The document discusses different types of crystalline solids and their structures. It defines key terms like unit cell, lattice, space lattice, and basis. It describes one, two and three dimensional lattices and the different types of unit cells in two and three dimensions. It also discusses crystal structures, Miller indices for planes and directions, Bravais lattices, and provides examples of rock salt and zinc blende structures.
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.
Space lattice, Unit cell, Bravais lattices (3-D), Miller indices, Lattice planes, Hexagonal closed packing (hcp) structure, Characteristics of an hcp cell, Imperfections in crystal: Point defects (Concentration of Frenkel and Schottky defects).
X – ray diffraction : Bragg’s law and Bragg’s spectrometer, Powder method, Rotating crystal method.
Dear aspirants,
This presentation includes basic terms of crystallography, a brief note on unit cell and its type With derivation of its properties: APF, Coordination no., No. of atoms per unit cell and also its atomic radius. I also added 7 Crystal System, Bravais Lattice and finally Miller Indices concept.
Hope this presentation is helpful.
Any questions or clarifications are welcomed.
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.
Space lattice, Unit cell, Bravais lattices (3-D), Miller indices, Lattice planes, Hexagonal closed packing (hcp) structure, Characteristics of an hcp cell, Imperfections in crystal: Point defects (Concentration of Frenkel and Schottky defects).
X – ray diffraction : Bragg’s law and Bragg’s spectrometer, Powder method, Rotating crystal method.
Dear aspirants,
This presentation includes basic terms of crystallography, a brief note on unit cell and its type With derivation of its properties: APF, Coordination no., No. of atoms per unit cell and also its atomic radius. I also added 7 Crystal System, Bravais Lattice and finally Miller Indices concept.
Hope this presentation is helpful.
Any questions or clarifications are welcomed.
The study of crystal geometry helps to understand the behaviour of solids and their
mechanical,
electrical,
magnetic
optical and
Metallurgical properties
The crystal structure notes gives the basic understanding about the different structures crystalline materials and their properties and physics of crystals. It also throw light on the basics of crystal diffraction
The study of crystal geometry helps to understand the behaviour of solids and their
mechanical,
electrical,
magnetic
optical and
Metallurgical properties
The crystal structure notes gives the basic understanding about the different structures crystalline materials and their properties and physics of crystals. It also throw light on the basics of crystal diffraction
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The word crystallography is derived from the Ancient Greek word κρύσταλλος (krústallos; "clear ice, rock-crystal"), with its meaning extending to all solids with some degree of transparency, and γράφειν (gráphein; "to write"). In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography.
Arrangement of atoms can be most simply portrayed by Crystal Lattice, in which atoms are visualized as, Hard Balls located at particular locations
Space Lattice / Lattice: Periodic arrangement of points in space with respect to three dimensional network of lines
Each atom in lattice when replaced by a point is called Lattice Point, which are the intersections of above network of lines
Arrangement of such points in 3-D space is called Lattice Array and 3-D space is called Lattice Space
Inner Transition Element by Dr.N.H.BansodNitin Bansod
Inner Transition Element, electronic configuration lanthanide and actinide, lanthanide contraction & consequences, oxidation state, magnetic properties, ion-exchange method for separation, similarities, and differences of lanthanide and actinide
The topic is important for UG students. it covers almost all concepts of metallurgy. The important method of separation of ores, Ellingham diagram and its application.
Colligative properties of dilute solution is important topic of physical chemistry. mainly cover types with application of it day to day life... must to watch and share
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
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.
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.
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.
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 .
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.
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
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.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
3. 3
SOLIDS
can be divided into two catagories.
