THE KINETICS AND MECHANISM OP THE CONVERSION OF DIOXIDE TO TITANIUM

DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By

David Leslie Douglass, B.S., M.S.

The Ohio State University 1958

Approved by:

*

V Adviser Department of Metallurgical Engineering DEDICATION

This dissertation is devoted to my family— to my wife who spent many silent nights in the same room with her husband who "wasn't there," and to my two young daughters who didn't see too much of "Daddy" and couldn't understand his Inability to devote more time to them. The patience and forebearance of my family have been a driving force and motivation. To them I am deeply Indebted.

il ACKNOWLEDGMENTS

The writer wishes to express his gratitude and sincere appreciation to Dr. George R. St.Pierre who acted as thesis adviser and whose sincere interest and many discussions were invaluable and provided much of the stimulus for this work. The contributions of Professor Rudolph Speiser proved extremely valuable and are gratefully acknowledged. Appreciation is expressed for the assistance of Gerald Gordon, fellow graduate student, in providing Innumerable experimental facilities and aids. The many interesting and pertinent.discussions with Lyle L. Marsh, another student, also proved very beneficial, and his keen interest is appreciated. Lastly, the understanding and patience of my wife, Rebecca, during my entire graduate program made this work possible.

ill CONTENTS

Page INTRODUCTION ...... 1 LITERATURE SURVEY ...... 2 Preparation of Titanium Nitride ...... 2 Practical Significance of the Conversion . . 3 Manufacture of Abrasives ...... 3 Scaling of Titanium in A i r ...... 4 Surface Hardening of Titanium ...... 4 Recovery of Titanium from . . . 4 Previous Work ...... 6 Phase Equilibria ...... 8 Related Studies ...... 10 GAS-SOLID REACTIONS ...... 11 Rates of Reaction ...... 11 Dependence upon Gas Pressure ...... 15 MECHANISM OP GAS-SOLID REACTIONS ...... 19 Chemlsorption...... 19 Llnear-Rate Reactions ...... 20 Parabolic-Rate Reactions ...... 21 Logarithmic-Rate Reactions ...... 24 POSSIBLE METHODS OP APPROACH ...... 27 Topochemlcal Studies ...... 2?

iv Page Electrical Conductivity ...... 28 Kirkendall Effects ...... 29 Self-Diffusion...... 31 EXPERIMENTAL PROCEDURES ...... 33 M a t e r i a l s ...... 33 Rate-Constant Determination ...... 34 Topochemlcal and X-ray Diffraction Studies . . 35 RESULTS ...... 38 Nitridizatlon of R u t i l e ...... 38 Topochemlcal and X-ray Studies ...... 38 Reaction Kinetics ...... 46 Effect of temperature ...... 46 Effect of p r e s s u r e ...... 52 Rates of layer G r o w t h ...... 56

Nitridizatlon of T *2^3 and ...... DISCUSSION ...... 66 Dissociation of Ti02 to TiO^ ...... 66 Complex Intermediate Oxides ...... 68 Formation of T i O ...... 69 Nitride Formation from TiO ...... 71 Comparison of Nitride Growth on Various Starting Materials ...... 74 Effect of Temperature ...... 77 Effect of Pressure ...... 81

v SUMMARY AND CONCLUSIONS

REFERENCES . . . . LIST OP TABLES

Table Page

I. CHEMICAL ANALYSES OP . . 33

II. X-EAY SPECTROMETER RESULTS SHOWING BOTH TIO AND REFLECTIONS FROM SURFACE LAYERS OF T102 NITRIDED 6 MINS. AT 1010°C IN 1 ATM .... 42

III. THE ABSORPTION OF TIO REFLECTIONS BY THE NITRIDE LAYER FOR VARIOUS THICKNESSES OF THE NITRIDE ...... 44

vll LIST OP FIGURES

Figure Page 1. Schematic Representation of Experimental Equipment ...... 36 2. Multiple Layers In Partially Reacted Sample (5x) ...... 40 3. Same as Figure 2 (30x)...... 40 4. Lattice Parameter Determination: Plot of a0 versus Sin 6 ...... 43 5. Lattice Parameter-Composition Relation of the TiO P h a s e ...... 45 6. Individual Contributions tc Cumulative Weight Change: Rutile at 1010°C and 1 Atm Ammonia ...... 47 7. Comparative Weight Losses of Rutile in 1 Atm Ammonia at Various Temperatures 48 8. Test for Parabolic Rate Law. Rutile Reacted at 900° and 950°C .... 49 8.(cont'd.) Rutile at 1010°C and 1 Atm NH^ . . 50 8.(concluded) Rutile at 1070°C and 1 Atm NH^ . 51

9. Temperature-Dependency of Rate Constant . 53 10. Comparative Weight Losses of Rutile at 1010°C and Various Ammonia Pressures . 54 11. Test for Parabolic Rate Law. Rutile Reacted at Various Ammonia Pressures at 1010°C ...... 55 12. Pressure Dependency of Parabolic Rate Constant at 1010°C ...... 57 13 . Micrographs of Fractured Sections Showing the Thickness of Each layer at Two Different T i m e s ...... 39 viii Figure Page 1^. The Effect of Time on Layer Growth on TIOg at 1010°C ...... 60 1 5 . Test for Parabolic Bate Law. TiO Reacted at 1010°C and 1 Atm Ammonia ...... 62 16. The Effect of Time on Layer Growth on T12°3 63

lx THE KINETICS AND MECHANISM OP THE CONVERSION OP TITANIUM DIOXIDE TO TITANIUM NITRIDE

INTRODUCTION

The conversion of titanium dioxide to the nitride has important practical implications in several fields of metallurgical technology. Titanium nitride is a very hard, refractory compound which finds widespread use as the "hard metal" phase in cemented compacts. The nitride is the chief constituent of the hard case on nitrided titan­ ium and offers excellent wear resistance. Nitride for­ mation is also of interest in the high temperature scaling behavior of titanium and its alloys in air. Lastly, the selective formation of titanium nitride from ilmenite, an inexpensive, plentiful iron-titanium ore, gives promise of economical recovery of titanium. LITERATURE SURVEY

Preparation of Titanium Nitride

Several methods have been used to prepare the "hard metal" . The metals or metal hydride may be reacted with or ammonia. Agte and Moers^ prepared nitrides of titanium, zirconium, and tantalum by reacting high purity powders In pure nitrogen. Other groups, IV-a, V-a, and Vl-a (in the periodic chart), metal nitrides of hafnium, vanadium, niobium, , thorium, and uranium have been produced by reaction of the powders with ammonia.2»3»^»5»6,7»8,9 The hydrides have been used to produce the ni- h, Q trides by reaction with ammonia. *7 However, very high temperatures, 2000°C or more, are required. The most economical method of preparation In­ volves the reaction of the oxides with either nitrogen or ammonia in the presence of carbon. Unfortunately, the formation of the occurs simultaneously. In the case of titanium, the and nitride are lso- morphous, and an impure solid solution of nitride-carbide results. Early work by several investigators showed that titanium nitride could be.prepared by reacting Ti02 with ammonia. ^ 2 3 Deposition of the nitride from the vapor phase has been successfully achieved.^3*14,15#16 a mixture of TiCl^, nitrogen, and hydrogen will deposit titanium ni­ tride on an Incandescent tungsten filament at tempera­ ture of about 1100°-1700°C. Several investigators have produced the nitride by reacting titanium compounds such as the tetrachloride with ammonia.12»17»18 However, the present research was not aimed at the preparation of titanium nitride per se; rather, it was designed to convert the oxide to the ni­ tride for reasons which will be listed in the following section.

Practical Significance of the Conversion

Manufacture of Abrasives Abrasive manufacturers produce materials such as and titanium nitride from the metal as a starting material. Both silicon and titanium are expens­ ive, and if the abrasive nitrides could be made directly from the plentiful, low-cost oxides, a large economic gain would be realized. A knowledge of the mechanism of the conversion would enable the optimum conditions to be determined for the process. Scaling of Titanium In Air A study of the scaling behavior of titanium in air"^ indicated that the nitride formed either simultan­ eously with the oxides or subsequently from the oxides. Once again, a knowledge of the conversion mechanism would enable more oxidation-resistant or scale-resistant alloys to be designed.

Surface Hardening of Titanium Another Important aspect of this problem can be found in an analysis of the surface hardening studies of titanium. The depth of hardening was found to increase by the presence of oxygen.2® This behavior suggests the possible formation of an oxynitride, whose mechanism of formation is unknown.

Recovery of Titanium from Ilmenlte Perhaps the most important aspect of the oxide-to- nitride conversion lies in the field of extractive met­ allurgy. Titanium is still an expensive metal in spite of much research to develop new processes and to make present production practices more efficient. The cus­ tomary raw material, rutile, is essentially titanium dioxide and costs about $0.15 per pound of contained titanium. This material is subjected to an expensive, batch-type chlorination to form the tetrachloride, which is subsequently reduced by magnesium or some other costly reducing agent. A significantly cheaper raw material, ilmenlte, is available. However, even though the cost is only about $0.02 per pound of contained titanium, the ore con­ tains iron which is difficult to separate from the ti­ tanium. Ilmenlte is actually an iron , expressed chemically as FeTiO^. The removal of iron from ilmenlte is a costly process, hence no cost reduction is possible in the price of metallic titanium when ilmenlte is used as a raw material. Present practices involve either a direct chlorination of ilmenlte2! or chlorination of a titania-rich slag, produced by the smelting of ilmenlte.22 Chlorination has the disadvantage of forming large amounts of iron chloride in addition to the titanium tetrachlor­ ide. In fact, more FeCl^ than TiCl^ is formed during the chlorination of ilmenlte. An alternative method of recovering titanium from ilmenlte would be to form selectively a titanium compound which could be readily separated from the divalent (or reduced iron). Further, the use of a reactant which is cheaper than chlorine would be desirable. Thermodynamic calculations showed that a stable nitride of titanium would form In the presence of iron (which itself forms a relatively weak, unstable nitride) by nitriding with ammonia. The resultant products, ti­ tanium nitride and metallic iron, could be readily separated by crushing and by magnetic separation. The nitride could then be processed to produce metallic ti­ tanium in any of several ways: (1) The nitride could be the starting material in the Kroll process and could be converted to TiCljj, with no attendant formation of FeCl^. (2) The nitride could be oxidized and then chlorinated. (3) The nitride might serve as the starting material for a new process. An example of the latter would be the thermal dissociation of titanium nitride in a high tem­ perature arc, followed by a rapid quench of the gaseous products. Computations Indicate that dissociation should occur at about 5800°F.

