Question Bank of Solid state physics
Choose the right answer or Complete each of the following or Put ()or
() questions:
Solid state physics explains the properties of solid materials.
Solid state physics explains the properties of a collection of atomic nuclei
and electrons interacting with electrostatic forces.
Solid state physics formulates fundamental laws that govern the behavior of
solids.
Single crystals has Long range order and 3D translational periodicity exists.
The polycrystalline materials are single crystals assembly.
Quasicrystals has long range order but has no 3D translational periodicity.
Amorphous materials have disordered or random atomic structure
Crystalline materials are solids with an atomic structure based on a regular
repeated pattern.
Single crystals have a periodic atomic structure across its whole volume.
At long range length scales, each atom is related to every other equivalent
atom in the structure by translational or rotational symmetry.
The grains are usually 100 nm - 100 microns in diameter.
Polycrystals with grains less than 10 nm in diameter are nanocrystalline
Amorphous (Non-crystalline) solids are made up of randomly orientated
atoms, ions, or molecules that do not form defined patterns or lattice
structures.
Crystalline materials are solids with an atomic structure based on a regular
repeated pattern.
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More progress has been made in understanding the behavior of crystalline
solids than that of non-crystalline materials since the calculation is easier in
crystalline materials.
The electrical resistivity of metals and superconductors is increasing
proportionally with the temperature increase, while it is inversely
proportional with temperature in case of insulators.
Polycrystalline materials are made up of an aggregate of many small single
crystals called crystallites or grains.
Polycrystalline materials have a high degree of order over many atomic or
molecular dimensions.
Grains (domains) are separated by grain boundaries, the atomic order can
vary from one domain to the next.
Amorphous materials have order only within a few atomic or molecular
dimensions.
Amorphous materials do not have any long-range order, but they have
varying degrees of short-range order.
Crystallography is a branch of science that deals with the geometric
description of crystals and their internal atomic arrangement.
Crystal structures can be obtained by attaching atoms, groups of atoms or
molecules which are called basis (motif) to the lattice sides of the lattice
point.
In two dimentional lattice, the crystal Structure = Crystal Lattice + Basis
In three dimentional lattice, the crystal Structure = Bravais Lattice + Basis
In two dimentional lattice we have five Bravais Lattice.
The unit cell in two dimention is the smallest component of the crystal,
when stacked together with pure translational repetition reproduces the
whole crystal.
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There are three common unit cells in three dimention, simple cubic, bodycentered cubic and face-centered cubic
The unit cell and, consequently, the entire lattice, is uniquely determined by
the six lattice constants: a, b, c, α, β and γ.
In a unit cell only 1/8 of each lattice point can actually be assigned to that
cell.
For the simple cubic lattice, each unit cell is associated with (8)  (1/8) =
one lattice point.
In three dimention there is typical 14 bravais lattice crystal structures with
seven crystal types.
In Cubic Crystal System, 𝑎 = 𝑏 = 𝑐, ∝= 𝛽 = 𝛾 = 90°
In Hexagonal Crystal System, 𝑎 = 𝑏 ≠ 𝑐, ∝= 𝛽 = 90°, 𝛾 = 120°
In Triclinic Crystal System, 𝑎 ≠ 𝑏 ≠ 𝑐, ∝≠ 𝛽 ≠ 𝛾 ≠ 90°
In Monoclinic Crystal System, 𝑎 ≠ 𝑏 ≠ 𝑐, ∝= 𝛾 = 90° , 𝛽 ≠ 120°
In Orthorhombic Crystal System, 𝑎 ≠ 𝑏 ≠ 𝑐, ∝= 𝛽 = 𝛾 ≠ 90°
In Tetragonal Crystal System, 𝑎 = 𝑏 = 𝑐, ∝= 𝛽 = 𝛾 ≠ 90°
In Trigonal (Rhombohedral) Crystal System, 𝑎 = 𝑏 = 𝑐, ∝= 𝛽 = 𝛾 ≠
90°
Sodium chloride structure consists of equal numbers of sodium and chlorine
ions placed at alternate points of a simple cubic lattice.
