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

[rathorebc]

 

Dear Members,

It has never been possible to determine the elemental percent composition of multi component alloys of three or more metals from their densities alone using the Archimedes density method. It is because the multicomponent alloys constitute of underdetermined system of linear equations due to exceeding variables than the known values. On the other hand, they are always associated with infinite number of probable compositions, where determining correct composition with absolute certainty is not possible.

Our family's 25-year long research journey has led to the development of the Density Decoding System (DDS), a revolutionary advancement in materials science that offers a novel approach to characterizing and analysing multi-component alloys from their densities alone. By extending the Archimedes’ density method to multicomponent alloys and treating density as encoded information, the DDS overcomes the challenges of unsolvable underdetermined system of linear equations, incomputable infinite Probable Iso-density Compositions (PICs), and identifying true compositions in infinite composition space.

Our paper, titled "Awakening the Sleeping Giant: Rediscovering Archimedes' Density Method for Fingerprinting of Multicomponent Alloys", is currently under review for publication in a reputed journal and has been published as a preprint on ChemRxiv. The methodology, algorithm, and mathematics used in this research have already undergone rigorous peer review in our previous paper, "Theoretical Optimization of Constitution of Alloys by Decoding Their Densities", published in Materials Letters (Elsevier) in 2007.

Our current work has the potential to revolutionize materials characterization and design, with far-reaching implications for various industries.

 Key insights from our study include:

·     Coexistence of chaos and order, the butterfly effect, emergence of order from infinity, and fractal nature of the composition space in alloys.

·     Manifestation of quantum-like phenomena in the classical domain of alloy compositions.

·     Presence of multiple series of Probable Iso-density Compositions (PICs) interconnected through a "True Composition" that replicates as "Concordant Compositions," resembling centromere replication in chromosomes.

·     Establishment of density as a fundamental "genetic code" for alloys, opening new avenues for materials design and discovery.

 To facilitate your review process, we are sharing the following resources:

1.   Current research paper preprint: https://doi.org/10.26434/chemrxiv-2024-wxzt9

2.   Previous peer-reviewed paper: https://doi.org/10.1016/j.matlet.2006.10.052

Links removed

To facilitate a thorough examination and validation of our results, we cordially invite you to visit our DDS platform, which is designed to allow users to instantaneously generate the results presented in our research paper, enabling an extensive evaluation and verification of the veracity of our data and findings. The successful live demonstration at the University of Pennsylvania, USA, on July 26th, 2023, further highlights the significance of our research.

We would be incredibly grateful if you could provide your invaluable comments, views, and suggestions to help refine our research and identify areas for improvement. Your expertise and feedback will be instrumental in shaping the future of this work.

Please feel free to reach out if you have any questions or require further information. You may also frequently share this communication to your colleagues or other scholars or scholastic community for further examination, evaluation, comments or review of our findings.

Thanking you for your time and consideration. We look forward to hearing back from you.

 Best regards,

 Dr. B. C. Rathore (On behalf of authors)

[exchemist]

1 hour ago, rathorebc said:

 

Dear Members,

It has never been possible to determine the elemental percent composition of multi component alloys of three or more metals from their densities alone using the Archimedes density method. It is because the multicomponent alloys constitute of underdetermined system of linear equations due to exceeding variables than the known values. On the other hand, they are always associated with infinite number of probable compositions, where determining correct composition with absolute certainty is not possible.

Our family's 25-year long research journey has led to the development of the Density Decoding System (DDS), a revolutionary advancement in materials science that offers a novel approach to characterizing and analysing multi-component alloys from their densities alone. By extending the Archimedes’ density method to multicomponent alloys and treating density as encoded information, the DDS overcomes the challenges of unsolvable underdetermined system of linear equations, incomputable infinite Probable Iso-density Compositions (PICs), and identifying true compositions in infinite composition space.

Our paper, titled "Awakening the Sleeping Giant: Rediscovering Archimedes' Density Method for Fingerprinting of Multicomponent Alloys", is currently under review for publication in a reputed journal and has been published as a preprint on ChemRxiv. The methodology, algorithm, and mathematics used in this research have already undergone rigorous peer review in our previous paper, "Theoretical Optimization of Constitution of Alloys by Decoding Their Densities", published in Materials Letters (Elsevier) in 2007.

Our current work has the potential to revolutionize materials characterization and design, with far-reaching implications for various industries.

 Key insights from our study include:

·     Coexistence of chaos and order, the butterfly effect, emergence of order from infinity, and fractal nature of the composition space in alloys.

·     Manifestation of quantum-like phenomena in the classical domain of alloy compositions.

·     Presence of multiple series of Probable Iso-density Compositions (PICs) interconnected through a "True Composition" that replicates as "Concordant Compositions," resembling centromere replication in chromosomes.

·     Establishment of density as a fundamental "genetic code" for alloys, opening new avenues for materials design and discovery.

 To facilitate your review process, we are sharing the following resources:

1.   Current research paper preprint: https://doi.org/10.26434/chemrxiv-2024-wxzt9

2.   Previous peer-reviewed paper: https://doi.org/10.1016/j.matlet.2006.10.052

To facilitate a thorough examination and validation of our results, we cordially invite you to visit our DDS platform, which is designed to allow users to instantaneously generate the results presented in our research paper, enabling an extensive evaluation and verification of the veracity of our data and findings. The successful live demonstration at the University of Pennsylvania, USA, on July 26th, 2023, further highlights the significance of our research.

