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A supplier can report a small particle-size percentile while a second instrument reports a much larger value for the same mixed population. The results may use different weighting rather than describe different paste. Before comparing D10, D50 or D90 on a conductive silver paste report, identify what is being accumulated: particle count, estimated volume or optical intensity. A percentile without that definition is not a complete receiving-inspection requirement.
Measurement purpose
Make paste particle-size comparisons use the same measurand and expose unrepresented coarse-tail risks.
Specimens and conditions
- Container sample
- Traceable aliquot and known conditioning, settling and mixing state.
- Prepared population
- Documented dilution and dispersion without assuming the state equals material at the screen.
Equipment and records required
- Particle-sizing method: Known principle, diameter convention, native weighting and conversion settings.
- Independent coarse-object observation: Method and detection limits appropriate to the specific upper-tail concern.
Method sequence
- Match
Compare units, weighting and sample definitions.
Record: Measurand comparison sheet.
- Inspect
Review complete curves, repeats and preparation effects.
Record: Raw distributions and preparation history.
- Decide
Separate percentile comparability from coarse-tail and print-performance decisions.
Record: Resolved differences and remaining tests.
Decision and uncertainty
Do not disposition a material change from incomparable percentiles.
Sampling, particle-shape assumptions and conversions can dominate apparent differences.
Materials and incoming-inspection owners.
Traceable outputs
| Record | Required contents |
|---|---|
| Comparable particle report | Units, diameter, weighting, native signal and conversions. |
| Tail-risk review | Target objects, sampling basis, separate observations and print relevance. |
Method review decisions
- Match the weighting basis and diameter definition before comparing supplier and incoming results.
- Keep particle population, sample preparation and calculation model with every reported percentile.
- Treat the upper tail and agglomerates separately; D90 is neither a maximum size nor proof of screen passage.
State what the ninety percent actually measures
A cumulative distribution assigns a fraction of some total to sizes at or below a given diameter. For a number distribution, that total is the counted particles. For a volume distribution, it is the estimated particle volume. The diameter at which the cumulative fraction reaches ninety percent is therefore answering a different question in each case. Label the basis explicitly instead of writing only D90.
The same distinction applies to D10 and D50. A median by particle count is not necessarily a median by particle volume. Also define whether the report describes discrete particles, agglomerates or another dispersed entity under its preparation method. Do not compare an image count of separated grains directly with a report of clusters measured in a liquid and attribute the entire difference to supplier inconsistency.
Identify the diameter that the instrument can support
Irregular flakes and fused clusters do not have one self-evident diameter. An imaging method may report an equivalent projected-area diameter or a selected caliper dimension. A scattering method infers size through a physical and mathematical model. The report should identify its diameter convention, material assumptions and conversion steps. A numerical size alone does not reveal these choices.
This matters for printed conductor pastes that contain nonspherical particles. A volume-equivalent sphere and a flake's longest dimension do not impose the same restriction at an aperture. Avoid converting between methods with a fixed correction factor unless that relationship has been demonstrated for the actual material population and preparation. A repeatable instrument can still be reporting a different measurand from the drawing requirement.
Calculate a simple mixture in both weightings
Consider an illustrative population of ninety-nine spherical particles of diameter 1 micrometer and one spherical particle of diameter 10 micrometers. By number, the small particles make up 99 percent. Under a discrete step-quantile convention, the number-based D90 is therefore 1 micrometer. This example is not a proposed paste formulation or a claim that actual silver particles are spheres.
