Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
85 Cards in this Set
- Front
- Back
|
Describe a single crystal's isotropy |
An-isotropic. The degree of an-isotropy increases as the degree of crystal symmetry decreases. |
|
|
Describe a poly-crystalline material's isotropy. |
Normally isotropic. Each grain may be an-isotropic but as the grains are orientated randomly the material behaves isotropically. |
|
|
Describe the 5 different 2D Bravais lattice in terms of the 3 lattice constants a,b and γ. |
Oblique P: a≠b. y≠60°, 90° or 120°. Square P: a=b. y=90°. Rectangular C: a≠b. y=90°. Rectangular P: a≠b. y=90°. Hexagonal P: a=b. y=120°. Where P is primitive and C is centred.
|
|
|
3D Bravais Lattices How many different types of crystal system are there? How many types of basic unit cell are there? How many Bravais lattices are there? |
There are 7 types of crystal system. There are 4 basic types of unit cells. There are 14 Bravais lattices that describe all possible lattice networks. |
|
|
Describe the 3 possible 3D cubic unit cells in terms of the constants a,b,c and a,b,y. |
a=b=c. a=b=y=90°. Simple (P), Body Centred (I), Face centred (F). |
|
|
Describe the 2 possible 3D tetragonal unit cells in terms of the constants a,b,c and a,b,y. |
a=b≠c. a=b≠y=90°.
|
|
|
Describe the 4 possible orthorhombic unit cells in terms of the constants a,b,c and a,b,y. |
a≠b≠c. a=b=y=90°. Simple (P), Base Centred (C), Face Centred (F), Body Centred (I). |
|
|
Describe the 1 possible rhombohedral unit cellin terms of the constants a,b,c and a,b,y. |
a=b=c a=b=y≠90°. Simple (P). |
|
|
Describe the 1 possible hexagonal unit cell in terms of the constants a,b,c and a,b,y. |
a=b≠c. a=120°, b=y=90°. Simple (P).
|
|
|
Describe the 2 possible monoclinic unit cell in terms of the constants a,b,c and a,b,y. |
a≠b≠c. a=y=90°≠b Simple (P), Base Centred (C). |
|
|
Describe the 1 possible triclinic unit cell in terms of the constants a,b,c and a,b,y. |
a≠b≠c. a≠b≠y≠90°. Simple (P). |
|
|
Define Symmetry. Define a symmetry operation. |
An object is symmetrical if after some operation has been carried out the result is indistinguishable from the original object. A symmetry operation is on that leaves the crystal and its environment invariant. |
|
|
Define rotational symmetry. Define a rotational axis. |
Rotational symmetry is when a 2D shape can be rotated so that it looks identical to the original shape. The axis along which the rotation is preformed is an element of symmetry referred to as a rotational axis. |
|
|
Which rotational symmetries are possible in a crystal lattice? |
2-fold (180°) 3-fold (120°) 4-fold (90°) 6-fold (60°) |
|
|
Define mirror/reflection symmetry. |
A mirror symmetry is an imaginary operation to reproduce an object. The operation is done by imagining that you cut the object in half then place a mirror next to one of the halves of the object along the cut. If the reflection reproduces the other half then the object is said to have mirror symmetry. |
|
|
Define a mirror plane. |
The plane of the mirror is an element referred to as a mirror plane (m). In 2D mirror planes can be represented by line of symmetry. A mirror plane of symmetry divides a 3D shape into 2 congruent halves that are mirror images of each other. |
|
|
Define the centre of symmetry. How many centres can a crystal have? |
A point within a crystal through which any straight line extends to a point on opposite surfaces of the crystal at equal distances from it maybe the centre of symmetry. A crystal may possess a number of planes or axis of symmetry nut it can have only one centre of symmetry. |
|
|
Define translation symmetry. Define translating by a vector. |
An image has translation symmetry if it can be divided by straight lines into a sequence of identical figures. Results from moving a figure a certain distance in a certain direction is known as translating by a vector. |
|
|
Describe point group symmetry. |
An object may have no symmetry but point groups can be constructed to create motifs. All group symmetry elements pass through one point. In order for a motif to be appropriate the lattice must have at least the symmetry of the motif. |
|
|
Define a unit cell. Define an asymmetric unit. Define crystallographic symmetry. |
The smallest volume from which the entire crystal can be constructed by translation only. The smallest volume from which the unit cell can be constructed by application of crystallographic symmetry. Symmetry operators such as rotation axes that apply over the entire crystal. |
|
|
In 3D how many point groups are there? How is a 3D crystal formed? |
