How XRF Reads Alloy Composition: The Physics of Karat

An XRF analyzer returns a composition table in a few seconds: gold 74.8%, copper 15.1%, silver 10.1%. The speed makes it feel like a lookup rather than a measurement. It is not. Behind that table is a chain of atomic physics, and every link in the chain introduces assumptions that can break.

Understanding those assumptions is what separates an operator who trusts the screen from one who knows when the screen is lying. This guide walks through the physics from the moment an X-ray photon strikes a sample to the moment a percentage appears — and, more usefully, identifies where each step can fail on real material.

Step one: creating a vacancy in an inner shell

Atoms hold electrons in discrete shells, labelled K, L, M outward from the nucleus. The K shell sits closest and is bound most tightly; binding energy rises steeply with atomic number. For gold, ejecting a K-shell electron requires 80.7 keV, while ejecting an L-shell electron requires only about 11.9 keV.

The analyzer’s X-ray tube fires high-energy photons at the sample. When an incoming photon carries more energy than an electron’s binding energy, it can eject that electron entirely — the photoelectric effect. The atom is left ionized with a vacancy in an inner shell, and that configuration is unstable.

Why the excitation energy has to exceed the edge

A photon with less energy than the binding energy cannot eject that electron at all. This is a threshold, not a gradient. A tube operating at 40 kV can produce photons up to 40 keV, which is nowhere near gold’s 80.7 keV K edge — so gold K lines are simply never excited in most benchtop instruments.

This is why precious metals analysis relies on L-series lines for heavy elements. It is not a preference; it is a consequence of the tube voltage available. It also explains why instruments intended for gold use rhodium or tungsten tube targets and operate in a voltage range chosen to sit comfortably above the L edges of the elements that matter.

Where this breaks in practice

If an instrument’s tube voltage is set too low for an element of interest, that element reports as absent rather than as an error. A machine configured for a light-alloy application and then pointed at platinum-group material can silently under-report. The failure is invisible because the missing element simply does not appear in the table.

Step two: the atom refills the vacancy

An electron from a higher shell drops down to fill the hole. The energy difference between the two shells has to go somewhere, and there are two competing outcomes.

Fluorescence

The energy is emitted as a photon whose energy exactly equals the difference between the two shell energies. Because shell energies are fixed and unique to each element, the emitted photon energy is an unambiguous fingerprint. Gold Lα is always 9.71 keV. Copper Kα is always 8.05 keV. Nothing about the sample’s form, temperature, or chemistry shifts these values meaningfully.

This invariance is the entire foundation of XRF as an identification technique. Chemical state, crystal structure, and alloying all leave characteristic line energies essentially untouched.

The Auger effect

Alternatively, the energy is transferred to another electron, which is ejected instead of a photon being emitted. This is the Auger effect, and it produces no detectable X-ray.

The competition between these two outcomes is described by fluorescence yield, which rises sharply with atomic number. For light elements it is very low — most vacancies decay through the Auger channel and emit nothing the detector can see. For heavy elements like gold it approaches unity.

This is the fundamental physical reason XRF is excellent for precious metals and poor for light elements. It is not an engineering limitation that better instruments will overcome; it is atomic physics.

Step three: line series and Moseley’s law

Transitions are named by the shell where the vacancy sat and the shell the filling electron came from. A vacancy in K filled from L gives Kα; filled from M gives Kβ. A vacancy in L filled from M gives Lα.

Henry Moseley established in 1913 that the frequency of a characteristic line varies with the square of atomic number — Moseley’s law. The practical consequence is that line energies increase monotonically and predictably across the periodic table, which is why an energy value maps cleanly to an element.

Why every element produces multiple lines

A single element emits a family of lines: Lα, Lβ, Lγ, each with sub-components. This redundancy is analytically valuable. When one line is obscured by an overlap from another element, the software can quantify using a different line from the same series.

Gold, for example, presents Lα at 9.71 keV and Lβ at 11.44 keV. If something interferes at 9.71, the Lβ line provides an independent route to the same answer. Robust quantification software checks consistency between lines of the same element — a mismatch is a strong signal that an overlap is being mishandled.

The overlaps that cause real errors

Certain pairs sit close enough to challenge the detector’s resolving power:

• Tungsten Lα (8.40 keV) against gold Lα (9.71 keV) — relevant to counterfeit screening
• Lead Lα (10.55 keV) against arsenic Kα (10.54 keV) — effectively coincident, requiring secondary lines
• Rhodium, palladium and silver L lines within 2.70–2.98 keV — a crowded cluster affecting plated white gold
• Zinc Kβ (9.57 keV) against gold Lα (9.71 keV) — matters in brass-based counterfeits

Whether these can be separated depends on detector energy resolution, which is covered in detail in our detector technology comparison.

