Thursday, April 28, 2011

The Geometry of Snowflakes - Oxygen Structure

Diagram of binding energy distribution between the electrons in the oxygen molecule

One of the most amazing and plentiful phenomenons in nature, is a snowflake.  Formed in a freezing atmosphere of free water molecules, which lock themselves together in a hexagonally based crystal structure that is delicate and nearly perfectly balanced.  What mechanism creates such a structure?  Why do freezing water molecules arrange themselves so easily and consistently at the 120 degree angle that forms this hexagonal structure?  Our science does not yet provide a good explanation for that.  Ice forms in lots of other configurations too.  And the angles involved in those await explanation as well.

Probably the most important aspect of water -- the thing that causes most of it's unique properties -- is its electric polarity. When an Oxygen atom bonds with two Hydrogen atoms to form water, the Hydrogens always bond to the Oxygen atom at one end.  This makes the hydrogen side of the molecule electro-positive, and the other side, with free electrons, electro-negative.  The opposite charges of the two sides makes water molecules strongly attracted to each other -- and to many other electrically "polar" molecules, which makes water such a good solvent.  This electric attraction is the reason for water's exceptionally strong surface tension.  Which makes water droplets form such perfect spheres, that billions of these droplets reflect and refract sunlight so consistently that we see the whole visible spectrum of light displayed in rainbows all the time.

Like the 120 degree angle formed regularly in snowflakes, liquid or gaseous water has a consistent angular formation.  With the hydrogen atoms always sharing two  sets of two electrons on one side of the Oxgen nucleus.  And the  two Hydrogen nuclei always forming an angle of about 104.4 degrees with each other.

As I mentioned before, The geometry of the various angles in which the elements arrange themselves is not yet fully understood.  There are theories about how the angles result from the attractive and repulsive forces of the electrons in atoms.  But they don't work consistently across different elements.  But we do have descriptions of what the angles are for most elements.  And we know which elements can combine with each other.  As well as the angles that form between them when they do.  But we haven't understood in a convincing way, why the elements form the angles that they do.  We don't have anything that explains the source of the geometry.  We just know what the geometry is.
Below is a model of nuclear formation that goes beyond the current one.  A model that describes the three dimensional configuration of protons and neutrons in a nucleus -- and accounts for the resulting geometry of atomic bonds that science has already determined.  Oxygen is just one example of an element that this model explains the geometry of, more convincingly than the current model.  I'll give a brief description of the model, then focus on the resulting configuration for Oxygen, which determines the known bonding angles that form in both water and snowflakes.

In this model, protons and neutrons are composed of different numbers of the same elements -- called Hawkrings.  There are two types of Hawkrings.  Left(positive) rings and right(negative) rings.  A neutron consists of 4 left Hawkrings and 4 right Hawkrings, joined together in an alternating chain of 8 rings.  The chain joins end to end forming a circle of 8 rings.  The rings are bound together by gluons.  Below is a picture of a neutron in its natural state, a circle.  The shape it forms, if it's not attached to another hadron.  I'll use the term hadron here to refer to either protons or neutrons, or both -- though this term generally refers to anything inside a nucleus.
Proton - natural

A proton is formed from the same configuration as a neutron, except that an additional left ring joins the formation in the center, bonding to the 4 right rings in the outer ring.  This gives a proton a square shape, pictured below.


Neutrons are more flexible than protons.  They can assume the square shape of a proton, when they are bound to other hadrons, or they can accommodate themselves to other shapes.  In the spherical configuration of an Oxygen nucleus, neutrons do both of these things.  A squared proton is below.

Squared Neutron

In the formation of the elements, individual Hawkrings in protons and neutrons become bonded to rings in other hadrons. By gluons, that join these building blocks together in certain shapes.  The four Elements following Hydrogen, Helium(2), Lithium(3), Beryllium(4), and Boron(5), all have box-like shapes.  But the next 5, Carbon(6), Oxygen(8), Nitrogen(9), Fluorine(10) and Neon(11) are all spheres.  Carbon is built on a six-sided ring, with 6 more hadrons filling out the top and bottom.  And the others all built on a similar eight-sided ring, with differing numbers of protons and neutrons above and below, according to their atomic number.

