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In a hexagonal close-packed (HCP) structure, the number of tetrahedral voids per sphere is:
1
2
3
4
Answers (1)
In a hexagonal close-packed (HCP) structure, each unit cell contains two layers of spheres arranged in a hexagonal pattern. The spheres in the second layer lie in the depressions of the first layer, such that each sphere in the first layer is surrounded by three spheres in the second layer. This arrangement creates tetrahedral voids between the spheres in the first and second layers.
To determine the number of tetrahedral voids per sphere, we need to count the number of tetrahedral voids in a unit cell and divide by the total number of spheres in the unit cell.
In a HCP unit cell, there are two layers of spheres, with three spheres in each layer surrounding a central sphere. Thus, the total number of spheres in the unit cell is 6.
Each sphere in the first layer of the HCP structure is surrounded by three spheres in the second layer. Therefore, there are three tetrahedral voids between each sphere in the first layer and its neighbouring spheres in the second layer. Similarly, each sphere in the second layer is surrounded by three spheres in the first layer, creating three more tetrahedral voids between each sphere in the second layer and its neighbouring spheres in the first layer.
In a hexagonal close-packed (HCP) structure, each unit cell contains two layers of spheres arranged in a hexagonal pattern. The spheres in the second layer lie in the depressions of the first layer, such that each sphere in the first layer is surrounded by three spheres in the second layer. This arrangement creates tetrahedral voids between the spheres in the first and second layers.
To determine the number of tetrahedral voids per sphere, we need to count the number of tetrahedral voids in a unit cell and divide by the total number of spheres in the unit cell.
In a HCP unit cell, there are two layers of spheres, with three spheres in each layer surrounding a central sphere. Thus, the total number of spheres in the unit cell is 6.
Each sphere in the first layer of the HCP structure is surrounded by three spheres in the second layer. Therefore, there are three tetrahedral voids between each sphere in the first layer and its neighbouring spheres in the second layer. Similarly, each sphere in the second layer is surrounded by three spheres in the first layer, creating three more tetrahedral voids between each sphere in the second layer and its neighbouring spheres in the first layer.
In a hexagonal close-packed (HCP) structure, each unit cell contains two layers of spheres arranged in a hexagonal pattern. The spheres in the second layer lie in the depressions of the first layer, such that each sphere in the first layer is surrounded by three spheres in the second layer. This arrangement creates tetrahedral voids between the spheres in the first and second layers.
To determine the number of tetrahedral voids per sphere, we need to count the number of tetrahedral voids in a unit cell and divide by the total number of spheres in the unit cell.
In a HCP unit cell, there are two layers of spheres, with three spheres in each layer surrounding a central sphere. Thus, the total number of spheres in the unit cell is 6.
Each sphere in the first layer of the HCP structure is surrounded by three spheres in the second layer. Therefore, there are three tetrahedral voids between each sphere in the first layer and its neighbouring spheres in the second layer. Similarly, each sphere in the second layer is surrounded by three spheres in the first layer, creating three more tetrahedral voids between each sphere in the second layer and its neighbouring spheres in the first layer.
Thus, the total number of tetrahedral voids per unit cell in a HCP structure is:
Dividing the total number of tetrahedral voids by the total number of spheres, we get:
Number of tetrahedral voids per sphere = Total number of tetrahedral voids / Total number of spheres
Therefore, the number of tetrahedral voids per sphere in a hexagonal close-packed (HCP) structure is 1, which is equivalent to option (a).
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