Attention Please!. From: LAM, Mandi [mailto:suetmlam5@cityu.edu.hk] Sent: Thursday, October 10, 2013 3:46 PM To: Email List Subject: Reminder: Completion of Teaching and Learning Questionnaire (TLQ)  AP 5301 Dear Students,
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From: LAM, Mandi [mailto:suetmlam5@cityu.edu.hk] Sent: Thursday, October 10, 2013 3:46 PMTo: Email ListSubject: Reminder: Completion of Teaching and Learning Questionnaire (TLQ)  AP 5301
Dear Students,
To enable us to have a better understanding of your valuable comment on our teaching and learning activities, you are invited to complete the TLQ evaluation for AP 5301 as soon as possible and no later than 27 October 2013.
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Thank you very much for your cooperation in advance.
Regards,Mandi LamAP General Office
Properties and generation of Xray
Properties and generation of Xray
http://www.matter.org.uk/diffraction/Default.htm
http://www.youtube.com/watch?v=vYztZlLJ3ds ~3:10
Xray and Xray DiffractionXray was first discovered by W. C. Roentgen in 1895. Diffraction of Xray was discovered by W.H. Bragg and W.L. Bragg in 1912
Bragg’s law:n=2dsin
Photograph of the hand of an old man using Xray.
http://www.youtube.com/watch?v=IRBKN4h7u80
E = h = hc/
http://www.youtube.com/watch?v=lwV5WCBh9a0 to~1:08
A Modern Automated Xray DiffractometerXray Tube
Detector
Sample stage
Cost: $560K to 1.6M
http://www.youtube.com/watch?v=Bc0eOjWkxpU to~1:10 Production of Xrays
Production of XraysCross section of sealedoff filament Xray tube
W
filament

+
target
Xrays
Vacuum
Xrays are produced whenever highspeed electrons collide with a metal target.
A source of electrons – hot W filament, a high accelerating voltage (3050kV) between the cathode (W) and the anode, which is a watercooled block of Cu or Mo containing desired target metal.
http://www.youtube.com/watch?v=UjyHK7jy1Vw Xray tube
http://www.youtube.com/watch?v=Bc0eOjWkxpU at~1:10 Production of Xrays
Xray SpectrumI
Mo
k
characteristic
radiation
continuous
radiation
k
SWL  shortwavelength limit
http://www.youtube.com/watch?v=3fe6rHnhkuY Bremsstrahlung
http://www.youtube.com/watch?v=n9FkLBaktEY characteristic Xray
V – applied voltage
Mo
Z
K
K and K2 will cause
Extra peaks in XRD pattern, but can be eliminated by adding filters.
is the mass absorption coefficient of Zr.
I
K1
<0.001Å
K2
K
=2dsin
(Å)
Spectrum of Mo at 35kV
where I is the transmitted intensity;
I0 is the incident intensity
x is the thickness of the matter;
is the density of the matter;
(/) is the mass absorption coefficient (cm2/gm).
I0
I
I
,
x
x
incident beam
crystal
diffracted beam
film
http://www.matter.org.uk/diffraction/xray/x_ray_diffraction.htm
/
Absorption coefficients of Pb, showing K and L absorption edges.
K absorption edge of Ni
1.4881Å
No filter Ni filter
Comparison of the spectra of Cu radiation (a) before and (b) after passage through a Ni filter. The dashed line is the mass absorption coefficient of Ni.
A wave interacts with
A single particle
The particle scatters the incident beam uniformly in alldirections.
A crystalline material
The scattered beam may add together in a few directions and reinforce each other to give diffracted beams.
http://www.matter.org.uk/diffraction/introduction/what_is_diffraction.htm
The atomic planes of a crystal cause an incident beam of xrays (if wavelength is approximately the magnitude of the interatomic distance) to interfere with one another as they leave the crystal. The phenomenon is called xray diffraction.
Bragg’s Law:
n= 2dsin()
~ d
2B
atomic plane
B
Xray of
I
d
http://www.youtube.com/watch?v=1FwM1oF5e6o to~1:17 diffraction & interference
Constructiveinterference occurs only when the path difference of the scattered wave from consecutive layers of atoms is a multiple of the wavelength of the xray.
/2
Constructive Interference Destructive Interference
In Phase Out Phase
http://www.youtube.com/watch?v=kSc_7XBng8w
http://www.youtube.com/watch?v=hQUsnMzTdpU Production of Xrays
Bragg’s Law and Xray DiffractionHow waves reveal the atomic structure of crystalsninteger
Diffraction occurs only when Bragg’s Law is satisfied
Condition for constructive interference (Xrays 1 & 2) from planes with
spacing d
nl = 2dsin()
Xray1
Xray2
l
=3Å
=30o
Atomic
plane
d=3Å
2diffraction angle
http://www.youtube.com/watch?v=UfDW0kghmI at~3:005.50
Constructive interference
occurs only when
nl = AB + BC
Xray 1
Xray 2
AB=BC
nl = 2AB
Sin=AB/d
AB=dsin
nl =2dsin
l=2dhklsinhkl
n – integer, called the order of diffraction
http://www.youtube.com/watch?v=wJ1sZtxuzg crystal lattice Production of Xrays
Basics of Crystallographysmallest building block
c
Single crystal
d3
CsCl
b
a
Unit cell (Å)
z [001]
d1
y [010]
Lattice
d2
x [100]
crystallographic axes
A crystal consists of a periodic arrangement of the unit cell into a lattice. The unit cell can contain a single atom or atoms in a fixed arrangement.
