MSE 280
MSE 280
Spring 2022
Spring 2022
Lecture 4 / Lecture 4
Ionic Crystals / Ionic Crystals
1. Compute the atomic packing factor for the diamond cubic crystal structure. Assume that
bonding atoms touch one another, that the angle between adjacent bonds is 109.5°, and that
each atom internal to the unit cell is positioned at a/4 of the distance away from the two
atoms in
nearest cell faces (a is the unit cell edge length).
V01 of
cell
unit
App
+
42×6=1+3--4 atoms inside
:
.
unit cell
Y¥fr
diamond cubic
.
1+3+4=8 total atoms
length
:
4
=t
①
APF
YX
a
a
=
4×0.5771 d
=
4×0.5771×2 r
=
4.6168
=D sing
=
54 -15°
App
=
APF
3
( 110
+
=
I
=
→
8×14-3
✗
IT
*
r
:
ZR
••(
•
3)
}
)
ME
••
ooo
ttomm
••→
✗
fza
1
Boy
a
a
angle ?
Bond
0.3405
3
A.
0.5771 dnm
14.6168 r )
rnm
)
¥1T (r )
n
=
=D sin / 35.25
0--90-0=35.250
d=2r
=
✗
✗
109.5°
Bond angle :
cell
unit
V01 of
# :
coordination
Bond
:
=
2. What is the spacing between the (211) planes of lead? Would you expect to see this plane
diffract in an XRD experiment? Why or why not? Lead has a FCC crystal structure with an
atomic radius of 0.175 nm.
=
FI :
d=n÷E
a
a=:÷
a
of
2
=
2hr
T2 ( 0.175)
0.495
spacing
D= 0.202 nm
values
__
a.
wavelengths
spacing
Given
the
lies
the
region
so
x-ray
we
can
use
within the
it to
diffract
.
?⃝
MSE 280
MSE 280
Spring 2022
Spring 2022
3. At a fundraiser, there is the classic game of guessing how many marbles are in a container.
Looking at the container, you can estimate it to be a cylinder with an internal diameter of 15
cm and a height of 25 cm. For the marbles, you estimate that they are 1 cm in diameter. What
do you guess the number of marbles to be? Justify your answer.
Tirah
=
v.
=
ñ(
7-
um
=
(a)
4
>
r
=
Vm
-4311-(0-5)
m%
cm
#
d- Icm
-
3
APF of
=
marbles =
#
HCP __ 0.74
0.74
6242
4. Using the following table, predict crystal structures for the following materials: (a) CsI, (b)
0.170
KI, (c) NiO, (d) NiS. Justify your selections.
ros
a) CSI
=
r±
f!÷o=
0.220
=
0.773
8
coord #
Cesium
=
CSI
c)
NIO
[ oord #
=
µ , o
=
rn i
=
ro
=
6
0.069
-0.140
=
0.493
salt
ROCK
structure
's
,
>
-
marbles
| fiji
>
cm
0.5236
=
I
5) 425 )
4=4417.8647
15 =D
rni -0-069 "
b)
chloride
structure
=
KI
rk=
d) Nig
" =
""
=
RI
-
Nis
=
=
4
zinc blende
structure
-
138
0.220
6"
# = 6
§!}÷=0word
-
cord #
0
Rock salt
KI
=
structure