# Chapter 5: Diffusion. 5.1 Steady-State Diffusion

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 : Diffusion Diffusion: the movement of particles in a solid from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance Diffusion is process which is NOT due to the action of a force, but a result of the random movements of atoms (statistical problem) 1. Diffusivity and Fick s laws. Atomistic mechanisms of diffusion 3. Temperature dependence and Arrenius plot 4. Industrial applications - carburized steel, - dopants in silicon 5.1 Steady-State Diffusion Consider diffusion of solute atoms (b) in solid state solution (AB) in direction between two parallel atomic planes (separated by ) if there is no changes with time in C B at these planes such diffusion condition is called steady-state diffusion For a steady-state diffusion, flu (flow), J, of atoms is: dc J = D d J flu of atoms, atoms/(m s): the number of particles which pass through a unit area in a unit of time; D diffusivity or diffusion coefficient, m /s dc/d concentration gradient, atoms/m 4 Recall: Solvent the majority atom type (or host atoms): Solute the element with lower concentration Substitutional a solid solution in which the solute atoms are replaced by solute Interstitial solute atoms are located in gaps between host atoms 1

2 Fick s first law of diffusion dc J = D d atoms m J = D m s s - sign: flu direction is from the higher to the lower concentration; i.e. it is the opposite to the concentration gradient For steady-state diffusion condition (no change in the system with time), the net flow of atoms is equal to the diffusivity D times the diffusion gradient dc/d dc atoms 1 3 d m m Diffusivity D depends on: 1. Diffusion mechanism. Temperature of diffusion 3. Type of crystal structure (bcc > fcc) 4. Crystal imperfections 5. Concentration of diffusing species Non-Steady-State Diffusion In practice the concentration of solute atoms at any point in the material changes with time non-steady-state diffusion For non-steady-state condition, diffusion coefficient, D - NOT dependent on time: Second Fick s law of diffusion: If D D(), in 1D case: dc dt = dc dt d d dc D d C = D Change in concentration in semi-infinite rods of Cu and Ni caused by diffusion, From G. Gottstein Physical Foundations of Material Science The rate of compositional change is equal to the diffusivity times the rate of the change of the concentration gradient In 3D case: dc dt C C C D + + y z =

3 Non-Steady-State Diffusion (continued) With specific initial or boundary conditions this partial differential equations can be solved to give the concentration as function of spatial position and time c(, y, z, t) Let us consider two rods with different concentrations c 1 and c which are joined at =0 and both are so long that mathematically they can be considered as infinitely long The concentration profile at t = 0 is discontinuous at = 0: < 0, c = c 1 ; < 0, c = c dc We can obtain solution of: C = D dt c c(, t) c = where erf ( z) = z = Dt 1 c π 1 π z 0 Dt e e ξ ξ c dξ = c erf Dt dξ, is known as the error function Gas diffusion into a solid Let us consider the case of a gas A diffusing into a solid B Gas A Solid B Cs C C C S o = erf Dt = 0 C S surf. C of element in gas diffusing into the surface C o initial uniform concentration of element in solid - distance from surface D diffusivity of diffusing solute element t time erf mathematical function called error function 3

4 Error function Curve of the error function erf (z) for z = Dt Q: Consider the gas carburizing of a gear of 1018 steel (C 0.18 wt %) at 97 C. Calculate the time necessary to increase the C content to 0.35 wt % at 0.40 mm below the surface of the gear. Assume the C content at the surface to be 1.15 wt % and that the nominal C content of the steel gear before carburizing is 0.18 wt %. D (C in γ iron) at 97 C = m /s 4

5 5. Atomistics of Solid State Diffusion Diffusion mechanisms: 1. Vacancy (substitutional) diffusion migration of atom in a lattice assisted by the presence of vacancies E.: self diffusion of Cu atoms in Cu crystal. Interstitial diffusion movement of atoms from one interstitial site to another neighboring interstitial site without permanent displacement any of the atoms in the matri crystal lattice E.: C diffusion in BCC iron Vacancies The simplest point defect is the vacancy (V) an atom site from which an atom is missing Vacancies are always present; their number N V depends on temperature (T) N V = N e EV kt N V - # of vacancies N - number of lattice sites E V energy required to form a vacancy k Boltzmann constant k = J K -1 ; or ev K -1 T absolute temperature vacancy 5

