Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 3, Problem 39P
To determine
The
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Tungsten (W) crystallizes in cubic structure. The edge length of the unit cell of this crystal structure is a = 3.1648 Å. When the X-ray diffraction experiment is performed, scattering occurs from the following planes: (110), (200), (211), (220), (310), (222), (321), (400), (411), (420), (332), (431)
Which of the x-rays scattered from the (110) and (200) planes has the greatest intensity?
Hint: The intensity of the x-ray scattered from any atom decreases as the scattering angle increases. Also note that λ / 2d = sinθ.
A beam of X-rays of first-order wavelength 1.5406 Å is diffracted by a cubic crystal
with lattice constant of 4.2 Å. What is the relationship between the glancing angle if
the (002), (020), and (200) planes of the crystal diffract the X-ray? Given: (1) For a
cubic crystal, the lattice translation vector (a) relates lattice spacing (d) and Miller
indices (h k l) through the relation a? = d²(h? + k² + l²); (2) 1 Å = 10-1º m.
Q#03. (a) Show that the (hkl) plane is perpendicular to the [hkl] direction.
(b) Discuss the Laue method for X-ray diffraction to evaluate the crystal
structure and write its advantages over the other methods..
Chapter 3 Solutions
Modern Physics
Ch. 3.2 - Calculate the quantum number, n, for this pendulum...Ch. 3.2 - An object of mass m on a spring of stiffness k...Ch. 3 - Prob. 1QCh. 3 - Prob. 2QCh. 3 - Prob. 3QCh. 3 - Prob. 4QCh. 3 - Prob. 5QCh. 3 - Prob. 6QCh. 3 - Prob. 7QCh. 3 - Prob. 8Q
Ch. 3 - Prob. 9QCh. 3 - Prob. 10QCh. 3 - Prob. 11QCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Prob. 17PCh. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - As a single crystal is rotated in an x-ray...Ch. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48P
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- X rays from a copper X- ray tube (A =204 pm) were diffracted at an angle of 35 degrees by a crystal of silicon. Assuming first- order diffraction. Assuming ( n=2 in the bragg equation, what is the interplaner spacing (d) in silicon? (A) 219 pm (B) 217 pm (C) 215 pm (D) 213 pmarrow_forwardA beam of X-ray diffraction (XRD) with a CuKa radiation of wavelength, λ = 1.541 Å, falls on a powder of three samples (A, B and C) which crystallized in the following crystal structure: sample A: body center cubic (BCC) with lattice parameter a = 4 Å; sample B: tetragonal, with lattice parameters a = b = 4 Å and c = 6 Å and sample C: orthorhombic, with lattice parameters a = 4 Å, b = 6Å and c = 8 Å. 1. For the first order Bragg diffraction, which of the three sample will give the smallest Bragg angle on the plan (111)? 2. Explain clearly with some calculations, if there will be higher order reflections on the plan (111) for the three samples.arrow_forwardThe figure below is the X-ray diffraction (XRD) pattern of Nb, which has a BCC crystal structure. A monochromatic X-ray with a wavelength (^) of 0.1542 nm was used. The reflection order is 1. (a) Calculate the lattice spacing for the (110) plane from the XRD spectrum. (b) Calculate the lattice parameter of Nb. (c) What is the atom packing fraction (APF) of Nb? 8000 (110)Nb 38.3° 6000 4000 69.3° 55.3° (211)Nb 2000 (200)Nb 82.1° (220)Nb 30 40 50 60 70 80 90 20,degree Intensity 20arrow_forward
