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Questions and Answers
What does 'compacité' primarily represent in the context of crystal structures?
What does 'compacité' primarily represent in the context of crystal structures?
- The ratio of atomic mass to the unit cell volume.
- The proportion of space within a unit cell occupied by atoms. (correct)
- The total number of atoms within a unit cell.
- The surface area of the unit cell.
What is the range of possible values for compacité?
What is the range of possible values for compacité?
- Between 0 and 1. (correct)
- Between -1 and 1.
- Between 0 and infinity.
- Any positive real number.
Which formula correctly expresses the calculation of compacité ('c')?
Which formula correctly expresses the calculation of compacité ('c')?
- c = V_maille / V_atom
- c = V_atom / V_maille (correct)
- c = V_maille + V_atom
- c = V_atom * V_maille
In calculating compacité, if the atomic radius is given in nanometers, what unit should the lattice parameter 'a' be in?
In calculating compacité, if the atomic radius is given in nanometers, what unit should the lattice parameter 'a' be in?
If a unit cell is simple cubic with a lattice parameter 'a', how is the volume of the unit cell (V_maille) calculated?
If a unit cell is simple cubic with a lattice parameter 'a', how is the volume of the unit cell (V_maille) calculated?
What does the multiplicity 'z' represent in the context of calculating the total atomic volume within a unit cell?
What does the multiplicity 'z' represent in the context of calculating the total atomic volume within a unit cell?
A crystal structure has a higher compacité value compared to another. What does this imply?
A crystal structure has a higher compacité value compared to another. What does this imply?
For a face-centered cubic (FCC) structure, the multiplicity (z) is 4. What does this value directly contribute to when calculating compacité?
For a face-centered cubic (FCC) structure, the multiplicity (z) is 4. What does this value directly contribute to when calculating compacité?
A simple cubic structure has a compacité of approximately 0.52. If the atomic radius were to increase while the lattice parameter remains constant, what would happen to the compacité?
A simple cubic structure has a compacité of approximately 0.52. If the atomic radius were to increase while the lattice parameter remains constant, what would happen to the compacité?
To accurately compare the compacité of two different crystal structures, what condition must be met regarding the units used for atomic radius and lattice parameter?
To accurately compare the compacité of two different crystal structures, what condition must be met regarding the units used for atomic radius and lattice parameter?
Flashcards
What is Compacité?
What is Compacité?
The degree of space occupied by atoms within a crystal's unit cell structure.
Compacité Formula
Compacité Formula
c = V_atom / V_maille. It's the ratio of atomic volume to the unit cell volume.
Calculating Unit Cell Volume (V_maille)
Calculating Unit Cell Volume (V_maille)
Determined using lattice parameters. For a cube, V_maille = a^3, where 'a' is the edge length.
Calculating Total Atomic Volume
Calculating Total Atomic Volume
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Volume of a Sphere (Atom)
Volume of a Sphere (Atom)
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Compacité of Simple Cubic Structure
Compacité of Simple Cubic Structure
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Compacité of Face-Centered Cubic Structure
Compacité of Face-Centered Cubic Structure
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High Compacité Implies?
High Compacité Implies?
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Study Notes
- Compacité refers to the degree of space or void between atoms within a crystal's unit cell structure
- It represents the proportion of space within the unit cell occupied by atoms
Definition & Formula
- Compacité is denoted as 'c.'
- It is the ratio of the volume occupied by atoms in a unit cell to the total volume of the unit cell, expressed as c = V_atom / V_maille.
- Compacité is a dimensionless quantity, its value ranges between 0 and 1
Calculating Compacité
- Volumes are rarely provided directly and need to be derived from other quantities
- The volume of the unit cell (V_maille) is determined using lattice parameters, specifically 'a,' which represents the edge length of the cube, so V_maille = a^3.
- The total atomic volume is calculated by multiplying the number of atoms per unit cell (multiplicity 'z') by the volume of a single atom.
- Volume of sphere = (4/3) * pi * r^3, where 'r' is the atomic radius
- Both atomic radius 'r' and lattice parameter 'a' must be in the same units
Examples
- For a simple cubic structure with z = 1, compacité is approximately 0.52, meaning 52% of the unit cell is occupied by atoms.
- Face-centered cubic structure has z = 4, resulting in a compacité of approximately 0.74, or 74%.
- Higher compacité indicates less void space within the unit cell
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