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The Uncertainty Principle04:08

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the...
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This lesson delves into the geometry of a radical, which is influenced by the electronic structure of the molecule. The principle is similar to that of a lone pair, where the unpaired electron influences the geometry at the radical center.
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The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the 3s orbital, giving a 1s22s22p63s1 configuration. The electrons occupying the outermost shell orbital(s) (highest value of n) are called valence electrons, and those occupying the inner shell orbitals are called core electrons. Since the core electron shells correspond to noble gas electron configurations, we can abbreviate electron...
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Tetra-Germanene Study from First Principles: Structure, Electronics, Mechanics, and Vibrations.

Phi M Nguyen1, Hai Hoang2,3, Vladimir Bubanja4,5

  • 1Ho Chi Minh City University of Technology (HCMUT), VNU-HCM, Ho Chi Minh City 700000, Vietnam.

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|February 9, 2026
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Summary
This summary is machine-generated.

Tetra-germanene exhibits superior cohesive stability and metallic conductivity compared to hexagonal germanene. Its anisotropic mechanical properties and improved thermal performance make it promising for next-generation nanoelectronics and phononic devices.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Chemistry

Background:

  • Two-dimensional (2D) materials like germanene are explored for advanced electronic applications.
  • Understanding the properties of novel germanene allotropes is crucial for material design.

Purpose of the Study:

  • To theoretically investigate the structural, electronic, mechanical, and thermal properties of tetra-germanene.
  • To compare tetra-germanene with hexagonal germanene for potential applications.

Main Methods:

  • Density Functional Theory (DFT) calculations for structural optimization and property analysis.
  • Molecular Dynamics (MD) simulations to obtain the initial buckled rectangular unit cell.
  • Analysis of electronic band structure, density of states, orbital populations, elastic moduli, and phonon dispersions.

Main Results:

  • Optimized tetra-germanene structure with specific lattice constants, buckling height, and high cohesive energy (5.14 eV/atom).
  • Metallic electronic behavior without Dirac crossings, with minor d-orbital participation and enhanced coordination.
  • Anisotropic in-plane Young's and bulk moduli indicating moderate stiffness and flexibility.
  • Stable phonon dispersions and improved thermal performance compared to hexagonal germanene.

Conclusions:

  • Tetra-germanene demonstrates significant cohesive stability and metallic conductivity.
  • Its anisotropic elasticity and favorable thermal properties suggest potential for nanoelectronics, energy efficiency, and phononic devices.
  • Tetra-germanene is a promising candidate for strain-tunable conductive channels and thermal pathways.