[Enthalpy]

The K absorption edge detects Br and also Sb, and the plastic chips that contain these fire retardants would be separated just after PVC. But for lighter elements, photons around the K edge are too weak to shine through the chips. So on the spreadsheet (rename pdf to xls) and zoomed graphics, can the knee at 10-100keV distinguish C, N, O, P, Cl?

           Attenuation cm²/g
   C        N        O        P        Cl    |    MeV    Source
================================================================
4.06E+0  6.70E+0  1.03E+1  6.82E+1  9.59E+1  |  8.34E-3    Ni
1.43E+0  2.27E+0  3.43E+0  2.32E+1  3.31E+1  |  1.21E-2   W L1
3.19E-1  4.06E-1  5.27E-1  2.69E+0  3.86E+0  |  2.56E-2    Ag
2.03E-1  2.22E-1  2.48E-1  7.27E-1  9.93E-1  |  4.20E-2    Pr
7.76E-2  7.76E-2  7.77E-2  3.10E-1  3.81E-1  |  6.54E-2    Hf
================================================================

      Attenuation ratios
  P/C      Cl/P  (N-C)/(O-C) |    MeV    Source
================================================
1.68E+1  1.41E+0   4.23E-1   |  8.34E-3    Ni
1.63E+1  1.43E+0   4.20E-1   |  1.21E-2   W L1
8.44E+0  1.44E+0   4.20E-1   |  2.56E-2    Ag
3.58E+0  1.37E+0   4.18E-1   |  4.20E-2    Pr
4.00E+0  1.23E+0   4.29E-1   |  6.54E-2    Hf
================================================
  YES     Maybe     Doubt

Observation at several energies can distinguish P and Cl from the polymer, even in small concentration. Telling Cl from P is uneasy, as their ratio varies from 1.4 to 1.2 but they are minor constituents of the plastic and the chips attenuate little at these energies. This suffices anyway to sort out the chips with flame retardant.

Even after the chips containing Sb, Br, Cl or P are sorted out, observation at several energies to tell raw proportions of C, N, O is doubtful. The graph shows the attenuation by N at constant proportion from C and O, the figures confirm that N is at 0.418 to 0.429 in the C to O interval. A determinant would confirm that the system of three linear equations is very badly conditioned.

A conveyor belt with several smooth spikes per chip diameter could hold the chips more firmly as they pass at successive detectors. Or have small holes in the belt, as they also help the rays pass through.

There might be alternatives within X absorption. 1*N looks the same as 0.42*O, but usual polymers group around few compositions, so 1*N+0.42*O may suffice to tell ABS from PA. Also, H absorbs higher energies more (it has more electrons per nucleon, compare polyethylene with C on the graph), so the H/C ratio might tell ABS.

==========

X-ray fluorescence would detect Sb, Br, Cl, P in a chip. The raw proportions of C, N, O aren't obvious due to air and because energies are very low.

==========

Evaporating a tiny amount of every plastic chip with an ultrashort laser pulse to analyze the light emitted by the plasma might be better for C, N, O analysis in addition to Sb, Br, Cl, P.

Marc Schaefer, aka Enthalpy

[Enthalpy]

I suggested to detect phosphorus by its X-ray fluorescence. From the CRC Hdbk of Chem&Phys, the light element emits at 2013eV, 2014eV and 2139eV, so what shall detect that small energy?

A plain silicon PIN diode looks perfect for that task. The K edge at 1839eV lets absorb 2139eV with 2336cm²/g, so 2.33g/cm³ and 8µm depleted depth absorb 99% of incoming rays. <10¹³cm^-3 residual doping deplete the diode without external voltage nor leakage current. The top doping must be <<1.8µm, for instance <100nm to save photons. An aluminium top contact should be a grid to save photons, or if feasible, uniform 3µm thick beryllium would waste 6% of the X-rays but attenuate stray visible light by millions, and thicker Be would attenuate air fluorescence X-rays. Passivation could be 0.5µm of BN, or if airtight BeO or B₂O₃, losing only 3% of X-rays. If 3.5eV per carrier pair holds for X-rays in Si, each photon creates packets of 575q.

