When a circuit has a supermesh, you write two equations: the supermesh constraint equation and the supermesh KVL equation. You h
ave completed this task. To complete the description of this circuit, two more equations are required, one of which is the KVL equation for the mesh whose current is iziz. Write this KVL equation.
1 answer:
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Answer:
A) The sketches for the required planes were drawn in the first attachment [1 2 1] and the second attachment [1 2 -4].
B) The closest distance between planes are d₁₂₁=a/√6 and d₁₂₋₄=a/√21 with lattice constant a.
C) Five posible directions that electrons can move on the surface of a [1 0 0] silicon crystal are: |0 0 1|, |0 1 3|, |0 1 1|, |0 3 1| and |0 0 1|.
Compleated question:
1. Miller Indices:
a. Sketch (on separate plots) the (121) and (12-4) planes for a face centered cubic crystal structure.
b. What are the closest distances between planes (called d₁₂₁ and d₁₂₋₄)?
c. List five possible directions (using the Miller Indices) the electron can move on the surface of a (100) silicon crystal.
Explanation:
A)To draw a plane in a face centered cubic lattice, you have to follow these instructions:
1- the cube has 3 main directions called "a", "b" and "c" (as shown in the first attachment) and the planes has 3 main coeficients shown as [l m n]
2- The coordinates of that plane are written as: π:[1/a₀ 1/b₀ 1/c₀] (if one of the coordinates is 0, for example [1 1 0], c₀ is ∞, therefore that plane never cross the direction c).
3- Identify the points a₀, b₀, and c₀ at the plane that crosses this main directions and point them in the cubic cell.
4- Join the points.
<u>In this case, for [1 2 1]:</u>
<u>for </u><u>:</u>
B) The closest distance between planes with the same Miller indices can be calculated as:
With ,the distance is
with lattice constant a.
<u>In this case, for [1 2 1]:</u>
<u /><u />
<u>for </u><u>:</u>
C) The possible directions that electrons can move on a surface of a crystallographic plane are the directions contain in that plane that point in the direction between nuclei. In a silicon crystal, an fcc structure, in the plane [1 0 0], we can point in the directions between the nuclei in the vertex (0 0 0) and e nuclei in each other vertex. Also, we can point in the direction between the nuclei in the vertex (0 0 0) and e nuclei in the center of the face of the adjacent crystals above and sideways. Therefore:
dir₁=|0 0 1|
dir₂=|0 0.5 1.5|≡|0 1 3|
dir₃=|0 1 1|
dir₄=|0 1.5 0.5|≡|0 3 1|
dir₅=|0 0 1|
