Duane's hypothesis

In 1923, American physicist William Duane presented[1] a discrete momentum-exchange model of the reflection of X-ray photons by a crystal lattice. Duane showed that such a model gives the same scattering angles as the ones calculated via a wave diffraction model, see Bragg's Law.

The key feature of Duane's hypothesis is that a simple quantum rule based on the lattice structure alone determines the quanta of momentum that can be exchanged between the crystal lattice and an incident particle.

In effect, the observed scattering patterns are reproduced by a model where the possible reactions of the crystal are quantized, and the incident photons behave as free particles, as opposed to models where the incident particle acts as a wave, and the wave then 'collapses' to one of many possible outcomes.

Duane argued that the way that crystal scattering can be explained by quantization of momentum is not explicable by models based on diffraction by classical waves, as in Bragg's Law.

Duane applied his hypothesis to derive the scattering angles of X-rays by a crystal. Subsequently, the principles that Duane advanced were also seen to provide the correct relationships for optical scattering at gratings, and the diffraction of electrons.[2]

In the early days of diffraction fine details were not observable because the detectors were inefficient, and the sources were also of low intensities. Hence Bragg's law was the only type of diffraction observable, and Duane's approach could model it. Modern electron microscopes and x-ray diffraction instruments are many orders of magnitude brighter, so many find details of electron and x-ray diffraction are now known which cannot be explained by his approach.[3][4][5][6] Hence his approach is no longer used.

  1. ^ Cite error: The named reference Duane 1923 was invoked but never defined (see the help page).
  2. ^ Bitsakis, E.(1997). The wave-particle duality, pp. 333–348 in The Present Status of the Quantum Theory of Light: Proceedings of a Symposium in Honour of Jean-Pierre Vigier, edited by Whitney, C.K., Jeffers, S., Roy, S., Vigier, J.-P., Hunter, G., Springer, ISBN 978-94-010-6396-8, p. 338.
  3. ^ COWLEY, JOHN M. (1995), "Diffraction from crystals", Diffraction Physics, Elsevier, pp. 123–144, doi:10.1016/b978-044482218-5/50008-0, ISBN 9780444822185, retrieved 2023-08-13
  4. ^ Cullity, Bernard D.; Stock, Stuart R. (2001). Elements of X-ray diffraction (3rd ed.). Upper Saddle River, NJ: Prentice Hall. ISBN 978-0-201-61091-8.
  5. ^ Warren, Bertram Eugene (1990). X-ray diffraction. Dover books on physics and chemistry. New York: Dover. ISBN 978-0-486-66317-3.
  6. ^ Peng, L.-M.; Dudarev, S. L.; Whelan, M. J. (2011). High energy electron diffraction and microscopy. Monographs on the physics and chemistry of materials (1. publ. in paperback ed.). Oxford: Oxford Univ. Press. ISBN 978-0-19-960224-7.