Lecture 5. Selected aspects of thermodynamics for adsorption, diffusion and desorption

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1 Physics 986b Lecture 5 Selected spects of thermodynmics for dsorption, diffusion nd desorption Physisorption Chemisorption Surfce Bonding Mechnisms of dsorption/diffusion/desorption References: 1) Zngwill, Chpter 8, 9, 14 ) Attrd nd Brnes, p.1-17, 7-34, ) Woodruff & Delchr, Chpter 5, p.356 4) Kolsinski, Chpter 3 nd 4 5) Somorji, Chpter 3.8, 4, 5 1 Force nd Energy Digrm F net = F ttctive + F repulvise ( Z1e)( Ze) FATTR 4 nb FREP n1 n nd b re constnts; n 7 9 F NET n 9; o Z Z e bn 1 0 n1 4 o Z1Ze 9b ; 10 4 o 8 Z1Ze b 4 9 o 1 36 Z1Ze o 8 Lecture 5, Jnury 8, 013 1

2 Physics 986b 5.1 Bsics of Collision Process () Elstic Scttering (b) Inelstic Scttering Adsorb (c) Chemisorption (d) Physisorption Surfce diffusion Surfce rection Desorption Cf. Kolsinski Lecture 6 3 Physisorption vs Chemisorption Chemisorption Electron exchnge Chemicl bond formtion Strong > 1eV (100 kj mol -1 ) Highly corrugted potentil Anlogies with coordintion chemistry Second phse cn form for suitble T nd P Physisorption Polriztion Vn der Wls ttrctions Wek < 0.3 ev (30kJ mol -1 ) Stble only t cryogenic tempertures (N 77K, He 4K) Less strongly directionl Multilyers cn form O/Fe, Al, Si H/Pd NH 3 /Cu H / Fe, Au H O/Au NH x /Cu 4 Lecture 5, Jnury 8, 013

3 Physics 986b 5. Binding Sites nd Diffusion The binding energy of n dsobte depends on its position on the surfce, or on the binding site 5 Binding Sites nd Diffusion Adsorption sites seprted by energetic brriers cn be thought of diffusion brriers Effects of T on diffusion: Diffusion rte in system will increse with temperture: D D e o EA RT D diffusivity, m /s D 0- proportionlity constnt, m /s, independent of T E A ctivtion energy for diffusing species, J/mol R molr gs constnt; R = J mol-1 K-1 6 Lecture 5, Jnury 8, 013 3

4 Physics 986b Fick s first lw of diffusion dc J D dx toms m J D m s s - sign: flux direction is from the higher to the lower concentrtion; i.e. it is the opposite to the concentrtion grdient For stedy-stte diffusion condition (no chnge in the system with time), the net flow of toms is equl to the diffusivity D times the diffusion grdient dc/dx dc toms 1 3 dx m m Diffusivity D depends on: 1. Diffusion mechnism. Temperture of diffusion 3. Type of crystl structure (bcc > fcc) 4. Crystl imperfections 5. Concentrtion of diffusing species 7 Non-Stedy-Stte Diffusion In prctice the concentrtion of solute toms t ny point in the mteril chnges with time non-stedystte diffusion For non-stedy-stte condition, diffusion coefficient, D - NOT dependent on time: dcx Second Fick s lw of diffusion: dt If D D(x), in 1D cse: In 3D cse: dc x dt dc x dt C D x d dcx D dx dx The rte of compositionl chnge is equl to the diffusivity times the rte of the chnge of the concentrtion grdient C C C D x y z Chnge in concentrtion in semi-infinite rods of Cu nd Ni cused by diffusion, From G. Gottstein Physicl Foundtions of Mteril Science 8 Lecture 5, Jnury 8, 013 4

5 Physics 986b Non-Stedy-Stte Diffusion (continued) With specific initil or boundry conditions this prtil differentil equtions cn be solved to give the concentrtion s function of sptil position nd time c(x, y, z, t) Let us consider two rods with different concentrtions c 1 nd c which re joined t x=0 nd both re so long tht mthemticlly they cn be considered s infinitely long The concentrtion profile t t = 0 is discontinuous t x = 0: x < 0, c = c 1 ; x < 0, c = c We cn obtin solution of: c c( x, t) c where erf ( z) 1 c 1 z 0 dc x C D dt x x Dt e e c d c 1 1 erf x Dt x d, is known s the error functionz Dt 9 Gs diffusion into solid Let us consider the cse of gs A diffusing into solid B Element A Solid B Cs C C C S x o x erf Dt x = 0 C S surf. C of element in gs diffusing into the surfce C o initil uniform concentrtion of element in solid x - distnce from surfce D diffusivity of diffusing solute element t time erf mthemticl function clled error function 10 Lecture 5, Jnury 8, 013 5

