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Oxidation Kinetics of CopperAn Experiment in Solid State ChemistryY. Ebisuzaki an d W. B. SanbornNorthCarolina State University, Raleigh.NC 27695

Considerable research interes t has been shown recently insolid state chemistry due to its technological mportance; thus,it seems appropriate to introduce some solid state chemistryin the underg;aduate rurrirulum. The presrnt article dg-scrihes the oxidation kinetics in metals and illustrates the mledefects play in diffusion-controlled reactions. Copper isprobably th e most suitable metal for studen t study since the"xidation proceeds at muderately high t e n ~ ~ e r a t ~ l r end themechanism has herome the prototype for other metsls (1-6).The ex~)eriments suitahle for iuniors and seniors in uhvsiral"or inorganic chemistry laboratory.Theory

Let us first consider the nature of defects in c u~ ro usxideand the role they play in the diffusion of Cu+ ions in theoxi-dation Drocess. Thr oxide is nonstoichiometric, riolatinpl thelaw of definite proportions with the excess oxygen contentheing of the order of 0.1'70, thus giving a formula ofCut.99901.0007). Each excess oxygen removes two electronsfrom the electronic band of th e solid and t he resulting anionis incorporated in a regular lattice site (Fig. 1) ( I .The defi-ciency of Cu+ ions give rise to vacant cation lattice sites (0)and these a re shown schematically in Figure 1 (5, 6 ) . Th evacancies play an important role in the oxidation process sincean adiacent Cu+ ion can move into a vacant s ite and thenanother ion will move into the evacuated position and thusallow the cuprous ions to diffuse across the oxide layer. Duringthe oxidation process in Cu-Cu20-Ozsystem, a concentrationgradient of cation vacancies is established with the vacanciesheing created a t he oxide-gas interphase and the concentra-tion d r o ~ ~ i n eo a minimum a t the metal-oxide houndarv. Therate of oxid; growth is controlled by th e diffusion of Cu+across the oxide layer due to the concentration gradient ofvacancies and this mechanism is supported by the proposedexperiment.The oxidation process of Cu will now be considered. Whena clean surface of Cu is exposed to oxygen, the gas moleculesare rhemisorhed and a mckolayr of oxide is fo k ed . A rapidoxidation process follows in which the movement of Cu+ onsacross the oxide film is controlled by the strength of theelectric field between t he metal and t he chemisorhed oxygen(2,8).As the film thickness grows, th e effect of the electricfield diminishes as its gradient decreases and a slower, diffu-sion dependent process of the parabolic law becomes impor-

Figure 1. A schematic representation 01nonstoichiometric cuprousoxMe.Theexcess 0'- in Cu.0 lead to cation vacancies which aredesignatedas 0 .

tan t. Th e critical film thickness for the transition to the dif-fusion process depends upon the metal and the model em-ployed in describing thin film oxidation. In copper the tran -sition is assumed to take place a t around lo 2 o 103A, thus anoxide film of cm is considered thi ck (2,8).The reactions occurring in the Cu-Cuz0-02 system consistsof Cu+ ons and electrons entering the oxide a t he oxide-metalinternhase 1Cu- u+ + e-) and diffusine out to the oxide-eashi&dary where oxidation pn,ceeds (2&+ + 2e' + 11~0;'-Cu.10).The empirical oxidation rat e is aiven hv dx/d/ = k l x .where k (cm2s") is the parabolic ra te co ns ta t and r is theoxide film thickness. This r ate equation is in agreement withthe general observation that , as the oxide becomes thicker, therate of reaction hecomes slower. Integration of the rateequation results in a paraholic equation o r the parabolic law(Wagner) ( 4 4 )Equation (1) may be expressed in terms of weight increase(Aw)

MCUSA m z = 2k tMo PA (2 )

where p is the density of CuzO and A is the area' of thegrowing oxide film. A plot of Awz against t (time) maybeemployed to calculate the rate constant. The relationshipbetween the paraholic rate constan t and th e diffusion coeffi-cient (D) ill now he established.Derivation of the Rate Law

