(a)
Interpretation:
Wavelength of first order and second order diffraction for an incident angle of 45° and reflection of 25° is to be determined.
Concept introduction:
Calculation of wavelength is done by using the following formula:
Here,
m= diffraction order
λ= wavelength
i = angle of incidence
r = angle of reflection
d = spacing
(b)
Interpretation:
Wavelength of first order and second order diffraction for an incident angle of 45° and reflection of 0° is to be determined.
Concept introduction:
Calculation of wavelength is done by using the following formula:
Here,
m= diffraction order
λ= wavelength
i = angle of incidence
r = angle of reflection
d = spacing
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Chapter 7 Solutions
Principles of Instrumental Analysis
- When an electron beam penetrates a sample in the SEM microscope chamber, the properties of the electron beam (i.e., its energy, E, or equivalently, wavelengthe) are related to the spacing of the atomic planes, d, through the Bragg's diffraction relation: nλ = 2d sin 0 Where n is the integer order of diffraction. When Bragg's condition for a certain set of planes is met, a diffraction pattern can be produced and collected by a detector in order to analyze the crystal orientations and texture of the grains. Consider an incident beam energy of (1.47x10^1) keV, where the electron wavelength is given by the de Broglie equation: de = h 2m (Eo " where m is the mass of an electron and E is expressed in joules. If the electron beam is directed at a silicon crystal that has a diamond-cubic crystal lattice with a lattice parameter of (4.8800x10^-10) meters, what is the value of the incident angle (0) produced to satisfy the first order diffraction of the (220) plane? Express you answer in…arrow_forwardIn TEM, we can obtain a diffraction pattern of a thin sample through the use of objective apertures that act as a barrier for incoming electron radiation in the microscope column. Due to the small angle that the beam makes as it transmits through the crystal planes of TEM samples, the Bragg condition can be modified to: ηλ 2d0 = Determine the wavelength of electrons travelling through an objective aperture if the diffraction spot produced satisfies the Bragg condition at (1.20x10^-2) (0 in radians) for the first order (110) plane with a lattice parameter of (6.010x10^-10), and the camera length between the CCD camera and sample is {c}.arrow_forwardA first order reflection from the (123) planes of a cubic crystal was observed at an angle of e = 24.8 ° when X-rays of wavelength 154 pm were used. 1 h k? 1? d u? b? na = 2d sin e -= - hki (i) Determine the length of the side of the unit cell.arrow_forward
- a) It is considered that a solid substance has an orthorhombic structure. Since the edges of the unit cell are a = 3.50Å, b = 4.0 Å, c = 5.5 Å, calculate the d and 2θ positions for the 111 plane expected in the diffraction pattern as a result of CuKα radiation (λ = 1.54 Å). b) What is the Miller index of the plane intersecting the crystal axes (2a, 1b, -3c)?arrow_forwardWhat is the value of 0 for the first diffraction line (n = 1) in bcc iron (atomic radius 126 pm) when the X-ray wavelength is 58.0 pm? Hint: Consider the closest set of lattice planes.arrow_forwardDetermine the number of Frenkel and Schottky defects per cubic centimeter of a metal chloride at 40 deg Celcius. The energy for defect formation is 3.2 eV, and the density of the metal chloride is 7.80 g/mL at 40 deg Celcius.arrow_forward
- 2. A spherical metallic nanoparticle of diameter di = 100 nm melts at Tmi = 900 K. A smaller spherical nanoparticle of the same metal, of diameter dz = 50 nm, melts at Tm2 = 800 K. a) Explain why the smaller nanoparticle melts at a lower temperature. b) Calculate the melting point of the metal in bulk form.arrow_forwardA hypothetical metal made up of one chemical element has a BCC crystal structure. A diffractometer with monochromatic x-radiation having a wavelength of 0.1542 nm is used to examine the crystal structure of this metal. Given the atomic radius of this metal is 0.1363 nm, determine the expected diffraction angle for the first order reflection from the (110) set of planes.arrow_forwardWhich of the following factors increases the rate of adsorption? low concentration low temperature small surface area decreased pressurearrow_forward
- Briefly discuss the effect of thermodynamic on polymerization.arrow_forward(b) A sample of titanium monoxide has a unit cell dimension of 4.182 A, a Ti/O ratio of 1.005 and an experimental density of 5.764 x10° kg m. Determine whether the defect in this sample is due to Ti cation excess or oxide vacancies.arrow_forwardWhen the temperature is 20 ° C, water flows through an ostwald viscometer at 363 s, whose density and viscosity are given as 0.9982 g / cm3 and 1,000 cP, respectively. The flow time of OF2 from the same viscometer at -145.8 ° C was measured as 68 s. Since the density of OF2 at this temperature is 1.523 g / cm3, what is the value of its viscosity?arrow_forward
- Principles of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning