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Diamond crystal structure has the cubic edge of 3.56 angstrom. Which of the following planes gives XRD lines when x ray of wavelength 1.5 angstrong is used 1. (111) 2. (220) 3. (400) 4. (510)?
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Diamond crystal structure has the cubic edge of 3.56 angstrom. Which o...
Diamond Crystal Structure
The diamond crystal structure is a face-centered cubic (FCC) lattice. In this structure, each carbon atom is bonded to four neighboring carbon atoms, forming a tetrahedral arrangement. The cubic unit cell of diamond consists of eight atoms, with one atom at each corner and one atom in the center of each face.
Cubic Edge Length
Given that the cubic edge length of the diamond crystal structure is 3.56 Å (angstrom), we can use this information to determine the interplanar spacing for different crystallographic planes.
Interplanar Spacing
The interplanar spacing (d) for a crystallographic plane can be calculated using the formula:
d = a / √(h^2 + k^2 + l^2)
where a is the cubic edge length and (hkl) are the Miller indices that represent the crystallographic plane.
For the (111) plane:
d(111) = 3.56 Å / √(1^2 + 1^2 + 1^2)
d(111) = 3.56 Å / √3
d(111) ≈ 2.06 Å
For the (220) plane:
d(220) = 3.56 Å / √(2^2 + 2^2 + 0^2)
d(220) = 3.56 Å / √8
d(220) ≈ 1.26 Å
For the (400) plane:
d(400) = 3.56 Å / √(4^2 + 0^2 + 0^2)
d(400) = 3.56 Å / 4
d(400) = 0.89 Å
For the (510) plane:
d(510) = 3.56 Å / √(5^2 + 1^2 + 0^2)
d(510) = 3.56 Å / √26
d(510) ≈ 0.70 Å
XRD Lines
X-ray diffraction (XRD) occurs when X-rays interact with a crystal and undergo constructive interference due to their interaction with the crystal lattice planes. This interference produces diffraction patterns or XRD lines.
To observe XRD lines, the condition for constructive interference must be met, which is given by Bragg's law:
nλ = 2d sin(θ)
where n is the order of diffraction, λ is the wavelength of the X-ray, d is the interplanar spacing, and θ is the angle of incidence.
For the XRD lines to be observed, the condition for constructive interference is that the angle of incidence (θ) must satisfy the equation:
sin(θ) = nλ / (2d)
Given that the wavelength of the X-ray is 1.5 Å, we can calculate the angles of incidence for different planes and determine if they satisfy the condition for constructive interference.
For the (111) plane:
sin(θ) = 1 * 1.5 Å / (2 * 2.06 Å)
sin(θ) ≈ 0.36
θ ≈ 21.8°
For the (220) plane:
sin(θ) = 1 * 1.5 Å / (2 * 1.26 Å)
sin(
The diamond crystal structure is a face-centered cubic (FCC) lattice. In this structure, each carbon atom is bonded to four neighboring carbon atoms, forming a tetrahedral arrangement. The cubic unit cell of diamond consists of eight atoms, with one atom at each corner and one atom in the center of each face.
Cubic Edge Length
Given that the cubic edge length of the diamond crystal structure is 3.56 Å (angstrom), we can use this information to determine the interplanar spacing for different crystallographic planes.
Interplanar Spacing
The interplanar spacing (d) for a crystallographic plane can be calculated using the formula:
d = a / √(h^2 + k^2 + l^2)
where a is the cubic edge length and (hkl) are the Miller indices that represent the crystallographic plane.
For the (111) plane:
d(111) = 3.56 Å / √(1^2 + 1^2 + 1^2)
d(111) = 3.56 Å / √3
d(111) ≈ 2.06 Å
For the (220) plane:
d(220) = 3.56 Å / √(2^2 + 2^2 + 0^2)
d(220) = 3.56 Å / √8
d(220) ≈ 1.26 Å
For the (400) plane:
d(400) = 3.56 Å / √(4^2 + 0^2 + 0^2)
d(400) = 3.56 Å / 4
d(400) = 0.89 Å
For the (510) plane:
d(510) = 3.56 Å / √(5^2 + 1^2 + 0^2)
d(510) = 3.56 Å / √26
d(510) ≈ 0.70 Å
XRD Lines
X-ray diffraction (XRD) occurs when X-rays interact with a crystal and undergo constructive interference due to their interaction with the crystal lattice planes. This interference produces diffraction patterns or XRD lines.
To observe XRD lines, the condition for constructive interference must be met, which is given by Bragg's law:
nλ = 2d sin(θ)
where n is the order of diffraction, λ is the wavelength of the X-ray, d is the interplanar spacing, and θ is the angle of incidence.
For the XRD lines to be observed, the condition for constructive interference is that the angle of incidence (θ) must satisfy the equation:
sin(θ) = nλ / (2d)
Given that the wavelength of the X-ray is 1.5 Å, we can calculate the angles of incidence for different planes and determine if they satisfy the condition for constructive interference.
For the (111) plane:
sin(θ) = 1 * 1.5 Å / (2 * 2.06 Å)
sin(θ) ≈ 0.36
θ ≈ 21.8°
For the (220) plane:
sin(θ) = 1 * 1.5 Å / (2 * 1.26 Å)
sin(
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Diamond crystal structure has the cubic edge of 3.56 angstrom. Which of the following planes gives XRD lines when x ray of wavelength 1.5 angstrong is used 1. (111) 2. (220) 3. (400) 4. (510)?
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Diamond crystal structure has the cubic edge of 3.56 angstrom. Which of the following planes gives XRD lines when x ray of wavelength 1.5 angstrong is used 1. (111) 2. (220) 3. (400) 4. (510)? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Diamond crystal structure has the cubic edge of 3.56 angstrom. Which of the following planes gives XRD lines when x ray of wavelength 1.5 angstrong is used 1. (111) 2. (220) 3. (400) 4. (510)? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Diamond crystal structure has the cubic edge of 3.56 angstrom. Which of the following planes gives XRD lines when x ray of wavelength 1.5 angstrong is used 1. (111) 2. (220) 3. (400) 4. (510)?.
Diamond crystal structure has the cubic edge of 3.56 angstrom. Which of the following planes gives XRD lines when x ray of wavelength 1.5 angstrong is used 1. (111) 2. (220) 3. (400) 4. (510)? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Diamond crystal structure has the cubic edge of 3.56 angstrom. Which of the following planes gives XRD lines when x ray of wavelength 1.5 angstrong is used 1. (111) 2. (220) 3. (400) 4. (510)? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Diamond crystal structure has the cubic edge of 3.56 angstrom. Which of the following planes gives XRD lines when x ray of wavelength 1.5 angstrong is used 1. (111) 2. (220) 3. (400) 4. (510)?.
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