# A crystalline solid is one which has a crystal structure in which atoms or ions are arranged in a pattern that repeats itself in three dimensions.

Save this PDF as:

Size: px
Start display at page:

Download "A crystalline solid is one which has a crystal structure in which atoms or ions are arranged in a pattern that repeats itself in three dimensions."

## Transcription

1 CHAPTER ATOMIC STRUCTURE AND BONDING. Define a crstalline solid. A crstalline solid is one which has a crstal structure in which atoms or ions are arranged in a pattern that repeats itself in three dimensions..2 Define a crstal structure. Give eamples of materials which have crstal structures. A crstal structure is identical to a crstalline solid, as defined b the solution of Problem.. Eamples include metals, ionic crstals and certain ceramic materials.. Define a space lattice. A space lattice is an infinite three-dimensional arra of points with each point having identical surrounding points..4 Define a unit cell of a space lattice. What lattice constants define a unit cell? The unit cell of a space lattice represents a repeating unit of atomic spatial positions. The cell is defined b the magnitudes and directions of three lattice vectors, a, b, and c: aial lengths a, b, and c; interaial angles α, β,and γ..5 What are the 4 Bravais unit cells? The fourteen Bravais lattices are: simple cubic, bod-centered cubic, face-centered cubic, simple tetragonal, bod-centered tetragonal, simple orthorhombic, base-centered orthorhombic, bod-centered orthorhombic, face-centered orthorhombic, simple rhombohedral, simple heagonal, simple monoclinic, base-centered monoclinic, and simple triclinic..6 What are the three most common metal crstal structures? List five metals which have each of these crstal structures. The three most common crstal structures found in metals are: bod-centered cubic (BCC), face-centered cubic (FCC), and heagonal close-packed (HCP). Eamples of metals having these structures include the following. BCC: α iron, vanadium, tungsten, niobium, and chromium. FCC: copper, aluminum, lead, nickel, and silver. HCP: magnesium, α titanium, inc, berllium, and cadmium..7 How man atoms per unit cell are there in the BCC crstal structure? Smith Foundations of Materials Science and Engineering Solution Manual 2

2 A BCC crstal structure has two atoms in each unit cell..8 What is the coordination number for the atoms in the BCC crstal structure? A BCC crstal structure has a coordination number of eight..9 What is the relationship between the length of the side a of the BCC unit cell and the radius of its atoms? In a BCC unit cell, one complete atom and two atom eighths touch each other along the cube diagonal. This geometr translates into the relationship a= 4 R..0 Molbdenum at 20ºC is BCC and has an atomic radius of 0.40 nm. Calculate a value for its lattice constant a in nanometers. Letting a represent the edge length of the BCC unit cell and R the molbdenum atomic radius, a = 4 R or a= R= (0.40 nm) =0.2 nm. Niobium at 20ºC is BCC and has an atomic radius of 0.4 nm. Calculate a value for its lattice constant a in nanometers. For a BCC unit cell having an edge length a and containing niobium atoms, a = 4 R or a= R= (0.4 nm) =0.0 nm.2 Lithium at 20ºC is BCC and has an atomic radius of nm. Calculate a value for the atomic radius of a lithium atom in nanometers. For the lithium BCC structure, which has a lattice constant of a = nm, the atomic radius is, R= a = ( nm) =0.52 nm. Sodium at 20ºC is BCC and has an atomic radius of nm. Calculate a value for the atomic radius of sodium atom in nanometers. For the sodium BCC structure, with a lattice constant of a = nm, the atomic radius is, Smith Foundations of Materials Science and Engineering Solution Manual 22

3 R= a = ( nm) =0.86 nm.4 How man atoms per unit cell are there in the FCC crstal structure? Each unit cell of the FCC crstal structure contains four atoms..5 What is the coordination number for the atoms in the FCC crstal structure? The FCC crstal structure has a coordination number of twelve..6 Gold is FCC and has a lattice constant of nm. Calculate a value for the atomic radius of a gold atom in nanometers. For the gold FCC structure, which has a lattice constant of a = nm, the atomic radius is, 2 2 R = a = ( nm) =0.44 nm.7 Platinum is FCC and has a lattice constant of nm. Calculate a value for the atomic radius of a platinum atom in nanometers. For the platinum FCC structure, with a lattice constant of a = nm, the atomic radius is, 2 2 R = a = (0.929 nm) =0.9 nm.8 Palladium is FCC and has an atomic radius of 0.7 nm. Calculate a value for its lattice constant a in nanometers. Letting a represent the FCC unit cell edge length and R the palladium atomic radius, 2a = 4 R or a= R= (0.7 nm) =0.87 nm Strontium is FCC and has an atomic radius of 0.25 nm. Calculate a value for its lattice constant a in nanometers. For an FCC unit cell having an edge length a an containing strontium atoms, 2a = 4 R or a= R= (0.25 nm) =0.608 nm 2 2 Smith Foundations of Materials Science and Engineering Solution Manual 2