There are 32 point groups. By adding a motif to every lattice point. The symmetry of the motif can be different from that of the lattice. A crystal can have more than the essential symmetries of the system. |
|
|
Describe the family form of Miller Indices. |
Sometimes when the unit cell has rotational symmetry several non-parallel planes may be equivalent. These planes are grouped into families represented by {}. {hkl} represents all of the planes equivalent to the plane (hkl) through rotational symmetry. |
|
|
Describe the Miller Indices for an hexagonal lattice. |
In hexagonal systems symmetry reflected planes and directions do not have Miller Indices which are permutations. A 4th axis, u, in the plane of the x and y axis is introduced. A plane is therefore determined in terms of (hkil) where i=-(h+k) |
|
|
Define a zone axis. |
It is the common direction shared by 2 or more crystal planes when they intersect. Any 2 non-parallel planes will intersect. |
|
|
Describe a stereo-graphic projection. |
The circumference is called the primitive circle. The stereo-graphic projections of any circumference of the sphere are called the great circles (line of longitude). Lines of latitude correspond to small circles and represent the angular distance from the north and south poles. |
|
|
Describe a wulffnet. |
A collection of great and small circles which represent lines of longitude and line of latitude on a sphere. |
|
|
Describe a vacancy. |
Simplest point defect. All crystalline solids contain vacancies. It is a missing atom from an atomic site. A tensile stress field is produced in the vicinity. |
|
|
How are vacancies and entropy related? What is the equilibrium vacancy concentration? |
The formation of a vacancy increases the entropy of the crystal. The equilibrium vacancy concentration is shown to be that which results in the minimum free energy. |
|
|
Describe impurities. |
Impurity or foreign atoms will always be present. Alloying is used to improve a materials mechanical properties and corrosion resistance. The addition of impurity atoms to a metal will result in the formation of a solid solution. The solid solution is compositionly homogeneous and may comprise of substitution or interstitial impurities. |
|
|
What are the 4 Hume Rothery rules for the formation of a complete substitutional solid solution? |
1. Atomic size factor- Difference in atomic radius must be <15% 2. Crystal structure- Both metals must be the same crystal structure. 3. Electronegativity- Must have similar electronegativities. 4. Valences- Complete solubility occurs when the solvent and the solute have the same valency. |
|
|
What are the 2 Hume Rothery rules for the formation of an interstitial solid solution? |
1. Solute atoms must be smaller than the interstitial sites in the solvent lattice. 2. The solute and solvent should have similar electronegativities (metal solute). |
|
|
Define Frenkel defects in ceramics. |
A cation vacancy and a cation interstitial pair. The cation leaves its normal position and moves to an interstitial. No change in charge as cation maintains same charge as interstitial. |
|
|
Define Schottky defects in ceramics. |
A paired set of cation and anion vacancies. Removing one cation and one anion from crystal interior and placing them at the surface. Electronegativity and stoichiometry is maintained. |
|
|
Define stoichiometric ceramics. |
If Frenkel or Schottky defects occur only then the material is stoichiometric as these defects do not effect the ratio of cations to anions. |
|
|
Define non-stoichiometric ceramics. |
When there is a deviation from the formulaic compound. Can occur in some ceramics for which 2 valence/ionic states exist for one of the atom types. |
|
|
How does temperature effect the numbers of Frenkel and Schottky defects? |
The equilibrium numbers of both defects will increase with temperature. See Notes of equations. |
|
|
What is the condition for the formation of an interstitial defect in a ceramic? What is the condition for the formation of an substitutional defect in a ceramic? |
The ionic radius must be relatively small in comparison to the anion. The impurity must be similar to the atom it is replacing in an electrical sense. |
|
|
What are the conditions required to achieve appreciable solid solubility of substitutional impurity atoms? |
Ionic charge and size must be similar to those of the host ion. For an impurity having a very different charge the crystal must compensate so that electronegativity is maintained. This can be accomplished by the formation of another defect. |
|
|
Describe an edge dislocation. |
