Crystal Structures and Platinum Quiz

Questions and Answers

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

0.64

0.74

0.52

0.68 (correct)

Which material is commonly associated with face-centered cubic (FCC) structures?

Tantalum

Chromium (Cr)

Iron (Fe)

Copper (Cu) (correct)

In a body-centered cubic (BCC) unit cell, how many total atoms are there?

2 (correct)

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

12 Signup and view all the answers

In a BCC structure, what fraction of an atom is contributed by each corner atom?

1/8 Signup and view all the answers

What is the coordination number of atoms in a simple cubic structure?

6 Signup and view all the answers

Which metallic crystal structure is characterized by atoms touching each other along cube diagonals?

Body Centered Cubic Signup and view all the answers

Which statement correctly describes the atomic packing factor (APF) for a simple cubic structure?

APF is 0.52 Signup and view all the answers

What is a primary reason for the dense packing of metallic crystal structures?

Small nearest neighbor distances Signup and view all the answers

Which type of unit cell structure is rare due to its low packing density?

Simple Cubic Signup and view all the answers

What is the volume of atoms contained in one unit cell for a simple cubic structure?

1 atom Signup and view all the answers

What is a defining characteristic of metallic bonding that contributes to dense packing?

Bonding is not directional. Signup and view all the answers

The atomic packing factor (APF) is calculated using which formula?

Volume of atoms in unit cell / Volume of unit cell Signup and view all the answers

What is the total number of atoms per unit cell in a face-centered cubic (FCC) structure?

4 Signup and view all the answers

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

0.74 Signup and view all the answers

In a face-centered cubic structure, which of the following represents the stacking sequence?

ABCABC... Signup and view all the answers

What is the relationship between the edge length (a) of the unit cell and the atomic radius (R) in a close-packed direction for FCC?

$4R = 2a$ Signup and view all the answers

What is the stacking sequence of a hexagonal close-packed (HCP) structure?

ABABAB... Signup and view all the answers

How many corner atoms contribute to the total atom count in a face-centered cubic unit cell?

8 corner atoms Signup and view all the answers

Which of the following describes the volume of the unit cell in terms of atomic radius for FCC?

$a^3$ Signup and view all the answers

Which geometric structure corresponds to the arrangement of atoms in a FCC crystal system?

Cubic Signup and view all the answers

What is the atomic packing factor (APF) for hexagonal close-packed structures?

0.74 Signup and view all the answers

Which of the following materials demonstrates a body-centered cubic (BCC) structure?

Cr Signup and view all the answers

In the theoretical density formula, what does the variable 'n' represent?

The number of atoms per unit cell Signup and view all the answers

What is the formula to calculate the length 'a' of the unit cell in relation to the radius 'R' for a BCC structure?

a = 4R/3 Signup and view all the answers

What is the theoretical density of the example material given (molecular weight of 52.00 g/mol, n = 2, R = 0.125 nm)?

7.18 g/cm³ Signup and view all the answers

Which material is known for having a low packing density and often consists of lighter elements?

Polymers Signup and view all the answers

What is a key characteristic of single crystals compared to polycrystals?

Properties of single crystals vary with direction. Signup and view all the answers

Which of the following materials is specifically mentioned as being used for abrasives?

Diamond Signup and view all the answers

What type of materials typically exhibit intermediate packing density?

Composites Signup and view all the answers

Which statement about the packing density of materials is true?

Materials with lower density often consist of lighter elements. Signup and view all the answers

How does quartz behave compared to other crystals?

Quartz fractures more easily along certain crystal planes. Signup and view all the answers

Which of the following is NOT a characteristic of polymers?

High packing density Signup and view all the answers

What material is typically used in applications requiring high strength, such as turbine blades?

Single Crystals Signup and view all the answers

Study Notes

Platinum and Its Structure

Platinum is a noble metal characterized by a dense, metallic crystal structure.
Scanning Tunneling Microscope (STM) allows for detailed visualization of the platinum surface at the atomic level.
Platinum's crystal lattice influences its various applications in electronics, jewelry, and catalysis.

Crystal Lattice and Unit Cells

Unit cells are the smallest repeating units in a crystal lattice that define its structure.
Different types of lattices lead to varied physical properties in materials.

Metallic Crystal Structures

Dense packing in metallic structures arises from uniform atomic radii, non-directional metallic bonding, short nearest neighbor distances, and electron cloud shielding.
These structures are often the simplest among crystal forms, allowing for efficient packing of atoms.

Simple Cubic Structure (SC)

Rare structure found only in polonium (Po) due to low packing density.
Coordination number of 6, indicating each atom is surrounded by six neighbors.
Atomic Packing Factor (APF) for SC is 0.52.

Body Centered Cubic Structure (BCC)

In BCC, atoms contact along cube diagonals, providing a coordination number of 8.
Common elements include chromium (Cr), tungsten (W), and iron (Fe).
APF for BCC is 0.68.

Face Centered Cubic Structure (FCC)

Atoms in FCC arrange themselves along face diagonals, resulting in a high coordination number of 12.
Commonly found in elements like aluminum (Al), copper (Cu), and platinum (Pt).
APF for FCC is 0.74, representing the maximum achievable packing efficiency.

Close-Packing Sequences

FCC stacking sequence follows an ABCABC... pattern, while hexagonal close-packed (HCP) structure follows an ABAB... sequence.
Both structures have a coordination number of 12 and an APF of 0.74.

Hexagonal Close-Packed Structure (HCP)

Consists of six atoms per unit cell and is characterized by a specific height-to-width ratio (c/a = 1.633).
Examples include cadmium (Cd), magnesium (Mg), and titanium (Ti).

Theoretical Density of Crystals

Density can be calculated using atomic weight, atom radius, and the number of atoms per unit cell.
For example, chromium (BCC) has a theoretical density of 7.18 g/cm³, closely matching its actual density of 7.19 g/cm³.

Miller Indices

A notation system in crystallography used to denote the orientation of planes in a crystal lattice.
Essential for interpreting x-ray diffraction patterns which provide insights into crystal structure.

Applications of Crystal Structures

Single crystals, such as diamond, are crucial for various engineering applications due to their unique properties.
Anisotropic nature of single crystals leads to directional dependencies in mechanical and thermal properties.

Comparison of Single vs. Polycrystalline Structures

Single crystals exhibit varied properties based on orientation (anisotropic), while polycrystalline materials possess averaged properties (isotropic).
Each structure type offers distinct advantages in different applications, influencing material selection.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your knowledge on the crystal structure of platinum, including its surface properties and unit cells. This quiz covers essential concepts such as reciprocal lattices and types of lattices found in three-dimensional structures. Perfect for students studying material science or crystallography.