The document discusses the crystal structures of materials. It begins by explaining that the properties of some materials are directly related to their crystal structures. For example, magnesium and beryllium have different properties than gold and silver due to differences in their crystal structures. It then lists the key learning objectives which include describing different crystal structures, computing densities, and distinguishing between single crystals and polycrystalline materials. The document goes on to explain common metallic crystal structures like body centered cubic and face centered cubic, as well as non-metallic structures like rock salt and cesium chloride. It also discusses factors that determine crystal structure such as the relative sizes of ions to maximize interactions and maintain charge neutrality.
Crystal Material, Non-Crystalline Material, Crystal Structure, Space Lattice, Unit Cell, Crystal Systems, and Bravais Lattices, Simple Cubic Lattice, Body-Centered Cubic Structure, Face centered cubic structure, No of Atoms per Unit Cell, Atomic Radius, Atomic Packing Factor, Coordination Number, Crystal Defects, Point Defects, Line Defects, Planar Defects, Volume Defects.
Crystal Material, Non-Crystalline Material, Crystal Structure, Space Lattice, Unit Cell, Crystal Systems, and Bravais Lattices, Simple Cubic Lattice, Body-Centered Cubic Structure, Face centered cubic structure, No of Atoms per Unit Cell, Atomic Radius, Atomic Packing Factor, Coordination Number, Crystal Defects, Point Defects, Line Defects, Planar Defects, Volume Defects.
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.
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Crystal Structure
1
Crystalline Solid
• Crystalline Solid is the solid form of a substance in
which the atoms or molecules are arranged in a
definite, repeating pattern in three dimension.
• Single crystals, ideally have a high degree of order, or
regular geometric periodicity, throughout the entire
volume of the material.
Crystalline Solids
2
Macroscopic form reflects underlying atomic structure
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Crystal Structure
3
Polycrystalline Solid
Polycrystalline
Pyrite form
(Grain)
Polycrystal is a material made up of an aggregate of many small single crystals
(also called crystallites or grains).
Polycrystalline material have a high degree of order over many atomic or molecular
dimensions.
These ordered regions, or single crytal regions, vary in size and orientation wrt one
another.
These regions are called as grains ( domain) and are separated from one another
by grain boundaries. The atomic order can vary from one domain to the next.
The grains are usually 100 nm - 100 microns in diameter. Polycrystals with grains
that are <10 nm in diameter are called nanocrystalline
Crystal Structure
4
Amorphous Solid
• Amorphous (Non-crystalline) Solid is composed of randomly
orientated atoms , ions, or molecules that do not form defined
patterns or lattice structures.
• Amorphous materials have order only within a few atomic or molecular
dimensions.
• Amorphous materials do not have any long-range order, but they have
varying degrees of short-range order.
• Examples to amorphous materials include amorphous silicon,
plastics, and glasses.
• Amorphous silicon can be used in solar cells and thin film transistors.
http://www.alaskanessences.com/gembig/Pyrite.jpg
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Molecular Crystals
5
Formed from C60 or molecules,
Known as “buckyballs”
A molecular lattice of 1·KClO4.
Liquid Crystals & Polymers
6
Some properties of liquid,
some of solid
Polymer long chain of atoms
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7
Bonds between atoms: contents
• bonding in general, attractive and repulsive forces,
cohesive energy
• ionic bonding
• covalent bonding
• metallic bonding
• hydrogen bonding and van der Waals bonding
• relationship between bonding type and some physical
properties of a solid (in particular melting point)
at the end of this lecture you should understand....
8
Bonding in solids: the general idea
• valence electrons (of the outer shell) achieve bonding (like
in chemistry)
• decrease in total energy stabilises the solid (the solid’s
energy is lower than that of sum of atoms it is made of)
• so the energy gain by the bonding must be higher than the
energy it costs to promote electrons from the atomic orbitals
to the electronic states of the solid.
