Purity of Gold/Composition of Gold Alloy

Eureka!

Eureka!

History traces back as long as 240 BC this wonderful discovery when great mathematician Archimedes discovered the method to decode the density of binary Au-Ag alloy and successfully determined the purity of gold in Crown without de-shaping it in any manner.

But that time only Ag was used as baser metal and one might easily decode the binary alloys of known metals in straight forword manner. Now a days no. of metals are alloyed with gold due to different reasons which makes the alloy complex and its density becomes closely associated to a large no. of probable compositions where it is not possible to point out exactly as to which particular composition does actually belong to the given density.

The most straightforward method is to dissolve the alloy in some mixture of HCl and HNO3. Once in solution, it can be diluted and analyzed with Atomic Absorption or Ion-coupled Plasma Spectrometry. Any reason why this couldn't be done?

I think that the good doctor wants to determine the relative abundance of the component metals non-destructively. Dissolution in aqua regia & AAS, is a one of several ways to determine the composition, but would consume some of the material as a sample. XRF may be the solution, but one would imagine that the object to be analysed is a wrought object which would not allow accurate determination by XRF methods. My guess is that a linear programming solution might give the answer (non-destructively). It's been quite a few years since I did any, so...

If there are any bright young mathematicians out there, they may be able to give us the answer?

Only an exceeding small sample is required for mass spectrometer analysis, which any decent testing laboratory can do.

Bernie Katz

Reasons why not solvable.

Theoretical: Too many unknowns.
You are asking "19.32A + 10.5B + 8.96C + 7.14D = 18.63" .
You would need three more equations.

Practical: The densities are not exact No.s so the mathematical solution
suffers from greater inaccuracies than the No.s themselves.

With precision:

Alloy specific gravity -----18.63 -----14.4852

Minimum Gold wt% -------95.59----- 60.26

Maximum Zinc wt% --------2.19 -----19.57

Maximum Copper wt% ------3.2 ------28.87

Maximum Silver wt% -------4.41 -----39.74

There are a very large number of alloys of these 4 elements with sg 18.63 or 14.4852.

Without additional information the above is all that can be determined.

You cannot solve three unknowns with only a single measurement.

We are very much thankful to all of you who are trying your best to solve the problem in order to help us a lot. Mathematically it is quite untenable to find out more variables than the no. of equations. We have discovered a method, a software based Mathematical Model which has produced the following results:

For SG 18.63 Au=96.998%; Ag=1.001%; Cu=1.000%; Zn=1.000%

(probabilities at 1.0% interval of predefind mass fraction=16)

For SG 14.4852 Au=71.048%; Ag=15.952%; Cu=4.000%; Zn=9.000%

(probabilities at 1.0% interval of predefind mass fraction=727)

The software generates a long list of all probabilities for given density at the interval of 1% of predefined mass fractions (which may be further controlled for 0.1, 0.01 etc.) and then search out the best probability from this database. Surprisingly only single solution is obtained by this method.

This method has been fully described in our research paper entitled, Theoretical optimisation of constitution of alloys by decoding their densities available at following link:

Theoretical optimisation of constitution of alloys by decoding their densities
Materials Letters, In Press, Corrected Proof, Available online 7 November 2006
B.C. Rathore, Pratibha and Bharati doi:10.1016/j.matlet.2006.10.052

We do not intend to advertise our research paper but we are quite annexious to know the scientific merit and value of our findings whether we have done something new.

Dr. B. C. Rathore

A specific gravity of 14.4852 means that a cubic centimeter of alloy will weigh 14.4852 grams.

The weight of the 71.048% Au is 10.29144 grams or volume 0.53268 cm3.

The sum of the volumes of the four elements is only 0.941 cm3. There is a serious flaw in your calculation.

Respected Guest,

Thanks for your comments.

Serious differences are possible due to the variations in standard densities employed to calculate the bulk alloy. Let us calculate again as follows:

SG =14.4852

Software result: 71.0481%Au ; 15.952%Ag; 4.0%Cu; 9.0%Zn

Standard densities: Au=19.32, Ag=10.5, Cu=8.96, Zn=7.14

(g/cm3)

Total volume= 71.048/19.32+15.952/10.5+4.0/8.96+9.0/7.14

= 6.9036 cm3

Density(SG) of alloy= mass/volume=100/6.9036 =

=14.485196 g/cm3

We must also mention here that the software produced as many as 727 probabilities at the 1% interval in predefined mass fractions and each composition in turn shows the same specific gravity (i.e. 14.4852). The most important aspect and implication of our work is, as to how it may be taken as granted that only and only the result displayed is correct. We may explain if desired. Further suggestions shall be highly appreciated.

Dr. B. C. Rathore

Please do explain why only one aswer is consideered correct rather than say 10 results being high probabilities?

Respected Guest,

It is my pleasure to explain how may the best probability be sorted out amongst large no. of probabilities. Let us first understand the working of our technique. We hope that the abstract of our findings may help it. For further details you will have to go through the entire Research Paper as quoted above or contact us personally.

"The proposed computer-based Mathematical Model optimises constitution of multi-component alloys by decoding their densities into elemental percent compositions without prior knowledge of constituent metals. It executes mathematical equations to generate two entirely different series of probable compositions of alloys for their densities according to their standard elemental densities and predefined imaginary mass fractions of constituent metals. It finally compares the series to detect common (concordant) composition, which has always been found exactly equal to the actual composition of alloy. This concordant composition represents the actual composition of alloy, which also constitutes its fingerprints for given density. The technique may be employed for theoretical optimisation and forecasting the constitution of multi-component alloys, even if constituent metals are unknown."

The proposed technique has been regarded as the Density Finger-printing Technique (DFT), which establishes that each particular density value of a particular class of alloy (i.e. gold alloy, silver alloy, copper alloy etc) is always associated to a particular composition which constitutes the peculiar finger-prints of such alloy.

Dr. B. C. Rathore

It seems, the topic ends and there is nothing to say furthermore???????......

May any one suggest me a cheap and best densitometer available to measure the density/specific gravity of irregular solids upto 50g with imaculate precision of at least three decimal places.

We are glad to inform you that the research paper entitled "Theoretical optimisation of constitution of alloys by decoding their densities"
has now been published and may be tracked at the following link:

Materials Letters
Volume 61, Issues 14-15, June 2007, Pages 2956-2960

doi:10.1016/j.matlet.2006.10.052

(Dr. B.C.Rathore)