Unit Cells and Metallic Crystal Structures Quiz

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Questions and Answers

What describes a face-centered cubic crystal structure?

Atoms are arranged in a non-repetitive pattern

Atoms are randomly scattered throughout the structure

Atoms are situated in a repeating array over large distances (correct)

Atoms are only arranged in a linear pattern

What is a lattice in the context of crystal structures?

A disordered arrangement of atoms

A three-dimensional array of points coinciding with atom positions (correct)

A two-dimensional array of points coinciding with atom positions

The number of electrons present in a crystal lattice

What is the atomic structure of a face-centered cubic crystal lattice?

All atoms are arranged in a linear pattern

Each atom is isolated and not connected to neighboring atoms

Atoms are randomly scattered throughout the lattice

Atoms are located at the corners and centers of each face of the cube (correct)

How do atoms arrange themselves in an amorphous material?

In a non-repetitive pattern with short-range order Signup and view all the answers

What is the main difference between crystalline and amorphous materials?

Amorphous materials lack periodic arrangements of atoms Signup and view all the answers

What does 'long-range order' refer to in crystal structures?

The periodic arrangement of atoms over large atomic distances Signup and view all the answers

What is the relationship between the cube edge length (a) and the atomic radius (R) in a face-centered cubic (FCC) crystal structure?

a = 2R √2 Signup and view all the answers

What is the coordination number for a face-centered cubic (FCC) crystal structure?

12 Signup and view all the answers

How many atoms are assigned to a given unit cell in a face-centered cubic (FCC) crystal structure?

4 Signup and view all the answers

What is the purpose of a unit cell in a crystal structure?

It is the smallest repeating unit that makes up the crystal structure. Signup and view all the answers

Which of the following metals does NOT have a face-centered cubic (FCC) crystal structure?

Iron Signup and view all the answers

What is the atomic packing factor (APF) for a face-centered cubic (FCC) crystal structure?

APF = volume of atoms in a unit cell / total unit cell volume Signup and view all the answers

In a body-centered cubic (BCC) crystal structure, what is the relationship between the unit cell edge length (a) and the atomic radius (R)?

$a = 4R/\sqrt{3}$ Signup and view all the answers

For a hexagonal close-packed (HCP) crystal structure, what is the ideal ratio of the lattice parameters c and a?

$c/a = 1.633$ Signup and view all the answers

In a face-centered cubic (FCC) crystal structure, how many atoms are present in a conventional unit cell?

4 Signup and view all the answers

What is the atomic packing factor (APF) for a body-centered cubic (BCC) crystal structure?

0.68 Signup and view all the answers

If the atomic radius of iron (Fe) is 0.124 nm and its crystal structure is body-centered cubic (BCC), what is the length of the unit cell edge (a)?

$0.287\text{ nm}$ Signup and view all the answers

Which of the following crystal structures has the highest atomic packing factor?

Hexagonal close-packed (HCP) Signup and view all the answers

Study Notes

Atomic Structure

Protons are positively charged, neutrons are neutral, and electrons are negatively charged.
The nucleus of a hydrogen atom contains one proton and one electron in the 1st shell.
Charge magnitude is 1.60 x 10^-19 Columb.
Atomic number (Z) is the number of protons in the nucleus, which is the same for all atoms of the same element.
Mass of a proton or neutron is 1.67 x 10^-27 kg, and mass of an electron is 9.11 x 10^-31 kg.
Atomic mass (A) is the sum of the mass of protons and neutrons within a nucleus.

Crystalline Solids

Crystalline materials have atoms arranged in a repeating or periodic array over large atomic distances.
Examples of crystalline materials include metals, ceramics, and some polymers.
Amorphous materials have short-range order of atoms, but are not periodic.

Crystal Structure

Crystal structure refers to the 3D arrangement of atoms, ions, or molecules.
Lattice is a 3D array of points coinciding with atom positions (or sphere centers).
Unit cells are small repeat entities within the whole structure, typically parallelepipeds or prisms.
Face-centered cubic (FCC) crystal structure has a coordination number of 12, and an atomic packing factor (APF) of volume of atoms in a unit cell / total unit cell volume.

FCC Crystal Structure

FCC has a unit cell of cubic geometry, with atoms located at each of the corners and the centers of all the cube faces.
Examples of metals with FCC structure include copper, aluminum, silver, lead, nickel, platinum, and gold.
The aggregate of atoms in the unit cell represents a section of crystal consisting of many FCC unit cells.

Body-Centered Cubic (BCC) Crystal Structure

BCC crystal structure has a unit cell edge length (a) and atomic radius (R) related by 𝑎 = 4𝑅 / √3.
The atomic packing factor for BCC is 0.68.

Hexagonal Close-Packed (HCP) Crystal Structure

HCP crystal structure has an ideal c/a ratio of 1.633.
The atomic packing factor for HCP is 0.74.

Density Computations

Iron has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol.
Theoretical density of iron can be computed and compared to the experimental value of 7.87 g/cm³.
Radius of an iridium atom can be calculated given its FCC crystal structure, density of 22.4 g/cm³, and atomic weight of 192.2 g/mol.
Radius of a vanadium atom can be calculated given its BCC crystal structure, density of 5.96 g/cm³, and atomic weight of 50.9 g/mol.

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Description

This quiz covers different types of unit cells and metallic crystal structures, including face-centered cubic crystal structures. Learn about the small repeat entities within the whole structure and how they are represented in parallelepipeds or prisms.