Presentation on theme: "Materials Contributions by:"— Presentation transcript:
1 Materials Contributions by: John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO
2 Sample A is an equimolar physical mixture of Si and Ge Sample A is an equimolar physical mixture of Si and Ge. Sample B is a Si0.5Ge0.5 solid solution. Which measurements will be different for the two samples?Elemental analysis and x-ray diffractionX-ray diffractionAbsorption spectrumAbsorption spectrum and x-ray diffractionElemental analysisANSWER: D. Absorption spectrum and x-ray diffractionThe solid solution will have different lattice parameters and thus different XRD patterns.
3 Below is a 2-dimensional representation of a crystal structure where each circle represents a single atom. Each lattice/unit cell contains ________ atoms.1234ANSWER: A. 1The each corner of a unit cell contains an atom, but not all of the atom is within the unit cell. With each atom centered on the corner, only 1/4th of an atom in each cell. 4 x 1/4th means one atom per cell.
4 A unit cell of a simple cubic crystal is represented below A unit cell of a simple cubic crystal is represented below. If each corner contains an atom, how many atoms are there per unit cell?12348ANSWER: A. 1The each corner of a unit cell contains an atom, but not all of the atom is within the unit cell. With each atom centered on the corner, only 1/8th of an atom is in each cell. 8 x 1/8th means one atom per cell.
5 A unit cell of a simple cubic crystal structure is represented below A unit cell of a simple cubic crystal structure is represented below. If each corner contains an atom, what is the coordination number of each atom?4681012ANSWER: B. 6Coordination number of an atom is the number of other atoms in contact with the atom of interest. For a simple cubic structure, this is 6. For the unit cell pictured, each atom is currently connected to three other atoms, each 90° from each other. For a sphere, there can be 6 such connections.
6 In a space-filling representation, the unit cell size is limited by the close-packing of spherical atoms, where the surfaces of the atoms are in contact. For a simple cubic unit cell of this type, how are atom center distance, d, and atom radius, r, related?d = rd = 2rd = 3rd = 4rANSWER: B. d=2rd
7 A corner atom is part of how many unit cells in this simple cubic structure? 1248ANSWER: D. 8Each corner atom has 1/8th of its volume within the unit cell pictured. Therefore the rest of the atom will be contained within 7 other unit cells, bringing the total to 8.
8 In the face-centered cubic (FCC) crystal structure, an atom is on each corner and each side of the unit cell. How many atoms are in the unit cell?12414None of the aboveANSWER: C. 4Each corner atom is shared with 8 unit cells so 1/8th x 8 corner atoms = 1 atomEach atom on the face is shared with 2 unit cells. So ½ x 6 face atoms = 3 atomsTotal 3 + 1= 4 atoms
9 In a face-center cubic structure, the atoms are close-packed along the face diagonal. What is the coordination number of a metal atom in this structure?246812ANSWER: E.12The coordination number of an atom is the number of other atoms in contact with the atom of interest. For a face-center cubic structure, this is 12. Look at the bottom face-centered atom. It is touching the 4 green atoms in it’s same plane. It also touches 4 atoms in the plane above it, and 4 atoms in the plane below it for a total of 12.
10 In the body-centered cubic (BCC) crystal structure, an atom is on each corner and one atom (blue atom) is in the center of the unit cell. How many atoms are in the unit cell?12489ANSWER: B. 2Each corner atom is shared with 8 cells so 1/8th in each cell. The center atom is entirely within the unit cell so (1/8th x 8) + 1 = 2 atoms
11 In the body-centered cubic (BCC) crystal structure, an atom is on each corner and one atom (blue atom) is in the center of the unit cell. What is the coordination number for each atom?46812ANSWER: C. 8The center atom is in contact with all the corner atoms in the unit cell for a total of 8 atoms
12 Which crystal structure is body center cubic? ANSWER: A.The blue atom is at the center of the cell and coordinates with 8 total atoms
13 A zinc sulfide crystal structure is shown A zinc sulfide crystal structure is shown. What type of unit cell is defined by just the green sulfide ions?Simple cubicBody-centered cubicFace-centered cubicNone of the aboveANSWER: C. Face-centered cubicThe sulfide ions are on the corners and the faces of the structure shown.
