The document discusses various topics related to solid state structures including:
1. Solids have a definite shape, volume and order due to an ordered arrangement of atoms, molecules or ions.
2. A unit cell is the smallest repeating unit that makes up the structure of a crystal lattice. There are 7 possible shapes of unit cells.
3. There are 14 possible arrangements or lattices that unit cells can form in the 7 crystal systems while still maintaining symmetry.
The document discusses various topics related to crystal structures including:
1. The seven possible shapes of unit cells - cubic, orthorhombic, rhombohedral, tetragonal, triclinic, hexagonal, monoclinic.
2. The four possible arrangements of spheres in unit cells - primitive, body centered, face centered, end centered.
3. Close packing of spheres in cubic unit cells and the coordination numbers and packing fractions for each arrangement.
4. Structures of ionic compounds like NaCl, ZnS, CaF2, and relationships between ion sizes and structures.
1. Solids have a definite shape, volume, and ordered arrangement of atoms or molecules. Liquids have a definite volume but no definite shape, while gases have neither a definite shape nor volume.
2. Unit cells are the smallest repeating units that make up crystal structures. They must be identical and fit together without gaps. There are seven possible shapes of unit cells.
3. There are 14 possible unit cell arrangements across the seven crystal systems based on satisfying symmetry requirements. Primitive, face-centered, and body-centered are common arrangements.
In the topic there is a discussion about the solid state their compact molecules in molecular space their temperature and their imitations of electrons in cell
This document provides information on crystallography and the structure of crystalline solids. It defines key terms like crystalline solids, amorphous solids, space lattice, unit cell, and Bravais lattices. It describes the primary crystalline structures of metals including simple cubic, body centered cubic, face centered cubic, and hexagonal close packed. It provides details on the characteristics of each structure like atoms per unit cell, coordination number, and packing factor. Crystalline solids are described as having a regular orderly arrangement of atoms compared to the random arrangement in amorphous solids.
Crystal physics deals with the study of crystalline solids and their physical properties. Single crystals are needed because they exhibit uniform physical properties and directional properties. There are two main types of solids - crystalline and amorphous. Crystalline solids such as metals have a regular arrangement of atoms while amorphous solids like glass have an irregular arrangement. Crystalline solids can be single crystalline or polycrystalline. Important crystallographic concepts include the unit cell, lattice points, Miller indices, and Bravais lattices which describe the geometric arrangement of atoms in crystals. Common crystal structures are simple cubic, body centered cubic, face centered cubic, and hexagonal close packed.
The document discusses different types of crystal defects including point defects, stoichiometric defects, and non-stoichiometric defects. Stoichiometric defects include Schottky and Frenkel defects which involve cation-anion pairs missing or cation dislocations. Non-stoichiometric defects result from deviations from the ideal ratio of cations to anions and include metal excess or deficiency defects involving anion or cation vacancies. Common examples of different defect types in various crystals are provided.
The document summarizes key concepts related to crystal structure:
Crystalline materials have atoms or molecules arranged in a regular, orderly 3D pattern which gives them high strength, while non-crystalline materials have a random arrangement and lower strength. A crystal structure is a regular repetition of this 3D pattern defined by a unit cell and space lattice. Common crystal structures include simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed. Crystal defects such as point defects, dislocations, grain boundaries, and voids are also discussed.
The document discusses various topics related to crystal structures including:
1. The seven possible shapes of unit cells - cubic, orthorhombic, rhombohedral, tetragonal, triclinic, hexagonal, monoclinic.
2. The four possible arrangements of spheres in unit cells - primitive, body centered, face centered, end centered.
3. Close packing of spheres in cubic unit cells and the coordination numbers and packing fractions for each arrangement.
4. Structures of ionic compounds like NaCl, ZnS, CaF2, and relationships between ion sizes and structures.
1. Solids have a definite shape, volume, and ordered arrangement of atoms or molecules. Liquids have a definite volume but no definite shape, while gases have neither a definite shape nor volume.