• this energy difference is a measure for the strength of the
bond. It is called the cohesive energy.
cohesive en.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
2. WHY STUDY The Structure of Crystalline Solids?
The properties of some materials are directly related to their crystal
structures. For example, pure and undeformed magnesium and beryllium,
having one crystal structure, are much more brittle (i.e., fracture at lower
degrees of deformation) than are pure and undeformed metals such as gold
and silver that have yet another crystal structure.
Furthermore, significant property differences exist between crystalline and
noncrystalline materials having the same composition.
For example, noncrystalline ceramics and polymers normally are optically
transparent; the same materials in crystalline (or semicrystalline) form tend
to be opaque or, at best, translucent.
2
3. Learning Objectives
1. Describe the difference in atomic/
molecular structure between crystalline
and non-crystalline materials.
2. Draw unit cells for face-centered cubic,
body-centered cubic, and hexagonal close-
packed crystal structures.
3. Derive the relationships between unit
cell edge length and atomic radius for
face-centered cubic and body-centered
cubic crystal structures.
4. Compute the densities for metals having
face-centered cubic and body-centered
cubic crystal structures given their unit
cell dimensions.
5. Given three direction index integers,
sketch the direction corresponding to these
indices within a unit cell.
6. Specify the Miller indices for a plane
that has been drawn within a unit cell.
7. Describe how face-centered cubic and
hexagonal close-packed crystal structures
may be generated by the stacking of close-
packed planes of atoms.
8. Distinguish between single crystals and
polycrystalline materials.
9. Sketch/describe unit cells for sodium
chloride, cesium chloride, zinc blende,
diamond cubic, fluorite, and perovskite
crystal structures.
10. Given the chemical formula for a
ceramic compound and the ionic radii of
its component ions, predict the crystal
structure.
3
After studying this chapter, you should be able to do the following:
4. Structure of Crystalline Materials
• Crystal Structure of Metallic and Semiconductor
Elements:
– Cubic, Face-centered cubic (FCC), Body-centered cubic
(BCC) and
– Diamond cubic structures;
• Crystals Structures of Ceramics:
– Rock Salt,
– Cesium Chloride, Zinc Blende (Sphalerite),
– Fluorite and Perovskite Structures;
– Fullerenes and Carbon Nano-tube Structure
4
5. Crystal Structures
• The arrangement of atoms, ions or molecules
in a material constitute the Crystal Structure
• If the arranged pattern repeats itself in 3-
dimension, the result is a crystal structure.
• The properties of some materials are directly
related to their crystal structures.
• Significant property differences exist between
crystalline and non-crystalline materials
having the same composition.
5
6. Unit Cell and Space lattice of ideal
Crystalline solid
6
Space Lattice:
A 3-D regular arrangements of
atoms characteristic of a
particular crystal structure
(points of intersection of a
network of lines in 3-D).
14 such arrangements exist
called Bravais Lattice
Unit Cell:
The smallest building block of a crystal, consisting of
atoms, ions, or molecules, whose geometric
arrangement defines a crystal's characteristic symmetry
and whose repetition in space produces a crystal lattice.
7. Lattice Constants (Lattice Parameters)
• Three lattice vectors a, b, c and the inter-axial
angles α, β, γ are called the lattice constants or
lattice parameters of a unit cell.
7
A unit cell showing
lattice constants
8. 8
• This results in the fact that, in 3 dimensions, there are only
• 7 different shapes of unit cell which can be stacked
together to completely fill all space without overlapping.
• This gives the 7 crystal systems, in which all crystal structures
can be classified. These are:
• The Cubic Crystal System (SC, BCC, FCC)
• The Hexagonal Crystal System (S)
• The Triclinic Crystal System (S)
• The Monoclinic Crystal System (S, Base-C)
• The Orthorhombic Crystal System (S, Base-C, BC, FC)
• The Tetragonal Crystal System (S, BC)
• The Trigonal (or Rhombohedral) Crystal System (S)
Classification of Crystal Structures
Crystallographers showed a long time ago that in 3-D, there are
7 CRYSTAL SYSTEMS with
14 BRAVAIS LATTICES
12. Relation of the primitive cell in
the hexagonal system (heavy
lines) to a prism of hexagonal
symmetry. Here a1 = a2 ≠ a3.
