Composite Fermions as a foundation of the Periodic Table.

[elas]

Abstract

The aim is to show how the 2-dimensional incompressible fractions of composite fermions theory can be found in 3-dimensional atomic structure and the result used to show the cause of the nature of the elements with supporting comments on electronegativity, electron filling order, and van der Waal’s radii.

 

Introduction

Two problems with current understanding are:

1) The problem of transferring two dimensional Composite Fermions theory into the three dimensional frame of the real world. Jainendra K. Jain[1] found that:

 

‘comparing Composite Fermions[1] theory with real life experiments also necessitates an inclusion of the effects of nonzero thickness of the electron wave function, Landau2 level mixing, and disorder, which are not as well understood as the FQHE3, and the accuracy of quantitative comparisons between theory and experiment is determined largely by the accuracy with which these effects can be incorporated into theory. At present, the quantitative agreement between theory and laboratory experiment is roughly within a factor of two, although a 10-20% agreement has been achieved in some cases1.

 

We show that incompressible fractions of composite fermions can be found in the nonzero structure of atomic elements.

 

2) The second problem concerns the order in which the electron periods of atoms are filled. Dmitri Mendeleev[4] published the first periodic table (1869) based on the order of atomic weights (in rows) and the similarity of chemical properties (in columns), an arrangement that is still in use today.

With the development of modern quantum mechanical theories of electron configurations within atoms, it became apparent that each row in the periodic table corresponded to the filling of a quantum period by electrons; however the current quantum filling explanation is open to question as detailed by Eric R. Scerri5. Scerri emphasises that Pauli’s Noble Prize-winning work6 does not provide a solution to the “closing of the periods” and that the filling order has never been derived from quantum mechanics. Scerri3 also points out that there are more than twenty exceptions to the Madelung rule[4] not all of which have been explained by subsequent theories. We do not propose an alternative theory, but will show what causes current filling order theories to fail.

 

Internal and external compression

External magnetic force compresses electrons in Fractional Quantum Hall Effect3 (FQHE) experiments; internal magnetic force compresses electrons within an atom. The difference between internal and external compression is illustrated in Fig.1 where the positive and negative fractions (black) of the incompressible fractions1 found in Composite Fermions1 experiments are shown together with the Internal Field electron (IFe) and Outer Field electron (OFe) fractions (colour) of the atomic periods; this shows that each Landau level1has a central fractional constant and that all atomic periodic fractions occur at the lower Landau level1. This brings together incompressible classical fractions and the quantum theory incompressible fractions of Composite Fermions[1], both classical and quantum theories being proven by experiment.

 

Theory

In Table 1 cols. 2-8 the electron shells (not the number of electrons) are divided in half and the number of electrons in each half is referred to as Inner Field electrons (IFe) and Outer Field electrons (OFe). This reveals that the number of IFe on each period is constant (1, 2, 6, 10, 19, 28 and 44) and the number of OFe on each period increases in a 1:1 ratio with the increase in the number of protons (Fig.2). The number of protons acting on each field is the same in both the inner and outer fields, therefore the magnetic compression fractions are found by dividing the number of IFe and OFe in each period, by the total number of protons in the nucleus (Table 1 cols. 9-12).

In order to show a similarity with the approximate incompressible fractions of FQHE[3] experiments and Composite Fermions theory the Ife and OFe fractions are simplified to approximate atomic fractions, but it should be noted the exact fractions show that in all elements Inner Field Fraction (IFF) plus Outer Field Fraction (OFF) = 1±0; therefore the theory is non-perturbative and cannot be falsified2

 

Table of elements

The periodic table below shows that within periods 2 to 7 the elements are sandwiched between Alkali and Alkaline Earths at the beginning and the Metalloids and Noble Gases at the end, we interpret that as ‘those elements whose nature is determined by greater internal (nuclear) force and those elements whose nature is determined by greater external force’ respectively. In between are those elements whose nature is determined by overlapping moderate level internal and external forces.

The periodic table and Fig. 1 show that in periods 2, 4, and 6 the gap between the numbers of OFe repeated on the preceding and proceeding periods expands in the order 3:5:7 (Fig. 2:boxed in red). The Fig. 2 inset shows the number of OFe in col. (A) and the increase in the number of OFe in col. (B). The number of elements in each period is given in brackets with the increase in the number of elements in col. ©. This mathematical structure can be attributed to the existence of two opposing (internal and external) forces causing the pairing of non-nuclear periods seen in the periodic table. During formation periods 2, 4, and 6 (where the internal force is the major force) are subject to increasing force causing an expanding divide between the first two elements and the last two elements of each period. Periods 3, 5, and 7 where the constant external force is the major force there is no corresponding increase in the number of elements.

