KEY FIRST MIDTERM EXAM Chemistry February 2009 Professor Buhro

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1 KEY FIRST MIDTERM EXAM Chemistry February 2009 Professor Buhro Signature KEY Print Name Clearly ID Number: Information. This is a closed-book exam; no books, notes, other students, other student exams, or any other resource materials may be consulted or examined during the exam period. Calculators are permitted. Partial credit will be given for partially correct reasoning in support of incorrect or correct final answers. Additional space for answers is provided at the end of this exam; please clearly label any answers you place there. Please find Potentially Useful Information attached as the last pages of this exam. 1. (15 pts) 2. (15 pts) 3. (10 pts) 4. (15 pts) 5. (15 pts) 6. (15 pts) 7. (15 pts) Total (100 pts) 1

2 P ow der Cell total pts. The element lanthanum (La) exhibits an uncommon metallic crystal structure. The hexagonal unit cell for crystalline La is shown below, in two orientations. The lattice parameters are a = b = Å, c = Å, = = 90 o, and = 120 o. (2/3, 1/3, 3/4) (2/3, 1/3, 3/4) La(A) La(B) (1/3, 2/3, 1/4) (1/3, 2/3, 1/4) a. 03 pts. Is the structure of La a close-packed structure? Please explain your answer in one or two brief sentences. The structure of La is close packed (1 pt.). Each plane of atoms (perpendicular to z) is close packed (1 pt.), and each close-packed plane is correctly offset from the adjacent close-packed planes (1 pt.) by ± a/3 in both the x and y directions. b. 03 pts. The packing sequence for the hcp structure is AB, and the packing sequence for the ccp structure is ABC. Please give the packing sequence for the La structure. ABAC, ACAB, BABC, or other correct variant c. 06 pts. Please assign fractional coordinates to the atoms labeled La(A) and La(B). La(A) (1, 1, 1/2) (3 pts.) La(B) (0, 0, 1/2) (3 pts.) d. 03 pts. Please give the internuclear separation (distance) between La(A) and La(B) Å 2

3 2. 15 total pts. a. 10 pts. The table below lists the anion sublattice and cation site occupancy for several structure types. Please identify the structure type for each by writing a structure name or characteristic formula in the blank spaces in the table. If there is no common structure type having the lattice characteristics given for any specific case(s), then write none in the blank. Anion Sublattice Cation sites occupied Structure type ccp All T + or all T sites zinc blende hcp All T + or all T sites wurtzite ccp All O sites NaCl hcp All O sites NiAs Primitive cubic All cubic sites CsCl ccp All T sites antifluorite hcp All T sites none ccp hcp hcp ½ of O sites, in alternating layers of O sites ½ of O sites, in alternating layers of O sites ½ of O sites in each layer of O sites CdCl 2 CdI 2 rutile or none (2 pts. each correct response) b. 05 pts. Please briefly explain why the NiAs structure is commonly found for covalent (or metallic) compounds but not for ionic compounds. In the NiAs structure there are close contacts (short distances) between the metal atoms along the z axis (direction). If the structures (compounds) were ionic, the M z+ ions would experience destabilizing electrostatic repulsions. 3

4 3. 10 total pts. A partial unit cell for CaTiO 3 is given below. Only the positions of the O 2 ions are given. Please show all Ti positions by placing small circles on the unit cell diagram to represent the Ti 4+ ions. Please also show all Ca positions by placing larger circles on the unit cell diagram to represent the Ca 2+ ions. (1 pt. each) (2 pts.) total pts. Imagine a Mooser-Pearson plot for MX 2 compounds that contains structure fields for fluorite, rutile, and cadmium iodide structures. Please label the axes of the Mooser-Pearson plot (below), and sketch proposed locations of the three fields on the plot. Be sure to label the fields according to structure. n (3 pts.) rutile (2 pts.) fluorite (2 pts.) (3 pts. for orienting the fields along the proper diagonal) cadmium iodide (2 pts.) (3 pts.) 4

5 5. 15 total pts. A projection of a hexagonal lattice on the xy plane is shown below. Please assign Miller indices to the crystallographic direction indicated by each arrow. Place your answers in the appropriate blanks below. The arrows all lie in the xy plane. (a) (b) (c) y x (d) (e) a. [010] b. [120] c. [130] (3 pts. each) d. [1 1 0] e. [100] 5

6 6. 15 total pts. The XRD powder pattern of a metal, collected using Cu K radiation, is shown below. This pattern was obtained in the standard fashion, using a fixed x-ray wavelength and by scanning through a range in 2. A newer method exists for collecting XRD powder data very quickly, in which a fixed 2 value is used and the x-ray wavelength is scanned over a range of wavelengths. Imagine that the metallic specimen used to obtain the conventional powder pattern below was re-examined by the newer method, at a fixed 2 of 2.85, which is a typical value for this method. Please sketch the expected diffraction pattern in the empty graph box below. Place the calculations necessary to support your answer on the next page. Hint: 1 Å = 100 pm. d = Å d = Å d = Å Degrees 2 Counts x-ray wavelength (pm) [3 pts. for peak positions; 3 pts. for relative peak heights] 6

7 6. (cont.) Extra work space 2d sin 1 2(3.513 Å) sin(1.425 ) Å 17.5 pm 2 2(3.042 Å) sin(1.425 ) Å 15.1 pm 3 2(2.151 Å) sin(1.425 ) Å 10.7 pm [3 pts. each calculation] 7

8 7. 15 total pts. The XRD pattern of a common metal is shown below. The line at lowest 2 is indexed. Please identify the structure type, and calculate the lattice parameter(s) of this metallic specimen. Show your work and describe your reasoning clearly. Line No. Degrees A common metallic specimen having 100 as the lowest-angle reflection must have an hcp structure (04 pts.). The second line must be the 002 reflection (04 pts.), because the (tall) height of the third reflection identifies it as the 101. (continued on the next page) 8

9 7. (cont.) Extra work space Use the first two reflections to solve for the lattice parameters a and c: d d 2sin a 2 a combine : 3 a 2sin Å a Å (4 pts.) 3sin100 3sin similarly : 12 2 c d002 2 c c 2sin002 2(1.542 Å) c Å (3 pts.) 2sin002 2sin