Hexagonal System
In this Fig. the lattice vectors are:
a = a ≠ c
α = β = 90̊ and
γ = 120̊
13.
14. 14
• Non dense, random packing
• Dense, ordered packing
Dense, ordered packed structures tend to have lower energies.
Energy and Packing
Energy
r
typical neighbor
bond length
typical neighbor
bond energy
Energy
r
typical neighbor
bond length
typical neighbor
bond energy
15. 15
• atoms pack in periodic, 3D arrays
Crystalline materials...
-metals
-many ceramics
-some polymers
• atoms have no periodic packing
Noncrystalline materials...
-complex structures
-rapid cooling
crystalline SiO2
noncrystalline SiO2"Amorphous" = Noncrystalline
Materials and Packing
Si Oxygen
• typical of:
• occurs for:
17. 17
• Tend to be densely packed.
• Reasons for dense packing:
-Typically, only one element is present, so all
atomic radii are the same.
-- Metallic bonding is not directional.
-- Nearest neighbor distances tend to be small in
order to lower bond energy.
- The “electron cloud” shields cores from each
other
• They have the simplest crystal structures.
Metallic Crystal Structures
19. 19
• Rare due to low packing density only Polonium (Po, At. No. 84) has
this structure)
• Close-packed directions are cube edges.
Atoms per unit cell: 01,
• Coordination # = 6
(# nearest neighbors)
Simple Cubic Structure (SC)
20. 20
• APF for a simple cubic structure = 0.52
APF =
a3
4
3
p (0.5a) 31
atoms
unit cell
atom
volume
unit cell
volume
Atomic Packing Factor (APF)
APF =
Volume of atoms in unit cell*
Volume of unit cell
*assume hard spheres
close-packed directions
a
R=0.5a
contains 8 x 1/8 =
1 atom/unit cell
21. 21
• Coordination # = 8
• Atoms touch each other along cube diagonals.
All atoms are identical.
Body Centered Cubic Structure (BCC)
ex: Cr, W, Fe (), Tantalum, Molybdenum
2 atoms/unit cell: 1 center + 8 corners x 1/8
23. 23
Atomic Packing Factor: BCC
a
APF =
4
3
p ( 3a/4)32
atoms
unit cell atom
volume
a3
unit cell
volume
length = 4R =
Close-packed directions:
3 a
• APF for a body-centered cubic structure = 0.68
a
R
a2
a3
24. 24
• Coordination # = 12
• Atoms touch each other along face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.
Face Centered Cubic Structure (FCC)
ex: Al, Cu, Au, Pb, Ni, Pt, Ag
4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
33. Closed packed structures
33
A portion of a closed-packed plane of
atoms; A, B, and C position are indicated.
The AB stacking sequence for close-
packed atomic planes .
ABAB stacking sequence for hcp. ABCABC stacking
sequence for fcc.
A corner has been removed to show the
relation between the stacking of close-
packed planes of atoms and the fcc crystal
structure, the heavy triangle outlines a
(111) plane. .
34. Figure. Workflow for solving the structure of a molecule by X-ray crystallography.
Crystal
Diffraction pattern
Electron Density Map
Atomic Model
35. What are X-rays?
X-rays: Electromagnetic radiation with a wavelength from 0.1 Ǻ to
100 Ǻ (0.01 nm to about 10 nm).
36. What are X-rays
• Discovered in 1895 AD by Wilhelm Roentgen and got first Noble
prize in Physics in 1901 AD.
• X-rays are a part of the electromagnetic spectrum along with
visible light, Infra Red, Ultra Violet etc.
• The λ could be 10-8 to 10-11 meter (0.01 to 10 nm, which is almost
comparable to lattice parameter or interatomic distance).
• The frequencies are in the range of 3 x 1016 Hz to 3 x 1019 Hz and
energies in the range of 100 eV to 100 keV.
• The shorter λ’s are called hard x-rays while longer λ’s are known
as soft X-rays (the shorter the λ, more energy the radiation has).
