Homework Answers
dhkl = a / [h2 + k2 + l2]1/2
d111 = (432) / [12 + 12 + 12]1/2
d111 = 249 pm or 2.49 x 10-10 m
d211 = (432) / [22 + 12 + 12]1/2
d211 = 176.4 pm or 1.76 x 10-10 m
d100 = (432) / [12 + 02 + 02]1/2
d100 = 432 pm or 4.32 x 10-10 m
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Calculate the separations of planes {111},{211 }, and { 100 } in a crystal in which...
Problem 3: Draw specific (hkl) planes of (100), (020), (211), and (111) on below orthorhombic crystal...
Problem 3: Draw specific (hkl) planes of (100), (020), (211), and (111) on below orthorhombic crystal structure.
Discuss physically why an actual crystal cannot possess a fivefold axis of rotational symmetry. Draw sketches...
Discuss physically why an actual crystal cannot possess a fivefold axis of rotational symmetry. Draw sketches illustrating a (100) plane, a (110) plane, and a (111) plane in a cubic unit cell. How many equivalent {100}, {110}, and {111} planes are there in a cubic crystal? Regard planes (hkl) and (hkl) as identical. How many equivalent {123} planes are there in a cubic crystal? How many equivalent {111} planes are there in an orthorhombic crystal?
Two pairs of directions are given in a cubic crystal system: [100]-[121] and [011]-[111]. * Compute...
Two pairs of directions are given in a cubic crystal system: [100]-[121] and [011]-[111]. * Compute the Miller indices of the planes formed by each pair of directions. * What is the direction common to those two planes? * Repeat the exercise for a triclinic crystal system with lattice parameters {1,2,3,40,60,80}.
Niobium (Nb) has the BCC crystal with a lattice parameter a 0.3294 nm. Find the planar concentrations as the number of atoms per nm2 of the (100), (110) and (111) planes. Which plane has the most con...
Niobium (Nb) has the BCC crystal with a lattice parameter a 0.3294 nm. Find the planar concentrations as the number of atoms per nm2 of the (100), (110) and (111) planes. Which plane has the most concentration of atoms per unit area? Sometimes the number of atoms per unit area nsurface on the surface of a crystal is estimated by using the relation nsurface - nbulk2/3 where nbulk is the concentration of atoms in the bulk. Compare nsurface values with...
1. For each of the (100). (110), and (111) planes, state all of the < 100...
1. For each of the (100). (110), and (111) planes, state all of the < 100 >, < 110 >, and < 111 > directions that lie on each of the planes. Hint: the directions that lie on the plane are perpendicular to the plane normal. The normal direction of a cubic plane has the same indices as the plane.
9. Write the Miller indices for the family of close-packed planes in the FCC crystal. {hkl}...
9. Write the Miller indices for the family of close-packed planes in the FCC crystal. {hkl} Hexagonally Close-Packed (HCP) Structure 10. What are the Miller-Bravais indices for the basal planes (i.e., the six-sided top and bottom) and side planes (i.e., the six rectangles of sides a and c) of the HCP unit cell? Basal planes: {uvtw} = Side planes: {uvtw} = 11. Calculate the planar density for the most densely packed HCP planes in terms of atomic radius (R). (Show...
For an FCC single-crystal metal, do the following for both the (100) and the (111) surface plane:...
For an FCC single-crystal metal, do the following for both the (100) and the (111) surface plane: 5) What is the surface coordination number for an atom in each of the surface planes? 6) Hence determine the surface free energies for the (100) and (111) surfaces. Use the formula in the data sheet at the end of the assignment. Express your answer in terms of the bulk lattice parameter a and the cohesive energy HoCompare the surface energies of the...
Find (cubic); h2+k2 + 12 hkl 100 110 111 200 210 211 220 300, 221 *...
Find (cubic); h2+k2 + 12 hkl 100 110 111 200 210 211 220 300, 221 * The value 7 is missing in the sequence, since there is no possible integral value h2+k2 + 1 = 7
(20 pts.) Draw each question (a-d) on a separate set of axes. Be sure to label...
