Lecture 5 Current LectureChapter 12: Solids: Structures and ApplicationsThe Solids State:- Crystalline Solid: Substance exhibiting an ordered array of atoms, ions, or molecules.o Metallic elements generally form these kind of solids- Amorphous Solid: Substance with a random ordering of atoms.Stacking Patterns:- Crystal Lattice: Ordered three-dimensional array of particles in a crystalline solid. - Hexagonal Closest-Packed (hcp): A crystal structure in which the layers of atoms or ions have an a-b-a-b-a-b stacking pattern. - Cubic Closest-Packed (ccp): A crystal structure in which the layers of atoms, ions, have an a-b-c-a-b-c-a-b-c stacking pattern- Square Packed: A structure where the atoms are arranged in an a-a-a stacking pattern- Two square-packed: a structure where the atoms are arranged in an a-b pattern, This pattern is just like the square packed but with two different layers of atoms.Unit Cells:Basic repeating unit of the arrangement of particles in a crystalline solid.- Coordination number : The number of other particles each particle is in contact with o For ions, it is the number of oppositely charged ions an ion is in contact with - Higher coordination number means more interaction, therefore stronger attractive forces holding the crystal together - The packing efficiency is the percentage of volume in the unit cell occupied by particles o The higher the coordination number, the more efficiently the particles are packing togetherVolume of the unit cell and packing Efficiency: - Packing Efficiency: Percentage of the total volume of the unit cell occupied bythe atoms.o Equation: ((Volume Occupied by spheres)/ (Volume of Unit cell))*100%These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. Chem 108 1st EditionLecture 5 - Vsphere = 4/3 π r3 For simple cubic, with one atom per unit cell, this represents the volume of space occupied by the atom.o Example:With l = 2r: Volume of the unit cell is: V unit cell = l3 = (2 r)3 = 8 r3Packing efficiency = V sphere/ V unit cell = 4/3 π r3 /(8 r3 ) = π/6 = 52%Types of Unit Cells and their dimensions:- Hexagonal Unit Cell (hcp): unit cell for hexagonal closest packing.o Coordination number: 12o Packing Efficiency: 74%- Simple Cubic (sc): square-packing arrangement; particles located at 8 corners of cubic unit cell. Eight particles, one at each corner of a cubeo Atoms touch along cell edge. (radius of atom) × 2 = l (length of the unitcell)o # of total atoms in the cell: (1/8)*8=1 whole atomo Relationship between r and l: r = l/2 = 0.5lo Coordination number: 6o Packing Efficiency: 52%- Body-Centered Cubic (bcc): square packing arrangement in which particles are located at 8 corners and one in the center of cubic unit cell.o Atoms touch along body diagonal. (radius of atom) × 4 = l × √3o # of total atoms in the cell: ((1/8)*8) +1 =2 whole atomso Relationship between r and l: r = (l√3)/4 = 0.433lo Coordination number: 8 o Packing Efficiency: 68%- Face centered cubic (fcc):Closest packing unit cell in which atoms are located on the 8 corners and 6 faces of a cubeo Atoms touch along face diagonal. (radius of atom) × 4 = l × √2o # of total atoms in the cell: ((1/8)*8) + ((1/2)*6) =4 whole atomso Relationship between r and l: r = (l√2)/4 = 0.3536lo Coordination number: 12 o Packing Efficiency: 74%These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. Chem 108 1st EditionLecture 5 -Density of unit cells: - D=m/v o m is the weight of the atoms in the unit cell Ex: unit cell mass = (# of atoms) x (atomic mass of atom/ion in g/mole) / (6.022 x 1023 atoms/mole)v is the volume of the cube Ex: l3 just find l in terms of r if need be.These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. Chem 108 1st
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