6 Vacancy (Substitutional) Diffusion Mechanism Substitutional (in homogeneous system - self-diffusion, in heterogeneous system solid state solutions) Vacancies are always present at any T As T increases # of vacancies increases diffusion rate increases Move atom A (from (1) to ()) = move vacancy from () to (1)..? higher T melt stronger bonding between atoms high activation energy to move V Kirkendall effect Marker at the diffusion interface move slightly in the opposite direction to the most rapidly moving species vacancies can move! 6

7 Possible mechanisms of self-diffusion and their activation energy 1. Neighboring atoms echange sites. Ring mechanism 3. Vacancy mechanism 4. Direct interstitial mechanism 5. Indirect interstitial mechanism Migration Formation Total ev 1 ev - 1 ev 8 ev ev ev 3.4 ev 4 ev 6 0. ev 3.4 ev 3.6 ev Anisotropy Effects From G.Gottstein Physical Foundations of Material Science 7

8 Carbon diffusion in Fe Jump frequency Γ [s -1 ] of an atom is given by: Γ = ν kt e G m Usually ν [s -1 ] vibrational frequency of the atom There is a fundamental relationship between the jump frequency Γ and the diffusion coefficient D which is independent of mechanism and crystal structure: λ λ D = Γ = 6 6τ λ the jump distance of the diffusing atom τ =1/Γ the time interval between two jumps J = J MN - J NM A 1 J = C M Γ C 4 3 D = Γa 4 A N 1 Γ 4 3 Carbon diffusion in Fe Can be derived from an atomistic considerations of the diffusion processes C atoms are located on the octahedral interstitial sites (black circles) J = J MN - J NM Only ¼ of possible jumps of C atoms lead to flu in + Only /3 of all C atoms can jump in direction λ λ D = Γ = 6 6τ D = Γa 4 8

9 5.3 Effects of T on diffusion in solids Diffusion rate in a system will increase with temperature: D = D e o EA RT D diffusivity, m /s D 0- proportionality constant, m /s, independent of T E A activation energy for diffusing species, J/mol R molar gas constant R = J mol-1 K-1; or 1.987cal mol-1k-1 T absolute temperature Activation energy A + B C + D A (initial state) A* (final state) only a fraction of the molecules or atoms in a system will have sufficient energy to reach E* A thermally active process is one which requires a definite amount of thermal energy to overcome an activation energy barrier and enter the reactive state 9

10 Bolzmann s equation On the basis of statistical analysis, Bolzmann s results showed that the probability of finding a molecule or atom at an energy level E * > the average energy E of all the molecules or atoms in a system at a particular temperature T, K, was: Probability e * E E kt where k B = J/(atom K) - Boltzmann s constant The fraction of atoms or molecules in a system having energies > E* at a given T (where E* is much greater than the average energy of any atom or molecule: n N total = C e * E kt Arrhenius Rate Equation The rate of many chemical reaction as a function of temperature as follows: Rate _ of _ reaction = C e E A RT C rate constant, independent of T E A activation energy R molar gas constant R = J mol -1 K -1 ; or 1.987cal mol -1 K -1 T absolute temperature 10

11 If we rewrite in natural log plot: EA ln rate = ln C RT ln rate = a ln C = b y = b + m 1 = T Typical Arrhenius Plot or in logarithmic log plot: log rate = log10 C 10 EA.303RT Q.: The diffusivity of Ag atoms in solid silver metal is 1.0X10 17 m /s at 500 o C and m /s at 1000 o C. Calculate the activation energy (J/mole) for the diffusion of Ag in Ag in the T range 500 to 1000 o C. 11

12 5.4 Industrial applications Steel Hardening by Gas Carburizing In the gas carburizing process for steel parts, the parts are placed in a furnace in contact with a gas rich in CO-CH 4 miture at ~97ºC. Fe + CH 4 FeC ( = % C), T = 97 o C The C from the gas diffuses into the surface of the steel part and increases the C content of the outer surface region of the part. The higher C concentration at the surface makes the steel harder in this region A steel part can thus be produced with a hard outer layer and a tough low C steel inner core (important, for eample, for many types of gears) Dopants activation Dopants can be incorporated into Si wafer to change their electrical conducting characteristics mask B, P + Ion implantation Annealing 1