Each ion in sodium chloride structure has six of the other kind of ions as its
nearest neighbours.
the types of forces hold the atoms together includes various types: ionic
bonds, covalent bonding, metallic bonding, van der waals bonding, and
hydrogen bonding.
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When ions are very close to each other, other forces arise and called shortrange repulsive forces, due to rearrangement of electrons as nuclei
approach.
The equilibrium distance between two ions is point at which energy is
minimum, and the forces are balanced.
The energy of the crystal is lower than that of the free atoms by an amount
equal to the energy required to pull the crystal apart into a set of free atoms.
The binding energy of the crystal is the energy required to pull the crystal
apart into a set of free atoms.
Ionic bonding is the electrostatic force of attraction between positively and
negatively charged ions (between non-metals and metals).
Metallic elements have only valence electrons in their outer shell, when
losing their electrons they become positive ions.
Electronegative elements tend to acquire additional electrons to become
negative ions or anions.
According to Pauli Exclusion Principle repulsive force arises between the
nuclii, and the potential energy of the system increases very rapidly When
they are brought close together.
The covalent bonding is formed when the atoms share the outer shell
electrons rather than by electron transfer.
Covalent bonding takes place between atoms with small differences in
electronegativity which are close to each other in the periodic table
(between non-metals and non-metals).
In covalent bonding each electron in a shared pair is attracted to both nuclei
involved in the bond.
Metallic bonding is found in metal elements. This is the electrostatic force
of attraction between positively charged ions and delocalized outer
electrons.
4
The metallic bond is weaker than the ionic and the covalent bonds.
A metal may be described as a low-density cloud of free electrons.
Metals have high electrical and thermal conductivity.
Van der waals bonding are weak bonds with a typical strength of 0.2
eV/atom which occurs between neutral atoms and molecules.
Weak forces of attraction result from the natural fluctuations in the electron
density of all molecules that cause small temporary dipoles to appear within
the molecules.
The natural fluctuations of the electron density for all molecules attract
them to each other; causes temporary dipoles are called van der Waals'
forces.
The bigger the 'surface area' of a molecule, the greater the van der
Waal's forces will be and the higher the melting and boiling points of the
compound will be.
Van der Waal's forces are of the order of 1% of the strength of a covalent
bond.
Van der Waal's forces are due to the electrostatic attraction between the
nucleus of one atom and the electrons of the other.
A hydrogen atom, having one electron, can be covalently bonded to only one
atom. However, it can have an additional electrostatic bond with a second
atom of highly electronegative character such as fluorine or oxygen. This
second bond permits a hydrogen bond between two atoms or structures.
The strength of hydrogen bonding varies from 0.1 to 0.5 ev/atom.
Hydrogen bonds connect water molecules in ordinary ice.
Hydrogen bonding is also very important in proteins and nucleic acids and
therefore in life processes.
Dense, ordered packed structures tend to have lower energies & thus are
more stable.
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A Crystal structure is a periodic arrangement of atoms/ions over large
atomic distances Leads to structure displaying long-range order.
All metals, many ceramics, and some polymers exhibit “High Bond Energy”
and a More Closely Packed Structure.
Amorphous Materials are materials lacking long range order, of less
densely packed lower bond energy “structures” can be found in metals,
ceramic, glass and many “plastics”
The unit cell is the smallest repetitive volume which contains the complete
lattice pattern of a crystal.
For any lattice, the unit cell &, thus, the entire lattice, is uniquely determined
by six constants a, b, c, α, β and γ which depend on lattice geometry.
Primitive Unit Cell is determined by the parallelepiped formed by the
Primitive Vectors a1 ,a2, & a3.
Primitive unit cell can be used as a building block for the crystal structure.
Primitive Unit Cell can be repeated to fill space by periodic repetition of it
through the translation vectors T = n1a1 + n2a2 + n3a3.
The Primitive Unit Cell volume can be found by (V = a3)
The Primitive Unit Cell must contain only one lattice point.
Metallic crystal structures tend to be densely packed
In metallic crystal structures, metallic bonding is not directional.
In metallic crystal structures, the nearest neighbor distances tend to be small
to lower bond energy, and the electron cloud shields cores from each other.