- The structure factor defines the amount of scattering from the planes hkl in the direction e defined by Bragg's law and is given by: N Fnkl = 2f, (hkl) exp 2mi (hx + ky, + lz) J=1 where the unit cell in the crystal contains N atoms of which the jh atom has an atomic scattering factor, f(hkl) and fractional unit cell co-ordinates x, y, z;. Show clearly, that for a body-centred cubic (bcc) lattice, diffraction peaks will be systematically absent for all planes where (h+k+l) is odd and that diffraction peaks will occur for all planes where (h+k+1) is even. Note: exp (nrti) = +1 if n is even exp (nri) = -1 if n is oddarrow_forwardHome work 1: Beam of X- rays of A = 0.842A° is incident on a crystal at a grazing angle of 8.35 when the first Bragg's reflection occurs calculate the glancing angle for third order reflection. ImsuenM amsum Home work 2: X- rays with wave length of 0.58 A° are used for calculating d(200) in nickel .The reflection angle is 9.5° when is the size of unit cell Home work 3: The Bragg's angle corresponding to the first order reflection from (111) plane in a crystal is 30 when X- rays of wave length 1.75A° are used, calculate inter atomic spacing. Home work 4: Calculate the wave length that can analyses by a rock salt crystal of spacing d = 2.82 A° in the first order. DialerSarrow_forward5.3. A material of simple tetragonal Bravais lattice (a = 2.4 Å, c = 3.6 Å) is prepared in a plate shape so that the sample surface is parallel to (001). When the sample was symmetrically scanned in the 20 range from 20° to 100° using an X-ray beam at 1.54 Å, at which 20 positions will the diffraction peaks be observed? How will the diffraction pattern change if the sample is replaced by a crystal of body-centered tetragonal lattice? Assume that all the other condi- tions are the same.arrow_forward
- The spacing between atoms in KCl crystal is 3.1 x 10^-10 m. At what angle from the surface will a beam of 3.14 x 10^-11 m x-rays be constructively scattered? (Ans. 2.9 degrees)arrow_forwardQ. 1. An X-ray beam of wavelength 0.71 A is diffracted by a cubic KCL crystal of density 1.99x10^3 Kgm-3. Calculate the interplanner spacing for (200) planes and glancing angle for the second order reflection from these planes. The molecular weight of KCL is 74.6 amu and the Avagadro’s numberis 6.023x10^26 Kg-1 mole-1.arrow_forwardTungsten is a very high density, high melting point, and hard metal. These properties are partially due to its body centered cubic (BCC) crystal structure. Tungsten has an atomic number of 74 and an average mass of 183.8u. (1u = 1.661x10-27 kg). X-ray diffraction experiments determine that the Bravais lattice has a characteristic length of 3.155 Å (This means each side of the cube shown below has a length of 0.3155 nm.) How many complete tungsten atoms are there in each BCC unit cell?arrow_forward
- The Bragg's angle in the first order for (220) reflection from nickel (FCC) is (38.2° ). When X-rays of wavelength 1.54 A° are employed in a diffraction experiment. Determine the lattice parameter of nickel?arrow_forwardTungsten is a very high density, high melting point, and hard metal. These properties are partially due to its body centered cubic (BCC) crystal structure. Tungsten has an atomic number of 74 and an average mass of 183.8u. (1u = 1.661x10-27 kg). X-ray diffraction experiments determine that the Bravais lattice has a characteristic length of 3.155 Å (This means each side of the cube shown below has a length of 0.3155 nm.)What is the density of single-crystalline tungsten? (Give your answer in g/cm.) Note: Single-crystalline indicates that the BCC unit cell repeats indefinitely. In poly-crystalline metals there are multiple domains with boundaries where the crystal structures do not line up. These materials tend to be much more brittle.arrow_forwardThe vanadium crystallizes in the body centered cubic lattice with a lattice parameter a. The X-ray diffraction data were collected from this compound and the following first four Bragg positions 20 (degrees): 21.06, 30.17, 37.03 and 43.10 were registered. The wavelength of the used X-ray radiation is 2 = 1.54Á. 1- Give the Bragg's Law. 2- Determine the inter-planer spacing d of the family of lattice planes (hke) of the cubic system. hkt 3 - Using the structure factor, determine the allowed reflections of the body centered cubic. 4- Index the four Bragg angles given above and calculate the cell parameter a.arrow_forward
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