37. Generation of X-radiation for diffraction
measurements
• Sealed X-ray tubes tend to operate at 1.8
to 3 kW.
• Rotating anode X-ray tubes produce much
more flux because they operate at 9 to 18
kW.
– A rotating anode spins the anode at
6000 rpm, helping to distribute heat
over a larger area and therefore
allowing the tube to be run at higher
power without melting the target.
• The Cu (or Co, Mo, Cr) source generates
X rays by striking the anode target with an
electron beam from a tungsten filament.
– The target must be water cooled.
– The target and filament must be
contained in a vacuum.
Cu
H2O In H2O Out
e-
Be
XRAYS
window
Be
XRAYS
FILAMENT
ANODE
(cathode)
AC CURRENT
window
metal
glass
(vacuum) (vacuum)
38. The Principle of Bremsstrahlung Generation
X-ray, (continuous or Bremsstrahlung)
Fast incident
electron
nucleus
Atom of the anode material
electrons
Ejected
electron
(slowed down
and changed
direction)
41. X-Ray Diffraction and Determination of
Crystal Structure
41
Using X-ray diffractometry.
• Crystal structure,
• Inter-planar distance,
• Phase composition and
• many more parameters can be determined.
42. Xray-Tube
Detector
Sample
Bragg´s Equation
λ = 2dsinθ
d – distance between the same atomic planes
λ – monochromatic wavelength
θ – angle of diffracto-meter
Xray-Tube
Detector
Metal Target
(Cu or Co)
X-Ray Diffractometer
43. Diffraction of x-rays from two planes
43
Diffraction of x-rays by planes of atoms (A – A’ and B-B);
Bragg’s Law
49. 49
Theoretical Density, r
where
n = number of atoms/unit cell
A = atomic weight
VC = Volume of unit cell = a3 for a cubic structure
NA = Avogadro’s number
= 6.022 x 1023 atoms/mol
Density = r =
VC NA
n A
r =
CellUnitofVolumeTotal
CellUnitinAtomsofMass
50. 50
• Example: Cr (BCC)
A (atomic weight) = 52.00 g/mol
n = 2 atoms/unit cell
R = 0.125 nm
rtheoretical
a = 4R/ 3 = 0.2887 nm
ractual
a
R
r =
a3
52.002
atoms
unit cell
mol
g
unit cell
volume atoms
mol
6.022x1023
Theoretical Density, r
= 7.18 g/cm3
= 7.19 g/cm3
51. Ceramic Materials
• Name comes from Greek letter “Keramicos” mean burnt off. (so
these materials are fabricated at high temperature).
• Ceramic materials are inorganic and nonmetallic material,
• Metallic and non-metallic elements are bonded together,
• Materials could be totally ionic or predominantly ionic with
covalent character or totally covalent.
51
52. • Properties depend upon nature of bonding and crystal structure.
• In general, Ceramic are hard and brittle,
• Good electrical and thermal insulators.
• Have high melting point and high chemical stability.
• Being used in very harsh environments (say at high Temp.
52
54. 54
• Bonding:
-- Can be ionic and/or covalent in character.
-- % ionic character increases with difference in
electronegativity of atoms.
• Degree of ionic character may be large or small:
Atomic Bonding in Ceramics
SiC: small
CaF2: large
55. Ceramics materials have two major
categories
• Traditional and Engineering ceramic materials.
• Traditional Ceramics are fabricted from “clay”, silica (flint)
and feldspar (rock forming silicate of Al together with Na, K.
Ca, and Ba).
• Examples are:
– Porcelain, bricks, tiles, and in addition, glasses and high temperature
ceramics.
55
• Engineering Ceramics;
• These are pure or nearly pure compounds of Aluminum
Oxide Al2O3, Silicon Carbide (SiC), and Silicon Nitrate
(Si3Ni4).
• They are being used in:
• I.T. Technology (Al2O3)
• In high temperature areas (SiC), furnaces and many more.
