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MSU / Engineering and Tech / EGR 375 / when does diffusion occur

when does diffusion occur

when does diffusion occur

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School: Murray State University
Department: Engineering and Tech
Course: Materials Science
Term: Fall 2016
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Cost: 50
Description: Diffusion V – Diffusion Issues to address: • What is it? • How does diffusion occur (mechanisms)? • What is the mathematics of diffusion? • How can the rate of diffusion be predicted for some simple cases? • How does the temperature and structure influence the diffusion? 1) Diffusion It is mass transport through atomic motion a) Demonstrate the phenomenon of diffusion • Use a diffusion couple – joi
Uploaded: 07/24/2017
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• How can the rate of diffusion be predicted for some simple cases?




• What is the mathematics of diffusion?




• How does diffusion occur (mechanisms)?



Diffusion V – Diffusion Issues to address: • What is it? • How does diffusion occur (mechanisms)? • What is the mathematics of diffusion? • How can the rate of diffusion be predicted for some simple cases? • How does the temperature and structure influence the diffusion? 1) Diffusion It is mass transport through atoWe also discuss several other topics like Enumerate the techniques used in solving differential equations.
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Don't forget about the age old question of which of the following systems (i.e., pair of metals) would you expect to exhibit complete solid solubility? explain your answers.
mic motion a) Demonstrate the phenomenon of diffusion • Use a diffusion couple – joining bars of two different metals to have a contact between two faces: • Heat the couple for an extended period at an elevated temperature just below the melting point for both metals • Copper atoms migrate or diffuse into the nickel • Nickel diffused into copper Pure copper and nickel regions separated by an alloyed region. Right – concentrations of  both metals vary with position along a sigmoidal trend.• Cool the couple to reach room temperature Material Science Notes  Spring 2017 V. 1 Dr. George Bunget  Murray State University Diffusion Diffusion types: • Interdiffusion or impurity diffusion In an alloy, atoms tend to migrate from regions of high concentration to regions of low concentration Initially After some time • Self-diffusion The atoms of a pure metal also migrate Label some atoms C After some time C A D B A B DMaterial Science Notes  Spring 2017 V. 2 Dr. George Bunget  Murray State University Diffusion A. Diffusion Mechanisms Atomic perspective – diffusion is the stepwise migration of atoms from lattice site to lattice site. Two conditions must be met: 1. Requires an empty adjacent site 2. The atoms must have sufficient energy to: a) Break its bonds b) Distort the lattice during its migration How do we increase the atomic energy? Types of diffusion mechanisms: • Vacancy diffusion • Interstitial diffusion Material Science Notes  Spring 2017 V. 3Dr. George Bunget  Murray State University Diffusion 1) Vacancy Diffusion - atoms exchange with vacancies  • Applies to substitutional impurities atoms  • Rate depends on: • number of vacancies • activation energy to exchange. increasing elapsed time Diffusion Simulation Simulation of interdiffusion across an interface: Rate of substitutional diffusion depends on: -- vacancy concentration -- frequency of jumping This slide contains an animation that requires  Quicktime and a Cinepak decompressor. Click  on the message or image below to activate the  animation.(Courtesy P.M. Anderson) Material Science Notes  Spring 2017 V. 4 Dr. George Bunget  Murray State University Diffusion increasing elapsed time This slide contains an animation that requires  Quicktime and a Cinepak decompressor. Click  on the message or image below to activate the  animation.(Courtesy P.M. Anderson) Material Science Notes  Spring 2017 V. Dr. George Bunget  5 Murray State University Diffusion 2) Interstitial Diffusion - smaller atoms can diffuse between atoms. increasing elapsed timeMore rapid than vacancy diffusion Material Science Notes  Spring 2017 V. 6 Dr. George Bunget  Murray State University Diffusion B. Fick’s First Law • Diffusion is a time-dependent process.  • We need to know the rate of mass transfer called the diffusion flux: 1) Fick’s first law for STEADY-STATE diffusion Material Science Notes  Spring 2017 V. 7Dr. George Bunget  Murray State University Diffusion What is Steady-State? Material Science Notes  Spring 2017 V. 8Dr. George Bunget Murray State University Diffusion Diffusion Coefficient  • The proportionality constant for Fick’s first law Steady-state diffusion across a thin plate.Concentration gradient Material Science Notes  Spring 2017 V. 9 Dr. George Bunget  Murray State University Diffusion Example 1 – Fick’s First Law A sheet of BCC iron 2-mm thick was exposed to a carburizing gas atmosphere on one side and a decarburizing atmosphere on the other side at 675°C. After reaching steady state, the iron was quickly cooled to room temperature. The carbon concentrations at the two surfaces of the sheet were determined to be 0.015 and 0.0068 wt%, respectively. Compute the diffusion coefficient if the diffusion flux is 7.36 × 10–9 kg/m2.s. Material Science Notes  Spring 2017 V. 10Dr. George Bunget  Murray State University Diffusion C. Fick’s Second Law – NONSTEADY-STATE DIFFUSION In real life the diffusion flux and the concentration gradient vary with time. If the diffusion coefficient is independent of composition Concentration profiles for NONSTEADY STATE diffusion at three different times.Material Science Notes  Spring 2017 V. 11 Dr. George Bunget  Murray State University Diffusion Solution for Fick’s Second Law A practical solution is for a semi-infinite solid, i.e.  