Question

Consider the plane makes intercepts of 2Å, 3Å. 4 Å on the coordinate axis of the crystal
with a b c = 4:32. The crystal is orthorhombic crystal. Calculate the miller indices of
the given place of the crystal
(A) (4.11)
(B) (43.2)
(0) (4.2.1)
(D) (4.4.4​

Answer 1

Answer:

b

Explanation:

Answer 2

Answer:

Explanation:

To determine the Miller indices of the given plane in an orthorhombic crystal, we need to find the reciprocals of the intercepts made by the plane on the coordinate axes.

Given that the intercepts of the plane on the coordinate axes are 2A, 3A, and 4A, and the ratio of the crystallographic axes is a:b:c = 4:3:2, we can calculate the reciprocals of the intercepts as follows:

Reciprocal of intercept along the a-axis = 1 / 2A = 1/2

Reciprocal of intercept along the b-axis = 1 / 3A = 1/3

Reciprocal of intercept along the c-axis = 1 / 4A = 1/4

To convert the reciprocals to integers, we can find the least common multiple (LCM) of the denominators 2, 3, and 4, which is 12.

Multiplying the reciprocals by the LCM, we get:

Reciprocal of intercept along the a-axis = (1/2) * 12 = 6

Reciprocal of intercept along the b-axis = (1/3) * 12 = 4

Reciprocal of intercept along the c-axis = (1/4) * 12 = 3

Finally, we take the reciprocals and represent them as integers to obtain the Miller indices:

Miller indices of the given plane = (6, 4, 3)

Among the answer choices provided, the closest option is:

(A) (4, 1, 1)

However, the correct Miller indices for the given plane in the orthorhombic crystal are (6, 4, 3), so none of the provided options match the correct answer.