00:01
So, it has been asked to find the direction indices for a vector that passes from a point 1 by 3, 1 by 2, 0 to a point 2 by 3, 3 by 4, 1 by 2 in a tetragonal unit cell.
00:32
And in the second part, it has been asked to repeat the problem in case of a rhombohedral unit cell.
00:43
So, in part b, it has been asked to find the direction indices for the vector that passes from the point 1 by 3, 1 by 2, 0 to the point 2 by 3, 3 by 4, 1 by 2 in a rhombohedral unit cell.
01:01
So, in part a, so in case of tetragonal unit cell, the lattice parameters a is equal to b but not equal to c and alpha, beta, gamma is equal to 90 degree.
01:19
This is the tetragonal unit cell, these are the directions, the three axis, then this is a, this is a and this is c.
01:27
These are the angles alpha, beta and gamma, they all are 90 degree.
01:32
The tail coordinates of the vector represented by x1, y1, z1 would be a by 3, a by 2 and 0.
01:49
If we specify this point in the unit cell, then this point is, if these are x, y, z coordinates, then this point is.
01:59
So, they are intersecting the point where the intercepts a by 3 and y intercept a by 2, they intersect each other.
02:12
So, this is the point.
02:13
Similarly, the head coordinates of the vector represented by x2, y2 and z2, they are 2a by 3, 3a by 4 and a c by 2.
02:25
So, it would be this point.
02:28
So, half of this coming out, so this would be the point having the coordinates 2a by 3, 3a by 4 and c by 2.
02:37
So this is c, then the vector would be this and it has been asked to find the direction in this as of this vector.
02:52
Taking the point coordinate differences, we get x2 minus x1 would be 2a by 3 minus a by 3, that is a by 3.
03:07
Y2 minus y1 would be 3a by 4 minus a by 2, that is a by 4 and z2 minus z1 would be c by 2 minus 0, that is c by 2.
03:20
Here it is wrongly written as a, it is c by 2.
03:25
Now, the projections of the vector along x, y, z, it is a by 3, a by 4 and c by 2.
03:36
So, projection in terms of a, b, c or a and c would be 1 by 3, 1 by 4 and 1 by 2.
03:47
So if we reduce it to integers, we have to multiply it with a common multiple here in this case it is 12.
03:56
So it is 4, 3 and 6.
03:59
If we enclose it within brackets, then it would be 4, 3, 6 within square brackets.
04:05
So, this 4, 3, 6 is the direction indices of the vectors in a tetragonal unit cell.
04:15
Thus, the direction indices of the given vector in a tetragonal unit cell is within bracket 4, 3, 6...