Uncertainty of Measurement

Please bear with me … this is rather convoluted, but I think it raises some interesting issues which are quite widely relevant.

I have an amateur interest in micro-manipulation, both manual and mechanical. What these techniques have in common is that they both require appropriately microscopic tools. Useful tools range from natural spines &hairs to items crafted from metal or glass.

On my ‘project list’ is a glass-working station for making the tools.

These can be heated by gas, electricity, or both. … but for physical contact with molten glass the use of a heated Platinum wire is preferred, because it is not wetted by the glass.

So … I have been on the lookout for Platinum wire, and recently purchased this piece:

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It was described as 99.99% pure Platinum with approximate dimensions of 0.5mm diameter and 100mm length, and an approximate weight of 0.4g

For no particular reason I felt, and still feel, confident that the Seller was honest.

When it arrived, however, I decided to just check that the numbers tallied

The density of pure Platinum is quoted as 21.45 g/cc and therefore my piece should weigh around 0.42g

The Mitutoyo digital calliper suggested some variation between 0.49 and 0.51 diameter,but the wire will never be straight enough for it to be worth using the micrometer.

The length was simply checked against the plastic rule and is near-enough 100mm [it has been cut with nippers, and seeking better accuracy is probably futile]

I then weighed it on my good, but uncalibrated, scale at 0.40g

… which is also happens to be what the seller’s photo of his weighing showed.

All of this together suggests that the material is basically Platinum, but it goes nowhere near proving that it is 99.99% pure.

Using the nominal dimensions the weight is about 5% too low.

The questions that I invite you to ponder are:

What is the overall Uncertainty of Measurement in what I have done ?

and

Given that there is no traceable certification of purity for this piece, is there any affordable way of checking it more accurately.

Please note: I don’t expect any numerical answer to the first question, it is essentially rhetorical. …I just want you to think about the way we put trust in the numbers our instruments display, with little but blind faith.

MichaelG.

If not knowing bother you greatly take it down to a scrappy and offer them a drink to hit it with their xrf gun, if it will work on something that small. The gun will give you the composition percentages.

Thanks for the suggestion, Pete

I’m probably not sufficiently worried to bother doing that, but do you happen to know how accurate those xrf guns are ?

My main point was that attempting to check a claim of 99.99% purity, using ordinary measuring equipment is futile.

MichaelG.

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Edit:__ a bit of self-help here:

 https://ndtlibrary.asnt.org/scholar/access/2017/AccuracyPrecisionandConfidenceinXrayFluorescenceforPositiveMaterialIdentification.pdf

Edited By Michael Gilligan on 22/07/2023 13:47:30

Where I live I would not take it to a local scrap merchant. They know what platinum is and they know it has been nicked. It used to be stolen from my place of work until no scappy would touch it. The last platinum wire stolen was found as binding wire on a chicken run.

Contact your local university and ask if the physics or chemistry department can do a quick spectrographic analysis on it. Your local university is a good one.

However I think you are treating this as an academic exercise. Just melt some glass and see if it will wet the wire.

JA

Spectrography is an ordinary tool (for some). You just cannot use a balance and micrometer for such accuracy.

Edited By JA on 22/07/2023 13:54:46

Redundant

Edited By DiogenesII on 22/07/2023 13:58:29

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… and, regarding your edit: Obviously you are correct, but I was using ‘ordinary’ in the context of a general workshop.

MichaelG.

I think there are two uncertainties in this problem: uncertainty of mass and uncertainty of volume.

It would also be worth verifying the quoted density from a number of sources.

The volume is also a 'composite' number, calculated from a diameter and length.

It might help to think of the uncertainties in each of the sub-elements and see how they might contribute to the overall number.

Since the diameter is squared to find the cross-sectional area, the error in its measurement is also squared.

It is unlikely you would be 5% out on measuring the 100mm length.

If the scales are underweighing and the volume is overmeasured, the two errors conspire together to produce a lower density.

Do a very quick calculation to see how much the nipped ends might reduce the volume.