Assume the following INITIAL CONDITIONS:  • The diffusing solute atoms are uniformly distributed with concentration of • The length scale, x starts at the surface and increases with distance into the solid • The time scale starts at the instant before the diffusion process begins. Assume the following BOUNDARY CONDITIONS:  • At x = 0  Constant surface concentration • At x = ∞ Based on these conditions, the Fick’s second law has the solution Material Science Notes  Spring 2017 V. 12Dr. George Bunget Murray State University Diffusion The error function has tabulated values where z  Concentration profile for NONSTEADY-STATE  diffusion.What if we don’t find the value of z in the table? We could also use a software such as MATLAB/Octave to compute the integral Material Science Notes  Spring 2017 V. 13 Dr. George Bunget Murray State University Diffusion Example of Non-Steady State Diffusion: Carburizing the surface of a steel gear • Diffuse carbon atoms into the host iron atoms at the surface - interstitial diffusion • The carbon from the surrounding atmosphere diffuses into the outer surface layer. Results: • The increased carbon content in the layer raises the surface hardness ???? Improvement of wear resistance of the gear. • Residual compressive stresses are introduced within the case region ???? Resistance to failure by fatigue The “case” appears as the dark outer rim  of that segment of the gear that has been  sectioned.https://www.youtube.com/watch?v=pYQuqNFG2ro Consider one such alloy that initially has a uniform carbon  concentration of 0.25 wt% and is to be treated at 950⁰C (1750⁰F). If  the concentration of carbon at the surface is suddenly brought to  and maintained at 1.20 wt%, how long will it take to achieve a  carbon content of 0.80 wt% at a position 0.5 mm below the surface?  The diffusion coefficient for carbon in iron at this temperature is 1.6  × 10-11 m2/s; assume that the steel piece is semi-infinite. Material Science Notes  Spring 2017 V. 14 Dr. George Bunget  Murray State University Material Science Notes  Spring 2017 Diffusion V. Dr. George Bunget 15Murray State University Diffusion D. Factors That Influence Diffusion Diffusion Species Temperature Diffusion coefficient increases with increasing T D = Do exp-Qd R T D Do Qd R T= diffusion coefficient [m2/s] = pre-exponential [m2/s] = activation energy [J/mol or eV/atom]  = gas constant [8.314 J/mol-K] = absolute temperature [K] Activation Energy Material Science Notes  Spring 2017 V. 16 Dr. George Bunget  Murray State University Diffusion Table 5.2: Tabulation of  Diffusion Data Taking natural log of  Or in terms of log10 Material Science Notes  Spring 2017 V. 17Dr. George Bunget  Murray State University Diffusion D has exponential dependence on T 10-8 D (m2/s) 0 0510 0010 06T(°C) 003Dinterstitial >> D substitutional 10-14 10-20 0.5 1.0 1.5 C in α-Fe C in γ-Fe 1000K/T Al in Al Fe in α-Fe Fe in γ-Fe Material Science Notes  Spring 2017 V. 18 Dr. George Bunget  Murray State University Diffusion Example of Non-Steady State Diffusion Consider a diffusion couple composed of two cobalt-iron alloys; one has a composition of 75 wt% Co-25 wt% Fe; the other alloy composition is 50 wt% Co-50 wt% Fe. If this couple is heated to a temperature of 800°C (1073 K) for 20,000 s, determine how far from the original interface into the 50 wt% Co-50 wt% Fe alloy the composition has increased to 52 wt%Co-48 wt% Fe. For the diffusion coefficient, assume values of 6.6 ×10-6 m2/s and 247,000 J/mol, respectively, for the pre-exponential and activation energy. Material Science Notes  Spring 2017 V. 19Dr. George Bunget  Murray State University Material Science Notes  Spring 2017 Diffusion V. Dr. George Bunget  20Murray State University Diffusion Manufacturing Processes Using Diffusion - Doping of  Semiconductors Silicon doping with phosphorus for n-type semiconductors. Doping Process – typically two heat treatment process: Predeposition Step: • Impurities atoms (gas) are diffused into the silicon. • Temperature 900 – 1000C  for less than 1 hour. Drive-in Diffusion Step: • Higher temperature (1200C) in an oxidizing atmosphere to  form an oxide layer at the  surface 0.5mm  magnified image of a computer chip  light regions: Si atoms  light regions: Al atoms The Fick’s second law for drive-in diffusion takes the form where  Material Science Notes  Spring 2017 V. 21 Dr. George Bunget  Murray State University Diffusion Junction depth is another important diffusion parameter Material Science Notes  Spring 2017 V. 22Dr. George Bunget  Murray State University

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