Lecture 6. Thermodynamics and Kinetics for Adsorption, Diffusion and Desorption

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1 Physics 986 Lecture 6 Thermodynmics nd Kinetics for Adsorption, Diffusion nd Desorption Physisorption Chemisorption Surfce Bonding Kinetics of Adsorption/Diffusion/Desorption References: ) Zngwill, Chpter 8, 9, 4 ) Attrd nd Brnes, p.-7, 7-34, ) Woodruff & Delchr, Chpter 5, p.356 4) Kolsinski, Chpter 3 nd 4 5) Somorji, Chpter 3.8, 4, 5 Lecture 6 Force nd Energy Digrm F net = F ttctive + F repulvise ( Ze)( Ze) FATTR = 4πε nb FREP = n+ n nd b re constnts; n = 7 9 NET = 0 = = n+ 4πε o ZZe 9b = 9; = ; 0 4πε o F n o o Z Z e 8 ZZe b = = 4πε 9 36 bn ZZe πε o 8 Lecture 6 Lecture 6

2 Physics 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 echnge Chemicl bond formtion Strong > ev (00 kj mol - ) 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 - ) Stble only t cryogenic tempertures (N 77K, He 4K) Less strongly directionl Multilyers cn form O/Fe, Al, Si H/Pd NH3/Cu H / Fe, Au H O/Au NH /Cu Lecture 6 4 Lecture 6

of T on diffusion: Diffusion rte in system will increse with temperture: EA RT D = Do e D diffusivity, m /s D 0- proportionlity constnt, m /s, independent of T E A ctivtion energy for diffusing

3 Physics Binding Sites nd Diffusion The binding energy of n dsobte depends on its position on the surfce, or on the binding site sites seprted by energetic brriers cn be thought of diffusion brriers Effects of T on diffusion: Diffusion rte in system will increse with temperture: EA RT D = Do e 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 = 8.34 J mol- K- Lecture 6 5 Fick s first lw of diffusion dc J = D d toms m J = D m s s - sign: flu 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/d dc toms 3 d m m Diffusivity D depends on:. Diffusion mechnism. Temperture of diffusion 3. Type of crystl structure (bcc > fcc) 4. Crystl imperfections 5. Concentrtion of diffusing species Lecture 6 6 Lecture 6 3

4 Physics 986 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: dc Second Fick s lw of diffusion: = dt If D D(), in D cse: In 3D cse: dc dt dc dt d d C = D dc D d The rte of compositionl chnge is equl to the diffusivity times the rte of the chnge of the concentrtion grdient C C C D + + y z = Chnge in concentrtion in semi-infinite rods of Cu nd Ni cused by diffusion, From G. Gottstein Physicl Foundtions of Mteril Science Lecture 6 7 Non-Stedy-Stte Diffusion (continued) With specific initil or boundry conditions this prtil differentil eqns cn be solved to give the concentrtion s function of sptil position nd time c(, y, z, t) Let us consider two rods with different concentrtions c nd c which re joined t =0 nd both re so long tht mthemticlly they cn be considered s infinitely long The concentrtion profile t t = 0 is discontinuous t = 0: < 0, c = c ; < 0, c = c dc We cn obtin solution of: C = D dt c c(, t) c = where erf ( z) = z = Dt c π π 0 z Dt e e ξ ξ c dξ = c + erf Dt dξ, is known s the error function Lecture 6 8 Lecture 6 4

5 Physics 986 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 o = erf Dt = 0 C S surf. C of element in gs diffusing into the surfce C o initil uniform concentrtion of element in solid - distnce from surfce D diffusivity of diffusing solute element t time erf mthemticl function clled error function Lecture 6 9 Error function Curve of the error function erf (z) for z = Dt Lecture 6 0 Lecture 6 5

Physics 986 Atomistics of Solid Stte Diffusion Diffusion mechnisms:.

: self diffusion of Cu toms in Cu crystl.

site without permnent displcement ny of the toms in the mtri crystl lttice E.

homogeneous system - self-diffusion, in heterogeneous system solid stte solutions) Vcncies re lwys

6 Physics 986 Atomistics of Solid Stte Diffusion Diffusion mechnisms:. Vcncy (substitutionl) diffusion migrtion of tom in lttice ssisted by the presence of vcncies E.: 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 mtri crystl lttice E.: C diffusion in BCC iron Lecture 6 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 () to ()) = move vcncy from () to ()..? higher T melt stronger bonding between toms high ctivtion energy to move V Lecture 6 Lecture 6 6

de Lecture 6 3 Possible mechnisms of self-diffusion nd their ctivtion energy. Neighboring toms echnge sites.

7 Physics 986 Ehrlich-Schwoebel Brrier, E S Echnge mechnism of diffusion (importnt for metl-on-metl growth) STM imge of chromium decorted steps of Cu() Lecture 6 3 Possible mechnisms of self-diffusion nd their ctivtion energy. Neighboring toms echnge sites. Ring mechnism 3. Vcncy mechnism 4. Direct interstitil mechnism 5. Indirect interstitil mechnism Migrtion 8 ev ev 0.6 ev 0. ev Formtion - ev 3.4 ev 3.4 ev Totl 8 ev ev 4 ev 3.6 ev Lecture 6 4 Lecture 6 7

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

defects ffect dsoprtion energies D lloyed lyers, compound lyers cn eist when no such bulk phse is known Adsorption chemistry is

9 Physics 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 eist when no such bulk phse is known Adsorption chemistry is nlogous to cluster inorgnic chemistry Lecture 6 7 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 8 Lecture 6 9

Physics 986 Moleculr Oygen Chemisorption Three distinct vibrtionl frequencies three moleculr species Decresing frequency incresing M-O bonding dpted from Surf.Sci. 334, 9 Lecture 6 9 6.

10 Physics 986 Moleculr Oygen Chemisorption Three distinct vibrtionl frequencies three moleculr species Decresing frequency incresing M-O bonding dpted from Surf.Sci. 334, 9 Lecture Rective (Dissocitive) Chemisorption Chemisorption ssocited with moleculr decomposition Other Rective Processes: Ctlysis (A + B (ds) AB) Substrte rection (Oidtion, etc) Desorption (+ Chemistry with sledge hmmer!) Lecture 6 0 Lecture 6 0

11 Physics 986 Dissocite Adsorption Emples O on Al() At 80K pirs for oygen dtoms withintertomic distnces -3 Al spcing Cl on Si() At 80K pirs for oygen dtoms withintertomic distnces -3 Al spcing Surf.Sci. 478 (00) L PRB 68 (003) Lecture 6 Prediction from Het of Adsorption Given dissocitive dsorption: is moleculr or tomic desorption preferred? Is H ds < E A or H ds > E A Ni-H W-O Lecture 6 Lecture 6

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

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