We would be incredibly grateful if you could provide your invaluable comments, views, and suggestions to help refine our research and identify areas for improvement. Your expertise and feedback will be instrumental in shaping the future of this work.

Please feel free to reach out if you have any questions or require further information. You may also frequently share this communication to your colleagues or other scholars or scholastic community for further examination, evaluation, comments or review of our findings.

Thanking you for your time and consideration. We look forward to hearing back from you.

 Best regards,

 Dr. B. C. Rathore (On behalf of authors)

What is meant by treating density as encoded information? Density is just one number. Unless, I suppose, you superimpose knowledge of limits to the range of densities possible for given combinations of elements. Is what you have done something like that?

[swansont]

!

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[rathorebc]

1 hour ago, exchemist said:

What is meant by treating density as encoded information? Density is just one number. Unless, I suppose, you superimpose knowledge of limits to the range of densities possible for given combinations of elements. Is what you have done something like that?

Dear @exchemist,

Thank you for your insightful question. When we say "treating density as encoded information," we are referring to the inherent relationship between the density of an alloy and its elemental composition. Our research goes beyond simply superimposing knowledge of density limits for given combinations of elements.

One of the most significant findings of our work is the discovery of multiple Probable Iso-density Composition (PIC) series interconnected through a "True Composition" (TC) that replicates as "Concordant Compositions" (CCs) across each series. This phenomenon resembles the replication of centromeres during cell division, establishing density as the genetic code for non-living matter. This highlights the fundamental role of information in governing the properties and behavior of matter, as conspicuously affirmed in alloys.

Furthermore, our research demonstrates that density is not merely a numerical ratio between mass and volume but encompasses intrinsic fundamental information about the constitution and composition of matter, encoded within this unique numerical value. The Density Decoding System (DDS) developed in our work successfully decodes this information into elemental percent compositions with absolute accuracy and precision, suggesting that density can be regarded as the genetic code of matter.

By establishing density as the genetic code for non-living matter and bridging the gap between classical and quantum realms, the DDS represents a paradigm shift in materials science. It provides a powerful tool for combinatorial synthesis and characterization of multi-component alloys, opening up new avenues for materials discovery and optimization, and challenging our understanding of the nature of matter.

We hope this clarifies our perspective on treating density as encoded information and highlights the significant insights from our research. If you have any further questions, please do not hesitate to ask.

Best regards,

Dr. B. C. Rathore and Research Team

[exchemist]

1 minute ago, rathorebc said:

Dear @exchemist,

Thank you for your insightful question. When we say "treating density as encoded information," we are referring to the inherent relationship between the density of an alloy and its elemental composition. Our research goes beyond simply superimposing knowledge of density limits for given combinations of elements.

One of the most significant findings of our work is the discovery of multiple Probable Iso-density Composition (PIC) series interconnected through a "True Composition" (TC) that replicates as "Concordant Compositions" (CCs) across each series. This phenomenon resembles the replication of centromeres during cell division, establishing density as the genetic code for non-living matter. This highlights the fundamental role of information in governing the properties and behavior of matter, as conspicuously affirmed in alloys.

Furthermore, our research demonstrates that density is not merely a numerical ratio between mass and volume but encompasses intrinsic fundamental information about the constitution and composition of matter, encoded within this unique numerical value. The Density Decoding System (DDS) developed in our work successfully decodes this information into elemental percent compositions with absolute accuracy and precision, suggesting that density can be regarded as the genetic code of matter.

By establishing density as the genetic code for non-living matter and bridging the gap between classical and quantum realms, the DDS represents a paradigm shift in materials science. It provides a powerful tool for combinatorial synthesis and characterization of multi-component alloys, opening up new avenues for materials discovery and optimization, and challenging our understanding of the nature of matter.

We hope this clarifies our perspective on treating density as encoded information and highlights the significant insights from our research. If you have any further questions, please do not hesitate to ask.

Best regards,

Dr. B. C. Rathore and Research Team

OK, I have to say the attempt an an analogy with DNA sounds seriously overblown. I understand of course that alloys often have a range of possible compositions and so if you know the elements present you may be able to work out what combinations are possible that could give rise to a measured density. But this stuff about "encoded information" being present in a density makes no sense to me.

What are the symbols of the code? In DNA we have a 4 "letter" code: A,C,G,U, denoting the 4 base pairs. A density, being a single number, has no code whatever.  

Can you perhaps give an example of an alloy with, say, 3 components and show how you deduce its composition from density alone? 

 

[studiot]

I see you appear to use spectroscopy.

Can we compare with a simple ternary system eg copper/silver/gold, where colourimetry can be employed ?

Edited Wednesday at 02:49 PM by studiot

[rathorebc]

Dear @exchemist, and @studiot

Thank you for your thought-provoking kind response to our research. We appreciate your perspective and the opportunity to clarify our findings.