Fast electronics to count charge packets promises only worries here, but a simple charge integrator looks excellent. A banal TLC084 adds 23pF to the 4mm² diode's 52pF. With 500µs integration time, its 8.5nV/sqrt(Hz) sum over roughly 600Hz while the auto-zero removes the 1/F noise, so the charge noise is 150q rms, or 0.32 photon. With good routing, the 3pA input bias current integrates to 9400q, of which zeroing software leaves 97q fluctuation, or 0.17 photon. Both are well below the quantum noise, so the TLC084 suffices.

Air attenuates by 550cm²/g at 2013eV, so 5mm waste 29% of phosphorus' fluorescence, but it also attenuates air's fluorescence X-rays. A small and more constant distance results from sources and sensors below the plastic chips, observing through holes in the conveyor belt. More transparent media have drawbacks: H₂O, CH₄, He, H₂, vacuum. That would make the measurement of the plastic's C, N, O by X-ray fluorescence difficult.

Chlorine fluoresces at 2621eV, 2622eV and 2816eV (does the handbook mention fluorescence from valence electrons?) so it can use the same PIN diode design. Silicon absorb 2816eV with 1151cm²/g, so 8µm absorb 88% of incoming rays, while 12µm absorb 96%, still accept 5×10¹²cm^-3 residual doping, and fit phosphorus' fluorescence too. A filter of sulphur or phosphorus (or compounds) can discriminate phosphorus from chlorine.

==========

Bromine fluoresces up to 14.0keV, for which the exponential attenuation distance is inconvenient 340µm in Si but 17µm in GaAs or Ge, a bit more in GaP or GaN. 4×10¹¹cm^-3 residual doping and no external voltage deplete 40µm that detect 90% of the photons. Compensating the semiconductor is useful as long as the carriers recombine little.

Antimony fluoresces up to 30.5keV, and even InP has 70µm exponential attenuation distance, so a scintillator or other detectors should be considered. Or detect only the transitions to L shell around 4keV.

This applies to fluorescence and to transmission measurements.

Marc Schaefer, aka Enthalpy

[Enthalpy]

As light approaches a frequency that would excite or ionize atoms or compounds, electrons vibrate more strongly. This increases the refractive index of matter around the visible spectrum. X-ray lenses using the increased index near an absorption edge were also built few years ago. I had suggested it somewhere, and apparently the idea was long known and carries some name.

I propose to use atoms near their absorption edge to make more brilliant diffraction gratings, as crystals or as patterns made by semiconductor processes. For instance if the X-ray light results from fluorescence, atoms with but more protons than the source, or maybe as many protons, nearly resonate.

The other atoms would better absorb little light at that energy range. So as examples, silver nitrate would diffract fluorescence light from palladium, or tungsten carbide would diffract light from tantalum.

==========

At 7nm channel length, semiconductor processes aren't very far from the longest X-rays, and some patterned optics become more feasible if not useful.

2139eV from phosphorus fluorescence have λ=580pm, bigger than many crystal lattice constants. Rhenium weighs 21.0g/cm³ and absorbs 3800cm²/g there, so 90nm thickness attenuate ×0.49. 15+15nm grating period need a banal aspect ratio of 6. The transmitting grooves are 26λ wide for 4.4° individual main lobes, neither excellent nor ridiculous. The grating can have many periods for excellent selectivity, and it transmits much light, for instance to distinguish the elements in a compound.

The substrate could be several µm beryllium stretched over a hole (or several holes) in a silicon wafer. Maybe LiH can serve with precautions.

Zoned lenses are conceivable with similar processes. Again with 2139eV and minimum 15+15nm, they need L/D>13. A CCD retina can have 2µm×2µm×2µm pixels, and at 20mm focal length, it can have D = 2mm = 1000 pixels for S = 800 000 pixels. The 100µrad resolution results from the CCD pitch, not from the D=1mm lens.

A Fresnel refractive lens, maybe of (a compound of) sulphur, would of course be better if feasible.

Marc Schaefer, aka Enthalpy

[Enthalpy]

Maybe one could make an even finer grating by stacking many thin layers of alternating materials and cutting slices through the thickness.

