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Packing of Spheres

What does this statement means? The anisotropy in crystalline solid arises due to the different arrangement of particles in different directions.

Crystalline solid can be classified on the basis constituent particles and intermolecular force of attraction in between them. Constituent particles are molecules, ions, metal kernel in sea of electrons and atoms. Force of attraction operate in between the particles are dispersion force, dipole-dipole interaction, hydrogen bonding, electrostatic attraction, metallic bonding and covalent bonding. The term van der Waals forces include hydrogen bonding, dipole-dipole attraction and London dispersion forces.

All molecules experience London dispersion forces. In addition, polar molecules can also experience dipole-dipole interactions. So, the interactions that holds the molecule together in polar molecular solid are London dispersion force and dipole-dipole interactions. Metallic solid has typical metallic lustre. But ionic solid looks dull. That is the attraction of positively charged kernel with sea of delocalized electrons. In graphite, each carbon is covalently bonded with 3 atoms in same layer.

The fourth valence electron of each atom is free to move in between different layers.

The characteristic feature of crystalline solid is regular and repeating arrangement of constituent particles in space. The smallest part of the crystal lattice is known as unit cell. Look at the role of unit cell in crystal lattice. On the basis of 6 parameters 3 edges and 3 angles of unit cell mentioned above, total seven types of primitive unit cells are possible. The primitive unit cells show variations in form of centred unit cells.


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The total number of possible unit cells primitive and centred in 3-dimensional lattice is This is called Bravais Lattice. The detail of the lattice structure in tabular form is given below. Primitive unit cell : In Primitive unit cell, atoms are present at corner only. An atom is shared by 8 unit cell.

In brief. Atoms Y are at the corners of the cube and X at the body centre. What is the formula of the compound? Atoms Y anions are at the corners of the cube and X cations at present at face-centre of the cubic lattice. As we the constituent particles in solid are in form of sphere.

The spheres in solid are arranged in different way to leave minimum vacant space. These arrangements of spheres in different layers form the closed packed structure of solid. The crystals are formed in closed packed structures. Similarly spheres in solid are also arranged in 3-dimension to form close-packed structure. In this type of arrangement spheres of both the layers are perfectly aligned horizontally and vertically. This type of arrangement is known as AAA type closed packing of sphere in 3-dimension. The possible smallest geometrical 3-dimensional shape would be cube. Thus this type of arrangement generate simple cubic lattice with primitive type of unit cell.

Coordination number: The number of nearest neighbour touching a particle in closed packed structure is known as the coordination number of constituent particles. In both type of crystal lattice hcp, ccp or fcc the coordination number for the constituent particle is Formula of the compound is deduced by calculating number of atoms present at lattice point and number of atoms present in voids.

Generally anions are bigger and they occupy the lattice point while cations are occupied in voids. In a given compound, it is not necessary that all the voids are occupied by constituent particles. Some time only fraction of voids are occupied depend on the formula of compound. Therefore it is necessary to know the position of voids in crystal lattice. Element B occupy all the ccp position and element A occupy all the octahedral voids.


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Find the formula of compound. What is the formula of compound? In fcc the cations in voids touches 6 nearest neighbour as well as anion at lattice point also touches 6 nearest neighbour. Packing efficiency is defined as percentage of total space filled by the constituent particles in crystal. Packing efficiency in hcp and ccp structures :. Although in crystalline solid there is regular arrangement of constituent particles but yet the crystals are not perfect. There is always some king of irregularity in arrangement of constituent particles in small crystals.

Point Defects in Semiconductors I - Michel Lannoo - Paperback () » Bokkilden

Irregularities are known as defects in crystal. There are 2 types of defects known in crystal lattice. In our syllabus only point defects are included so we will focus our study on point defects only. Impurity defect: Impurity defect is arises due to addition of small amount of impurity in ionic solid. Edited by James H. Crawford, Jr, and Lawrence M.

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Skip to main content. Subscribe Search My Account Login. View Author Information. Kutateladze, 18, Novosibirsk , Russia. Pirogova, 2, Novosibirsk , Russia. Cite this: Chem. ACS AuthorChoice.

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Article Views Altmetric -. Citations PDF 23 MB. Biography After acquiring his Ph. Biography Dr. Transformation of energy into motion work is one of the basic processes of energy conversion in nature. Materials that are capable of stimuli-responsive mechanical effects are invaluable for the fabrication of mechanically tunable elements for actuation and energy harvesting, including flexible electronics, displays, artificial muscles, microfluidic valves and gates, dynamic components in the soft robotics, switchable reflector units for projective displays, and tunable components for contact printing.

Point Defects in Solids: Semiconductors and Molecular Crystals Volume 2

The advanced materials that will qualify for these applications in the future must fulfill an extended list of requirements including reversibility, rapid and controllable mechanical response that is proportional to the applied stimulus, and extended lifetime with insignificant fatigue. Their properties hinge on the capability for preservation of physical integrity and endurance to defects that normally accumulate to cause fatigue during prolonged exposure to mechanical stress, temperature, light, pH, and electric or magnetic fields.

In the past, photorestrictive effects in inorganic ceramic materials have been commonly employed to control actuators, which are known to be robust, stiff, and highly temperature resistant. More recently, thin strips or films of soft materials, such as organic polymers, elastomers, or liquid crystalline materials, were used for the same purpose.