While we understand your reservations about the DNA analogy, we kindly request that you thoroughly peruse the contents, results, discussions, and findings explained in detail in our research paper. Our work goes beyond simply comparing density to a genetic code and delves into the intricate relationships between density and elemental composition in alloys.

To facilitate a comprehensive examination and validation of our results, we cordially invite you to explore our Density Decoding System (DDS) platform, which is available on preprinted research paper in “supplementary weblinks”. The DDS platform is designed to allow the users to instantaneously generate the results presented in our research paper. By using the DDS platform, you can extensively evaluate and verify the veracity of our data and findings.

As mentioned in our paper (Section 3.4.4): "This consistent finding invariably underscores that density is not merely a numerical ratio between mass and volume but encompasses intrinsic fundamental information about the constitution and composition of matter, encoded within this magically unique and extraordinary numerical value. This information can be successfully decoded into elemental percent compositions with absolute accuracy and precision, fairly suggesting that density can be regarded as the genetic code of matter."

Furthermore, we encourage you to use the DDS platform to compose imaginary alloys of your own choice using the standard densities provided in the drop-down menu for each element. This hands-on experience will allow you to explore the capabilities of the DDS and gain a deeper understanding of how it decodes alloy compositions from density values.

To address your specific request for an example, we kindly refer you to the comprehensive results presented in our paper, particularly in Tables 3, 4, and 5, and Figures 9 through 13. These sections showcase the DDS's ability to accurately determine the elemental compositions of various alloys, including ternary, quaternary, and higher-order alloys, solely based on their densities.

We believe that a thorough examination of our research paper and hands-on experience with the DDS platform will provide you with a clearer understanding of our findings and the significance of treating density as encoded information in the context of alloy characterization and design.

We greatly appreciate your interest in our work and look forward to engaging in further scientific discourse. If you have any additional questions or concerns after reviewing our paper and exploring the DDS platform, please do not hesitate to reach out.

Best regards,

Dr. B. C. Rathore and Research Team

 

  

 

[exchemist]

24 minutes ago, rathorebc said:

Dear @exchemist, and @studiot

Thank you for your thought-provoking kind response to our research. We appreciate your perspective and the opportunity to clarify our findings.

While we understand your reservations about the DNA analogy, we kindly request that you thoroughly peruse the contents, results, discussions, and findings explained in detail in our research paper. Our work goes beyond simply comparing density to a genetic code and delves into the intricate relationships between density and elemental composition in alloys.

To facilitate a comprehensive examination and validation of our results, we cordially invite you to explore our Density Decoding System (DDS) platform, which is available on preprinted research paper in “supplementary weblinks”. The DDS platform is designed to allow the users to instantaneously generate the results presented in our research paper. By using the DDS platform, you can extensively evaluate and verify the veracity of our data and findings.

As mentioned in our paper (Section 3.4.4): "This consistent finding invariably underscores that density is not merely a numerical ratio between mass and volume but encompasses intrinsic fundamental information about the constitution and composition of matter, encoded within this magically unique and extraordinary numerical value. This information can be successfully decoded into elemental percent compositions with absolute accuracy and precision, fairly suggesting that density can be regarded as the genetic code of matter."

Furthermore, we encourage you to use the DDS platform to compose imaginary alloys of your own choice using the standard densities provided in the drop-down menu for each element. This hands-on experience will allow you to explore the capabilities of the DDS and gain a deeper understanding of how it decodes alloy compositions from density values.

To address your specific request for an example, we kindly refer you to the comprehensive results presented in our paper, particularly in Tables 3, 4, and 5, and Figures 9 through 13. These sections showcase the DDS's ability to accurately determine the elemental compositions of various alloys, including ternary, quaternary, and higher-order alloys, solely based on their densities.

We believe that a thorough examination of our research paper and hands-on experience with the DDS platform will provide you with a clearer understanding of our findings and the significance of treating density as encoded information in the context of alloy characterization and design.

We greatly appreciate your interest in our work and look forward to engaging in further scientific discourse. If you have any additional questions or concerns after reviewing our paper and exploring the DDS platform, please do not hesitate to reach out.

Best regards,

Dr. B. C. Rathore and Research Team

rathorebc@hotmail.com

  

 

No, present an example here please. This is a discussion forum  and we should not be required to go off and read other material in order to understand your claims. You should be able to describe the principle your technique uses and give one simple example of how it is used. 

Secondly, the passage you quote, which I have highlighted in red,  is nonsensical. You cannot say something is "encoded" if there is no code present, which there is not in a single number such as density.  If you are drawing on other information, such as limits on possible ranges of density of certain alloys, or on compositional ranges, then that information is not present in the density number but in the other information you are drawing on. 

Furthermore the generalisation describing density as a "magically unique and extraordinary numerical value"  conveying compositional information about, not just a limited range of alloys, but matter in general, is absurd and completely unwarranted.   

 

Edited Wednesday at 05:19 PM by exchemist

[studiot]

38 minutes ago, rathorebc said:

We greatly appreciate your interest in our work and look forward to engaging in further scientific discourse. If you have any additional questions or concerns after reviewing our paper and exploring the DDS platform, please do not hesitate to reach out.

What's the point of asking further questions since you have failed/refused to answer the first ones ?