Miller Indices are reciprocals of the (three) axial intercepts for a plane,
cleared of fractions & common multiples.
All parallel planes have the same Miller indices.
Miller indices are a shorthand notation to describe certain crystallographic
directions and planes in a material.
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Miller Indices are a symbolic vector representation for the orientation of an
atomic plane in a crystal lattice.
Miller Indices are defined as the reciprocals of the fractional intercepts,
which the plane makes with the crystallographic axes.
Diffraction gratings must have spacing comparable to the wavelength of
diffracted radiation.
Von Laue method is mainly used to determine the orientation of large
single crystals while radiation is reflected from, or transmitted through a
fixed crystal.
In Von Laue method The Bragg angle is fixed.
In the transmission Laue method, the film is placed behind the crystal to
record beams which are transmitted through the crystal.
The Lattice constant a of the crystal can be determined by rotating crystal
method.
By rotating crystal method one can determine the shape & size of unit cell
as well as the arrangement of atoms inside the cell.
In crystals the typical interatomic spacing ~ 2-3 Å so the X-rays is suitable
radiation.
Bragg’s angle is (θ) and the experimentally measured diffraction angle is
(2θ).
Bragg’s low states that:
n  2d hkl sin 
Powdered crystal is used instead of a single crystal, then there is no need to
rotate it, because there will always be some small crystals at an orientation
for which diffraction is permitted.
X-rays powder method is used to determine the lattice parameters
accurately.
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For every set of crystal planes in the powder method, by chance, one or
more crystals will be in the correct orientation to give the correct Bragg
angle to satisfy Bragg's equation.
X-ray diffraction XRD distinguishing between crystalline & amorphous
materials.
X-ray diffraction XRD determine the structure of crystalline materials.
X-ray diffraction XRD determine the electron distribution within the
atoms, & throughout the unit cell.
X-ray diffraction XRD determine the orientation of single crystals.
X-ray diffraction XRD determine the texture of polygrained materials.
X-Rays are the least expensive, the most convenient & the most widely
used method to determine crystal structures.
X-Ray is not absorbed very much by air, so the sample need not be in an
evacuated chamber.
X-Rays do not interact very strongly with lighter elements.
Atomic motions are governed by the forces exerted on atoms when they are
displaced from their equilibrium positions.
It is necessary to determine the wave functions and energies of the
electrons within the crystal to determine the forces exerted on atoms.
One of the properties of elasticity is that it takes about twice as much force
to stretch a spring twice as far. This linear dependence of displacement upon
stretching is called Hooke's law.
Sound waves are mechanical waves, which propagate through a material
medium (solid, liquid, or gas) at a wave speed, which depends on the elastic
and inertial properties of that medium.
At a given frequency and in a given direction in a crystal it is possible to
transmit three sound waves, differing in their direction of polarization and
in general in their velocity.
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The speed with which a longitudinal wave moves through a liquid of density ρ is
𝐵
𝑣𝜄 = 𝜆𝑓 = √
𝜌
The larger the elastic modules and smaller the density, the more rapidly
can sound waves travel.
An equation of motion for any displacement can be produced by means of
considering the restoring forces on displaced atoms.
The dispersion relationship between frequency and wavelength, or
between angular frequency and wave vector.
The simplest crystal is the one-dimensional chain of identical atoms.
In a chain of two types of atoms, the acoustic branch has this name
because it gives rise to long wavelength vibrations - speed of sound.
In a chain of two types of atoms, the optical branch has higher energy
vibration (the frequency is higher, and you need a certain amount of energy
to excite this mode).
Phonons are quanta of lattice vibrations, while photons are quanta of
electromagnetic radiation.
In solids, the energy associated with this vibration and perhaps also with the
rotation of atoms and molecules is called thermal energy.
In gases, the translational motion of atoms and molecules contribute to
vibrational and rotational energy of atoms.
Thermal expansion is an example to the anharmonic effect.
In a harmonic approximation phonons do not interact with each other, in
the absence of boundaries, lattice defects and impurities (which also scatter
the phonons), the thermal conductivity is infinite.
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In anharmonic effect phonons collide with each other and these collisions
limit thermal conductivity which is due to the flow of phonons.
