UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering. Professor R. Gronsky Fall Semester 2000

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1 UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering Professor R. Gronsk Fall Semester 2000 ENGINEERING 45 MIDTERM #1 NAME: (Please Print Clearl) This is a closed book Eam. You must work independentl, and no reference materials are permitted. Please use onl the pages given here, and write our answers in the spaces provided.

2 NAME: E45 Midterm # Question 1 a b c d e f g h Choose the best answer. (2 points for each correct answer) The directional atomic bonds include 1 ionic bonds. 2 covalent bonds. 3 metallic bonds. Metallic bonding is generall NOT responsible for 1 translucenc. 2 malleabilit. 3 ductilit. The van der Walls bond is a 1 primar bond in polmeric materials. 2 dipole-dipole interaction. 3 charge-transfer fluctuation. The near-neighbor distances between anions and cations in a ceramic 1 are established b a force balance. 2 are established b a charge balance. 3 are established b the coordination number. Crstal structure is conventionall described using 1 onl one unit cell of the Bravais lattices. 2 lattice and motif. 3 fcc, bcc, or hcp. During elastic deformation, a metal eperiences 1 necking. 2 bond breaking. 3 bond stretching. Plastic deformation in metallic allos is the result of 1 necking. 2 dislocation motion. 3 the uniaial tensile test. Hardness is a measure of 1 resistance to surface penetration. 2 resistance to deformation in the elastic limit. 3 resistance to formation of circular indentations.

3 NAME: E45 Midterm # i j k l Young's modulus characteries what propert of a material? 1 slope. 2 rigidit. 3 elasticit. Materials with the greatest toughness 1 have the greatest ductilit 2 have the highest Young's modulus. 3 have a combination of strength and ductilit. The percent elongation of a material at failure defines its 1 fracture strength. 2 tougness. 3 ductilit. Structural engineering steels are sometimes found to be brittle 1 at high values of strain 2 at low ambient temperatures. 3 at moderate concentrations of carbon. m Edge and screw dislocations differ in what wa? 1 magnitude of their Burgers vectors. 2 line direction is straight (edge) or curved (screw). 3 angle between Burgers vector and line direction. n o Interstitial defects 1 come from impurit atoms on lattice sites 2 are usuall associated with vacant lattice sites. 3 are found between lattice sites. Diffraction distinguishes fcc allos from bcc allos b 1 the number of hkl peaks. 2 the angular positions of the hkl peaks. 3 the shape of the hkl peaks.

4 NAME: E45 Midterm # Question 2 (20 points) A pieoelectric ceramic is suspected to have ogen anions (O 2- ) at locations , , , barium cations (Ba2+ ) at 000, and titanium cations (Ti 4+ ) at Draw and label the contents of a unit cell of this material (5 points) What is its chemical formula? (5 points) Chemical formula = Specif and draw the Bravais lattice (5 points) and motif (5 points) that defines this structure. Bravais Lattice = Motif =

5 NAME: E45 Midterm # Question 3: (30 points) Identif each of the lattice directions and planes in the following figures relative to the coordinate aes shown. All intersections between the vectors and the unit cells occur at corners or midpoints of cell edges or face centers. Use appropriate Miller indices or Miller-Bravais notation and write answers in boes provided. Lattice Directions (3 points each) a 3 c a 1 a 2 a b c d e Lattice Planes (3 points each) a 3 c a 1 a 2 f g h i j

6 NAME: E45 Midterm # Question 4: (20 points) Consider the following schematics showing the deformation sequence of a crstal in response to an applied shear stress. In each case: label the direction of the shear load that caused the deformation (1 point); draw the dislocation line and label ξ the dislocation line direction (2 points); draw and label b the Burgers vector (2 points); identif the slip plane b shading it in (1 point); show with arrows the motion of the dislocation during continued slip (2 points); and specif the tpe of dislocation (edge or screw) represented b our figure (2 points). (a) (10 points) Tpe of dislocation = (b) (10 points) (Corrupted file) Tpe of dislocation =

7 UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering Professor R. Gronsk Fall Semester 2001 ENGINEERING 45 Midterm #1 NAME: (Please Print Clearl) This is a closed book Eam. You must work independentl, and no reference materials are permitted. Please use onl the pages given here, and write our answers in the spaces provided.