Crystals consist of planes of atoms that are spaced a distance d apart, but can be resolved into many atomic planes, each with a different dspacing.
a,b and c (length) and , and (angles between a,b and c) are lattice constants or parameters which can be determined by XRD.
http://www.youtube.com/watch?v=Rmi1c7zr6Q&list=TLyPTUJ62VYE4wC1snHSChDl0NGo9IKNl
SystemAxial lengths Unit cell
and angles
Rhombohedral
a=b=c
==90o
a
Cubic
a=b=c
===90o
a
Hexagonal
a=bc
=120o
c
Tetragonal
a=bc
===90o
c
a
Monoclinic
a
abc
==90o
c
b
Orthorhombic
a
c
abc
===90o
Triclinic
abc
90o
c
a
a
b
b
Miller indicesthe reciprocals of the
fractional intercepts which the plane
makes with crystallographic axes
(010)
a b c
a b c
Axial length 4Å 8Å 3Å
Intercept lengths 1Å 4Å 3Å
Fractional intercepts ¼ ½ 1
Miller indices 4 2 1
h k l
4Å 8Å 3Å
8Å
/4 1 /3
0 1 0
h k l
http://www.youtube.com/watch?v=C9h1gLQmUto Miller indices of a given plane

a
http://www.matter.org.uk/diffraction/geometry/planes_in_crystals.htm
(111)
c
c
[111]
(110)
b
b
[110]
a
a
a direction [uvw]
a set of equivalent
directions <uvw>
<100>:[100],[010],[001]
[100],[010] and [001]
a plane (hkl)
a set of equivalent
planes {hkl}
{110}:(101),(011),(110)
(101),(101),(101),etc.
BaTiO3 at T>130oC
(hkl)
Simple Cubic
I
40o
2
60o
20o
dhkl
Bragg’s Law:
l=2dhklsinhkl
l(Cu K)=1.5418Å
http://www.youtube.com/watch?v=nstYtUFELVQ
Fix l (Cu k)=1.54Å dhkl = 1.54Å/2sinhkl
For a simple cubic (a=b=c=a0)
a0 = dhkl/(h2+k2+l2)½
e.g., for BaTiO3, 2220=65.9o, 220=32.95o,
d220 =1.4156Å, a0=4.0039Å
Note: Most accurate dspacings are those calculated
from highangle peaks.
Determine crystal structure and atomic arrangement in a unit cell
Peak IntensityXray intensity: Ihkl lFhkll2
Fhkl  Structure Factor
N
Fhkl = fjexp[2i(huj+kvj+lwj)]
j=1
fj – atomic scattering factor
fjZ, sin/
Low Z elements may be difficult to detect by XRD
N – number of atoms in the unit cell,
uj,vj,wj  fractional coordinates of the jthatom
in the unit cell
I f
Direction of incident beam
atom
Simple Cubic Bodycentered Cubic Facecentered Cubic
BCC FCC
[001]
z axis
a
a
[010]
y
a
1 atom 2 atoms 4 atoms
[100]
x
8 x 1/8 =1 8 x 1/8 + 1 = 2 8 x 1/8 + 6 x 1/2 = 4
Location: 0,0,00,0,0,½, ½, ½,0,0,0,½, ½, 0,
½, 0, ½,0, ½, ½,
 corner atom, shared with 8 unit cells
 atom at facecenter, shared with 2 unit cells
8 unit cells
[001] axis
l = 2dhklsinhkl
(001) plane
d010
Mo
Cu
a
d001
(010)
plane
(002)
a
d002 =
½ a
[010]
axis
[010]
a
BCC FCC
[100]
h,k,l – integers, Miller indices, (hkl) planes
(001) plane intercept [001] axis with a length of a, l = 1
(002) plane intercept [001] axis with a length of ½ a, l = 2
(010) plane intercept [010] axis with a length of a, k = 1, etc.
Sometimes, even though the Bragg’s condition is satisfied, a strong diffraction peak is not observed at the expected angle.
Consider the diffraction peak of (001) plane of a FCC crystal.
Owing to the existence of the (002) plane in between, complications occur.
1
1’
2
2’
3
3’
d001
d002
z
Structure factor and intensity of diffraction(001)
(002)
FCC
ray 1 and ray 3 have path difference of a strong diffraction peak is not observed at the expected angle.
but ray 1 and ray 2 have path difference of /2. So do ray 2 and ray 3.