2. Unit cells are the smallest repeating units that make up crystal structures. They must be identical and fit together without gaps. There are seven possible shapes of unit cells.
3. There are 14 possible unit cell arrangements across the seven crystal systems based on satisfying symmetry requirements. Primitive, face-centered, and body-centered are common arrangements.
In the topic there is a discussion about the solid state their compact molecules in molecular space their temperature and their imitations of electrons in cell
This document provides information on crystallography and the structure of crystalline solids. It defines key terms like crystalline solids, amorphous solids, space lattice, unit cell, and Bravais lattices. It describes the primary crystalline structures of metals including simple cubic, body centered cubic, face centered cubic, and hexagonal close packed. It provides details on the characteristics of each structure like atoms per unit cell, coordination number, and packing factor. Crystalline solids are described as having a regular orderly arrangement of atoms compared to the random arrangement in amorphous solids.
Crystal physics deals with the study of crystalline solids and their physical properties. Single crystals are needed because they exhibit uniform physical properties and directional properties. There are two main types of solids - crystalline and amorphous. Crystalline solids such as metals have a regular arrangement of atoms while amorphous solids like glass have an irregular arrangement. Crystalline solids can be single crystalline or polycrystalline. Important crystallographic concepts include the unit cell, lattice points, Miller indices, and Bravais lattices which describe the geometric arrangement of atoms in crystals. Common crystal structures are simple cubic, body centered cubic, face centered cubic, and hexagonal close packed.
The document discusses different types of crystal defects including point defects, stoichiometric defects, and non-stoichiometric defects. Stoichiometric defects include Schottky and Frenkel defects which involve cation-anion pairs missing or cation dislocations. Non-stoichiometric defects result from deviations from the ideal ratio of cations to anions and include metal excess or deficiency defects involving anion or cation vacancies. Common examples of different defect types in various crystals are provided.
The document summarizes key concepts related to crystal structure:
Crystalline materials have atoms or molecules arranged in a regular, orderly 3D pattern which gives them high strength, while non-crystalline materials have a random arrangement and lower strength. A crystal structure is a regular repetition of this 3D pattern defined by a unit cell and space lattice. Common crystal structures include simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed. Crystal defects such as point defects, dislocations, grain boundaries, and voids are also discussed.
The document provides information on crystal structures including:
- Crystalline solids have atoms arranged in an orderly, periodic manner while amorphous solids do not.
- Dense, regularly packed structures have lower energy than non-dense, randomly packed structures.
- A unit cell is the smallest repeating unit that defines the lattice structure. There are 14 possible Bravais lattice structures.
- Common crystal structures for metals include body centered cubic (BCC), face centered cubic (FCC), and hexagonal close packed (HCP).
- Properties of unit cells include the number of atoms, effective number of atoms, coordination number, and atomic packing factor.
The document provides information about different types of solids and their properties. It discusses crystalline solids which have a regular arrangement of particles and sharp edges, as well as amorphous solids which have an irregular arrangement and no distinct shape. It also describes different classifications of crystalline solids such as molecular, ionic, metallic and covalent solids. Unit cells, lattice structures, coordination numbers and packing fractions are explained. Close packing arrangements in 2D and 3D are discussed.
Solid state 12th Maharashtra state boardFreya Cardozo
- Solids can be crystalline or amorphous. Crystalline solids have long-range order while amorphous solids have short-range order.
- There are four main types of crystalline solids: ionic, molecular, metallic, and covalent networks. They differ in the type of particles that make them up and the nature of bonding between the particles.
- Crystalline solids can form different crystal structures depending on how the particles are packed together in the lattice. Common structures include simple cubic, body-centered cubic, and face-centered cubic.
