Homework assignment(released on May 14th,due on May 21st,2019) (Use an A4 sheet) 1.When dynamic effects are considered,the solution for the intensity of the diffracted beam under two-beam conditions is given by: t2sin2(πtSeffecve) 1g=(0 (ntseffective)2 Where Seffective= s2+(1/),is the extinction distance for the selected reflection g. The following picture is a dark-field TEM micrograph of the edge of an aluminium sample recorded under two-beam diffracting conditions,and a selected area diffraction(SAD)pattern of the grain which contains the reflection used to form the two-beam image.Solve the diffraction pattern.Use the thickness fringes in the image and the data in Table to estimate the thickness profile of the sample.How would your results be changed if the material was gold rather than aluminium? (b) 200nm ● Table 4.1 Extinction distance for prominent lattice planes in aluminium and gold at 100kV. Material Extinction distance for reflection hkl(nm) 110 111 200 220 400 A Au 二 56.3 68.5 18.3 20.2 好8 2.In a TEM study of polycrystalline molybdenum(BCC,a=0.3147 nm),a low-angle grain boundary was found.The boundary geometry is sketched in figure(a).In order to identify the dislocations composing the boundary,two-beam diffraction images were recorded.The first image was obtained after orienting the sample to align a [1 0 1]zone axis parallel to the incident electron beam.The SAD pattern is shown in figure(b).Use of reflection 1 resulted in the sub-boundary dislocations
Homework assignment (released on May 14 th , due on May 21 st, 2019) （Use an A4 sheet） 1. When dynamic effects are considered, the solution for the intensity of the diffracted beam under two-beam conditions is given by: = th MMgtU MMgtU Where MMgtU = h , is the extinction distance for the selected reflection g. The following picture is a dark-field TEM micrograph of the edge of an aluminium sample recorded under two-beam diffracting conditions, and a selected area diffraction (SAD) pattern of the grain which contains the reflection used to form the two-beam image. Solve the diffraction pattern. Use the thickness fringes in the image and the data in Table to estimate the thickness profile of the sample. How would your results be changed if the material was gold rather than aluminium? 2. In a TEM study of polycrystalline molybdenum (BCC, a=0.3147 nm), a low-angle grain boundary was found. The boundary geometry is sketched in figure (a). In order to identify the dislocations composing the boundary, two-beam diffraction images were recorded. The first image was obtained after orienting the sample to align a [1 0 1] zone axis parallel to the incident electron beam. The SAD pattern is shown in figure (b). Use of reflection 1 resulted in the sub-boundary dislocations
going out of contrast.The sample was then tilted by 18.430 into a new zone axis, from which a two-beam image was recorded using the reflection 2 shown in the second SAD pattern(figure(c)).Again,no diffraction contrast was detected from the sub-boundary dislocations under these diffracting conditions.The sample was then tilted to bring the boundary parallel to the incident electron beam. a)Determine the Miller indices for 1 and 2. b)Determine the Burgers vector of the sub-boundary dislocations. c)The distance between the dislocations in the sub-boundary(h)depends on the Burgers vector(b)and the relative misorientation of the two crystals(0) h=-b 2sin(0/2) Sketch the SAD pattern that you would expect from the boundary region when aligned with a [0 0 1]zone axis parallel to the electron beam. o)● (a) ● d-0.225mm GrainA Grain B -15.6mm 。4=a.573 3.Note that both the mass-density and the diffraction contrast require only a transmitted beam to pass through the objective aperture.How can you know you have the diffraction contrast without checking selected area diffraction(SAD)? 4.A bright field image of a single crystal superalloy and its corresponding SAD pattern are shown below.According to the images,mark the crystallographic orientation of the cuboidal phase in the image. 10000元 500nm
going out of contrast. The sample was then tilted by 18.43 o into a new zone axis, from which a two-beam image was recorded using the reflection 2 shown in the second SAD pattern (figure (c)). Again, no diffraction contrast was detected from the sub-boundary dislocations under these diffracting conditions. The sample was then tilted to bring the boundary parallel to the incident electron beam. a) Determine the Miller indices for 1 and 2. b) Determine the Burgers vector of the sub-boundary dislocations. c) The distance between the dislocations in the sub-boundary (h) depends on the Burgers vector (b) and the relative misorientation of the two crystals (): = sin . Sketch the SAD pattern that you would expect from the boundary region when aligned with a [0 0 1] zone axis parallel to the electron beam. 3. Note that both the mass-density and the diffraction contrast require only a transmitted beam to pass through the objective aperture. How can you know you have the diffraction contrast without checking selected area diffraction (SAD)? 4. A bright field image of a single crystal superalloy and its corresponding SAD pattern are shown below. According to the images, mark the crystallographic orientation of the cuboidal phase in the image
5.(optional)Following is a series of diffraction patterns acquired from an aluminum grain which contains a single dislocation.After recording the first pattern(SAD1) the sample was tilted 36+2 to acquire the second pattern(SAD2).The sample was then tilted a further 22+2 to obtain the third pattern (SAD3).On each of these three diffraction patterns a reflection used to form a two-beam image is indicated for which the dislocation contrast was absent. a)Solve all three diffraction patterns. b)Determine the Burgers vector of the dislocation. (a)SAD1●●● (b)SAD2 ● ● ● 。。。(●)· ● ●●● ●●● (c)SAD3
5. (optional) Following is a series of diffraction patterns acquired from an aluminum grain which contains a single dislocation. After recording the first pattern (SAD1) the sample was tilted 362 o to acquire the second pattern (SAD2). The sample was then tilted a further 22 2 o to obtain the third pattern (SAD3). On each of these three diffraction patterns a reflection used to form a two-beam image is indicated for which the dislocation contrast was absent. a) Solve all three diffraction patterns. b) Determine the Burgers vector of the dislocation