13 Q: If boron, B, is diffused into a thick slice of Si with no previous B in it at a temperature of 1100 C for 5 h, what is the depth below the surface at which the concentration is atoms/cm 3 if the surface concentration is atoms/cm3? D = cm /s for B diffusing in Si at 1100 C. Summary Diffusion: the movement of particles in a solid from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance Fick s first diffusion law: for steady-state diffusion condition (no change in the system with time), the net flow of atoms is equal to the diffusivity D times the diffusion gradient dc/d J = D Fick s second diffusion law: The rate of compositional change is equal to the diffusivity times the rate of the change of the concentration gradient Diffusion rate in a system will increase with temperature: D = D e o dc d dc C = D dt EA RT 13

### Chapter Outline. Diffusion - how do atoms move through solids?

Chapter Outline iffusion - how do atoms move through solids? iffusion mechanisms Vacancy diffusion Interstitial diffusion Impurities The mathematics of diffusion Steady-state diffusion (Fick s first law)

### THE WAY TO SOMEWHERE. Sub-topics. Diffusion Diffusion processes in industry

THE WAY TO SOMEWHERE Sub-topics 1 Diffusion Diffusion processes in industry RATE PROCESSES IN SOLIDS At any temperature different from absolute zero all atoms, irrespective of their state of aggregation

### Introduction To Materials Science FOR ENGINEERS, Ch. 5. Diffusion. MSE 201 Callister Chapter 5

Diffusion MSE 21 Callister Chapter 5 1 Goals: Diffusion - how do atoms move through solids? Fundamental concepts and language Diffusion mechanisms Vacancy diffusion Interstitial diffusion Impurities Diffusion

### In order to solve this problem it is first necessary to use Equation 5.5: x 2 Dt. = 1 erf. = 1.30, and x = 2 mm = 2 10-3 m. Thus,

5.3 (a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion. Solution (a) With vacancy diffusion,

### Lecture 3: Introduction to Diffusion

Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP6, Kinetics and Microstructure Modelling, H. K. D. H. Bhadeshia Lecture 3: Introduction to Diffusion Mass transport in

### MAE 20 Winter 2011 Assignment 3 solutions

MAE 20 Winter 2011 Assignment 3 solutions 4.3 Calculate the activation energy for vacancy formation in aluminum, given that the equilibrium number of vacancies at 500 C (773 K) is 7.57 10 23 m -3. The

### DIFFUSION IN SOLIDS. Materials often heat treated to improve properties. Atomic diffusion occurs during heat treatment

DIFFUSION IN SOLIDS WHY STUDY DIFFUSION? Materials often heat treated to improve properties Atomic diffusion occurs during heat treatment Depending on situation higher or lower diffusion rates desired

### Materials Science and Engineering Department MSE , Sample Test #1, Spring 2010

Materials Science and Engineering Department MSE 200-001, Sample Test #1, Spring 2010 ID number First letter of your last name: Name: No notes, books, or information stored in calculator memories may be

### 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.

### Ch. 4: Imperfections in Solids Part 1. Dr. Feras Fraige

Ch. 4: Imperfections in Solids Part 1 Dr. Feras Fraige Outline Defects in Solids 0D, Point defects vacancies Interstitials impurities, weight and atomic composition 1D, Dislocations edge screw 2D, Grain

### Defects Introduction. Bonding + Structure + Defects. Properties

Defects Introduction Bonding + Structure + Defects Properties The processing determines the defects Composition Bonding type Structure of Crystalline Processing factors Defects Microstructure Types of

### CHAPTER 4 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS

4-1 CHAPTER 4 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Vacancies and Self-Interstitials 4.1 In order to compute the fraction of atom sites that are vacant in copper at 1357 K, we must employ Equation

### Imperfections in atomic arrangements

MME131: Lecture 8 Imperfections in atomic arrangements Part 1: 0D Defects A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Occurrence and importance of crystal defects Classification

### Surface Treatments. Corrosion Protective coatings for harsh environments (catalytic converters, electrochemical cells )

Surface Treatments Applications Biomedical (biocompatible coatings on implants, drug coatings for sustained release ) Mechanical Tribological friction and wear (tool steels, implants ) Fatigue minimize

### CHAPTER 6: DIFFUSION IN SOLIDS. Inter-diffusion. Simple Diffusion. Diffusion- Steady and Non-Steady State ISSUES TO ADDRESS...