The document discusses different types of solids and crystal structures. It begins by stating that everything around us is matter, which is made of molecules and exists in four main types. It then discusses crystalline and amorphous solids, and the key differences between them. Crystalline solids like metals can have either a single crystal or polycrystalline structure. The document also covers various crystal structures like simple cubic, body centered cubic, face centered cubic, and diamond cubic. It defines important concepts such as unit cell, lattice points, Miller indices, coordination number and packing factor.
This document discusses different types of solids and their crystal structures. It describes crystalline solids as having long-range periodic atomic arrangements, while amorphous solids lack long-range order. Polycrystalline solids consist of many small crystallites. Common crystal structures include body-centered cubic, face-centered cubic, and hexagonal close-packed arrangements. Defects in crystal structures like point defects and dislocations are also summarized.
- The document discusses different crystal structures including simple cubic, body-centered cubic, face-centered cubic, and hexagonal closely packed.
- Key properties like number of atoms per unit cell, atomic radius, coordination number, and atomic packing factor are defined and calculated for each structure.
- There are seven basic crystal systems that materials can belong to depending on their lattice parameters and angles between axes. The most common systems are cubic, hexagonal, and tetragonal.
Crystals are solids with atoms arranged in regular repeating patterns in all directions. There are several key concepts in crystallography:
1) Crystals have a crystal lattice structure defined by lattice vectors and a unit cell that repeats to form the crystal.
2) Unit cells have lattice constants and contain one or more atoms. Primitive, body-centered, and face-centered unit cells have different atomic packing factors.
3) Crystal structures demonstrate symmetry operations like translation and rotation that leave the structure unchanged. Miller indices represent crystallographic planes and directions.
This document discusses crystal and amorphous structures in materials. It begins by defining crystals as having long-range order while amorphous solids lack long-range order. Examples of common crystalline and amorphous solids are provided. The document then goes into extensive detail about different types of unit cells and crystal structures including body centered cubic, face centered cubic, and hexagonal close packed. It discusses topics such as lattice constants, atomic packing factors, Miller indices, and crystallographic directions. Finally, it briefly discusses polymorphism and how x-ray diffraction can be used to analyze crystal structures.
undamentals of Crystal Structure: BCC, FCC and HCP Structures, coordination number and atomic packing factors, crystal imperfections -point line and surface imperfections. Atomic Diffusion: Phenomenon, Fick’s laws of diffusion, factors affecting diffusion.
This document provides an overview of solid state structures. It discusses the two main types of solids - crystalline and amorphous - and explains their distinguishing characteristics. Crystalline solids have a definite, orderly arrangement of atoms while amorphous solids do not. The document then covers various topics related to crystalline solids, including crystal structures, unit cells, Bravais lattices, and the structures of materials like NaCl, diamond, and graphite. It also discusses crystal imperfections and different types of defects that can occur in ionic crystals.
This document discusses different crystal structures and materials. It begins by describing three common crystal structures - face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) - and provides examples of metals that adopt each structure. It then discusses ceramic crystal structures and how the size and charge of ions influence the structure. Key ceramic structures described include rock salt, cesium chloride, and zinc blende. The document also examines properties of carbon including different allotropes like diamond, graphite, fullerenes, and carbon nanotubes.
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.
Contains information about various crystal types in solid state chemistry like Rock Salt, Wurtzite, Nickel Arsenide, Zinc Blende etc. It also gives a brief description of lattice energy and Born Haber cycle.
This document provides an overview of crystallography and crystal structures. It discusses how crystals form periodic arrangements that can be described by unit cells defined by lattice parameters. The most common crystal structures for metals are face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) since metals form dense, ordered packings with low energies. These crystal structures differ in their unit cell contents and atomic packing factors (FCC has the highest at 0.74). Directions in crystals are described by Miller indices written as [uvw].
This document provides an introduction to solid state physics and crystallography. It defines key terms like crystalline, non-crystalline, lattice, basis, unit cell and discusses common crystal structures including simple cubic, body centered cubic, and face centered cubic. It also covers topics like Miller indices, atomic packing fraction, coordination number, and examples of crystal structures in sodium chloride and cesium chloride.