Layers are even finer than the channel length of presently 7nm, and reverse engineering achieves clear slices through them. That would make periods under 10nm.

200 000 layers for 1mm grating length is unheard of in semiconductor manufacturing. I hope evaporation or sputtering achieve it by passing the target alternately over two sources of material, say by a rotation, with a few screens in vacuum. A progressive transition improves the grating's selectivity.

During the paleomonolithic era, evaporating 1µm aluminium took about 500s, so I hope 5nm take 2.5s and 200 000 layers 6 days. Atomic layers need time to consolidate since the atoms land at random locations, but I imagine this time is a constant per atomic layer. Each target provides many gratings as the slices need little thickness.

The targets must also be warm to consolidate the layers, so the deposited materials should creep at compatible temperatures. Based imperfectly on the melting point, for instance beryllium might pair with nickel, yttrium, palladium, gold and more. Some diffusion is desireable.

Marc Schaefer, aka Enthalpy

[Enthalpy]

As the divergence is a drawback, the zoned lens of 27 October 2019, 21:17:49 can improve X-ray sources too, soft ones in a first time. The energy selectivity is often an advantage.

At the source too, diffraction gratings are useful, first as monochromators. Atoms used just below the K or other absoption edge, as proposed on 27 October 2019, 21:17:49, absorb energies but stronger, which is often an advantage.

The multilayer stack of 28 October 2019, 00:21:57 can be a mirror. It wouldn't be sliced then. Grazing incidence uses to reflects better than normal incidence. The energy selectivity is often an advantage. Such a mirror could use lithium rather than beryllium, it would be much thinner than the length of the previously suggested grating, and it would keep its support. The support can be shaped as a converging or diverging mirror, even if not wavelength accurate.

To bridge the gap between few nm and interatomic distances, both for gratings and mirrors, the multilayer stack of 28 October 2019, 00:21:57 can be further thinned, by mechanical means. Rolling and hammering come to mind. How much thinner depends on the regular behaviour of the support, which might also cover the multilayer during thinning for protection. Very malleable support materials should behave regularly when thinned; some are easier to remove than gold.

==========

Mirrors, even at grazing incidence, would enable or improve X-ray laser oscillators. I vaguely believe that existing X-ray lasers are superradiant oscillators.

I had already suggested elsewhere to dope lasing media with lasing centres only at the antinodes of electric field. For an X-ray laser oscillator, superradiant oscillator or amplifier, the multilayer can use a more transparent material at the nodes of electric field. At the antinodes, it might also dilute the fluorescent atoms among more transparent ones to reduce the power density required from the pumping power and the cooling.

A multilayer amplifying medium can be made by the same machine as the optional end mirror(s), possibly in the same operation. Data seems to indicate that elements' most fluorescence energies are below the own absorption step, then the same element could fluoresce and reflect, so the mirrors would resemble much the amplifying medium, except maybe for the concentration of active atoms. A flat laser would radiate in directions that let match the atoms' transition wavelength with the layers' imperfect thickness.

Electrons would pump the lasing atoms more directly than primary X-rays, but any net advantage depends on many physical and technological limits like cooling - better beryllium or a carbon allotrope as the transparent medium. Or the lasing medium could be very close to the anode emitting the primary X-rays, possibly deposited on the anode. If the lasing medium is deposited on a thin anode, at the side not exposed to electrons, hydrogen may perhaps cool the anode, with pressure and speed, and with a vacuum pump at the electrons' side because of diffusion. As usual, the electron beam can sweep quickly at the anode, or the anode rotate.

Would that expand to higher energies and to crystals instead of multilayers? Shorter fluorescence times must be the barrier.

Marc Schaefer, aka Enthalpy

[Enthalpy]

A possible aspect of the resonant circuit or cavity of 04 October 2019, 00:17:26 is appended.

The chip can cross the gap in different directions, with hollow poles at the right option. As a guiding insulating tube, alumina, PE, PP, PS have low losses, but the chips may deposit lossy dirt on abrasive alumina, so PP seems better.

