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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 ______.
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A concentration gradient may be created when two materials of different ______ are placed in contact.
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The flux at a particular temperature is constant only if the concentration gradient is also ______.
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In practical cases, compositions vary as atoms are ______.
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The flux is initially high and then gradually decreases as the concentration gradient is ______.
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The minimum thickness of the membrane is ______ cm.
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The maximum thickness of the membrane that will permit 90% of the hydrogen to pass is ______ cm.
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The diffusion coefficient (D) was given as ______ cm2/s.
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J (flux) is calculated using the formula J = - D______.
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H atom loss per hour can be calculated as (0.90)(35.343 * 10______).
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From Equation 5-4, DH equals ______ cms.
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The flux can also be stated as J = ______ H cm^2/s.
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The value of ¢c is essential for calculating ¢x, where ¢x = - D______/J.
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An iron membrane with a thickness between ______ and 0.073 cm will be satisfactory.
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The calculated maximum thickness of the membrane for hydrogen diffusion is ______ cm.
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The diffusion couple for carbon in FCC iron has a D0 value of ______ cm2/s.
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The self-diffusion of Pb in FCC Pb has a Q value of ______ cal/mol.
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For nitrogen in BCC iron, the D0 value is recorded as ______ cm2/s.
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The Q value for carbon in C in covalent diffusion is ______ cal/mol.
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In heterogeneous diffusion, the Q value for copper in nickel is ______ cal/mol.
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Hydrogen in FCC iron has a Q value of ______ cal/mol.
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Zinc in BCC iron shows a self-diffusion D0 value of ______ cm2/s.
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The diffusion of oxygen in Al2O3 is characterized by a D0 value of ______ cm2/s.
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Magnesium in MgO has a Q value of ______ cal/mol.
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Aluminum in alumina (Al2O3) has a D0 value of ______ cm2/s.
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In the processing of silicon (Si), we create a thin layer of ______ on top of a silicon wafer.
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We create a window by removing part of the ______ layer.
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The silica layer is essentially impervious to the dopant atoms such as ______ and boron (B).
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Slower diffusion in most ______ and other ceramics is advantageous in high-temperature applications.
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When the temperature of a material increases, the diffusion coefficient ______ increases.
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At higher temperatures, the thermal energy supplied to the diffusing atoms allows them to overcome the activation energy ______.
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An increase in temperature results in an increase in the flux of ______.
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Diffusion coefficients for different dopants in silicon are affected by ______.
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The lattice parameter of BCC tungsten is ______ Å.
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The number of tungsten atoms per cm³ is calculated to be ______ * 10²².
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In the tungsten-1 at% thorium alloy, the concentration of thorium atoms is ______ * 10²⁰ Th atoms/cm³.
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The concentration gradient is calculated to be ______ * 10²² Th atoms/cm³ per cm.
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In pure tungsten, the number of thorium atoms is ______.
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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.
