Mineralogy Database

Fermion Index

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Fermion Index

Definition

The Fermion Index calculated for each species is the sum of all fermion atomic isotopes in the mineral species' empirical formula. This calculation assumes the following:
  1. The overall contribution for each isotope in each mineral matches the natural abundance (no isotopic fractionation) of that element.
  2. Each unit cell is electrically neutral.
  3. Lattice effects on the position of each element are ignored.

Calculation of Fermion Index

The calculation of the fermion index is fairly straightforward, each element in the periodic table is generally composed of a mixture of isotopes. Each neutral isotope is either a fermion atom or a boson atom.

  •  Fermion Atom - Sum of all neutrons, protons, and electrons is an odd number.
    • Has an odd half integer spin (i.e. 1/2, 3/2, 5/2, etc.).
    • Obeys Fermi-Dirac quantum mechanical statistics.
  •  Boson Atom - Sum of all neutrons, protons, and electrons is an even number.
    • Has an even net spin (i.e. 1, 2, 3, etc.).
    • Obeys Bose-Einstein quantum mechanical statistics.

For each element, the fermion index is the sum of all fermion atomic isotopes times the natural abundance. See Example for:

Naturally Occurring Sodium (Na) Isotopes
Isotope Protons Neutrons Electrons Fermion/Boson % Natural Abundance Fermion Index
11Na23 11 12 11 (11+12+11=34) Boson 100.00 % 0.0

Fermion Index for Naturally Occurring Sodium

 0.0

Naturally Occurring Barium (Ba) Isotopes
Isotope Protons Neutrons Electrons Fermion/Boson % Natural Abundance Fermion Index
56Ba130 56 74 56 (56+74+56=186) Boson 0.1060 % 0.0
56Ba132 56 76 56 (56+76+56=188) Boson 0.1010 % 0.0
56Ba134 56 78 56 (56+78+56=190) Boson 2.4170% 0.0
56Ba135 56 79 56 (56+79+56=191) Fermion 6.5920% 0.06592
56Ba137 56 81 56 (56+81+56=193) Fermion 11.2300% 0.11230
56Ba138 56 82 56 (56+82+56=194) Boson 71.7000% 0.0

Fermion Index for Naturally Occurring Barium

 0.17822

For each mineral, the fermion index for each element is summed from the mineral's empirical formula and is presented in the Calculated Property section on the Mineral Species page. The boson index for each mineral is simply calculated as (1 - fermion index).

Table of Fermion Index Values for each Element

Element Symbol Fermion Index Boson Index Element Symbol Fermion Index Boson Index

