Dear Chinedu Onyeke ,

let us first bring the things in the right order...

a) In an reflectivity experiment there is in general no thing like an inverse wavelength or other length involved.

Here you have the incident angle (e.g. alpha) and the reflection angle (e.g. beta) being equal (alpha = beta). Both angles refer to the surface of the sample. The reflected intensity is measured and presented vs the angle alpha.

However in some publications, especially when discussing the Kiessig fringes, the magnitude of the Q-vector is used for the presentation (see section 'd)' below).

b) In scatter experiments*), such as XRD, GID, SAXS and GISAXS, you measure the scattered x-ray intensity as a function of the scatter angle phi, and present this dependence as the XRD or scatter pattern.

c) In the case of XRD the x-axis is phi=2theta, which directly gives the relation to the Bragg angle theta of diffraction.

d) For the other scatter experiments one uses the magnitude q of the momentum transfer vector Q as x-axis in the presentation of the scatter pattern; q is defined by**):

q = (4pi/lamda)*sin(phi/2) = (4pi/lamda)*sin(theta)

Taking here 'theta' (=phi/2) as the incident angle**), similar to an XRD experiment, one is able to solve the above equation for theta:

theta = arcsin(q*lamda/(4pi))

In your case you have qmax = 0,5Å-1 ; lambda(Cu K-alpha) ~ 1,54Å;

so thetamax = arcsin(0,5Å-1*1,54Å/(4pi)) ~ 3,5°

*) see for example my answer in

https://www.researchgate.net/post/What_are_exactly_is_the_difference_between_GID_AND_GISAXS

**) see for example page 3 of:

https://www-ssrl.slac.stanford.edu/conferences/workshops/scatter2006/talks/hufnagel.pdf

Best regards

G.M.

Dear Chinedu Onyeke

In a typical X-ray specular reflectivity measurement (regardless of the type of source used), the observed pattern consists of a plateau from 0 up to the critical angle, where the X-ray beam is fully reflected. Beyond this point, as the beam penetrates the sample, oscillations known as Kiessig fringes become visible. These fringes provide valuable information about the sample's depth, including the thickness of each thin film in a multilayer, their scattering length density (SLD), and their roughness etc...

The oscillations continue until reaching a specific angle Theta_max, which would depend on the wavelength of the source and the response of the sample materials at that wavelength. It would also depend on other factors like the collimation and the resolution of the experimental setup.

Past this Theta_max angle, the X-ray beam penetrates further into the sample, causing the reflectivity signal to be dominated by background noise.

To expand the range of the useful signal, I would recommended to review the experimental setup and the collimation and/or performing a complementary off-specular measurement, then subtract the off-specular from the specular signal. This will allow you to obtain a cleaner measurement with significantly reduced background noise and a slightly extended range.

Best regards,

Elhoucine HADDEN

The scanning range is the maximum distance from the scanner to the barcode which still allows for error-free scanning. For typical powder patterns, data is collected at 2θ from ~5° to 70°...

Dear Chinedu Onyeke,

The angle range for reflectivity is specific to your experimental setup and the quality of sample. For example, higher the roughness of your sample, less angle range will be required to measure as the intensity reflected by the sample will drop very fast. As a general rule, you should measure reflectivity till you stop seeing any Kiessig fringes and the reflected intensity is almost flat on logarithmic scale (which refers to background noise). This will allow you to determine the quantitative information about the sample.