CHAPTER 6: DIFFUSION IN SOLIDS Diffusion- Steady and Non-Steady State ISSUES TO ADDRESS... Gear from case-hardened steel (C diffusion) Diffusion - Mass transport by atomic motion How does diffusion occur?

### Solution: ΔG = a 3 ΔG v. + 6a 2 γ. Differentiation of this expression with respect to a is as. d ΔG da = d(a3 ΔG v. + d(6a2 γ) = 3a 2 ΔG v.

14:440:407 ch10 Question 10.2: (a) Rewrite the expression for the total free energy change for nucleation (Equation 10.1) for the case of a cubic nucleus of edge length a (instead of a sphere of radius

### The University of Western Ontario Department of Physics and Astronomy P2800 Fall 2008

P2800 Fall 2008 Questions (Total - 20 points): 1. Of the noble gases Ne, Ar, Kr and Xe, which should be the most chemically reactive and why? (0.5 point) Xenon should be most reactive since its outermost

### - in a typical metal each atom contributes one electron to the delocalized electron gas describing the conduction electrons

Free Electrons in a Metal - in a typical metal each atom contributes one electron to the delocalized electron gas describing the conduction electrons - if these electrons would behave like an ideal gas

### 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

### Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied

Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Stress and strain fracture or engineering point of view: allows to predict the

### Chapter 3: Kinetics of Electrode Reactions

Goal: To understand the observed behavior of electrode kinetics with respect to potential and concentration. = i/nfa (mol/s-cm 2 ) Rate = f(e) Dynamic Equilibrium A k f k b B s -1 f = k f C A (M/s) b =

### Vysoká škola báňská Technická univerzita Ostrava. Physical Metallurgy. Didactic Text. Jaroslav Sojka

Vysoká škola báňská Technická univerzita Ostrava Physical Metallurgy Didactic Text Jaroslav Sojka Ostrava 2013 Physical Metallurgy Review: Prof. Ing. Ludmila Hypecká, DrSc. Description: Physical Metallurgy

### Mechanisms of Diffusion in Materials 3.205 L4 11/7/06

Mechanisms of Diffusion in Materials 1 A final point on interdiffusion The composition profiles resulting from interdiffusion are generally constrained by phase equilibria. Consider the an Ir Re diffusion

### Chapter Outline: Phase Transformations in Metals

Chapter Outline: Phase Transformations in Metals Heat Treatment (time and temperature) Microstructure Mechanical Properties Kinetics of phase transformations Multiphase Transformations Phase transformations

### Chapter Outline. Defects Introduction (I)

Crystals are like people, it is the defects in them which tend to make them interesting! - Colin Humphreys. Defects in Solids Chapter Outline 0D, Point defects vacancies interstitials impurities, weight

### Chapter Outline Dislocations and Strengthening Mechanisms

Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip

### Met-2023: Concepts of Materials Science I Sample Questions & Answers,(2009) ( Met, PR, FC, MP, CNC, McE )

1 Met-223: Concepts of Materials Science I Sample Questions & Answers,(29) ( Met, PR, FC, MP, CNC, McE ) Q-1.Define the following. (i) Point Defects (ii) Burgers Vector (iii) Slip and Slip system (iv)

### Phase Transformations in Metals and Alloys

Phase Transformations in Metals and Alloys THIRD EDITION DAVID A. PORTER, KENNETH E. EASTERLING, and MOHAMED Y. SHERIF ( г йс) CRC Press ^ ^ ) Taylor & Francis Group Boca Raton London New York CRC Press

### Iron-Carbon Phase Diagram (a review) see Callister Chapter 9

Iron-Carbon Phase Diagram (a review) see Callister Chapter 9 University of Tennessee, Dept. of Materials Science and Engineering 1 The Iron Iron Carbide (Fe Fe 3 C) Phase Diagram In their simplest form,

### Chapter Outline Dislocations and Strengthening Mechanisms

Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip

### 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

### Processing of Semiconducting Materials Prof. Pallab Banerji Department of Metallurgy and Material Science Indian Institute of Technology, Kharagpur