4 .20 Calculate the atomic packing factor for the FCC structure. B definition, the atomic packing factor is given as: volume of atoms in FCC unit cell Atomic packing factor = volume of the FCC unit cell These volumes, associated with the four-atom FCC unit cell, are 4 6 Vatoms = 4 πr = πr and Vunit cell = a 4R where a represents the lattice constant. Substituting a =, 2 64R Vunit cell = a = 2 2 The atomic packing factor then becomes, πr 6 2 π 2 APF (FCC unit cell) = = 2R 6 = How man atoms per unit cell are there in the HCP crstal structure? The heagonal prism contains si atoms..22 What is the coordination number for the atoms in the HCP crstal structure? The coordination number associated with the HCP crstal structure is twelve..2 What is the ideal c/a ratio for HCP metals? The ideal c/a ratio for HCP metals is.6; however, the actual ratios ma deviate significantl from this value..24 Of the following HCP metals, which have higher or lower c/a ratios than the ideal ratio: Zr, Ti, Zn, Mg, Co, Cd and Be? Cadmium and inc have significantl higher c/a ratios while irconium, titanium, magnesium, cobalt and berllium have slightl lower ratios..25 Calculate the volume in cubic nanometers of the titanium crstal structure unit cell. Titanium is HCP at 20ºC with a = nm and c = nm. For a heagonal prism, of height c and side length a, the volume is given b: Smith Foundations of Materials Science and Engineering Solution Manual 24

5 V = (Area of Base)(Height) = [(6 Equilateral Triangle Area)(Height)] 2 = (a sin 60 )( c) 2 = ( nm) (sin 60 )(0.468 nm) = 0.06 nm.26 Rhenium at 20ºC is HCP. The height c of its unit cell is nm and its c/a ratio is.6 nm. Calculate a value for its lattice constant a in nanometers. The rhenium lattice constant a is calculated as, c nm a = = =0.27 nm c/ a.6.27 Osmium at 20ºC is HCP. Using a value of 0.5 nm for the atomic radius of osmium atoms, calculate a value for its unit-cell volume. Assume a packing factor of From the definition of the atomic packing factor, volume of atoms in HCP unit cell HCP unit cell volume = APF Since there are si atoms in the HCP unit cell, the volume of atoms is: V atoms 4 = 6 πr = 8 π(0.5) = nm The unit cell volume thus becomes, nm HCP unit cell volume = = nm How are atomic positions located in cubic unit cells? Atomic positions are located in cubic unit cells using rectangular,, and aes and unit distances along the respective aes. The directions of these aes are shown below Smith Foundations of Materials Science and Engineering Solution Manual 25

6 .29 List the atom positions for the eight corner and si face-centered atoms of the FCC unit cell. The atom positions at the corners of an FCC unit cell are:, (, 0, 0), (,, 0), (0,, 0), (0, 0, ), (, 0, ), (,, ), (0,, ) On the faces of the FCC unit cell, atoms are located at: (,, 0), (, 0, ), (0,, ), (,, ), (,, ), (,, ).0 How are the indices for a crstallographic direction in a cubic unit cell determined? For cubic crstals, the crstallographic direction indices are the components of the direction vector, resolved along each of the coordinate aes and reduced to the smallest integers. These indices are designated as [uvw].. Draw the following directions in a BCC unit cell and list the position coordinates of the atoms whose centers are intersected b the direction vector: (a) [00] (b) [0] (c) [] (,, ) (, 0, 0) (,, 0) (a) Position Coordinates: (b) Position Coordinates: (c) Position Coordinates:, (, 0, 0), (,, 0), (,, ).2 Draw direction vectors in unit cubes for the following cubic directions: (a) [ ] (b) [0] (c) [2] (d) [] (a) (b) = + = - = - = + = - = 0 [ ] [ 0] Smith Foundations of Materials Science and Engineering Solution Manual 26

7 (c) (d) [] Dividing b 2, = - = = - [2] Dividing b, = = =. Draw direction vectors in unit cubes for the following cubic directions: (a) [ 2] (d) [02] (g) [0] (j) [0 ] (b) [2 ] (e) [22] (h) [2 ] (k) [2 2] (c) [] (f) [2] (i) [2] (l) [22] (a) Dividing [2] b 2, =, =, = 2 2 (b) Dividing [2] b, 2 =, =, = (c) Dividing [] b, =, =, = (d) Dividing [02] b 2, = 0, =, = 2 (e) Dividing [2 2] b 2, =, =, = 2 (f) Dividing [2] b, 2 =, =, = Smith Foundations of Materials Science and Engineering Solution Manual 27

8 (g) For [ 0], =, = 0, = (h) Dividing [2] b 2, =, =, = 2 2 (i) Dividing [2] b, 2 =, =, = (j) Dividing [0] b, =, = 0, = (k) Dividing [22] b 2, =, =, = 2 (l) Dividing [22] b, 2 2 =, =, =.4 What are the indices of the directions shown in the unit cubes of Fig. P.4? (a) a ¾ d c b (b) e f g ¾ h ¾ Smith Foundations of Materials Science and Engineering Solution Manual 28

9 a / 6 b c New 0 New 0 a. Vector components: = -, =, = 0 Direction indices: [0] b. Moving direction vector down, vector components are: =, = -, = Direction indices: [44] c. Moving direction vector forward, vector components are: = - / 6, =, = Direction indices: [66] ¾ d e New 0 f - New 0 d. Moving direction vector left, vector components are: =, =, = Direction indices: [22] New 0 e. Vector components are: = -¾, = -, = Direction indices: [44] New 0 f. Moving direction vector up, vector components are: = -, =, = - Direction indices: [] ¾ ¾ g -¾ h ¾ g. Moving direction vector up, vector components are: =, = -, = - Direction indices: [44] h. Moving direction vector up, vector components are: = ¾, = -, = -¾ Direction indices: [4] Smith Foundations of Materials Science and Engineering Solution Manual 29