The perfect crystal is cut and an extra plane of atoms is inserted. Results from a mismatch in the rows of atoms. Caused by the termination of a plane of atoms in the middle of a crystal. The adjacent planes bend around the terminating plane. The magnitude of distortion decreases with distance from the dislocation line. |
|
|
Describe a screw dislocation. |
A distortion where the upper front region of the crystal is shifted one atomic distance to the right relative to the bottom portion. |
|
|
What are the Burger's vectors orientation for screw and edge dislocations? |
For edge dislocations the Burger's vector is perpendicular to the dislocation line. For screw dislocation the Burger's vector is parallel to the dislocation line. |
|
|
Describe a mixed dislocation. |
A dislocation that is both edge and screw in character. The Burger's vector is neither perpendicular nor parallel. |
|
|
Define a transverse wave. Define a longitudinal wave. |
A wave in which the vibration direction is perpendicular to the direction in which the wave travels in. A wave in which the vibration direction is parallel to the direction in which the wave travels in. |
|
|
Define a travelling wave. Define a harmonic wave. |
A travelling wave in one dimension is a distance that moves along a direction, x, with a constant speed, v. A simple wave where the profile is a sine or cosine function. See notes for equations. |
|
|
Describe a spherical wave. |
In 3D consider a small pulsating sphere surrounded by a fluid. As this source expands and contracts it generates pressure vibrations in the fluid that propagate outwards as spherical waves. |
|
|
Define superposition. Define reflection. |
The principle of superposition states that the resultant of several waves at any point is given by the sum of their effects at that point. For a monochromatic plane wave arriving at a surface the reflected ray lies in the plane of incidence. The angle of incidence is equal to the angle of reflection. |
|
|
Describe internal reflection. |
As the angle of incidence increases the angle of refraction also increases. Thus there is a value for the angle of incidence for which the angle of refraction is 90° and the emerging ray is transmitted to the interface. This is called the critical angle. For all angles of incidence greater than this critical angle the incident ray will not emerge into the rarer medium but is reflected back into the denser medium giving rise to total internal reflection. |
|
|
Define Huygens' Principle. |
Every point on a wave front can be thought of as a new point source for waves generated in the direction the wave is travelling or being propagated. |
|
|
Describe Bragg diffraction. |
The atomic planes of atoms in crystals are assumed to reflect the incident wave. For constructive interference the path difference for reflections from successive planes must be an integral number of wavelengths. For Bragg equation see notes. |
|
|
Describe 2D array diffraction. |
Can be considered as the superposition of diffraction from rays in two directions. For constructive interference for all rays it is necessary to satisfy two simultaneous equations. See written notes for equations. |
|
|
Describe diffraction in 3D. |
Diffraction from a 3D array requires the solution to 3 simultaneous equations. The wave equations show the directions in which incident waves can travel through the crystal and exit in phase to give constructive interference. Thus for teh equations to be satisfied all points in a plane (hkl) must act in phase and scattering from successive (hkl) planes must also be in phase. See written notes for equations. |
|
|
Describe the reciprocal lattice. |
The lattice vectors d* can be defined by drawing lines perpendicular to all the real space (hkl) planes with lengths 1/d. The vectors define a series of the lattice points in reciprocal space known as the reciprocal lattice. |
|
|
Describe diffraction using wave vectors. |
A wave vector is equal to the reciprocal of the wavelength. In the special case where the Braggs' law is satisfied the wave vector is equal to the reciprocal of the distance between the lattice planes. This is also equal to the distance of the reciprocal lattice points from the origin of the reciprocal lattice. |
|
|
Describe an Ewald Sphere. |
It is a geometric construction used in electron, neutron and x-ray crystallography. It demonstrates the relationship between: the wave vector of the incident and diffracted x-ray beams; the diffraction angle for a given reflection; the reciprocal lattice of the crystal. The aim of the sphere is to determine which lattice planes will result in a diffracted signal for a given wavelength of incident radiation. |
|
|
Describe how a Ewald Sphere is constructed. |