[rathorebc]

Dear exchemist,

We appreciate your perspective and the opportunity to address your concerns directly in this forum. To provide a simple example of how our Density Decoding System (DDS) works, let's consider a ternary alloy with a density of 15.56 g/cm³, composed of gold (Au), silver (Ag), and copper (Cu).

Given:

• Alloy density: 15.56 g/cm³
• Constituent elements: Au, Ag, Cu
• Standard densities: Au (19.32 g/cm³), Ag (10.50 g/cm³), Cu (8.96 g/cm³)

Using the DDS, we input the alloy density and the constituent elements with their respective standard densities. The system then computes the Probable Iso-density Compositions (PICs) using a mathematical framework based on modified Archimedes' density equations. The PICs are organized into three distinct series, each containing the "True Composition" (TC) of the alloy as "Concordant Compositions" (CCs).

Through a comprehensive analysis of the PICs and CCs, the DDS identifies the TC of the alloy as Au₇₅Ag₁₅Cu₁₀, meaning the alloy is composed of 75% gold, 15% silver, and 10% copper by mass.

Regarding your second point, we acknowledge that the term "encoded" may have caused some confusion. Our intention was to emphasize that the density value, along with the knowledge of the constituent elements and their standard densities, contains sufficient information to determine the alloy's composition. We apologize for any misunderstanding caused by our choice of words.

You are correct in stating that the information used to determine the alloy's composition is not solely present in the density value itself but also draws upon the knowledge of the constituent elements and their standard densities. The DDS leverages this additional information along with the alloy's density to compute the PICs and identify the TC.

We hope this example and clarification help to address your concerns. If you have any further questions, please feel free to ask, and we will do our best to provide clear and concise answers within the context of this discussion.

Best regards,

Dr. B. C. Rathore and Research Team

rathorebc@hotmail.com

 

[studiot]

12 minutes ago, rathorebc said:

Given:

• Alloy density: 15.56 g/cm³
• Constituent elements: Au, Ag, Cu
• Standard densities: Au (19.32 g/cm³), Ag (10.50 g/cm³), Cu (8.96 g/cm³)

Using the DDS, we input the alloy density and the constituent elements with their respective standard densities. The system then computes the Probable Iso-density Compositions (PICs) using a mathematical framework based on modified Archimedes' density equations. The PICs are organized into three distinct series, each containing the "True Composition" (TC) of the alloy as "Concordant Compositions" (CCs).

Through a comprehensive analysis of the PICs and CCs, the DDS identifies the TC of the alloy as Au₇₅Ag₁₅Cu₁₀, meaning the alloy is composed of 75% gold, 15% silver, and 10% copper by mass.

Thank you for this.

 

How does this compare with the following

268 × 262

 

 

Does it identify the phases since there is no 'alloy' for the greater part of the ternary diagram.

[rathorebc]

18 minutes ago, studiot said:

What's the point of asking further questions since you have failed/refused to answer the first ones ?

Dear @studiot,

We apologize for any confusion or inconvenience caused by our previous responses. We appreciate your interest in our work and the opportunity to address your question directly.

Regarding your suggestion to compare our Density Decoding System (DDS) with a simple ternary system like copper/silver/gold using colorimetry, we believe this is an interesting idea worth exploring. The figure you provided illustrates the relationship between the color and composition of Cu-Ag-Au alloys, which is indeed a well-established method for estimating the composition of these alloys based on their visual appearance.

While colorimetry can be a useful tool for qualitative analysis of certain ternary alloys, our DDS aims to provide a more quantitative and generalizable approach for determining the composition of a wider range of alloys, including those with more than three components. The DDS relies on the precise measurement of an alloy's density and the knowledge of the constituent elements' standard densities to compute the Probable Iso-density Compositions (PICs) and identify the True Composition (TC).

To directly address your question, let's consider an example of a ternary Cu-Ag-Au alloy with a density of 15.56 g/cm³, as mentioned in our previous response. The DDS would input the alloy density and the constituent elements (Cu, Ag, Au) with their respective standard densities (Cu: 8.96 g/cm³, Ag: 10.50 g/cm³, Au: 19.32 g/cm³). By analyzing the computed PICs and Concordant Compositions (CCs), the DDS would identify the TC of the alloy as Au₇₅Ag₁₅Cu₁₀, indicating a composition of 75% gold, 15% silver, and 10% copper by mass.

In this case, the colorimetry method might also provide an estimate of the alloy's composition based on its color. However, the accuracy of the colorimetry method may be limited, especially for compositions near the boundaries between different color regions in the ternary diagram. In contrast, the DDS aims to provide a more precise determination of the composition based on the quantitative measurement of density.

Furthermore, the DDS has the potential to be applied to a broader range of alloys, including those with more than three components, where colorimetry may not be applicable or effective.

We hope this explanation helps to clarify the relationship between our DDS and the colorimetry method for ternary Cu-Ag-Au alloys. We value your input and the opportunity to engage in scientific discourse. If you have any further questions or suggestions, please feel free to ask, and we will do our best to provide clear and concise answers.