10 .5 A direction vector passes through a unit cube from the ( ¾, 0, ) to the (,, 0 ) positions. What are its direction indices? The starting point coordinates, subtracted from the end point, give the vector components: = = = 0= = 0 = 2 The fractions can then be cleared through multiplication b 4, giving =, = 4, =. The direction indices are therefore [4]..6 A direction vector passes through a unit cube from the (, 0, ¾ ) to the (,, ) positions. What are its direction indices? Subtracting coordinates, the vector components are: = = = 0= = = 2 Clearing fractions through multiplication b 4, gives =, = 4, = 2. The direction indices are therefore [ 4 2]..7 What are the crstallographic directions of a famil or form? What generalied notation is used to indicate them? A famil or form has equivalent crstallographic directions; the atom spacing along each direction is identical. These directions are indicated b uvw..8 What are the directions of the 00 famil or form for a unit cube? [0 0], [00], [00], [00], [00], [00].9 What are the directions of the famil or form for a unit cube? [], [], [], [], [], [ ], [], [] [ 0] [0 ].40 What 0 -tpe directions lie on the () plane of a cubic unit cell? [0], [0], [0], [0], [0], [0 ] [ 0 ] [ 0] [0] [0] Smith Foundations of Materials Science and Engineering Solution Manual 0

11 .4 What -tpe directions lie on the (0) plane of a cubic unit cell? [], [], [ ], [] [] [] [] [].42 How are the Miller indices for a crstallographic plane in a cubic unit cell determined? What generalied notation is used to indicate them? The Miller indices are determined b first identifing the fractional intercepts which the plane makes with the crstallographic,, and aes of the cubic unit cell. Then all fractions must be cleared such that the smallest set of whole numbers is attained. The general notation used to indicate these indices is (hkl), where h, k, and l correspond to the, and aes, respectivel..4 Draw in unit cubes the crstal planes that have the following Miller indices: (a) ( ) (d) (2) (g) (20) (j) () (b) (0 2) (e) (2) (h) (22) (k) ( 2) (c) ( 2 ) (f) (0 2) (i) (22) (l) () - - ( ) (02) - + ( 2 ) - a. For ( ) reciprocals are: =, = -, = (2) + b. For (02) reciprocals are: =, =, = - - (2) + + c. For ( 2 ) reciprocals are: =, = -, = - + (02) - d. For (2)reciprocals e. For (2) reciprocals f. For (02) reciprocals are: =, =, = - are: =, = -, = are: =, =, = - Smith Foundations of Materials Science and Engineering Solution Manual

12 + - (20) g. For (20)reciprocals are: =, =, = (22) h. For (22)reciprocals are: =-, =, = (22) i. For (22) reciprocals are: =-, =, = () j. For () reciprocals are: =, =, = - - (2) + k. For (2) reciprocals are: =, = -, = - () k. For ()reciprocals are: = -, =, = -.44 What are the Miller indices of the cubic crstallographic planes shown in Fig. P.44? (a) a d c ¾ ¾ (b) a b c d b Smith Foundations of Materials Science and Engineering Solution Manual 2

13 Miller Indices for Figure P.44(a) Plane a based on (0,, ) as origin Plane b based on (,, 0) as origin Planar Intercepts = = - = 4 Reciprocals of Intercepts Planar Intercepts Reciprocals of Intercepts 0 = = - = = 5 2 = = = = 0 = The Miller indices of plane a are (04). The Miller indices of plane b are (5 2 0). Plane c based on (,, 0) as origin Plane d based on as origin Planar Intercepts = = - = Reciprocals of Intercepts Planar Intercepts Reciprocals of Intercepts 0 = = = = = = = 2 = = 2 The Miller indices of plane c are (0 ). The Miller indices of plane d are (22). Miller Indices for Figure P.44(b) Plane a based on (, 0, ) as origin Plane b based on (0,, ) as origin Planar Intercepts = - = = Reciprocals of Intercepts Planar Intercepts Reciprocals of Intercepts = = = 0 = = = 2 = = 2 The Miller indices of plane a are (0). The Miller indices of plane b are (22). Smith Foundations of Materials Science and Engineering Solution Manual

14 Plane c based on (0,, 0) as origin Plane d based on (0,, 0) as origin Planar Intercepts = 5 = 2 = Reciprocals of Intercepts Planar Intercepts Reciprocals of Intercepts = = = 2 = = - 5 = 0 = = 2 2 = The Miller indices of plane c are ( 5 2 0). The Miller indices of plane d are ( 2)..45 What is the notation used to indicate a famil or form of cubic crstallographic planes? A famil or form of a cubic crstallographic plane is indicated using the notation {hkl}..46 What are the {00} famil of planes of the cubic sstem? (00), (00), (00), (00), (00), (00).47 Draw the following crstallographic planes in a BCC unit cell and list the position of the atoms whose centers are intersected b each of the planes: (a) (00) (b) (0) (c) () a. (, 0, 0), (, 0, ), (,, 0), (,, ) b. (, 0, 0), (, 0, ), (0,, 0), (0,, ), (,, ) c. (, 0, 0), (0, 0, ), (0,, 0).48 Draw the following crstallographic planes in an FCC unit cell and list the position coordinates of the atoms whose centers are intersected b each of the planes: (a) (00) (b) (0) (c) () Smith Foundations of Materials Science and Engineering Solution Manual 4

