structures, woods, matrices Flashcards
what is tribology?
surface friction
how are samples prepared for use?
- a single crystal cleaved to expose a particular facet
- aligned by x-ray diffraction before cutting
- crystal is under ultra high vacuum (UHV)
- crystal is cleaned by sputtering and annealing
what is sputtering and annealing?
sputtering = surface bombarded with Ar^+ to remove any adsorbed species
annealing = heating then cooling of the surface to reorder it and make it smooth
what is monolayer coverage?
all possible sites are covered
how are surface planes and directional integers represented?
surface planes = (hkl)
directions = [pqr]
NOTE THE BRACKET TYPES
in which crystal type are the real and reciprocal lattice vectors the same in the same directions?
cubic crystals
how does the miller indices indicate the position of the plane relative to the axes?
(100) = plane is parallel to y and z
(110) = plane is parallel to z
what are the shapes of the unit cells for simple cubic?
(100) = square
(111) = triangular/parallelogram
(110) = rectangular
What elements have FCC arrangement?
Cu, Ni, Rh, Pt
what are the shapes of the unit cells for FCC?
(100) = square orientated like a diamond
(111) = parallelogram
(110) = rectangle
What are the layer spacings for (100) FCC?
a|2/ 2 = a/|2
| = root symbol
= root symbol
What are the layer spacings for (111) FCC?
L/|3 = a|2 / |3
| = root symbol
= root symbol
What are the layer spacings for (110) FCC?
a/2
What is the most densely packed FCC surface and so the lowest energy?
(111)
What does a high density within a layer mean?
the layers can’t get closer together
What is the conventional labelling direction for a1 in FCC (111)?
pointing down
What is the conventional labelling direction for a2 in FCC (110)?
must be the longer side of the rectangle
What is an atop site?
the top layer
What is a bridge site?
the gaps/overlaps between atoms of the same layer
What is a hollow site?
the bottom layer(s)
the no. fold = how many atoms it has overlapping on top of it
What are the shapes of the unit cells for BCC?
(100) = square
(111) = parallelogram
(110) = rectangular diamond (horizontal)
What is quasi-hexagonal or quasi close-packed?
BCC (110)
What is the order of density of BCC arrangments?
(110) > (100) > (111)
What metals arrange in BCC (100)?
Na and W (tungsten)
How many nearest neighbours for FCC (100) surface and second layer?
4 NN for both
How many nearest neighbours for FCC (111) surface and second layer?
6 on surface, 3 on second layer
How many nearest neighbours for FCC (110) surface and second layer?
2 on surface, 7 NN total
How many bonds broken for (100) FCC?
4 bonds broken (from second layer NN)
How many bonds broken for (111) FCC?
3 bonds broken (from second layer NN)
How many bonds broken for (110) FCC?
5 bonds broken
Which has the lowest energy conformer of the FCC? The order of the other two?
(111) < (100) < (110)
What is the bulk vs the surface?
surface = the very top layer
bulk = the rest of the layers
How do the spacings between surfaces change when bonds break?
the surface moves closer to the bulk - so the spacings between the 2nd and 3rd layers are larger than in the bulk
(bc the 1st layer is closer to the 2nd)
What is the selvedge?
where the differences between the surface and the bulk are noticeable
How does (110) FCC reconstruct?
by adding an extra row inbetween rows of three of the original layer
how do the lattice vectors change for FCC (11) reconstructed surface?
a1 = b1
b2 = 2a2 (the space between two of the original rows)
Why does reconstruction occur?
to minimise the energy cost of the surface being separated from the bulk
How does FCC (100) reconstruct?
so the top layer is hexagonal on top of the normal square lattice
where is a2 on stepped surfaces?
pointing along the steps
how are the steps arranged on (100) vs (111) FCC?
(100) = square lattice
(111) = hexagonal stacking
What are vicinal structures?
where the cut of the crystal is slightly “off” and this can lead to steps
how do you work out the spacing of steps?
by trigonometry
How can you fix steps in the structure?
by annealing
How does reconstruction occur with covalent bonds?
The atoms are moved so that the top layer atoms are connected horizontally, giving more than 2 NN
What is the rutile structure?
TiO2
How does TiO2 reconstruct?
extra rows of Ti2O3 are added on top of the layers - gives a lower oxygen content
How to identify the overlayer type?
By the number of atoms the overlayer atoms are apart:
one atom apart (rare) = (1x1)
two apart horizontally but one apart vertically = (2x1 or 1x2)
two apart = (2x2)
What is the most common overlayer arrangement?
(2x2) bc the atoms are likely the same so repel each other
What is the clean surface ?
no overlayer/adsorbate atoms at all on it (ie. in one section of the surface)
what are the clean surface vectors vs the overlayer vectors?
clean surface = a1, a2
overlayer = b1, b2
Why is the M(100) c (2x2) surface known as that?
M = the metal
(100) = miller indices
c refers to the central atom in the overlayer unit cell
(2x2) bc the square containing the central atom is twice the size of the unit cell (in both directions)
why is a(root)2 often used as a length?
root 2 is always a factor for the diagonal of a square - so a(root)2 is that vector relative to a
What does the angle in Woods notation refer to?
the angle of rotation from the clean surface that the overlayer vectors are offset by
How do you convert between Woods and matrix notations?
the integers for a1 and a2 for b1 are written along the top of the matrix
the integers for a1 and a2 of b2 are written along the bottom of the matrix
e.g. (1x2) = (10//02) see notes
what is the standard directions for a1 and a2 to point for all structures?
a1 down, a2 across
for FCC(110) the a2 must be the longer side and anticlockwise to a1
for RECIPROCAL space, how is the matrix labelled?
M*
how do you deal with decimal values for a1 or a2 etc?
multiply all of the values by the same number to make the decimals whole numbers