Previous Work

The separation of titanium from iron in titaniS- erous mineral by the formation of titanium nitride is not a new idea. P. Farup23 received a patent in 1920 for .the preparation of titanium compounds from titan- iferous materials by heating the mineral with carbon in 7 an atmosphere of nitrogen. The iron was separated by the -nitride product by solution of the iron in acid. The residue was heated with sulfuric acid to form titanium sulfate, which when dissolved in water formed a hydrate. The hydrate was then calcined to yield crystalline T102. This process was designed primarily to obtain pigment-grade TiOg. Metallic titanium was a laboratory curiosity at that time, and no efforts were made to produce the metal. Bichowsky and Harthan^ obtained a patent in 1922 for forming titanium nitride from ilmenlte by reaction with carbon, nitrogen, and sodium carbonate. Andreu and Paquet2^ received a patent in 1924 for virtually the same process. Numerous methods have been patented for the pro­ duction of Ti02 from ilmenlte. These methods all entailed the use of aqueous and will not be covered here. Still other attempts have been reported on the separation of iron and titanium in ilmenlte.2^*2?*2® None have proved eminently successful. Unfortunately, a study of the mechanism by which titanium nitride forms during the reaction of ilmenlte with ammonia would be extremely complex. A five-component system exists and is difficult to analyze. It was there­ fore decided to initiate the problem of titanium recovery 8 from ilmenlte by a comprehensive study of the conversion of the oxide to the nitride. Once this aspect is clear­ ly defined, the study of the ilmenlte conversion will become much more feasible. Further, the presence of carbon was also excluded. Calculations have shown that the energy requirements are lowered considerably when carbon is present. However, titanium carbide and titan­ ium nitride are isomorphous2* and form solid solutions during the reaction of TiO£ with carbon and nitrogen.

Phase Equilibria

The phase equilibria between Ti(X> and TIN have been determined^® and indicated complete solid solubility be­ tween the two compounds. A more recent study^l has re­ ported the limit of solubility of 60 mol per cent TIN in TiO. The lattice constants were observed to vary from 4.16 kX for pure TIO to 4.24 kX at 60 mol per cent TIN, and remained constant up to 100 per cent TIN. The ter­ nary equilibrium diagram has been explored only in the titanium-rich portion.32 No data exist on the phase equil­ ibrist between TiO and TIN. The binary titanium-oxygen and titanium-nitrogen systems have been .reported.33»3^

According to the summary by DeVries and R o y , 33 the following oxides of titanium have been observed: two crystallographic forms of TIO, two forms of TigO^, Ti^O^, and two equilibrium forms of Ti02 (rutile and anatase). Recent work at Massachusetts Institute of Technology has shown that the phase change in Ti20^ at 200°C does not exist as previously reported, but that an unusual change in the lattice parameters does occur over a range of tem­ perature. 35 The same prevailed at tem­ peratures as high as 400°C that was observed at room tem­ perature. It can thus be concluded that a phase change does not occur in Ti20^ but that some other second-order effect takes place. A recent publication^? reports the observation of many new titanium oxides. An homologous series of com­ pounds, having the formula Tin02n_^, exists. These are Ti2°3, ti3o5, Ti4o7, ti5o9, ti6ou ) ti3o15.

Ti^O^, and Ti10°19* In addltlon» Ti2° 321(1 T10o 65 have been observed. These oxides were observed in arc-melted buttons of rutile and were stable at room temperature. It is not known whether all or any of these oxides are actually equilibrium products and should appear on the phase diagram. The titanium-nitrogen system shows a wide range of homogeneity of TIN. A questionable nitride is also 10 Indicated on the phase diagram at about 26 atomic per cent nitrogen.

Belated Studies

Tungsten oxynitride was formed by Kiessling and Peterson36 by reducing either ammonium paratungstate or tungsten trioxlde with ammonia. The latter process has also been described in a patent Journal.37 The product of their work was approximated by the formula /frPrt oo had the sodium chloride structure. v • 02 U «02 0 • jjO Only 62 per cent of the tungsten sites were filled and all the X sites (MeX type of compound) were filled, 62 per cent by nitrogen and 38 per cent by oxygen. Al­ though this study is very similar to the one to be described, no attempts were made to discern the reaction mechanism by which tungsten oxynitride formed. GAS-SOLID REACTIONS

The reaction of solids with gases has received much attention, particularly the oxidation of metals and the reverse process, the gaseous reduction of metal ox­ ides to metal. In addition, the reaction of many metals with nitrogen has been extensively studied. The theoret­ ical basis of these reactions and their mechanisms are well established for many conditions. Because the pres­ ent study falls within the same general category of gas- solid reactions, the methods of experimentation, presentation, and interpretation are essentially the same as for oxidation and/or reduction studies. In essence, the only difference is that one compound is converted to a second compound. Analogous studies have been made on the mechanism of the roasting of metal sulfides.3®»39

Rates of Reaction

If a given solid reacts with a gas to form, a : second solid, the rate at which the reaction proceeds de­ pends upon the extent to which the new solid protects the original solid from the gas. The manner and rate of

11 12 growth of the covering layer actually determine the over­ all rate of reaction. Initially, a forms, and according to Cabrera and Mott,^® a number of rate laws may be possible from the physical nature of the solid-solid composite. The rate equations may be linear, parabolic, cubic, or logarithmic. During the course of reaction under a fixed set of conditions the various laws may apply in time sequence as the film thickens. The linear relationship is given as

k,, d t ° (1)

where Am * weight change/unit area t = time k^ = constant or, in terms of the increase in film thickness, it may be expressed as

d ( & « ) - L' T T ‘ ‘ (2)

The relation between the film thickness and weight in­ crease may be approximated as

A ™ . % A €g yTfy ' (3)

where MAY = molecular weight of the ^ surface compound = molecular weight of the negative component per mole of surface compound $ * of the surface compound. 1 3 The parabolic relationship, discovered indepen­ dently by Tammann^l and by Pilling and Bedworth,^2 is given as <4 (Am) . k’fA , S i — S** <*> or, in integrated form,

(/tfrnf"* kf'tt (5)

2 which represents a straight line when (Am) is plotted against time. If the line does not intersect the origin, a more general form exists,

w)*» k f t + C ♦ ($)

C is a constant but not necessarily the integration con­ stant. Another form of the parabolic equation is given (a, b, and kp are constants) as,

_ k f (7) JX +* © > which, upon integration, gives

A combination of constants gives 14

( a rf * ka A'to* k^t9 (9)

The simplest parabolic relation, equation (4), states that the increase in weight (or film thickness) with time is Inversely proportional to the weight change (or film thickness). This relation assumes that a dif­ fusion process is rate controlling; that a coherent, continuous film forms; that the surface area remains constant; and that the diffusion coefficient is constant. The last assumption is not valid because the diffusion coefficient varies with changes in concentration in the layer. The diffusivity is also sensitive to structural changes and defects. Bates of reaction seldom follow a given rate equation but rather involve two or more differ­ ent processes. For example, equation (9) may hold when the interfacial reaction (given by the term k.Am)cl is rate- controlling in the early stages, and when the film be­ comes thicker, the parabolic behavior (given by the term Am^) becomes rate-determining. Cubic and logarithmic laws have also been found to agree with experimental data. These relations are of the form 15

(a w )’= kct (1 0 ) and Am* ke (at+i) (11) respectively. There are two main theories of logarithmic oxida­ tion. Mott and Cabrera**0 treat the exponential oxidation behavior on the basis of a complex theory of thin films, whereas Evans**3 has based his theory on the formation of mechanical imperfections in the oxide layer. Three basic relationships have been shown to exist to which a gas-solid reaction may conform to form a new solid. These three forms are the linear, parabolic, and logarithmic laws. Most gas-solid reactions follow one of these relations or some sub-form. Physical significance may be associated with each law, although other factors are operative in the actual mechanism. Lastly, combinations of these laws may occur successively or even simultaneously.

Dependence on Gas Pressure

If the reaction at the gas-solid Interface is rate- controlling, the rate would increase with some power of 16 the partial pressure of the gas. Any other relationship between rate and pressure would imply that some other step was rate-controlling. If, on the other hand, the process were diffusion- controlled, the rate-pressure relation might be similar to the high-root relationships as postulated by Wagner The exact root relationship depended upon the nature of the surface compound which forms. Wagner has shown that the pressure-electrical conductivity relationship is sim­ ilar to the pressure-diffusion relationship in certain semi-conducting surface compounds. He has shown that electrical current is carried in cuprous oxide by the cations which move through vacant lattice sites.^ The vacant lattice sites are produced by the migration of cuprous ions and electrons from the interior to the in­ terface of adsorbed oxygen on the Cu2®* The concentration of defects was shown from the mass action law to be pro­ portional to the one-eighth power of the oxygen pressure. But, inasmuch as the conductivity is proportional to the number of defects, the conductivity is proportional to the one-eighth power of the oxygen pressure. Wagner and Grunewald^ measured a linear variation of the parabolic rate constant for copper oxidation with the 7th-root of oxygen pressure. This represents reasonable agreement for such high-root relationships. It may be concluded from these data that a high-root relationship between the rate constant and pressure may be expected for a reaction which is controlled by diffusion via lattice vacancies through a metal-deficient semiconducting layer. The type of relation to be expected in a metal-excess layer depends upon the mechanism of diffusion and the method by which vacancies are created. Generally, the influence of pressure in the range 1-760 mm mercury on the oxidation rate of most metals is small. Pressure effects are usually different at very low pressures than at higher pressures. Lustman and Mehf^ observed in the oxidation rate of copper a critical pres­ sure above which the rate decreased rather than Increased with increasing pressure. At very low pressures the frac­ tion of surface covered by the adsorbed gas becomes sig­ nificant. On the other hand, high pressures may result in a change in the rate law from parabolic to linear or vice versa.The oxidation of metals is not ideal, i.e., does not rigorously follow a particular rate law, but usually is a combination of two laws. Hence, the prac tice of discarding early readings in the weight-change­ time relationship may lead to erroneous Interpretations. The subject of pressure effects on gas-solid 18 reactions is very complex. A complete understanding is dependent upon a knowledge of the reaction mechanism, which in turn is dependent upon the mechanism of diffusion through the freshly formed surface layers. Many facets of solid-state physics and physical chemistry are inter­ related, and they must be studied simultaneously in order to gain a complete picture of the chain of events. MECHANISMS OP GAS-SOLID REACTIONS

Chemlsorption

Prior to any reaction In a heterogeneous gas- solid system, contact of the gas must occur with the solid. Thus the first step In the sequence, regardless of the subsequent steps, Is chemlsorption of the gas or evaporation of the solid. Chemlsorption of oxygen during oxidation results in the removal of electrons from the surface of the lat­ tice to form the gas-solid bond. The withdrawal of the electrons results in an increased valence of some cations and the generation of positive holes. These defects im­ part semi-conductivity to the compound. In the case of reducing gases, such as hydrogen or carbon monoxide, the -2 chemlsorption forms a bond between OH” ions or CO^ ions, respectively, and surface oxide anions.^ The additional valence electrons are incorporated into the lattice by a decrease In the valence of some cations. The excess of electrons or a deficiency of electrons imparts semi­ conductivity to the compound. Because both oxidation and reduction gas-sohd reactions may result in the forma­ tion of semi-conducting compounds, the study of the electrical conductivity may help to understand the chemi- sorption process.

