Atomic Structure and Crystal Lattice can be Explained after we know about the atomic structure. Although the number of protons is fixed for an element, the number of neutrons may vary, which is called isotopes. i.e., the same atomic number with a different atomic mass of an element. So the atomic weight is the weighted average of all the isotopes of an element that exists.
That is why most of the element has an atomic mass in fraction. E.g., the Helium atom has two protons and two neutrons in the nucleus and two-electrons revolving around the nucleus. So the atomic number and mass of Helium are 2 and 4, respectively.
Atom a smallest constituent of matter consists of three subatomic particles - Electron, Proton, and Neutron. Proton and neutron constitute the center part of an atom known as the nucleus. At the same time, electron revolves around the nucleus in an orbit of discrete energy value describe by the Bohr Atomic Model. Proton is a positively charged species with one atomic mass unit; the neutron has no charge with a mass equivalent to a proton. Electron is a negatively charged species with negligible mass. The number of electrons is equal to the number of protons in an atom. They are thus making an atom overall neutral. The volume of the nucleus is small is compare to the volume of an atom where the mass of an atom resides. The electromagnetic force of attraction exists between the electron and nucleus that keeps electrons revolving around it. The nuclear force binds the proton with the neutrons in the nucleus. It is a short-range force (10-15 m) as compared to the electromagnetic force of attraction. Each element made of various atoms, the mass of an atom denoted as an atomic mass (A). Atomic Mass if the summation of the protons plus neutrons in an element. Additionally, each element has a unique atomic number (Z), which equals the number of protons in an atom.
Atomic Model
The Bohr model of the atom proposed by Niels Bohr in the year 1915 called a planetary model just similar to the planets revolving around the sun. Erwin Schrodinger proposed the Electron cloud model of an atom in the year 1926. It states that a dense cloud of an electron surrounds the nucleus at various energy levels in the orbitals, where the probability of finding an electron is maximum. He gives the quantum mechanics model of an atom through mathematical wave equations.
The electron revolves in fixed orbits or shells represented by the letters K, L, M, N,.. around the nucleus, which corresponds to n = 1, 2, 3, 4. It gives the average distance between the electron and the nucleus. The maximum of electrons in orbit is given by 2n2 where n is the number of the orbit from the nucleus, and outermost shell cannot have more than eight electrons.
Each orbit contains different orientations of the electron called orbital denoted as s, p, d, f. It gives the number and shape of the orbital. s has one orbital centered towards the nucleus, p has three orbital with a dumbbell shape, d has five orbital with more complex shape.
According to Pauli’s Exclusion Principle, each orbital accommodates at two electrons with an opposite spin at maximum. Thus s, p, d, f can have a maximum of 2, 6, 10, 14 electrons, E.g., Chlorine has an atomic number 17, so its electronic configuration is 1s2, 2s2, 2p6, 3s2 3p5.
The outermost electrons in the shell are called a valence electron that takes part in a chemical reaction and bond formation between different atoms and molecules. These valence electrons decide the properties of an element and classify them into metal, semiconductor, non-metal, etc. The element having stable electronic configuration (8 electrons in the last shell) are non-reactive chemically inert.
The Crystal Lattice
Crystal structure determines the property of a crystalline material through spatial arrangements of atoms/molecules or ions. The word lattice also used in context with the crystal structure. If atom or groups of atoms (Motif) are 3D periodic translated in space, we get a crystal while the 3D translational periodic arrangement of points in space is called the lattice.
Unit Cell refers to a small volume of the crystal, which by periodic repetitions, generates the entire crystal. It is a building block of a crystal structure. The periodic repetition of a unit cell is without any gap or overlaps. In a nutshell, lattice gives the idea of the repetitions and motif, which together constitute the crystal.
Classification of Lattice
The crystal structure has been divided based on unit cell configuration. Six parameters can define the unit cell; three edge length denoted as a, b, c, and three angles indicated by α, β, and γ. These also called lattice parameters of the crystal structure. A crystal structure can consist of up to 14 different types of unit cells given by the French physicist Auguste Bravais. On this basis, the lattice has been classified into seven crystal systems and 14 Bravais lattices. The seven crystal systems are seven distinct point groups of Bravais lattice.
Crystal Lattice Vibrations
Ideally, the atomic displacement from the position of the crystal lattice is not considered. Still, for determining any thermal and electrical properties of any materials, lattice mobility plays a vital role. Although the vibrational amplitude is small, their wavelength is in the range of interatomic distances. At temperatures above 0 Kelvin, the atoms vibrate about their mean position in a crystal lattice at the frequency around ~ 1014 Hz. It determines the solid-state properties of any material like heat capacity, thermal expansion, and transport properties (electric and thermal conductivity). This vibrational mode of atoms in a crystalline lattice is called phonons.
For understanding the concept of the lattice vibration in a simple way, let us consider an infinite periodic lattice in a linear chain of atoms.
The energy of lattice vibrations is quantized; it is called phonons, just like photons are the quantization of the electromagnetic field.
The intensity of these vibrations is characterized by Brillouin scattering (acoustic phonons) and Raman spectroscopy (optical phonons). They are classified as acoustic phonons and optical phonons. In acoustic phonons, atoms in init cell move in phase contrary to optical phonons where atoms move out of phase in the unit cell. The optical phonons have much higher frequencies than the acoustic phonons frequency lies in the optical range.
Lattice Vibration with One Atomic Species
If an atom of mass M connected through spring having spring constant in a 1-d linear chain of atoms. The mean position distance between two atoms is a. the displacement of the nth atom is n from the mean position. This model representing one atomic species is called Acoustic phonons.
Lattice Vibration with Two Atomic Species
If there exist two or more different atoms in the unit cell in a chain. They may give to vibrations out of phase (opposite) to their mean position. When coupled with opposite charges. They can interact with electromagnetic radiation showing optical properties in a crystal. This model called optical phonons.
3 –Dimensional Lattice Vibrations
Suppose an atom vibrates in the 3-dimensional axis. There is one longitudinal mode of vibration with two transverse modes of vibrations perpendicular to propagation. This vibration can be explained through phonon band structure, just like electronic structure. In the linear chain, there is only longitudinal vibration along the axis. In polyatomic, the vibrations of different atoms against each other give rise to phonon band structure. It interacts with the electron in the crystals; this creates the generation of holes or vacancies in the crystal structure of materials. The optical phenomenon absorption, dispersion, and transmission can be explained. It is very useful in the development of the optical study of any materials
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Featured Image: Atomic Structure and Crystal Lattice
Research Scholar
Metallurgical & Materials Engineering Dept.
Indian Institute of Technology, Patna
M.Tech, Mechanical Engineering
