REVIEW INVITATION : Awakening the Sleeping Giant: Rediscovering Archimedes' Density Method for Fingerprinting of Multicomponent Alloys

[exchemist]

I'm amazed this is still going on. A pattern has emerged. A simple question is asked -  and the answer is several paragraphs of verbiage, dancing around the issue and  introducing newly invented terminology, but not answering the question.

At the end of the day, no answer has been given to explain how, given that, as @John Cuthber and others have pointed out, a range of compositions can have the identical density, one composition can be positively identified without any extra information being provided. Unless a succinct answer to this can be provided, one is forced to conclude this is all bullshit.   

 

 

Edited November 23, 2024 by exchemist

[JaiHind15]

On 11/23/2024 at 4:36 PM, exchemist said:

a range of compositions can have the identical density, one composition can be positively identified without any extra information being provided

Dear @exchemist and @John Cuthber

Kindly refer the following paragraph and Table 2 in the paper given below:

"On comparing the two Series, values seem to intersect each other at a point where the mass fractions of constituent metals in both compositions become exactly equal to each other (Fig. 2). Thus, only single composition emerges as common (concordant) composition within the two series, which stands as the ‘best probability’ among such a large number of probabilities. Its numerical values have also been found exactly equal to the actual composition of alloy for which the theoretical density was originally calculated. This peculiar pattern constitutes the finger-prints of alloy for a given density. It has also been observed that high precision and accuracy in densities are essentially required because a fractional variation may lead to incorrect results."

Reference:

B.C. Rathore, Pratibha and Bharati, “Theoretical optimisation of constitution of alloys by decoding their densities”, Materials Letters, Volume 61 (June 2007), 2956-2960. https://doi.org/10.1016/j.matlet.2006.10.052

 

[exchemist]

44 minutes ago, JaiHind15 said:

Dear @exchemist and @John Cuthber

Kindly refer the following paragraph and Table 2 in the paper given below:

"On comparing the two Series, values seem to intersect each other at a point where the mass fractions of constituent metals in both compositions become exactly equal to each other (Fig. 2). Thus, only single composition emerges as common (concordant) composition within the two series, which stands as the ‘best probability’ among such a large number of probabilities. Its numerical values have also been found exactly equal to the actual composition of alloy for which the theoretical density was originally calculated. This peculiar pattern constitutes the finger-prints of alloy for a given density. It has also been observed that high precision and accuracy in densities are essentially required because a fractional variation may lead to incorrect results."

Reference:

B.C. Rathore, Pratibha and Bharati, “Theoretical optimisation of constitution of alloys by decoding their densities”, Materials Letters, Volume 61 (June 2007), 2956-2960. https://doi.org/10.1016/j.matlet.2006.10.052

 

No, that paper is behind a paywall, so not acceptable here. Kindly explain how you overcome the objection we are raising, here on the forum, in your own words, with reference to the diagram posted by @John Cuthber.

 

[JaiHind15]

Surely. This should be available without paywall.

Kindly refer the following paragraph, Table 1&2 and Figures 3&4 in the paper given below:

"3.1.1 Decoding Au75 Ag18 Cu7 and Au90 Ag5 Cu3 Zn2 Alloys: Proof of Concept
The Density Decoding System (DDS) was initially put to the test by decoding the densities of imaginary ternary and quaternary alloys into their elemental percent compositions. The alloy Au₇₅Ag₁₈Cu₇ (D=15.68) was subjected as an input parameter in 3-Metals System, selected for Au, Ag, and Cu, with their respective standard densities of 19.32, 10.5, and 8.96, at a 1% scale of discretization (i.e., iterative step, i=1). The system generated three distinct series containing 21, 29, and 8 Probable Iso-density Compositions (PICs), with each series invisibly holding the Most Probable Composition (MPC) as Concordant Compositions (CCs) at serial numbers 8, 19, and 3, respectively, as shown in Table 1. Similarly, the quaternary alloy Au₉₀Ag₅Cu₃Zn₂ (D=17.3928) was tested in 4-Metals System, selected for Au, Ag, Cu, and Zn (d=7.14), at the same scale of discretization. The system yielded six series with 42, 56, 17, 43, 30, 8 and 86 PICs, each series containing MPC as CCs at serial numbers 23, 32, 10, 23, 17, and 46, respectively, as shown in Table 2"

Reference:

Rathore JH, Rathore P, Rathore B, Rathore BC. Awakening the Sleeping Giant: Rediscovering Archimedes’ Density Method for Fingerprinting of Multicomponent Alloys. ChemRxiv. 2024; doi:10.26434/chemrxiv-2024-wxzt9

Edited November 30, 2024 by JaiHind15
Inconsistencies in indentations from reference text

[John Cuthber]

JaiHind15

Never mind all that tripe.
I have a piece of metal with a density of 10.49 exactly.
It's made from all 3 metals Ag, Au, Cu
What is its composition?
If you don't know, just say so.