Crystalline
Amorphous
Crystalline has long range order
Amorphous materials have short range order
Effect of Crystallinity on Physical properties - ex. Polyethylene
4. 4
Crystal
Type
Particles Interparticle
Forces
Physical Behaviour Examples
Atomic
Molecular
Metallic
Ionic
Network
Atoms
Molecules
Atoms
Positive and
negative
ions
Atoms
Dispersion
Dispersion
Dipole-dipole
H-bonds
Metallic bond
Ion-ion
attraction
Covalent
• Soft
• Very low mp
• Poor thermal and electrical
conductors
Fairly soft
Low to moderate mp
Poor thermal and electrical
conductors
Soft to hard
Low to very high mp
Mellable and ductile
Excellent thermal and
electrical conductors
Hard and brittle
High mp
Good thermal and electrical
conductors in molten condition
• Very hard
• Very high mp
• Poor thermal and electrical
conductors
Group 8A
Ne to Rn
O2, P4, H2O,
Sucrose
Na, Cu, Fe
NaCl, CaF2,
MgO
SiO2(Quartz)
C (Diamond)
TYPES OF CRYSTALLINE SOLIDS
7. 7
CRYSTAL STRUCTURE
Crystal structure is the periodic arrangement of atoms in the
crystal. Association of each lattice point with a group of
atoms(Basis or Motif).
Lattice: Infinite array of points in space, in which each point has
identical surroundings to all others.
Space Lattice Arrangements of atoms
= Lattice of points onto which the atoms are hung.
Elemental solids (Argon): Basis = single atom.
Polyatomic Elements: Basis = two or four atoms.
Complex organic compounds: Basis = thousands of atoms.
+
Space Lattice + Basis = Crystal Structure
=
• • •
• • •
• • •
14. The “unit cell” is the basic repeating unit of the
arrangement of atoms, ions or molecules in a
crystalline solid.
The “lattice” refers to the 3-D array of particles in a
crystalline solid. One type of atom occupies a
“lattice point” in the array.
19. 19
COUNTING ATOMS IN THE THREE DIMENTIONAL
UNIT CELL
Vertex(corner) atom shared by 8 cells 1/8 atom per cell
Edge atom shared by 4 cells 1/4 atom per cell
Face atom shared by 2 cells 1/2 atom per cell
Body unique to 1 cell 1 atom per cell
Atoms in different positions in a cell are shared by
differing numbers of unit cells
21. Contributions of Atoms to Cubic Unit Cells
Position of Atoms
in Unit Cell
Contribution to
Unit Cell
Unit-Cell Type
Center 1 bcc
Face 1/2 Fcc
Corner 1/8
fcc, bcc, simple
cubic
How many total atoms are found in a simple cubic
unit cell? Face centered cube? Body centered cube?
22. 22
Number of Atoms per unit cell in cubic
crystal system(z)
1.For SCC( Simple Cubic Crystal Lattice)
Vertex(corner) atom shared by 8 cells 1/8 atom per cell
Z = 1/8 × 8 = 1
2. For FCC (Face Centred Cubic lattice)
Vertex(corner) atom shared by 8 cells 1/8 atom per cell
Face atom shared by 2 cells 1/2 atom per cell
Z = 1/8 × 8 + 1/2 × 6 = 1+3 = 4
23. Unit Cells
A body-centered
cubic (bcc) unit cell
has atoms at the 8
corners of a cube and
at the center of the
cell
A simple cubic unit
cell has atoms only at
the 8 corners of a
cube.
24. Number Atoms in a Unit Cell
In the simple cubic cell
there are only the 8
atoms at the corners.
1/8 x 8 = 1 atom in cell
In bcc, 8 atoms at the
corners and 1 in center.
1/8 x 8 + 1 x 1 = 2 atoms
in the cell
25. 25
3.For BCC(Body Centred Cubic lattice)
Vertex(corner) atom shared by 8 cells 1/8 atom per cell
And Body unique to 1 cell 1 atom per cell
Z = 1/8 × 8 + 1 × 1 = 1+1 = 2
26. 26
Density of crystal matter (D)
Density = Mass of the Unit cell
………………………………
Volume of the Unit cell
Mass of unit cell = Z × mass of each atom
= Z × M/N0
Volume of unit cell = a3 = where a is edge length is in pm
1pm = 10-12 m.
D = Z × M where M –molecular weight
……….
No × a3 No- Avogadro's Number(6.023×10-23
27. 27
Numerical problem:
1.The length of side of unit cell of a cubic crystal is 4×10-3 m.
the density of crystal matter is 1.2× 10-3 kg m-3.if molar mass
is 2.4×10-2 mole-1 then find out i) type of lattice ii) number of
atoms in each unit cell
Solution :
28. 28
Numerical problem:
1. The corner of a face centred cubic Crystal has atoms
of elements X while at centre of face has of element
Y. find out the formula of crystal compound.
29. The Chemistry of Solids
Miller Indices (l,m,n) are a
way of denoting planes in
crystal lattices.