It is constructed with radius 1/wavelength and with the incident beam wave vector, ki, spanning from the centre of the sphere to the origin of the reciprocal lattice (000) corresponding to the direct beam. kd is the wave vector for the diffracted electron beam. For diagram see written notes. |
|
|
Define electromagnetic waves. |
They are self propagating waves in a vacuum or in matter. The consist of electric and magnetic waves which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. |
|
|
Describe powder x-ray diffraction. |
By using a powdered sample for x-ray diffraction crystals are arranged in all orientations giving the whole range of possible angles. This finely produced powdered sample is loaded in a thin walled glass capillary. |
|
|
Describe the impact of atomic positions on the diffraction results. |
Atomic positions can be considered lattice planes. Lattice planes 0 and 0' are scattering in phase. Atoms from plane A which is between 0 and 0' will scatter x-rays so that the resulting wave is partially out of phase with x-rays from the lattice planes 0 and 0'. This will effect the intensity of the resulting diffraction spot and could even reduce in to zero. Thus in a primitive lattice reflections are shown for all inter-planar spacings but for non-primitive lattices expected diffraction beams may not appear. |
|
|
Describe the impact of a single atom on the diffraction results. |
The type of atom also effects the diffracted intensity. X-ray photons are EM waves and so are scattered by the electron cloud around an atom. The scattering power increases as the number of electrons increases. |
|
|
Describe the impact of atoms in a crystal on the diffraction results. |
For atoms arranged regularly in a crystal the periodicity of the lattice results in x-rays scattered by the unit cells interfering destructively in all direction except those given by the Bragg law. The positions or angles of the diffracted beams are determined by the size and shape of the unit cells of the crystals. For any particular reflection (hkl), each atom in the unit cell contributes to a scattered wave with a particular phase difference determined by its amplitude that is proportional to the value of the scattering factor for that atom. See written notes for equations. |
|
|
Describe structure factor. |
Structure factor is the summation of scattering over all atoms in the unit cell. See written notes for equations. |
|
|
Indexing a cubic diffraction pattern. |
Follow instructions in written notes. |
|
|
Describe how thermal vibrations effect the diffraction intensities. |
Thermal vibrations smear diffraction intensities by disturbing the order in the lattice planes. |
|
|
Describe how absorption and fluorescence effect the diffraction intensities. |
X-rays may have sufficient energy to eject a photo-electron resulting in an x-ray with a different wavelength to that of the incident ray. |
|
|
Describe how shape and size effect the diffraction intensities. |
The dimensions of the crystal affects the width of the scattered intensity. Small crystals give broad diffraction maxima. Large crystals produce sharp diffraction maxima. |
|
|
What did Rontgen discover in 1895? |
He discovered that x-rays are penetrations able to pass through materials that are opaque to visible light. That they are invisible to the human eye. Cause many materials to fluoresce. Cause shadows of absorbing materials on photosensitive paper. |
|
|
Describe a Coolidge Tube. |
Electrons are produced by thermionic emission from a tungsten filament which is heater by an electric current. A voltage difference is used to get the electrons to accelerate towards and hit a target. When they hit the target about 1% of the electrons kinetic energy is converted into x-rays. The rest of the energy is converted into heat and so the system needs to be cooled. See lecture notes of diagram. |
|
|
Describe the production of EM by atoms. |
It is produced by oscillating charges, normally electrons. This can be the oscillation of valence electrons in atoms or conduction electrons in metals or of free electrons in 'beam' devices. |
|
|
What is the De Broglie hypothesis? |
The hypothesis states that all matter can exhibit wave-like behaviour. See written notes for equations. |
|
|
Describe the typical continuous x-ray spectrum. |
The continuous spectrum is due to the deceleration of electrons in the target material. Some electrons are stopped by one impact and lose all their energy. Some undergo a large number of smaller impacts and lose fractions of their energy until it is all gone. This gives rise to x-rays with a range of energies. |
|
|
Describe the typical sharp line x-ray spectrum. |