6 Physics 986b Error function Curve of the error function erf (z) for z x Dt Lecture 6 11 Exmple If boron is diffused into thick slice of Si with no previous Bin it t T=1100 C for 5 h, wht is the depth below the surfce t which the concentrtion is toms/cm 3 if the surfce concentrtion is toms/cm 3? D = cm /s for B diffusing in Si t 1100 C. Lecture 5 1 Lecture 5, Jnury 8, 013 6

7 Physics 986b Atomistics of Solid Stte Diffusion Diffusion mechnisms: 1. Vcncy (substitutionl) diffusion migrtion of tom in lttice ssisted by the presence of vcncies Ex.: self diffusion of Cu toms in Cu crystl. Interstitil diffusion movement of toms from one interstitil site to nother neighboring interstitil site without permnent displcement ny of the toms in the mtrix crystl lttice Ex.: C diffusion in BCC iron 13 Vcncy (Substitutionl) Diffusion Mechnism Substitutionl (in homogeneous system - self-diffusion, in heterogeneous system solid stte solutions) Vcncies re lwys present t ny T As T increses # of vcncies increses diffusion rte increses Move tom A (from (1) to ()) = move vcncy from () to (1)..? higher T melt stronger bonding between toms high ctivtion energy to move V 14 Lecture 5, Jnury 8, 013 7

8 Physics 986b Ehrlich-Schwoebel Brrier, E S Exchnge mechnism of diffusion (importnt for metl-on-metl growth) STM imge of chromium decorted steps of Cu(111) 15 Possible mechnisms of self-diffusion nd their ctivtion energy 1. Neighboring toms exchnge sites. Ring mechnism 3. Vcncy mechnism 4. Direct interstitil mechnism 5. Indirect interstitil mechnism Migrtion Formtion Totl 1 8 ev - 8 ev 3 1 ev 1 ev ev ev 3.4 ev 4 ev 6 0. ev 3.4 ev 3.6 ev 16 Lecture 5, Jnury 8, 013 8

9 Physics 986b 5.3 Physisoption Physisorption rises from dispersion forces d+ d- r E d+ d- C ; r where C f ( Instntneous fluctutions in chrge distribution interct with instnteneous dipole moments in neighboring species, ) ATTR 6 i i The 6-1 Lennrd-Jones potentil is commonly used to describe both Vn der Wls nd steeply rising repulsive interction potentil E 4 r 1 6 r r E V substrte D r 1 6 C Ndv r dv i 17 Physisorption energy of Xe on metl surfce Lecture 6 18 Lecture 5, Jnury 8, 013 9

10 Physics 986b 5.4 Nondissocitive Chemisorption Sequentil filling of binding sites top bridge hollow Binding energies depend on crystl fce Steps, defects ffect dsoprtion energies D lloyed lyers, compound lyers cn exist when no such bulk phse is known Adsorption chemistry is nlogous to cluster inorgnic chemistry 19 The Blyholder Model of CO Chemisorption CO hs longed served s model dsorbte Isolted CO: MO of gs-phse CO The wvefunction chnges sign in going from the region shown by different color Lecture 6 0 Lecture 5, Jnury 8,

11 Physics 986b Moleculr Oxygen Chemisorption Three distinct vibrtionl frequencies three moleculr species Decresing frequency incresing M-O bonding dpted from Surf.Sci. 334, Rective (Dissocitive) Chemisorption Chemisorption ssocited with moleculr decomposition Other Rective Processes: Ctlysis (A + B (ds) AB) Substrte rection (Oxidtion, etc) Desorption (+ Chemistry with sledge hmmer!) Lecture 5, Jnury 8,

12 Physics 986b Dissocite Adsorption Exmples O on Al(111) At 80K pirs for oxygen dtoms withintertomic distnces 1-3 Al spcing Cl on Si(111) At 80K pirs for oxygen dtoms withintertomic distnces 1-3 Al spcing Surf.Sci. 478 (001) L PRB 68 (003) Prediction from Het of Adsorption Given dissocitive dsorption: is moleculr or tomic desorption preferred? Is DH ds < E A or DH ds > E A Ni-H W-O 4 Lecture 5, Jnury 8, 013 1

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