30. Types of planes of cubic Crystal or indexing the planes
(110) planes (130) planes
a
b
(-210) planes
37. 37
Law of crystallography :
1. Law of constancy of interfacial angles:
2. Law of symmetry :
3. Law of rational indices
38. Face intercepts I
Crystal faces are defined by indicating their intercepts on the crystallographic axes. The
units along the axes is determined by the periodicity along theses axes:
- c
- b
- a
Intercepts: 5a : 3b : 2c = 5 : 3 : 2
+ c
+ b
+ a
2c
3b
5a
39. Face intercepts II
Faces parallel to an axis have an intercept with that axis at infinity
+ c
- c
+ b- b
+ a
- a
a
Intercepts: 3a : b : c = 3 : :
c
b
40. Face intercepts III
Intercepts are always given as relative values, e.g. they are divided until they have no common fac
Parallel faces in the same quadrant have, therefore, the same indices
+ c
+ b- b
+ a
- a
a
4c
2b1b
2a
2c
Intercepts: 4a : 2b : 4c = 4 : 2 : 4
div. by 2
2 : 1 : 2
- c
Intercepts: 2a : 1b : 2c = 2 : 1: 2
Intercept ratios are called Weiss indices
42. Miller indices I
The Miller indices of a face are derived from the Weiss indices by inverting the latter
and, if necessary, eliminating the fractions.
Reason for using Miller indices:- avoiding the index
- simplifies crystallographic calculations
- simplifies the interpretation of x-ray diffraction
Example:
Weiss indices Miller indices
1 1 1
1 1 1 0 0
1 1 1
1 2 3 1 2 3 1 0.5 0.333 x 6 6 3 2
Miller indices are placed in round brackets, e.g. (1 0 0). Commas are only used, if two
digit indices appear, e.g. (1,14,2)
Negative intercepts are indicated by a bar above the number, e.g. (1 0 0).
Indices, which are not precisely known, are replaced by the letters h, k, l. This system
is also used to indcate indices of faces with common orientation properties e.g.
(0, k, 0) all faces parallel to the a- and c-axis
(0, k, l) all faces parallel to the a- axis
43. Find intercepts along axes → 2 3 1
Take reciprocal → 1/2 1/3 1
Convert to smallest integers in the same ratio → 3 2 6
Enclose in parenthesis → (326)
(2,0,0)
(0,3,0)
(0,0,1)
Miller Indices for planes
45. Interplaner Distances for Cubic Crystal or Spacing of planes
222
lkh
a
dhkl
Here a = length of any side of a cube in Angstrom (A0 )
h – intercept made by plane on x- axis
k- – intercept made by plane on y- axis
l - – intercept made by plane on z- axis
46. Index
Number of
members in a
cubic lattice
dhkl
(100) 6
(110) 12 The (110) plane bisects the
face diagonal
(111) 8 The (111) plane trisects the
body diagonal
(210) 24
(211) 24
(221) 24
(310) 24
(311) 24
(320) 24
(321) 48
100d a
110 / 2 2 / 2d a a
111 / 3 3 /3d a a
49. very small wavelengths of
radiation.
Why are electrons go for studying matter?
Why are electrons not ideal?
What could be used instead?
Xrays made by slamming electrons into metals.
50. Bragg’s Law
nλ = 2 d sin θ
Constructive interference only occurs for certain θ’s
correlating to a (hkl) plane, specifically when the path
difference is equal to n wavelengths.
54. path difference=nλ give constructive
interference.
for different angles path difference varies. Some angles give constructive some
destructive.
Braggs Law Path difference =2dsinθ=nλ
55. The Braggs realised that by sending the X rays in at different angles they should get periods of constructive
and destructive interference.
X ray tube target
Turntable
Collimating
Slits
The Bragg Spectrometer
This would help them
determine the lattice
structure including d.