15 a. (, 0, 0), (, 0, ), (,, 0), (,, ) (,, ) b. (, 0, 0), (, 0, ), (0,, 0), (0,, ), (,, 0), (,, ) c. (, 0, 0), (0, 0, ), (0,, 0), (, 0, ) (,, 0), (0,, ).49 A cubic plane has the following aial intercepts: a =, b = -, c =. What are the Miller indices of this plane? Given the aial intercepts of (, -, ), the reciprocal intercepts are:,, 2. = = 2 = Multipling b 2 to clear the fraction, the Miller indices are (64)..50 A cubic plane has the following aial intercepts: a = -, b = -, c =. What are the Miller indices of this plane? Given the aial intercepts of (-, -, ), the reciprocal intercepts are: 2, 2,. = = = 2 Multipling b 2, the Miller indices are (44)..5 A cubic plane has the following aial intercepts: a =, b =, c = -. What are the Miller indices of this plane? Given the aial intercepts of (,, -), the reciprocal intercepts are:,, 2. = = 2 = Multipling b 2, the Miller indices are (24)..52 Determine the Miller indices of the cubic crstal plane that intersects the following position coordinates: (, 0, 0 ); (,, ); (,, 0 ). First locate the three position coordinates as shown. Net, connect points a and b, etending the line to point d and connect a to c and etend to e. Complete the plane b Smith Foundations of Materials Science and Engineering Solution Manual 5

16 connecting point d to e. Using (,, 0) as the plane origin, = -, = - and =. The intercept reciprocals are thus =, =, = 2. The Miller indices are ( 2). (, 0, 0) (,, ) (,, 0) a b d c e (,, 0).5 Determine the Miller indices of the cubic crstal plane that intersects the following position coordinates: (, 0, ); ( 0, 0, ); (,, ). First locate the three position coordinates as shown. Net, connect points a and b and etend the line to point d. Complete the plane b connecting point d to c and point c to b. Using (, 0, ) as the plane origin, = -, = and =. The intercept reciprocals are thus =, =, =. The Miller indices are (). (0, 0, ) (,, ) (, 0, ) a b c (, 0, ) d.54 Determine the Miller indices of the cubic crstal plane that intersects the following position coordinates: (,, ); (, 0, ¾ ); (, 0, ). After locating the three position coordinates, connect points b and c and etend the line to point d. Complete the plane b connecting point d to a and a to c. Using (, 0, ) as the plane origin, = -, = and = -. The intercept reciprocals then become =, = 2, = 2. The Miller indices are (22). Smith Foundations of Materials Science and Engineering Solution Manual 6

17 d (, 0, ¾) b (, 0, ) (, 0,,) c (,, ) a.55 Determine the Miller indices of the cubic crstal plane that intersects the following position coordinates: ( 0, 0, ); (, 0, 0 ); (,, 0 ). After locating the three position coordinates, connect points b and c and etend the line to point d. Complete the plane b connecting point d to a and a to b. Using as the plane origin, =, = and =. The intercept reciprocals are thus =, = 2, = 2. The Miller indices are therefore (2 2). a d (0, 0,,) c (, 0, 0) (,, 0) b (0,, 0).56 Rodium is FCC and has a lattice constant a of nm. Calculate the following interplanar spacings: (a) d (b) d 200 (c) d nm nm d = = = nm (a) nm nm d = = = 0.90 nm (b) nm nm d = = = 0.5 nm (c) 220 Smith Foundations of Materials Science and Engineering Solution Manual 7

18 .57 Tungsten is BCC and has a lattice constant a of nm. Calculate the following interplanar spacings: (a) d 0 (b) d 220 (c) d nm nm d = = = nm (a) nm nm d = = = 0.2 nm (b) nm nm d = = = 0.00 nm (c) 0.58 The d 0 interplanar spacing in a BCC element is nm. (a) What is its lattice constant a? (b) What is the atomic radius of the element? (c) What could this element be? (a) (b) a= d0 h + k + l = (0.587 nm) =0.502 nm a (0.502 nm) R = = =0.27 nm (c) The element is barium (Ba)..59 The d 422 interplanar spacing in a FCC metal is nm. (a) What is its lattice constant a? (b) What is the atomic radius of the metal? (c) What could this metal be? (a) (b) a= d422 h + k + l = ( nm) =0.408 nm 2a 2(0.408 nm) R = = =0.44 nm (c) The element is gold (Au). Smith Foundations of Materials Science and Engineering Solution Manual 8

### It is possible to map the surfaces of conducting solids at the atomic level using an

3 C H A P T E R Crstal Structures and Crstal Geometr It is possible to map the surfaces of conducting solids at the atomic level using an instrument called the scanning tunneling microscope (STM). The

### CHAPTER 3 THE STRUCTURE OF CRYSTALLINE SOLIDS PROBLEM SOLUTIONS

CHAPTER THE STRUCTURE OF CRYSTALLINE SOLIDS PROBLEM SOLUTIONS Fundamental Concepts.6 Show that the atomic packing factor for HCP is 0.74. The APF is just the total sphere volume-unit cell volume ratio.

### Chapter Outline. How do atoms arrange themselves to form solids?

Chapter Outline How do atoms arrange themselves to form solids? Fundamental concepts and language Unit cells Crystal structures Simple cubic Face-centered cubic Body-centered cubic Hexagonal close-packed

### Relevant Reading for this Lecture... Pages 83-87.

LECTURE #06 Chapter 3: X-ray Diffraction and Crystal Structure Determination Learning Objectives To describe crystals in terms of the stacking of planes. How to use a dot product to solve for the angles

### Solid State Theory Physics 545

Solid State Theory Physics 545 CRYSTAL STRUCTURES Describing periodic structures Terminology Basic Structures Symmetry Operations Ionic crystals often have a definite habit which gives rise to particular

### Chapter 3: Structure of Metals and Ceramics. Chapter 3: Structure of Metals and Ceramics. Learning Objective

Chapter 3: Structure of Metals and Ceramics Chapter 3: Structure of Metals and Ceramics Goals Define basic terms and give examples of each: Lattice Basis Atoms (Decorations or Motifs) Crystal Structure

