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How many unit cells are possible for the...

How many unit cells are possible for the crystallographic dimensions as `a ne b ne c alpha=gamma =90^(@),alphane beta`

A

1

B

2

C

3

D

4

Text Solution

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The correct Answer is:
To solve the problem of determining how many unit cells are possible for the given crystallographic dimensions, we can follow these steps: ### Step 1: Understand the Given Conditions The problem states: - \( a \neq b \neq c \) (the lengths of the unit cell edges are not equal) - \( \alpha = \gamma = 90^\circ \) (the angles between the edges are right angles) - \( \alpha \neq \beta \) (the angle between the edges \( a \) and \( b \) is not equal to \( 90^\circ \)) ### Step 2: Identify the Crystal System Based on the conditions: - The condition \( a \neq b \neq c \) indicates that the unit cell edges are of different lengths. - The angles \( \alpha \) and \( \gamma \) being \( 90^\circ \) and \( \alpha \neq \beta \) suggests that this is a monoclinic crystal system. ### Step 3: Determine the Number of Unit Cells In crystallography, each crystal system has a specific number of unique unit cells. For the monoclinic system: - There is only **one unique unit cell** that fits the given parameters. ### Conclusion Therefore, for the crystallographic dimensions provided, there is only **one possible unit cell**. ### Final Answer The answer is: **1 unit cell**. ---
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The regular three dimensional arrangement of points in a crystal is known as crystal lattice and the smallest repeating pattern in the lattice is called unit cell. The unit cells are characterised by the edge lengths a, b, c and the angles between them alpha, beta and gamma respectively. Based on this, there are seven crystal systems. In a cubic unit cell: a=b=c and alpha = beta=gamma=90^(@) The number of points in simple, body centred and face centred cubic cells are 1,2 and 4 respectively In both the hcp and ccp of spheres, the number of tetrahedral voids per sphere is two while the octahedral voids is one. The C.N of cation occuppying an octahedral vois is: