Cubic Atom and Crystal Structures

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A possible electron configuration is result of resonance of electronic mass waves and nuclear internal waves. The ground state electron configuration for an element has maximum resonance. Noticeably, the crystal structures of the metals are related to the electron configuration and their orbit angle to the vertical line of the octahedron faces.

2. Results

2.1. Electron Movements

Since the nuclei are octahedron shape ^{[1, 2]}, the electronic primary movement direction is vertical to the eight faces of the octahedron. In the other word, an electron collides with one of eight faces of proton and bounces like a ball. Even though an electron has a steady straight line “orbit”, mass waves create wave patterns as they interact with three axes. The “orbit” of electron is from nucleus to a fixed high possibility point of wave pattern.

When the atomic number is one, the nuclei of hydrogen isotopes are shaped as dot or line. The movement of electron makes the nucleus constantly spinning in the gas state in normal temperature. Helium isotopes have line shaped nucleus. When the atomic number (proton count) is greater than two, the nuclei become 2D symmetrical plate or 3D octahedron piles.

The topology of nuclei provides an important clue to re-exam the existing theories [9-41]^[9].

2.2. Cubic Atom

When each octahedron face has an outer shell electron vertical to the face, the outer shell electrons form a cubic for a noble gas elements with eight out most s/p orbits (except helium).

2.3. Triangle Grids and Electron Orbits

The three axes of nucleus interact with the electron mass waves and create diffraction pattern that is similar to the crystalline diffraction. The charged axis has one electronic field interaction, the two uncharged axes have two charged interactions each, positive and negative. Therefore, the charged axis has one wave and uncharged axes have two waves each. The proton/electron diffraction pattern is a triangle pattern. Various electron orbits are related to the layers of triangle strips. Each triangle node represents an “orbit”. Each node is mirrored with a node on the opposite side of proton face.

p: 3*2, d: 5*2, f: 7*2

Figure 2. Electron Diffraction Triangle Grids and Zeeman Splitting

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Electrons are evenly distributed vertical to eight octahedron faces. The possibility of the various electron orbits are based on the strength of electron’s mass wave. The orbit s has highest priority for its high possibilities. The priority order is:

s, p, d and f

In many cases, due to the shape of nucleus, there are exceptions to Madelung rules.

2.4. Orbit Allocations

To simplify the case, the wave function of the orbit on the shell is:

Wx + Wy + Wz

Wx = (2/3)Pi sin (16N Ax)

Wy = (2/3)Pi sin (16N Ay)

Wz = (2/3)Pi sin (8N Az)

N: shell count

Ax: Angle relative to X

Ay: Angle relative to Y

Az: Angle relative to Z (charged axis)

These three waves are independent waves.

Figure 3. Triangle Grids Location

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Even though the electron field vector is from the center of the triangle due to the resonance of the forces, the S orbit is closer to the charged axis.

2.5. Multi-Atom Resonance

When two atoms are close enough, the overlapped shells will have wave resonance as electrons are shared between the two atoms. The wave resonance not only provides straight orbits for the shared electrons, but also merges overlapped triangle grids from two neighboring atoms.

As result the new wave function is:

W1 + W2

When different chemical atoms are mixed together, the molecule structure and wave resonance are related.

3. Discussion

3.1. Quantum Tunnel Effects

As electrons collide with nucleus, the collisions between outer electrons and inner electrons are unavoidable. These collisions are one of reasons for tunneling effect of inner electrons to get out of their orbits.

3.2. Orbit Overlaps

Since the mass waves do not stop at the nodes, the orbit of S, P, D and F extend themselves. The orbit extensions of the neighboring atoms overlap themselves.

Figure 4. Grids overlap

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The above model tells us how tilted axes give a straight orbit for a shared electron.

The orbits are distorted by the nuclear forces, but they are mostly straight and symmetrical to have better resonance.

3.3. Multiple Shells’ Overlaps

The D orbits’ overlaps coexist with the S orbit and inner orbit overlap. For the element of the same period in element periodic table, the electron count is reverse proportional to the distance of the neighboring atom, as the overlapping increases the stabilities.

Propensities as follow reverse proportional to the wave strength of the orbits:

Wave interactions need the similar propensity values to make interaction waves with better contrasts. Most of interactions of the same elements neighboring to one another are the orbits with same quantum numbers, mainly the ones with high propensities. As the waves of these orbits can impact the configuration of electrons and the electron configuration is less stable.

3.4. Crystal Structures of Beryllium

Beryllium has a pair of S orbit with angle of A against the line vertical to an octahedron face. It makes Beryllium Proton axes not perfectly line up with the neighboring atoms even with higher temperature. Beryllium has HCP structure under the room temperature.

Figure 5. Beryllium HCP Crystal

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3.5. Crystal Structures of Calcium

Calcium has a pair of S orbit. It makes Calcium’s Proton axes not perfectly line up with the neighboring atoms. Unlike BCC Potassium, Calcium has FCC structure under the room temperature.

3.6. Crystal Structures of Lithium

The crystal structure of Lithium [42-51]^[42] near 0K is hR9. The hR9 crystal is largely due to the S orbit of the outmost shell is not at the center of the orbital triangle grids. At the room temperature, the rotation movement of nuclei allows nuclei “catch” the off central single S orbit electron when the structure [52-61]^[52] is bcc.

Figure 6. Lithium Phase Diagram

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The existing crystallization theories [62-70]^[62] provide explanations for the crystal preferences under the pressure mainly based on entropy. The topology of atom provides visual explanations. Under the pressure of 10 to 40 Pa, inner shell S orbit electrons become main factors. FCC crystal structure is the result of inner 1S electron interactions. Since the 1S electron has angle A, it prefers FCC structure which does not have perfectly lined up octahedron faces.

When the pressure reaches to 30Pa, the structure becomes complex cl16 and each octahedron face bind with two neighboring atoms. Lithium phase diagram is complex, but its complexities are topology of octahedron nuclei.

4. Methods

4.1. S Orbit Angle and Phase

S orbit is tilted an angle (“A” in Figure 5). As proton count increases, the angle is decreasing as the more protons join the interaction processes to bring S orbit to the center:

Be hcp

Mg hcp

Ca fcc

Sr fcc

Ba bcc

Ra bcc

Figure 7. BCC, FCC and HCP Crystal

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