# Carsten Aveda Institute WK3 Primary Bonding Models Lattice and Miller Worksheet

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Carsten Aveda Institute - New York

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please finish these two set of simple questions.......................................................................................................

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Problem worksheet for Week 2 Due Tuesday Week 3 1) 2) 3) 4) 5) 6) 7) 8) 9) List primary bonding models How do allowed energy levels of electrons relate to each bonding model? Sketch cubic, bcc, and fcc crystal models. Sketch cubic case of unit cell showing included atom portions only. How many full spheres are inside the unit cell? Describe/discuss the anticipated electronic effects that defects in crystalline materials may have? (How might energy level populations change?) What fundamental theorem does the relation P1V1=P2V2 describe? PV=(N/NA)RT & KE=.5mv2=(3/2)(R/NA)T=(3/2)kT, where T represents “heat”. Note volume is constant. How might you expect bonds to react to added heat? e-(EA/kT) a) Describe the active terms in this relation. b) What did its namesake accomplish such that it is forever associated with him? Give two examples of constant temperature of something while heat is applied. Why is each occurring? Electronic Materials – EE Science 1 Lattice and Miller Worksheet Use the below diagrams and the textbook to answer the questions on the second page. Summer 2020 1. Sketch the cubic and face-centered cubic lattice structures. 2. Given the diagram below, provide a possible explanation as to why the (010) planes do not need unique identifiers. 3. Draw a line from the origin in the [111] direction. In a face-centered cubic lattice, how many atoms are encountered without leaving the first unit cell? 4. For a body-centered cubic lattice, what is the volume density (atoms/unit volume) assuming the lattice constant is 5.4 Å. 5. For a face-centered cubic lattice, what is the surface density (atoms/unit area) for the (111) plane assuming the same lattice constant as problem 4. 6. Silicon naturally forms a diamond lattice, which is two FCC lattices overlaying one another. How many atoms have their center inside the diamond lattice? Summer 2020
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This is the solution for week 2 problem sheet. Please go through it and revert back if you have any problems.

1) The primary bonding models are covalent bonding, ionic bonding and metallic bonding.
2) For every bonding model, the potential wells for the interatomic interactions have different
depths and points of minima. Hence, the spatial distribution and the density of the energy
eigenstates of the system will be different for the three bonding models. For example, we
know that stability order of primary bonding models is ionic bonding > covalent bonding >
metallic bonding. Thus, the depth of the potential energy minima will be in the order ionic
bonding > covalent bonding > metallic bonding. Hence, the density of the energy levels (how
closely the energy levels are packed) will be in the order ionic bonding < covalent bonding <
metallic bonding.
3)

4)

There are 8 corners. Each of the corners is occupied by 1 octant (= 1/8th of an atom). Hence,
total number of full spheres (atoms) = 8 × 1/8 = 1
5) Electronic defects (crystal defects in which electrons participate) occur in case of metal
excess defects. Due to electronic defects, crystal lattices house unpaired electrons that result
in paramagnetism and color due to incident light. These electrons occupy energy states both
in between and higher than the natural energy levels of the ideal crystal, hence they allow for
easier electronic transitions to higher energy levels, which is a phenomenon similar to doping
in semiconductors.
6) P1V1 = P2V2 is the mathematical expression of Boyle’s law, which states that the pressure
of a given mass of an ideal gas is inversely proportional to its volume at a constant
temperature. One can use thi...

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Very useful material for studying!

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