(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.

Question
(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.
Expand
Transcribed Image Text

(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.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Science
Advanced Physics

Other

Related Advanced Physics Q&A

Find answers to questions asked by students like you.

Q: Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag fo...

A: Given drag force acting on the body is Fdrag=kmv Since the direction of drag force is always opposit...

Q: In solid carbon monoxide, each CO molecule has two possible orientations: CO or OC. Assuming that th...

A: Given: The Carbon monoxide has two different orientations, which was assumed as random orientations....

Q: = 0 at infinity, what are the electric potential and electric field at the center C of the circle du...

A: Click to see the answer

Q: A new type of force was discovered by physicists with the following expression: a Fnew + Be* + 3x4 %...

A: Given: The value of new force is Fnew=αx+βex+3x4. The formula to calculate the work done on a part...

Q: A tennis ball of mass 57.0 g is held just above a basketball of mass 597 g. With their centers verti...

A: Click to see the answer

Q: 6. A child of mass m starts from rest from the top of a water slide. The water slide is 7.6 meters h...

A: Given: The mass of the child is m. The height of the water slide s = 7.6 m.

Q: An ice cube (mass 30 g) at 0°C is left sitting on the kitchen table, where it gradually melts. The t...

A: Given: The mass of ice cube is m=30 g. The temperature of the kitchen is Ti=25∘C. The temperature o...

Q: Juan, Jose, and Jokoy are pushing a table with a constant 475 N force. Juan is pushing the table eas...

A: Given, Juan, Jose and Jokoy are pulling a table and they move it by 6 m along the east.

Q: Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points east...

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. ...

Q: A cylinder contains 0.300 mol of an ideal gas. The cylinder has a movable piston on top, which is fr...

A: Click to see the answer

Q: A body falls in a medium offering resistance proportional to the speed at any time. If the limiting ...

A: Click to see the answer

Q: what is field dimension/distance to field in-camera lens?

A: Answer:   Introduction:   The field dimension/distance to field in-camera lens is introduced and dis...

Q: Power is defined as the rate of doing work. That is, P = dW/dt. Note that doing work can be interpre...

A: Part (a) Given: The force applied on the body is F=40 N. The speed of the body is v=3.5 m/s. The po...

Q: Estimate the thermal properties of a food with the following composition: carbohydrate 17.1%, protei...

A: Given data: The percentage of carbohydrate is A=17.1%. The percentage of protein is B=2.1%. The per...

Q: 5- please help with parts c and d only thank you!

A: In the first three frames, it is seen that the ball is moving horizontally on the floor. Thus, there...

Q: Assume that the top of your head has a surface area of 25 cm x 25 cm. How many newtons of force push...

A: The expression of force in terms of pressure and area is. F=PA           (I)               P=pressur...

Q: Suppose you could convert the 495 C in the cheeseburgeryou ate for lunch into mechanical energy with...

A: (a) The energy in cheeseburger is 495C. 495 C=495C×4.18 J1 C          =2069 J The expression for pot...

Q: A 10,000 kg railroad car is moving at 2.00 m/sec when a 4000 kg load of gravel is suddenly dropped i...

A: Click to see the answer

Q: A uniform electric field of magnitude 3.8 * 105N>C pointsin the positive x direction. Find the ch...

A: Given: Electric field E=3.8×105 N/C The charge q=7.5μC

Q: Block B (mass 4.00 kg) is at rest at the edge of a smooth platform, 2.60 m above the floor. Block A ...

A: Given data: Height of platform, h=2.60 m. Mass of block A, MA=2.00 kg. Mass of block B, MB=4.00 kg....

Q: A rubber hose is attached to a funnel, and the free end is bent around to point upward. When water i...

A: Introduction: Fluid Flow is a part of fluid mechanics and deals with fluid dynamics. It involves the...

Q: (III) Show that the kinetic energy KE of a particle of mass m is related to its momentump by the equ...

A: The equation is given by, E=KE+mc2...(1) Here, mc2= rest mass of the particle KE = kinetic energy of...

Q: Angular momentum (L) of a thin slice rotating around an axis is given by 1. L = mr"wm where w is ang...

A: The angular momentum can be defined as the linear momentum of rotating system. The angular momentum ...

Q: Man A and Man B are trying to pull Man C out of a hole). Man A is pulling with a force of 18 lb and ...

A: Given that,Man A and Man B are trying to pull Man C out of a holeMan A is pulling with a force of 18...

Q: A student throws a 120 gram snowball at 7.5 m/s at the side of the schoolhouse, where it hits and st...

A: The magnitude of the average force is given by Where  = Magnitude of the change in linear momentum,...

Q: Here is a new twist on the question. Suppose we want to cool our hot coffee to 100 °F as quickly as ...

A: Given that:Tnew=137.8°F   (as found in 12)Value of k=0.125

Q: An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of ...

A: Click to see the answer

Q: 1 20° 8" X- Locate the centroid of the shaded area shown resulting from removing the circular segmen...

A: Given Data: The radius of the circular plate is R = 8 in. The radius of the circular segment is r =...

Q: 2. Two weights (750 g each) are tied together by a string and swung at a high rate of speed in a ver...

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,...

Q: solve and explain in detail: (a) Can we observe diffusion for point particles? Point particles are d...

A: Answer:  (a) Point particles are the particles with zero radii and zero mass. for example: when we v...

Q: A man weighing 600 N is using a ladder to fix the light bulb. If the position of the ladder is as sh...

A: from the given figure ∠A=60°∠B=60°then ∠C=60° (using property of triangle)Let, consider Ladder will ...

Q: A 93.0-kg fullback running east with a speed of 5.20 m/s is tackled by a 95.0-kg opponent running no...

A: (a) In a successful tackle there must be maximum loss of kinetic energy so as to prevent the opponen...

Q: Find the Fourier series of the periodic function x(t) of fundamental period T. Assume any arbitrary ...

A: Assuming a rectangular wave as a function of fundamental period 1 as below, Here period p = 2L=1, w...

Q: A particle of mass m is placed in a finite spherical well: - Vo. if r a. V(r) = Find the ground sta...

A: Given: v(r) =-V0,        if r≤a;0,             if r>a.

Q: The 30N force P is applied perpendicular to the portion BC on the bent bar . Determine The moment of...

A: Given: P=30 N The P is the force applied at bent perpendicularly to the portion of BC. The Moment of...