The formation of an Oxygen nucleus is pictured below.  First an alternating ring of 4 protons and 4 neutrons forms a ring.    On top, two protons attach to two opposing neutrons in the ring.  Then two neutrons attach to the ring and to the corners of the protons.  Tying the top together.  And leaving the two protons facing up at almost exactly 45 degrees from horizontal.  Perhaps a little bit higher than that because the neutrons are not attached to the ring as symmetrically as the protons.  The bottom is the same configuration, but rotated 90 degrees relative to the top.
Oxygen Formation

Oxygen(8) is the most perfectly symmetrical of all the spheres.  And it's easy to see how the geometry of the Oxygen nucleus creates the amazing properties of water.  The location of the proton faces in a nucleus determines where an element's electrons will be arranged. In Oxygen, The 8-ring of alternating protons and neutrons means, if you were standing in the center of the nucleus, directly in front, behind and to your right and left, there would be a proton, and an electron extending directly out from each of those.  Above, would be two more protons and electrons.  If you turn 45 degrees left and raise your arms up 45 degrees above horizontal, that's where the two top electrons will be.  Same for the bottom, but you'd rotate 45 degrees right from your original position.  So the top and bottom proton faces are oriented at 90 degrees to one another.  The angles formed by these eight lines fit perfectly with what science has determined about the bonding angles in water and in snowflakes.

Below is a simplified picture of an Oxygen atom. Protons and neutrons are represented as either a red(neutron) or blue(proton) square.  On the top and bottom, only the protons are shown.  Extending from each proton is a line representing the direction of the proton's electron.  With each line, is a small x, y, x axis to show the direction of the electron toward the nucleus.  Either toward you or away from you.  On the number 1 electron, the z axis arrow is pointing down, toward you.  The numbering scheme is present to designate each electron so it can be easily identified in discussing the angles that form around the Oxygen nucleus.
Oxygen Numbered

The next image is a simplified picture of a water molecule.  The two single blue squares are Hydrogen nuclei -- single protons.  Each shares two electrons with the Oxygen atom in covalent bonds. The electrons are single negative Hawkrings.  One bonded to the 1 and 3 electrons.  The other to the 2 and 4 electrons.

H20 Molecule

In liquid or gas form, an Oxygen atom shares two sets of its eight electrons with two hydrogen nuclei in covalent bonds.  Where each Hydrogen nucleus shares two electrons with the Oxygen nucleus.  These two bonds form the  well known angle between the two hydrogen atoms in a water molecule, which is about 104.4 degrees.  The natural angle between the 1, 3 covalent bond and the 2, 4 covalent bond, if the formation was perfect, would be 105 degrees.  But as described earlier, the angle is very slightly changed due to the imperfect neutron formation on the top and bottom of the Oxygen nucleus.
So, the covalent bonds between Oxygen and Hydrogen in liquid water give water molecules the shape seen above, which makes the molecule electrically polar.  The leads to the formation of what is called the Hydrogen bond.  Causing water molecules to stick to each other.  The Hydrogen end of the molecule is electrically positive and the two Hydrogen nuclei form a wedge at 104.5 degrees.  When this wedge is near another water molecule, it is attracted to the negative end of the other molecule, the end on the opposite side of that molecule's Hydrogen end.  The positively charged wedge shares electric energy with the electrons on the negative side of the other water molecule when the molecules come into contact.  The Hydrogen bond is more easily broken and reformed than the covalent bonds that hold each molecule together.  This allows liquid water molecules to move around each other easily, yet they are still strongly attracted or bound to each other.

