KEY. FIRST MIDTERM EXAM Chemistry March 2012 Professor Buhro. ID Number:

Transcription

1 KEY FIRST MIDTERM EXAM Chemistry March 2012 Prfessr Buhr _ KEY Signature _ KEY Print Name Clearly ID Number: Infrmatin. This is a clsed-bk exam; n bks, ntes, ther students, ther student exams, r any ther resurce materials may be cnsulted r examined during the exam perid. Calculatrs are permitted. Partial credit will be given fr partially crrect reasning in supprt f incrrect r crrect final answers. Additinal space fr answers is prvided at the end f this exam; please clearly label any answers yu place there. Please find Ptentially Useful Infrmatin attached as the last pages f this exam. 1. (20 pts) 2. (15 pts) 3. (10 pts) 4. (30 pts) 5. (10 pts) 6. (15 pts) Ttal (100 pts) 1

2 1. 20 ttal pts. Cngratulatins! Yu have discvered a new metallic element, which yu have named turbnium (chemical symbl Trb ). Turbnium pssesses an unusual crystal structure fr a metal. The structure cnfrms t a primitive tetragnal lattice, with a Trb atm placed n each lattice pint. (a) 04 pts. A prjectin n the xz plane f the Trb crystal structure is shwn belw. Upn this prjectin (and in different regins f the prjectin) please sketch and label the fllwing families f planes: (002), (200), ( 1 11), and (102). (002) (200) (1 1 1) (102) z x [1 pt. each family f planes] The indexed XRD pwder pattern f crystalline turbnium is shwn belw. Line psitins in 2 are given in the adjacent table. Please cnsider this pattern as yu answer the questins n the next page. Cunts hkl 2 (º) Degrees 2 2

3 1. (cnt.) (b) 05 pts. Why is the 100 reflectin present in the XRD pattern f turbnium, whereas this reflectin is ften absent in the XRD patterns f ther metals? Please give yur answer in ne r tw brief sentences. The 100 reflectin is generally present in structures cnfrming t primitive lattices. (c) 05 pts. Why is the 010 reflectin nt shwn in the indexed XRD pattern f turbnium? Is it systematically absent? Please give yur answer in ne r tw brief sentences. The 010 reflectin is cincident (by symmetry) with the 100 reflectin in the tetragnal crystal system. It is nt systematically absent. (d) 06 pts. Please calculate the lattice parameters fr the turbnium structure. Shw sufficient wrk t justify yur answers A a d A A c d A [3 pts. each crrect calculatin. 1 pt. each minr errr.] 3

4 2. 15 ttal pts. Within hcp r ccp anin sublattices, the O sites themselves cnstitute clse-packed layers when they are fully ccupied. Thus, the packing sequence in NaCl may be described as AcBaCbAcBaCb, where the capital letters dente the anin-sublattice packing sequence (ABC), and the lwer-case letters dente the clse-packed layers frmed by the O-site ccupancy f the catins. This ntatin fr describing the packing sequences in inic, nnmlecular crystal structures is knwn as Ramsdell ntatin, and can be used t describe a variety f structures. (a) 03 pts. Please identify the crystal structure, using a mineral name r chemical frmula, fr the structure having the Ramsdell ntatin: AcB/AcB/ The slash (/) in the ntatin indicates a cmpletely empty layer f O sites. CdI 2 (b) 03 pts. Please identify the crystal structure, using a mineral name r chemical frmula, fr the structure having the Ramsdell ntatin: AcB/CbA/BaC The slash (/) in the ntatin indicates a cmpletely empty layer f O sites. CdCl 2 (c) 03 pts. Please identify the crystal structure, using a mineral name r chemical frmula, fr the structure having the Ramsdell ntatin: AcBcAcBc NiAs (d) 03 pts. Please identify the crystal structure, using a mineral name r chemical frmula, fr the structure having the Ramsdell ntatin: A(1/2c)B(1/2c )A(1/2c)B(1/2c ). The (1/2c) and (1/2c ) represent layers in which ne-half f the O sites are ccupied. The c and c represent different subsets f O sites. Rutile [2 pts. fr TiO 2 ] (e) 03 pts. Imagine remving the catins (Ti 4+ ins, fr example) frm the O sites in the rutile structure, and replacing them with catins f apprpriate charge such that all available O sites becme fully ccupied. Please identify the resulting crystal structure, using a mineral name r chemical frmula. NiAs 4

5 3. 10 ttal pts. Prjectins f bcc (left) and fcc (right) metallic structures n the (001) planes are shwn belw. The 110 reflectin in bcc metals is very prminent, whereas the 110 reflectin is systematically absent in fcc metals. Please explain in n mre than a few sentences why the 110 reflectin is present in the bcc structure but absent in the fcc structure. Include sketches n the frames belw in supprt f yur answer. y z ut (up) x [2 pts. fr adding 110 lines ] [2 pts. fr adding 110 lines ] Lines representing the (110) planes are drawn n each prjectin abve. In the bcc structure (left), there are n atms psitined at halfway psitins between the (110) planes, and s the 110 reflectin is bserved (3 pts.). In the fcc structure (right), there are identical (but shifted) planes f atms psitined exactly halfway between the (110) planes, which result in cmplete destructive interference f the diffracted intensity frm these planes, r in a systematic absence f the 110 reflectin (3 pts.). 5