19 20 An equilibrium number of defects is found at each temperature and is given by^®

^ t (12)

where N = number of atoms in the crystal Es = energy required to move an atom from an Interior lattice site to a surface site k = Boltzman constant T = temperature, degrees Kelvin As chemlsorption proceeds, additional defects are formed at the surface, the total number being in excess of that in equation (12). The defects then migrate into the lattice slowly, according to the diffusion rate and con­ centration of the defects. This process may be followed in some cases by the change in conductivity with time of contact between gas and solid.

Llnear-Rate Reactions

After the initial chemlsorption, reaction takes place at the surface to form the new solid. If the ratio of the molar volume of the new solid to the molar volume of the substrate is less than unity, a non-coherent layer of solid is formed.**2 The surface layer offers no protec­ tion against further contact between gas and solid sur­ face. The thickness of the layer does not influence the rate of reaction, and integration of equation (1 ) gives 21 a zero order reaction

(13)

A similar behavior occurs when newly formed solid vaporizes and leaves exposed substrate. The mechanism for reaction when porous, non-coherent, or volatile prod­ ucts are formed is simply a chemical reaction at the gas-solid interface.

Parabollc-Bate Reactions

When the volume ratio is greater than unity, and a coherent layer is formed, further access of the gas to —V the substrate is prevented. The only mechanism whereby the gas can reach the substrate is by diffusion through the layer. Either the gas diffuses as an anion through the layer or the cations of the substrate diffuse through the layer to the gas. The simultaneous inward diffusion of anions and outward diffusion of cations is also poss­ ible, having been observed by Davies et al.-^ in layers of magnetite during the scaling of iron in air. The theory of parabolic oxidation has been careful­ ly outlined by Wagner and co-workers^*^5*52,53 and although it is well known by all workers in this field, it deserves attention and will be presented here in its simplest form. 22 A true parabolic reaction is diffusion-controlled, and in order to maintain electrical neutrality during diffusion, electrons must diffuse concurrently with the positive ions in the same direction through the oxide lattice. The diffusion rate is determined by the rate of movement of cations to the vacant cation sites. How­ ever, a concentration gradient must exist in the oxide for diffusion to occur. Some relationship between trans­ port and the thickening of the film must therefore exist. Wagner has obtained an expression relating the rate of film thickening to the film conductivity, transport num­ bers, and the free energy change during oxidation. Hoar and Priced treat Wagner's relationship* on the basis of current flow through a cell, where the film serves as the electrolyte, and the electrons provide the external circuit by electronic conduction;. The cell emf is represented by the free energy decrease (expressed as E0 , the electrode potential). The cathodic reaction is the formation of anions, and the anodic reaction is the ionization of metal at the metal-layer interface. The total resistance per unit area (cm ) of film (cm) is

^ W»tc ) A 9 (I**)

* Summarized in Reference 55* 23

where ^ i ectr0lytic = ©le°tr°lyfcic conductivity ^electronic = ©iectronic conductivity.

Substitution of transport numbers for cations, an­ ions, and electrons ( X . % , and X , respectively) gives

n r,

But **c+ ^ 4 + "2t - 1» and

(16) R a ( Z * r c) % r A .

If the film growth-rate is equivalent to the current, the number of gram equivalents, , of film formed in t sec­ onds is ^*1 iE._£s. (17) Tit* f * FK and J?c+rA)%

K S * > & 4: 4 (18)

The relationship between and the parabolic constant for the formation of an oxide Me20 is Zk where V = volume of 1 gm-equivalent of Me20 z = valency of oxygen ion M = atomic weight of oxygen. The variation of conductivity with pressure of the gas cannot be disregarded and is given by tr*

where » conductivity of i at 1 atm n = constant. Wagner*s derived relationship is then corrected for pres­ sure and finally is given as

S Z S T z v * * <21)

where Px(s) = pressure of x at outer oxide surface Px (m) = pressure of x at film-metal Interface.

Excellent agreement has been achieved between ex­ perimental results and values of kp calculated from Wagner's theory.53»56 These results tend to confirm the assumptions and postulated mechanism of Wagner’s theory.

Logarlthmlc-Rate Reactions

The logarithmic rate-law mechanism is based upon the thin film theory of Cabrera and Mott.2*0 Wagner had previously assumed an even distribution of electric charges 25 in thick films. Mott, however, suggests that a strong electric field exists in thin films, and that at low tem­ peratures the ions cannot diffuse through the film but that electrons can pass through by the quantum-mechanical "tunnel effect." Cations would then form at the metal- oxide interface, and oxygen ions at the oxide-gas inter­ face. The electrons tunnel out of the thin film, leaving an equivalent number of cations behind, and form 0 —2 from the adsorbed oxygen at the surface. An electric field is established across the film. The strong field may cause a forced migration of cations when normal diffusion is not possible. The rate of film growth is given by

(22)

where n^ = concentration of ions at a distance from the metal- oxlde interface = diffusivity of ions V = electrostatic potential v = volume of oxide per ion e = electron charge . But,

(23)

where = energy to remove an ion from its position in the oxide. Equation (22) is therefore exponential. At thicknesses greater than 2.1 x 10“^ cm the relation becomes parabolic (terms in brackets become constant). The logarithmic-rate mechanism will always govern the Initial oxidation behavior during the thin film stage. As the film thickens, the behavior tends toward parabolic behavior according to the Wagner theory. POSSIBLE METHODS OF APPROACH

The mechanism of gas-solid reactions may be studied in any of several methods. Actually, no single technique is entirely adequate, but rather several techniques when used together provide sufficient information to piece the Jmzzle together. Each technique will be discussed briefly on its relative merit and will be documented with refer­ ences from the literature.

Topochemical Studies

The topochemical method entails the study of par­ tially reacted and subsequently sectioned massive samples. Examination of each layer and of the sequence of forma­ tion of component layers can yield a valuable insight into the relative rates of formation of each zone, the thermo­ dynamic stability of phases, and the variation in prop­ erties across each layer. For example, Peretti38 studied the roasting of cupric sulfide. It was previously thought that cupric sulfate formed directly from cupric sulfide. However, Peretti observed the rapid partial reduction of cupric sulfide to cuprous sulfide with the evolution of sulfur gas. When the partial reduction had been completed, the cuprous sulfide oxidized to cuprous oxide, which then

2? 28 oxidized to cupric oxide, which finally reacted with SO^ to form the sulfate. This sequence of events was studied by examination of partially reacted massive samples and by studying the relative positions, etc. of each phase.

McCabe and Morgan reported virtually the same sequence^ in their study by topochemical methods. Gurnick and Baldwin-’® studied the relative thick­ nesses of oxide layers in the oxidation behavior of manganese and were then able to write an over-all rate constant in terms of the rate constants for the formation of each layer, according to Valensi's method.-9 Bitsianes and Joseph^0 *61,62,63 have made a compre­ hensive study on reduction mechanisms and solid phase identification in iron oxides. The presence of wustite vias detected only above 570°C, and X-ray diffraction pat­ terns taken across the layer revealed a marked variation in oxygen content of wustite between the iron layer and the magnetite layer.

Electrical Conductivity

As noted previously, the electrical conductivity is closely associated with diffusion behavior in semiconduc­ tors. The pressure-dependency of conductivity was correla­ ted with the pressure-dependency of the reaction rate- constant for cuprous oxide and was found to agree remarkably well. The technique, however, Is more or less limited to semiconductors. In this particular research Its utility may be doubtful, especially when the pseudo-metallic ni­ tride is concerned. It would be particularly valuable in the study of the rutlie matrix. Johnson and Weyl meas­ ured the change in electric&l'conductivity in rutile^ when minor additions were made to the rutile lattice. Johnson^ reported variations of several orders of magnitude by the addition of 1 mol per cent of various trivalent or penta- valent ions. Such a technique would prove very useful:in the determination of nitrogen effects and solubility lim­ its in rutile, but the measurements could be meaningful only if they were taken on the rutile core after removal of the high conductivity nitride or titanium monoxide. Measurement of the Hall coefficient would also be very useful in establishing the type of semi-conductivity, i.e., "P" or "N" type.

Kirkendall Effects

Smigelskas and Kirkendall observed the migration of inert molybdenum markers relative to the original brass- copper interface during diffusion studies of zinc in alpha brass.^6 Darken^? offered a phenomenological explanation 30 on the basis that two diffusion coefficients should be used when markers are used as a reference point. If a difference exists between the two diffusion coefficients, a mass flow occurs relative to the markers. The Kirkendall effect may be used to study mass transport and reaction mechanism during gas-solid reactions. Davies, simnad, and Birchenall^ investigated the mechan­ ism of the scaling of iron in air by using radioactive silver as an inert marker and measuring the relative move­ ment of the radioactive tracer. They found that the mi­ gration of Fe+^ ions was the rate-controlling step in the formation of wustite, FeO. They also observed migration of both iron and oxygen ions in magnetite, and Just the diffusion of oxygen ions through hematite. Dunnington and Fontana^® detected voids by the con­ densation of vacancies after iron had diffused outward through the FeO layer during oxidation of iron wires. In fact, they observed an extreme case where a hollow, cylin­ drical shell of iron oxides remained after the oxidation of iron had taken place. Inert markers have been used successfully in other cases to determine the reaction mechanism. Simnad and Spilners^9 used radioactive silver in oxidation studies of molybdenum and found that the silver remained on the surface throughout the oxidation process. This proved that the reaction occurred by the diffusion of oxygen ions through the oxide lattice. Jones et. al.?° made a similar study on molybdenum using chromic oxide as an inert marker. They concluded also that the process was controlled by diffusion of oxygen through the oxide.