 

 

Period force fields

In the graphs below, electron numbers (Fig. 2) are replaced with IFe and OFe fractions to show how the nature of the elements is determined. There are four fractional sequences in both inner and outer field due to the division of the middle period in the odd numbered periods.

Boxed on fractional sequence 1 of the outer field are:

 

(A) 1H and 2He the first two electrons will be compressed to form the nuclear shell on all elements with higher atomic numbers.

 

(B) The Alkali and Alkaline Earths.

 

© The Metalloids, Other Metals and Non-Metals which change group with compression, and Halogens and Noble gases which retain their group on periods 2 – 7 inclusive.

 

Boxed on fractional sequence 2 is found:

 

(D) The Transitional Metals.

 

On fractional sequence 3 is found:

 

(E) The Lanthanides.

 

(F) The Actinides.

 

It is proposed that the unboxed fractions are responsible for changing the nature of the elements within each group of elements.

Compression of the inner field electrons determines the length of each pair of periods as the electrons of each pair of periods reach the maximum incompressible fraction for each pair of periods on the lower Landau level.

A composite fermium consists of an electron and a vortex, in order to explain why the fractions of atomic electrons occur on the same Landau level as some composite fermions; it is proposed that atomic electron are separated by vortices therefore atoms contain composite fermions.

 

 

Electronegativity, Alkali Earths and Filling Order

With the inner and outer fields in their natural overlapping position, the solid arrows the graph below mark the elements with the highest electronegativity values4 of each period, they precede the first overlapping pair with the highest combined fractional value on each period or, in the case of 9F the element with the highest single fractional value (dashed arrow).

Alkali Earths (dashed boxes) have one less OFe than IFe allowing the nuclear force to compress one electron below the lower force line.

Period’s 1-4 inclusive show that the Madelung rule5 breaks down in areas of high compression where electrons are forced below the lower force line (solid line boxes). 24Cr and 29Cu are unique in that a second electron is forced above the upper force line indicating that the outer force field of 24Cr and 29Cu is too weak to retain more than seven electrons.

 

Calculated and van der Waals radii

On Fig. 9 (A) marks the first element of each period and a peak in the van der Vaal’s radii. (B) marks the first low point of the van der Waal’s radii and occurs where each new force line crosses the lower force line. © marks the second van der Waal’s peak which occurs where two force lines are separated vertically, by one space (shown in triangles).

 

Summary

It has been shown that incompressible fractions can be produced from the known atomic structure and that atomic incompressible fractions occur on the lower Landau level. It has also been shown that the cause of the periodic table can be explained in terms of Atomic incompressible fractions. Additional comments hint at the possibility of using atomic incompressible fractions to explain Electronegativity, Alkali Earths, Filling Order and van der Waals radii.

 

References

[1] Composite Fermions, Jainendra K. Jain. Cambridge University Press, 2007. ISBN-978-0-521-86232-5

[2] Karl Popper, Conjectures and Refutations, London; Routledge ane Keagan Paul, 1963. ISBN 0-415-28593-3

[4] E. Clementi, D.L.Raimondi,, W.P. Reinhardt (1967). "Atomic Screening Constants from SCF Functions. II.

[5] Meek, Terry L.; Allen, Leland C. (2002). "Configuration irregularities: deviations from the Madelung rule and inversion of orbital energy levels". Chem. Phys. Lett. 362 (5-6): 362–64. doi:10.1016/S0009-2614(02)00919-3

[6] Landau, L. D.; E. M. Lifshitz (1977). Quantum Mechanics: Nonrelativistic Theory. Pergamon Press

 

 

Edited May 12, 2010 by elas

[Phi for All]

Thanks for posting this, elas. In the past when you've expended so much effort on a concept, you've had a tendency to bring it up in threads outside of Speculations. Please be reminded that this speculation needs to stay contained in this thread alone.

[elas]

Thanks for posting this, elas. In the past when you've expended so much effort on a concept, you've had a tendency to bring it up in threads outside of Speculations. Please be reminded that this speculation needs to stay contained in this thread alone.

 

Lesson learnt; problem was that I thought that rearranging known data in a novel manner was not speculation, For example, I did not think that the periodic table published here was speculation because all the data used is experimentally proven and no different to the data used to support a number of unsatisfactory theories (see Scerri). The rest is of course speculation based on the re-arrangement.