Processing of Semiconducting Materials Prof. Pallab Banerji Department of Metallurgy and Material Science Indian Institute of Technology, Kharagpur Lecture - 8 Diffusion and Ion Implantation II (Refer

### Chapter 8. Phase Diagrams

Phase Diagrams A phase in a material is a region that differ in its microstructure and or composition from another region Al Al 2 CuMg H 2 O(solid, ice) in H 2 O (liquid) 2 phases homogeneous in crystal

### ELEC-D Principles of materials science- Thermodynamics and diffusion. ELEC-D Principles of materials science

Thu 3.3 Mon 7.3 ELEC-D8710 - Principles of materials science- Thermodynamics and diffusion Thu 10.3 Exercise 5 Mon 14.3 Thu 17.3 Exercise 6 Mon 21.3 Thermodynamics - Principles (T,xi) equilibrium diagrams

### Module - 01 Lecture - 23 The Diffusion Equation

Electronic Materials Devices and Fabrication Layering: Thermal Oxidation Dr. S. Parasuraman Department of Metallurgical and Materials Engineering Indian Institute of Technology, Madras Module - 01 Lecture

### Kinetic Molecular Theory of Matter

Kinetic Molecular Theor of Matter Heat capacit of gases and metals Pressure of gas Average speed of electrons in semiconductors Electron noise in resistors Positive metal ion cores Free valence electrons

### Ch 3. Rate Laws and Stoichiometry

Ch 3. Rate Laws and Stoichiometry How do we obtain r A = f(x)? We do this in two steps 1. Rate Law Find the rate as a function of concentration, r A = k fn (C A, C B ). Stoichiometry Find the concentration

### Question 6.5: A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm

14:440:407 Ch6 Question 6.3: A specimen of aluminum having a rectangular cross section 10 mm 12.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.

### Reaction Mechanism (continued) CHEMICAL KINETICS. Pt 2. Reaction Mechanisms. Often Used Terms. Reaction Mechanisms. The reaction

Reaction Mechanism (continued) CHEMICAL KINETICS Pt The reaction C H O + 5O 6CO + 4H O 3 4 3 has many steps in the reaction mechanism. Objectives! Be able to describe the collision and transition-state

### Solid-liquid Interface Energy of Metals at Melting Point and Undercooled State

Materials ransactions, Vol. 43, No. 4 (2002) pp. 721 to 726 c 2002 he Japan Institute of Metals Solid-liquid Interface Energy of Metals at Melting Point and Undercooled State Zengyun Jian 1, Kazuhiko Kuribayashi

### Ref. Ch. 11 in Superalloys II Ch. 8 in Khanna Ch. 14 in Tien & Caulfield

MTE 585 Oxidation of Materials Part 1 Ref. Ch. 11 in Superalloys II Ch. 8 in Khanna Ch. 14 in Tien & Caulfield Introduction To illustrate the case of high temperature oxidation, we will use Ni-base superalloys.

### Figure 10.1. Process flow from starting material to polished wafer.

Figure 10.1. Process flow from starting material to polished wafer. 1/11/003 Ettore Vittone- Fisica dei Semiconduttori - Lectio XI 1 Starting material: silicon dioxide (SiO ): pure form of sand (quartzite)

### Chapter 14 Chemical Kinetics

Chapter 14 Chemical Kinetics Chemical kinetics: the area of chemistry dealing with the speeds or rates at which reactions occur. Rates are affected by several factors: The concentrations of the reactants:

### Chemical Kinetics. Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant Products A B

Reaction Rates: Chemical Kinetics Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant Products A B change in number of moles of B Average rate = change in

### Physical Vapor Deposition (PVD): SPUTTER DEPOSITION

We saw CVD PECVD Physical Vapor Deposition (PVD): SPUTTER DEPOSITION Gas phase reactants: P g 1 mtorr to 1 atm. Good step coverage, T > > RT Plasma enhanced surface diffusion without need for elevated

### Physics 610/Chemistry 678 Semiconductor Processing and Characterization Quiz I July 18, 2014

Physics 610/Chemistry 678 Semiconductor Processing and Characterization Quiz I July 18, 2014 Part I: Short-answer questions on basic principles. (5 points each) 1. Briefly describe the CZ method and the

### Chapter 13 Properties of Solutions. Classification of Matter

Chapter 13 Properties of Solutions Learning goals and key skills: Describe how enthalpy and entropy changes affect solution formation Describe the relationship between intermolecular forces and solubility,

### CHAPTER 4 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS. C Zn A Cu C Zn A Cu C Cu A Zn. (30)(63.55 g /mol) (30)(63.55 g /mol) (70)(65.