Self-Diffusion

The determination of self-diffusion coefficients in oxides will in many cases enable the mechanism of dif­ fusion (and the reaction mechanism) to be determined. Carter and Richardson?^ have measured the self-diffusion coefficients in wustite and cobaltous oxide by the de­ crease in surface-activity method. They found that the diffusion coefficient of cobalt in cobaltous oxide was proportional to the 0.26 power of the oxygen pressure. This was similar to their previous observation that the concentration of excess oxygen in cobaltous oxide was proportional to the same power of the oxygen pressure. They concluded that the nonstoichiometry was caused by vacant cation sites, and that cation diffusion occurred by migration of the cations by way of the vacant sites. The determination of self-diffusion coefficients is more laborious than the other suggested experimental techniques, but useful data are obtained which may help to explain the mechanism of reaction. EXPERIMENTAL PROCEDURES

Materials

Two grades of titanium dioxide were used. These were "C. P." and ceramie-grade rutile. Analyses are listed in Table I.

Table I CHEMICAL ANALYSES OP TITANIUM DIOXIDE

Impurity Per Cent C.P. Grade Grade Zr02 - 1.6A Si02 - 1.12 Pe203 0.002 2.25 Al203 - 0.50 As203 0.0002 0.03 Cr203 - 0.11 MgO - 0.10 CaO - 0.08 CuO - 0.001 PbO 0.01 0.002 Na20 - 0.005 Cb20c - 0.10 V20t - O.kZ ZnO 0.006

The powders were dry-pressed at 5000 psi into bars i x £ x 6 inches and fired eight hours in air at 1400°C. The were measured by the Archimedes method and varied from 96 to 99 per cent of theoretical (^.26 gm/cm3). Samples were cut from the sintered bars on a diamond

33 34 cut-off wheel. The sample size and shape was varied, depending upon the type of test conducted. Thin reci- langular wafers, about 1-2 gms, were used for the determination of rate constants; cubes or rectangular prisms were used for topochemical and X-ray diffrac­ tion studies.

Rate-Constant Determination

The gravimetric method was used to measure con­ tinuously the decrease In weight during nitridlzation. Samples were suspended by Nlchrome wires In a vertical tube furnace, and the total weight change of wire and sample was measured. A dummy Nlchrome wire was run at each temperature and partial pressure of ammonia, and the weight gain of the wire was then added to the cumulative weight change of sample plus wire to give the sample weight loss.**

* Nlchrome was used even though it nitrlded. Plat­ inum wires failed within an hour or less from hydrogen embrittlement, and pure iron, which is relatively inert to nltriaing, failed by oxidation by reacting with the water vapor (product of nitridlzation of T102) toP of the furnace. The net curve consisted of a weight loss from the sample and a weight gain from the Nlchrome nitrid- ization. The sample welght-loss was the cumulative change plus the Nlchrome weight gain. Mixtures of argon and ammonia were used to give various partial pressures of ammonia. Each gas was in­ troduced at the same pressure (controlled by a blow-off tower through mineral oil) and at some predetermined flow rate. The flow rates were controlled by resistances which consisted of capillary tubes of given sizes which were inserted into the gas train. Inasmuch as the fur­ nace effluent was vented at atmospheric pressure* and the gases were introduced at the same pressures, the partial pressure of ammonia was then equal to its flow rate divided by the total flow rate. The total flow rate was adjusted to about 400 cm3 per minute. Calibration of flow rates was performed by the soap-film technique which consists of timing the movement of a film of soap through a calibrated, narrow cylinder. The experimental equipment is shown schematically in Figure 1.

Topochemical and X-ray Diffraction Studies

Samples were nitrided for various times under a given set of temperature-pressure conditions and then sec­ tioned for examination of the layers. Samples were ex­ amined in the fractured condition after unsuccessful attempts were made to polish the section. Representative micrographs of fractured sections will be shown in a later section. PIG. 1. SCHEMATIC REPRESENTATION OP EXPERIMENTAL EQUIPMENT 37 X-ray diffraction samples were made for both Debye- Scherrer powder patterns and for the diffractometer. Powder samples were taken from scrapings of the various layers. The powders were crushed and screened through a 325 mesh net and placed in a 0.3 mm glass capillary tube.

A 57.3 mm diameter camera was used, and the Straumanis, unsymmetrlcal type of loading was employed. Filtered, copper Ka radiation was used. Powder patterns were taken at 40 kv and 15 milliamps for six hours. Film shrinkage was less than 0.01 mm. Clear back-reflections were ob­ tained for the nitrides and monozide, and lattice param- eters were determined by extrapolating a plot of sin2 © versus to 180°=2©. The diffractometer was used to obtain patterns of the samples at various intervals beneath the surface. The samples were abraded on silicon carbide paper, and patterns were taken at intervals of 0.003 inch below the surface. Filtered copper Ka radiation was used throughout. The patterns obtained by the diffractometer were not solely from the surface constituents. Calculations showed that 0.0016 inch of titanium nitride was sufficient to reduce the strongest reflection of any phase to the background level. Hence, it may be concluded that the patterns obtained represented the phases present for a depth of 0.0016 inch below the scanned surface. RESULTS

Nitridlzation of Butlle

Topochemical and X-ra.v Diffraction Studies

Sintered, massive samples of rutile were reacted

In ammonia at 1 0 1 0°C for times ranging from 10 seconds to

5000 minutes. The samples were quenched In water Immedi­ ately after the desired time had elapsed, and subsequently examined visually, microscopically, and by X-rays.

The first step In the sequence was found to be a rapid partial reduction, or probably, more properly called dissociation, of rutile. The straw-yellow, fully oxidized rutile readily lost oxygen as evidenced by a change to a blue-black color. This black phase was T10^ ^ according to Assayag, Dode, and Falvre?^ and has the same tetragonal rutile structure. In fact, It Is difficult, If not Impos­ sible, to detect the loss of oxygen by X-ray diffraction.

Samples reacted for less than four minutes consisted of two zones, an Inner core of yellow T1 0 2 and an outer layer of black T1 0^ ^5 * No nitride formed during this time. X-ray diffraction measurements of lattice parameters re­ vealed no difference between the two phases, and the pat­ terns agreed perfectly with the ASTM card Index.

38 39 After the Initial dissociation had been completed, ammonia further reduced TIO^ ^ through a sequence of

complex oxide structures to give ultimately the face-

oentered cubic TiO phase. The overall reduction may be

represented as

TiOi + %NU,~TiO->-HtO+'kNx (24)

Beactlon (24) consisted of several steps, each of which represents a reduction from one oxide to a lower oxide. The oxides which were detected by X-ray diffraction of samples which had been abraded through 0 .0 0 3-lnch inter­ vals from the surface to the center were Tl02 t Ti^O^,

T 1 8°1 5* T1 7°1 3» t 1 2°3 * 831(1 Tl0» >nie schematic sequence may be represented as

T102 ■*'T1001>95 -|-T19017 -^TIqO^ TlyO^ -¥>T120j -►•TiO.

Multi-layered samples were observed where nearly all the oxides in the above sequences were present. Fig­ ure 2 shows a color nitrograph of a fractured sample

reacted 5500 minutes at 1010°C. The buff center is Ti^O^;

T180i5 was detected at the purple-buff Interface; Ti^O^ was observed at the blue-purple interface; the blue layer

is TigO^, the gold layer is TIO, and the outer gray layer

is Tin. A higher magnification of the zones is shown

in Figure 3* 40

5X PIG. 2. MULTIPLE LAYERS IN PARTIALLY REACTED SAMPLE (Rutile reacted 5500 mine, at 1010°C in 1 atm. ammonia)

30X PIG. 3. MULTIPLE LAYERS IN PARTIALLY REACTED SAMPLE (Rutile reacted 5500 mlns. at 1010°C in 1 attn. ammonia) 41 The formation of the nitride occurred only as a product"of the reaction of TiO with ammonia. Nitride lay­ ers were observed only adjacent to TIO layers. The re­ maining layers in each sample were in the proper order as indicated in the previous sequence.

The nature of the nitride was firmly established by

X-ray diffraction. Titanium nitride with a lattice param­ eter of 4.238 1 was formed; no evidence of an oxynitride phase was detected. This result was surprising in view of the known complete misclblllty of TiO and TIN and of the formation of tungsten oxynitride by Klessling and Peterson-^

Several samples which were run on the spectrometer- gonlometer showed both TiO and TIN reflections from the surface layers. If an oxynitride had existed, either of two phenomena would have been observed. First, the identi­ cal crystal structures and very nearly identical lattice parameters would give rise to line broadening due to con­ centration gradients from the pure TIN at the surface to tne pure TiO at the other edge of the solid-solutlon band.

Second, if no gradients existed,'and a solid solution had formed, a sharp peak for each "d" spacing would have been observed at values intermediate to pure TiO and to pure TIN.

However, only sharp peaks from both'phases were present.

A typical example is shown in Table II. 42 Table II

X-RAY SPECTROMETER RESULTS SHOWING BOTH TiO AND TIN REFLECTIONS FROM SURFACE LAYERS OF TiOo NITRIDED 6 MINS. AT 1010°C IN 1 ATM. AMMONIA

TIN (hkl) TiO H H 20 dhk l 20 N V I o O dh k l 111 36.8 40 2.440 37.52 100 2.395 200 42.9 60 2.106 43.57 7 0 2 .0 7 6 220 62.25 40 1.490 63.20 15 1.470 311 74.50 8 1 .2 7 2 75.70 5 1.255 222 78.40 5 1.219 79.80 60 1.201 400 93.8 2 1.055 95.55 2 1.040 331 105.1 1 0.9702 107.5 4 0.9551 420 1 0 9 .2 8 0.9449 111.4 5 0.9324 511 126.5 5 0.8626 129.6 3 0.7969

2 A plot of lattice parameter versus sin © (Fig. 4) gives values of the lattice parameters, after extrapolation to sin2© = 1, of 4.238 and of 4.178 I for TIN and TiO, re­ spectively. These agree very closely with values reported for the pure compounds. The relative intensities of reflections from a given

(hkl) give an indication of the thickness of the nitride layer. The calculated mass absorption coefficient of TIN is 161 for copper Ka radiation. Values of I^/IQ &**© tabu­ lated in Table III for various thicknesses of TIN, employing a value of 5.4 grn/caP for the density of the nitride. A value of Ij/I0 ■ 0 .0 3 would be sufficient to reduce the *3

TIO kl I- M 4 .170 Z <

4 .1*0 »- <

4. ISO 0 0.2 0 .4 0.6 0. • 1.0

4 .2 40 TIN

4 .2 50

M 0

1

0 0.2 0.4 0.* 0.* IjO SIN *

FIG. 4 LATTICE PARAMETER DETERMINATION: PLOT

OF CL VERSUS SIN* 0 Zi4 Table III

THE ABSORPTION OP TIO REFLECTIONS BY THE NITRIDE LAYER FOR VARIOUS THICKNESSES OF THE NITRIDE

Thickness *l/*o

0.01 mm. 0.419 0.02 0.194 0.03 0.0735 0.04 0.0308 0.05 0.0129 0.10 0.00017 1^ = intensity of a given TIO reflection through the Indicated thickness of TIN.