### Experiment: Crystal Structure Analysis in Engineering Materials

Experiment: Crystal Structure Analysis in Engineering Materials Objective The purpose of this experiment is to introduce students to the use of X-ray diffraction techniques for investigating various types

### Chapters 2 and 6 in Waseda. Lesson 8 Lattice Planes and Directions. Suggested Reading

Analytical Methods for Materials Chapters 2 and 6 in Waseda Lesson 8 Lattice Planes and Directions Suggested Reading 192 Directions and Miller Indices Draw vector and define the tail as the origin. z Determine

### The Structure of solids.

Chapter S. The Structure of solids. After having studied this chapter, the student will be able to: 1. Distinguish between a crystal structure and an amorphous structure. 2. Describe the concept of a unit

### Chapter 3. 1. 3 types of materials- amorphous, crystalline, and polycrystalline. 5. Same as #3 for the ceramic and diamond crystal structures.

Chapter Highlights: Notes: 1. types of materials- amorphous, crystalline, and polycrystalline.. Understand the meaning of crystallinity, which refers to a regular lattice based on a repeating unit cell..

### 12.524 2003 Lec 17: Dislocation Geometry and Fabric Production 1. Crystal Geometry

12.524 2003 Lec 17: Dislocation Geometry and Fabric Production 1. Bibliography: Crystal Geometry Assigned Reading: [Poirier, 1985]Chapter 2, 4. General References: [Kelly and Groves, 1970] Chapter 1. [Hirth

### The Crystal Structures of Solids

The Crystal Structures of Solids Crystals of pure substances can be analyzed using X-ray diffraction methods to provide valuable information. The type and strength of intramolecular forces, density, molar

### X-Ray Diffraction HOW IT WORKS WHAT IT CAN AND WHAT IT CANNOT TELL US. Hanno zur Loye

X-Ray Diffraction HOW IT WORKS WHAT IT CAN AND WHAT IT CANNOT TELL US Hanno zur Loye X-rays are electromagnetic radiation of wavelength about 1 Å (10-10 m), which is about the same size as an atom. The

### Sample Exercise 12.1 Calculating Packing Efficiency

Sample Exercise 12.1 Calculating Packing Efficiency It is not possible to pack spheres together without leaving some void spaces between the spheres. Packing efficiency is the fraction of space in a crystal

### Chapter 8 Atomic Electronic Configurations and Periodicity

Chapter 8 Electron Configurations Page 1 Chapter 8 Atomic Electronic Configurations and Periodicity 8-1. Substances that are weakly attracted to a magnetic field but lose their magnetism when removed from

### Crystal Structure Determination I

Crystal Structure Determination I Dr. Falak Sher Pakistan Institute of Engineering and Applied Sciences National Workshop on Crystal Structure Determination using Powder XRD, organized by the Khwarzimic

### 47374_04_p25-32.qxd 2/9/07 7:50 AM Page 25. 4 Atoms and Elements

47374_04_p25-32.qxd 2/9/07 7:50 AM Page 25 4 Atoms and Elements 4.1 a. Cu b. Si c. K d. N e. Fe f. Ba g. Pb h. Sr 4.2 a. O b. Li c. S d. Al e. H f. Ne g. Sn h. Au 4.3 a. carbon b. chlorine c. iodine d.

### LECTURE SUMMARY September 30th 2009

LECTURE SUMMARY September 30 th 2009 Key Lecture Topics Crystal Structures in Relation to Slip Systems Resolved Shear Stress Using a Stereographic Projection to Determine the Active Slip System Slip Planes

### ATOMIC THEORY. Name Symbol Mass (approx.; kg) Charge

ATOMIC THEORY The smallest component of an element that uniquely defines the identity of that element is called an atom. Individual atoms are extremely small. It would take about fifty million atoms in

### Structure of Metals 110

Structure of Metals 110 Welcome to the Tooling University. This course is designed to be used in conjunction with the online version of this class. The online version can be found at http://www.toolingu.com.

### ME 612 Metal Forming and Theory of Plasticity. 1. Introduction

Metal Forming and Theory of Plasticity Yrd.Doç. e mail: azsenalp@gyte.edu.tr Makine Mühendisliği Bölümü Gebze Yüksek Teknoloji Enstitüsü In general, it is possible to evaluate metal forming operations

### The Periodic Table and Periodic Law

The Periodic Table and Periodic Law Section 6.1 Development of the Modern Periodic Table In your textbook, reads about the history of the periodic table s development. Use each of the terms below just

### Solid State Device Fundamentals

Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1 Solids Three types of solids, classified according to atomic

### CRYSTALLINE SOLIDS IN 3D

CRYSTALLINE SOLIDS IN 3D Andrew Baczewski PHY 491, October 7th, 2011 OVERVIEW First - are there any questions from the previous lecture? Today, we will answer the following questions: Why should we care

### Electroceramics Prof. Ashish Garg Department of Material Science and Engineering Indian Institute of Technology, Kanpur.

Electroceramics Prof. Ashish Garg Department of Material Science and Engineering Indian Institute of Technology, Kanpur Lecture - 3 Okay, so in this third lecture we will just review the last lecture,

### CHAPTER 7 DISLOCATIONS AND STRENGTHENING MECHANISMS PROBLEM SOLUTIONS

7-1 CHAPTER 7 DISLOCATIONS AND STRENGTHENING MECHANISMS PROBLEM SOLUTIONS Basic Concepts of Dislocations Characteristics of Dislocations 7.1 The dislocation density is just the total dislocation length

### v kt = N A ρ Au exp (

4-2 4.2 Determination of the number of vacancies per cubic meter in gold at 900 C (1173 K) requires the utilization of Equations 4.1 and 4.2 as follows: N v N exp Q v N A ρ Au kt A Au exp Q v kt (6.023

### CHEM 10113, Quiz 7 December 7, 2011

CHEM 10113, Quiz 7 December 7, 2011 Name (please print) All equations must be balanced and show phases for full credit. Significant figures count, show charges as appropriate, and please box your answers!