14 A layer sequence for an FCC metal is shown A layer sequence for an FCC metal is shown. A close-packed plane is comprised of six atoms. If atoms 2, 4, 5 are three of the six atoms, which other three atoms are need to define the plane?Z = 01243511, 13, 146, 9, 127, 8, 146, 9, 10Z = 1/2Z = 1ANSWER: D.These atoms form the close packed (111) plane. Along this plane that cuts diagonally through the FCC structure, atoms 2, 5, 4 are the base and atoms 6 and 9 nestle into the spaces diagonally (and to the viewer’s left) and above those atoms. Atom 10 nestles between 6 and 9 on the same diagonal to form a close-packed plane along the (111) plane. Note: atom 1 is the origin.67981011141312
15 Which structure is the FCC (110) plane? BANSWER: B. The (110) plane cuts along the bottom, horizontal plane of the unit cell. This means that the green atom is surrounded on all sides by blue atoms, all on the same plane. Picture B shows this repeating pattern.FCC unit cell
16 Which structure is the FCC (001) plane? BANSWER: A. The plane (001) cuts through vertically from the back left corner to the front right corner of the shown unit cell. This means that the blue atoms form a square grid, as shown in A.FCC unit cell
17 Which structure is the FCC (111) plane? BANSWER: C. The (111) plane cuts diagonally through the unit cell with the blue atoms forming a triangle at each “corner” of the plane and the green, face centered atoms forming a projected triangle that fills in between the blue atoms. This is the close packing plane.FCC unit cell
18 In a zinc sulfide (ZnS) crystal structure, each zinc ion (blue) sits between four sulfide ions (white). Given a ZnS layer sequence, which sulfide ions surround the indicated zinc ion?124531, 4, 7, 81, 3, 4, 71, 3, 6, 71, 4, 7, 9Z = 0Z = 1/4ANSWER: C. 1, 3, 6, 7 The layer sequences show that at z = ¼ the indicated zinc ion nestles between the sulfide ions 1 and 3. The next plane up is z = ½ , and the sulfide ions 6 and 7 would be touching on either side of the indicated zinc ion.6879Z = 1/2Z = 3/4
19 How many sulfide ions (green) are in a zinc sulfide unit cell? 1234ANSWER: D. 4Sulfide ions are the green ones. Each corner atom is shared with 8 unit cells so 1/8th x 8 corner atoms = 1 atomEach atom on the face is shared with 2 unit cells. So ½ x 6 face atoms = 3 atomsTotal 3 + 1= 4 atoms
20 Vanadium, molybdenum, and sodium all have a body-centered cubic structure. Given the following atomic radii, which two metals are most likely to form a sold solution?MetalAtomic radiiV0.131Mo0.136Na0.186Vanadium, molybdenumVanadium, sodiumMolybdenum, sodiumANSWER: A. Vanadium, molybdenumVanadium and molybdenum have similar atom radii. Therefore, they are more likely to be able to form a BCC crystal structure together and thus form a solid solution
21 For a two-plane, octahedron arrangement of identical spheres, there will be two differently-sized gaps. One gap will be within the plane, the other gap will be between planes. Which gap will be smaller?Between planesWithin planeWithin the planeBetween the planesThe gaps are the same sizeANSWER: B. Between the planesWithin the plane x radiusBetween the planes– x radius
22 When a copper wire is heated, it becomes more malleable because ___________________________. the bonds have been weakenedthe wire has fewer atomic level defectsthe wire has more atomic level defectsthe density is lowerthere is more space inside the crystal latticeANSWER: B. the wire has fewer atomic level defects. Heating the metal allows the atoms to settle into a more regular arrangement which decreases the number of grain boundaries, or defects. Fewer grain boundaries means a softer metal.
23 Atoms in a solid _____________________________. cannot move, only electrons movemay move through vacancies in a crystal latticemay move in the spaces between atoms in a crystal latticecan move through both vacancies and in the spaces between atoms in a crystal latticenone of the aboveANSWER: B. may move through vacancies in a crystal lattice. These are called dislocations.
24 If 0 < x < 1, which gallium alloys could be solid solutions? Gallium(Ga) can be mixed with two other elements to form a solution. Possible elements include aluminum(Al), arsenic(As), and phosphate(P).If 0 < x < 1, which gallium alloys could be solid solutions?B6 C7 N8 O13 Al14 Si15 P16 S31 Ga32 Ge33 As34 Se49 In50 Sn51 Sb52 TeGaxAl1-xAs ; GaAlxAs1-xGaxAl1-xAs ; GaPxAs1-xGaPxAs1-x ; GaAlxAs1-xGaPxAs1-x ; GaxP1-xAsANSWER: B.The structure has the compostion of GaAs or AlP or any replacement of Ga by Al or As by P so that the sum of Ga + Al =1 and the sume of P + As = 1
25 Buckminsterfullerene, C60, is face-centered cubic in crystalline form Buckminsterfullerene, C60, is face-centered cubic in crystalline form. If a fullerene was saturated with potassium, by placing a potassum atom in every tetrahedral hole and every octahedral hole, the chemical formula would be ____.KC60K2C60K3C60K4C60K6C60ANSWER: C. K3C60The FCC structure has 2 tetrahedral sites and one octahedral site for each atom for a total of 3 sites.