IQ = intensity of a given reflection from TiO in the absence of a nitride layer.

intensity of a given reflection from the substrate of TiO through the nitride layer to the background level of the spectrometer. This fraction corresponds to a value of

0.04 mm or about 0.0016 inch of nitride. In other words, if the nitride layer is thicker than 0.04 mm, no TIO re­ flections are observed. The composition of the TIO from which the nitride formed may be determined from Rostoker's plot of the lattice parameter of T10 versus oxygen content?3 as shown in Figure

5. A value of 47 atomic per cent oxygen is obtained and indicates that a metal-excess compound exists, which, I. LTIE ARAMEER- TON RELATION N ITIO S O P M O -C R ETE M A R PA LATTICE 5 FIG. LATTICE PARAMETER, A 4.160 4.160 4.170 F H TO PHASE TiO THE OF 44 46 ATOMIC % OXYGEN 504 8 52 64

46 7U according to Ehrlich,' has approximately only 86 per cent of the oxygen sites occupied. The significance of this statement will be covered subsequently in the discussion of the nitridization of TiO.

Beaction Kinetics

Effect of temperature. The weight loss as a function of time was measured at 900°, 950°, 1010°, and 1070°C. How­ ever, in order to obtain the true weight change of the sample a correction for the weight gain of the supporting

Nlchrome wire was required. A typical example is shown in

Figure 6, which shows the cumulative curve and the individ­ ual contributions of both wire and sample to the cumulative curve. All data were treated in the same manner after dummy wires had been exposed under the same experimental conditions for each run. The corrected weight loss versus time curves are shown in Figure 7. Parabolic-type curves were obtained at all temperatures.

A test for the diffusion-controlled parabolic law was made by plotting the weight loss squared against time, in Figure 8. A straight line, indicating parabolic behav­ ior, was observed for each temperature. However, a break was present in the curves at 1010° and 1070°C, Indicating a possible change in mechanism. The time at which the T O T A L . WCIOHT CHAN# E, M # FIG. INDIVIDUAL 6 CONTRIBUTIONS CUMULATIVE TO WEIGHT -eo 0 5 - 30 -3 0 4 - -20 -10 o CHANGE: RUTILE AT IOIO*C AND I ATM. AMMONIA 100 LE IL T U R C A. IHOE IE 5#. .) M C .0 # (5 WINE NICHROME . «A SC >00 ME, NS. S IN M , E IM T 300 CUMULATIVE CHANOE CHANOE CUMULATIVE NUTIE 4 WI ) E IR W 4- ILE T U IN 400 500 •00 700

24. -

1010 «c

20

1 0 7 0 *C 9 a m 9 9 O J H X 9 9 9 • 8 0 • C

• 0 0 a C

0 too 4 0 0 •00 • 00 1000 1200 1400 lioo l«00 TIMK, MINS. FIG. 7 COMPARATIVE WEIGHT LOSSES OF RUTILE IN I ATM. AMMONIA AT VARIOUS TEMPERATURES 4?

so

2.0 900* C

*5 “

- > X

S '•» ec « 3 a w

«5E u » 0.0

o O » 20 90 40 80 00 70

t i m e, M IM S. FIG. 8 TEST FOR PARABOLIC RATE LAW. RUTILE REACTED AT 900 AND 950* C (I ATM. AMMONIA) 700

COO *

5 0 0

z 4 0 0 Om Khi 3 300 a m

too

£ hi 9 100

K, ■ 4*§X 10

too 4 0 0 COO •00 1000 It 00 1400 I COO ItOO

TIME, MIN8.

FIG. 8 (CONT’D) RUTILE AT 1010 #C AND I ATM. NH^ X FIG. 8 (CONCLUDED) (CONCLUDED) FIG. 8 WEISHT LOSS SQUARED, M<• 100 ISO 0 2 60 so 0 4 O 10 SO RUTILE I E, TIM MINS. 90 00C AM ^ H N ATM. I D N A I070*C T A ^ 52 X 10 X 5.24 1^* 1 090 40 _e SO 70 52 breaks occurred was dependent upon the temperature, de­ creasing with Increasing temperature.

The temperature dependency of the rate constants was determined on an Arrhenlus-type plot of log k versus reciprocal temperature In Figure 9» Values of k were plot­ ted for both portions of the weight squared-tlme curves at

1010° and 1070°C. Two straight line curves were obtained on the Arrhenius plot, giving values of the activation energy of 76,000 and 91,000 calories for the Initial and longer time steps, respectively. The values of k were based on the average of three runs per temperature. Agree­ ment between duplicate runs was generally not too good, being about ±50 per cent. However, In some cases excellent agreement (±5/0 was achieved.

Effect of pressure. The effect of partial pressure of ammonia on the nltrldlzatlon of rutlle was determined at 1010°C on both C.P. rutlle and ceramlc-grade rutlle.

The weight loss-tlme curves are presented In Figure 10 for pressures of ammonia ranging from 0 .0 3 2 to 1.0 atm.

The test for parabolic behavior was made In the conventional manner of plotting weight loss squared against time and checking for a linear relationship. These data are shown in Figure 11. PARABOLIC RATE CONBTANT, ^ /C H ^ % £ C . I 9 EPRTR-EEDNY OFRATE TEMPERATURE-DEPENDENCY FIG 9 I riO 7.4 7 . 8 I 4 I0 X T / l 8. O 8.8 8.4 CONSTANT 8.6

140 Ito RUTILE AT RUTILE P«0.03t ATM. OF 100 P - O .M A T N . >0.007 ATM.

P •o m TIMff, MM«. WEIGHT LOSSES • ■ 1.0 ATM. 4 0 ao KMO*C AND VARDUS AMMONIA PRESSURES COMPARATIVE o 10 4 9

t 0 FIG. ‘ ••0 1 1HWSM so

tft

A z • o w 53 0 • 3 o

»>X S M» P * 0097 ATM.

P *0 .0 3 2 ATM.

o to 40 •0 •0 100 ISO 140

TIME, MINS. no. II TEST FOR PARABOLIC RATE LAW. RUTILE REACTED AT VARIOUS AMMONIA PRESSURES AT 1010'C 5 6

The pressure dependency of the rate constants was plotted on a log-log scale In Figure 12 for hoth C.P. and ceramic-grade rutlle. A linear relationship was obtained for the C.P. rutlle for the Initial rate constants ( k ^ up to 0.29 atm with a slope of 0.75. The plot then showed a departure from the earlier linearity, the slope continu­ ously decreasing up to 1 atm ammonia. A straight line was drawn through the points representing the long-time rate constants, although a linear relationship may be questioned.

The slope of this line, according to the method of least squares, was 0.80. The ceramlc-grade rutlle showed no change In mechanism as evidenced by the lack of breaks In the weight loss squared versus time plots. The slope of the resulting linear relationship between log k and log Pjjh^ was 1.09. This value probably represents a linear relation­ ship between k and PNH~ inasmuch as the slope determination ^ j. is probably accurate only to -0.1.

Rates of Laver Growth

The thickness of each layer of the sectioned samples was measured In order to obtain data on the relative rates of growth of each zone. According to Valensi59 the relative thickness of the various layers is Independent of time.

Each layer will form according to Its Individual rate con­ stant, and Inasmuch as there are several layers, the FIG. PARABOLIC RATI OONBTANT txro 6X10 SXIO EX 10EX

12 0.01 RSUE EEDNY F PARABOLIC OF RATE DEPENDENCY PRESSURE OSAT AT CONSTANT MMONA t Am. m A , E R ttU E R P NIA O M AM CCRAIHC-RR 1010 *C c l i t u r 0.1 s .. UIE K RUTILE, C.P. 1.0

58 over-all rate constant Is some function of the Individual rate constants.

It was possible to obtain data on the rates of layer growth for only TIN, TiO, and TigO^ as seen in the micro­ graphs of Figure 13 . The constancy of the thickness ratios may be seen by comparing the two samples which were nitTid­ ed at times of 100 and 1000 mins. at 1010°C. The thick­ ness of each layer as a function of time is shown graphic­ ally in Figure 14.

Nltrldlzatlon of T1?0? and TIP

The measurements of the thickness of the various layers on T102 were very uncertain for shorter reaction times. In addition, the effect of the presence of other oxides undoubtedly influenced the rate of growth of TIN and T10. It was therefore deemed necessary to make simi­ lar measurementson pure T120^ and on TiO as starting materials. Buttons of these oxides were prepared by triple arc-melting stoichiometric amounts of rutlle and metallic titanium. Prisms of TiO were made by the use of a diamond cut-off wheel. However, the Ti-jO^ was too friable and could not be cut without irregular fractures taking place.