56. Crystal structure of Ceramics
• The metallic ion could be;
– Cation: Positively ion, (e- has left the atom)
– Anion: Negatively ion (e- is gained in the atom.
• In ionic compounds, packing of ions determine by:
– The relative size of the ions in the ionic solid.
– The need to balance electrostatics charges to maintain
electrical neutrality in the ionic solid.
56
57. 57
Table 12.3: Ionic Radii for Several Cations and Anions for a
Coordination Number of 6
• The size of an ion depends on
several factors.
• One of these is coordination
number: ionic radius tends to
increase as the number of
nearest-neighbor ions of
opposite charge increases.
• Ionic radii given in Table 12.3
are for a coordination number
of 6.
• Therefore, the radius is
greater for a coordination
number of 8 and less when
the coordination number is 4.
In addition, the charge on an ion will influence its radius. For example, from Table 12.3, the
radii for Fe2+and Fe3+ are 0.077 and 0.069 nm, respectively, which values may be contrasted to
the radius of an iron atom—0.124 nm.
When an electron is removed from an atom or ion, the remaining valence electrons become
more tightly bound to the nucleus, which results in a decrease in ionic radius.
Conversely, ionic size increases when electrons are added to an atom or ion.
58. 58
Factors that Determine Crystal Structure
1. Relative sizes of ions – Formation of stable structures:
--maximize the # of oppositely charged ion neighbors.
- -
- -
+
unstable
- -
- -
+
stable
- -
- -
+
stable
2. Maintenance of
Charge Neutrality :
--Net charge in ceramic
should be zero.
--Reflected in chemical
formula:
CaF2: Ca2+
cation
F-
F-
anions+
AmXp
m, p values to achieve charge neutrality
59. • For a Bravais Lattice,
The Coordinatıon Number
The number of lattice points closest to a given point
(the number of nearest-neighbors of each point).
• Because of lattice periodicity, all points have the same
number of nearest neighbors or coordination number.
(That is, the coordination number is intrinsic to the lattice.)
Examples
Simple Cubic (SC) coordination number = 6
Body-Centered Cubic coordination number = 8
Face-Centered Cubic and HCP, coordination number = 12
Coordination Number
60. 60
• Coordination # increases with
Coordination # and Ionic Radii
2
rcation
ranion
Coord
#
< 0.155
0.155 - 0.225
0.225 - 0.414
0.414 - 0.732
0.732 - 1.0
3
4
6
8
linear
triangular
tetrahedral
octahedral
cubic
rcation
ranion
To form a stable structure, how many anions can
surround a cation?
(Zinc blende)
62. 62
Computation of Minimum Cation-Anion
Radius Ratio
• Determine minimum rcation/ranion for an octahedral site
(C.N. = 6)
a = 2ranion
2ranion 2rcation = 2 2ranion
ranion rcation = 2ranion
rcation = ( 2 1)ranion
arr 222 cationanion =
414.012
anion
cation ==
r
r
a
Measure the radii (blue and
yellow spheres)
Substitute for “a” in the
above equation
63. 63
• On the basis of ionic radii, what crystal structure would you
predict for FeO?
• Answer:
5500
1400
0770
anion
cation
.
.
.
r
r
=
=
Example Problem: Predicting the Crystal
Structure of FeO
Ionic radius (nm)
0.053
0.077
0.069
0.100
0.140
0.181
0.133
Cation
Anion
Al3+
Fe2+
Fe3+
Ca2+
O2-
Cl-
F-
based on this ratio,
-- coord # = 6 because
0.414 < 0.550 < 0.732
-- crystal structure is similar to NaCl
64. AX type Crystal Structure
64
• The ceramic materials with AX type Crystal Structure have;
• Number of Cation = Number of Anions
• Where ‘A’ denotes cations and ‘X’ the anion
• Several different AX compounds exist,
• Each is normally named after a common material that assumes the
particular structure
Examples:
• Rock Salt, NaCl
• Cesium Chloride, CsCl
• Zinc Blende (ZnS)
65. 65
Rock Salt Structure
Same concepts can be applied to ionic solids in general.