26 How many zinc ions (green) are in a zinc sulfide unit cell? 1234ANSWER: D. 4There is an atom on every corner, with only 1/8th of that atom contributing to unit cell. 8 * 1/8th = 1 atomThere is a zinc atom on each face contributing ½ to the unit cell. 6 * ½ = 3 atomsTotal atoms = = 4 atoms
27 How many atoms are in the following layer sequence of a diamond structure? 46813Z = 0Z = 1/4ANSWER: C. 8 atoms.1 atom from corner atoms (8 corner atoms, shared with 7 other unit cells, so 1/8th of each corner atom in this unit cell)3 atoms from faces (6 atoms, each shared with another unit cell so 6 x ½)4 atoms inside the unit cell (atoms on the z =1/4 and z= ¾ levels)Z = 1/2Z = 3/4
28 What is the coordination number for a diamond structure? 46810ANSWER: AThe diamond structure can be considered an FCC lattice with half the tetrahedral holes filled by four interstitial C atoms. Each carbon atom bonds to 4 other carbon atoms
29 What is the coordination geometry of a diamond structure? TetrahedralSquareOctahedralCubicANSWER: A. Tetrahedral The inner carbon atoms are at the center of a tetrahedron.
30 In the two-dimensional square packing shown below, what is the coordination number of the central atom?2468ANSWER: B. 4 The central atom is actually only in contact with 4 atoms, not all 8 that surround it.
31 Which part of a face-centered cubic crystal surface is likely to chemically etch faster? 111 plane100 planeGrain boundaryVacancyANSWER: C. Grain BoundaryThe etching solution will attack the surface at dislocations. These dislocations occur at grain boundaries in crystal structures.
32 A system contains an equimolar vapor/liquid mixture of components A and B. The saturated pressure of A is greater than that of B. If the system is an ideal gas, which plot represents the effect of raising the system pressure on the vapor/liquid fractions of component A?1.01.0yAxAC.1.0xAyAyAxAA.B.ANSWER: A.The mole fraction of A in the vapor should be higher than in the liquid and high pressure should be all liquid with the same compostion as the starting vaporPPP1.01.0yAxAyAxAPasat > PBsatD.E.PP
33 TemperatureLiquidSolid100%Cu100% Ni50/50For this Cu/Ni phase diagram, which cooling curve results for a 50/50 mixture?Temp.TimeATimeBTemp.TimeCTemp.ANSWER: D.The slope should change and the temperature should drop more slowly as solid starts to form. From the phase diagram, solidificaiton takes place over a temperature range. The slope should change again when all solid and change based on the heat capacity of the solid.TimeDTemp.TimeETemp.
34 Magnesium and silicon form Mg2Si under certain conditions Magnesium and silicon form Mg2Si under certain conditions. What phases and how much of each will be present for a 60 mol% Si mixture at 1000 K?xSiTemperature (K)1Liquid80017001 phase that is 57% Si2 phases; 57% is Mg2Si2 phases; 40% is Mg2Si2 phases; 57% is pure Mg2 phases; 57% is pure SiANSWER: B.Mixture of 2 solid phases, Mg2Si and pure Si. Lever rule indicates more Mg2Si than Si so B is correct answer. It’s about 57% Mg2Si.MgSi
35 A Pt/Ag alloy containing 62% Ag is initially at 1600°C A Pt/Ag alloy containing 62% Ag is initially at 1600°C . As it cools, what phases are observed? L represents liquid and α and β are solids.1800L+α, L+α+β, L+β, β, α+βL+α, L+β, α, α+βL+α, L+α+β, L+β, α+βL+α, L+β, α+βL+α, L+β, β , α+βLL+ααTemp. (°C)L+βα+βANSWER: A. L+α, L+α+β, L+β, β, α+βIn the transition from L + alpha to L + beta, must have L +alpha+betaβWt % Ag100
36 (β) solid. Given some of the phases, what phase(s) Cu/Pb alloys can form several combinations of phases between two liquids (L1 and L2) and alpha (α) and beta(β) solid. Given some of thephases, what phase(s)is/are present at the pointindicated?Wt % Pb100TemperatureL+ αLα + βL2+αL1+βL1+L2α+βANSWER: C. L1+L2In the region that has liquid on both sides, get two liquid phases that do not mix so the indicated point represents liquid phases L1 and L2.
37 A Si-Mg mixture containing 40 mol% Si at 1000 K (the blue dot in the figure) contains ____________. 1700Liquida single solid phasea mixture of pure Si and pure Mga mixture of Si and Mg2Sinone of the aboveTemperature (K)ANSWER: C.At 40 mol% Si and 1000 K, the mixture is in the rectangular region, which is all solid. It is mostly solid Mg2Si with some solid pure Si. There are two solid phases present.800xSi1Mg2Si
38 For the binary phase diagram for components A and B, what fraction of the mixture is liquid at point indicated by the black dot?1Weight frac BTemperatureLiquidSolid30%45%50%55%70%ANSWER: EUse the lever rule to determine the amount. The black dot is much closer to the liquid line than the vapor line so only possible answer is E.