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# Condensed matter magnetism problem

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The existence of the surface of a piece of magnetizable material profoundly alters the internal magnetic field, H(int).
Mostly this is a nuisance as in the demagnetization correction required to determine the true, (i.e. internal) susceptibility of a sample.

Demagnetization can however be put to good use. One example is the magnetic shielding of instruments and experimental chambers.

Following the method used to derive the field of a uniformly magnetized sphere, derive the field in the cavity of a hollow sphere (see attached pdf).

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https://brainmass.com/physics/magnetic/condensed-matter-magnetism-problem-561591

#### Solution Preview

Please see either of the attached documents for the solution.

Problem: Consider a spherical shell made of a material with magnetic permeability  and with an inner and outer radius of a and b, respectively. This object is placed in a uniform and constant magnetic field Ha. Determine the field H inside the spherical shell (r < a). Figure 1 illustrates the geometry.

Figure 1

Solution: In this steady-state problem, no currents exist (J = 0). This means that the magnetic field H is constant and is determined from the scalar potential

H = -. (1)

As B = r0H = H and  ∙ B = 0 yields

 ∙ H =  ∙ (r0H) =  ∙ H = 0, (2)

where r (is the relative (absolute) magnetic permeability of the shell material and 0 is the permeability of free space. Combining eq. (1) and (2) gives

 ∙( ) = 2 = 0, ...

#### Solution Summary

The solution assists with deriving the field in the cavity of a hollow sphere.

\$2.19

## Rate Limiting Steps in Metal Oxide Epitaxy

On the bottom right-hand side of the third page of the pdf attached (page 2 of the article), the author states:

"Metal deposition rates are easily converted into the oxide growth rate under the assumption that the metal arrival rates are the rate limiting steps, which is true for growth under oxygen- rich conditions."

I am having trouble understanding this, so please answer the following questions to clarify it for me.

(a) What is meant by metal arrival rates being "rate limiting steps?" (Does this refer to oxidation?)

(b) Why is this true? (Why are metal arrival rates rate limiting steps?)

(c) What exactly is meant by an "oxygen-rich environment?" I haven't seen a technical definition of an "oxygen-rich environment" anywhere in the literature.

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