Tentamen. TFYA47 Ytor och gränsskikt, TEN2. 28 oktober 2015 kl Skrivsal: Kårallen

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1 Thomas Ederth IFM / Molekylär Fysik ted@ifm.liu.se Tentamen TFYA47 Ytor och gränsskikt, TEN2 28 oktober 2015 kl Skrivsal: Kårallen Tentamen omfattar 5 problem som vardera kan ge 10 poäng. För godkänt krävs totalt 22 poäng samt minst 3 poäng per uppgift. Tentamen består av 3 sidor (inklusive denna). Lösningar läggs ut på kurshemsidan efter skrivtidens slut. Skrivningsresultat meddelas senast 12 arbetsdagar efter tentamenstillfället. Tillåtna hjälpmedel: Physics Handbook Räknedosa (med tömda minnen) Kursansvarig: Thomas Ederth, som finns tillgänglig på ankn eller telefon under skrivtiden. Kursadministratör: Lena Wide, ankn. 1229, lena.wide@liu.se. Lösningar skall om möjligt åtföljas av figur, införda beteckningar skall definieras, ekvationer motiveras och numeriskt svar alltid skrivas ut med enhet. Orimligt svar medför noll poäng på uppgiften. Lycka till!

2 Tentamen i TFYA47 Ytor och gränsskikt, TEN2, 28 oktober 2015 (English translation on next page!) 1. a) Figuren till höger visar ett plan inlagt i ett enkelt kubiskt gitter. Bestäm Millerindex för planet. [3p] b) Ange riktningen som är vinkelrät mot planet i a). [2p] c) Järn har bcc-struktur, där den kubiska enhetscellen är 286 pm. Beräkna antalet atomer per m 2 förkristallplanen Fe(100) och Fe(111). [5p] 2. a) Woods notation kan användas för att beskriva antingen en rekonstruktion eller ett överlager. Vad är det för skillnad mellan dessa? [2p] b) En komplett beskrivning av ett överlager ser ut som följer. Vad står de olika termerna för? [3p] ( a0 M(hkl) a s b ) 0 Rα A θ b s c) Figuren visar sticking -koefficienten för molekylär kemisorption av syre på wolfram, som funktion av molekylernas kinetiska energi. Skissa växelverkanspotentialen mellan syremolekylerna och ytan. [4p] d) Sticking föregås i regel av en process där kinetisk energi absorberas av ytan, vad kallas detta? [1p] 3. a) Vid IRAS-mätning av etan adsorberat på Cu fås detta spektrum. Figuren visar också de två C Hsträckningar som indikerats i spektrumet. Förklara hur detta kan visa hur etan är orienterat på ytan. [5p] b) Visa hur vinkelberoende XPS fungerar, och varför det är användbart för ytstudier. [5p] 4. a) Vad är oleofobicitet och hydrofobicitet? [2p] b) Vad är kontaktvinkelhysteres, och hur uppstår det? [4p] c) Förklara hur en Zisman-plot konstrueras, och hur den kan användas för att uppskatta ytenergin. [4p] 5. a) Vid ytmodifiering med silaner skiljer man mellan klorosilaner och alkoxysilaner. Beskriv dessa, och nämn viktiga skillnader mellan dem. [4p] b) Ange två metoder som kan användas för att avgöra kvaliteten på ett silanmonolager; beskriv vilka egenskaper eller storheter som bestäms med respektive metod, samt åtminstone en nackdel med var och en av dem. [6p]

3 Examination TFYA47 Surfaces and Interfaces, TEN2, 28 October a) The figure shows a plane in a simple cubic lattice. Determine the Miller index for the plane. [3p] b) Specify the direction perpendicular to the plane in a). [2p] c) Iron has bcc structure, with the cubic unit cell lattice parameter 286 pm. Calculate the number of atoms per m 2 for the planes Fe(100) and Fe(111). [5p] 2. a) Wood s notation can be used to specify either a reconstruction or an overlayer. What is the difference between these? [2p] b) A complete descrption of an overlayer looks like this. What do the different terms represent? [3p] ( a0 M(hkl) a s b ) 0 Rα A θ b s c) The figure shows the sticking coefficient for molecular chemisorption of oxygen on tungsten, as a function of the kinetic energy of the molecules. Sketch the interaction potential between the molecules and the surface. [4p] d) Sticking is typically preceded by a process where kinetic energy is absorbed by the surface, what is this called? [1p] 3. a) IRAS measurement of ethane on Cu yields the spectrum on the right. The figure also shows the two C H-stretching modes that are indicated in the spectrum. Explain how this can tell us the orientation of ethane on the surface. [5p] b) Explain how angle-resolved XPS works, and why it is useful for surface studies. [5p] 4. a) What are oleophobicity och hydrophobicity? [2p] b) What is contact angle hysteresis, and how does it occur? [4p] c) Explain how a Zisman plot is constructed, and how it can be used to estimate the surface energy. [4p] 5. a) Upon surface modification with silanes we differ between chlorosilanes and alkoxysilanes. Describe these types, and also some important differences between them. [4p] b) Specify two methods that can be used to determine the quality of a silane monolayer; describe what properties each method provides, and also at least one disadvantage of each method. [6p]

