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Chapter 8: Q. 8.19 (page 345)

The critical temperature of iron is 1043K. Use this value to make a rough estimate of the dipole-dipole interaction energy 蔚, in electron-volts.

Short Answer

Expert verified

The dipole interaction energy of iron =0.011eV

Step by step solution

01

Step 1. Given information

Formula for critical temperature,

kTc=n蔚

Here,

k=Boltzmann constant,

n= number of nearest neighboring dipole

蔚= interaction energy.

02

Step 2. To find the dipole interaction energy of iron

We have,

蔚=kTcn

Iron is BCC structure, and the value of nis 8.0,

Substituting the value of 8.617脳10-5eV/k=k,1043kfor critical temperature of ironTcand8.0forn

蔚=8.617脳10-5eV/k(1043k)(8)

=0.011eV

The dipole interaction energy of iron ==0.011eV

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Most popular questions from this chapter

At T = 0, equation 8.50 says that s炉=1. Work out the first temperature-dependent correction to this value, in the limit 尾鈭�n鈮�1. Compare to the low-temperature behaviour of a real ferromagnet, treated in Problem 7.64.

Starting from the partition function, calculate the average energy of the one-dimensional Ising model, to verify equation 8.44. Sketch the average energy as a function of temperature.

For a two-dimensional Ising model on a square lattice, each dipole (except on the edges) has four "neighbors"-above, below, left, and right. (Diagonal neighbors are normally not included.) What is the total energy (in terms of 蔚) for the particular state of the 4脳4square lattice shown in Figure 8.4?

Figure 8.4. One particular state of an Ising model on a 4脳4square lattice (Problem 8.15).

Consider an Ising model in the presence of an external magnetic field B, which gives each dipole an additional energy of -渭BB if it points up and +渭BB if it points down (where渭B is the dipole's magnetic moment). Analyse this system using the mean field approximation to find the analogue of equation 8.50. Study the solutions of the equation graphically, and discuss the magnetisation of this system as a function of both the external field strength and the temperature. Sketch the region in the T-B plane for which the equation has three solutions.

Use a computer to plot s炉 as a function of kT/蔚, as predicted by mean field theory, for a two-dimensional Ising model (with a square lattice).
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