Now I'lll describe the formation of snowflake crystals.  And here I'll depart slightly from the way our science describes this formation.  As far as I've been able to understand the current thinking on this formation, the bonds between water molecules in snowflakes, remain as they are in liquid water, they just become more static.  That is, the covalent bonds in individual molecules remain intact.  As do the Hydrogen bonds with other molecules.  The only difference is that the molecules become arranged in a hexagonal pattern and stay locked in it while the snowflake is frozen.  But I can't find any explanation of why these bonds form the 120 degree angle required for the snowflake crystal formation.  If anyone reading does understand the reasoning behind this, I'd appreciate hearing about it in comments.
In my model, the bonds between molecules change as water turns to ice.  Instead of a mixture between covalent and Hydrogen bonds, All the bonds are converted to univalent bonds.  Where only one electron is shared between each  Oxygen and Hydrogen nucleus.  Just like in the liquid formation, each Oxygen  nucleus bonds with Hydrogen nuclei among 4 of its electrons.  But, two of the covalent bonds in the liquid formation become univalent with one of the electrons it was bound to as a liquid.  And two new univalent bonds are formed with two other freezing molecules.

Let's look at a picture to see how this would happen.  Below are a few water molecules in the liquid state.

H2o Pre-freeze

All the Oxygen nuclei are covalently bonded to their two Hydrogen nuclei.  The upper two molecules are Hydrogen bonded to the middle molecule.  The middle and lower molecules are also Hydrogen bonded.  The covalent bonds are between the 1, 3 electrons and the 2, 4 electrons for all the molecules.  As the molecules freeze, the 1, 3 bond in the middle molecule becomes univalent with the upper one.  Now it is bound to that molecule with just the number 1 electron.  The 2, 4 bond is similarly reduced to the number 4 electron, which opposes the number 1 electron at 120 degrees.  The number 7 electron's Hydrogen bond also becomes univalent.  The 7 electron opposes both the 1 and 4 electrons at 120 degrees -- they are all in one plane, dividing 360 degrees into 3 120 degree angles -- this is the source of the hexagonal snowflake formation.  The number 7 electron had been Hydrogen bonded to the middle molecule.  Now that bond becomes univalent with the number 7 electron and we have 3 Oxygen molecules rigidly bound in a plane at 120 degrees to each other.  One more univalent bond forms in the middle molecule, with either the 3 or 5 electron.  This bond is not at 120 degrees to any of the other bonded electrons.  It is at roughly 80 degrees to the plane those electrons are in.  This bond is what connects the layers of hexagonal formations in the snowflake structure.

In a single hexagonal snowflake ring, each of the six molecules will have two electrons bonded to two others in the ring.  And they will have one more electron bonded to other molecules forming other hexagons in the same plane.  Each of the six will also have one more bond to a molecule in a ring above or below it.  Three of the six will be bonded above and 3 will be bonded below.  The up or down orientation of these bonds in a single ring alternates as you go around the ring.  This crystal snowflake lattice formation results from the nearly perfect symmetrical geometry of the Oxygen nucleus.

In regular ice, like you have in your freezer -- hexagonal type 1, the formation of water molecules is not as open as in snow. It's more tightly packed, as if you folded a flat hexagon in a weird way.  And joined those together in a tighter formation.  This structure is more dense and stronger than a snowflake structure.  It's strength comes from a simple, sound architectural formation, based on the angles of the Oxygen nucleus.  It also comes from the change to univalent bonds that occurs when water freezes.  When these bonds are formed, water molecules are pushed out of the way so the structure has room to form.  And the crystalized structure of all ice is more open than the arrangement of liquid water.  This is why water has the unusual property of expanding by about 10 percent when it freezes.  This increase in the volume of water begins to take place when the temperature of water drops below 4 degrees Celsius.  And is complete at 0 degrees.  As this bond shifting occurs, the volume of water increases as the bonded molecules become rigidly locked in crystal formations.
In snowflake crystals, the Hydrogens are bonded to the number 1 and 4 electrons.  These two are at almost exactly 120 degrees from each other.  and the number 7 electron opposes both of those at the same angle.  This electron becomes the focus of another bond.  This results in the hexagonal lattice structure in snowflakes, pictured below.  Some of the Oxygen nuclei are turned upside down to make the angles come out right.  And all the bonds are shown as single covalent bonds between oxygen atoms for simplicity.  In an actual snowflake hexagon, Hydrogen atoms would be between the bonds. The purpose of this diagram is to show that the angles in an Oxygen nucleus are the source of the hexagonal lattice crystal structure in snowflakes.

