THE FORMATION OF THIN FILMS OF IRON OXIDE' ABSTRACT It is assumed that the free energy of a thin film of iron oxide is a function of its thickness. The effect on the dissociation pressure is calculated and the condition for stability of thickness is stated. A possible method for measuring the free energy change involved in oxide film formation on metal surfaces is presented which is based on measurements of the e.m.f. of the dry cell metal (oxide(oxygen. INTRODUCTION At ordinary temperatures and pressures the system iron+oxygen is unstable and will go spontaneously to one or more of the various iron oxides. For example, the equilibrium dissociation pressure of a Fe203 is about 10-80mm. pressure of oxygen. Hence, when the process of oxidation halts it is natural to assume that kinetic conditions have imposed a very slow speed on the process, slow enough to give the appearance of a halt. The influence of resistance to change can be seen very clearly in the formation of iron oxide films on massive iron at pressures of around, say, 3 cm. oxygen and at temperatures around 370 C. In this region the clear-cut result is obtained, by a variety of methods, that the rate of increase of the film thickness is inversely proportional to the thickness. The most reasonable interpretation of this result is that the rate is controlled by the diffusion of the reagents through the film. Subsidiary experiments on transport processes, such as conduction, in oxides have checked this conclusion directly. This simple diffusion mechanism holds over a very wide range of film thicknesses-under the conditions mentioned above, from 800 A up to thicltnesses of the order of fractions of a millimeter where the film begins to lift: from the metal and to scale off the surface. The range from 0 to 800 A behaves anomalously, not following the diffusion law. Fig. 1 shows an oxidation for which the diffusion law is valid; the weight increase varies linearly with the square root of the time which follows from the varying of the rate of increase with the thicltness. Fig. 2 can be regarded as a "blown-up" view of the anomalous region in Fig. 1; the data were obtained from observation of interference colors and the ordinate is plotted directly as Angstrom units since the interference colors can be correlated with film thickness. It is seen that the anomalous region has been divided into two stages. At any rate, from Fig. 1 it is clear that given a certain thickness iron oxide will limit the rate of its own further growth. It is tempting to apply this conclusion to the data on iron oxidation at room temperature. At room temperature and below, iron will take up oxygen to form a film in the manner shown in Fig. 3. It is seen that the rate slows 'Manuscript received September 16, 1954. Contvibution from Division of Applied Chemistry, National Research COZL?LC~~, Ottawa, Canadn. Issued as N.R.C. No. 3495. This paper was presented at the Symposirtm on Problents Relating to the Adsorption of Gases by Solids, held at Kingston, Ontario, September 10-11, 1954.
CAULE AND COHEN: FILMS OF IRON OXIDE 800 FIG. 1. Measurements of weight gain as a function of square root ofitime. Total area of specimen 15 ~ rn.~ - STAGE 2 STAGE 3 3 TIME - MINUTES FIG. 2. Curve of oxide thickness as function of time; thickness derived from color observations.
300 CANADIAN JOURNAL OF CHEMISTRY. VOL. 33 ROOM TEMP. I \I t, minutes FIG. 3. Curve of weight gain as function of square root of time. Total area of specimen 15 cmz Specimen oxidized and reduced once previously. practically to zero in the time shown. It is natural to assume that the process here is exactly the same as the high-temperature diffusion process, modified and reduced in scale by the drop in temperature, since the diffusion process has been found to have an activation energy of about 40 kcal. This paper will present an alternative explanation of the low-temperature phenomena, which can be extended to explain the initial section of the high-temperature curve. It will be claimed (a) that the film initially formed on iron at any temperature attains an equilibrium thickness, whose magnitude is a function of temperature and pressure, and (b) that a process of recrystallization transforms the initial oxide to a second variety not possessing an equilibrium thickness and that in this second form the diffusion process of the type shown in Fig. 1 takes place. Unless, then, process (b) occurs, growth of the film will cease entirely at a certain thickness which is truly stable in the absence of the second phase. The most striking fact to consider is that all of the iron oxide phase is concentrated at an interface, where it is subject to peculiarly unbalanced forces. From this consideration comes the first assumption, that the free energy of the iron oxide per unit of weight or volume is a function of the thickness. Let the free energy of the oxide phase, Fox, be divided into two parts, one the free energy of the equivalent amount of iron oxide in the bulk phase, Fb, and the other the amount of free energy attributable to the existence of the oxide at an interface, F,. [I] Then Fox = Fb+ F,. [21 Similarly, pox = pb+p,. The number of moles, N, of oxide can be related to the thickness, r, by the following equation : 131 N = ~.A.P/M where A is the area considered, p is the density, and M the molecular weight. From [3] there is obtained: dn = (Ap/M).dr.