HAPTER 4 IMPERFETIONS IN SOLIDS PROBLEM SOLUTIONS wt% u? 4.7 What is the composition, in atom percent, of an alloy that consists of 30 wt% Zn and 70 4.6 as In order to compute composition, in atom percent,

### Fatigue :Failure under fluctuating / cyclic stress

Fatigue :Failure under fluctuating / cyclic stress Under fluctuating / cyclic stresses, failure can occur at loads considerably lower than tensile or yield strengths of material under a static load: Fatigue

### Lecture 12. Physical Vapor Deposition: Evaporation and Sputtering Reading: Chapter 12. ECE 6450 - Dr. Alan Doolittle

Lecture 12 Physical Vapor Deposition: Evaporation and Sputtering Reading: Chapter 12 Evaporation and Sputtering (Metalization) Evaporation For all devices, there is a need to go from semiconductor to metal.

### CHEMICAL KINETICS (RATES OF REACTION)

1 CHEMICAL KINETICS (RATES OF REACTION) Introduction Chemical kinetics is concerned with the dynamics of chemical reactions such as the way reactions take place and the rate (speed) of the process. Collision

### University of Cambridge, Materials Science & Metallurgy. Dilatometry

University of Cambridge, Materials Science & Metallurgy H. K. D. H. Bhadeshia Dilatometry The dilatometric method utilises either transformation strains or thermal strains; the basic data generated are

### Crystal Structure and Growth

Crystal Structure and Growth Source: USNA EE 452 Course on IC Technology EE-452 13-1 Atomic Order of a Crystal Structure EE-452 13-2 Amorphous Atomic Structure EE-452 13-3 Unit Cell in 3-D Structure Unit

### phys4.17 Page 1 - under normal conditions (pressure, temperature) graphite is the stable phase of crystalline carbon

Covalent Crystals - covalent bonding by shared electrons in common orbitals (as in molecules) - covalent bonds lead to the strongest bound crystals, e.g. diamond in the tetrahedral structure determined

### Basic laws and electrical properties of metals (I) Electrical properties. Basic laws and electrical properties of metals (II)

Electrical properties Electrical conduction How many moveable electrons are there in a material (carrier density)? How easily do they move (mobility)? Semiconductivity Electrons and holes Intrinsic and

### Free Electron Fermi Gas (Kittel Ch. 6)

Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals -- they are the glue that hold the nuclei together Types of binding (see next slide)

### Chemistry 4th Edition McMurry/Fay

13 Ch a pt e r Chemical Equilibrium Chemistry 4th Edition McMurry/Fay Dr. Paul Charlesworth Michigan Technological University The Equilibrium State 01 Chemical Equilibrium: A state achieved when the rates

### Phase Transformations

Vysoká škola báňská Technická univerzita Ostrava Phase Transformations Didactic Text Vlastimil Vodárek Ostrava 2013 Review: Prof. Dr. Ing. Jaroslav Sojka Description: Phase Transformations Author: Vlastimil

### FACTORS AFFECTING REACTION RATES

QUESTIONSHEET 1 a) Rate at which the molar concentration of a reactant decreases with time FACTORS AFFECTING REACTION RATES Or r = - dc dt where dc is a concentration change occurring in a time interval

### Lecture 3: Models of Solutions

Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP4, Thermodynamics and Phase Diagrams, H. K. D. H. Bhadeshia Lecture 3: Models of Solutions List of Symbols Symbol G M

### 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

### Martensite in Steels

Materials Science & Metallurgy http://www.msm.cam.ac.uk/phase-trans/2002/martensite.html H. K. D. H. Bhadeshia Martensite in Steels The name martensite is after the German scientist Martens. It was used

### Silicon dioxide, SiO2

Silicon dioxide, SiO2 Sand (silica) one of the most common minerals in the earth. Main component in common glass mixed with sodium carbonate and calcium oxide (lime) to make soda-lime glass for window