Oxygen Hex Ring

These hexagon structures also form layers one on top of the other.  If you connected another water molecule to the number 5 electron in the leftmost Oxygen nucleus above, and also every alternating nucleus in the circle, they would all join to form another hexagon behind this one. Same thing with the number 5 electron beginning a formation of another hexagon in front of this one.

Two oxygen rings

This idea is also picture below in a diagram borrowed from a website at the following Url.

Snowflake Lattice

And here is a picture of a dendrite snowflake, borrowed from:

Snowflake - Dendrite

In the model I've begun to describe here, each element has a specific three dimensional configuration that produces the arrangement of electrons around its nucleus.  The arrangement of the electrons and their bonding tendencies and angles are easily seen in the nuclear configurations.  And of the 20 or so elements I have figured out so far, the properties all match with those already determined by science.  Other effects, such as magnetism, electric and thermal conductivity and density are also explained by the configurations.
I'm currently working out the angles and bonds in the other organic elements: Carbon, Nitrogen, Phosphorus and Sulfur.  I plan to have another diary up soon describing the bonds in some organic molecules, including DNA.

I also have several diaries describing the whole theory behind this nuclear model.  Including a more thorough description of the mechanics of the nuclear aspect of it.  Anyone interested can find them by searching for diaries by Sneelock, or the tags: Einstein, Physics, Chemistry and Science.  I would recommend reading them in the following order.


New Science

On the Machinery of Motion

Feynman Force

Types of Snowflakes


   A hexagonal prism is the most basic snow crystal geometry
(see the

Snowflake Primer
).  Depending on how fast the different facets
grow, snow crystal prisms can appear as thin hexagonal plates, slender
hexagonal columns (shaped a lot like wooden pencils), or anything in
between.  Simple prisms are usually so small they can barely be
seen with the naked eye.

examples at right show two stubby prisms and one thin plate.  Snow
crystal facets are rarely perfectly flat, being more typically decorated
with various indents, ridges, or other features.

Stellar Plates

   These common snowflakes are thin, plate-like crystals with
six broad arms that form a star-like shape.  Their faces are often
decorated with amazingly elaborate and symmetrical markings.

snowflakes form when the temperature is near -2 C (28 F) or near -15 C
(5 F), as dictated by the

snow crystal morphology diagram

Sectored Plates

   Stellar plates often show distinctive ridges that point to
the corners between adjacent prism facets.  When these ridges are
especially prominent, the crystals are called sectored plates.

simplest sectored plates are hexagonal crystals that are divided into
six equal pieces, like the slices of a hexagonal pie.  More complex
specimens show prominent ridges on broad, flat branches. 


   Dendritic means "tree-like", so stellar dendrites are
plate-like snow crystals that have branches and sidebranches. 
These are fairly large crystals, typically 2-4 mm in diameter, that are
easily seen with the naked eye.

dendrites are clearly the most popular snow crystal type, seen in
holiday decorations everywhere.  You can see these crystals for
yourself quite well with just a simple magnifier.  (See

Snowflake Watching
for more about observing snowflakes.)

Stellar Dendrites

   Sometimes the branches of stellar crystals have so many
sidebranches they look a bit like ferns, so we call them fernlike
stellar dendrites.  These are the largest snow crystals, often
falling to earth with diameters of 5 mm or more.  In spite of their
large size, these are single crystals of ice -- the water molecules are
lined up from one end to the other.

snowfalls contain almost nothing but stellar dendrites and fernlike
stellar dendrites.  It can make quite a sight when they collect in
vast numbers, covering everything in sight.

The best powder snow, where you sink to your knees while skiing, is made
of stellar dendrites.  These crystals can be extremely thin and
light, so they make a low density snowpack.

