# How to add a hump to the background Append a `HumpComponent` to `Instrument.extra_components`, and free `instrument.extra_components.*` in a stage after the peak widths have refined. A hump is one broad Gaussian added on top of whichever background model you use. Use it for scattering with no Bragg peaks behind it: an amorphous phase, a glass or polymer capillary, a cryostat window or a sample holder. Other programs call it a background peak. ## Declare the hump Give it a starting position, height and width. Seed the position where the feature is, from a blank scan or from the pattern itself: ```python import rietx as rx from rietx.schemas.instrument import HUMP_FWHM_MIN capillary = rx.Instrument.debye_scherrer(wavelength=0.412359) capillary.extra_components = [rx.HumpComponent( label="Kapton halo", position=rx.Parameter(value=5.0, unit="deg"), height=rx.Parameter(value=50.0, min=0.0, unit="counts"), fwhm=rx.Parameter(value=2.0, min=HUMP_FWHM_MIN, unit="deg"))] assert capillary.extra_components[0].height.vary is False ``` `position` and `fwhm` are in degrees 2θ, and `height` is the peak value in counts. Keep the `min` bounds: a height of zero switches the hump off, and the width is floored at `HUMP_FWHM_MIN` because the Gaussian divides by it. `label` is free text and never part of a parameter’s name. The parameters are named `instrument.extra_components.0.position`, `.height` and `.fwhm`, numbered by the hump’s place in the list. All three start fixed, and a declared hump at zero height changes nothing. ## Free it after the peak widths `mccusker_structural` frees declared humps in its `extra_components` stage, after the zero shift, cell and peak widths. No other preset frees them, so with another plan add a stage for `instrument.extra_components.*`, as [How to add a stage to a refinement plan](plan.html.md) shows. Freeing the hump earlier lets its free position chase misfit from a wrong zero shift or cell. For the same reason `instrument.background.*`, which most presets free in their first stage, does not reach the humps. No plan ever adds a hump. A plan frees only the humps you declared. ## Compare it with more polynomial terms A free position, height and width will lower Rwp on any pattern, so compare the hump with the same number of extra polynomial terms. This runs APS 11-BM’s scan of NIST SRM 640c silicon in a Kapton capillary, which shows the capillary’s halo near 5° 2θ. `rietx.examples.fetch` downloads the file, about 1.5 MB, the first time it is asked for. ```python import rietx as rx from rietx.examples import fetch from rietx.schemas.instrument import HUMP_FWHM_MIN data = rx.read_pattern(fetch("11BM_Si640c.xy")) def silicon(): """SRM 640c at its certified lattice parameter, 5.4311946 Å.""" a = rx.Parameter(value=5.4311946) right = rx.Parameter(value=90.0) return rx.Structure(phases=[rx.Phase( name="Si", space_group="F d -3 m :2", cell=rx.Cell(a=a, b=a, c=a, alpha=right, beta=right, gamma=right), scale=rx.Parameter(value=3e-4, min=0.0), atoms=[rx.Atom(label="Si", species="Si", x=rx.Parameter(value=0.125), y=rx.Parameter(value=0.125), z=rx.Parameter(value=0.125), biso=rx.Parameter(value=0.44, min=0.0))])]) def halo(): """Seeded where the empty capillary's scan peaks, near 5° 2θ.""" return rx.HumpComponent( label="Kapton halo", position=rx.Parameter(value=5.0, unit="deg"), height=rx.Parameter(value=50.0, min=0.0, unit="counts"), fwhm=rx.Parameter(value=2.0, min=HUMP_FWHM_MIN, unit="deg")) def fit_with(n_terms, humps): instrument = rx.Instrument.debye_scherrer(wavelength=0.412359) instrument.background = rx.BackgroundChebyshev.with_terms(n_terms) instrument.extra_components = humps ref = rx.Refinement(silicon(), instrument) ref.hold("phases.0.cell.*") return ref.fit(data, plan="mccusker_structural", two_theta_limits=(1.997, 49.996)) bisos = {} for label, n_terms, humps in [("3 terms", 3, []), ("3 terms + hump", 3, [halo()]), ("6 terms", 6, [])]: biso = bisos[label] = fit_with(n_terms, humps).parameter("phases.0.atoms.0.biso") print(f"{label:<15} Biso {biso.value:.3f} ± {biso.stderr:.3f} Ų") ``` ```text 3 terms Biso 0.443 ± 0.100 Ų 3 terms + hump Biso 0.446 ± 0.018 Ų 6 terms Biso 0.448 ± 0.039 Ų ``` Silicon’s Biso is the only structural parameter in this fit. Its value barely moves, and its esd falls by a factor of 5.6 with the hump, against 2.5 with three more polynomial terms. A background that cannot describe the halo trades against the Bragg intensities, and the hump ends that trade. ## Check what the hump is Rwp cannot tell a container halo from a missed reflection, so look for evidence outside the fit. For this pattern, 11-BM’s scan of the same capillary empty peaks near 5.0° 2θ, d ≈ 4.7 Å, the amorphous halo of the polyimide the capillary is made of. A scan of the beam path with no capillary shows no feature at all. Without such a check, a hump is three parameters that lower Rwp. A hump narrower than 4.0 times the instrumental peak width at its position is reported as [`HUMP_TOO_NARROW`](../reference/diagnostics-refinement.html.md#hump-too-narrow). That width belongs to a reflection, so model it as a second phase instead. ## Read the fitted position with care The refined position and width describe the background model, not the halo on its own: ```python humps = {} for n_terms in (3, 6): result = fit_with(n_terms, [halo()]) position, fwhm = humps[n_terms] = tuple( result.parameter(f"instrument.extra_components.0.{name}") for name in ("position", "fwhm")) print(f"{n_terms} terms: hump at {position.value:.2f} ± {position.stderr:.2f}°, " f"FWHM {fwhm.value:.2f} ± {fwhm.stderr:.2f}°") ``` ```text 3 terms: hump at 4.16 ± 0.10°, FWHM 5.59 ± 0.25° 6 terms: hump at 5.24 ± 0.04°, FWHM 1.91 ± 0.11° ``` Against three polynomial terms, the hump also absorbs the rise of the direct beam below 3°, which pulls its centre low and widens it. Against six, the polynomial takes the rise, and the hump moves onto the halo and narrows to a third of the width. Its esds cover neither shift. Quote the blank’s envelope for where the halo is, and keep the background low-order if you mean to quote the hump’s parameters. The full script is `examples/guides/hump.py`. ## See also - [How to use a measured blank as the background](blank.html.md) holds the empty capillary’s whole scan under the pattern, which describes the halo without three free parameters. - `save_instrument_profile` leaves humps out, because a hump belongs to the specimen and its holder, not to the diffractometer.