### Chapter 6 An Overview of Organic Reactions

John E. McMurry www.cengage.com/chemistry/mcmurry Chapter 6 An Overview of Organic Reactions Why this chapter? To understand organic and/or biochemistry, it is necessary to know: -What occurs -Why and

### Introduction to Materials Science, Chapter 9, Phase Diagrams. Phase Diagrams. University of Tennessee, Dept. of Materials Science and Engineering 1

Phase Diagrams University of Tennessee, Dept. of Materials Science and Engineering 1 Chapter Outline: Phase Diagrams Microstructure and Phase Transformations in Multicomponent Systems Definitions and basic

### Chem 115 Sample Examination #1

_ Chem 115 Sample Examination #1 Student number This exam consists of seven (7) pages, including this cover page. Be sure your copy is complete before beginning your work. If this test packet is defective,

### Boltzmann Distribution Law

Boltzmann Distribution Law The motion of molecules is extremely chaotic Any individual molecule is colliding with others at an enormous rate Typically at a rate of a billion times per second We introduce

### Chemistry 102 Chapter 13 CHEMICAL KINETICS

CHEMICAL KINETICS Chemical Kinetics: I. The study of the Rates of Chemical Reactions: how fast do chemical reactions proceed to form products II. The study of Reaction Mechanisms: the steps involved in

### 8. Kinetic Monte Carlo

8. Kinetic Monte Carlo [Duane Johnsons notes in web; Per Stoltze: Simulation methods in atomic-scale physics; Fichthorn, Weinberg: J. Chem. Phys. 95 (1991) 1090; Bortz, Kalos, Lebowitz, J. Computational

### Name Class Date. In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question.

Assessment Chapter Test A Chapter: States of Matter In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1. The kinetic-molecular

### 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

### Energy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids)

Energy Transport Focus on heat transfer Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Conduction Conduction heat transfer occurs only when there is physical contact

### Major chemistry laws. Mole and Avogadro s number. Calculating concentrations.

Major chemistry laws. Mole and Avogadro s number. Calculating concentrations. Major chemistry laws Avogadro's Law Equal volumes of gases under identical temperature and pressure conditions will contain

### Vacuum Evaporation Recap

Sputtering Vacuum Evaporation Recap Use high temperatures at high vacuum to evaporate (eject) atoms or molecules off a material surface. Use ballistic flow to transport them to a substrate and deposit.

### Reaction Rates and Chemical Kinetics. Factors Affecting Reaction Rate [O 2. CHAPTER 13 Page 1

CHAPTER 13 Page 1 Reaction Rates and Chemical Kinetics Several factors affect the rate at which a reaction occurs. Some reactions are instantaneous while others are extremely slow. Whether a commercial

### [ A] 2. [ A] 2 = 2k dt. [ A] o

Chemistry 360 Dr Jean M Standard Problem Set 3 Solutions The reaction 2A " P follows second-order kinetics The rate constant for the reaction is k350 0 4 Lmol s Determine the time required for the concentration

### This is the 11th lecture of this course and the last lecture on the topic of Equilibrium Carrier Concentration.

Solid State Devices Dr. S. Karmalkar Department of Electronics and Communication Engineering Indian Institute of Technology, Madras Lecture - 11 Equilibrium Carrier Concentration (Contd.) This is the 11th

### SOLIDIFICATION. (a)formation of stable nuclei. Growth of a stable nucleus. (c) Grain structure

SOLIDIFICATION Most metals are melted and then cast into semifinished or finished shape. Solidification of a metal can be divided into the following steps: Formation of a stable nucleus Growth of a stable

### CHEMISTRY STANDARDS BASED RUBRIC ATOMIC STRUCTURE AND BONDING

CHEMISTRY STANDARDS BASED RUBRIC ATOMIC STRUCTURE AND BONDING Essential Standard: STUDENTS WILL UNDERSTAND THAT THE PROPERTIES OF MATTER AND THEIR INTERACTIONS ARE A CONSEQUENCE OF THE STRUCTURE OF MATTER,

### Composition Solidus Liquidus (wt% Au) Temperature ( C) Temperature ( C)

10.4 Given here are the solidus and liquidus temperatures for the copper gold system. Construct the phase diagram for this system and label each region. Composition Solidus Liquidus (wt% Au) Temperature

