InternationalMathematical, physical and chemical tablesTables for Crystallography Volume C Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C, ch. 2.9, p. 129
## Section 2.9.6. Resolution in real space |

From Fig. 2.9.2.3, the period δ*Q* of the reflectivity oscillation (in the region where the Born approximation becomes valid, sufficiently far away from the critical angle) is inversely proportional to the thickness *t* of the film. That is, 2π/(δ*Q*) = *t*. Consequently, in order to be able to resolve reflectivity oscillations for a film of thickness *t*, the instrumental *Q* resolution Δ*Q* [from equation (2.9.5.1)] must be approximately 2π/*t* or smaller. With sufficiently good instrumental resolution, even the thickness of a film with non-abrupt interfaces can be accurately determined, as demonstrated by the hypothetical case depicted in Fig. 2.9.6.1
(where the instrumental resolution is taken to be perfect): an overall film-thickness difference of 2 Å (between 42 and 40 Å films) is clearly resolved at a *Q* of about 0.2 Å^{−1}. In practice, differences even less than this can be distinguished. Note, however, that to `see' more detailed features in the scattering-density profile (such as the oscillation on top of the plateau shown for the long-dash profile in the inset of Fig. 2.9.6.1), other than the overall film thickness, it can be necessary to make reflectivity measurements at values of *Q* corresponding to 2π/(characteristic dimension of the feature).