Only the positive ions and the electrons are appreciablymobile in Cu9O and need he included in the derivation oft herate law (I, 2:4,6). A current of charged particles per unit areaoer un it time or the flux. i. consists of two terms. one due todiffusion along the con&tration gradient ( d ~ f d x ) ith rbeina measured from th e metal surface and the other due tothe Gotion in an electric field, E:0 - D

dCej --0 -- ECepe (electron current)dl. (3)dCjj . = -D.-+EC. .&I (ionic current)dx (4)

wherep is the mobility or velocity per unit field. Th e followingsteps will lead to a s imple flux equation:(1) Eliminate E using eqns. (3) and (4); substitute for p from

Einstein relation (Dlu = k'Tle) and assume a stead" statewhew j , = I , = J ( I ) , where e is electronrr charge and k ' isRollzmann constant.(2 ) We may set r,o =PC.@,, ,a = PC,~ , ,. + t , and r, I . whereo is conductivity and t is transference numhpr.(31 Finally [he concentration of mobile electrons (C,) isequal tothe concrntration of cation vacancies(C,):, = C, = C.

'When a thin copper sheet with a fairly large surface area is oxidizedon the surface, he change in the area between that of the metal andthe oxide is quite small, although the thickness of the film increasesowing to the outward diffusionof the cuprous ions.A s a first approxi-mation, me area (A) may be assumed to be that of the metal sheet andthat it remains constant during the reaction in which an oxide scaleforms.Volume 62 Number 4 April 1965 341

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Figwe 2.The square of lheweight increase ( A s ) s ploned agsinst time (0 woxidation a t 807V (smallest slope), 913C and 1000'C (highest do pe).

Now the following flux equation is obtained:

Equation ( 5 ) may be rewritten (1,2)as

When the substitut ion is made for the concentration gradientin eqn. ( 6 ) ,we obtain = 2D(C1- Co)/x, where Cl an d Co areth e concentration of vacancies a t the metal-oxide and oxide-gas interphase, respectively. Th e oxide growth rate, d d d t , isequal to the fluxmultiplied by th e volume of oxide (V). Tha tis,

The relation between the measured rate constant and thediffusion coefficient is k = 2DV(C1- Co). Th e dependenceof k on the concentration of vacancies (C) may be tested bychanging the oxygen pressure (4 ,6) .The rate law for t he diffusion process and t he effect oftemperature on the rate cons tant in air can he measured in alaboratory experiment. The temperature effect is given by thefamiliar Arrhenius' equation k = koexp(-EJRT), where E .is th e activation energy. A convenient temperature range forcopper is 500 to 1000C.Experlmenlal

A small copper shee t (-0.1 X 1 X 3 cm) is cleaned (dil.HN 03 and HzO) and th e area measured with a micrometer.The samole is sus~ end ed v a fine wire in a furnace and al-lowed toix idiz e. 6 u r apparatus consisted of a modified dou-ble-oan anahtical balance sitting on a cement laboratory tahleto pk it h avertical furnace below one of the balance pans. Asa precaution, considerable separation (12 in.) was providedbetween th e furnace and t he tab le top.2 The sample was sus-pended from the balance pan and hung freely in the furnace.The oxidation rate of Cu in air or the weight increase wasobtained in reference to the apparent weight of the sample a tth e commencement of the experiment. As an alternative tothe above procedure, the individual samples were also re-moved from the oxidation furnace and the increase in weiehtmeasured a t room temperature. A tube furnace (1 in. iyd.)heated with nickel-chromium (Nichrome) wire with uDnertemperature of approximately 1 0 0 0 ~ ~as employed.A~h ethermocou~leti^ was laced directlv below the sa m ~ l endthe temper&e.was f&owed with ast ude nt poc ent ihe ter .If a chromel-alum~lhermocouple isemployed, it should not

