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Consider the following statements about FCC and HCP crystal structure:
1. Both have same coordination number and atomic packing fraction.
2. Both represent closely packed crystal structures.
3. Both structures are generated by stacking of close packed plants on top of one another,but only the stacking sequence is different.
Which of the statements given above are correct?
1. Both have same coordination number and atomic packing fraction.
2. Both represent closely packed crystal structures.
3. Both structures are generated by stacking of close packed plants on top of one another,but only the stacking sequence is different.
Which of the statements given above are correct?
- a)1 and 2
- b)2 and 3
- c)1 and 3
- d)1, 2 and 3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the following statements about FCC and HCP crystal structure:...
1, 2 and 3
Explanation:
1. Both FCC (Face-Centered Cubic) and HCP (Hexagonal Close-Packed) structures have the same coordination number (12) and atomic packing fraction (0.74). Coordination number refers to the number of nearest neighbor atoms to a central atom, and atomic packing fraction refers to the proportion of volume occupied by atoms in a crystal structure.
2. Both FCC and HCP represent closely packed crystal structures, which means that the atoms are arranged in a way that minimizes empty space and maximizes the packing efficiency.
3. Both structures are indeed generated by stacking close-packed planes on top of one another. The difference between FCC and HCP lies in the stacking sequence. In FCC, the stacking sequence is ABCABC, while in HCP, the stacking sequence is ABAB. This difference in stacking sequence affects the overall symmetry and properties of the crystal structures.
Explanation:
1. Both FCC (Face-Centered Cubic) and HCP (Hexagonal Close-Packed) structures have the same coordination number (12) and atomic packing fraction (0.74). Coordination number refers to the number of nearest neighbor atoms to a central atom, and atomic packing fraction refers to the proportion of volume occupied by atoms in a crystal structure.
2. Both FCC and HCP represent closely packed crystal structures, which means that the atoms are arranged in a way that minimizes empty space and maximizes the packing efficiency.
3. Both structures are indeed generated by stacking close-packed planes on top of one another. The difference between FCC and HCP lies in the stacking sequence. In FCC, the stacking sequence is ABCABC, while in HCP, the stacking sequence is ABAB. This difference in stacking sequence affects the overall symmetry and properties of the crystal structures.
Most Upvoted Answer
Consider the following statements about FCC and HCP crystal structure:...
Statement 1: Both have the same coordination number and atomic packing fraction.
The coordination number refers to the number of nearest neighbors that each atom in a crystal structure has. In both the face-centered cubic (FCC) and hexagonal close-packed (HCP) structures, the coordination number is 12. This means that each atom is surrounded by 12 other atoms that are in direct contact with it.
The atomic packing fraction is a measure of how efficiently the atoms are packed in a crystal structure. It is defined as the ratio of the volume of atoms to the total volume of the unit cell. In both FCC and HCP structures, the atomic packing fraction is approximately 0.74. This indicates that both structures have a high level of packing efficiency.
Therefore, statement 1 is correct.
Statement 2: Both represent closely packed crystal structures.
Both the FCC and HCP structures are examples of closely packed crystal structures. In these structures, the atoms are arranged in a way that maximizes the packing efficiency, leading to a high density of atoms. The FCC structure consists of closely packed layers of atoms arranged in a cubic lattice, while the HCP structure consists of closely packed planes of atoms arranged in a hexagonal lattice.
Therefore, statement 2 is correct.
Statement 3: Both structures are generated by stacking of close-packed planes on top of one another, but only the stacking sequence is different.
In both the FCC and HCP structures, the crystal is generated by stacking close-packed planes of atoms on top of one another. However, the stacking sequence is different between the two structures.
In the FCC structure, the stacking sequence is ABCABC..., where each layer is offset by half of the lattice parameter in both the x and y directions. This results in a cubic close-packed arrangement of atoms.
In the HCP structure, the stacking sequence is ABAB..., where each layer is offset by one-third of the lattice parameter in the x and y directions. This results in a hexagonal close-packed arrangement of atoms.
Therefore, statement 3 is correct.
Conclusion:
All three statements are correct. Both the FCC and HCP structures have the same coordination number and atomic packing fraction, and they represent closely packed crystal structures. The main difference between the two structures lies in their stacking sequences.
The coordination number refers to the number of nearest neighbors that each atom in a crystal structure has. In both the face-centered cubic (FCC) and hexagonal close-packed (HCP) structures, the coordination number is 12. This means that each atom is surrounded by 12 other atoms that are in direct contact with it.
The atomic packing fraction is a measure of how efficiently the atoms are packed in a crystal structure. It is defined as the ratio of the volume of atoms to the total volume of the unit cell. In both FCC and HCP structures, the atomic packing fraction is approximately 0.74. This indicates that both structures have a high level of packing efficiency.
Therefore, statement 1 is correct.
Statement 2: Both represent closely packed crystal structures.
Both the FCC and HCP structures are examples of closely packed crystal structures. In these structures, the atoms are arranged in a way that maximizes the packing efficiency, leading to a high density of atoms. The FCC structure consists of closely packed layers of atoms arranged in a cubic lattice, while the HCP structure consists of closely packed planes of atoms arranged in a hexagonal lattice.
Therefore, statement 2 is correct.
Statement 3: Both structures are generated by stacking of close-packed planes on top of one another, but only the stacking sequence is different.
In both the FCC and HCP structures, the crystal is generated by stacking close-packed planes of atoms on top of one another. However, the stacking sequence is different between the two structures.
In the FCC structure, the stacking sequence is ABCABC..., where each layer is offset by half of the lattice parameter in both the x and y directions. This results in a cubic close-packed arrangement of atoms.
In the HCP structure, the stacking sequence is ABAB..., where each layer is offset by one-third of the lattice parameter in the x and y directions. This results in a hexagonal close-packed arrangement of atoms.
Therefore, statement 3 is correct.
Conclusion:
All three statements are correct. Both the FCC and HCP structures have the same coordination number and atomic packing fraction, and they represent closely packed crystal structures. The main difference between the two structures lies in their stacking sequences.
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Consider the following statements about FCC and HCP crystal structure:1. Both have same coordination number and atomic packing fraction.2. Both represent closely packed crystal structures.3. Both structures are generated by stacking of close packed plants on top of one another,but only the stacking sequence is different.Which of the statements given above are correct?a)1 and 2b)2 and 3c)1 and 3d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?
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