### Electron Configurations

SECTION 4.3 Electron Configurations Bohr s model of the atom described the possible energy states of the electron in a hydrogen atom. The energy states were deduced from observations of hydrogen s emissionline

Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Chemistry/Additional Science Unit C2: Discovering Chemistry Foundation Tier Wednesday 7 November 2012 Morning Time:

### UNIT (2) ATOMS AND ELEMENTS

UNIT (2) ATOMS AND ELEMENTS 2.1 Elements An element is a fundamental substance that cannot be broken down by chemical means into simpler substances. Each element is represented by an abbreviation called

### Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

### Each grain is a single crystal with a specific orientation. Imperfections

Crystal Structure / Imperfections Almost all materials crystallize when they solidify; i.e., the atoms are arranged in an ordered, repeating, 3-dimensional pattern. These structures are called crystals

### Chapter 6: The Periodic Table Study Guide

Chapter 6: The Periodic Table Study Guide I. General organization of table A. Modern periodic table 1. Increasing atomic number B. 3 major blocks 1. Metals a. Mostly solids at room temperature b. Conduct

### Warm Up: Using your periodic table, answer the following quetsions

Warm Up: Using your periodic table, answer the following quetsions 1. Element 21's state 2. Number of metalloids 3. Number of liquids 4. Element 4 is a metal/nonmetal/metalloid. 5. Order from least to

### Chem 106 Thursday Feb. 3, 2011

Chem 106 Thursday Feb. 3, 2011 Chapter 13: -The Chemistry of Solids -Phase Diagrams - (no Born-Haber cycle) 2/3/2011 1 Approx surface area (Å 2 ) 253 258 Which C 5 H 12 alkane do you think has the highest

### Chapter 2: Crystal Structures and Symmetry

Chapter 2: Crystal Structures and Symmetry Laue, ravais December 28, 2001 Contents 1 Lattice Types and Symmetry 3 1.1 Two-Dimensional Lattices................. 3 1.2 Three-Dimensional Lattices................

### LMB Crystallography Course, 2013. Crystals, Symmetry and Space Groups Andrew Leslie

LMB Crystallography Course, 2013 Crystals, Symmetry and Space Groups Andrew Leslie Many of the slides were kindly provided by Erhard Hohenester (Imperial College), several other illustrations are from

### ATOMS A T O M S, I S O T O P E S, A N D I O N S. The Academic Support Center @ Daytona State College (Science 120, Page 1 of 39)

ATOMS A T O M S, I S O T O P E S, A N D I O N S The Academic Support Center @ Daytona State College (Science 120, Page 1 of 39) THE ATOM All elements listed on the periodic table are made up of atoms.

### 14:635:407:02 Homework III Solutions

14:635:407:0 Homework III Solutions 4.1 Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 37 C (600 K). Assume an energy for vacancy formation of 0.55 ev/atom.

### Material Expansion Coefficients

17 Material Expansion Coefficients Linear Thermal Expansion Coefficients of Metals and Alloys Table 17-1 provides the linear thermal expansion coefficients of the most frequently used metals and allows.

### Addition and Subtraction of Vectors

ddition and Subtraction of Vectors 1 ppendi ddition and Subtraction of Vectors In this appendi the basic elements of vector algebra are eplored. Vectors are treated as geometric entities represented b

### Find a pair of elements in the periodic table with atomic numbers less than 20 that are an exception to the original periodic law.

Example Exercise 6.1 Periodic Law Find the two elements in the fifth row of the periodic table that violate the original periodic law proposed by Mendeleev. Mendeleev proposed that elements be arranged

### Chemistry CP Unit 2 Atomic Structure and Electron Configuration. Learning Targets (Your exam at the end of Unit 2 will assess the following:)

Chemistry CP Unit 2 Atomic Structure and Electron Learning Targets (Your exam at the end of Unit 2 will assess the following:) 2. Atomic Structure and Electron 2-1. Give the one main contribution to the

### CHAPTER 7: DISLOCATIONS AND STRENGTHENING

CHAPTER 7: DISLOCATIONS AND STRENGTHENING ISSUES TO ADDRESS... Why are dislocations observed primarily in metals and alloys? Mech 221 - Notes 7 1 DISLOCATION MOTION Produces plastic deformation, in crystalline

### Lecture Outline Crystallography

Lecture Outline Crystallography Short and long range Order Poly- and single crystals, anisotropy, polymorphy Allotropic and Polymorphic Transitions Lattice, Unit Cells, Basis, Packing, Density, and Crystal

### CLASSIFICATION OF ELEMENTS

CLASSIFICATION OF ELEMENTS Matter is classified into solids, liquids and gases. However this is not the only way of classification of the matter. It is also classified into elements, compounds and mixtures

### 2.5 The Modern View of Atomic Structure: An Introduction

2.5 The Modern View of Atomic Structure: An Introduction Figure 2.13 a & b (a) Expected Results of the Metal Foil Experiment if Thomson's Model Were Correct (b) Actual Results Copyright Houghton Mifflin

### *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

### Theory of X-Ray Diffraction. Kingshuk Majumdar

Theory of X-Ray Diffraction Kingshuk Majumdar Contents Introduction to X-Rays Crystal Structures: Introduction to Lattices Different types of lattices Reciprocal Lattice Index Planes X-Ray Diffraction:

