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Homework Assignment #3
MEMS 1054 ‘ NAME: Return by next Wednesday! 7 Questions in total! This is an
important homework for you in MEMS 1054. Get Started
early, especially since I uploaded it only today, Friday! 1) Many concentrated solid solutions of metal atom species form chemically ordered phases
at low temperatures. The chemical ordering involves changes from a statistically random
distribution of the atoms among the atom sites to a regular distribution in which
designated sites are occupied by one kind of atom. Thus, atomic sites, which are
equivalent in the disordered solid solution are no longer equivalent in the ordered
structures. These phenomena can be monitored and studied with diffraction techniques
using X—rays, neutrons and electrons. ﬁr'sprdzred {Tutc
Svoh'q'r 5¢Futian~ cu” . Atemt. in. A“? A”
Figure 1 As shown schematically in the section of the binary phase—diagram (Figure 1), both Cu
and Au have cubic close—packed structures and at temperatures above 410°C a complete
solid solution exists between them across the entire composition range. Below critical
temperatures of 390°C and 410°C ordered phases occur at the compositions of about
CuAu and Cu3Au. Just as the disordered Cu and Au phases unit cells with lattice
parameters 0t=[3=y=90° and a=b=c can be used HERE to good approximation to describe
the ordered phases. Continued next page a) In the AB—compound CuAu the atomic ordering a crystal structure where Cu atoms
occupy the positions 0&0 and IA, 1/2, 0 and the Au atoms occupy the sites 1/2 , 0, 1A and 0, r 1/6, 1/2 in the unit cell. .__.—— \ .___¢——~ Draw a unit cell of ordered CuAu and determine the lattice type (P, C, LP) and crystal
system of this crystal structure. [oat] :i ‘ ‘9 '0
“7‘ 'W WWW” my“; my am 2/ > / ‘5
’5 W14 #3:? W m.) a; 44 W! mazezm,
/ ‘ 3 m
#22!“ “252/: M to w r a M w“ M"
Z: m>la 0/ Mil ‘ #6:: WW affaixwmf [a1 a/LNC)\
I l I m I o ‘ ‘ ‘
vita/w?” [7,,” f _ WW b) n the A3B—compound Cu3Au the a omic ordering a crystal structure where Au atoms
occupy the positions 0,0,0 and Cu atoms occupy 1/2, 1A, 0 and 1A , 0, 1/5 and O, 1/2, IA in
the unit cell. Draw a unit cell of ordered CuAu and determine the lattice type (P, C, I F) and crystal
system of this crystal structure. 2) Consider the ionically bonded crystal structure of rock salt, NaCl. A conventional unit
cell representation of this cubic structure is shown on the next page inclusive of some information regarding the atomic and ionic radii. Size effect in ionically bonded structures: e.g. NaCl
Na Cl —> Na+ Cl
electron transfer
[Ne3s1] [Ne3823p5] [Ne] [Ar]
0.099 0.095 0.181 r [nm] 0.192
/7 a) How many lattice points are contained in this conventional unit cell? How many chemical units of NaCl are contained in this unit cell? % and? b) Determine by inspection of the unit cell the coordination (represents the number of nearest neighbors) for each of the two ion species in the NaCl structure. How many cations (anions) are nearest neighbors to the anion (cation) sites? Mn‘ W [Z /V£+Wm)£rém My]. 44. m“ a” a'M/f
42‘“ «ce'« 4 ,~5¢’/Mé/m‘/M<
c) Is the cation coordination characteristic of NaCl structures called tetrahedral, cubic
octahedral or polyhedral? arm/m ﬂ/ 7%} f; oer/WfEDML eawamg; ’ {44/1 MVLMM 1'; AWM/ 5/ “A’Ké” d) For the sketched unit cell of NaCl define a coordinate system and indicate the direction
[1 2 0] by an arrow, draw into it the (101) plane and list all the planes contained in the form {111} using their Miller indices. 3) Compare the three cubic cystal structures shown below as unit cell representations.
What are the atom positions and species? What are the Bravais lattices for these
structures (cP, cI, CF)? How many atoms of each species (where applicable) are contained in the unit cell? 4) Find descriptions of the archetype closepacking related structure of ﬂuorite (a) and
for perovskite (b). The are in the notes I used in lecture and you can also find them
per book and/or intemet research. Identify for each the Bravais LATTICE (there are 14 of these) and describe the
MOTIF for each structure. . r 111 FJEZ" WwJeaA
a)CaF2(ﬂuor1te) 6F; Japalg‘ FM‘ ’1” 2‘ 116; V,“ q 11
d) CaTi03 (perovskite) C CL, «)‘l M” M y 4“ if?!) g 21/”. 5' 0’7'
0 — M5” 0v MW 5) The unit cell of a tetragonal crystal has three orthogonal axes (0L=[3=y=90°) with lattice
constants a, b, and c equal to 3A, 3A, and 7A, respectively. a) Make a perspective sketch of one or more unit cells of this crystal. Outline planes with
Miller indices (110) and (011). b) List six different orientations of planes, which have Miller indices that are
permutations of i1 , :lzl , and O. For this tetragonal crystal, group these six planes into forms of crystallographically equivalent planes {hkl}. '_ / n .
101°), 1070) , 1‘ (la/)1 i (m7), i (911)]: (WI) 100/} #Jﬂ’j Mt
/ {In} i101} Jag/“ML
c) Find the angles between each of the pairs of the [100] direction with the [101], [011],
[110] and [111] in this tetragonal crystal. :1 I \ p z .
(14/[[Ioo3itl00)=> 2‘3 : com, : 3m : “31.1 a d! ' {i at (Mm): o , =6...» 0114/
L4. I ) q 33 0 / «msmm»? W. WW7? ' a 1/ a ' .
“(9 ¥ZEWJIEW3>$ 5050/9: W 3 {7 ’W d) Is the normal of the (101) plane parallel to the [101] direction in this tetragonal
crystal? I
M I
. / 6) Draw the atomic arrangements of the close—packed planes in the elemental cF crystal
of Cu and use it as a representation of the crystal in the projection along the normal to
this close—packed plane. What are the Miller indices, (hkl), of the close packed plane you drew? ( n ) Now mark the three close—packed directions in this close—packed plane (hkl). m iElTojl iftwjﬁ
i [0713 / 7) Miller indices problems from the textbook by Callister. .. 3.33, 3 .34
3.33 Determine the Miller indices for the planes shown in the following unit cell:
a ‘3 3.34, Determine the Miller indices for the planes , Shown in the following unit cell:
w v +2 ...
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This note was uploaded on 01/07/2011 for the course MEMS Mems1054 taught by Professor Wiezorek during the Fall '10 term at Pittsburgh.
 Fall '10
 Wiezorek

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