A 20mm×20mm×20mm gap can resonate at 2.45GHz with 24nH resulting from roughly 60mm height of the openings. Gold plating creates some 45mOhm for Q≈9000. A metal shield at moderate distance suppresses stray radiation. The resonant circuit can also have cylindrical symmetry, better for higher GHz and needing no shield, or ferrite or coils for lower frequencies. Several frequencies may discriminate polymers better.

A short antenna or loop can couple the cavity with a feed cable, as usual. I'd rather have two such ports, distant from an other, to excite the resonance and to observe it.

From the excelentísimo Carlowitz, Kunststoff-Tabellen, alas at 1MHz:

Loss     Permitt    Polymer
10-4
====================================
 0.5-1     2.5      PS
 0.4-1.3   2.34     PE-HD, MD
   1.8     2.3      PE-LD
  <5       2.25     PP
5-10     2.8-3.1    ABS
  40       2.6      PS flame retard
 180       3.0      PVC hard
 300       3.0      PVC shock proof
1200       4.2      PVC plasticized
 300       3.2      PA11, PA12 dry
 800       3.4      PA11, PA12 damp
 280       3.6      PA6, PA66 dry
2500       6        PA6, PA66 damp
====================================

We see that the polymer families difficult to separate by flotation, ABS and PA, have a very different dielectric loss. Even flame retardants might be detected that way.

The permittivity differs too little to discriminate the material whatever the chip size, but it can estimate the chip size to better measure the dielectric loss.

The ε=3 of a 10mm×10mm×3mm chip in the 20mm×20mm×20mm gap would change the resonant frequency by roughly 7%, so I suggest to excite the circuit by a burst 100 periods short, or 40ns at 2.45GHz. The electronics shall then observe the decay time and the natural frequency. Misusing the 1MHz loss factor, already 10^-4 from PE reduces the Q-factor by measurable /1.06, 5×10^-4 from ABS by /1.3, 280×10^-4 from PA6 by /19. This must be better modelled, and above all calibrated. At 2.45GHz and Q=9000, 5µs repetition rate is possible.

Even if the chips fly through at 20m/s, one measurement per mm needs only 50µs repetition rate and suffices to pick the best chip position. If the sorting actuator is as fast as the sensor, one 10mm×10mm×3mm chip every 80mm lets sort 75g/s = 270kg/h = 6.5t/day, and a recycling company can afford many such sensors.

Marc Schaefer, aka Enthalpy

[Enthalpy]

Permittivity can also separate the plastic chips by electrostatic force.

Take again ABS (ε_r=3.0) and PA66 (ε_r=3.6) because they have a similar density. Other materials would already be separated by flotation. The chips shall float in a liquid of similar density, excellent insulator (hence hydrophobic), runny, with permittivity between both plastic families, here ε_r=3.3.

Combs of electrodes apply a strong electric field in the liquid, like 30MV/m. This can be the rms value of an AC field that stresses the insulators less. Frequencies higher than 50Hz are less dangerous to humans, for instance a few 10kHz. Capacitors can feed the electrodes and limit the current in a short-circuit, while insulated electrodes would be less efficient.

The rms energy of 30MV/m in vacuum is 4kJ/m³. Simplifying quite a bit, 0.3 more or less in ε_r changes this energy by 1.2kJ/m³, or for a 10mm×10mm×3mm chip ±0.36mJ. The electrodes attract the PA66 chips, while the liquid pushes the ABS chips away. If the shape and period of the comb let the field drop over 5mm, the electrostatic force is ±0.07N.

If ABS and PA are ±50kg/m³ away from the liquid's density, the 10mm×10mm×3mm chip weighs ±0.15mN. If the runny liquid moves with at most 1.1m/s versus the 10mm×10mm chip with C_d=1, the drag is smaller than the electrostatic force.

So the separator would have electrode combs that move gently in the liquid, plus something like a perforated conveyor belt or net to fish the lower-permittivity chips repelled from the electrodes, and at places where the voltage is removed or reduced at the electrodes, an other fishing device to extract the higher-permittivity chips. Gradual voltage reduction can allow further separation, for instance of dirt.

