Chapter 5 Diffusion Flashcards
(18 cards)
Why study diffusion?
To enhance material properties through processes like heat treatment, steel hardening (carburizing, nitriding), sintering, and plating. These processes involve atomic diffusion, which is the transport of materials through atomic movement.
What are some examples of diffusion in different states of matter?
Diffusion in gases: Scent spreading in air.<br></br>Diffusion in liquids: Ink spreading in water.<br></br>Diffusion in solids: The main focus of this chapter.
What is solid-state diffusion?
Solid-state diffusion occurs when atoms move in a solid material, typically from a region of high concentration to a region of low concentration. Also called interdiffusion or impurity diffusion.
What is self-diffusion?
Self-diffusion is the migration of atoms within a pure elemental solid. It does not change the chemical composition of the material.
What are the two primary diffusion mechanisms?
Vacancy Diffusion: Requires an adjacent vacant site for an atom to move into. The process is temperature-dependent.<br></br>Interstitial Diffusion: Small atoms like hydrogen, carbon, nitrogen, and oxygen move between larger atoms in the structure. This is typically faster than vacancy diffusion.
What is an example of interstitial diffusion?
Case Hardening: Carbon atoms diffuse into iron atoms at the surface of a material, making it harder. Example: A case-hardened gear.
What is diffusion flux, and how is it quantified?
Diffusion flux quantifies the rate of diffusion and is defined as:<br></br>J = dM / (A * dt)<br></br>Where:<br></br>J is the diffusion flux<br></br>dM is the mass diffused<br></br>A is the surface area<br></br>dt is the time.
What is Fick’s First Law?
Fick’s First Law applies to steady-state diffusion where the concentration profile does not change with time:<br></br>J = -D (dC / dx)<br></br>Where:<br></br>J is the diffusion flux<br></br>D is the diffusion coefficient<br></br>dC/dx is the concentration gradient.
What is an example problem using Fick’s First Law?
A plate of iron is exposed to a carburizing atmosphere on one side and a decarburizing atmosphere on the other side at 700°C. If the diffusion coefficient is 3 × 10⁻¹¹ m²/s, and the carbon concentrations at 5 mm and 10 mm are 1.2 kg/m³ and 0.8 kg/m³, respectively, the diffusion flux is calculated as:<br></br>J = -D (C_A - C_B) / (x_A - x_B)<br></br>J = - (3 × 10⁻¹¹) (1.2 - 0.8) / (5 × 10⁻³ - 10⁻²)<br></br>J = 2.4 × 10⁻⁹ kg/m²·s.
What is Fick’s Second Law?
Fick’s Second Law applies to non-steady-state diffusion, where concentration changes over time:<br></br>(∂C / ∂t) = D (∂²C / ∂x²)<br></br>This describes how the concentration of a diffusing species depends on both position and time.
What is the solution for a semi-infinite diffusion case?
For a semi-infinite medium where diffusion starts at t = 0, the solution is:<br></br>(C(x,t) - C₀) / (C_s - C₀) = 1 - erf(x / (2√(D t)))<br></br>Where:<br></br>C(x,t) is the concentration at depth x at time t<br></br>C_s is the surface concentration<br></br>C₀ is the initial concentration<br></br>D is the diffusion coefficient<br></br>erf is the error function.
What is an example of carburizing using Fick’s Second Law?
A steel part initially has a uniform carbon concentration of 0.25 wt% and is treated at 950°C. If the surface concentration is maintained at 1.20 wt%, how long will it take for the carbon content to reach 0.80 wt% at a depth of 0.5 mm?<br></br>Using the diffusion equation and solving for time, the answer is 7.1 hours.
What is the Arrhenius equation for reaction rate?
The reaction rate follows an Arrhenius-type expression:<br></br>R = R₀ e^(-Q / RT)<br></br>Taking the natural log:<br></br>ln R = ln R₀ - (Q / RT)<br></br>Where:<br></br>R is the reaction rate<br></br>R₀ is the pre-exponential factor<br></br>Q is the activation energy<br></br>R is the gas constant (8.314 J/mol·K)<br></br>T is the absolute temperature in Kelvin.
What is the temperature dependence of the diffusion coefficient?
The diffusion coefficient increases with temperature according to:<br></br>D = D₀ e^(-Q_d / RT)<br></br>Where:<br></br>D is the diffusion coefficient [m²/s]<br></br>D₀ is the pre-exponential factor [m²/s]<br></br>Q_d is the activation energy [J/mol]<br></br>R is the gas constant [8.314 J/mol·K]<br></br>T is the absolute temperature [K].
What is the experimental determination of activation energy?
From the temperature dependence equation:<br></br>ln D = ln D₀ - (Q_d / R) (1 / T)<br></br>A plot of ln D vs. 1/T gives a straight line with slope -Q_d / R.
What is an example problem for determining temperature from diffusion data?
Given:<br></br>- Initial carbon concentration: 0.20 wt%<br></br>- Surface concentration: 1.0 wt%<br></br>- Carbon content at 4 mm after 49.5 hours = 0.35 wt%<br></br>Using diffusion equations, solving for T gives 1027°C.
What is the importance of diffusion in semiconducting devices?
Diffusion is used in doping silicon to modify its electrical properties. Steps include:<br></br>1. Predeposition: Diffusing impurity atoms into the silicon at approximately 900°C.<br></br>2. Drive-in diffusion: Moving impurities deeper into the material at approximately 1200°C, forming an oxide layer to prevent outward diffusion.
What factors affect diffusion speed?
Faster diffusion occurs in:<br></br>- Open crystal structures<br></br>- Materials with secondary bonding<br></br>- Smaller diffusing atoms<br></br>- Lower density materials<br></br>Slower diffusion occurs in:<br></br>- Close-packed structures<br></br>- Materials with covalent bonding<br></br>- Larger diffusing atoms<br></br>- Higher density materials.
