Diffusion and Concentration Gradients
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Diffusion and Concentration Gradients

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The ______ of diffusing species is from higher to lower concentrations.

flux

The thermodynamic driving force for diffusion is the ______ gradient.

concentration

A net or observable flux is created depending upon ______ and the concentration gradient.

temperature

The concentration gradient shows how the composition of the material varies with ______.

<p>distance</p> Signup and view all the answers

A concentration gradient may be created when two materials of different ______ are placed in contact.

<p>composition</p> Signup and view all the answers

The flux at a particular temperature is constant only if the concentration gradient is also ______.

<p>constant</p> Signup and view all the answers

In practical cases, compositions vary as atoms are ______.

<p>redistributed</p> Signup and view all the answers

The flux is initially high and then gradually decreases as the concentration gradient is ______.

<p>reduced</p> Signup and view all the answers

The minimum thickness of the membrane is ______ cm.

<p>0.013</p> Signup and view all the answers

The maximum thickness of the membrane that will permit 90% of the hydrogen to pass is ______ cm.

<p>0.073</p> Signup and view all the answers

The diffusion coefficient (D) was given as ______ cm2/s.

<p>1.86 * 10-4</p> Signup and view all the answers

J (flux) is calculated using the formula J = - D______.

<p>¢c/¢x</p> Signup and view all the answers

H atom loss per hour can be calculated as (0.90)(35.343 * 10______).

<p>20</p> Signup and view all the answers

From Equation 5-4, DH equals ______ cms.

<p>0.0012</p> Signup and view all the answers

The flux can also be stated as J = ______ H cm^2/s.

<p>0.125 * 10^18</p> Signup and view all the answers

The value of ¢c is essential for calculating ¢x, where ¢x = - D______/J.

<p>¢c</p> Signup and view all the answers

An iron membrane with a thickness between ______ and 0.073 cm will be satisfactory.

<p>0.013</p> Signup and view all the answers

The calculated maximum thickness of the membrane for hydrogen diffusion is ______ cm.

<p>0.073</p> Signup and view all the answers

The diffusion couple for carbon in FCC iron has a D0 value of ______ cm2/s.

<p>0.23</p> Signup and view all the answers

The self-diffusion of Pb in FCC Pb has a Q value of ______ cal/mol.

<p>25,900</p> Signup and view all the answers

For nitrogen in BCC iron, the D0 value is recorded as ______ cm2/s.

<p>0.0047</p> Signup and view all the answers

The Q value for carbon in C in covalent diffusion is ______ cal/mol.

<p>163,000</p> Signup and view all the answers

In heterogeneous diffusion, the Q value for copper in nickel is ______ cal/mol.

<p>61,500</p> Signup and view all the answers

Hydrogen in FCC iron has a Q value of ______ cal/mol.

<p>10,300</p> Signup and view all the answers

Zinc in BCC iron shows a self-diffusion D0 value of ______ cm2/s.

<p>4.1</p> Signup and view all the answers

The diffusion of oxygen in Al2O3 is characterized by a D0 value of ______ cm2/s.

<p>1900.0</p> Signup and view all the answers

Magnesium in MgO has a Q value of ______ cal/mol.

<p>79,000</p> Signup and view all the answers

Aluminum in alumina (Al2O3) has a D0 value of ______ cm2/s.

<p>28.0</p> Signup and view all the answers

In the processing of silicon (Si), we create a thin layer of ______ on top of a silicon wafer.

<p>silica</p> Signup and view all the answers

We create a window by removing part of the ______ layer.

<p>silica</p> Signup and view all the answers

The silica layer is essentially impervious to the dopant atoms such as ______ and boron (B).

<p>phosphorus</p> Signup and view all the answers

Slower diffusion in most ______ and other ceramics is advantageous in high-temperature applications.

<p>oxides</p> Signup and view all the answers

When the temperature of a material increases, the diffusion coefficient ______ increases.

<p>D</p> Signup and view all the answers

At higher temperatures, the thermal energy supplied to the diffusing atoms allows them to overcome the activation energy ______.

<p>barrier</p> Signup and view all the answers

An increase in temperature results in an increase in the flux of ______.

<p>atoms</p> Signup and view all the answers

Diffusion coefficients for different dopants in silicon are affected by ______.

<p>temperature</p> Signup and view all the answers

The lattice parameter of BCC tungsten is ______ Å.

<p>3.165</p> Signup and view all the answers

The number of tungsten atoms per cm³ is calculated to be ______ * 10²².

<p>6.3</p> Signup and view all the answers

In the tungsten-1 at% thorium alloy, the concentration of thorium atoms is ______ * 10²⁰ Th atoms/cm³.

<p>6.3</p> Signup and view all the answers

The concentration gradient is calculated to be ______ * 10²² Th atoms/cm³ per cm.

<p>6.3</p> Signup and view all the answers

In pure tungsten, the number of thorium atoms is ______.

<p>zero</p> Signup and view all the answers

Study Notes

Diffusion and Concentration Gradient

  • Diffusion is the movement of atoms or ions from one place to another, driven by a concentration gradient.
  • Diffusion occurs in solids, liquids, and gases.
  • The flux (J) of diffusing species is from higher to lower concentrations.
  • The concentration gradient 𝝙c, is the difference in concentration over the distance 𝝙x.
  • Concentration gradient can be created when two materials of different composition are placed in contact.

Factors Affecting Diffusion

  • Temperature: Higher temperatures increase the diffusion coefficient (D) and therefore the flux of atoms.
  • Concentration gradient: A larger concentration gradient increases diffusion.
  • Diffusion coefficient: The diffusion coefficient (D) is a material-specific property that influences its rate of diffusion.
  • Diffusion path: Atoms can diffuse through the bulk of a material (volume diffusion), along grain boundaries, or on the surface of a material.
  • Type of diffusion: Interstitial diffusion is the movement of atoms between the spaces in a crystal lattice; vacancy diffusion is the movement of atoms into vacant lattice sites.
  • Activation energy: The activation energy (Q) is the minimum energy needed for an atom to jump from one site to the next.

Diffusion coefficient

  • The diffusion coefficient (D) is dependent on the material, the temperature, and the type of diffusion.
  • Equation 5-4: D = D0 exp(- Q/RT)
  • D0 (cm2/s) is a constant that takes into account the frequency of atomic vibrations.
  • Q (cal/mol) is the activation energy.
  • R (1.987 cal/K*mol) is the gas constant.
  • T (K) is the temperature in Kelvin.

Summary of Relevant Data

  • In BCC iron, the diffusion coefficient of carbon is 0.011 cm2/s at 2000°C (1273 K).
  • In FCC iron, the diffusion coefficient of carbon is 0.23 cm2/s at 2000°C (1273 K).
  • The diffusion of silicon in the bulk crystal is 1800.0 at 2000 °C (see Table 5-1).

Example Application: Tungsten Thorium Diffusion Couple

  • A tungsten-thorium alloy was exposed to heat at 2000°C.
  • The diffusion of the thorium atoms in the tungsten was studied.
  • Flux of thorium atoms was calculated for volume diffusion, grain boundary diffusion, and surface diffusion.
  • The flux through each pathway was used to determine whether a transition zone of 0.01 cm thickness was established.

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Description

Explore the concepts of diffusion and concentration gradients in various states of matter. Understand the factors affecting diffusion, including temperature, concentration gradient, and diffusion coefficients. This quiz will help solidify your knowledge of how substances move and interact on a molecular level.

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