CAULE AND COHEN: FILMS OF IRON OXIDE 301 Consequently p, in [2] above can be expressed as a function of r: At a fixed pressure of oxygen, Po,, the condition for equilibrium is This assumes that the oxide formed is FePO,, which below 550 C. is very probable. Hence ~PF~+~P:,+~RT In p = 2p,, = 2pb+2p,, from which 161 4pke+3p;, -2pi = 2 p8-3rt In p. But the left-hand side of this equation is then -LIFO, which is equal to RT In K. Hence [7] RT In K = 2 p,-3rt In p. For bulk oxide equation [7] reduces to K = p-3 which gives the equilibrium pressure when the free energy is not dependent on the thickness of film. Here, because of the introduction of 2p8, p will not have the value it would have for bulk oxide. If pa has a positive value, 9 will have to have a more positive value-and correspondingly for a negative value of p,. There is a second important factor to be considered, namely, the slope of the pa VS. r curve. (a) If ap/ar is negative in a range, no equilibrium can be established in the range at a given value of applied oxygen pressure, since an increase in r will result in a lower value of p and thus a lower value of equilibrium pressure. (b) On the other hand, a positive value of ap/ar in a certain range does permit the system to come to equilibrium at definite values of p which then define values of r. From the above considerations there are seen (iii) p, < 0 (iv) PB> 0 a~ ar 0 -> ar 0.%> Equilibrium Equilibrium No equilibrium No equilibrium possible possible P< h P> lh 9 < Pb P> fib
302 CANADIAN JOURNAL OF CHEMISTRY. VOL. 33 to be four possibilities which are shown in Fig. 4. In the caption to this figure, pb represents the dissociation pressure of the bulk oxide. It will be seen that the most probable situation is represented by (iv). In the discussion so far the definition of p, has been by means of the differential equation [4]. It is important that it be emphasized that p, includes not only the free energy connected with the formation of the top layer of oxide but also the "reorganization" energy of the inner layers and of the metaloxide interface. Another major assumption must now be made in order to account for the experimental facts; the primary stable film is considered to be not a normal oxide, but one of higher total free energy content, perhaps amorphous in character. There are several reasons for this condition, one of which is that it is extremely difficult to obtain a definite and recognizable electron diffraction pattern from such thin films. Another is to be found in the results of hightemperature oxidation; a striking graph from a series of experiments is shown in Fig. 5, where there is clearly an induction period between stages 1 and 2. TEMP. PRE5SURE 32b0c. 3 cms. FIG. 5. Color measurement of thickness as function of time. Mott (2) has obtained the same result for copper, by a method of direct weighing of oxygen uptake. In general, our results indicate that stage 2 can be explained on the basis of a nucleation and recrystallization process occurring to the oxide, assumed amorphous, formed in stage 1. The induction period demonstrates that the oxide in stage 1 is stable in the absence of the type of oxide formed in stage 3, which is the normal bulk crystalline a-ferric oxide.
CAULE AND COHEN: FILMS OF IRON OXIDE 303 At low temperatures the transformation does not occur readily and stable films are left on the metal. The assumptions brought into the discussion so far could be tested if there were a direct method of measuring free energy as a function of thickness. Normally one of the most direct measurements is that of e.m.f., which is, of course, related to free energy by: AF = -n FE. There is a possibility of such a measurement here since the oxidation of iron is electrical in character and a current normally does flow in the oxide (3). An over-all equation showing the transfer of electrons can be written: 4(Fe-3e)+3(0?+4e) -+ 2FenOa. In Mott's theory of oxidatioil (2) electrons are emitted from the metal through the oxide to combine with adsorbed oxygen on the oxide surface; the negative ions then set up a field across the oxide which pulls iron ions through the oxide. Unfortunately the electron current, which normally is in the external circuit, is here in the cell itself together with the ion current. This rules out direct measurement of the cell e.m.f. and destroys any simple analogy to cells containing liquid solutions. There have been many measurements made, notably by Haclcerman (I), of the contact potential difference between a noble reference electrode and an electrode of iron or other metal undergoing oxidation. The resultant readings, while showing that changes are taking place, have not been able to be interpreted. It is possible to set up a circuit which in most respects simulates the oxidizing system and produces an e.m.f. analogous to contact potential. Fig. 6 shows the proposed analogue. FIG. 6. Electrical analogue to pair of contacting metals, one of which is osidizirlg in osygen. In this circuit the contact potential would appear across C2, which is a condenser of very low capacity similar to the electrodes ordinarily used in contact potential measurements. Condenser C, represents the capacity of
304 CAN.4DIAX JOURNAL OF CHEMISTRY. VOL. 33 the oxide film. R1 is the resistance to electron flow of the oxide film, and Iiz is the resistance to positive ion flow of the same film. El is the e.m.f. responsible for electron flow and according to Mott (2) is to be equated to W+EO- 4 where W is the binding energy of an adsorbed oxygen ion, E0 is the electron affinity of oxygen, and 4 is the work function of the metal against vacuum. Ez is the e.m.f. equivalent to the free energy change of removing an iron ion from the metal and bringing it to the outer layer of the oxide. It is equal to L- WFe, where L is the sublimation energy of an iron ion and WFe is the binding energy in the external layer. E3 is the contact potential difference between iron and the reference metal. Before the system comes to equilibrium, growth occurs by the passage of a current around the circuit including El and E2. Growth will stop when this current drops to zero. The condenser C1 allows simulation of the building-up of the charge on the surface of the oxide which is a feature of Mott's theory. The potential actually measured across C2, the "contact potential", is the algebraic sum of e.m.f.'s around the circuit-it is the negative of the voltage which must be inserted to cause no current to flow when the capacity of C? is altered (which is the common method of measurement of contact potentials by the vibrating plate method). At equilibrium, then, the measured contact potential will be E3-El or E3-E2 since E2 and El must be equal and opposed. At other non-equilibrium stages, the measured contact potential will be Es - E2 +potential drop across XI. The free energy change involved in the oxide growth is proportional to the algebraic sum of E1+E2. At equilibrium this sum is zero; consequently the relative magnitudes must change as the thickness increases. The analogue is not too useful as yet but further study may prove its validity and increase its usefulness. The assumptions involved in the early part of this paper may be extreme and based on faulty experimental data, since accurate oxidation experiments are difficult to do. They too await Eurther trial and proof. REFERENCES 1. ANTES, L. and HACKERMAN, N. J. Appl. Phys. 22: 1395. 1951. 2. CABRERA, N. and MOTT, N. F. Repts. Progr. in Phys. 12: 163. 1948-49. 3. WAGNER, C. Corrosio~~ and Material Protect. 5 (5): 9. 1948.