If one of the bombarding incident electrons has sufficiently high energy a collision can also result in the excitation of inner shell electrons from the atoms in the target material. The inner shell electron is knocked out. To fill the vacancy left behind the other electrons within the atom move down from higher energy states and release their excess energy in the form of x-rays. As the energy levels for a particular atom are fixed these x-rays have characteristic wavelengths for each atom type so appear as sharp lines on the x-ray spectrum. |
|
|
Describe characteristic x-ray labels. |
The x-ray wavelengths are termed k,l,m this refers to the quantum number of the energy level that the initial electron is ejected from. The electron that fills the vacancy can come from any of the outer shells. The energy of the radiation which is emitted depends on the shell from which the electron comes. |
|
|
Define the critical excitation energy. Describe Moseley's law |
The energy required to excite k radiation is called the critical k excitation energy. Moseley's law quantitatively justified the nuclear model of the atom with positive charges in the nucleus and explained the atomic number. See written notes for equation. |
|
|
Describe x-ray absorption. |
When x-rays are incident on matter they are partly transmitted and partly absorbed. Scattering occurs in all directions and is referred to as absorption as scattered rays don't appear in the transmitted beam. True absorption is produced by electronic transmissions and fluorescent radiation which radiates in all directions. See written notes for equations. |
|
|
How does the wavelength effect the absorption of the x-rays? |
Shorter wavelengths are absorbed less because higher energy photons travel through the material more easily. However if the incoming x-ray is equal to the energy difference between a specific electron state and the vacuum level then more x-rays will be absorbed below this particular wavelength. For equations see written notes. |
|
|
Describe absorption edges. |
Near to the critical wavelength the change in the linear absorption coefficient leads to a huge change in the transmitted intensity. This is called an absorption edge and is a discontinuity superimposed on the linear coefficient Vs wavelength^3 relation. A large fraction of the incident photons are absorbed and their energy converted into fluorescent radiation and into kinetic energy of the photo-electrons. Can be used to remove unwanted x-ray energies. |
|
|
How can diffraction help solve crystal structures? |
It can determine the size of the unit cell. It can determine the symmetry of the crystal. It can determine the atomic positions. It can provide information about defects. When used with a database it can be used as a 'finger print' to identify the material. |
|
|
What can be determined from diffraction? |
Phases present. Lattice parameters. Thermal expansion coefficient. See written notes for more detail. |
|
|
Describe a synchotron. |
Brightest x-ray sources. X-rays are produce through centripetal acceleration with charged particles travelling at high speed around a ring. The x-ray radiation is projected along beam lines at tangents to the ring. |
|
|
What are the advantages to electron diffraction? |
Electrons are easily produced. Scattering of electrons depends on atomic number. Electrons interact much more strongly with matter hence a smaller volume sample can be used and structural information on a nm scale can be determined. |
|
|
What are the disadvantages to electron diffraction? |
Insensitive to elements lighter than boron. Electrons interact more with matter so specimens have to be thin to be electron transparent and diffraction is likely to contain dynamical interactions. |
|
|
Describe diffraction in the TEM. |
TEM can obtain highly localised diffraction information and see a good resolution image of the features that the diffraction information is coming from simply by switching lens settings. The wavelength is much less than the spacing between planes thus the Bragg angle is very small. Sample must be thin to prevent many scattering centres interacting with the beam. |
|
|
Indexing TEM diffraction ring patterns. |
See written notes and lecture slides |
|
|
What are the advantages to neutron diffraction? |
Scattering depends on the isotope of the element. Good differentiation of adjacent elements. Neutrons have a magnetic moment and are therefore sensitive to magnetic fields. |
|
|
What are the disadvantages to neutron diffraction? |
Expensive. Produced by spallation source or nuclear reactor. Weak flux so large sample required. |