Actinium

Ac

0.0000

1.0000

Manganese

Mn

0.0000

1.0000

Silver

Ag

0.0000

1.0000

Molybdenum

Mo

0.2547

0.7453

Aluminum

Al

0.0000

1.0000

Nitrogen

N

0.9963

0.0037

Americium

Am

0.0000

1.0000

Sodium

Na

0.0000

1.0000

Argon

Ar

0.0000

1.0000

Niobium

Nb

0.0000

1.0000

Arsenic

As

0.0000

1.0000

Neodymium

Nd

0.2048

0.7952

Astatine

At

0.5290

0.4710

Neon

Ne

0.0027

0.9973

Gold

Au

0.0000

1.0000

Nickel

Ni

0.0113

0.9887

Boron

B

0.1990

0.8010

Nobelium

No

0.0000

1.0000

Barium

Ba

0.1782

0.8218

Neptunium

Np

0.0000

1.0000

Beryllium

Be

1.0000

0.0000

Oxygen

O

0.0005

0.9995

Bismuth

Bi

0.0000

1.0000

Osmium

Os

0.1770

0.8230

Berkelium

Bk

0.0000

1.0000

Phosphorus

P

0.0000

1.0000

Bromine

Br

0.0000

1.0000

Protactinium

Pa

0.0000

1.0000

Carbon

C

0.0110

0.9890

Lead

Pb

0.2210

0.7790

Calcium

Ca

0.0014

0.9987

Palladium

Pd

0.2233

0.7767

Cadmium

Cd

0.2503

0.7497

Promethium

Pm

0.0000

1.0000

Cerium

Ce

0.0000

1.0000

Polonium

Po

0.0000

1.0000

Calfornium

Cf

0.0000

1.0000

Praeseodymium

Pr

0.0000

1.0000

Chlorine

Cl

0.0000

1.0000

Platinum

Pt

0.3380

0.6620

Curium

Cm

0.0000

1.0000

Plutonium

Pu

0.0000

1.0000

Cobalt

Co

0.0000

1.0000

Radium

Ra

0.0000

1.0000

Chromium

Cr

0.0950

0.9050

Rubidium

Rb

0.0000

1.0000

Cesium

Cs

0.0000

1.0000

Rhenium

Re

0.0000

1.0000

Copper

Cu

0.0000

1.0000

Rare Earth Elements

REE

0.1861

0.8139

Dysprosium

Dy

0.4380

0.5620

Rhodium

Rh

0.0000

1.0000

Erbium

Er

0.2295

0.7705

Radon

Rn

0.0000

1.0000

Einsteinium

Es

0.0000

1.0000

Ruthenium

Ru

0.2980

0.7020

Europium

Eu

0.0000

1.0000

Sulfur

S

0.0075

0.9925

Fluorine

F

0.0000

1.0000

Antimony

Sb

0.0000

1.0000

Iron

Fe

0.0212

0.9788

Scandium

Sc

0.0000

1.0000

Fermium

Fm

0.0000

1.0000

Selenium

Se

0.0760

0.9240

Francium

Fr

0.0000

1.0000

Silicon

Si

0.0467

0.9533

Gallium

Ga

0.0000

1.0000

Samarium

Sm

0.2880

0.7120

Gadolinium

Gd

0.6935

0.3065

Tin

Sn

0.1662

0.8338

Germanium

Ge

0.0780

0.9220

Strontium

Sr

0.0700

0.9300

Hydrogen

H

0.0002

0.9999

Tantalum

Ta

0.0001

0.9999

Helium

He

0.0000

1.0000

Terbium

Tb

0.0000

1.0000

Hafnium

Hf

0.3223

0.6777

Technetium

Tc

0.0000

1.0000

Mercury

Hg

0.3020

0.6980

Tellurium

Te

0.0799

0.9201

Holmium

Ho

0.0000

1.0000

Thorium

Th

0.0000

1.0000

Iodine

I

0.0000

1.0000

Titanium

Ti

0.1293

0.8707

Indium

In

0.0000

1.0000

Thallium

Tl

0.0000

1.0000

Iridium

Ir

0.0000

1.0000

Thulium

Tm

0.0000

1.0000

Potassium

K

0.0001

0.9999

Uranium

U

0.0072

0.9928

Krypton

Kr

0.1185

0.8815

Vanadium

V

0.0025

0.9975

Lanthanum

La

0.0009

0.9991

Tungsten

W

0.1428

0.8572

Lithium

Li

0.0750

0.9250

Xenon

Xe

0.4760

0.5240

Lawrencium

Lr

0.0000

1.0000

Yttrium

Y

0.0000

1.0000

Lutetium

Lu

0.0259

0.9741

Ytterbium

Yb

0.3050

0.6950

Mendelevium

Md

0.0000

1.0000

Zinc

Zn

0.0410

0.9590

Magnesium

Mg

0.1000

0.9000

Zirconium

Zr

0.1122

0.8878

Other References to Fermion Index

There are additional references to the Fermion Index. Caution: Some of these references are based on pseudo-scientific principles.

ORMUS (orbitally rearranged monatomic elements)
Fermion Atoms or Fermi Condensate
Boson Atoms or Bose Condensate

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Example: "fermion index-0.0" finds all minerals that have a FI index value from 0 to 0.09

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