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Perovskite, an oxide mineral, is shown below. The light gray spheres are oxygen anions in edge positions. The dark spheres are calcium cations in corner positions. The small sphere in the body is a titanium cation.   1.  What type of unit cell do the calcium ions define? 2.  What is the empirical formula of the ionic compound formed by calcium, titanium, and oxygen? 3. If the edge length of the unit cell is 3.84Å, what is the density of perovskite (g/cm3)?

Perovskite, an oxide mineral, is shown below. The light gray spheres are oxygen anions in edge positions. The dark spheres are calcium cations in corner positions. The small sphere in the body is a titanium cation.   1.  What type of unit cell do the calcium ions define? 2.  What is the empirical formula of the ionic compound formed by calcium, titanium, and oxygen? 3. If the edge length of the unit cell is 3.84Å, what is the density of perovskite (g/cm3)?

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Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Perovskite, an oxide mineral, is shown below. The light gray spheres are oxygen anions in edge positions. The dark spheres are calcium cations in corner positions. The small sphere in the body is a titanium cation.

 

1.  What type of unit cell do the calcium ions define?

2.  What is the empirical formula of the ionic compound formed by calcium, titanium, and oxygen?

3. If the edge length of the unit cell is 3.84Å, what is the density of perovskite (g/cm3)?

  1.  
### Band Structure of Graphene **Description:** The image illustrates a model of the band structure of graphene. Graphene is a single layer of carbon atoms arranged in a two-dimensional honeycomb lattice. The specific arrangement of the atoms in this model helps to explain some of its remarkable electronic properties. **Model Explanation:** - **Nodes and Colors:** - The red and blue spheres represent carbon atoms in the graphene lattice. - The green sphere at the center represents a point of overlap or intersection in the model, showing where the band structures meet. - **Connections:** - The black lines connecting the spheres represent the covalent bonds between carbon atoms. - The intricate pattern of connections highlights the hexagonal geometry of graphene, where each carbon atom is bonded to three other carbon atoms. - **Geometrical Layers:** - The outer layer formed by red spheres signifies the outer edges of the graphene sheet. - The inner layer formed by blue spheres aids in visualizing the layer of carbon atoms beneath the outer shell. - The triangulated internal structure emphasizes the symmetrical nature of the lattice. Understanding the band structure of graphene is crucial for predictions of electrical, thermal, and optical properties. The geometrical representations in this image offer insights into how electrons behave in the graphene lattice and help explain why graphene is an excellent conductor of electricity. Further study into this model assists in the exploration of new materials and the potential applications of graphene in various fields, including electronics, material science, and nanotechnology. _For more detailed educational content, please refer to our sections on Carbon Nanomaterials and Quantum Physics._
Transcribed Image Text:### Band Structure of Graphene **Description:** The image illustrates a model of the band structure of graphene. Graphene is a single layer of carbon atoms arranged in a two-dimensional honeycomb lattice. The specific arrangement of the atoms in this model helps to explain some of its remarkable electronic properties. **Model Explanation:** - **Nodes and Colors:** - The red and blue spheres represent carbon atoms in the graphene lattice. - The green sphere at the center represents a point of overlap or intersection in the model, showing where the band structures meet. - **Connections:** - The black lines connecting the spheres represent the covalent bonds between carbon atoms. - The intricate pattern of connections highlights the hexagonal geometry of graphene, where each carbon atom is bonded to three other carbon atoms. - **Geometrical Layers:** - The outer layer formed by red spheres signifies the outer edges of the graphene sheet. - The inner layer formed by blue spheres aids in visualizing the layer of carbon atoms beneath the outer shell. - The triangulated internal structure emphasizes the symmetrical nature of the lattice. Understanding the band structure of graphene is crucial for predictions of electrical, thermal, and optical properties. The geometrical representations in this image offer insights into how electrons behave in the graphene lattice and help explain why graphene is an excellent conductor of electricity. Further study into this model assists in the exploration of new materials and the potential applications of graphene in various fields, including electronics, material science, and nanotechnology. _For more detailed educational content, please refer to our sections on Carbon Nanomaterials and Quantum Physics._
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