Hollow Columns

   Hexagonal columns often form with conical hollow regions in
their ends, and such forms are called hollow columns.  These
crystals are small, so you need a good magnifier to see the hollow

how the two hollow regions are symmetrical in each column. 
Sometimes the ends grow over and enclose a pair of bubbles in the ice,
as seen in the last picture on the right.


   Needles are slender, columnar ice crystals that grow when
the temperature is around -5 C (23 F).  On your sleeve these
snowflakes look like small bits of white hair.

of the amazing things about snow crystals is that their growth changes
from thin, flat plates to long, slender needles when the temperature
changes by just a few degrees.  Why this happens remains something
of a scientific mystery.


   These crystals first grow into stubby columns, and then
they blow into a region of the clouds where the growth becomes
plate-like.  The result is two thin, plate-like crystals growing on
the ends of an ice column.  Capped columns don't appear in every
snowfall, but you can find them if you look for them.

first example at right shows three views of a capped column.  The
first view is from the side, showing the central column and the two
plates edge-on.  The other two views show the same crystal from one
end, with the microscope focused separately on the two plates.

Double Plates

   A double plate is basically a capped column with an
especially short central column.  The plates are so close together
that inevitably one grows out faster and shields the other from its
source of water vapor.  The result is one large plate connected to
a much smaller one.  These crystals are common -- many snowflakes
that look like ordinary stellar plates are actually double plates if you
look closely.

first picture at right shows a double plate from the side.  The
second picture shows a double plate with the microscope focused on the
smaller plate.  In the third picture, note the slightly
out-of-focus hexagon that is about one-sixth as large as the main
crystal.  This hexagon is the second side of a double plate,
connected to the main plate by a small axle.

Split Plates
and Stars

   These are forms of double plates, except that part of one
plate grows large along with part of the other plate.  The picture
at right shows all eight ways to make a split star.  Split plates
and stars, like double plates, are common but often unnoticed.

may have to stare at these pictures a bit to see how the two distinct
pieces fit together.  Note how in each case the crystals are
connected in the center with short axles.


   Plates sometimes grow as truncated triangles when the
temperature is near -2 C (28 F).  If the corners of the plates
sprout arms, the result is an odd version of a stellar plate crystal. 
These crystals are relatively rare.

no one knows why snow crystals grow into these three-fold symmetrical
shapes.  (Note however that the molecular structure of triangular
crystals is no different from ordinary six-sided crystals.  The
facet angles are all the same.) 


   Sometimes capped columns form with a twist, a 30-degree
twist to be specific.  The two end-plates are both six-branched
crystals, but one is rotated 30 degrees relative to the other. 
This is a form of crystal twinning, in which two crystals grow
joined in a specific orientation.

crystals are quite rare, but sometimes a snowfall will bring quite a
few.  The picture at the far right shows a 12-sider where the two
halves are widely separated.


   The nucleation of an ice grain sometimes yields multiple
crystals all growing together at random orientations.  When the
different pieces grow into columns, the result is called a bullet
rosette.  These polycrystals often break up to leave isolated
bullet-shaped crystals.

a bullet rosette can become a capped rosette, as shown in the example at
the far right.


   When the pieces of a polycrystal grow out into dendrites,
the result is called a radiating dendrite (also called a spatial

first example on the right shows radiating plates.  The second
example shows a fernlike stellar dendrite with two errant branches
growing up out of the main plane of the crystal.


   Clouds are made of countless water droplets, and sometimes
these droplets collide with and stick to snow crystals.  The frozen
droplets are called rime.  All the different types of snow crystals
can be found decorated with rime.  When the coverage is especially
heavy, so that the assembly looks like a tiny snowball, the result is
called graupel.

first two pictures at right have relatively light rime coverage. 
The final example is completely covered with rime, but you can still see
the six-fold symmetry of the underlying stellar crystal.

Irregular Crystals

   The most common snow crystals by far are the irregular
crystals.  These are small, usually clumped together, and show
little of the symmetry seen in stellar or columnar crystals.