Homework assignment(released on May 28th,due on June 4th,2019) (Use A4 sheet) 1.(optional)The specimen used in the TEM lab is an Alo3CoCrFeNi high entropy alloy (HEA).Powder X-ray diffraction indicates that it is fcc structure without noticeable second phase.By examining it in TEM,we have obtained a BF image (fig.(a)),a corresponding SAD pattern(fig.(b))and a high resolution TEM image of the matrix region (fig.(c))as follows. a)Explain the contrast indicated by the arrows in fig.(a) b)Solve the diffraction pattern in fig.(b)and explain the weak spots. c)Do you find precipitates in fig.(c)?Try to locate them (a) 200nm (b) 51/nm (c) m 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
Homework assignment (released on May 28 th , due on June 4 th , 2019) （Use A4 sheet） 1. (optional) The specimen used in the TEM lab is an Al0.3CoCrFeNi high entropy alloy (HEA). Powder X-ray diffraction indicates that it is fcc structure without noticeable second phase. By examining it in TEM, we have obtained a BF image (fig. (a)), a corresponding SAD pattern (fig. (b)) and a high resolution TEM image of the matrix region (fig. (c)) as follows. a) Explain the contrast indicated by the arrows in fig. (a). b) Solve the diffraction pattern in fig. (b) and explain the weak spots. c) Do you find precipitates in fig. (c)? Try to locate them. 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 [00 1]zone axis parallel to the electron beam. (b) ● ⊙g20 ● (a) =02225nm d=0.1573nm Grain A Grain B 1h-15.6nm ● 3.In an SEM,what is the minimum magnification required to resolve spherical particles with a radius of 10 nm?Assuming that reasonable resolution is achieved when an image feature covers 3x3 pixels,what is the probe size required to resolve 10 nm particles? 4.Depth of field D refers to the range of position for an object in which image sharpness does not change.An important feature of SEM is the ability to image topographic information of specimen clearly. (1)Derive the equations for Dy based on Raleigh resolution criterion and explain why the of SEM is larger than optical microscope under the same magnification; (2)Compare the different factors that affect D in SEM and optical microscope. 5.On p.129,figure 4.2 compares OM image and SEM image of the same specimen under the same magnification.Why does the SEM image reveal somewhat topographic information?
shown in figure (b). Use of reflection 1 resulted in the sub-boundary dislocations going out of contrast. The sample was then tilted by 18.43 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 h . 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. In an SEM, what is the minimum magnification required to resolve spherical particles with a radius of 10 nm? Assuming that reasonable resolution is achieved when an image feature covers 3x3 pixels, what is the probe size required to resolve 10 nm particles? 4. Depth of field Df refers to the range of position for an object in which image sharpness does not change. An important feature of SEM is the ability to image topographic information of specimen clearly. (1) Derive the equations for Df based on Raleigh resolution criterion and explain why the of SEM is larger than optical microscope under the same magnification; (2) Compare the different factors that affect Df in SEM and optical microscope. 5. On p.129, figure 4.2 compares OM image and SEM image of the same specimen under the same magnification. Why does the SEM image reveal somewhat topographic information?
6.The following SEM pictures are the same area imaged under back-scattered electron(BSE)mode and secondary electron(SE)mode,respectively.Explain the different contrast imaged in the two pictures. BSE 2 m0 SE2 2um 7.Suppose you are a representative of SEM manufacturer and want to demonstrate to your customers the power of your SEM.Suggest the specimen type,signal used to form the image and the operation conditions in the following picture to show the highest resolution possible. 6/30/2009
6. The following SEM pictures are the same area imaged under back-scattered electron (BSE) mode and secondary electron (SE) mode, respectively. Explain the different contrast imaged in the two pictures. 7. Suppose you are a representative of SEM manufacturer and want to demonstrate to your customers the power of your SEM. Suggest the specimen type, signal used to form the image and the operation conditions in the following picture to show the highest resolution possible