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(a) One way of treating the vibrational modes of a linear diatomic solid is to assume that the atoms have the same masses, but the springs on either side of an atom have spring constants K and G, respecti vely. Show that the dispersion relation of such a lattice is given by K+G =()+(K + G)* - 4KGsin"ka} M where M is the mass of the ion, G and K the lattice constants, a is the periodic distance between masses and k the lattice wave vector. (i) Sketch the dispersion relation Discuss what happens when K = G and K >> G. (ii) (b) In diatomic (linear) lattice, why do we assume same o and k.

(a) One way of treating the vibrational modes of a linear diatomic solid is to assume that the atoms have the same masses, but the springs on either side of an atom have spring constants K and G, respecti vely. Show that the dispersion relation of such a lattice is given by K+G =()+(K + G)* - 4KGsin"ka} M where M is the mass of the ion, G and K the lattice constants, a is the periodic distance between masses and k the lattice wave vector. (i) Sketch the dispersion relation Discuss what happens when K = G and K >> G. (ii) (b) In diatomic (linear) lattice, why do we assume same o and k.

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3. (a) One way of treating the vibrational modes of a linear diatomic solid is to assume that the atoms have the same masses, but the springs on either side of an atom have spring constants K and G, respectively. Show that the dispersion relation of such a lattice is given by (K+G` +G)' - 4KGsin ka M where M is the mass of the ion, G and K the lattice constants, a is the periodic distance between masses and k the lattice wave vector. (i) (ii) Sketch the dispersion relation Discuss what happens when K = G and K >> G. (b) In diatomic (linear) lattice, why do we assume same o and k.
Transcribed Image Text:3. (a) One way of treating the vibrational modes of a linear diatomic solid is to assume that the atoms have the same masses, but the springs on either side of an atom have spring constants K and G, respectively. Show that the dispersion relation of such a lattice is given by (K+G` +G)' - 4KGsin ka M where M is the mass of the ion, G and K the lattice constants, a is the periodic distance between masses and k the lattice wave vector. (i) (ii) Sketch the dispersion relation Discuss what happens when K = G and K >> G. (b) In diatomic (linear) lattice, why do we assume same o and k.
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