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The orthorhombic crystal has axial units in the ratio of 0.424 : 1: 0.367. The miller indices of a crystal face whose intercepts are in the ratio 0.212 :1 :0.183 will be : -
- a)2 : 1 : 2
- b)1 : 2 : 1
- c)4 : 1 : 4
- d)2 : 1 : 1
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The orthorhombic crystal has axial units in the ratio of 0.424 : 1: 0....
a : b : c :: 0.424 :1 : 0.367
p x 0.424 = 0.212
Similarly bq = 1
q x 1
∴ q= 1
& rc = 0.183
p x 0.424 = 0.212
Similarly bq = 1
q x 1
∴ q= 1
& rc = 0.183
Most Upvoted Answer
The orthorhombic crystal has axial units in the ratio of 0.424 : 1: 0....
Given:
- Ratio of axial units in the orthorhombic crystal: 0.424 : 1 : 0.367
- Ratio of intercepts on a crystal face: 0.212 : 1 : 0.183
To find:
- Miller indices of the crystal face
Solution:
Step 1: Determine the Miller indices for each axis
- The Miller indices for each axis can be determined by taking the reciprocal of the axial unit ratios.
For the first axis:
- Reciprocal = 1 / 0.424 = 2.358
For the second axis:
- Reciprocal = 1 / 1 = 1
For the third axis:
- Reciprocal = 1 / 0.367 = 2.727
Step 2: Determine the multiples of the intercept ratios
- Multiply the intercept ratios by the smallest integer that will make all the values whole numbers.
For the first intercept:
- Multiple = 1 / 0.212 = 4.717
- Smallest integer multiple = 5
For the second intercept:
- Multiple = 1 / 1 = 1
- Smallest integer multiple = 1
For the third intercept:
- Multiple = 1 / 0.183 = 5.464
- Smallest integer multiple = 5
Step 3: Determine the Miller indices
- The Miller indices are the multiples of the reciprocal values for each axis.
For the first axis:
- Miller index = 2.358 * 5 = 11.79 ≈ 12
For the second axis:
- Miller index = 1 * 1 = 1
For the third axis:
- Miller index = 2.727 * 5 = 13.635 ≈ 14
Step 4: Simplify the Miller indices
- Divide all the Miller indices by their smallest common factor to simplify.
For the first axis:
- Dividing by 2, Miller index = 12 / 2 = 6
For the second axis:
- Dividing by 1, Miller index = 1 / 1 = 1
For the third axis:
- Dividing by 2, Miller index = 14 / 2 = 7
Step 5: Write the Miller indices in the form of a:b:c
- The Miller indices of the crystal face are 6:1:7
Answer:
- The correct option is A) 2:1:2
- Ratio of axial units in the orthorhombic crystal: 0.424 : 1 : 0.367
- Ratio of intercepts on a crystal face: 0.212 : 1 : 0.183
To find:
- Miller indices of the crystal face
Solution:
Step 1: Determine the Miller indices for each axis
- The Miller indices for each axis can be determined by taking the reciprocal of the axial unit ratios.
For the first axis:
- Reciprocal = 1 / 0.424 = 2.358
For the second axis:
- Reciprocal = 1 / 1 = 1
For the third axis:
- Reciprocal = 1 / 0.367 = 2.727
Step 2: Determine the multiples of the intercept ratios
- Multiply the intercept ratios by the smallest integer that will make all the values whole numbers.
For the first intercept:
- Multiple = 1 / 0.212 = 4.717
- Smallest integer multiple = 5
For the second intercept:
- Multiple = 1 / 1 = 1
- Smallest integer multiple = 1
For the third intercept:
- Multiple = 1 / 0.183 = 5.464
- Smallest integer multiple = 5
Step 3: Determine the Miller indices
- The Miller indices are the multiples of the reciprocal values for each axis.
For the first axis:
- Miller index = 2.358 * 5 = 11.79 ≈ 12
For the second axis:
- Miller index = 1 * 1 = 1
For the third axis:
- Miller index = 2.727 * 5 = 13.635 ≈ 14
Step 4: Simplify the Miller indices
- Divide all the Miller indices by their smallest common factor to simplify.
For the first axis:
- Dividing by 2, Miller index = 12 / 2 = 6
For the second axis:
- Dividing by 1, Miller index = 1 / 1 = 1
For the third axis:
- Dividing by 2, Miller index = 14 / 2 = 7
Step 5: Write the Miller indices in the form of a:b:c
- The Miller indices of the crystal face are 6:1:7
Answer:
- The correct option is A) 2:1:2
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Community Answer
The orthorhombic crystal has axial units in the ratio of 0.424 : 1: 0....
a : b : c :: 0.424 :1 : 0.367
p x 0.424 = 0.212
Similarly bq = 1
q x 1
∴ q= 1
& rc = 0.183
p x 0.424 = 0.212
Similarly bq = 1
q x 1
∴ q= 1
& rc = 0.183
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The orthorhombic crystal has axial units in the ratio of 0.424 : 1: 0.367. The miller indices of a crystal face whose intercepts are in the ratio 0.212 :1 :0.183 will be : -a)2 : 1 : 2b)1 : 2 : 1c)4 : 1 : 4d)2 : 1 : 1Correct answer is option 'A'. Can you explain this answer?
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