubic, and it has a body center, cubic body center.

00:29 And from here, what we can learn is how many atoms in one.

00:35 Unit cell.

00:37 We know for body centered, the atoms occupies the corner, all the corners, and each corner only accounts for one eighth of the atom.

00:50 There are eight corners in the cubes.

00:53 And also, the atom will also occupy the body center of the cube.

01:00 And that atom accounts for one atoms.

01:03 So in one unit cell, there are totally two atoms.

01:13 And the second piece of information gives us is the edge lens of this unit cell, which equals to 379 picometers.

01:27 And normally when we do the calculation, we need to convert it to meters.

01:33 So it's 10 to minus 12 meters.

01:41 And the third piece of information is an atomic mass, which given here is 1905 amu.

01:59 And of course, we have to convert it into the grams, which is 195 times 1 .67 times 10 .3.

02:13 To minus 24, and we can use the calculator to do the calculations.

02:20 195 times 1 .67, it actually equals to around 300 and 25 .65 times 10 minus 24 grams.

02:40 And now we get all the information we need to calculate the density...

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