8 E45 Midterm #1, 2001 NAME: Question 1 The mechanical properties of materials are described in engineering terms using simple concepts and normalied parameters. Choose the best answers from those presented below for 2 points each. a. The data at right could have been obtained from a uniaial tensile test three-point bend test Brinell hardness test b. This data reveals that the sample had a ield strength of 350 MPa 400 MPa 450 MPa c. Necking would have been observed in this sample when the stress reached 350 MPa 400 MPa 450 MPa ε d. Dislocations began to move in this sample when the strain eceeded e. The construction at right represents percent elongation to failure estimate of toughness modulus of elasticit

9 E45 Midterm #1, 2001 NAME: Question 2 A lattice is an arra of points in space with identical environment. A primitive unit cell, also called simple, is one that contains onl a single lattice point. a. Label the lattice (4 points) and a primitive unit cell (2 points). (4 points) Number of atoms in the unit cell = b. Label the lattice (4 points) and a primitive unit cell (2 points). (4 points) Number of atoms in the unit cell = 3

10 E45 Midterm #1, 2001 NAME: Question 3 Identif the lattice directions and lattice planes shown in the sketches below for 3 points each. Note especiall the scale markings and use them to precisel identif an fractional intercepts. Be sure that our answer satisfies the special requirement of the four-inde Miller-Bravais notation that h + k = -i. a. b. c. d. e. c a 3 a 1 a 2 f. g. h. i. j. 4

11 E45 Midterm #1, 2001 NAME: Question 4 An allo of copper and gold forms a special ordered crstal structure known as L12 in the Strukturbericht notation. It has a cubic unit cell with Au atoms at the corners and Cu atoms at the face centers. a. Draw and label the contents of the unit cell (5 points) b. Show how to count all of the atoms in the unit cell and use our result to specif the chemical formula of this ordered allo? (5 points) c. Now specif a Bravais lattice (5 points) AND a motif (5 points) that appropriatel describe this ordered L12 crstal structure. 5

12 E45 Midterm #1, 2001 NAME: Question 5 Consider the following schematic of the atomic arrangements in an fcc crstal (lattice constant = a) that has been subjected to an eternal load of sufficient magnitude to eceed the critical resolved shear stress for motion of dislocations on the slip plane pictured here. Find the edge dislocation in the fcc crstal illustrated below... a. Locate and label the etra half plane (5 points). b. Locate and label the slip plane (5 points). c. Trace an FSRH Burgers circuit and draw in the Burgers vector (5 points). d. Now specif the Burgers vector s magnitude and direction with respect to the fcc crstalline coordinate sstem indicated here (5 points). Remember that b is a lattice vector representing the shortest lattice translation. [111] [101] 6

13 UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science & Engineering Professor R. Gronsk Fall Semester, 2005 Engineering 45 Midterm 01 Name: (Please print) INSTRUCTIONS LATTICE seating... Please be seated with occupied seats to our front and back, vacant seats to our left and right. CLOSED BOOK format... All ou need are writing instruments and a straightedge. Please store all books, reference materials, calculators, PDAs, cell phones (OFF), and ipods. NO DISRUPTION rule... Questions cause too much of a disturbance to others in the room. Instead of asking questions, write an concerns or alternative interpretations in our answers. PROFESSIONAL protocol... Engineers do not cheat on the job and the certainl don t cheat on eams. Do not open until START is announced.

14 E 45 Midterm 01, 2005 Initials: 1. Mechanical Properties (20 points) Mark the ballot bo corresponding to the best answer. Two (+2) points for correct answers, -1 if wrong, 0 if blank. (a) The compressive stress induced in the volume element shown below is defined b which epression? σ = P (w t) σ = P (l w) σ = P (l t) w (b) The shear stress induced in the volume element shown below is defined b which epression? σ = P (w t) σ = P (l w) σ = P (l t) w (c) In order to convert the data from a load vs elongation plot to a stress vs strain plot, the following information is essential. the cross-sectional area of the sample the ield strength of the sample the geometr of the sample (d) Elastic deformation is? linear recoverable time-dependent (e) The gage length of a metallic allo sample used in the standard uniaial tensile test has the smallest cross-sectional area establishes the initial length of the sample calibrates the sample s elongation to failure l l t t P P (f) True stress differs from engineering stress in the wa tensile test data is collected in the wa tensile test data is reported in the wa tensile test data represents the actual sample (g) The following data from a uniaial tensile test of a low carbon steel sample indicates that Stress, " (MPa) Strain,! (mm/mm) it has a lower ield point of 450 MPa it has an 0.2% offset ield point of 450 MPA it fractured at precisel 0.02% offset (h) For the same steel sample as above, an observer in the room would have observed necking in the sample just before the sample fractured at 400 MPa just when the sample ielded at 500 MPa just as the stress eceeded 600 MPa (i) An aluminum allo produced the following stress-strain plot during a uniaial tensile test. Its ield strength is Stress, " (MPa) MPa 450 MPa 500 MPa Strain,! (mm/mm) (j) Comparing the above plots from a steel sample and an Al allo sample, it can be concluded that the Al allo has greater elastic recover after fracture the Al allo has a larger elastic modulus the Al allo deforms more before it fails page 2 of 7