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Filling order

 

Diversions from Madelung rule are dealt with more fully in diagram below. Which shows that 24Cr, 29Cu and 46Pd have one electron raised one level on the Inner 1 line, and one electron lowered one level on the Outer 4 line.

 

57La and 64Gd have one electron raised one level on the Outer 3 line.

 

78Pt and 79Au have one electron lowered one level on the Outer 4 line.

 

90Th has an electron raised two levels on the Outer 3 line.

 

89Ac, 91Pa, 92U, 93Np and 96Cm have one electron raised one level on the Outer 3 line.

110Ds and 111Rg have one electron lowered one level on the Outer 4 line and therefore are predicted to disagree with the Madelung rule.

 

This leaves 41Nb, 42Mo and 43Tc which having one electron lowered one level on Outer 4 and should disagree with Madelung, but do not. It is suggested that where two theories have different sequences it is possible at some stage that an error of one sequence agrees with the correct sequence.

 

58Ce and 103Lr do have one electron raised one level on Outer 2 and Outer 3 respectively, but as this is part of a climbing sequence in both cases, it would be questionable to claim that as the cause of disagreement with Madelung.

 

19K, 37Rb, 55Cs, and 87Fr Being Alkaline Earths have one less outer electron than inner electrons and therefore one electron forced below the lower force line.

 

Finally it should be noted that diversions from Madelung increase with increases in density; periods 1. 2 and 3 have no diversions, period 4 has 2 diversions, period 5 has 3 diversions, period 6 has 5 diversions and period 7 has 9 diversions.

 

This proposal explains the cause of the diversions from the Madelung filling order by explaining how compression forces electrons into positions above or below their expected filling position.

 

Edited May 14, 2010 by elas
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[elas]

Not made clear in the foregoing is that both inner and outer electron fields are situated in the outer half of the atomic field as shown in the graph below. The next step is to use this proposal to show how neutrons are distributed in a balanced manner within the atomic nuclii. As that does not involve the use of fractions it will be the subject of a separate submission in the near future.

 

[elas]

Submission number 4 on my Periodic Table thread: http://www.scienceforums.net/forum/showthread.php?t=51884

Ended with a graph to illustrate the proposal that the proposed ‘inner’ and ‘outer’ electron fields were both situated in the outer half of a balanced atomic field, in order to do so it was necessary to use a secondary axis.

The graphs below show that the secondary axis can be removed by multiplying ‘force times mass’ (Fm). In the Periodic Table graphs it is the innermost electron shell (excluding the nuclear shell) that follows the only undisturbed force line, this time it is again the innermost electron shell, which now follows the Fm line (top graph). The bottom graph shows all the sub-shell lines given in ‘The Elements' by John Emsley.

 

 

The next step combines the Fm and EBE 2s scales by expressing EBE 2s as a percentage of Fm and compares the result with the number of neutrons for each atomic number; the result is a pairing similar to that found in the Periodic Table with one notable difference. By including a large number of elements that do not occur naturally, the Periodic Table creates a false (i.e. unnatural) pairing of the periods (2:3, 4:5, and 6:7), but the graph below being restricted to naturally occurring elements, shows how neutrons determine the true natural pairing by dividing period 6 into two groups of 16 elements each. Period 7 contains only those radioactive elements that compression has forced well away from both structure lines.

 

 

Edited May 19, 2010 by elas
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[John Cuthber]

Have you tried applying for an Arts Council grant for this work?

 

 

Anyway, I think it remains speculative until this theory

"The aim is to show how the 2-dimensional incompressible fractions of composite fermions theory can be found in 3-dimensional atomic structure "

becomes established.

[elas]

Much to my embarrassment I missed the great simplicity predicted by Newton even though it was blindingly obvious, the equation is:

 

inner field fraction minus outer field fraction equals the periodic fraction

 

the periodic fractions is so-called because this single column of fractions contains the periods in their correct order. A graph of this single column and the Table of Fractions is shown below.

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Have you tried applying for an Arts Council grant for this work?

 

 

Anyway, I think it remains speculative until this theory

"The aim is to show how the 2-dimensional incompressible fractions of composite fermions theory can be found in 3-dimensional atomic structure "

becomes established.

 

1) No grant, but I have heard T shirt printing mentioned.

2) Is there any other classical mathematical theory that produces the periodic table and predicts the nature of the transuranium elements?

3)The link with Composite Fermion theory is intended to solve a problem of that theory; my work is classical physics and will stand alone without CF theory.

 

PS Anyway, it's good to see you are still on your usual form! All I want now is a comment from insane alien to make my day complete.