4 Solutions to Examination TFYA47 TEN2, 28 October a) The plane intersects the axes at (2,5,4). Inverting these numbers, and multiplying to obtain the least common denominator (20) yields the Miller index as: ( ) ( 1 10 = ) 5 20 (10 4 5) b) In a cubic lattice, the direction perpendicular to a plane specified with the Miller index (10 4 5) is given as [10 4 5] (the direction can also be found via the cross product of any two vectors in the plane). The surface normal is obtained after normalization: ˆn = (10 4 5) = (10 4 5) c) Let a = 286 pm denote the lattice parameter. In bcc, only the corner atoms in the side of the cubic cell lie in the (100) plane. The area of one such cube side is 286 pm 286 pm = 8, m 2. This area corresponds to one atom (each corner contributing 1/4 atom), and hence the number of atoms per area is 1/8, = 1, atoms/m 2. The (111) plane in a bcc unit cell is shown to the right. The center atom does not lie in the (111) plane, and should not be counted. The diagonals x = 2a. Each corner of the triangle indicated in the figure contributes 1/6 atom, and hence the whole triangle contributes 1/2 atom. If x is the base, its height h is obtained via Pythagoras theorem: ( ) ( ) x 2 ( ) h = x 2 = = = pm Thus, the area occupied by one atom in the plane is twice the shaded triangle, 2 A = 2 x h 0,5 = 1, m 2. The number of atoms per m 2 is then the inverse of this; 7, atoms/m a) A reconstruction is a rearrangement of surface atoms which are of the same type as the bulk atoms. An overlayer is formed by adsorbed atoms. b) See the literature, e.g. notes from lecture 9. Bonus point to those who spotted the omission of the c,p identifier in the question... c) From the diagram it is apparent that sticking is less likely for energies less than approximately 0,4 ev, suggesting that there is a barrier of this height inthe potential. Taking this into account, an approximate potential looks like the figure on the right. There must be a minimum in the potential behind the barrier, otherwise the molecules would not be retained. There may or may not be a shallow minimum outside the potential, though this is indeed very common. d) Trapping.

5 3. a) In IRAS, only those vibrational modes are visible with transition dipoles (changes in the dipole moments) perpendicular to the surface (the surface selection rule). The ν s mode induces a change in dipole moment which is orientedalongthec-caxisofthemolecule, whiletheν as modehasatransition dipole moment which is perpendicular to the molecular axis. In the spectrum, the ν s mode is suppressed, and ν as has a large magnitude, indicating that the ν s mode is oriented parallel to the surface, which is consistent with ethane lying flat, with the C-C-bonds parallel to the surface. b) See the literature, e.g. notes from lecture 13 on surface spectroscopy. An important point (i.e. acommon mistake) isthat it isthe angleofemission from the sample to the detector that is varied to obtain the sensitivity to different depths; the X-ray excitation radiation penetrates deeply into the sample, but it is the photoelectrons that have a limited path length. 4. a) Oleophobicity is when a material is not wetted by hydrocarbons, while hydrophobicity is when a material is not wetted by water. (Literally, these terms refer to imbibition, or bulk uptake, but both meanings are considered correct, due to widespread use of this terminology.) b) The difference between advancing and receding contact angles. This occurs as a result of surface heterogenenity (either chemical or topographical), or due to reorganization of functional groups at the interface. c) In a Zisman plot, the cosines of the contact angles of several probe liquids (on a given solid) are plotted versus the surface energy of the probe liquids. Using the rule that low energy liquids spread on high energy surfaces one then extrapolates to the highest liquid surface energy that completely wets the sample, and this surface tension is taken as the free energy of the surface (the critical surface tension ). 5. a) See the literature, e.g. notes from lecture 12 on SAMs. b) There is a large number of methods to investigate, for example, structure, chemistry, or wettability. Of particular relevance is that silane layers are usually formed on oxides, which are typically electrical insulators, excluding most uses of methods such as STM or IRAS.