Step four: from peak intensity to concentration

Identifying elements is the straightforward part. Converting peak intensities into percentages is where most of the difficulty lives, because intensity is not proportional to concentration in any simple way.

The matrix effect

Every element in a sample affects the measured intensity of every other element. Two mechanisms operate simultaneously and in opposite directions.

Absorption

Fluorescent X-rays generated inside the sample must escape before reaching the detector. On the way out they can be absorbed by other atoms. A heavy matrix absorbs strongly, suppressing the apparent intensity of elements within it. Copper fluorescence emerging from a gold-rich alloy is attenuated far more than the same copper fluorescence emerging from an aluminium matrix.

Secondary fluorescence (enhancement)

The reverse also happens. If element A emits a photon energetic enough to excite element B, then B fluoresces from A’s emission in addition to the tube’s. B’s apparent concentration is inflated.

In gold alloys, gold L emission at 9.71 keV sits above the copper K absorption edge at 8.98 keV, so gold actively enhances copper. Without correction, the copper reading is systematically high and, since totals normalize to 100%, the gold reading is correspondingly low.

Why this matters commercially

Matrix effects are not small. Uncorrected, they routinely shift results by several percent — far larger than the counting statistics that dominate the error bars people usually worry about. On a settlement basis, a systematic 2% error on gold content is a permanent margin leak on every transaction.

Step five: the correction models

Two families of approach exist, and knowing which one an instrument uses tells you a great deal about when to trust it.

Empirical calibration

The instrument is calibrated against certified reference materials of known composition, and regression coefficients are fitted to reproduce those known values. Within the compositional range covered by the standards this approach is highly accurate — often the most accurate available.

Its weakness is extrapolation. Present a sample outside the calibrated range and accuracy degrades without warning. An instrument calibrated on 14K–24K yellow gold will produce a number for a palladium white gold sample, and that number may be substantially wrong. The instrument does not know it is extrapolating.

Fundamental parameters

The FP method calculates expected intensities from first principles — tube spectrum, absorption cross-sections, fluorescence yields, detector efficiency — then iterates the assumed composition until calculated intensities match measured ones.

FP handles unknown and unusual compositions far more gracefully because it is not bound to a calibration range. It is generally slightly less accurate than a well-built empirical calibration operating within its designed range, but far more reliable outside it.

Most commercial instruments use a hybrid: FP as the backbone, with empirical adjustment applied for the alloy families the machine is expected to encounter most.

The tube: where the incident radiation comes from

Everything described so far assumes photons arriving at the sample. Their source shapes what the instrument can and cannot do, and tube choice is one of the least discussed variables in instrument specification.

Bremsstrahlung and the characteristic contribution

An X-ray tube accelerates electrons into a metal target. Two emission mechanisms result. Electrons decelerating in the target’s electric field emit a continuous spectrum called bremsstrahlung, spanning from near zero up to the applied voltage. Simultaneously, the electrons ionize the target’s own atoms, producing that element’s characteristic lines superimposed on the continuum.

Both components excite the sample. The continuum provides broad coverage; the characteristic lines provide intense excitation at specific energies. Where those target lines fall relative to the absorption edges of the elements you care about determines sensitivity.

Why rhodium targets dominate precious metals instruments

Rhodium’s K lines sit at approximately 20.2 keV and its L lines at around 2.7 keV. The K emission falls comfortably above the L absorption edges of gold, platinum, and the surrounding heavy elements, providing efficient excitation exactly where precious metals analysis needs it.

Tungsten targets are also used and offer higher output, but tungsten’s own L lines at 8.40 keV land inconveniently close to gold’s Lα at 9.71 keV. The tube’s own emission scatters off the sample and appears in the spectrum, and separating tube-scattered tungsten from sample tungsten requires care. For counterfeit screening where tungsten is the element of interest, this is a genuine complication.

Filters and why they change results

Primary beam filters sit between tube and sample, selectively absorbing part of the incident spectrum. A filter that removes the low-energy continuum reduces background in the region where light-element lines appear, improving their detection. A filter that removes the tube’s characteristic lines prevents those lines from swamping a nearby region of interest.

Instruments typically switch filters automatically according to the selected measurement mode. The practical implication for operators is that mode selection is not cosmetic. Running a plating-detection measurement in a bulk-alloy mode changes the excitation conditions and can change the answer. When results look wrong, verifying that the correct mode was active is a faster diagnostic than recalibration.

Geometry: the variable operators actually control

Tube, detector, and correction model are fixed at manufacture. Sample geometry is decided fresh with every measurement, and it is the largest source of avoidable variation in daily use.