It was possible to obtain weight change data on only TiO

Inasmuch as the area of the regular geometric shapes could a. Butile nitrlded 100 mlns. at 1010°C

b. Butile nitrlded 1000 mlns. at 1010°C

PIG. 13. MICBOGBAPHS OP PBACTUBED SECTIONS SHOWING THE THICKNESS OF EACH LAYER AT TWO DIPPEBENT TIMES I. 3 E H T 13 FIG. THICKNKtC, MM 1.0 O.t 0.4 EFFECT to

OF IE N O TIME IE MINS. TIME, 40 1 TIO. l AE GROWTH LAYER I

ON I2 T 1010* AT TI02 61 be easily measured, whereas, it was not possible to de­ termine the area on Ti2°3 samples. Lumps of both oxides were reacted for various times and then sectioned. Meas­ urements of the growth rate of the layers was possible for both starting materials. The change in weight of TiO was a gain and is shown in Figure 15 as weight gain squared versus time. Parabolic behavior was indicated by the ensuing linear relationship. Growth curves for various layers on TigO^ are given in Figure 1

I.1 THE EFFECT OF TIME ON LAYER E Y A L N O E M I T F O T C E F F E E H T 16 FIG. THICKNESS, MM. O.C .4 0 1.0 1.4 IS l.t I O N Ti O A T 1010 *C 1010 T A O Ti N O lf, MINS. TllfC, 10 T50 IN T 100

GROWTH 64 cause marked changes In color. Even if no solid solubil­ ity can be detected by X-ray measurements, small amounts of undetected impurity are quite capable of creating color changes. It is interesting to compare the difference in thick­ ness between layers on the rutile and on Tl2°3 samP^es* The nitride layer on TigO^ is about 2& to 3 times thicker than on the rutile sample. A similar comparison of the TiO layers showed that TiO on TiO, was about 4 times 2 3 greater than on rutile. The lesser amount of each layer on rutlle implies that some other process in addition to Inward diffusion of either nitrogen or hydrogen is influ­ encing the rate. Such factors as the effect of oxygen on the dlffusivity of nitrogen can not be neglected. The layers of nitride which formed on the TiO sample were too thin to be measured at times of less than 195 min­ utes. A value of 0.008 mm was obtained by means of a filar eyepiece for a TiO sample nitrlded 195 minutes at 1010°C. This thickness is much less than that observed on Ti20^ for similar times and implies that some factor is inhibiting nitride growth in the absence of TigO^. The volume changes as a result of reaction of rutile were less than 2 per cent. In all cases the volume de­ creased and may be accounted for by the formation of layers 65 having a greater density than the original material, The following densities are known: TIN— 5,4; TiO— 4,9 TigO^— 4.56. The densities and structure of Ti^O^ TlgO^, and Ti^o^ are presently unknown. DISCUSSION

Dissociation of T102 to T101 Qc,

The Initial step In the nitriding sequence was found to be the partial reduction of rutile to TiO^ The process Is rapid and may occur even under moderately oxidiz­ ing conditions. The lower oxide is a semiconductor of the metal-excess variety. The rutile structure may be visualized as a close- packed array of oxygen ions held together by highly-charged Ti ions. As oxygen is lost, the cation to anion ratio decreases from 1:2 to l:(2-x) where x is small and represents the number of anion vacancies. According to Marshall, Enright and Weyl?2 the following process takes place in the initial partial reduction

The blue-black color is the result of interactions between Ti+^ and Ti+i* ions. ^ * ^ 2 The high conductivity as­ sociated with the defect structure is due to quasl-free electrons in the vicinity of the missing oxygen ion. The large number of anion vacancies permits ready diffusion of oxygen via the vacancies.

6 6 The mechanism hy which the partial reduction occurs is apparently two-fold. First, the inherent instability of Ti02, even in an oxidizing atmosphere, implies that a certain characteristic tendency exists for the fully oxi­ dized lattice to lose oxygen. Second, the removal of oxygen from the lattice has been shown to be due, in part, to a photochemical reaction at the oxide surface.^ Ultra­ violet light reacts with rutlie to form atomic oxygen ac­ cording to the following relation,

0 * = 0 + a ®' > (26) the intensity of short wave length radiation increasing at higher temperatures. Two Ti+^ ions are then reduced to two Ti+3 ions by the two electrons which are trapped in the lattice. + 4 43 1T\ . (27)

Oxygen is readily removed from the surface as atomic oxygen and causes a depletion of oxygen. A concentration gradient exists and provides the driving force for diffu­ sion of oxygen from the interior of the crystal to the surface. The rapid rate of the dissociation may be linked to the low activation energy for self-diffusion of oxygen 68 76 in rutile of 26 kcal/mol. Although the activation en­ ergy is low, it is still too high to account for the high rate of dissociation by itself. Undoubtedly, the combina­ tion of instability, photochemical surface behavior, and activation energy all contribute to this rapidity.

Complex Intermediate Oxides

The effect of the Ti^O^, TigO^, and phases on the reaction rate and mechanism is unknown. These com­ pounds are very complex, having tricllnlc, monoclinic, or orthorhombic structures. However, the observed thickness of nitride layers on rutile compared to the nitride layer on TiO indicates that the rate of nitride formation is en­ hanced by the presence of either these oxides or by TlgO^. A further examination of nitride layers formed on suggests that the presence of Ti202 is most favorable for nitride formation. It can therefore be concluded that the complex oxides diminish the reaction rate moderately over that observed on Tl^O^. This is not unexpected on the basis of the complex structures and perhaps Intricate atom move­ ments required to form the structures. Further, the lack of symmetry in the structures strongly suggests the possi­ bility of anisotropic diffusion behavior. Any preferred orientation of these oxides in such a direction that was 69 unfavorable for diffusion would strongly retard nitride formation. An indication of the anisotropy of diffusion to be expected for low-symmetry structures is given by Seith and Kell's work?? on self-diffusion in bismuth paral­ lel and normal to the c-axis. Values of the activation energy were 31,000 and 140,000 cal, respectively.

Formation of TlO

As mentioned previously, nitride formation occurs only by reaction with TiO. Hence, conditions favorable for T10 formation would be favorable for nitride growth. Fig­ ures 14 and 16 showed the rate of growth of both TiO and TIN starting with rutile and TigO^, respectively, the growth rate of both T10 and TIN being greater with TigO^ as the starting material. The ratio of the thickness of TiO on T^O^ and rutile was about 3& to 1 , and the nitride thick­ ness ratio was slightly greater than 2 :1 . The rate at which TiO forms would seemingly depend upon the outward diffusion of oxygen from TigO^ or inward migration of titanium ions to the TIO/T^O^ interface. 60th types of mitratlon are possible in TiO according to Wagner ,->2 due to the fact that TiO is stable both as a metal-excess, and as a metal-deficient compound. The compound is very unusual in its ability to exist over a wide range of homogmn- reity on both sides of the stoichiometric composition. Most 70 compounds which exist over a range of compositions are

found on one side or the other of the Ideal composition

such as wustlte, NiO, ZnO, etc. Stoichiometric TiO con­

tains about 15 per cent of e&ch type of lattice vacancy

On the titanium side, the fraction of anion vacancies is

higher, and on the oxygen side the fraction of cation va­

cancies Is higher. The type of disorder existing in this

crystal is similar to that of the alkali halides?8 but is

much higher. Schottky found that both cations and anions participate in the conduction of electrical current in so­

dium chloride, and due to the same type of disorder, a

similar behavior is likely for T l O . ? ^ Mostly cations will migrate from the TiO/NH^ interface to the Tio/TigO^ Inter­ face, and predominantly anions will move in the opposite

direction. Of course electrons must migrate with the cat­

ions in order to maintain electrical neutrality. No sharp

composition boundary should exist where one type of migra­

tion would proceed In preference to the other type.

Although Wagner claims that either cation or anion

migration in T10 is possible, depending upon whether the

compound is metal-deficient or metal-excess, respectively,

it is unlikely that in this study cations will migrate in

the metal-excess T10. The atomic radius of titanium in TIO

is 1.48 A and the atomic radius of oxygen 0.66 1, and if 71 nearly all metal sites were filled, the larger titanium

atom could not fit through the oxygen sites which are about O 0.66 A in radius. Because of size considerations alone, it

appears that only oxygen atoms will diffuse to an appreci­

able extent.

Nitride Formation from TIP

Titanium nitride growth on TiO as the. starting mater­

ial was shown to be parabolic by the linearity of the weight

gain squared versus time relationship. As stated in the

section on reaction mechanism, a parabolic behavior results when the reaction is diffusion-controlled by migration of

some specie through a boundary layer. Two possible mechan­

isms could account for parabolic behavior. First, the

reaction is controlled by diffusion of nitrogen through the nitride to the T1N/T10 Interface where further reaction

takes place. The second alternative involves the outward

diffusion of titanium ions through the nitride layer to the

surface, at which point additional reaction ensues. It was hoped to gain an insight into the relative

movements of anions and cations by the Klrkendall effect.

However, volume changes associated with the reaction were

insufficient to draw any conclusions about the relative move­

ment of the TiN/TiO interface. The thickness of the nitride 72 layers on pure TiO was surprisingly small even at 1200

minutes.

The rather striking similarity between the proper­

ties and structure of TIN and TiO permit an analysis similar

to that of TiO in the preceding section; namely, the depar­

ture of TIN on both sides from the stoichiometric composi­

tion would allow both cations and anions to migrate.

But, once again, an analysis of the size relation­

ships between atoms in TiN gives the same argument as was

stated for TIO. The titanium atom is much larger than the nitrogen atom, and unless considerable titanium atoms were missing, it is unlikely that titanium could diffuse through

the smaller nitrogen sites. 80 The diffusion of nitrogen is TiN has been measured and is given by the expression

<28)

No data are available for the dlffuslvlty of titanium in

TiN.

The weight gain— time relation observed in the ther­ mobalance for TiO is puzzling. If the following reaction were to occur, T;0+NHt‘TlM+H>0-+tH%> (29) the formation of TiN from TiO would Involve a simple ex­ change of nitrogen for oxygen. The net result upon substitu­ tion of an atom of atomic weight 14 for an atom of atomic weight 16 would be a decrease in weight and not the ob­ served increase. The anomalous weight increase could result then only by the formation of an oxynitride in which case the solution of nitrogen in TiO would take place. As stated previously, however, the presence of an oxynitride could be detected by line broadening of X-ray patterns or by a lattice parameter which would be intermediate to those of the pure phases. A continuous change in lattice parameter of wustlte was observed by Bitsianes and Joseph^ during the reduction of magnetite. Wustite always contains more oxygen than the stoichiometric 50 per cent, and both reduc­ tion of magnetite or oxidation of iron occur by diffusion +2 of Fe ions through the vacant iron sites in wustite. As the iron ions are used up at the respective interface, the wustite phase changes in oxygen content with a continuous change in the lattice parameter.

The only logical conclusion in this study is that nitrogen dissolved in the TIO lattice by occupying the 15 per cent vacant oxygen sites and that no change in lattice parameter occurred which could be detected by X-ray diffrac­ tion. it therefore appears that a small amount of nitrogen 74 had dissolved in TiO to form an oxynitride, and that the formation of TIN took place by reaction of ammonia with the oxynitride surface.