Caution: Organic solvents should not be used near the hot fur-nace.

be left in the furnace for long duration. I t will be necessary toform a new fused thermocouple ti p after many hours of usea t high temperatures.Results and Discussion

When the square of the weight increase (Aw2) is plottedagainst time, a straight line is obtained, confirming the par-abolic law as reauired by ean . (2). The results a t three tem-peratures are pr&ented.in Figure 2. The paraholic rate con-sta nts ( k ) were calculated and thp results were found to bereprod"cible. The rate constants at various temperatures from687 to lO0OoC are summarized in the table. A straight line isobtained when the logarithm of the rate constants (loglo k)are plotted against the reciprocal of absolute temperature (Fig.3). The temperature dependence of the rate constant issummarized by

34.5 * 0.9 keal mol-'k = (6.0f .2 ) X 10V2 xp - (cm2s-')RTThe parabolic law was followed in the present temperaturerange, however, a more complex relationship is reported toexist a t ow temperatures (several hundred OC), especially inth e earlv staees of oxidation (8)..Several points should he made concerning the manner inwhich the oxidation experiment was performed. The literaturereports various furnace-hnlancearrangements in an attemptto minimize the effect of heat on the balance operation ( 9 ) . Wehave found it is sufficient to employ a large spacing betweenthe furnace and th e balance along with a n insulating screenabove the furnace. The buoyancy effect concerned us, thus therate constants were measured with the balance arrangementdiscussed and also individual samples were removed from thefurnace and weighed. The ra te constants obtained by bothmethods are shown in Figure 3. Within experimental preci-sion, we could not distinguish the two types of results. Theoresent observation is in aereement with the ~ ub li sh ed n-formation that the buoyancy corrections are quire small in thisexoeriment ( 9 ) .The ~ubl ishe d ate constants (@ ) areshown

Parabolic Rate Constants for Cu (k)Temperature (OC) k (cm2C1)

687 8.85 X 1 0 P0696 9.67 X742 2.24 X lo-'742 1.94X lo-*864 1.19X892 2.10 X900 1.98X949 4.02 X949 5.15 X 10-a

1000 6.37 X

Fbure 3. me rate eonstants liw.. k )are oioRBd as a function of temosrature, .~~~ ~(it-')) The open cwcles (0 ) epe sen l tne rate constants determined in misrepon and W e closed c rcles 1 are litaratws values 19).

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Acknowledgment (2) ~ o t t , F..and G U ~ ~ Y ,w., ' " E I ~ ~ ~ ~ ~ ~ ~m c ~n h i e c r y s ~ , "O V ~ ~ .WYork, 1964,CbaptPrVIII.One of the authors (YE)expresses her appreciation to the (s ~ . ~ W ,., Brsttain,W. ., and S ~ ~ ~ I W ,.,J them phys.. 14,714 (1916).students whohavesuccessfullyarried outhe experimentand (4) Kubaxhemki. 0..and HopLms. B. E., "Oxidation of Metals andAUoya,"Buttewonhs.London.LPs2.made this report possible. (5 ) M W ~ , . J.,J.m ~ .o u c . , 2 3 21961).(6) Hauffe, K.."Oxidation olMe tals,"Pienum. New York, 1965,Chapter 111.(7) O'Keeffe, M.,and Mm m, W. J.,J. Chem. Phys., 36 .3 W (1962).Literature Clted (8) ~ ~ t t ,. F., nd F ~ ~ I ~ ~ ~ ,., "oxidation a[ M ~ ~ ~ I Snd AII~~~." ~ ~ ~ .ac.M ~ ~ AMetals Par k, OH, 1970,pp. 37-60.(I)Moare,W. .. "Seven Solid States," Benjamin,New York, 1967,Chapter 5. (9) Tylecote, .F.. il Inst Met.,8.327 (1950).

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