This document provides an overview of key concepts in crystallography and crystal systems. It defines a crystal as a solid with a repeating pattern of atoms in all directions. Crystals can be single crystals, polycrystalline, or amorphous. A crystal lattice describes the repeating points in space upon which atoms are arranged in a crystal structure. Unit cells are the smallest repeating units that make up the crystal lattice. Lattice constants, symmetry operations, packing factors, and Miller indices are also discussed in the context of describing crystal structures and properties.
Crystalline structures can be classified as crystalline, polycrystalline, or amorphous. Crystalline structures have repeating arrangements of atoms or molecules. There are seven crystal systems and fourteen Bravais lattices that describe how points in the unit cell are arranged in three-dimensional space. Common metal structures include body centered cubic, face centered cubic, and hexagonal close packed. Ceramic and semiconductor structures often involve ionic bonding between metals and nonmetals. Polymeric structures can be crystalline but typically have disordered regions as well.
This document provides a summary of key topics in solid state chemistry, including the three phases of matter, types of solids (crystalline and amorphous), crystal structures (ionic, covalent, molecular, metallic), symmetry elements, Bragg's equation, and allotropes of carbon (diamond, graphite, fullerene). It describes characteristics of each topic in 1-3 sentences, with accompanying diagrams and examples. Key definitions include crystalline lattices, unit cells, coordination numbers, radius ratio rule for predicting structure, and the seven crystal systems.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
The document provides information on crystal structures including:
- Crystalline solids have atoms arranged in an orderly, periodic manner while amorphous solids do not.
- Dense, regularly packed structures have lower energy than non-dense, randomly packed structures.
- A unit cell is the smallest repeating unit that defines the lattice structure. There are 14 possible Bravais lattice structures.
- Common crystal structures for metals include body centered cubic (BCC), face centered cubic (FCC), and hexagonal close packed (HCP).
- Properties of unit cells include the number of atoms, effective number of atoms, coordination number, and atomic packing factor.
The document provides information about different types of solids and their properties. It discusses crystalline solids which have a regular arrangement of particles and sharp edges, as well as amorphous solids which have an irregular arrangement and no distinct shape. It also describes different classifications of crystalline solids such as molecular, ionic, metallic and covalent solids. Unit cells, lattice structures, coordination numbers and packing fractions are explained. Close packing arrangements in 2D and 3D are discussed.
Solid state 12th Maharashtra state boardFreya Cardozo
- Solids can be crystalline or amorphous. Crystalline solids have long-range order while amorphous solids have short-range order.
- There are four main types of crystalline solids: ionic, molecular, metallic, and covalent networks. They differ in the type of particles that make them up and the nature of bonding between the particles.
- Crystalline solids can form different crystal structures depending on how the particles are packed together in the lattice. Common structures include simple cubic, body-centered cubic, and face-centered cubic.
The document discusses different types of solids and crystal structures. It begins by stating that everything around us is matter, which is made of molecules and exists in four main types. It then discusses crystalline and amorphous solids, and the key differences between them. Crystalline solids like metals can have either a single crystal or polycrystalline structure. The document also covers various crystal structures like simple cubic, body centered cubic, face centered cubic, and diamond cubic. It defines important concepts such as unit cell, lattice points, Miller indices, coordination number and packing factor.
This document discusses different types of solids and their crystal structures. It describes crystalline solids as having long-range periodic atomic arrangements, while amorphous solids lack long-range order. Polycrystalline solids consist of many small crystallites. Common crystal structures include body-centered cubic, face-centered cubic, and hexagonal close-packed arrangements. Defects in crystal structures like point defects and dislocations are also summarized.
- The document discusses different crystal structures including simple cubic, body-centered cubic, face-centered cubic, and hexagonal closely packed.
- Key properties like number of atoms per unit cell, atomic radius, coordination number, and atomic packing factor are defined and calculated for each structure.