Edited December 1, 2024 by John Cuthber

[JaiHind15]

4 hours ago, John Cuthber said:

JaiHind15

Never mind all that tripe.
I have a piece of metal with a density of 10.49 exactly.
It's made from all 3 metals Ag, Au, Cu
What is its composition?
If you don't know, just say so.

We decoded density = 10.49 for Au-Ag-Cu and the algorithm found Au_11.5Ag_57.4Cu_31.1 as the composition of the alloy for i=0.1. The results are provided below.

10.49.pdf

[John Cuthber]

17 hours ago, JaiHind15 said:

We decoded density = 10.49 for Au-Ag-Cu and the algorithm found Au_11.5Ag_57.4Cu_31.1 as the composition of the alloy for i=0.1. The results are provided below.

 

10.49.pdf 699.44 kB · 4 downloads

How do you know it isn't a 50:50 mixture of that alloy and pure silver (which has a density of 10.49)?

[JaiHind15]

Hi @John Cuthber,

For 50% Au_11.5Ag_57.4Cu_31.1 + 50% Ag₁₀₀, the resultant density of the alloy is 10.49499847 which is different than ‘10.49 exact’ as provided before. Please see the calculations below:

50% Au_11.5Ag_57.4Cu_31.1 + 50% Ag₁₀₀

Au_5.75Ag_28.7Cu_15.55 + Ag₅₀

Au_5.75Ag_78.7Cu_15.55

[latex]\frac{100}{\frac{5.75}{19.32}+\frac{78.7}{10.5}+\frac{15.55}{8.96}}=10.49499847[/latex]

Please see the details and the reasoning of pure silver computations 10.5 in the previous response:

On 11/14/2024 at 1:50 AM, rathorebc said:

The DDS, effectively displayed the presence of Ag₁₀₀ in result along with three discrete PIC series, each one showing presence of Ag₁₀₀ as Concordant Compositions (CCs), the density spectrum revealing fingerprints of Ag₁₀₀, the triangular plot of PICs showing the Isopycnic Region (IR) of Ag₁₀₀ and 2D projection of two PIC series. The detailed results are enclosed as Figure-1.

The performance of an algorithm that identifies a unique solution for an underdetermined system (mathematically impossible task) is being evaluated here. To ascertain that the result produced is correct or not, the composition of the alloy must be known beforehand for testing purposes, so that after identification the result obtained from DDS can be matched, verified and authenticated accordingly.

 

For instance,

A pure metal or an alloy: Ag₁₀₀ has density of 10.5 (in this case taken as standard density for the DDS).

On subjecting this density (10.5) in DDS as input density with Au=19.32, Ag=10.5 and Cu=8.96 as constituents, it produces numerous compositions from pure metal to ternaries and conclusively determines the only concordant composition i.e. Ag₁₀₀ as the unique solution confirming that the algorithm or the methodology of finding concordance between series effectively works accurately.

If you wish to evaluate the functioning efficiency of this algorithm by testing the alloys of you own compositions, you may access our DDS platform (www.densityfingerprinting.com).

We have evaluated many alloys (from pure metals up to 8-metal alloys) using DDS to understand the functioning and those results are also presented in both papers.

Sincerely,

Jai

Edited December 5, 2024 by JaiHind15
latex issues

[John Cuthber]

On 12/5/2024 at 4:42 AM, JaiHind15 said:

For 50% Au_11.5Ag_57.4Cu_31.1 + 50% Ag₁₀₀, the resultant density of the alloy is 10.49499847 which is different than ‘10.49 exact’ as provided before. Please see the calculations below:

50% Au_11.5Ag_57.4Cu_31.1 + 50% Ag₁₀₀

Au_5.75Ag_28.7Cu_15.55 + Ag₅₀

Au_5.75Ag_78.7Cu_15.55

1005.7519.32+78.710.5+15.558.96=10.49499847

Please see the details and the reasoning of pure silver computations 10.5 in the previous response:

Are you deliberately missing the point?
The actual density of silver is 10.49

You can invent any alloy you like with that density, and I will tell you that you have got it wrong because the real alloy it has more silver (Or less) than you suggest.
Changing the silver content  does not ( to a first order approximation) change the density at all.
If you choose to be a bit more precise then adding silver changes  the density slightly. But you can always get it back to exactly 10.49  by adding either copper or gold.

