Flashcards

ICMP Week 1 LNs

R S C ICMP Year 4 Inglês 38 flashcards

State the relation to describe for a lattice appearing unchanged by this relation (in terms of translation vectors and…

Flashcards do conjunto (38)

1What is the overall aim of condensed matter physicsTo develop physical concepts and models to describe and predict physical properties
2Describe atoms of crystalsAn ordered arrangement of atoms
3Describe angles and shape of mineral crystalsSymmetric Shape
Discrete angles between facets
4Define a crystalAny solid with an essentially ordered arrangement of atoms or molecules that extends in three spatial directions and has a diffraction pattern of sharp spots
5Define a Periodic CrystalAny solid with essentially ordered arrangement of atoms that extends periodically in three spatial directions. Its periodicity is the lattice and the set of atoms is the basis.
6Describe a crystal LatticeRegular array of points in space, it describes 3D crystal periodicity.
7State the relation to describe for a lattice appearing unchanged by this relation (in terms of translation vectors and arbitrary integers)
8For the following crystal systems state the min symmetry and restrictions on unit cell properties Cubic, Hexagonal, Trigonal. Tetragonal, Orthorhombic, Monoclinic, Triclinic
9For BCC, state the relations for conventional and primitive translation vectors
10Describe the difference between direct and reciprocal latticeDirect/Real: Translation vectors have dimension of length. Lattice describes periodicity of atomic arrangement.
Rec: Tran vectors have dimension I / length. Lattice is in fourier space of crystal.
11(N) Define condensed mattersystems comprising a large number of particles with strong interactions between
them
12How can we 'create' a crystalby repeating a certain set
of atoms (the basis) periodically in all three spatial directions. The crystal lattice
describes only the spatial periodicity
13Define Spatial periodicitydescribed with three (non-coplanar) translation vectors.
They also span a basic volume, the unit cell, which fills space without gaps when
repeated periodically. For every lattice, there is an infinite number of possible
translation vectors and corresponding unit cells, which are mathematically all
equivalent.
14Describe the symmetry of a crystals shapeThe symmetries of crystal shapes reflect symmetries in the atomic arrangements.
A symmetry operation is a geometrical operation that transforms the “object”
to a state that is indistinguishable from the starting point. This can be applied
both to a crystal as a whole and to the atomic arrangement within a crystal.
15Define Mirror SymmetryMirror symmetry leaves an object unchanged upon reflection about a line (in two
dimensions) or a plane (in three dimensions). A cube has three mirror planes
parallel to its faces and six mirror planes that are parallel to the face diagonals.
16Define rotational symmetryRotational symmetry leaves an object unchanged upon rotation about an axis,
where the rotation angle is necessarily an integer fraction of 360°.
17Define inversion symmetryInversion symmetry leaves an object unchanged upon reflection through a point,
which is called the inversion centre.
18Describe a centred lattice revealing hidden symmetriesthe unit cell spanned
by the translation vectors contains more than one lattice point. The benefit is
that this can uncover some restriction on the translation vectors.
19For the following crystal systems state centring and restrictions on unit cell properties Cubic, Hex, Trigonal, tetra, Ortho, Mono, Triclinic
20Describe forming the HCP and FCC closed pack structures via layersstart with a first hexagonal layer of spheres — layer a. A second,
identical layer is then placed above layer a and displaced such that every sphere
in the new layer b is above a gap between three spheres in layer a. One has now
a choice how to proceed to the next layer. (i) If one adds another layer of type a,
and proceeds to create a sequence ababab. . . of layers, one obtains the hcp crystal
structure. (ii) If one places the third layer such that every sphere is above the
remaining gaps in the ab double layer, and proceeds to create an abcabcabc. . .
sequence, one obtains the fcc crystal structure.
21Define Crystal PlanesCrystal planes are sets of parallel planes on which all the atoms of a crystal can
be located
22Answer the following; What does interplanar spacings determine Describe electrical and thermal conductivity of graphene Describe plastic deformation in crystals Factors of Crystal surfaces
23what do miller indices describe?an infinite set of parallel planes
also used to describe directions in a crystal.
24What can be used for diffraction from crystals?xrays
neutrons
electrons
25Describe diffraction as a wave phenomenon? Sketch the waves interactingRadiation is scattered by atoms
Each atom becomes a new source
Theres interference of all scattered radiation.
Diffraction from crystals is a wave phenomenon employing electromagnetic
or particle waves of a wavelength similar to the interatomic spacing or lattice
periodicity $Describe diffraction as a wave phenomenon? Sketch the waves interacting$
26Why is modelling diffraction intensities for electrons more difficult than xrays and neutrons?electrons interact more strongly with
a crystal than x-ray and neutrons
27What are the short comings of Braggs Lawbased on the unexplained premise that the
incoming radiation is reflected specularly by the crystal planes. Bragg’s law also
yields no information on the relative intensities of the reflections from different
crystal planes, which is the crucial information for determining the positions of
the atoms in the unit cell. That said, Bragg’s law allows us to determine the unit
cell dimensions from measured diffraction angles and thus the lattice part of the
crystal structure.
28Describe the x ray diffraction processConsider
an electromagnetic (EM) plane wave entering and propagating through the crystal.
At every point 𝒓 in the crystal, there is a certain chance that the EM radiation gets
scattered into a secondary spherical wave, which scales with the electron density
𝑛(𝒓) at that point. All scattered contributions will then interfere in some way in
the direction of the outgoing beam, which means that we need to take into account
the phase differences between all contributions. In order to obtain a measure of
the “diffraction strength”, one integrates all phase-weighted contributions over
the whole crystal. Interpret “diffraction strength” as a measure of the diffracted
EM field amplitude relative to that of the incoming wave. We will eventually
square it to obtain a measure of the diffracted intensity, which is what one can
obtain in an experiment. $Describe the x ray diffraction process$
29For xray diffraction intensities state the scattering amplitude strength $For xray diffraction intensities state the scattering amplitude strength$
30Describe a periodic signal in terms of Fourier coefficients, how does the electron density distribution occur here?A periodic function can be expanded as a Fourier series. A periodic signal in the
time domain can be represented by a series of Fourier coefficients (numbers) that
describe the relative weight of the discrete frequency components of the signal.
The electron density distribution in a periodic crystal is a three-dimensional
periodic function. We will see later that an x-ray diffraction experiment measures
the Fourier coefficients of the electron distribution.
31For xrays, what is the con of Fourier component measurementswe can only
measure the the absolute values of the Fourier components. The signs or phase
information is lost because we can only measure x-ray intensities, not electric
field amplitudes
32For the square wave, state the following relations Periodicity in a Fourier series general formula Cp, Co and Sp (Inversion of FS)
33What does the charge distribution provide in an xray diffraction experimenta
discrete set of diffraction intensities.
34State the relations for the Complex Fourier series and coefficients
35Describe a Fourier Series for non orthogonal latticessimple Fourier series in terms of Cartesian coordinates cannot be used for
functions on a non-orthogonal lattice (hexagonal or oblique). The problem here
is that 𝑛(𝑥, 𝑦) is necessarily aperiodic with respect to at least one of the Cartesian
coordinates. The solution is to create a non-orthogonal reciprocal lattice (i.e. in
frequency space), which can then be used for Fourier series.
36YB State the translational vector formula State reciprocal lattice point formula Reciprocal vector lengths
37How is the interplanar spacing determineddetermined conveniently from the corresponding reciprocal lattice vector
38YB State the following Complex Fourier Expansion in 1D Fourier Series in 3D Fourier Coefficients