- There are seven basic crystal systems that materials can belong to depending on their lattice parameters and angles between axes. The most common systems are cubic, hexagonal, and tetragonal.
Crystals are solids with atoms arranged in regular repeating patterns in all directions. There are several key concepts in crystallography:
1) Crystals have a crystal lattice structure defined by lattice vectors and a unit cell that repeats to form the crystal.
2) Unit cells have lattice constants and contain one or more atoms. Primitive, body-centered, and face-centered unit cells have different atomic packing factors.
3) Crystal structures demonstrate symmetry operations like translation and rotation that leave the structure unchanged. Miller indices represent crystallographic planes and directions.
This document discusses crystal and amorphous structures in materials. It begins by defining crystals as having long-range order while amorphous solids lack long-range order. Examples of common crystalline and amorphous solids are provided. The document then goes into extensive detail about different types of unit cells and crystal structures including body centered cubic, face centered cubic, and hexagonal close packed. It discusses topics such as lattice constants, atomic packing factors, Miller indices, and crystallographic directions. Finally, it briefly discusses polymorphism and how x-ray diffraction can be used to analyze crystal structures.
undamentals of Crystal Structure: BCC, FCC and HCP Structures, coordination number and atomic packing factors, crystal imperfections -point line and surface imperfections. Atomic Diffusion: Phenomenon, Fick’s laws of diffusion, factors affecting diffusion.
This document provides an overview of solid state structures. It discusses the two main types of solids - crystalline and amorphous - and explains their distinguishing characteristics. Crystalline solids have a definite, orderly arrangement of atoms while amorphous solids do not. The document then covers various topics related to crystalline solids, including crystal structures, unit cells, Bravais lattices, and the structures of materials like NaCl, diamond, and graphite. It also discusses crystal imperfections and different types of defects that can occur in ionic crystals.
This document discusses different crystal structures and materials. It begins by describing three common crystal structures - face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) - and provides examples of metals that adopt each structure. It then discusses ceramic crystal structures and how the size and charge of ions influence the structure. Key ceramic structures described include rock salt, cesium chloride, and zinc blende. The document also examines properties of carbon including different allotropes like diamond, graphite, fullerenes, and carbon nanotubes.
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.
Contains information about various crystal types in solid state chemistry like Rock Salt, Wurtzite, Nickel Arsenide, Zinc Blende etc. It also gives a brief description of lattice energy and Born Haber cycle.
This document provides an overview of crystallography and crystal structures. It discusses how crystals form periodic arrangements that can be described by unit cells defined by lattice parameters. The most common crystal structures for metals are face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) since metals form dense, ordered packings with low energies. These crystal structures differ in their unit cell contents and atomic packing factors (FCC has the highest at 0.74). Directions in crystals are described by Miller indices written as [uvw].
This document provides an introduction to solid state physics and crystallography. It defines key terms like crystalline, non-crystalline, lattice, basis, unit cell and discusses common crystal structures including simple cubic, body centered cubic, and face centered cubic. It also covers topics like Miller indices, atomic packing fraction, coordination number, and examples of crystal structures in sodium chloride and cesium chloride.
This document provides an overview of key concepts in crystallography and crystal systems. It defines a crystal as a solid with a repeating pattern of atoms in all directions. Crystals can be single crystals, polycrystalline, or amorphous. A crystal lattice describes the repeating points in space upon which atoms are arranged in a crystal structure. Unit cells are the smallest repeating units that make up the crystal lattice. Lattice constants, symmetry operations, packing factors, and Miller indices are also discussed in the context of describing crystal structures and properties.
Crystalline structures can be classified as crystalline, polycrystalline, or amorphous. Crystalline structures have repeating arrangements of atoms or molecules. There are seven crystal systems and fourteen Bravais lattices that describe how points in the unit cell are arranged in three-dimensional space. Common metal structures include body centered cubic, face centered cubic, and hexagonal close packed. Ceramic and semiconductor structures often involve ionic bonding between metals and nonmetals. Polymeric structures can be crystalline but typically have disordered regions as well.
