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A Dynamical Theory Approach to the Berg-Barrett Technique

  • B. Roessler (a1) and R.W. Armstrong (a2)

Abstract

Crystals with a dislocation density low enough so that individual dislocations can be resolved by X-ray diffraction contrast techniques should be regarded as highly perfect crystals. A complete description of the diffraction process, therefore, requires the approach of the dynamical theory of X-ray diffraction. In the Berg-Barrett arrangement each point on the crystal surface integrates the incident X-ray intensity over the angular range received from the X-ray source. For most experimental arrangements this range is about 1/2 degree and corresponds, therefore, to integrating over the entire range of reflection of the crystal, which is of the order of a minute or so of arc. The Berg-Barrett image is a recording of a localized integrated intensity, integrated over the complete range of incident angles. We consider as essential, however, primarily the range of total reflection, since it makes the major contribution to the integrated intensity.

The dynamical theory shows that the details of the diffraction process depend very strikingly on the boundary ocnditions at the crystal surface through two angles of incidence - one between the incident beam and the crystal surface, the other between the incident beam and the diffracting plane of atoms. Calculations of the parameters of the dynamical theory which describe the diffraction process in the Berg-Barrett arrangement show that the description depends very strongly on the details of the specific boundary conditions employed. In particular, two parameters seem especially important in dislocation image formation: 1) ΔθR, the angular range of the exit beam diffracted from the crystal, which we call the range of total rejection to distinguish It from ΔθA, the angular range over which the entrance beam is totally accepted, and 2) σe, the extinction coefficient, the parameter which describes the X-ray penetration depth. Both parameters are extremely sensitive to the specific boundary conditions employed.

This dynamical theory approach suggests that, by suitable choice of the experimental conditions, the boundary conditions can be advantageously adjusted so that satisfactory Berg-Barrett images can be obtained.

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References

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1. Bonse, U.K., Hart, M., and Newkirk, J.B., “X-Ray Diffraction Topography”, in J.B. Newkirk and G.R. Mallett, Editors, Advances in X-Ray Analysis, Vol. 10, Plenum Press, New York, 1967, p. 18.
2. Austerman, S.B. and Newkirk, J.B., “Experimental Procedures in X-Ray Diffraction Topography”, ibid., p. 134-152.
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6. Pope, D.P., Vreeland, T. Jr., and Wood, D.S., “Mobility of Edge Dislocations in the Basal-Slip System of Zinc”, J. Appl. Phys. 38:40114018, 1967.
7. Michell, D. and Ogilvie, G.J., “The Effect of Exposure to Air on Dislocations-in Zinc and Cadmium Crystals”, phys. stat. sol. 15:8394, 1966. .
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10. James, R.W., “The Dynamical Theory of X-Ray Diffraction”, in F. Seitz and D. Turnbull, Editors, Solid State Physics. Vol. 15, Academic Press, New York, 1963, p. 53220.

A Dynamical Theory Approach to the Berg-Barrett Technique

  • B. Roessler (a1) and R.W. Armstrong (a2)

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