### Crystalline Structures Crystal Lattice Structures

Jewelry Home Page Crystalline Structures Crystal Lattice Structures Crystal Habit Refractive Index Crystal Forms Mohs Scale Mineral Classification Crystal Healing Extensive information on healing crystals,

### B) atomic number C) both the solid and the liquid phase D) Au C) Sn, Si, C A) metal C) O, S, Se C) In D) tin D) methane D) bismuth B) Group 2 metal

1. The elements on the Periodic Table are arranged in order of increasing A) atomic mass B) atomic number C) molar mass D) oxidation number 2. Which list of elements consists of a metal, a metalloid, and

### Learning Guide 3A Salts Chem 1010. If you could look at them more closely, here's what you would see.

Introduction Learning Guide 3A Salts Chem 1010 Look at the samples in the two bottles you were given. What observations can you make about them? A: B: If you could look at them more closely, here's what

### Periodic Table, Valency and Formula

Periodic Table, Valency and Formula Origins of the Periodic Table Mendelѐѐv in 1869 proposed that a relationship existed between the chemical properties of elements and their atomic masses. He noticed

### Atomic Theory: The Nuclear Model of the Atom

Chapter 5 Atomic Theory: The Nuclear Model of the Atom Section 5.1 Dalton s Atomic Theory Goal 1 Precursors to John Dalton s atomic theory Law of Definite Composition The percentage by mass of the elements

### Summer Assignment Coversheet

Summer Assignment Coversheet Course: A.P. Chemistry Teachers Names: Mary Engels Assignment Title: Summer Assignment A Review Assignment Summary/Purpose: To review the Rules for Solubility, Oxidation Numbers,

### Ionic and Metallic Bonding

Ionic and Metallic Bonding BNDING AND INTERACTINS 71 Ions For students using the Foundation edition, assign problems 1, 3 5, 7 12, 14, 15, 18 20 Essential Understanding Ions form when atoms gain or lose

### Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

### Chapter 6. Periodic Relationships Among the Elements

Chapter 6. Periodic Relationships Among the Elements Student: 1. The nineteenth century chemists arranged elements in the periodic table according to increasing A. atomic number. B. number of electrons.

### Instructions and Sequence for Using the Atom Board

Instructions and Sequence for Using the Atom Board Bohr s atomic model is a representation of protons, neutrons, and electrons and their relationships within an atom. Because these particles are so small

### ELECTRONIC STRUCTURE OF THE ATOM

Note that the periodic table is arranged based on the way electrons arrange themselves around the nucleus of an atom (to differ from the idea that elements are solely based on atomic number). For example,

Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Chemistry/Additional Science Unit C2: Discovering Chemistry Higher Tier Wednesday 7 November 2012 Morning Time: 1 hour

### Unit 12 Practice Test

Name: Class: Date: ID: A Unit 12 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1) A solid has a very high melting point, great hardness, and

### Concepts of Stress and Strain

CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS Concepts of Stress and Strain 6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original

### Standard Solutions (Traceable to NIST)

Standard Solutions (Traceable to NIST) - Multi Element ICP Standard Solutions (Inductively Coupled Plasma Spectroscopy) - Single Element ICP Standard Solutions (Inductively Coupled Plasma Spectroscopy)

### Nuclear reactions determine element abundance. Is the earth homogeneous though? Is the solar system?? Is the universe???

Nuclear reactions determine element abundance Is the earth homogeneous though? Is the solar system?? Is the universe??? Earth = anion balls with cations in the spaces View of the earth as a system of anions

### Calculating Molar Mass of a Compound

Instructions for Conversion Problems For every conversion problem Write the number in the problem down with unit and a multiplication sign Decide which conversion factor you should use, Avagadro s or molar

### 2.1 Three Dimensional Curves and Surfaces

. Three Dimensional Curves and Surfaces.. Parametric Equation of a Line An line in two- or three-dimensional space can be uniquel specified b a point on the line and a vector parallel to the line. The

### Chapter 13 The Chemistry of Solids

Chapter 13 The Chemistry of Solids Jeffrey Mack California State University, Sacramento Metallic & Ionic Solids Crystal Lattices Regular 3-D arrangements of equivalent LATTICE POINTS in space. Lattice

### The Atom Atomic Number Mass Number Isotopes

The Atom Atomic Number Mass Number Isotopes 1 Atomic Theory Atoms are building blocks of elements Similar atoms in each element Different from atoms of other elements Two or more different atoms bond in

### Success criteria You should be able to write the correct formula for any ionic compound

Chemical Formulas and Names of Ionic Compounds WHY? Going back to pre-historic times, humans have experimented with chemical processes that helped them to make better tools, pottery and weapons. In the

Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Chemistry/Additional Science Unit C2: Discovering Chemistry Foundation Tier Tuesday 10 June 2014 Afternoon Time:

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

### Electrons in Atoms & Periodic Table Chapter 13 & 14 Assignment & Problem Set

Electrons in Atoms & Periodic Table Name Warm-Ups (Show your work for credit) Date 1. Date 2. Date 3. Date 4. Date 5. Date 6. Date 7. Date 8. Electrons in Atoms & Periodic Table 2 Study Guide: Things You

### Rectangle Square Triangle

HFCC Math Lab Beginning Algebra - 15 PERIMETER WORD PROBLEMS The perimeter of a plane geometric figure is the sum of the lengths of its sides. In this handout, we will deal with perimeter problems involving

