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