(20 pts.) Draw each question (a-d) on a separate set of axes. Be sure to label all axes, directions, planes, etc. appropriately. a. (5 pts.) Draw the following crystallographic directions in a cubic unit cell: [112],[010], [100]. b. (5 pts.) Draw all directions in the family <110> in a cubic crystal on a single set of axes. C. (5 pts.) Draw the following planes in a cubic unit cell: (110), (112), (010). d. (5 pts.) Draw all the planes in...
Units: NA= 6.02×1023 atoms/mol Walter White who lives in Simeranya (a utopic city in Anarres) prepares...
Units:
NA= 6.02×1023 atoms/mol
Walter White who lives in Simeranya (a utopic city in Anarres) prepares blue crystals, named as myth, which adopt a side-centered cubic (scc) cell with a molecular formula of A.B Side-centered cubic (scc) cell Top view 1. Determine the molecular formula of myth. 2. Calculate the atomic packing factor (APF) of scc unit cell. The atomic radii of A and B are equal to 120 and 132 pm, respectively. 3. Calculate the density of the myth...
Problem 3: Draw specific (hkl) planes of (100), (020), (211), and (111) on below orthorhombic crystal structure.
Discuss physically why an actual crystal cannot possess a fivefold axis of rotational symmetry. Draw sketches illustrating a (100) plane, a (110) plane, and a (111) plane in a cubic unit cell. How many equivalent {100}, {110}, and {111} planes are there in a cubic crystal? Regard planes (hkl) and (hkl) as identical. How many equivalent {123} planes are there in a cubic crystal? How many equivalent {111} planes are there in an orthorhombic crystal?
Niobium (Nb) has the BCC crystal with a lattice parameter a 0.3294 nm. Find the planar concentrations as the number of atoms per nm2 of the (100), (110) and (111) planes. Which plane has the most concentration of atoms per unit area? Sometimes the number of atoms per unit area nsurface on the surface of a crystal is estimated by using the relation nsurface - nbulk2/3 where nbulk is the concentration of atoms in the bulk. Compare nsurface values with...
1. For each of the (100). (110), and (111) planes, state all of the < 100 >, < 110 >, and < 111 > directions that lie on each of the planes. Hint: the directions that lie on the plane are perpendicular to the plane normal. The normal direction of a cubic plane has the same indices as the plane.
9. Write the Miller indices for the family of close-packed planes in the FCC crystal. {hkl} Hexagonally Close-Packed (HCP) Structure 10. What are the Miller-Bravais indices for the basal planes (i.e., the six-sided top and bottom) and side planes (i.e., the six rectangles of sides a and c) of the HCP unit cell? Basal planes: {uvtw} = Side planes: {uvtw} = 11. Calculate the planar density for the most densely packed HCP planes in terms of atomic radius (R). (Show...
For an FCC single-crystal metal, do the following for both the (100) and the (111) surface plane: 5) What is the surface coordination number for an atom in each of the surface planes? 6) Hence determine the surface free energies for the (100) and (111) surfaces. Use the formula in the data sheet at the end of the assignment. Express your answer in terms of the bulk lattice parameter a and the cohesive energy HoCompare the surface energies of the...
Find (cubic); h2+k2 + 12 hkl 100 110 111 200 210 211 220 300, 221 * The value 7 is missing in the sequence, since there is no possible integral value h2+k2 + 1 = 7
(20 pts.) Draw each question (a-d) on a separate set of axes. Be sure to label all axes, directions, planes, etc. appropriately. a. (5 pts.) Draw the following crystallographic directions in a cubic unit cell: [112],[010], [100]. b. (5 pts.) Draw all directions in the family <110> in a cubic crystal on a single set of axes. C. (5 pts.) Draw the following planes in a cubic unit cell: (110), (112), (010). d. (5 pts.) Draw all the planes in...
Units:
NA= 6.02×1023 atoms/mol
Walter White who lives in Simeranya (a utopic city in Anarres) prepares blue crystals, named as myth, which adopt a side-centered cubic (scc) cell with a molecular formula of A.B Side-centered cubic (scc) cell Top view 1. Determine the molecular formula of myth. 2. Calculate the atomic packing factor (APF) of scc unit cell. The atomic radii of A and B are equal to 120 and 132 pm, respectively. 3. Calculate the density of the myth...
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