This document provides a summary of key topics in solid state chemistry, including the three phases of matter, types of solids (crystalline and amorphous), crystal structures (ionic, covalent, molecular, metallic), symmetry elements, Bragg's equation, and allotropes of carbon (diamond, graphite, fullerene). It describes characteristics of each topic in 1-3 sentences, with accompanying diagrams and examples. Key definitions include crystalline lattices, unit cells, coordination numbers, radius ratio rule for predicting structure, and the seven crystal systems.
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A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
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1. Solid State
Gases: no definite shape and volume
Solids: definite shape, volume and order.
Order: definite pattern of arrangement of atoms or molecules or
ions.
Liquids: no definite shape but definite volume
Solids: definite shape and volume
2. Intensive properties: do not depend on the amount.
Unit Cells
• Smallest Repeating Unit
• Unit Cells must link-up − cannot have gaps between them
• All unit cells must be identical
11. Crystal Systems Lattice Parameters
Crystal Intercepts Crystal Angles
Cubic a = b = c α = β = γ = 90o
Orthorhombic a ≠ b ≠ c α = β = γ = 90o
Rhombohedral a = b = c α = β = γ ≠ 90o
Tetragonal a = b ≠ c α = β = γ = 90o
Triclinic a ≠ b ≠ c α ≠ β ≠ γ ≠ 90o
Hexagonal a = b ≠ c α = β = 90o,
γ = 120o
Monoclinic a ≠ b ≠ c α = γ = 90o,
β ≠ 90o
12. There are not more than 4 ways of arranging
spheres in any shape of unit cell
These are Primitive, Body Centered, Face
Centered & End Centered
23. Packing Fraction
Volume occupied by a corner sphere in the unit cell
Volume occupied by the central sphere in the unit cell
Total Volume occupied by the spheres in the unit cell
Packing Fraction
28. Packing Fraction
Volume occupied by a corner sphere in the unit cell
Volume occupied by a face centered sphere in the unit
cell
Total Volume occupied by the spheres in the unit cell
Packing Fraction
Highest Packing Fraction of all shapes and of
all arrangements
32. Out of all the twenty eight possible unit cells only
14 exist !
Those arrangements in a given shape that violate even
one symmetry element of that shape do not exist in
that shape
90o axis of symmetry
33.
34.
35.
36.
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63.
64. If we do the same with BCC & FCC we will get the
same result.
Lets try with End Centered
65.
66.
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71.
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89.
90.
91. Like this 13 other arrangements in various shapes
were rejected.
We are left with only 14 unit cells
105. r
O
A
B
AB = r
OA = r tan30o < r
Packing Fraction − same
Rank of unit cell − 2
Volume of unit cell − 1/3 of previous
mass of unit cell − 1/3 of previous
density − same
106.
107. Two types of voids:
Octahedral
Tetrahedral
Found only in FCC & Hexagonal primitive unit cells
Octahedral void in FCC
108. Each octahedral void located at the edge center is shared by 4 unit
cells
Total contribution of edge centre voids =
Contribution of central void
Total contribution of all octahedral voids per unit cell of FCC = 4
No. of Octahedral voids per unit
cell = Rank of unit cell
111. With each corner as origin there are 8 tetrahedral voids in FCC unit
cell
∴ No. of tetrahedral voids = 2 × no. of Octahedral voids
112. Voids in Hexagonal Primitive
Let us assume that this is the unit cell
then according to what we have done in FCC no. of
Octahedral voids = 6 & no. of tetrahedral voids = 12
Octahedral voids
Octahedral
void
113. Voids in Hexagonal Primitive
Let us assume that this is the unit cell
then according to what we have done in FCC no. of
Octahedral voids = 6 & no. of tetrahedral voids = 12
Tetrahedral voids
Contribution of tetrahedral voids formed inside the unit
cell is 1 each. The ones formed on the corners of the
hexagon have a contribution of 1/3.