The coupling of normal modes by the unharmonic terms in the interatomic
forces can be pictured as collisions between the phonons associated with the
modes.
A flow of heat takes place from a hotter region to a cooler region when
there is a temperature gradient in a solid.
The most important contribution to thermal conduction comes from the flow
of phonons in an electrically insulating solid.
Thermal conductivity is a transport coefficient and it describes the flow.
The thermal conductivity of a phonon gas in a solid will be calculated by
means of the elementary kinetic theory of the transport coefficients of
gases.
Give the Scientific term of
The binding energy of the crystal is the energy required to pull the crystal
apart into a set of free atoms.
Ionic bonding is the electrostatic force of attraction between positively and
negatively charged ions (between non-metals and metals).
Covalent bonding takes place between atoms with small differences in
electronegativity, which are close to each other in the periodic table
(between non-metals and non-metals).
Metallic bonding is found in metal elements. This is the electrostatic force
of attraction between positively charged ions and delocalized outer
electrons.
10
Van der waals bonding are weak bonds with a typical strength of 0.2
eV/atom which occurs between neutral atoms and molecules.
A Crystal structure is a periodic arrangement of atoms/ions over large
atomic distances Leads to structure displaying long-range order.
Amorphous Materials are materials lacking long range order.
The unit cell is the smallest repetitive volume which contains the complete
lattice pattern of a crystal.
Miller Indices are reciprocals of the (three) axial intercepts for a plane,
cleared of fractions & common multiples.
Miller indices are a shorthand notation to describe certain crystallographic
directions and planes in a material.
Miller Indices are defined as the reciprocals of the fractional intercepts
which the plane makes with the crystallographic axes.
One of the properties of elasticity is that it takes about twice as much force
to stretch a spring twice as far. This linear dependence of displacement upon
stretching is called Hooke's law.
Sound waves are mechanical waves, which propagate through a material
medium (solid, liquid, or gas) at a wave speed, which depends on the elastic
and inertial properties of that medium.
Phonons are quanta of lattice vibrations.
photons are quanta of electromagnetic radiation.
Dulong-Petit law states that the specific heat of a given number of atoms of
any solid is independent of temperature and is the same for all materials.
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Compare between ionic and covalent bonding with respect to the shape,
polarity, formation, types of atoms, state at room temperature and melting
point.
Shape
Polarity
Covalent Bonds
As in fig
Low
Ionic Bonds
As in fig
High
Formation
A covalent bond is formed
between two non-metals that
have similar
electronegativities. For
stabilization, the atoms share
their electrons from outer
molecular orbit with others.
An ionic bond is formed
between a metal and a nonmetal. Non-metals(-ve ion)
are "stronger" than the
metal(+ve ion) and can get
electrons very easily from the
metal. These two opposite
ions attract each other and
form the ionic bond.
Types of atoms
Two non-metals
One metal and one non-metal
State at room temperature
Liquid or gaseous
Solid
Melting point
Very high
High
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Compare between X-Ray Diffractıon Methods of Von Laue, Rotating
Crystal, and Powder method with respect to type of crystal lattice used,
beam of incidence, and angle of incidence. (lec. 6,7 p. 37)
Compare between phonons and photons with respect to their nature and
energies. (lec. 8,9 p. 20)
Draw the normal mode frequencies of a chain of two types of atoms masses
M and m, clarify on the curve the three states of atoms oscillations and the
optical and acoustical branches.
Problems:
Calculate the atomic Packing Factor (APF) for a Simple Cubic structure
(SC)?
Calculate the atomic Packing Factor (APF) for a Body Centered Cubic
Structure (BCC)?
Calculate the atomic Packing Factor (APF) for a Face Centered Cubic
Structure (FCC)?
EX p32 (lec.3)
Calculate the Theoretical density 𝜌 for Cr (BCC), using that their atomic
weight A= 52g/mole and Avogadro’s number NA = 6.023 x 1023 atoms/mol ?
Draw the following crystallographic planes and directions:
Ex (Lec.4) p23 +
(110), (111), (634), (100), (210), (100), (1̅00), (200)
[110], [111], [634], [100], [210], [100], [1̅00], [200]
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