56. In two dimensions this type of
pattern is produced.
typical lattice diffraction pattern for iron
57. 57
a) ROCK SALT STRUCTURE (NaCl)
• CCP Cl- with Na+ in all Octahedral
holes
• Lattice: FCC
• Motif: Cl at (0,0,0); Na at (1/2,0,0)
• 4 NaCl in one unit cell
• Coordination: 6:6 (octahedral)
• Cation and anion sites are topologically
identical
STRUCTURE TYPE - AX NaCl
CLOSE PACKED STRUCTURES
58. 58
• CCP S2- with Zn2+ in half Tetrahedral holes ( T+ {or T-}
filled)
• Lattice: FCC
• 4 ZnS in one unit cell
• Motif: S at (0,0,0); Zn at (1/4,1/4,1/4)
• Coordination: 4:4 (tetrahedral)
• Cation and anion sites are topologically identical
b) SPHALERITE OR ZINC BLEND (ZnS) STRUCTURE
59. 59
• HCP with Ni in all Octahedral holes
• Lattice: Hexagonal - P
• Motif: 2Ni at (0,0,0) & (0,0,1/2) 2As at (2/3,1/3,1/4)
& (1/3,2/3,3/4)
• 2 NiAs in unit cell
• Coordination: Ni 6 (octahedral) : As 6 (trigonal
prismatic)
c) NICKELARSENIDE (NiAs)
60. 60
• HCP S2- with Zn2+ in half Tetrahedral holes ( T+ {or T-}
filled )
• Lattice: Hexagonal - P
• Motif: 2 S at (0,0,0) & (2/3,1/3,1/2); 2 Zn at (2/3,1/3,1/8) &
(0,0,5/8)
• 2 ZnS in unit cell
• Coordination: 4:4 (tetrahedral)
d) WURTZITE ( ZnS )
62. 62
STRUCTURE TYPE - AX
NON – CLOSE PACKED STRUCTURES
CUBIC-P (PRIMITIVE) ( eg. Cesium Chloride ( CsCl ) )
• Motif: Cl at (0,0,0); Cs at (1/2,1/2,1/2)
• 1 CsCl in one unit cell
• Coordination: 8:8 (cubic)
• Adoption by chlorides, bromides and iodides of larger cations,
• e.g. Cs+, Tl+, NH4
+
63. 63
• CCP Ca2+ with F- in all Tetrahedral holes
• Lattice: fcc
• Motif: Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4)
• 4 CaF2 in one unit cell
• Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral)
• In the related Anti-Fluorite structure Cation and
Anion positions are reversed
STRUCTURE TYPE - AX2
CLOSE PACKED STRUCTURE eg. FLUORITE (CaF2)
64. 64
• CCP Ca2+ with F- in all Tetrahedral holes
• Lattice: fcc
• Motif: Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4)
• 4 CaF2 in one unit cell
• Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral)
• In the related Anti-Fluorite structure Cation and
Anion positions are reversed
STRUCTURE TYPE - AX2
CLOSE PACKED STRUCTURE eg. FLUORITE (CaF2)
65. 65
ALTERNATE REPRESENTATION OF FLUORITE
STRUCTURE
Anti–Flourite structure (or Na2O structure) – positions of
cations and anions are reversed related to Fluorite structure
67. 67
• HCP of Iodide with Cd in Octahedral holes of alternate layers
• CCP analogue of CdI2 is CdCl2
STRUCTURE TYPE - AX2
NON-CLOSE PACKED STRUCTURE
LAYER STRUCTURE ( eg. Cadmium iodide ( CdI2 ))
69. 69
HCPANALOGUE OF FLOURITE (CaF2) ?
• No structures of HCP are known with all Tetrahedral sites (T+
and T-) filled. (i.e. there is no HCP analogue of the Fluorite/Anti-
Fluorite Structure).
• The T+ and T- interstitial sites above and below a layer of close-
packed spheres in HCP are too close to each other to tolerate the
coulombic repulsion generated by filling with like-charged species.