Distance and the inverse square relationship

Measured intensity falls roughly with the square of the distance between sample and detector. A sample sitting 2 mm higher than the calibration geometry does not produce a slightly different reading; it produces a substantially weaker signal in every channel.

Quantification normalizes across elements, so uniform intensity loss partially cancels. But the cancellation is imperfect, because absorption in the intervening air is energy-dependent — low-energy lines are attenuated more than high-energy ones. The net effect is a composition shift, not merely a noisier reading.

Surface angle and shadowing

Curved surfaces such as ring shanks and bangles present a varying angle to the beam. Part of the illuminated area may be angled away from the detector, and raised features can shadow the region being measured.

This is why a flat, presented surface consistently outperforms a curved one, and why readings taken on the inside of a ring band frequently disagree with readings from a flat outer face. Neither is wrong; they are different measurements.

Sample size relative to beam spot

If a sample is smaller than the analyzed spot, part of the beam misses it entirely and the detector sees the sample holder, the chamber floor, or air. Small items — chain links, earring posts, tiny findings — are especially prone to this, and the contamination is not always obvious in the result.

The reliable habit is checking that the item fully covers the measurement aperture before accepting any number from it.

Why two instruments disagree on the same item

This question arises constantly in disputes between buyer and seller, and the physics above explains most cases without either instrument being faulty.

• Different calibration families. One machine calibrated on yellow gold, the other on a broader alloy set, will diverge on an unusual composition — and the yellow-gold machine gives no indication it is extrapolating.
• Different measurement spots. On a plated, soldered, or surface-enriched piece, two spots genuinely differ. Both readings are correct measurements of different material.
• Different detector resolution. Where an overlap exists, a lower-resolution instrument may be deconvolving a blended peak while a higher-resolution one separates it cleanly.
• Different measurement duration. A short reading has wider statistical scatter. Two short readings can differ by more than their apparent precision suggests.
• Different modes or filters. Excitation conditions differ, so sensitivity differs across the element range.

Resolving a dispute therefore starts with establishing whether the two measurements were comparable at all, before anyone concludes an instrument is out of calibration. Measuring the same certified reference material on both machines settles the question quickly and objectively.

The assumption nobody states: infinite thickness and homogeneity

Every quantification model above rests on two conditions that a great deal of real jewelry violates.

Infinite thickness

The models assume the sample is thick enough that making it thicker would not change the measured signal. This threshold is the critical depth, and it depends on both the matrix and the energy of the line being measured.

For gold L lines in a gold matrix, critical depth is on the order of 20–60 microns. Anything thinner and the substrate underneath contributes to the signal.

A hollow bangle with a 0.3 mm wall satisfies infinite thickness comfortably. A gold-filled item with a 40-micron layer sits right at the boundary. An electroplated item with a 0.5-micron layer violates it completely — and the instrument will still return a confident-looking number.

Homogeneity

The models assume composition is uniform throughout the analyzed volume. Real pieces routinely are not:

• Solder joints are typically lower karat and silver-rich compared to the body
• Surface enrichment from pickling or polishing depletes base metals in the top few microns, making the surface read higher than the bulk
• Plating and rhodium flash present an entirely different composition at the surface
• Casting porosity and segregation produce genuine local composition variation

Because XRF only sees the top tens of microns, surface enrichment is a systematic bias toward higher apparent purity. On a heavily polished piece the effect can reach a full karat. This is the physical reason a multi-spot protocol is not optional — see our plated versus solid gold tutorial for the practical procedure.

Where the light-element blind spot bites

Because fluorescence yield collapses for low atomic numbers, elements below roughly sodium (Z=11) are effectively invisible to a standard benchtop instrument. Even magnesium, aluminium and silicon are marginal without vacuum or helium purge.

The consequence is not that these elements are reported as zero. It is that they are excluded from the normalization entirely. Results are typically normalized so detected elements sum to 100%, which means any undetected mass is silently redistributed among the elements that were detected.

Practical failure modes:

• A hollow piece filled with lac or resin reports the metal shell composition, telling you nothing about how much of the item’s weight is filler
• A lacquered or epoxy-coated surface attenuates signal without appearing in the results
• Organic residue, polishing compound or skin oil on the test surface shifts readings downward with no indication why

None of these produce an error message. They produce a plausible number. This is why weight cross-checks remain essential alongside XRF for filled and hollow items, a point developed further in our 22K wedding gold guide.

Counting statistics and what precision really means

X-ray emission is a random process governed by Poisson statistics. If N counts are collected in a peak, the standard deviation is √N, so relative precision is 1/√N.