The electrodes could be on slowly rotating cylinder(s). Fishing can occur several times per turn. The throughput looks promising.

The power consumption is very small. 30MV/m seem plethoric. Coils can compensate the reactive energy, as a resonant circuit or in a more subtle combination with active power components. The coils can be parts of transformers that create the high voltage locally, possibly immersed.

This is a very nice small experiment, cheap, spectacular and quickly done at a university for instance. Drawings should follow.

Marc Schaefer, aka Enthalpy

[Enthalpy]

I suggested here on 28 October 2019 to cycle a target over sources of varied materials to deposit many thin layers and make gratings or, on 29 October 2019, mirrors. A possible aspect of the machine is appended here.

For instance evaporation in vacuum is well known. Some processes can also deposit compounds of the desired elements to improve the chemical, thermal, mechanical resistances, reduce the diffusion, etc. Screens between zones for varied materials let deposit only one material at a location, but opening them more provides a smoother transition between the layers compositions to improve the adherence and reduce higher order diffraction modes, or to reduce a mirror reflectivity at unwanted energies. The materials can have different thicknesses to favour higher order and even modes.

There could be more deposition zones, maybe for more uniform thickness, or to deposit more varied layers. I've drawn several sources per zone for more uniform thickness along the radius; there could be more sources farther from the axis than nearer. Diffraction gratings could be cut along the machine's azimuthal direction for uniform thickness.

The carrousel can hold many targets or a continuous one. They are usually heated for adherence and uniformity. The substrates can be curved, in one or two dimensions, especially to make mirrors. Very flat substrates exist for microelectronics, of semiconductors or ceramics, some expanding little over temperature.

Marc Schaefer, aka Enthalpy

[Enthalpy]

I proposed that the force of an electric field separates chips of different permittivity in a liquid, here on 03 November 2019, 18:38:34. A possible aspect of the machine is appended.

The materials of close density, here PA and ABS for instance, must just float in a liquid. The optional left part on the sketch uses that to separate first chips denser and lighter than the electrostatic separation candidates.

The electric field acts on the right part on the sketch. Rotating cylinders are one way to bring electrodes near to the chips and have a quiet flow. The electrodes can be on the cylinders or just below its surface, with smooth shapes and no bubbles nor voids. Three phases would make a mean force more uniform.

Horizontal axes combine nicely with the decantation pool and ease the outlet. Vertical axes would allow many cylinders, for instance with positions and rotation directions like a chessboard. This leaves little room for inlets and outlets.

The very high voltage is better created at the electrodes, within the liquid or the cylinders. Electronics could switch a common 2 or 3-phase supply, or make local 2 or 3-phase power from a common DC supply, and send it to transformers that make the very high voltage for the electrodes that currently need it. An other transformer may provide power to a cylinder without slip rings. Synchronous phases among the cylinders reduce the field at their midline.

The field gradient can move the chips at more than 0.5m/s as already evaluated. With 2*25mm between the cylinders, 0.1s suffices, and D=0.2m cylinders can rotate in 2s. 2m wide cylinders treat 31dm³/s, so with 10cm³ per chip, one cylinder pair separates 3.5t/h. Or four D=0.4m W=3m cylinder pairs around one decantation pool separate 42t/h = 13 000 t/month in 2 shifts and 20 days.

Marc Schaefer, aka Enthalpy

[Enthalpy]

I proposed here on 27 October 2019, 21:17:49
https://www.chemicalforums.com/index.php?topic=101272.msg356774#msg356774
that semiconductor processes make zoned lenses for soft X rays. The wide emission lines, i.e. short time coherence, limit the size of a zoned lens because it doesn't compensate travel times.

From the CRC Hdbk of Chem&Phys, I take as an example the strongest Kα_I (2p->1s) emission. For P at 2014eV, the line shall be 0.5eV wide as extrapolated from Ca and heavier. This lets the photon last 0.7fs or 0.2µm. F=1mm focal length lets all zones interfere if the lens radius is <20µm, F=100mm allow 200µm.

If the lens is wider, it catches and focusses more light, but not to the theoretical spot size.