Comparison of Nitride Growth on Various Startlntr Materials

The rate of growth of TIN on TigO^, TiOg, and TiO was observed to have the ratio of 9000 : 3000 : 1. In each case the nitride formed from TIO regardless of the material from which TiO formed. In the case of TigO^ and TIOg the sesquloxlde was adjacent to the TiO layer, whereas, no ses- quioxlde was present in the TiO startteg material. The obvious question then is why does T1 0 have such a pro- Z j nounced effect on nitride growth. In order to answer this question it is necessary to consider the nature of the bond­ ing in the various compounds.

Ti20^ is an ionic crystal (corundum structure) in which the titanium and oxygen ions are 0.69 and I.3 2 £ in 81 radius, respectively. * TiO and TIN are interstitial com- 82 pounds of the electron deficient variety. They may be regarded as compounds of the light elements which are in holes between the larger metallic atoms. The face-centered cubic, sodium chloride structure is assumed so that the light elements may take up positions in the octahedral inter­ stices^ and so that the metal atoms may have mutually 75 perpendicular bonds with six neighbors.®3 Hume-Eothery 2 3 suggests that the bonding is d sp-' covalent. Bundle claims that the high hardness and high melting points coupled with the anomalous high electrical conductivity stem from the delocalization of bonding as the ratio of low energy orbi­ tals to valence electrons increases. The "excess" orbitals are introduced by the metal, and interstitial compounds of carbon and nitrogen (occasionally oxygen) occur only with metals having unfilled d-subshells. A comparison of the metal-metal distances in the interstitial phases shows that the distance is increased in the phase over that in the metal, and according to Pauling,®** the bond should be weak­ ened when an Increase in the length occurs. The high melt­ ing points and hardnesses are difficult to rationalize unless the structure is strengthened by strong metal-non- metal bonding. Further, to explain both hardness and high conductivity it is necessary to retain quasl-free electrons and to have directionality in the bonding. Bundle suggests that the orbitals which would provide the necessary require­ ments for the above bonding are the three 2p-orbitals of the non-metal atom. The orbitals are mutually perpendicular, and each orbital has equal concentration of electrons in two directions at 180°. However, for interstitial compounds better bonding might be achieved with two hybrid sp-orbitals 76 and the two remaining p-orbitals. This type of bonding would enable two of the six bonds formed to be of the usual electron-pair variety. Extreme resonance would make all six bonds equivalent. In other words, if one orbital is used with one electron pair to form two bonds, each bond is a half-bond of bond number 1/2. For the interstitial com­ pounds the bonding would be one-third electron pair and two-thirds of an ordinary bond. The bond number will then be 2/3. Rundle gives the conditions for forming half-bonds in interstitial compounds as follows:

1. One element must have more orbitals than valence electrons.

2. The other element must have fewer orbitals than valence electrons.

3. The electronegativities must not differ appreciably.

The suggested bonding of two electron-pair bonds and four half-bonds is apparently considerably stronger than the equivalent number of single bonds. The bonds which are di­ rectional are also resonating and provide quasi-free elec­ trons which explains the high electrical conductivity.

The presence of a nitrogen atom in TiO results in 7 bonding electrons (3 from nitrogen and from titanium)in a directed titanium-nitrogen covalent bond. The oxygen-tItan­ ium bond involves 8 bonding electrons per titanium atom. The number of bonding electrons Increases from 7 to 8 to

10 for TIN, TIO, and TlgO^, respectively. An explanation

for the effect of may be as fo^ ows< nitrogen dissolves In the TiO lattice, the nitrogen may take up a pseudo-oxygen structure®? by acquiring an extra electron.

Apparently nitrogen will enter the TiO lattice more readily

if an extra electron can be obtained from some other source.

The primary source of electrons is the Ti^O^, which releases

two electrons per titanium atom as the reduction to TiO oc­

curs. These electrons can move through the T10 layer and will then associate with the nitrogen. The slowness of the

TlO-ammonla reaction may then be attributed to the absence

of an electron supply such as Ti^O^.

Effect of Temperature

A change in slope was observed in the test for para­ bolic behavior at 1010° and 1070°C. The rate constants

for both portions of the curve were plotted on th®

Arrhenius-type diagram, giving two straight line®. The

calculated activation energies were 76,000 and 9 1 ,0 0 0

calories for the initial and final rate constants, respec­

tively. The change in slope of the test for parabolic behavior may be taken as a change in mechanism or different

reactions coming into play at different times, although, as will be shown subsequently, this is not necessarily true. 78

The first rate constant, k^, probably represents the formation of TiN in view of the fact that the nitride was formed within 6 minutes at 1010°C. The second rate constant, kg, probably represents the cumulative nitrid­ ing and reduction reactions. The rate constants are composite quantities representing the product of both dif­ fusion and concentration differences. The concentration gradient across any given field is dictated to a certain extent by the equilibrium requirements of the interfaces and to the composition of the gaseous components. In addi­ tion, several simultaneous reactions are taking place, each of which has its own individual rate constant.

The activation energies for both and k2 do not agree with that of nitrogen diffusion in TIN. In fact, the overall complexity of the system makes it surprising that linear relations were observed at all on the Arrhenius plot, much less that the activation energies should agree. Valensl^? showed that no simple linear relation between log k and reciprocal temperature should be expected when conjugate layers form, and that this does not necessarily

Imply a change in the reaction mechanism.

The calculated dlffuslvity of nitrogen in TIN from the rate constant for the growth of TiN on TigO^ S^ve8

D * 10*"®, compared to D ■ 10“*^° as calculated at 1010°C 79 from equation (28). The value of D calculated from the growth rate of TiN on TIO gives a value of D = 6 x 10**11.

The failure of either to agree with the measured data of

Wasllewski and Kehl Indicates that nitrogen diffusion is not solely rate determining.

Surface effects cannot be ignored and may be markedly

Influencing the rate. Barrer®-5 offers several possible rate controlling processes which are as follows: — -

(1.) An adsorbed atom enters the lattice,

Rate cl) (30)

where 0 = the fraction of surface covered by adsorbed atoms = the concentration of gas Just inside the surface Cg = the concentration of gas in the metal at saturation.

(2.) A dissolved atom re-enters the surface,

Rate <*(*-*). (31)

(3 ») A molecule strikes the surface and is absorbed as atoms,

Rate = k9P 0 -9 )%. (32)

(4.) Adsorbed atoms evaporate as a molecule,

Rate * M * 0 3 ) 80

(5.) A molecule strikes the surface, one atom

being adsorbed and the other dissolved,

Rate =fcsf>0~&)0~2r9')* (3*0

(6.) A dissolved atom combines with adsorbed atoms

and evaporates as a molecule,

Rate * (3 5)

Barrer further points out that the probability of

the necessary sorption site, being vacant next to a given

interstitial site so that diffusion may occur, is

0 6 )

In an ideal interstitial compound the diffusivity is then

.P-A (37)

D is dependent upon the concentration, and a combined equa­ tion of steady state diffusion and of the adsorption iso­

therm is necessary. Unfortunately data which could be used in such an analysis are unavailable. These possibilities do show, however, that other factors besides diffusion may be significant and may even be rate-controlling. 81

Effect of Pressure

It is unlikely that the pressure dependency is due to a simple solution behavior such as that given by Sievert's law. Ammonia is largely dissociated at 1000°C (K=8000), giving 1/2 mol of nitrogen and 3/2 mol hydrogen. The par­ tial pressure of nitrogen is proportional to the square root of the ammonia pressure. If Sievert's law were valid, the solubility of nitrogen would be proportional to the 1/2 power of the nitrogen pressure or to the 1/4 power of the ammonia pressure. If the rate-controlling step were the solution of nitrogen, the rate constant would be pro­ portional to the 1/4 power of the ammonia pressure and not to the O .75 power. Calculations were made on the variation of nitrogen pressure with the mol fraction of ammonia for two condi­ tions: 1 ) the dissociation of ammonia to diatomic gasls and 2 ) the dissociation of ammonia to monatomlc gases. The pressure of nitrogen for the first case is

. i J j S i - (38) I*K. where N° is the original mol fraction of ammonia. The NH 3 pressure of nitrogen in terms of the mol fraction of ammonia 82 for the second case is

r p* ft ^ V*

The nitrogen pressures are always less than the ammonia pressure and when incorporated into Sievert's law give a very low pressure dependency. The type and nature of lattice vacancies could be altered by the variation in nitrogen pressure similar to that of cuprous oxide according to Wagner.^ The effect of pressure on the diffuslvlty of zinc in zinc oxide was 86 determined and was found to be proportional to the 0.65 power of the zinc pressure. Although the structure of zinc oxide (wurtzite) is different from that of TiO, it is of interest to note the similarity in the 0.65 power and of the 0.75 power in this investigation for the pressure de­ pendency of the rate constant. The effect of nitrogen pressure on the diffuslvlty of nitrogen in titanium nitride is unknown and should be investigated in future work. It may actually be that the relationship is approximated by the 0.75 power of the nitrogen pressure. The variation of diffuslvlty with pressure in either cuprous oxide or zinc oxide is related to the num­ ber of defects in the crystal and to the mobility of the defects. The number of defects Is a thermodynamic quan­ tity determined by the free energy of formation of a defect, whereas, the mobility of the defects Is dependent upon the energy of activation for the movement of the defect. The observed diffuslvlty Is then a composite quantity of both the concentration and mobility. One last consideration of the pressure effect may be made In connection with the apparent Importance of a source of electrons. If the rate of growth of a composite layer is due predominantly to the outer layer, the rate constant will be pressure-dependent. On the other hand, if the growth Is due primarily to an inner layer, the rate constant will be Independent of pressure. The observed pressure dependency therefore Indicated that the overall growth was due mainly to the growth of nitride which was the outermost layer. The Importance of TlgO^ seemingly interrelates the electron transfer and the pressure effect. This relationship may stem from the chemisorptlon of the gas, which results in the In­ troduction of electrons Into the surface to form the gas- solid bond. The chemisorbed reducing gases are bonded as radicals^ and Introduce extra electrons into the lattice. This may be the only source of electrons when TIO is the starting material for the nitriding process. When rutile or TlgO^ is used as a starting material, the supply of elec­ trons could originate from both chemisorptlon and from the Ti 0 lattice. 2 3 The preceding discussion on the pressure dependency is largely speculative. At best, the system is very com­ plex. Diffusion is important, as indicated by the para­ bolic behavior, but it should be pointed out that oxygen must also diffuse outward in addition to the inward dif­ fusion of nitrogen. Undoubtedly, the diffuslvlty of the rate-controlling specie is affected by the concentration of the specie which is diffusing countercurrently. The diffusivities of both species would be pressure-sensitive also. No concise explanation can be offered on the basis of the available data. SUMMARY AND CONCLUSIONS