Unknown HCP
analogue of FluoriteFluorite
71. 71
Formula Type and fraction of sites
occupied
CCP HCP
AX All octahedral
Half tetrahedral (T+ or T-)
Rock salt (NaCl)
Zinc Blend (ZnS)
Nickel Arsenide (NiAs)
Wurtzite (ZnS)
AX2 All Tetrahedral
Half octahedral (ordered
framework)
Half octahedral (Alternate
layers full/ empty)
Fluorite (CaF2),
Anti-Fluorite (Na2O)
Anatase (TiO2)
Cadmium Chloride
(CdCl2)
Not known
Rutile (TiO2)
Cadmium iodide (CdI2)
A3X All octahedral & All
Tetrahedral
Li3Bi Not known
AX3 One third octahedral YCl3 BiI3
SUMMARY OF IONIC CRYSTAL STRUCTURE TYPES
72. 72
Rock salt(NaCl) – occupation of all octahedral holes
• Very common (in ionics, covalents & intermetallics )
• Most alkali halides (CsCl, CsBr, CsI excepted)
• Most oxides / chalcogenides of alkaline earths
• Many nitrides, carbides, hydrides (e.g. ZrN, TiC, NaH)
Fluorite (CaF2) – occupation of all tetrahedral holes
• Fluorides of large divalent cations, chlorides of Sr, Ba
• Oxides of large quadrivalent cations (Zr, Hf, Ce, Th, U)
Anti-Fluorite (Na2O) – occupation of all tetrahedral holes
• Oxides /chalcogenides of alkali metals
Zinc Blende/Sphalerite ( ZnS ) – occupation of half tetrahedral holes
• Formed from Polarizing Cations (Cu+, Ag+, Cd2+, Ga3+...) and
Polarizable Anions (I-, S2-, P3-, ...)
e.g. Cu(F,Cl,Br,I), AgI, Zn(S,Se,Te), Ga(P,As), Hg(S,Se,Te)
Examples of CCP Structure Adoption
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Examples of HCP Structure Adoption
Nickel Arsenide ( NiAs ) – occupation of all octahedral holes
• Transition metals with chalcogens, As, Sb, Bi e.g. Ti(S,Se,Te);
Cr(S,Se,Te,Sb); Ni(S,Se,Te,As,Sb,Sn)
Cadmium Iodide ( CdI2 ) – occupation half octahedral (alternate) holes
• Iodides of moderately polarising cations; bromides and chlorides of
strongly polarising cations. e.g. PbI2, FeBr2, VCl2
• Hydroxides of many divalent cations. e.g. (Mg,Ni)(OH)2
• Di-chalcogenides of many quadrivalent cations . e.g. TiS2, ZrSe2, CoTe2
Cadmium Chloride CdCl2 (CCP equivalent of CdI2) – half octahedral holes
• Chlorides of moderately polarising cations e.g. MgCl2, MnCl2
• Di-sulfides of quadrivalent cations e.g. TaS2, NbS2 (CdI2 form as well)
• Cs2O has the anti-cadmium chloride structure
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PEROVSKITE STRUCTURE
Formula unit – ABO3
CCP of A atoms(bigger) at the corners
O atoms at the face centers
B atoms(smaller) at the body-center
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• Lattice: Primitive Cubic (idealised structure)
• 1 CaTiO3 per unit cell
• A-Cell Motif: Ti at (0, 0, 0); Ca at (1/2, 1/2, 1/2);
3O at (1/2, 0, 0), (0, 1/2, 0), (0, 0, 1/2)
• Ca 12-coordinate by O (cuboctahedral)
• Ti 6-coordinate by O (octahedral)
• O distorted octahedral (4xCa + 2xTi)
PEROVSKITE
• Examples: NaNbO3 , BaTiO3 ,
CaZrO3 , YAlO3 , KMgF3
• Many undergo small distortions:
e.g. BaTiO3 is ferroelectric
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SPINEL STRUCTURE
Formula unit AB2O4 (combination of Rock Salt
and Zinc Blend Structure)
Oxygen atoms form FCC
A2+ occupy tetrahedral holes
B3+ occupy octahedral holes
INVERSE SPINEL
A2+ ions and half of B3+ ions
occupy octahedral holes
Other half of B3+ ions occupy
tetrahedral holes
Formula unit is B(AB)O4