Is there a practical method to measure it in a different way, perhaps using Archimedes method with distilled water?

What impurities are likely in platinum? Do all likely impurities have densities less than platinum?

Finally, we have had numerous definitions of the inch on this forum in the past. On the same lines, are you using the correct value for pi?

Good response DC31k

I suspect, but cannot currently demonstrate, that the weighing is the biggest contributor to the error [if error it is] … the machine consistently reads 0.40g for repeated weighings, but its ‘minimum division’ is specified as 20mg

Take that, along with the fact that it is uncalibrated, and it seems to be the prime suspect.

It is difficult to visualise either the diameter or length measurement contributing a 5% error, but of course the final answer involves all of them.

For your comfort I would add that most [not all] metals are less dense than Platinum, but in the quantities required to reduce the weight by 5% the wire would surely not perform as Platinum.

MichaelG.

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P.S. my calculator used 3.14159265358979 for Pi

also see: https://www.bullionbypost.co.uk/index/platinum/density-of-platinum/

Edited By Michael Gilligan on 22/07/2023 15:56:28

Michael , Regarding the purity , would your local assay office be able to help ? There used to be one in Chester .

Thanks Trevor; but it’s really of no great concern, … I will in due course, [hopefully] confirm that this piece is not wetted by molten glass, and in that case I will be content to use it.

I might, however, write to the Assay office [or trawl their website] to find out how they would test it for purity.

The acid test using a black stone looks to be very subjective, so I would expect they have moved with the times.

MichaelG.

Edited By Michael Gilligan on 22/07/2023 16:30:17

I think that you would be doing well to measure the volume to within 5%, so that is where any error is likely to lie.

Don't forget that density changes with temperature.

Maybe you should have purchased it from a company that will issue a C of C with it, you will then know exactly what you have.

What you have not told us is the resolution and accuracy of your measuring instruments. If the scale only reads to 0.01g that is a resolution of +_1% on 1gram or +_2.5% on tour 0.4g measurement. And that is just the +_1 count error of ANY digital instrument (quantisation error). You have to add the accuracy of the sale on top of that.
Likewise your digital caliper has a resolution variance of 2%.. As it is squared that is a +_ 4% variance on area. You have to add accurcy on top of that. A micrometer would be a better instrument for this measurement.

Your instruments are not up to the task. As a rule of thumb you need ten times the resolution / accuracy of the measurement you want. I doubt your measurements are within 10%.

Robert.

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Well, Robert, I did tell you about the resolution of weighing scale, and I identified the other two well-known measuring sticks … what I could not [and cannot] tell you is the accuracy and precision of any of them.

Edit: __ and I also explained why I chose not to use the micrometer.

You have highlighted the whole point of the thread … Thank You

MichaelG.

Edited By Michael Gilligan on 22/07/2023 19:34:26

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At what price ?

MichaelG.

perhaps quite cheaply if they realise you have no way to accurately check it!

I'm sure you'll know that a good source of information (and the metal itself) is Johnson Matthey and their website. Therein there's a section "how can I tell if a metal is platinum?" Unfortunately the simple suggested methodology is rather naive and concludes with recommending that density is confirmed to be 21.45 g cm^–3 which was the subject of your original posting : - (
Link

Nevertheless, the website does provide a huge bibliography of articles on platinum and its many alloys.

My purchase of some Pt wire from JM many years ago, came with a certification of purity.

Caveat emptor....

I agree with Robert, you're at the limit of what you can measure with retail equipment. There are 4 measurements, so even 1% per measurement will get you a total of 4%. Getting it right to within 5% is pretty decent.

There is 8% uncertainty in cross sectional area from the diameter measurements...

Can you check density using the Archimedes principle? (Weight in air vs weight in water) You would probably need access to a 4DP balance - N.B. don't assume that the density of water is 1g/cm^3 - it isn't when trying to work to these accuracies.

Anyway, on a separate note, Pure Pt *is* wetted by molten glasses. There is a specific, non-wetting alloy that is Pt5%Au.