It turns out that it is in fact a destructive condition, i.e. having an intensity of 0.
the diffraction peak of a (001) plane in a FCC crystal can never be observed.
1
1’
2
2’
3
3’
d001
d002
Structure factor and intensity of diffraction/4
/4
/2
/2
e.g., Aluminium (FCC), all atoms are the same in the unit cell
four atoms at positions, (uvw):
A(0,0,0),B(½,0,½),
C(½,½,0)& D(0,½,½)
Structure factor and intensity of diffraction for FCCz
D
B
y
A
C
x
For a certain set of plane, (hkl) cell
F = f () exp[2i(hu+kv+lw)]
= f () exp[2i(hu+kv+lw)]
= f (){exp[2i(0)] + exp[2i(h/2 + l/2)]
+ exp[2i(h/2 + k/2)] + exp[2i(k/2 + l/2)]}
= f (){1 + ei(h+k) + ei(k+l) + ei(l+h)}
Since e2ni = 1 and e(2n+1)i = 1,
if h, k & l are all odd or all even, then (h+k), (k+l), and (l+h) are all even and F = 4f; otherwise, F = 0
Structure factor and intensity of diffraction for FCC2i
Ihkl lFhkll2
A(0,0,0),B(½,0,½),
C(½,½,0) & D(0,½,½)
(FWHM)
Determine
grain size
2. Residual
strain
As rolled
300oC
As rolled
t
Grain
size
200oC
I
K1
B
K2
(FWHM)
250oC
Grain
size
450oC
300oC
0.9
Peak
broadening
B =
t cos
450oC
As grain size decreases
hardness increases and
peak become broader
2
(331) Peak of coldrolled and
annealed 70Cu30Zn brass
No Strain
Uniform Strain
(d1do)/do
Peak moves, no shape changes
Nonuniform Strain
d1constant
Peak broadens
Crystal
Constructive interference
Structural periodicity
Diffraction
Sharp maxima
2
Liquid or amorphous solid
Lack of periodicity One or two
Short range orderbroad maxima
Monatomic gas
Atoms are arranged Scattering I
perfectly at random decreases with
http://www.youtube.com/watch?v=UfDW0kghmI at~1:203:00
Backreflection Laue
crystal
Film
Xray
[001]
Transmission Laue
Film
crystal
http://www.youtube.com/watch?v=2JwpHmT6ntU
Diffraction of Xrays by WidthPolycrystals
2
2
Powder Diffraction (most widely used)A powder sample is in fact an assemblage of small crystallites, oriented at random in space.
d3
d1
d2
Powder
sample
d1
crystallite
d2
d3
Polycrystalline
sample
http://www.youtube.com/watch?v=lwV5WCBh9a0 at~1:081:46
Xray Width
detector
Sample
holder
Detection of Diffracted Xray by A DiffractometerXray
tube
xray
2
http://www.youtube.com/watch?v=lwV5WCBh9a0 at~1:441:56 and 15:4416:16
One of the most important uses of XRD
Quality of data Width
JCPDS Card1.file number 2.three strongest lines
3.lowestangle line 4.chemical formula and name 5.data on dif
fraction method used 6.crystallographic data 7.optical and other
data 8.data on specimen 9.data on diffraction pattern.
Lattice parameters (104Å), strain, grain size, expitaxy,
phase composition, preferred orientation
orderdisorder transformation, thermal expansion
Detection limits: ~3% in a two phase mixture; can be
~0.1% with synchrotron radiation.
Lateral resolution: normally none
XRD is a nondestructive technique
a b c Width
Phase Identification Effect of Symmetry on XRD Patterna=b=c, (a)
b. Tetragonal
a=bc (a and c)
c. Orthorhombic
abc (a, b and c)
2
ZnO+ M23C6+
Grain
Random orientation
Preferred orientation
I
Simple cubic
Random orientation
Texture
20 30 40 50 60 70
PbTiO3 (001) MgO (001)
highly caxis
oriented
2
I
I
(110)
PbTiO3 (PT)
simple tetragonal
(111)
Preferred orientation
Figure 1. Xray diffraction 2 scan profile of a PbTiO3 thin film grown on MgO (001) at 600°C.
Figure 2. Xray diffraction scan patterns from (a) PbTiO3 (101) and (b) MgO (202) reflections.
By rotating the specimen about the three major axes as shown, these spatial variations in diffraction intensity can be measured.
4Circle Goniometer
For polefigure measurement
(330)
Single Crystal Ferroelectric 92%Pb(Zn1/3Nb2/3)O3 8%PbTiO3
E=6kV/cm
(330) peak splitting is due to
Presence of <111> domains
Rhombohedral phase
No (330) peak splitting
Tetragonal phase
K1
K2
E=10kV/cm
K1
K2
Powders: 0.1m < particle size <40 m
Peak broadening less diffraction occurring
Double sided tape
Glass slide
Bulks: smooth surface
after polishing, specimens should be
thermal annealed to eliminate any
surface deformation induced during
polishing.
http://www.youtube.com/watch?v=lwV5WCBh9a0 at~2:005:10