Sphere volume scales with diameter cubed. The combined small-particle volume is proportional to 99, while the single large particle contributes 1000. The large particle accounts for 1000/1099, approximately 90.992 percent of total volume. The cumulative volume fraction at 1 micrometer is only about 9.008 percent, so the volume-based D90 is 10 micrometers. Neither report is contradictory; their denominators differ.
| Quantity | Small particles | Large particle | Interpretation |
|---|---|---|---|
| Count | 99 | 1 | Number weighting emphasizes the numerous small particles |
| Relative volume | 99 × 1³ = 99 | 1 × 10³ = 1000 | The large particle dominates estimated volume |
| Number fraction | 99% | 1% | Number D90 = 1 µm |
| Volume fraction | 9.008% | 90.992% | Volume D90 = 10 µm |
Do not relabel a converted curve as a direct measurement
Some instruments produce one native signal weighting and offer software conversions to other distributions. Those conversions depend on the model and can be sensitive to measurement noise and assumptions. Keep the original result and conversion settings together. A volume curve calculated from an intensity measurement is not the same evidence as directly measuring each particle's volume.
Do not apply a universal diameter-to-the-sixth rule to every optical instrument or size range. Scattering behavior depends on the method and regime. If a supplier changes the analysis software, refractive-index assumptions or distribution model, assess comparability before treating a shifted percentile as proof of a changed manufacturing lot. Conversely, a similar converted D90 does not prove that the underlying measured signals are unchanged.
Keep sampling and dispersion from changing the population unnoticed
A paste is not automatically ready for a particle-sizing method developed for a dilute suspension. The selected carrier, dilution, mixing and dispersion can alter clusters, dissolve binder components or preferentially lose part of the population. Define a preparation procedure appropriate to the material and method, with the supplier's handling and safety requirements preserved. Record the actual preparation rather than only the final instrument setting.
Compare aliquots and repeats that can reveal nonuniform sampling or unstable dispersion. A sample drawn from the top of a settled jar may not represent the solids distribution throughout the container. If a preparation step intentionally breaks agglomerates, its result describes that prepared state; it does not by itself establish the size of clusters reaching the production screen. Link container sampling to its separate handling procedure rather than using a polished percentile report to bypass it.
Ask a separate question about coarse particles and agglomerates
A D90 value allows ten percent of the chosen weighting to lie above that diameter. It places no finite maximum on the remaining tail. Two pastes can have the same D90 while containing different rare coarse particles, fibers or dried fragments. If the concern is aperture blockage, streaks or local film defects, define an additional observation that addresses those objects rather than tightening D90 without a mechanism.
The relevant method may include a separately justified coarse-particle screen, microscopy or a controlled print assessment. Its detection limit and sampling amount matter when the objects are rare. Do not infer a screen-opening safety factor solely from a percentile and a nominal mesh count. Aperture geometry, emulsion, agglomerate strength, rheology and process state remain separate contributors to print transfer.
Classify a disagreement before changing the material disposition
Start a discrepant-report review by matching units, weighting, diameter convention and population preparation. If those differ, label the comparison as method-mismatched and request like-for-like data. If they match, examine raw distributions, repeatability and the tail rather than reducing the investigation to one percentile. A shift confined to a conversion setting requires a different response from an observed new coarse population.
Keep a retained comparison material where justified and measure it through the same preparation and instrument sequence. This can help distinguish a method change from a lot change, but it does not independently validate the method. Record which difference was actually resolved. A successful recalculation of the same data is not a new physical observation of the incoming paste.
Write a receiving requirement that another laboratory can reproduce
Specify the material state, sampling location and amount, preparation, instrument principle, diameter definition and distribution weighting. Name the percentile calculation convention and any coarse-tail requirement separately. Include the allowed comparison method and the handling of results near a decision limit. A supplier certificate and incoming measurement should refer to this same measurand before their numbers are compared for acceptance.
For a thick film conductor review, provide the substrate, intended printed features and finished-film requirements alongside the particle report. The useful outcome is a defensible interpretation of the material data and its connection to the actual printing question. It is not a claim that one D90 establishes conductivity, fired adhesion, fine-line capability or the acceptability of a stored container.
Send the complete particle-size report
Include the distribution basis rather than only a D90 number.
- Paste identity, sampling and preparation records.
- Raw size distribution, weighting, diameter convention and analysis settings.
- Supplier and incoming methods with their repeat observations.
- Printed feature/aperture concern and any separately observed coarse objects.
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