Solid State Physics, FCC or BCC and why?

In summary, solid state physics is the study of the physical properties of solid materials and their microscopic components. FCC (face-centered cubic) and BCC (body-centered cubic) are two common crystal structures found in metals, which greatly influence the properties of a material. FCC structures tend to be more ductile and have higher melting points, while BCC structures are more brittle and have lower melting points. Some examples of materials with FCC and BCC structures include aluminum, copper, gold, iron, chromium, and tungsten. However, other factors such as impurities and defects can also affect the properties of a material.
  • #1
Alvis
9
1

Homework Statement


Based on sizes for Na(.97 Angstroms), Cs(1.67 Angstroms), and Cl(1.81 Angstroms), which lattice type would you expect for NaCl and CsCl and why?

Homework Equations


My equation for the hole size for a bcc is (4/sqrt(3))(radius)-2(radius), I assume you put in the radius of Cl in since the positive ions are the ones that fill the holes?

For fcc I got 2(sqrt(2))(radius)-2(radius), again, (assuming this equation is correct) I think you input the Cl as radius.

The Attempt at a Solution


So I know NaCl is supposed to be fcc and CsCl is bcc. For NaCl, I got the hole size (using fcc formula) to be 1.49 Angstroms and that is bigger than .97 Ang for Na.

For CsCl, I got the hole size to be 5.6x10^-11 using bcc forumula. The ion Cs is much bigger than the hole size which is what we want I believe.

I'm not sure NaCl and CsCl are the structure they are? my prof said it was based off of the hole size and my equation for bcc one is correct but not sure about fcc.
 
Physics news on Phys.org
  • #2


I would approach this problem by first looking at the sizes of the ions and the expected lattice types for each. NaCl is expected to have a face-centered cubic (fcc) lattice, while CsCl is expected to have a body-centered cubic (bcc) lattice.

To confirm this, I would calculate the hole sizes for each lattice using the equations provided. For NaCl, the hole size for fcc is 1.49 Angstroms, which is larger than the size of the Na ion (0.97 Angstroms). This suggests that the Na ions would not fit perfectly into the holes of the lattice, supporting the idea that NaCl has an fcc structure.

Similarly, for CsCl, the hole size for bcc is 5.6x10^-11 Angstroms, which is smaller than the size of the Cs ion (1.67 Angstroms). This indicates that the Cs ions would fit perfectly into the holes of the lattice, supporting the idea that CsCl has a bcc structure.

In conclusion, the sizes of the ions and the calculated hole sizes support the expected lattice types for NaCl and CsCl. However, it is always important to verify these assumptions through experimental data and further research.
 

Related to Solid State Physics, FCC or BCC and why?

1. What is solid state physics?

Solid state physics is the study of the physical properties of solid materials, such as metals, semiconductors, and insulators. It examines the behavior of electrons, atoms, and molecules within these materials and how they contribute to their macroscopic properties.

2. What is an FCC crystal structure?

FCC (face-centered cubic) is a common crystal structure found in metals, in which the lattice points are located at the corners and centers of each face of a cube. This results in a close-packed structure with a high packing efficiency, making it a stable and efficient arrangement for many metals.

3. What is a BCC crystal structure?

BCC (body-centered cubic) is another common crystal structure found in metals, in which the lattice points are located at the corners and one in the center of a cube. This results in a slightly less dense structure compared to FCC, but it still has a high packing efficiency and is a stable arrangement for many metals.

4. How do FCC and BCC structures affect the properties of materials?

The crystal structure of a material can greatly influence its physical and mechanical properties. For example, FCC structures tend to be more ductile and have higher melting points compared to BCC structures, which are typically more brittle and have lower melting points. This is due to the different ways in which the atoms are arranged and the resulting bonding between them.

5. What are some examples of materials with FCC or BCC structures?

FCC structures are commonly found in metals such as aluminum, copper, and gold. BCC structures are often seen in metals such as iron, chromium, and tungsten. However, it is important to note that not all materials with these structures exhibit the same properties, as other factors such as impurities and defects can also affect the overall properties of a material.

Similar threads

Solid State Physics: Draw the Dispersion Relation from the Fermi Surface
    • Advanced Physics Homework Help
Replies
1
Views
2K
How Does Compression Transform FCC Lattice to BCC and Affect Miller Indices?
    • Advanced Physics Homework Help
Replies
17
Views
6K
Solid state physics, lattice constants, ionic radii, nacl
    • Advanced Physics Homework Help
Replies
1
Views
5K
Packing fraction in ionic structure
    • Advanced Physics Homework Help
Replies
19
Views
4K
Solid state physics - FFC structure of NaCl
    • Advanced Physics Homework Help
Replies
1
Views
3K
Dispersion relation ~ modern phyics (solid state physics)
    • Introductory Physics Homework Help
Replies
1
Views
4K
Why is the volume of FCC and BCC different in reciprocal space?
    • Atomic and Condensed Matter
Replies
1
Views
29K
Solid State Physics: X-Ray scattering
    • Advanced Physics Homework Help
Replies
5
Views
1K
Solid State Physics | ionic crystal bonding | Born & Meyer equation
    • Advanced Physics Homework Help
Replies
1
Views
3K
I A question on elasticity from Kittel's Solid State Physics book
    • Atomic and Condensed Matter
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top