### Chemistry 102 Chapter 13 CHEMICAL KINETICS

CHEMICAL KINETICS Chemical Kinetics: I. The study of the Rates of Chemical Reactions: how fast do chemical reactions proceed to form products II. The study of Reaction Mechanisms: the steps involved in

### Semiconductor doping. Si solar Cell

Semiconductor doping Si solar Cell Two Levels of Masks - photoresist, alignment Etch and oxidation to isolate thermal oxide, deposited oxide, wet etching, dry etching, isolation schemes Doping - diffusion/ion

### Next, solid silicon is separated from other solid impurities by treatment with hydrogen chloride at 350 C to form gaseous trichlorosilane (SiCl 3 H):

University Chemistry Quiz 5 2014/12/25 1. (5%) What is the coordination number of each sphere in (a) a simple cubic cell, (b) a body-centered cubic cell, and (c) a face-centered cubic cell? Assume the

### 3. Apply phase rule to the two phase field of a binary isomorphous diagram. What conclusion can be drawn?

ecture 18-22: Solidification of binary alloys: Solidification of binary alloys: limits of solubility, isomorphous system, lever rule, constitutional super cooling, effect of non equilibrium cooling, eutectic,

### Phase Diagrams & Thermodynamics

Phase Diagrams & Thermodynamics A phase diagram is a graphical representation of the equilibrium state of a system using the intensive variables T and i while p is kept constant. The equilibrium may be

Problem Set 7 Materials101 1.) You wish to develop a gold alloy (mostly gold) that can be precipitation strengthened to provide high strength - high conductivity electrical leads to integrated circuits

### Oxide Growth. 1. Introduction

Oxide Growth. Introduction Development of high-quality silicon dioxide (SiO 2 ) has helped to establish the dominance of silicon in the production of commercial integrated circuits. Among all the various

### Aerogel an excellent thermal insulator (known as frozen smoke)

Aerogel an excellent thermal insulator (known as frozen smoke) 2 Thermal images of a dog (top) and a snake wrapped around a human arm (bottom) Thermal Properties (1) Heat Capacity Heat Capacity When heated,

### Lecture 3: Electron statistics in a solid

Lecture 3: Electron statistics in a solid Contents Density of states. DOS in a 3D uniform solid.................... 3.2 DOS for a 2D solid........................ 4.3 DOS for a D solid........................

### Theory of Chromatography

Theory of Chromatography The Chromatogram A chromatogram is a graph showing the detector response as a function of elution time. The retention time, t R, for each component is the time needed after injection

### 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

### Chapter 13 Rates of Reaction

Chapter 13 Rates of Reaction Chemical Kinetics: Rates of Chemical Reactions & Factors that Affect Rates of Reactions How fast does a chemical reaction occur? rates of reactants consumed rates of products

### Semiconductors, diodes, transistors

Semiconductors, diodes, transistors (Horst Wahl, QuarkNet presentation, June 2001) Electrical conductivity! Energy bands in solids! Band structure and conductivity Semiconductors! Intrinsic semiconductors!

### Lecture 14. Chapter 8-1

Lecture 14 Fatigue & Creep in Engineering Materials (Chapter 8) Chapter 8-1 Fatigue Fatigue = failure under applied cyclic stress. specimen compression on top bearing bearing motor counter flex coupling

### 5.6 Isobaric thermal expansion and isothermal compression (Hiroshi Matsuoka)

5.6 Isobaric thermal expansion and isothermal compression Hiroshi Matsuoka 1 5.6.2 he coefficient of thermal expansion as a response function to a temperature change he coefficient of thermal expansion

### Lecture 19: Eutectoid Transformation in Steels: a typical case of Cellular

Lecture 19: Eutectoid Transformation in Steels: a typical case of Cellular Precipitation Today s topics Understanding of Cellular transformation (or precipitation): when applied to phase transformation

### 1A Rate of reaction. AS Chemistry introduced the qualitative aspects of rates of reaction. These include:

1A Rate of reaction AS Chemistry introduced the qualitative aspects of rates of reaction. These include: Collision theory Effect of temperature Effect of concentration Effect of pressure Activation energy