So, whatever composition you suggest, I can say you are wrong.

Your method simply can not work.

[rathorebc]

On 12/6/2024 at 11:13 PM, John Cuthber said:

Are you deliberately missing the point?
The actual density of silver is 10.49

You can invent any alloy you like with that density, and I will tell you that you have got it wrong because the real alloy it has more silver (Or less) than you suggest.
Changing the silver content  does not ( to a first order approximation) change the density at all.
If you choose to be a bit more precise then adding silver changes  the density slightly. But you can always get it back to exactly 10.49  by adding either copper or gold.

So, whatever composition you suggest, I can say you are wrong.

Your method simply can not work.

Dear @John Cuthber,

This entire analysis was done with the following Metal Densities: Au:19.32, Ag:10.5, Cu:8.96. 

If you are saying that the density used for silver is wrong, that's fine, it can be changed to 10.49 but then it will change all the resultant compositions accordingly. Still, it will identify pure Silver, no problem with that! 

I was wondering why 10.49 was asked all of a sudden. This makes more sense based on the gold copper additions you were proposing to get back to the density of silver with a different composition.

What you propose is definitely correct that there are multiple compositions that share same densities in the continuum that is Iso-pycnic Region, but the moment it is discretized, it shows different behavior allowing DDS to pinpoint the composition.

To your question regarding the DDS excluding any other composition produced for a given density, I would like to reiterate that:
1)    The remaining compositions produced using the equation are probable compositions (in the continuum, there are infinite of them) and they have non-terminating mass percents as a result or reciprocals in the equation.
2)    The termination of the non-terminating numbers produce a deviation ∆D in the alloy density of the remaining compositions (which is completely irrelevant to the functioning of the DDS)
3)    If we go back a bit, @sethoflagos mentioned how taking integer combinations will reduce the remaining number of solutions but there will be multiple solutions left still, well, if you take an equation with reciprocals as we have, then your solutions spread out even farther away to the point that their values go out of bounds [0%,100%] which is evident in ternary plot.
4)    Now, integer combination as the solution is not the best solution as a composition can have fractional mass percents, and we have found that with this same methodology, fractional mass percents also show unique solution condition in the bounds [0,100].

This is why when we take a random alloy -> compute density using equation -> feed density and the metal densities used in computation to DDS -> we get the same exact resultant alloy back regardless of how many metals there are.
This might not be the best solution for this kind of problem or you might think that we manipulated our data, but you can perform your own analysis using our governing equation and you will reach the same conclusions.

What you propose is definitely correct that there are multiple compositions that share same densities in continuum, but the moment it is discretized, it shows different behavior allowing DDS to pinpoint the composition.

[studiot]

Just now, rathorebc said:

What you propose is definitely correct that there are multiple compositions that share same densities in continuum, but the moment it is discretized, it shows different behavior allowing DDS to pinpoint the composition.

I don't know what you mean by 'discretized'   but density has no meaning at the atomic and molecular scale.

You need a sufficiently large sample to use a density model of composition, which is why I asked earlier about sample size.

I am not aware of a satisfactory answer to this issue.

[KJW]

28 minutes ago, studiot said:

I don't know what you mean by 'discretized'

What @rathorebc is referring to is the notion that alloy compositions have discrete value percentages of the individual components, similar to the high-resolution mass example I posted earlier, where the molecular formula can be obtained because the number of atoms of each type in the molecule is discrete (an integer). But to be successful, the density measurements of the alloy and of the individual components of the alloy needs to be very accurate.

 

[studiot]

Just now, KJW said:

What @rathorebc is referring to is the notion that alloy compositions have discrete value percentages of the individual components, similar to the high-resolution mass example I posted earlier, where the molecular formula can be obtained because the number of atoms of each type in the molecule is discrete (an integer). But to be successful, the density measurements of the alloy and of the individual components of the alloy needs to be very accurate.

 

Thank you, that was very clear. +1

Edited December 8, 2024 by studiot

[John Cuthber]

8 hours ago, rathorebc said:

I was wondering why 10.49 was asked all of a sudden.

It's the actual density of silver

 

8 hours ago, rathorebc said:

, but the moment it is discretized, i

What does that mean?
Is it something your model does?
Do you  realise that your model does not affect the density or composition of a piece of metal?
 

 

8 hours ago, rathorebc said:

Still, it will identify pure Silver, no problem with that! 

How can it identify pure silver?
It  can't distinguish it from a silver/ copper/ gold alloy with the same density, and there are essentially an infinite series of those.