4. Sketch and identify the crystal structures represented by the following lattice vectors, wherea is the lattice constant: (a) a₁ = ax, a₂ = aŷ, a3 = az^ (b) a₁ = (c) a₁ = (x+y), ā₂ = ½ (ŷ + 2), ã3 = (x + 2) (x + y + 2), a₂ = (x −ý + 2), ã³ = (x + y − 2)
4. Sketch and identify the crystal structures represented by the following lattice vectors, wherea is the lattice constant: (a) a₁ = ax, a₂ = aŷ, a3 = az^ (b) a₁ = (c) a₁ = (x+y), ā₂ = ½ (ŷ + 2), ã3 = (x + 2) (x + y + 2), a₂ = (x −ý + 2), ã³ = (x + y − 2)
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Transcribed Image Text:4. Sketch and identify the crystal structures represented by the following lattice vectors,
wherea is the lattice constant:
(a) a₁ = ax, a₂ = ay, a3 = az^
(b) a₁ = (x+y), a₂ = (y + 2), ã³ = (x + 2)
(c) a = ;(-x+y+z), a,=; (x-y+z), a}= ; (x+y-2)
(d) a₁ = (√3x +ŷ), a₂ = (-√³x + y)
(e) Consider (d) but with two atoms are located at each lattice point. The atoms are located
₁d₂ = ax
at d₁
=
O and de
(e) is the crystal structure of graphene, one of the most exciting up-and-coming electronic materials
due to its very high electron mobility (we will talk about mobility later - briefly, it is a measure of how
fast electrons can move in the material). Graphene is a single 2D sheet of carbon atoms (a monoatomic
layer of graphite). The scientists who discovered and did the first experiments on graphene were
awarded the Nobel Prize in physics in 2010. For graphene, |d₂| = 1.42 °A, the length of the carbon-
carbon bond. A carbon nanotube, which some of you may have heard of, is graphene curled up into a
roll.
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