we know that metal or non-metallic materials can be identified by examining the Fermi surface and solid bands. According to this information, Cu crystallizes in FCC structure and has about 1 free electron in its unit cell. Diamond (or Si) has an FCC crystal lattice while it has about 8 electrons in its unit cell. Graphene has 2 free electrons. In the light of this information, what can you say about Cu, Diamond and Graphene about whether they are metallic or not?

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### Understanding Metal and Non-Metal Classification through Fermi Surfaces and Solid Bands

Metal or non-metallic materials can be identified by examining specific characteristics such as the **Fermi surface** and **solid bands**. Here's a detailed explanation based on different materials:

#### Copper (Cu)

- **Structure**: Copper crystallizes in an *FCC (Face-Centered Cubic)* structure.
- **Electrons**: It has about *1 free electron* in its unit cell.

#### Diamond (or Silicon)

- **Structure**: Diamond (or Silicon) also forms an *FCC crystal lattice*.
- **Electrons**: It contains about *8 electrons* in its unit cell.

#### Graphene

- **Structure**: Not specifically stated, but derives from graphite, typically known for its *hexagonal lattice structure*.
- **Electrons**: Graphene has *2 free electrons*.

### Analysis

Given this information, we can infer the following about the metallic nature of these materials:

- **Copper (Cu)**: With a crystalline FCC structure and 1 free electron, Copper behaves as a **metal** due to the presence of free electrons which facilitate electrical conductivity.
- **Diamond (or Silicon)**: Despite having an FCC lattice, it has 8 electrons bound within its structure, making it a **non-metal**. This configuration results in a lack of free electrons necessary for electrical conductivity.
- **Graphene**: With its 2 free electrons, Graphene exhibits some metallic characteristics, leading to it being classified as a **semi-metal**. This unique electronic structure makes Graphene highly conductive and gives it metallic properties under certain conditions.

### Conclusion

By analyzing the structure and electron configuration, we conclude that Copper is metallic, Diamond (or Silicon) is non-metallic, and Graphene holds properties of a semi-metal.
Transcribed Image Text:### Understanding Metal and Non-Metal Classification through Fermi Surfaces and Solid Bands Metal or non-metallic materials can be identified by examining specific characteristics such as the **Fermi surface** and **solid bands**. Here's a detailed explanation based on different materials: #### Copper (Cu) - **Structure**: Copper crystallizes in an *FCC (Face-Centered Cubic)* structure. - **Electrons**: It has about *1 free electron* in its unit cell. #### Diamond (or Silicon) - **Structure**: Diamond (or Silicon) also forms an *FCC crystal lattice*. - **Electrons**: It contains about *8 electrons* in its unit cell. #### Graphene - **Structure**: Not specifically stated, but derives from graphite, typically known for its *hexagonal lattice structure*. - **Electrons**: Graphene has *2 free electrons*. ### Analysis Given this information, we can infer the following about the metallic nature of these materials: - **Copper (Cu)**: With a crystalline FCC structure and 1 free electron, Copper behaves as a **metal** due to the presence of free electrons which facilitate electrical conductivity. - **Diamond (or Silicon)**: Despite having an FCC lattice, it has 8 electrons bound within its structure, making it a **non-metal**. This configuration results in a lack of free electrons necessary for electrical conductivity. - **Graphene**: With its 2 free electrons, Graphene exhibits some metallic characteristics, leading to it being classified as a **semi-metal**. This unique electronic structure makes Graphene highly conductive and gives it metallic properties under certain conditions. ### Conclusion By analyzing the structure and electron configuration, we conclude that Copper is metallic, Diamond (or Silicon) is non-metallic, and Graphene holds properties of a semi-metal.
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