15 E 45 Midterm 01, 2005 Initials: 2. Bonding (20 points) Mark the ballot bo corresponding to the best answer. Two (+2) points for correct answers, -1 if wrong, 0 if blank. (a) Primar bonds are formed b the transfer of primar electrons primaril between individual atoms or ions during primar chemical reactions (b) Secondar bonds are so-named because the require secondar electrons to complete the charge transfer necessar for bonding the occur between groups of atoms after primar bonding has occurred the result in secondar reactions with reduced efficienc relative to primar bonds (f) During the formation of covalent bonds, a bonding model called hbridiation eplains wh some bonds show both covalent and metallic character carbon has more than one isotope silicon atoms are tetrahedrall coordinated (g) The metallic bonding model eplains ductilit on the basis of lack of bonding electrons, ielding weaker bonds ecess of mobile electrons, causing fluid bonds lack of bond directionalit (c) Consider the following bonding energ curves for two allos, A and B. + A B (h) The basis for the van der Waals interaction that causes molecular bonding is mutual charge smmetr induced electric dipoles distortion in electron orbitals Bonding energ - 0 A has a higher tensile strength than B A has a lower elastic modulus than B A has a smaller lattice constant than B a 0 a (i) One eplanation for wh graphite powder acts so well as a solid lubricant is carbon atoms in graphite are covalentl bonded within planar laers but have weaker secondar bonds between laers finel-powdered carbon has man unsatisfied bonds at the particle surfaces, which act as a sea of electrons to cause lubrication when crushed into a fine powder, graphite establishes a polar distribution of charge, leading to Coulombic repulsion between powder particles (d) The octet rule predicts that Group IV elements form bonds with four near neighbors have eight bonding electrons reside in octahedral sites (j) The following schematic shows two water molecules in a bonded configuration due to (e) When compared with materials that form ionic bonds, metallic allos melt at higher temperatures ehibit greater bond directionalit have higher coordination numbers covalent bond angles a functional hdrogen bridge the ideal radius ratio, 0 < r/r < page 3 of 7

16 E 45 Midterm 01, 2005 Initials: 3. Lattice Planes (20 points) The triangles drawn here are sections of planes through cubic and heagonal lattices. Identif the relevant planes b their Miller indices or Miller-Bravais indices. Four (4) points for correct answers in the boes provided. (c) c (a) a 3 a 2 (d) a 1 c (b) a 3 a 2 (e) a 1 page 4 of 7

17 E 45 Midterm 01, 2005 Initials: 4. Lattice Directions (20 points) Identif the following directions through both cubic and heagonal lattices using the appropriate Miller inde or Miller-Bravais inde notation. Four (4) points for correct answers in the boes provided. (c) (a) c a 3 a 2 (d) a 1 c (b) a 3 a 2 (e) a 1 page 5 of 7

18 E 45 Midterm 01, 2005 Initials: 5. Crstal Structure (20 points) An allo of nickel and tin adopts a number of different structures, one of which is cubic, designated b the Strukturbericht smbol DO3, where the first inde D is reserved for the more complicated crstal structures. In this case, the larger Sn atoms are located at all face-centered-cubic lattice sites, and the smaller Ni atoms are found in all of the tetrahedral interstices and all of the octahedral interstices. A perspective sketch of the positions is shown below on the left. (a) On the grid provided to the right, draw a cube-ais projection of the structure, and label the elevation of each atom from the bottom plane (elevation 0 ) to the top plane (elevation 1 ). [Hint: On this scheme, for eample, the side faces would be occupied b a single Sn atom at elevation ½. ] (5 points) r Ni = nm r Sn = nm (b) How man Sn atoms are there in this unit cell? Ans: (2 points) (Show how ou count the atoms occuping the lattice points in the unit cell) How man Ni atoms are there in this unit cell? Ans: (2 points) (Show how ou count the atoms occuping the interstitial sites in the unit cell) Now write the chemical formula with the stoichiometr of the Ni-Sn allo shown here. Ans: (1 point) (c) Using our evaluation above, specif both a Bravais lattice and motif that full describes this D03 crstal structure. Lattice: (5 points) Motif: (5 points) page 6 of 7

19 E 45 Midterm 01, 2005 Initials: Worksheet No points will be given or deducted for work shown here. Please enter answers in the spaces provided. DO NOT WRITE BELOW THIS LINE Problem # Possible Points Your Score Total 100 page 7 of 7