A lens opaque at the centre is rarely useful. With F=1mm too, rings starting at r=40µm can reach R=45µm. The collecting area is the same, the angular resolution increases even more if the source or detector sizes don't limit it, and the lens' rings get even narrower. For F=1mm and full r=20µm at 2014eV they need 30nm period, for F=100mm and full r=200µm it's 300nm.

==========

I proposed here on 29 October 2019
https://www.chemicalforums.com/index.php?topic=101272.msg356879#msg356879
to use the thin multilayer stack as a mirror, for a wavelength I didn't specify.

Imagine layers 2nm thin, the period is 4nm and a wave bouncing back travels 8nm more if the incidence is normal. If this adds one wavelength, then the photon has 8nm or 155eV only, at very deep UV or extremely soft X-rays. A nonzero incidence multiplies the energy by 1/cos.

Already before 1keV, a crystal fits better the wavelength. For instance LiCl is cubic with 257pm between neighbours. The <111> planes contain only Li or only Cl to define a multilayer reflector. The period between Cl planes is 257pm×2/sqrt(3)=297pm. 2×297pm make 2088eV photon energy. A 2622eV photon, from the strongest Kα_I emission by Cl, arriving at 37° from normal is reflected at 37°. A submultiple of the wavelength would fit the crystal, provided the halfwave is longer than the K=1s shell.

==========

The Kα_I emission is a 2p->1s transition if I interpret properly data in the CRC Hdbk of Chem&Phys. It can happen after an electron or photon knocks a 1s electron away. If an element has its 2p being full in ground state, 1s->2p is impossible and can't absorb the 2p->1s emission line. So the same element can emit a line and filter it, contrary to what I wrote previously and had read.

For Cl, tables give indeed a Kα_I emission at 2622eV and an absorption edge at 2822eV, logically from 1s->valence. This doesn't hold for line energies very close to the maximum, especially at transition elements.

[Enthalpy]

I proposed on 27 October 2019, 13:04:39
https://www.chemicalforums.com/index.php?topic=101272.msg356752#msg356752
to use atoms near an energy absorption edge, but how brilliant are they?

With the detection of flame retardant in mind, I consider the Kα_I emission by ₁₅P at 2014eV=616pm with 0.2µm coherence time.

• The K (1s->valence) absorption edge of ₁₅P is at 2146eV or 1.066× above the emission line. Numerically, strong reflection would take much more than 0.2µm phosphorus thickness, but the decoherence prevents it.
• The L (2s->valence) edge of ₃₉Y is at 2080eV or 1.033×. Here the 0.2µm are a few times too short, imperfect.
• The M (3d->valence) edge of ₇₇Ir is at 2040eV or 1.013× and the path in a mirror is but more than 0.2µm. Considered here.
• The emission by ₁₇Cl instead of ₁₅P fits the absorption edge of unstable elements only, bad luck.
• Freely chosen emitting and resonating elements would fit much better than 1.013×.

I model the ₇₇Ir near-resonance brutally with electrons 0.91×10^-30kg heavy and 8.7MN/m stiff to resonate at 492PHz=2040eV. Well below the resonance, 1V/m move the electron by 1.8×10^-26m. 1m³ Ir contains 117kmol for 7.0×10²⁹ 3d electrons, so 1V/m induces 2.1fC×m displacement. The resulting permittivity is ε=(1+2.3×10^-4)×ε₀.

As a quick check, electrons in optical materials resonate at 5eV instead of 2keV, they are 400² times less stiff, so their permittivity would be 38 - compare with 3 usually, not bad for such a model. Maybe only one 3d electron from Ir moves per atom. More probably, few valence electrons per atom move at optical materials.

With F=2040eV/2014eV=1.013, the near-resonance multiplies the movement amplitude by 1/(F-1/F)=39 so the permittivity becomes ε=(1+9.1×10^-3)×ε₀. The near-resonating 10 electrons are more brilliant than the 67 others. This improves the diffraction by crystals and, at lower energies, by gratings.