Best regards,

Dr. B. C. Rathore and Research Team

 

[exchemist]

1 hour ago, rathorebc said:

Dear exchemist,

We appreciate your perspective and the opportunity to address your concerns directly in this forum. To provide a simple example of how our Density Decoding System (DDS) works, let's consider a ternary alloy with a density of 15.56 g/cm³, composed of gold (Au), silver (Ag), and copper (Cu).

Given:

• Alloy density: 15.56 g/cm³
• Constituent elements: Au, Ag, Cu
• Standard densities: Au (19.32 g/cm³), Ag (10.50 g/cm³), Cu (8.96 g/cm³)

Using the DDS, we input the alloy density and the constituent elements with their respective standard densities. The system then computes the Probable Iso-density Compositions (PICs) using a mathematical framework based on modified Archimedes' density equations. The PICs are organized into three distinct series, each containing the "True Composition" (TC) of the alloy as "Concordant Compositions" (CCs).

Through a comprehensive analysis of the PICs and CCs, the DDS identifies the TC of the alloy as Au₇₅Ag₁₅Cu₁₀, meaning the alloy is composed of 75% gold, 15% silver, and 10% copper by mass.

Regarding your second point, we acknowledge that the term "encoded" may have caused some confusion. Our intention was to emphasize that the density value, along with the knowledge of the constituent elements and their standard densities, contains sufficient information to determine the alloy's composition. We apologize for any misunderstanding caused by our choice of words.

You are correct in stating that the information used to determine the alloy's composition is not solely present in the density value itself but also draws upon the knowledge of the constituent elements and their standard densities. The DDS leverages this additional information along with the alloy's density to compute the PICs and identify the TC.

We hope this example and clarification help to address your concerns. If you have any further questions, please feel free to ask, and we will do our best to provide clear and concise answers within the context of this discussion.

Best regards,

Dr. B. C. Rathore and Research Team

rathorebc@hotmail.com

 

OK, thank you for clarifying that  you are indeed using other input data relating to the constituents. That makes sense now. Saying it was "encoded" in the density number was misleading. You are combining density data on the alloy with density data on the compenents.

But tell me, what are "Archimedes' density equations"? I am aware of Archimedes' Principle (not equation), but that relates to the upthrust due to buoyancy on an immersed object. That does not seem relevant here. Are you referring to something else? 

[studiot]

6 minutes ago, exchemist said:

But tell me, what are "Archimedes' density equations"? I am aware of Archimedes' Principle (not equation), but that relates to the upthrust due to buoyancy on an immersed object. That does not seem relevant here. Are you referring to something else? 

Archimedes was famous for using density to test the purity of the gold supplied to the King.

 

24 minutes ago, rathorebc said:

Dear @studiot,

We apologize for any confusion or inconvenience caused by our previous responses. We appreciate your interest in our work and the opportunity to address your question directly.

Regarding your suggestion to compare our Density Decoding System (DDS) with a simple ternary system like copper/silver/gold using colorimetry, we believe this is an interesting idea worth exploring. The figure you provided illustrates the relationship between the color and composition of Cu-Ag-Au alloys, which is indeed a well-established method for estimating the composition of these alloys based on their visual appearance.

While colorimetry can be a useful tool for qualitative analysis of certain ternary alloys, our DDS aims to provide a more quantitative and generalizable approach for determining the composition of a wider range of alloys, including those with more than three components. The DDS relies on the precise measurement of an alloy's density and the knowledge of the constituent elements' standard densities to compute the Probable Iso-density Compositions (PICs) and identify the True Composition (TC).

To directly address your question, let's consider an example of a ternary Cu-Ag-Au alloy with a density of 15.56 g/cm³, as mentioned in our previous response. The DDS would input the alloy density and the constituent elements (Cu, Ag, Au) with their respective standard densities (Cu: 8.96 g/cm³, Ag: 10.50 g/cm³, Au: 19.32 g/cm³). By analyzing the computed PICs and Concordant Compositions (CCs), the DDS would identify the TC of the alloy as Au₇₅Ag₁₅Cu₁₀, indicating a composition of 75% gold, 15% silver, and 10% copper by mass.

In this case, the colorimetry method might also provide an estimate of the alloy's composition based on its color. However, the accuracy of the colorimetry method may be limited, especially for compositions near the boundaries between different color regions in the ternary diagram. In contrast, the DDS aims to provide a more precise determination of the composition based on the quantitative measurement of density.

Furthermore, the DDS has the potential to be applied to a broader range of alloys, including those with more than three components, where colorimetry may not be applicable or effective.

We hope this explanation helps to clarify the relationship between our DDS and the colorimetry method for ternary Cu-Ag-Au alloys. We value your input and the opportunity to engage in scientific discourse. If you have any further questions or suggestions, please feel free to ask, and we will do our best to provide clear and concise answers.

Best regards,

Dr. B. C. Rathore and Research Team

 

Thank you so much for a much better reply in our discussion forum.

Yesw I rather gathered that you were using modern computer algorithms to search a database of previously observed and tabulated values for a match when presented with a new sample. You and your team deserve full credit for the hard work to determine and tabulate such data.

This of course is also true of colourimetry and spectroscopy more generally.

And yes your method ranges much more widely than colourimetry.

So well done.

[exchemist]

1 hour ago, studiot said:

Archimedes was famous for using density to test the purity of the gold supplied to the King.