Total contribution
In 3 layers
114. Minimum rc/ra for various coordination numbers
2r
a
B
O
A
Coordination number - 3
118. Final Radius Ratios
Radius Ratio, rc/ra
Co-ordination No.
<0.155 2
[0.155, 0.225) 2 or 3
[0.225, 0.414) 2 or 3 or 4 Td
[0.414, 0.732) 2 or 3 or 4 Td, 4 sq. pl or 6 Oh
[0.732, 0.99) 2 or 3 or 4 Td, 4 sq. pl or 6 Oh
or 8
119. For ionic compounds of the general formula AxBy the ratio of the
coordination number of A to that of B will be the ratio of y:x.
1. Rock Salt Structure (NaCl) − Cl-
− Na+
Cl- is FCC
Na+ occupies Octahedral voids
No. of Cl- per unit cell = 4
No. of Na+ per unit cell = 4
∴ formula is NaCl
Coordination no. of Na+ = 6
Coordination no. of Cl- = 6
120. Other compounds which have this structure are: all halides of alkali metals
except cesium halide, all oxides of alkaline earth metals except beryllium
oxide, AgCl, AgBr & AgI.
121. Consider the unit cell with Cl- as FCC.
Consider the unit cell with Na+ as FCC.
Similarly, rany alkali metal = rany halide
rany akaline earth metal = roxide
Comparing
122. 2. Zinc Blende (ZnS)
− S2-
− Zn2+
S2- is FCC
Zn2+ occupies alternate tetrahedral
voids
No. of S2- per unit cell = 4
No. of Zn2+ per unit cell = 4
∴ formula is ZnS
Coordination no. of Zn2+ = 4
Coordination no. of S2- = 4
Other compound which have this structure is: BeO
123. 3. Fluorite (CaF2)
− F-
− Ca2+
Ca2+ is FCC
F- occupies all tetrahedral voids
No. of Ca2+ per unit cell = 4
No. of F- per unit cell = 8
∴ formula is CaF2
Coordination no. of F- = 4
Coordination no. of Ca2+ = 8
Other compounds which have this structure are: UO2,
ThO2, PbO2, HgF2 etc.
124. 4. Anti-Fluorite (Li2O)
− O2-
− Li+
O2- is FCC
Li+ occupies all tetrahedral voids
No. of O2- per unit cell = 4
No. of Li+ per unit cell = 8
∴ formula is Li2O
Coordination no. of Li+ = 4
Coordination no. of O2- = 8
Other compounds which have this structure are: Na2O,
K2O, Rb2O
125. 5. Cesium Halide
− Cl-
− Cs+
Cl- is Primitive cubic
Cs+ occupies the centre of the unit cell
No. of Cl- per unit cell = 1
No. of Cs+ per unit cell = 1
∴ formula is CsCl
Coordination no. of Cs+ = 8
Coordination no. of Cl- = 8
Other compounds which have this structure are: all halides
of Cesium and ammonium
126. 6. Corundum (Al2O3)
Oxide ions form hexagonal primitive unit cell and trivalent ions (Al3+) are
present in 2/3 of octahedral voids.
No. of O2- per unit cell = 2
No. of Al3+ per unit cell = 4/3
Coordination no. of Al3+ = 6
Coordination no. of O2- = 4
Other compounds which have this structure are: Fe2O3, Cr2O3, Mn2O3 etc.
127. 7. Rutile (TiO2)
Oxide ions form hexagonal primitive unit cell and tetravalent ions (Ti4+)
are present in 1/2 of octahedral voids.
