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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?

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?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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