 

 

Yes I know the story. The Greeks didn't do algebra, so I was baffled by the reference to "density equations" attributed to Archimedes.

What he did for the king was to measure the volume of a complex object by the water it displaced. There is no obvious equation to be derived from that other than V(crown) = V(water)!  

And Archimedes's Principle is just F = ρgV, which seems to have no bearing on an alloy composed of 2 or more metals, not submerged in any fluid. 

[JaiHind15]

Hi all!

Archimedes proved that the crown was not pure gold by doing the following:
1. Measuring the volume of the crown using immersion in water (Archimedes's Principle)
2. Compare the density obtained from the volume and mass for the crown with that of pure gold

D(crown) ≠  D(pure gold)

Therefore the crown can not be pure gold!

The events could be subject to speculation but, using density, he was able to prove that the crown was not gold.

The density of the alloy is dependent on many factors such as composition, temperature, in some cases even pressure.

Archimedes' work was a qualitative analysis based on the density - composition relationship. Any perturbations in the composition of an alloy will affect its density. Since, the mass percents of each constituent affects the density, this means that the information of constituents is already naturally "encoded" in the form of density, all we need to do is "decode" this information by understanding the dynamics of density-constituent relationship.

The work of Archimedes as described above has been quantified already for binary alloys which utilizes conservation of mass from constituents to alloy and assumes conservation of volume. We extended this relationship further for ternary, quaternary etc. This produces the governing equation:

V=v1+v2+v3...           ---(1)
M=m1+m2+m3...       ---(2)

Rewriting into density terms:

D=M/(m1/d1 +m2/d2 +m3/d3 +....)

In terms of mass percents, this shows a linear relationship. Since there are two equations (1) & (2), only two variables can be uniquely identified, i.e. binary alloys! Extending this for multi-component alloy makes this an underdetermined system.

We tackled the problem of underdetermined system by first considering mass percents (M=100), so the alloy space (VAS) constricts to the area in ternary plot (3-metals), tetrahedral plot (4-metals) etc. Then we discretized. This is Density Decoding System (DDS).

The results of this are the following:

Test alloy: Produce a theoretical alloy density based on the governing equation e.g., Au90Ag5Cu3Zn2 -> 17.3928 [Au:19.32, Ag:10.5, Cu:8.96, Zn:7.14]

 

1) Calibrate DDS: Metal Densities, Iterative Step (used in convergence, dictates the discretization)
     e.g., selected: Au(19.32), Ag(10.5), Cu(8.96), Zn(7.14); i=1

2) Input: Alloy Density (Theoretical)
    e.g., Density: 17.3928

3) Output: Percent Composition for multi-component alloy
    e.g., Alloy: Au90Ag5Cu3Zn2

We have presented upto 8-metal alloy identification using density in the paper.

I hope this clears things as this has been peer reviewed already in 2006. In this paper we delved deeper into the functioning of the algorithm and tried to understand why this method works. In this pursuit, we have found evidences of chromosomal structure of probability distributions of the probable iso-density compositions, butterfly effect stemming from alloy density, principle of vernier caliper in multi-dimensions etc. We wish to share these findings through this paper. Please take a look as we believe it is a fascinating find.

Sincerely,

Jai on behalf of research team

[rathorebc]

On 10/16/2024 at 11:16 PM, studiot said:

Thank you for this.

 

How does this compare with the following

268 × 262

 

 

Does it identify the phases since there is no 'alloy' for the greater part of the ternary diagram.

Dear @studiot,

Thank you for sharing the Cu-Ag-Au ternary diagram, which provides a valuable perspective on the relationship between composition and various properties, such as color and immiscibility, in this alloy system.

To address your question more directly, let's consider how the Density Decoding System (DDS) would approach the analysis of a Cu-Ag-Au alloy with a specific composition, such as 30% gold, 50% silver and 20% copper by weight (Au₃₀Ag₅₀Cu₂₀).

Using the standard densities of the constituent elements (Au: 19.32, Ag: 10.50 g/cm³ and Cu: 8.96 g/cm³ g/cm³), we may calculate the theoretical density of this alloy using the modified Archimedes' density equation:

D = (30 + 50 +20) / (30/19.32 + 50/10.50 + 20/8.96) = 11.7 g/cm³

On inputting the calculated alloy density (11.7 g/cm³) as input parameter along with the constituent elements (Au, Ag and Cu) with their respective standard densities, the DDS executes the modified Archimedes Density equations and calculates all possible Probable Iso-density Compositions (PICs) for input density.

For calculations, DDS supplies Successively increasing Predefined Imaginary Numerical values (SPIN-values) ranging from 1-100 to the third metal and utilises standard densities of constituent metals to calculate PICs.

We have discovered that each density of non-binary alloy essentially consists of multiple PIC series based on ⁿC₂ combinatorial notation, where, n denotes the number of constituent metals in multicomponent alloy. It means that each multicomponent alloy consists of at least three distinct PIC Series, each series containing unique PICs. Interestingly, All the PIC series are essentially containing a common PIC, which we regard as Concordant Composition (CC). All PICs in each series constitute probabilities associated with single input density.