6 4. 30 ttal pts. The XRD pwder pattern belw crrespnds t a mixture f tw metallic elements, A and B, each f which exhibits a cmmn, cubic structure. The first line in the pattern (27.361º) belngs t metal A. A sin 2 ()-rati table is prvided, frmed frm every line in the cmbined pattern. Please assign hkl indices and A r B t each line in the pattern, and calculate the lattice parameter a fr metal A and metal B. 111 B [1 pt. each crrect label] Cunts 110 A 200 B 311 B 200 A 211 A 321 A 220 B 222 B 220 A 310 A 222 A 400 B 331 B Degrees 2 Line N. 2 sin 2 () primitive bcc fcc m hkl /m 100 * m hkl /m 100 m hkl /m m hkl = (h 2 + k 2 +l 2 ) *Assume first reflectin is 100 Assume first reflectin is 110 Assume first reflectin is 111 6

7 4. Cntinued. Place additinal wrk here. Inspectin f the table n page 6 indicates small integer m values fr lines 1, 4, 5, 7, 10, 11, and 13, which are assigned t metal A. All three slutins give integer m values; the primitive slutin is rejected because it is nt a cmmn metallic structure, and the fcc slutin is rejected because it des nt index fr allwed fcc reflectins. The structure fr metal A is thus bcc. The table n the right prvides the hkl indices fr these reflectins. [4 pts. fr crrectly identifying the lines belnging t metal A.] Line n. bcc m hkl The remaining lines 2, 3, 6, 8, 9, 12, and 14 must therefre belng t metal B. A new set f m hkl /m 100 values is determined by dividing the sin 2 () values fr these lines by that fr line 2 ( ; see the table n the right). Multiplicatin f the new m hkl /m 100 values by 3 gives integer values, and thus an fcc slutin. The lines index crrectly fr allwed fcc reflectins; hkl all even r all dd (see table). [4 pts. fr crrect reasning abut the structure f metal B.] Line n. m hkl /m 100 fcc m hkl Bragg s law: d sin hkl hkl The d-spacing frmula fr the cubic system: d a( h k l ) hkl Cmbine and slve fr a: ( h k l ) a 2 hkl 2 a a A B ( A) ( A) A [4 pts.] A [4 pts.] 7

8 5. 10 ttal pts. The XRD pattern f an equal-vlume mixture f CsCl (lightweight curve), CsBr (medium-weight curve), and CsI (heavy-weight curve) shwn belw. Several peaks are labeled. Cunts Cunts 111, CsI 100, CsI 20 Degrees 2 111, CsBr 100, CsCl 100, CsBr 111, CsCl (a) 05 pts. In general, the XRD pattern f CsI has the highest intensity, and the CsCl pattern has the lwest intensity (see, fr example, the 111 reflectins fr each phase near 30º 2). Please explain in n mre than tw sentences why the CsI pattern is generally the mst intense, and the CsCl pattern the least intense. The scattering factr r diffractin prbability is higher fr heavier elements because they cntain mre electrns than d lighter elements. Cnsequently, the idide-cntaining CsI has the mst-intense pattern verall, and the chlride-cntaining CsCl has the least. (b) 05 pts. Despite the much greater verall intensity f the CsI pattern, its 100 reflectin is extremely weak. The inset in the graph abve shws the 100 reflectins fr CsI, CsBr, and CsCl at a greatly expanded vertical scale. The CsI 100 reflectin (marked by an arrw) is barely discernable in the baseline f the pattern. Please explain in n mre than tw sentences why this reflectin is s weak. Cs + and I have the same number f electrns, making their scattering factrs nearly identical, such that the diffracted intensity frm the 100 reflectin is nearly quenched by destructive interference between the Cs + and I planes. (A bcc-like situatin is created.) 2 (º) 8

9 6. 15 ttal pts. Cngratulatins! Yu have just synthesized the first cmpund f the element turbnium (Trb; see prblem 1). The new cmpund has the frmula TrbCl (1:1 stichimetry). Yu have btained the XRD pwder pattern, and have successfully indexed the reflectins in the pattern t a cubic unit cell using the sin 2 ()-rati methd. The XRD pwder pattern cntains a 100 reflectin at , which crrespnds t a d spacing f Å. (a) 05 pts. This cmpund exhibits a cmmn structure. Please identify it, and prvide a brief justificatin fr yur answer. The new cmpund TrbCl apparently has the CsCl structure, because the 100 reflectin is present. This reflectin wuld be systematically absent if the cmpund pssessed the zinc blende r NaCl structure. (b) 05 pts. Please determine the lattice parameter a, and prvide a brief justificatin fr yur answer. The d spacing fr the 100 reflectin = a = Å. (c) 05 pts. Please calculate the nearest-neighbr Trb Cl distance (internuclear separatin) in this structure. Shw yur wrk. The M X distance equals ne-half the unit-cell bdy diagnal. M X = (bdy diagnal)/2 = 3 a 3 = ( Å) = Å (5 pts.) 9