### rotation,, axis of rotoinversion,, center of symmetry, and mirror planes can be

Crystal Symmetry The external shape of a crystal reflects the presence or absence of translation-free symmetry y elements in its unit cell. While not always immediately obvious, in most well formed crystal

### 100% ionic compounds do not exist but predominantly ionic compounds are formed when metals combine with non-metals.

2.21 Ionic Bonding 100% ionic compounds do not exist but predominantly ionic compounds are formed when metals combine with non-metals. Forming ions Metal atoms lose electrons to form +ve ions. Non-metal

### The atomic packing factor is defined as the ratio of sphere volume to the total unit cell volume, or APF = V S V C. = 2(sphere volume) = 2 = V C = 4R

3.5 Show that the atomic packing factor for BCC is 0.68. The atomic packing factor is defined as the ratio of sphere volume to the total unit cell volume, or APF = V S V C Since there are two spheres associated

### Naming and Writing Formulas for Ionic Compounds Using IUPAC Rules

Naming and Writing Formulas for Ionic Compounds Using IUPAC Rules There are three categories of ionic compounds that we will deal with. 1.Binary ionic o simple ions (only single charges) o multivalent

### ACT Math Vocabulary. Altitude The height of a triangle that makes a 90-degree angle with the base of the triangle. Altitude

ACT Math Vocabular Acute When referring to an angle acute means less than 90 degrees. When referring to a triangle, acute means that all angles are less than 90 degrees. For eample: Altitude The height

### Chapter 15 Mensuration of Solid

3 Chapter 15 15.1 Solid: It is a body occupying a portion of three-dimensional space and therefore bounded by a closed surface which may be curved (e.g., sphere), curved and planer (e.g., cylinder) or

### We shall first regard the dense sphere packing model. 1.1. Draw a two dimensional pattern of dense packing spheres. Identify the twodimensional

Set 3: Task 1 and 2 considers many of the examples that are given in the compendium. Crystal structures derived from sphere packing models may be used to describe metals (see task 2), ionical compounds

### MAT 1341: REVIEW II SANGHOON BAEK

MAT 1341: REVIEW II SANGHOON BAEK 1. Projections and Cross Product 1.1. Projections. Definition 1.1. Given a vector u, the rectangular (or perpendicular or orthogonal) components are two vectors u 1 and

### Lösungen Übung Verformung

Lösungen Übung Verformung 1. (a) What is the meaning of T G? (b) To which materials does it apply? (c) What effect does it have on the toughness and on the stress- strain diagram? 2. Name the four main

### Sample Exercise 2.1 Illustrating the Size of an Atom

Sample Exercise 2.1 Illustrating the Size of an Atom The diameter of a US penny is 19 mm. The diameter of a silver atom, by comparison, is only 2.88 Å. How many silver atoms could be arranged side by side

### Study Guide For Chapter 7

Name: Class: Date: ID: A Study Guide For Chapter 7 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The number of atoms in a mole of any pure substance

### Chapter 3 Applying Your Knowledge- Even Numbered

Chapter 3 Applying Your Knowledge- Even Numbered 2. Elements in a specific compound are always present in a definite proportion by mass; for example, in methane, CH 4, 12 g of carbon are combined with

### Chapter Outline. 3 Elements and Compounds. Elements and Atoms. Elements. Elements. Elements 9/4/2013

3 Elements and Compounds Chapter Outline 3.1 Elements A. Distribution of Elements Foundations of College Chemistry, 14 th Ed. Morris Hein and Susan Arena Copyright This reclining Buddha in Thailand is

### Understanding Chemical Equations

Connections Understanding Chemical Equations Have you ever... Seen the result of mixing baking soda and vinegar? Used friction to light a match? Seen a car eaten through by rust? Chemical equations model

### MODERN ATOMIC THEORY AND THE PERIODIC TABLE

CHAPTER 10 MODERN ATOMIC THEORY AND THE PERIODIC TABLE SOLUTIONS TO REVIEW QUESTIONS 1. Wavelength is defined as the distance between consecutive peaks in a wave. It is generally symbolized by the Greek

### Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Chemistry/Additional Science Unit C2: Discovering Chemistry Foundation Tier Monday 21 May 2012 Morning Time: 1 hour

### b) What is the trend in melting point as one moves up the group in alkali metals? Explain.

Problem Set 2 Wed May 25, 2011 1. What is the rough trend in the number of oxidation states available to the elements (excluding the noble gases) as you move a) to the right and b) down the periodic table?

### What is the atomic mass of Iridium? What is the atomic number Chromium? What is the charge of a neutron?

How many protons are in oxygen? 1 What is the atomic mass of Iridium? 192 What is the number of protons and neutrons in Niobium? 93 How many electrons in Potassium? 19 What is the atomic number Chromium?

### Properties of Atomic Orbitals and Intro to Molecular Orbital Theory

Properties of Atomic Orbitals and Intro to Molecular Orbital Theory Chemistry 754 Solid State Chemistry Dr. Patrick Woodward Lecture #15 Atomic Orbitals Four quantum numbers define the properties of each

### The Interactive Periodic Table of the Elements Teacher s Guide

Teacher s Guide Grade Level: 9 12 Curriculum Focus: Chemistry Description Disc 1. Alkali Metals and Alkaline-Earth Metals These elements are highly reactive and rarely found uncombined in nature. The alkaline-earth

### Chapter 2 Atoms, Ions, and the Periodic Table

Chapter 2 Atoms, Ions, and the Periodic Table 2.1 (a) neutron; (b) law of conservation of mass; (c) proton; (d) main-group element; (e) relative atomic mass; (f) mass number; (g) isotope; (h) cation; (i)

### CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news