Example: NaCl (rock salt) structure
rNa = 0.102 nm
rNa/rCl = 0.564
cations (Na+) prefer octahedral sites
rCl = 0.181 nm
66. 66
MgO and FeO
O2- rO = 0.140 nm
Mg2+ rMg = 0.072 nm
rMg/rO = 0.514
cations prefer octahedral sites
So each Mg2+ (or Fe2+) has 6 neighbor oxygen atoms
MgO and FeO also have the NaCl structure
67. 67
CsCl Crystal Structures
939.0
181.0
170.0
Cl
Cs ==
r
r
Cesium Chloride structure:
Since 0.732 < 0.939 < 1.0,
cubic sites preferred
So each Cs+ has 8 neighbor Cl-
CsCl is an AX-type Crystal Structures
68. Zinc blende (ZnS) Crystal Structure
68
A unit cell for the zinc blende (ZnS)
crystal structure
• Zinc blende or Sphalerite structure
• Coordination No. = 4,
• All corner's and face positions occupied by S
atoms,
• Zn atoms fill interior tetrahedral position.
• Reverse structure is also possible (Zn, S
position reversed)
• Each Zn atom is bonded to 4 S atoms,
• Atomic bonding is highly covalent;
• Include:
• ZnS,
• ZnTe,
• SiC
69. 69
AX2 Crystal Structures
• Calcium Fluorite (CaF2)
• Calcium ions in cubic sites
• Fluorine ions at the corners
• Similar to CsCl, except that only half the
center cube positions occupied by Ca2+ ions
• Charges on cation ≠ anions
• UO2, ThO2, ZrO2, CeO2, PuO2
• Coordination No. = 8
• Antifluorite structure also exists
• in which positions of cations and
anions are reversed.
Fluorite structure
71. ABX3 Crystal Structures
• More than one type of cation.
• For two types of Cations (represented by A and B), chemical
formula is listed above.
• Examples are;
– CaTiO3, BaTiO3, SrZrO3, SrSnO3 etc.
• Perovskite Crystal Structure is shown on R.H.S.
• Ca2+ and O2- ions at the center of the faces of the unit cell.
• The highly charged Ti4+ ion is located at the octahedral interstitial
site at the center of the unit cell and is coordinated to six O2- ions.
• BaTiO3 has the perovskite structure above 1200 C, but below, it is
slightly changed.
71
73. 73
• Atoms may assemble into crystalline or amorphous structures.
• We can predict the density of a material, provided we know the
atomic weight, atomic radius, and crystal geometry (e.g., FCC,
BCC, HCP).
SUMMARY
• Common metallic crystal structures are FCC, BCC and HCP.
Coordination number and atomic packing factor are the same
for both FCC and HCP crystal structures.
• Ceramic crystal structures are based on:
-- maintaining charge neutrality
-- cation-anion radii ratios.
• Interatomic bonding in ceramics is ionic and/or covalent.
75. Silica (SiO2)
75
• Most simple silicate material
• 3-D network generated when every corner O2 atom of one
tetrahedron is shared by adjacent tetrahedron.
• Electrically, material is neutral, so stable electronic
structure is formed.
• Three primary polymorphic structures of silica,
• a). Quartz, b). Cristobalite, and c). Tridymite.
• Complicated and relatively open structure
• Low densities,
• Due to strong Si-O interatomic bonds, melting
• point is relatively high 17100 C.
The arrangement of silicon
and oxygen atoms in a unit
cell of cristobalite, a
polymorph of SiO2.
76. Silica Glass
• A form of silica which is non-crystalline solid or glass.
• Having high degree of atomic randomness.
76
Search out what type of
materials are:
Network Formers
Network modifiers,
Intermediates
78. 78
A unit cell for the diamond cubic crystal structure
Carbon Structures
• Diamond, Graphite,
Fullerene, Carbon Nanotube
(CNT)
• In diamond, each C atom is
bonded to 4 other C atoms.
• 4 tetrahedral sites with
covalent bonding
• Ge, Si and Gray tin (below
13̊ C) have this structure.