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In 1962, Riccardo Giacconi and colleagues flew three Geiger counters to search for lunar X-ray fluorescence. Different mica thicknesses tested penetration; lampblack blocked ultraviolet. Each counter sat in an anticoincidence detector using a scintillation counter to reject cosmic rays. There was no mechanical collimator. Rotation scanned the sky; optical sensors supplied orientation.^[ref]

Counts were sorted by azimuth; a faulty counter and tumbling descent data were excluded. A directional peak lay above a diffuse component. Window, altitude and angular responses tested X-rays against charged particles; the Moon's nondetection checked optical leakage. The authors argued for an origin outside the Solar system, while residual cosmic ray background was not directly measured and source size, position and spectrum remained assumption-dependent.^[ref]

A simple original forward problem makes the distinction precise. Let $\varphi$ be the scan azimuth, let $g(\varphi )$ be a dimensionless directional response with maximum one, let $F$ be a source's band-integrated photon arrival rate per unit area, let $A_0$ be its on-axis X-ray effective area, and let $b$ be a constant accepted background rate. The expected rate isFor a broad illustrative response $g(\varphi )=\max (0,\cos \varphi )$, the full width at half maximum is $120^{\circ }$: $\cos \varphi =1/2$ at $\varphi =\pm 60^{\circ }$. For a one-dimensional ideal collimator model $g(\varphi )=\max (0,1-|\varphi |/{\theta }_c)$, the full width at half maximum is ${\theta }_c$. Choosing ${\theta }_c=20^{\circ }$ narrows the response sixfold without focusing any additional photons. These are teaching response functions, not reconstructions of the rocket's window transmission or geometry. A narrower scan peak can reflect the instrument response even when the source is unresolved.

An absorption edge is an abrupt change in photon absorption as incident photon energy crosses an electronic excitation threshold. For inner-shell photoionization, a new vacancy-production channel opens near the shell's binding energy. This threshold concerns incident energy; a Characteristic X-ray concerns a subsequent difference of atomic energies. They are different observations. Barkla's lecture explicitly treats characteristic emission as requiring a critical excitation condition, while discussing characteristic radiation separately from scattering.^[ref]

In the stipulated X-ray fluorescence model, the K threshold is $10.0\mathrm{keV}$, whereas the K lines are $8.5$ and $9.7\mathrm{keV}$. An absorber made of a different material could have its own absorption edge between those line energies, preferentially removing the upper line. Actual near-edge structure and attenuation values require material data; the following deliberately chosen coefficients are not such data.

Derek E. Haycock coauthored research on X-ray emission spectroscopy.^[ref]

X-ray emission spectroscopy studies the frequency spectrum of emitted X-rays. The spectral line positions identify electronic energy differences; their strengths also depend on excitation, photon absorption inside the sample, geometry and detector response. An X-ray tube may excite a sample with electrons, while X-ray fluorescence uses incident photons. The distinction matters when choosing what the experiment measures: identifying a chemical element from a line position is different from determining its abundance from a line strength.

The sixth allowed family is $400$. For the two lattice constants, use $2{\theta }_{400}=2{\sin }^{-1}(2\lambda /a)$:ConsequentlyThe larger lattice constant shifts the AlAs reflection to lower scattering angle. As a differential check, $\Delta (2\theta )\simeq -2\tan \theta \Delta a/a$ in radians.

If the angular displacement is unresolved, use the intensity contrast. With the same $f\simeq Z$ model, a difference reflection has basis amplitude $13-33=-20$ for AlAs, versus $31-33=-2$ for GaAs. Its squared amplitude is therefore one hundred times greater before overall sample normalization. More robustly, compare a weak and a strong reflection within each specimen. Neglecting their almost identical angular corrections,The contrast in this internal ratio is about a factor $194$. Element-specific X-ray fluorescence, for example testing for a Ga characteristic line with a suitably energetic incident beam, or an X-ray absorption spectroscopy scan through an element-specific absorption edge, also distinguishes composition. Such scans can change incident energy; one must not assume every core shell can be excited by the original $8\mathrm{keV}$ beam.

SEM with energy-dispersive X-ray spectroscopy can identify gold versus silver through their characteristic X-ray energies. Acquire spectra and maps from representative regions: two compositionally distinct regions would support the two-phase interpretation of B. With standards or validated matrix corrections it can estimate local compositions and, with representative sampling, an overall composition. Surface topography and the interaction volume limit spatial interpretation.

X-ray fluorescence provides a complementary more bulk-averaged elemental measurement. Gold and silver produce different characteristic lines; calibrated intensities can yield their mass fractions, with corrections for absorption, excitation and specimen geometry. It does not by itself determine whether an element occupies one or two crystallographic phases.

Both methods supply elemental information missing from a lattice-parameter-only identification. A purely morphological micrograph could reveal phase separation but would not alone give a reliable numerical chemical composition.

X-ray emission spectroscopy studies the frequency spectrum of emitted X-rays. The spectral line positions identify electronic energy differences; their strengths also depend on excitation, photon absorption inside the sample, geometry and detector response. An X-ray tube may excite a sample with electrons, while X-ray fluorescence uses incident photons. The distinction matters when choosing what the experiment measures: identifying a chemical element from a line position is different from determining its abundance from a line strength.

X-ray fluorescence is Characteristic X-ray emission following excitation by incident photons. In a simple initially unexcited chemical atom, photoionization can eject an inner electron if the incident photon supplies its binding energy. An outer electron can then fill the vacancy, releasing an emitted photon with the difference of shell binding energies. Nonradiative relaxation competes with this route, so one absorbed incident photon need not yield one escaping characteristic photon.

Choose a separate stipulated electron shell model with values $B_K=10.0$, $B_L=1.5$ and $B_M=0.3$, all in $\mathrm{keV}$. Ignore subshell splitting, recoil and changes of binding energy during relaxation. The possible shell differences areThese labels denote simplified shell groups, not resolved subshell electronic transitions. With $hc=1.23984\mathrm{keV}\mathrm{nm}$, their calculated wavelengths are respectively $0.145864$, $0.127819$ and $1.03320\mathrm{nm}$. An incident $9.8\mathrm{keV}$ photon exceeds both K-line energies but cannot directly create the K vacancy in this initially unexcited model. A $12.0\mathrm{keV}$ photon can, leaving approximately $2.0\mathrm{keV}$ of photoelectron kinetic energy. This comparison fixes neither the excitation probability nor the radiative branching probability.