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Do both unit cells shown below represent the same compound? Titanium Calcium Охygen

Do both unit cells shown below represent the same compound? Titanium Calcium Охygen

Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
10th Edition
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Chapter12: The Solid State
Section12.1: Crystal Lattices And Unit Cells
Problem 12.1CYU: (a) Determining an Atom Radius from Lattice Dimensions: Gold has a face-centered unit cell, and its...
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### Do both unit cells shown below represent the same compound? #### Unit Cell Diagrams In the figure below, two unit cell structures are displayed side by side. Each diagram represents a crystallographic unit cell, which is the smallest repeating unit that constitutes the entire crystal structure. The coloring scheme for the atoms in the unit cells is as follows: - **Titanium:** Represented by grey spheres. - **Calcium:** Represented by yellow spheres. - **Oxygen:** Represented by red spheres. #### Explanation of Each Unit Cell **1. Left Unit Cell:** - Composition: - The corners of the unit cell are occupied by yellow spheres (Calcium). - Inside the unit cell, red spheres (Oxygen) are placed at the face centers and body-centered positions. - Grey spheres (Titanium) are located inside the unit cell but not at symmetrical positions. **2. Right Unit Cell:** - Composition: - The corners and the centers of the faces of the unit cell are occupied by red spheres (Oxygen), forming an arrangement of atoms in the cubic structure. - Grey spheres (Titanium) are positioned at the face centers. - A single yellow sphere (Calcium) is centered inside the cell. #### Analysis To determine whether both unit cells represent the same compound, we need to evaluate the relative positions of Titanium, Calcium, and Oxygen atoms in each structure. The arrangement and connectivity of these atoms must be consistent across both unit cells for them to represent the same compound. #### Conclusion Both unit cells illustrate different arrangements of Titanium, Calcium, and Oxygen atoms, which need further examination to conclude if they form the same compound or different compounds. Comparing their atomic ratios, lattice constants, and symmetry will provide additional insights into their crystallographic equivalence.
Transcribed Image Text:### Do both unit cells shown below represent the same compound? #### Unit Cell Diagrams In the figure below, two unit cell structures are displayed side by side. Each diagram represents a crystallographic unit cell, which is the smallest repeating unit that constitutes the entire crystal structure. The coloring scheme for the atoms in the unit cells is as follows: - **Titanium:** Represented by grey spheres. - **Calcium:** Represented by yellow spheres. - **Oxygen:** Represented by red spheres. #### Explanation of Each Unit Cell **1. Left Unit Cell:** - Composition: - The corners of the unit cell are occupied by yellow spheres (Calcium). - Inside the unit cell, red spheres (Oxygen) are placed at the face centers and body-centered positions. - Grey spheres (Titanium) are located inside the unit cell but not at symmetrical positions. **2. Right Unit Cell:** - Composition: - The corners and the centers of the faces of the unit cell are occupied by red spheres (Oxygen), forming an arrangement of atoms in the cubic structure. - Grey spheres (Titanium) are positioned at the face centers. - A single yellow sphere (Calcium) is centered inside the cell. #### Analysis To determine whether both unit cells represent the same compound, we need to evaluate the relative positions of Titanium, Calcium, and Oxygen atoms in each structure. The arrangement and connectivity of these atoms must be consistent across both unit cells for them to represent the same compound. #### Conclusion Both unit cells illustrate different arrangements of Titanium, Calcium, and Oxygen atoms, which need further examination to conclude if they form the same compound or different compounds. Comparing their atomic ratios, lattice constants, and symmetry will provide additional insights into their crystallographic equivalence.
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