In hundreds of thousands of cases, we have persistently and precisely observed that all the PIC series of a single input density are interconnected together through a Concordant Composition (CC). Which replicates as CCs during computation of PIC series and appears in each individual series akin to the replication of centromere in chromosome.

The corresponding plot of PIC series (trigonal and tetrahedral in case of ternary and quaternary alloys) show convergence (superimposition, Vernier co-incidence, wave interference) in corresponding plots. The point of concordance shows highest probability of being True Composition of alloy, therefore we regard it as Most Probable Composition (MPC) unless conclusively proved being True Composition (TC)

This MPC always constitutes True Composition (TC) of input density when the iterative step (i) is set at the correct accuracy level of such composition. In order to conclusively verify the correctness of result, the DDS fine tunes the process by decreasing iterative step to higher accuracy levels, unless the composition shows convergence. This complex process may not be reproduced here in limited space.

A pdf copy is enclosed herewith to demonstrate the functioning of DDS exhibiting various steps to decode density (11.7 g/cm³) of Au₃₀Ag₅₀Cu₂₀.

In this example, the DDS provides a quantitative determination of the alloy composition based on the density calculation and the PIC analysis. The ternary diagram, on the other hand, offers a graphical representation of the composition space and the expected properties of the alloy at different compositions.

The immiscibility dome in the Cu-Ag-Au system, as shown in the diagram, you have shown in query, indicates a region where the alloy may separate into two distinct phases with different compositions. This information is valuable for understanding the microstructure and phase behavior of the alloy, which can influence its properties and performance.

While the DDS focuses on the quantitative determination of alloy composition based on density, the ternary diagram provides complementary information about the expected properties and phase behaviour of the alloy at different compositions. Combining the insights from both approaches can lead to a more comprehensive understanding of the alloy system and guide the design and optimization of alloys with desired properties.

We appreciate your engagement and the opportunity to discuss the relationship between our DDS and the graphical representation of alloy systems. If you have any further questions or observations, please feel free to share them, and we will be happy to continue the discussion.

 

Dr. B. C. Rathore and Research Team

rathorebc@hotmail.com

 

Dcoding density of ternary alloy by DDS.pdf

[exchemist]

19 hours ago, JaiHind15 said:

Hi all!

Archimedes proved that the crown was not pure gold by doing the following:
1. Measuring the volume of the crown using immersion in water (Archimedes's Principle)
2. Compare the density obtained from the volume and mass for the crown with that of pure gold

D(crown) ≠  D(pure gold)

Therefore the crown can not be pure gold!

The events could be subject to speculation but, using density, he was able to prove that the crown was not gold.

The density of the alloy is dependent on many factors such as composition, temperature, in some cases even pressure.

Archimedes' work was a qualitative analysis based on the density - composition relationship. Any perturbations in the composition of an alloy will affect its density. Since, the mass percents of each constituent affects the density, this means that the information of constituents is already naturally "encoded" in the form of density, all we need to do is "decode" this information by understanding the dynamics of density-constituent relationship.

The work of Archimedes as described above has been quantified already for binary alloys which utilizes conservation of mass from constituents to alloy and assumes conservation of volume. We extended this relationship further for ternary, quaternary etc. This produces the governing equation:

V=v1+v2+v3...           ---(1)
M=m1+m2+m3...       ---(2)

Rewriting into density terms:

D=M/(m1/d1 +m2/d2 +m3/d3 +....)

In terms of mass percents, this shows a linear relationship. Since there are two equations (1) & (2), only two variables can be uniquely identified, i.e. binary alloys! Extending this for multi-component alloy makes this an underdetermined system.

We tackled the problem of underdetermined system by first considering mass percents (M=100), so the alloy space (VAS) constricts to the area in ternary plot (3-metals), tetrahedral plot (4-metals) etc. Then we discretized. This is Density Decoding System (DDS).

The results of this are the following:

Test alloy: Produce a theoretical alloy density based on the governing equation e.g., Au90Ag5Cu3Zn2 -> 17.3928 [Au:19.32, Ag:10.5, Cu:8.96, Zn:7.14]

 

 

 

1) Calibrate DDS: Metal Densities, Iterative Step (used in convergence, dictates the discretization)
     e.g., selected: Au(19.32), Ag(10.5), Cu(8.96), Zn(7.14); i=1

2) Input: Alloy Density (Theoretical)
    e.g., Density: 17.3928

3) Output: Percent Composition for multi-component alloy
    e.g., Alloy: Au90Ag5Cu3Zn2

We have presented upto 8-metal alloy identification using density in the paper.

I hope this clears things as this has been peer reviewed already in 2006. In this paper we delved deeper into the functioning of the algorithm and tried to understand why this method works. In this pursuit, we have found evidences of chromosomal structure of probability distributions of the probable iso-density compositions, butterfly effect stemming from alloy density, principle of vernier caliper in multi-dimensions etc. We wish to share these findings through this paper. Please take a look as we believe it is a fascinating find.

Sincerely,

Jai on behalf of research team

I see a bit of problem with this. The density of an alloy will in generral not be a simple linear interpolation between the densities of the components. There will be a degree of interaction between the different elements present, according to their mutual chemical affinity or otherwise, and effects due to the packing of atoms of dissimilar size in the metal lattice. This is addressed for example in this piece of work: https://www.sciencedirect.com/science/article/pii/S0364591619302524. in which the enthalpy of mixing is used as a way to estimate these effects.