X-ray lenses were reported using this near-resonance. Here a Fresnel lens made by semiconductor process needs steps 68nm thick, nicely transparent, and its 30nm to 300nm wide rings as in the previous message fit the thickness. More transparent than a zoned lens but limited by the coherence time too and narrowband. 30% loss allow only 156nm thickness, no good alternative. Better matched element pairs would improve. ₃₉Y is more transparent in this use.

An X-ray mirror must provide atomic planes spaced by multiples of the half-wave on the path of the ray. Fcc Ir spaces the planes by 192pm along <100>, less in the others. That's too small for 616pm wavelength, so some iridium compound is needed, with lighter atoms for transparency, maybe O, F, Cl, B, C, a metal... The incident and reflected angle makes the fine tuning. The ray shall encounter a dense iridium plane every 308pm in some adequate crystal.

I treat this as a dichroic mirror. The 3d shells are small and of higher index, but for the reflection they can be taken as 308/2=154pm layers of permittivity 1+11×10^-3 that alternate with 154pm layers of vacuum. The index is 1+55×10^-4 and the field reflection amplitude 28×10^-4 at each interface.

Over 0.2µm coherence time, 62% iridium attenuates ×0.75, nice. The ray encounters 325 Ir layers and as many on the return leg. The 650 interfaces reflect 28×10^-4 field each so the reflection is strong.

Marc Schaefer, aka Enthalpy

[Enthalpy]

Wrong link in my previous post. It was on 27 October 2019, 22:17:49
https://www.chemicalforums.com/index.php?topic=101272.msg356774#msg356774

[Enthalpy]

And the L edge of ₃₉Y at 2080eV is from 2p->valence.

[Enthalpy]

For the main emission line by ₁₅P, ₇₇Ir has an absorption edge 1.013× higher to build components. How common is such a near resonance?

The other fire-retardant elements ₁₇Cl, ₃₅Br, ₅₁Sb have resonating elements too. For the alpha lines of ₁₇Cl the elements are radioactive, but for the beta line 0.08× as bright, ₄₄Ru is stable.

    Emission line     |     Absorption edge     |   Ratio
   eV   name Element  |     eV   name  Element  |
===========================================================
 2815.6  Kß     Cl    |   2837.9   L      Ru    |  1.0079×
11877.6  Kα2    Br    |  11918.7   L      Au    |  1.0035×
 3886.4  Lß4    Sb    |   3928.2   L      Sn    |  1.011×
26359.1  Kα1    Sb    |  26711.2   K      Cd    |  1.013×
===========================================================


Even for Br and Au, the absorption edge is 18 half-widths away from the line centre.

I also checked the refractory elements ₇₃Ta, ₇₄W and ₇₅Re to see how usual a close absorption edge is. Here's a pick.

    Emission line     |     Absorption edge     |   Ratio
   eV   name Element  |     eV   name  Element  |
===========================================================
 9212.4  L1ß4   Ta    |   9244.1   L      Lu    |  1.0034×
67194    Kß4    Ta    |  67416.4   K      Ta    |  1.0033×
 9525.2  L1ß4    W    |   9560.7   L      Hf    |  1.0037×
59318.2  Kα1     W    |  59389.6   K      Tm    |  1.0012×
 9846.3  L1ß4   Re    |   9881.1   L      Ta    |  1.0035×
61140.3  Kα1    Re    |  61332.3   K      Yb    |  1.0031×
69310    Kß1    Re    |  69525.0   K       W    |  1.0031×
===========================================================

For W and Tm, the absorption edge is 3.1 half-widths away from the line centre.

From this short but time-consuming sample, heavy elements seem to have some near-resonating element less than 1.004× away, while 1.001× needs limited luck and begins to encroach upon the line width. The K edge of lighter elements was rather 1.020× over the L lines of heavy elements, but more trials would bring luck.

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The already described multilayer or crystal mirror can narrow down an emission line without wasting much power. It must then be thicker than the source's coherence time but still transparent, favouring a light element like ₃₉Y over ₇₇Ir in the December 01, 2019 example, and can serve at the transmitted or reflected rays. The many bounces let each light pulse last longer.

The longer coherence of a narrower line eases subsequent components like zoned lenses.

Marc Schaefer, aka Enthalpy