The arithmetic is unforgiving:

• 10,000 counts gives 1% relative precision
• 100,000 counts gives 0.32%
• 1,000,000 counts gives 0.1%

Improving precision by a factor of ten requires one hundred times the counts. This is why measurement times lengthen so sharply when high precision is demanded, and why detector count-rate capability translates directly into how long an operator waits.

Precision is not accuracy

This distinction causes more misplaced confidence than any other concept in XRF. Counting statistics describe repeatability — how tightly repeated measurements cluster. They say nothing about whether that cluster sits at the correct value.

An instrument with a calibration error, an unrecognized matrix effect, or a plated sample will produce beautifully repeatable wrong answers. Ten readings agreeing to 0.05% feels authoritative and may all be a full karat off.

The only defense against systematic error is verification against certified reference material, which is a scheduled discipline rather than a property of the instrument. Our calibration guide covers building that routine.

Reading a spectrum rather than a table

The composition table is an interpretation. The spectrum is the measurement. Operators who develop the habit of glancing at the spectrum catch problems the table conceals.

Peak shape

A genuine single-element peak is close to symmetric. Shoulders, asymmetry, or a flattened top usually indicate two unresolved peaks being reported as one.

The scatter region

Coherent and incoherent scatter peaks from the tube target appear at the high-energy end. Their ratio is sensitive to the average atomic number of the matrix, and an unexpected shift there is an early warning that the sample is not what the calibration assumes.

Unexplained peaks

A small peak at an energy no expected element accounts for deserves attention. It may be a genuine trace element, a pile-up artifact, or an escape peak. All three are informative; none should be ignored.

Background level

An unusually high background relative to peak height suggests poor sample-to-detector geometry, an unclean window, or an inappropriate filter setting.

Frequently asked questions

Why can XRF not measure the karat of a plated item?

XRF only interrogates the top few tens of microns of a sample. If the surface layer is thicker than roughly a micron, the instrument measures the plating rather than the substrate. The result is a real measurement of the wrong material, which is why it looks plausible rather than obviously wrong.

Does XRF damage the sample?

No. The photoelectric interactions involved are non-destructive and leave no mark, no heating of consequence, and no residual radioactivity. The sample is unchanged and can be measured repeatedly.

Why do gold analyzers use L lines instead of K lines?

Gold’s K absorption edge is at 80.7 keV, far above the tube voltage of a typical benchtop instrument. L lines, requiring around 11.9 keV, are readily excited within the available voltage range. This is a hardware constraint, not an analytical preference.

What is the matrix effect in simple terms?

Elements in a sample interfere with each other’s measured signal. Heavy elements absorb the fluorescence of lighter ones on its way out, suppressing them; and an element can be excited by a neighbor’s emission, inflating it. Both happen at once, and correction models exist specifically to unwind them.

Can XRF distinguish gold alloys from gold-plated tungsten?

At the surface, yes — tungsten Lα at 8.40 keV is resolvable from gold Lα at 9.71 keV by a good detector. For a tungsten core buried under substantial gold, no. XRF cannot see deeper than a few tens of microns, so density, ultrasonic, or destructive methods are required.

Why do readings differ between two spots on the same item?

Either the item is genuinely non-homogeneous — plating, solder, surface enrichment, casting segregation — or the measurement geometry changed between readings. Both are real effects. Consistent variation across spots is diagnostic information, not instrument noise.

What does normalization to 100% hide?

Any element the instrument cannot detect is excluded from the sum, and its mass is implicitly redistributed among detected elements. Light elements, organic fillers, and coatings therefore inflate the apparent concentration of everything else without generating any warning.

Is a longer measurement always more accurate?

Longer measurement improves precision, following the 1/√N relationship, but does not correct systematic error. If a calibration is wrong or a sample is plated, a longer count produces a more precisely wrong answer. Accuracy comes from correct calibration and sound sampling, not from time.

What the physics implies for daily practice

Three conclusions follow directly from everything above, and they are worth stating plainly:

XRF measures the surface, always. Every claim about bulk composition is an inference that rests on the sample being homogeneous. When that assumption is unsafe — plating, solder, filled hollows, heavy polish — multi-spot testing and cross-checks are mandatory rather than cautious.

The instrument cannot tell you when it is extrapolating. A calibration built for one alloy family will return a confident number for a sample outside it. Knowing which families your instrument was calibrated against is part of knowing what its results mean.

Repeatability is not correctness. Tight agreement between readings tells you the measurement is stable, not that it is right. Only reference material verification tells you the latter.

For how detector hardware determines which of these overlaps can be resolved at all, see our SDD versus Si-PIN comparison. For the depth constraint in quantitative detail, see plating thickness measurement limits.