Edited May 19, 2010 by elas
Consecutive posts merged.

[elas]

Have you tried applying for an Arts Council grant for this work?

 

 

Anyway, I think it remains speculative until this theory

"The aim is to show how the 2-dimensional incompressible fractions of composite fermions theory can be found in 3-dimensional atomic structure "

becomes established.

 

I hope the following will help.

 

IQHE refers to an electron or to the number of electrons. FQHE refers to the quasi particle or vortex between bodies. Composite Fermions consist of both particle and vortex.

 

The number of inner field electrons taken from the proposed table of element (Table 2) can be used to illustrate the difference between FQHE and IQHE on one hand and CFs on the other hand. by using the number of atomic electrons on each shell to find the Hall resistance of electrons, and the fraction formed by adjacent shell electron numbers to find the Hall resistance of electron plus vortex.

 

The table below shows the fractions produced using the inner field electrons. 1/3, 3/5, and 10/19 appear in a Table of Incompressible Fractions (Table 7.1 of ‘Composite fermions’ by Jainendra K Jain); 19/28 simplifies to 2/3 which does match the approximate 2/3 fraction found in FQHE and is therefore acceptable (because FQHE produces only approximate fractions). 7/11 is a continuation of the n7 sequence (7/15 and 7/13 appear in Jain’s table). CF states are shown on the left of the table; 4CF-7 being a prediction. Fractions derived from atomic structure are not approximations; they are exact fractions.

 

Atomic fractions are found in Tables of Composite Fermions fractions, but they are not found in the FQHE fractional sequences found by Laughlin, Tsui or Heseilberg, the reason for this is that CF fractions include particle and attached vortex whereas the work of Laughlin et al produces fractions related to either particles or vortex, but not both together . This leads to the conclusion that atomic electrons are attached to (or separated by) vortices. (Composite Fermions by Jainendra K Jain section 1.4).

 

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Vortices shown in the table are found on atomic radials, it follows that similar vortices should be present between electrons on atomic concentrics where they would replace vacuum or Casimir force currently thought to separate electrons. In this interpretation concentric vortices would play a major role in determining the nature of the elements.

Edited July 8, 2010 by elas

[elas]

supplement

 

At present there is no explanation of why periods of the elements start and end at their particular points, an explanation is offered on:

 

http://www.scienceforums.net/topic/50848-gravity-as-the-fundamental-force/page__p__555536__fromsearch__1#entry555536

Edited July 28, 2010 by elas

[John Cuthber]

"At present there is no explanation of why periods of the elements start and end at their particular points"

There was when I was at school.

 

http://en.wikipedia.org/wiki/Aufbau_principle

[mississippichem]

 

 

At present there is no explanation of why periods of the elements start and end at their particular points...

 

 

Its beacause at the end of each period the p-orbitals are full with 6e^- and the aufbau principle states that the next n-level s-orbital must be filled. There are three available m_l quantum #'s for the set of p-orbitals each p-orbital can hold 2 e^-, so then the pauli exclusion principle takes over and electrons must be filled under a different angular momentum quantum number, i.e. the next available s-orbital.

[elas]

"At present there is no explanation of why periods of the elements start and end at their particular points"

There was when I was at school.

 

http://en.wikipedia.org/wiki/Aufbau_principle

 

Your ref. also refers to the paper by Sciara which contains the following:

 

"Of course, most of what I have said so far is well known.

Nevertheless, I hope to have given these issues a new perspective

by adopting an almost perversely rigorous approach

in demanding that every aspect of electronic configurations

should be strictly deducible from quantum mechanics. Although

I am not in a position to propose a better explanation,

I do not think that we should be complacent about what

the present explanation achieves. As I have tried to argue, in

terms of deduction from theoretical principles, the present

semi-empirical explanation is not fully adequate".

 

Please refer the reply to John Cuthber On two submissions¹ we have shown that using magnetic compression to form fractions (following the practice used in the interpretation of FQHE and Composite Fermions experiments); we have produced an explanation that has greater accuracy than the current teaching. This has be done using a single force and a single elementary particle; as the single force is gravity (Relativity) and Composite Fermions theory is part of QED we have a crossover of the two theories. Current models and teachings treat particles and atoms as entities that can be explained without reference to the cause of their structure, by showing the relationship between internal and external forces the proposed theory is fully causal.

 

¹http://www.scienceforums.net/topic/50848-gravity-as-the-fundamental-force/page__p__555536__fromsearch__1#entry555536

Edited July 30, 2010 by elas