I am also rather confused by the following sentence in your post: " In this pursuit, we have found evidences of chromosomal structure of probability distributions of the probable iso-density compositions, butterfly effect stemming from alloy density, principle of vernier caliper in multi-dimensions etc."  

What is meant by chromosomal structure of probability distributions?

What is meant by a butterfly effect in this context?

What is meant by principle of vernier caliper in multi-dimensions?

 

 

[rathorebc]

On 10/17/2024 at 12:32 AM, studiot said:

Archimedes was famous for using density to test the purity of the gold supplied to the King.

 

Thank you so much for a much better reply in our discussion forum.

Yesw I rather gathered that you were using modern computer algorithms to search a database of previously observed and tabulated values for a match when presented with a new sample. You and your team deserve full credit for the hard work to determine and tabulate such data.

This of course is also true of colourimetry and spectroscopy more generally.

And yes your method ranges much more widely than colourimetry.

So well done.

Dear @Exchemist and @Studiot,

Thank you very much for your kind interest in our work and for taking the time to discuss our research. We appreciate your insights and the opportunity to clarify any misunderstandings.

To address the confusion regarding our methodology, we want to emphasize that the Density Decoding System (DDS) does not rely on exploring a preserved or stored large database to search for the composition corresponding to an input density. Instead, the DDS automatically creates its own real-time database of multiple series of Probable Iso-density Compositions (PICs) based on the ⁿC₂ combinatorial notation, where n represents the number of constituent metals in the alloy associated with the input density.

The DDS explores this instantly created real-time database to conclusively determine the correct composition using the principles of Vernier's coincidence, superimposition, concordance, and wave-interference patterns. The determination of the correct composition with an absolute degree of certainty and accuracy from the real-time database of numerous PICs is a significant achievement, unprecedented in the history of materials science.

It is crucial to note that the number of PICs in the real-time database increases exponentially in higher-order multicomponent alloys due to the gradual increase in the number of constituent metals and PIC series generated for input densities. For example, the densities of octonary alloys consist of 28 PIC series, and sometimes a single series can contain millions of PICs, leading to an NP-Hard situation in decoding the densities of higher-order alloys.

Our work extends the classical Archimedes' density method, which was primarily used merely for qualitative analysis based on the density-composition relationship in binary alloys. We have quantified and extended this relationship further for ternary, quaternary, and higher-order alloys by developing the modified Archimedes' density equations. These equations relate the density of an alloy to the densities and mass fractions of its constituent elements, allowing us to establish a mathematical relationship between composition and density.

The DDS effectively tackles the problem of underdetermined systems by first considering mass percentages (M=100), which constricts the alloy space (VAS) to the area in a ternary plot (3-metals), tetrahedral plot (4-metals), and so on. The system then discretizes the composition space and condenses the infinity by slicing it in various increasing accuracy levels, enabling the computation of PIC series based on ⁿC₂ combinatorial notation and the identification of the True Composition (TC) through the analysis of Concordant Compositions (CCs).

Our research has not only demonstrated the successful identification of alloy compositions up to octonary systems using density alone but has also uncovered fascinating insights into the functioning of the algorithm. We have found evidence of chromosomal structure in the probability distributions of PICs, the manifestation of the butterfly effect stemming from alloy density, perfect order beyond the infinity and the principle of Vernier calliper in multi-dimensions.

We hope this clarifies our methodology and addresses any misunderstandings about our work. We invite you to explore our research paper further, as we believe it presents a fascinating and novel approach to alloy characterization and design. Kindly feel free to reach out if you have any questions or require further clarification/information

Thank you once again for your kind engagement and the opportunity to discuss our research.

Best regards,

 

Dr. B. C. Rathore and Research Team

rathorebc@hotmail.com

[sethoflagos]

4 hours ago, exchemist said:

I see a bit of problem with this. The density of an alloy will in generral not be a simple linear interpolation between the densities of the components. There will be a degree of interaction between the different elements present, according to their mutual chemical affinity or otherwise, and effects due to the packing of atoms of dissimilar size in the metal lattice. This is addressed for example in this piece of work: https://www.sciencedirect.com/science/article/pii/S0364591619302524. in which the enthalpy of mixing is used as a way to estimate these effects.

+1

The referenced discussion document makes no allowance that I can find for alloy density being a function of a lattice structure specific to that alloy. Rather, as you seem to suspect, alloy densities are simply assumed to be mass weighted averages of elemental densities.

As far as I can tell, such a weighted average is calculated from an alloy composition constructed from integer component percentages, and of the infinite potential compositions that match that density, the composition that most closely yields integer percentage values is picked as the 'Most Probable Composition'. It's a few years since I studied statistical analysis techniques and I think I must have missed the lecture on the Hogwarts Sorting Hat.

4 hours ago, exchemist said:

What is meant by chromosomal structure of probability distributions?

What is meant by a butterfly effect in this context?

What is meant by principle of vernier caliper in multi-dimensions?

Best guess:- deadcatting.