No. of O2- per unit cell = 2
No. of Ti4+ per unit cell = 1
Coordination no. of Ti4+ = 6
Coordination no. of O2- = 3
Other compounds which have this structure are: MnO2, SnO2, MgF2, NiF2
∴ formula is TiO2
128. 8. Pervoskite (CaTiO3)
− O2-
− Ca2+ (divalent ion)
Ca2+ is Primitive cubic
Ti4+ occupies the centre of the unit cell
No. of O2- per unit cell = 3
No. of Ca2+ per unit cell = 1
∴ formula is CaTiO3
Coordination no. of O2- = 6
Coordination no. of Ti4+
Other compounds which have this structure are: BaTiO3,
SrTiO3
− Ti4+ (tetravalent ion)
O2- occupies face centres
No. of Ti4+ per unit cell = 1
= 6
Coordination no. of Ca2+ = 12
129. 9. Spinel & Inverse Spinel (MgAl2O4)
O2- ion is FCC
Mg2+(divalent ion) 1/8th of tetrahedral voids
Al3+ (trivalent ion) 1/2 of octahedral voids
O2- per unit cell = 4
Mg2+ per unit cell = 1
Al3+ per unit cell = 1
∴ formula is MgAl2O4
Spinel Inverse Spinel
O2- ion is FCC
divalent ion 1/8th of tetrahedral voids
trivalent ion 1/4th of octahedral voids & 1/8th of
tetrahedral voids
O2- per unit cell = 4
Divalent per unit cell = 1
Trivalent per unit cell = 1
130. (i) Lattice of atoms
(a) Vacancy − an atom is missing from its position
− density decreases
− percentage occupancy decreases
(b) Self interstitial − an atom leaves its lattice site & occupies interstitial space
− density & percentage occupancy remains same
(c) Substitutional impurity − foreign atom substitutes a host atom & occupies its lattice
− density & percentage occupancy may change
(c) Interstitial impurity − foreign atom occupies occupies the interstitial space
− density & percentage occupancy increases
131. (i) Ionic structures
(a) Schottky Defect − Cation – anion pair are missing
− electro neutrality is maintained
− density decreases
(b) Frenkel Defect − ion leaves lattice position & occupies interstitial space
− electro neutrality is maintained
− density maintained
(c) Substitutional Impurity Defect − Ba2+ is replaced by Sr2+
− electro neutrality is maintained
− density changes
(d) Interstitial Impurity Defect − H2 is trapped in TiC
− electro neutrality is maintained
− density increases
(a) F-Centre
− electron replaces anion
− electro neutrality is maintained
− density decreases
− colour is imparted
132. 1. Assuming diamond to be FCC of carbon atoms
and that each carbon atom is sp3 hybridized
then which of the following statements is
correct.
(a) all voids are empty
(b) 100% octahedral voids are filled
(c) 50% octahedral voids are filled
(d) 100% tetrahedral voids are filled
(e) 50% tetrahedral voids are filled
Sol: If no void is filled then each carbon would be in contact with 12 carbon atoms. This is
not possible as each carbon is sp3 hybridized.
If octahedral voids are filled then those carbons in the voids would be in contact with
6 carbon atoms. This also is not possible.
If 100% tetrahedral voids are filled then the FCC carbons would be in contact with 8
carbon atoms as they are shared in 8 unit cells and would be in contact with 8
tetrahedral voids. Not possible. ∴ (e)
133. 2. In NaCl calculate:
The distance between the first 9 nearest neighbors
in a unit cell & their total number in all unit cells
135. 3. Iron crystallizes in FCC lattice. The figures given below shows
the iron atoms in four crystallographic planes.
Draw the unit cell for the corresponding structure and identify
these planes in the diagram. Also report the distance between
two such crystallographic planes in each terms of the edge length
‘a’ of the unit cell.
136. distance between two such planes
is a/2
distance between two such planes
is a/2
138. 3. Marbles of diameter 10 mm are to be placed on a flat surface
bounded by lines of length 40 mm such that each marble has its
centre within the bound surface. Find the maximum number of
marbles in the bound surface and sketch the diagram. Derive an
expression for the number of marbles per unit area.
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