The rates of nitride formation on TiO_, Ti-O.., and fa fa ^ TiO were studied in the temperature range of 900° to 1070°C. Parabolic behavior was observed for each substance; how­ ever, the parabolic rate constants were vastly different, being in the ratio of

“riaOj ! *iio2 ! ^ 1 0 " 9000 ! 3000 : 1 •

The initial step was a rapid, partial-dissociation of Ti02 to TIO^ ^ and was attributed to the inherent insta­ bility of fully oxidized rutile and to a photochemical sur­ face reaction.^-* The next step in the sequence was the reduction of through a series of complex intermediate oxides to ultimately give TiO. Nitride formation was only observed when TiO was present and adjacent to the nitride. No oxynitride was detected by X-ray diffraction, only patterns from TIN and TIO which contained 47 atomic per cent oxygen. A small anomalous weight gain was observed when TiO was nltrided directly. This Indicated the formation of some oxynitride which was probably formed by the solution of nitro­ gen in vacant oxygen sites and was undetected by X-rays. The slow nitride formation from TiO was attributed to the absence

85 86 of an electron source such as Tl^O^ which was present in the other starting materials. The electrons are necessary in order for both oxygen and nitrogen to enter the covalent- metallic TiO and TiN structures. The larger 0“2 ions of the Ti 0 require electrons in order to form TiO. The plots of the test for parabolic rate behavior showed breaks at both 1010° and 1070°C, indicating either a change in mechanism or a complex system associated with conjugate layers. ^ The energies of activation were 76,000 and 91.000 cal for the short and long-time curves, respec­ tively, Both of these values were greater than the activa­ tion energy reported for the diffusion of nitrogen in the nitride.®® The higher values were attributed to possible rate-controlling surface reactions in addition to diffusion. The pressure dependency was Investigated at 1010°C for rutile between 0.032 and 1.0 atm ammonia. The relation­ ship of the rate constant to pi ressure is of the form

k = Ap°*75 .

The exponent of 0.75 may be due to the pressure dependency of the diffusion coefficient. An exact analysis has not been developed. REFERENCES

1. Agte, C. and Moers, K., Z. Anorg. allg. Chem., 198. 233 (193D. ; 2. Ehrlich, P., Z. anorg. Chem., 259. 1 (1949). 3* Chiotti, P., J. American Ceramic Society, 35, 123 (1952). 4. Duwez, P., and Odell, P., Journal Electrochemical Society, 21, 299 (1950). 5. Hahn, H., Z. anorg. Chem., 258. 58 (1949). 6 . Brauer, G . , Z. Electrochem., 46, 397 (1940). 7. Friederlch, E. and Sittig, L., Z. Anorg. allg. Chem., 142, 293 (1925). 8. Bllx, H., Z. physlk. Chem. (B), 2t 229 (1929). 9. Bundle, R. E., Baenziger, N. C., Wilson, A. S., and McDonald, B. A., J. Am. Chem. Society. 70. 99 (1948). 10. Friedel, C. and Guerin, J., Compt. rend., 82, 972 (1876). 11. Montemartini, C. and Losana, L . , Giorn. Chim. Ind. Appl. i, 323 (1924); Notizario Chim. Ind., 1, 237 (1924). 12. Buff, 0. and Eisner, F., Ber, Dtsch. Chem. Ges., 41, 2250 (1908); 42, 900 (1909). 13* van Arkel, A. E., Physlca, 4, 286 (1924).

14. Moers, K., Z. anorg. allg. Chem., 198. 243 (’1931 )• 15. Campbell, I. E., Powell, C. F., Nowlcki, D. H., and Gonser, B. W., J. Electrochem. Soc., 2£» 318 (1949). 16. Pollard, F. H. and Woodward, P., J. 4m. Chem. Soc., ZQt 1709 (1948).

87 88 17. Brager, A., Acta Physiochim. U.S.S.R., 10. 887 (1939); 11, 617 (1939). 18. Olson, C. M., U. S. Patent 2,413, 778 (1947). 19. Morton, P. H. and Baldwin, W. M., Jr., "The Scaling of Titanium In Air," Trans. ASM, 44, 1004 (1952). 2 0 . Slede, A. and Pulslfer, v., "Surface Hardening of Titanium with Metalloid Elements,” Watertown Arsenal Laboratory Report, 401/84/55. 2 1 . Aagard, L. and Rowe, L. W., "Process for Chlorinating Titaniferous Material," U. S. Patent 2,622,005 (1952). 22. Eoberson, A. H. and Banning, L. W., "Preparation and Chlorination of Titaniferous Slags from Idaho Ilmen- ites," Trans. AIME, 203. 1335 (1955).

23. Farup, P., "Process of Producing Titanium Compounds," U. S. Patent 1,343,441 (1920). 24. Bichowsky, F. and Harthan, J., U. S. Patent 1,408,661 (1922).

25. Andreu, P. and Paquet, Eene, "Fixation of Nitrogen by Means of Titanium and its Transformation Into Indus­ trial Products," U. S. Patent 1,487,521 (1924). 2 6 . Traill, R. J. and McClelland, J., "Metallization of Fe Oxide in FeTiOo," Pamphlet, Amer. Electrochem. Soc. (1929). . 27. Suirokowski, V. S., Snopova, E. V., and Eotkov, N. E., "Reduction of FeTiO-a in Gaseous phase,” Mineral Suiv'e, £, 522 (193D. 28. Michaud, G. G. and Pidgeon, L. M., "Selective Reduc­ tion of Iron in Ilmenlte," Trans. Can. Inst. Min. Met. Bull., 50£, 307 (195*0.

29. Belyakova, E. P., Komar, A., and Mikhailov, V. V., Metallurg., No. 4, 5 (1940). 3°. Dahwihl, W., "Hard Metals," London, H. M. Stationery Off., (1955). 89 31. Schmidtz-Dumont and Steinberg, Naturwissenschaften, 41, 117 (1954). 32. Stone, L. and Margolin, H., "Titanium-Rich Regions of the Ti-C-N, Ti-C-O, and Ti-N-0 Phase Diagrams," Trans. AIME, 122., 1498 (1953). 33* DeVries, R. C. and Roy, R., "A Phase Diagram for the System Ti-Ti(>2 Constructed from Data in the Literature*" Bull. Amer. Cer. Soc., 33. 370 (1954).

34. Palty, A. E. , Margolin, H., and Nielson, J. P., "Ti- tanlum-Nltrogen and Titanium-Boron Systems," Trans. ASM, 46, 312 (1954).

35. Pearson, A. D., "Studies on the Lower Oxides of Titan­ ium," Technical Report 120, Laboratory for Insulation Research, M. I. T., Cambridge, Mass. (1957).

36. Kiessling, R. and Peterson, L., "The Nitrides and Oxide-Nitrldes of Tungsten," Acta Metallurgica, 2, 675 (1954). 37. British Patent 635.221 (1946).

38. Peretti, E. A., "A New Method for Studying the Mechan­ ism of Roasting Reactions," Discussions, Faraday Soc., 4, 174 (1948).

39. McCabe, C. L., and Morgan, J. A., "Mechanism of Sul­ fate Formation During the Roasting of Cuprous Sulfide," Trans. AIME, 206 (1956).

40. Tammann, G., Z. anorg. Chem., 111. 78 (1920).

41. Tammann, G., and Koster, W., Z. anorg. Chem., 123. 196 (1922). 42. Pilling, N. B., and Bedworth, R. E., J. Inst. Metals, 22., 529 (1923). 4 3. Evans, U. R., Trans. Electrochem. Soc., 2i, 547 (1947).

44. Dunwald, H., and Wagner, C., Z. phys. Chem., B22, 212 (1933). 4 5. Gunderman, J., Hauffe, K. , and Wagner, C., Z phys. Chem., B37. 148 (1937). 90 46. Lustman, B., and Mehl, R. F., Trans. AIME, 143. 246 (1941). 47. Baur, J. P., Bridges, W., and Fassell, F. W., Jr., "High Pressure Oxidation of Metals— Oxidation of Met­ als Under Conditions of a Linear Temperature Increase," J. Electrochem. Soc. (1955)* 48. Reed, N. L., "High Pressure Oxidation," Report, Ord­ nance Materials Research Office, Watertown Arsenal (1956). 49. Garner, J., J. Chem. Soc., 1239 (1947). 50. Klttel, C., "Introduction to Solid State Physics," J. Wiley and Sons, New York, Chap. 17 (1957). 51. Davies, M. H., Simnad, M. T.« and Blrchenall, C. E., "On the Mechanism and Kinetics of the Scaling of Iron," Trans. AIME, 191. 889 (1951). 52. Wagner, C., Seminar on Atom Movements, ASM, Cleveland, 151 (1951). 53. Wagner, C., Z phys Chem., B21. 25 (1933). 54. Hoar, T. P. and Price, L. E., Trans. Faraday Soc., 2il» 867 (1938). 55. Kubaschewski, 0. and Hopkins, B. E., "Oxidation of Metals and Alloys," Academic Press, New York, 120 (1953)- 5 6 . Wagner, C. and Grunewald, K., & phys. Chem., B40. 455 (1938). 5 7 . Andersson, Collen; Kruuse, Kuylenstlema, Hagnelli, Restnalls* and Asbrlnk, "Identification of Titanium Oxides by X-ray Powder Patterns," Acta Chem. Scand., 11, 1653 (1957). 58. Gurnick, R. S. and Baldwin, W. M., Jr., "The High Tem­ perature Oxidation of Manganese," Trans. ASM, 310 (1950). 59. Valensi, G., International Conference on Surface Reac­ tions, Pittsburgh (19**8). 91 60. Bltsianes, G. and Joseph, T. L., "Topochemical Aspects of Iron Ore Seduction," Trans. AIME, 203. 639 (1955). 61. Edstrom, J. 0. and Bltsianes, G., "Solid State Diffu­ sion in the Reduction of Magnetite," Trans. AIME, 203 . 760 (1955). 62. Bltsianes, G. and Joseph, T. L., "Solid Phase Identi­ fication in Partially Reduced Iron Ore," Trans. AIME, 197. 1641 (1953). 63* Bltsianes, G. and Joseph, T. L., "The Wustite Phase in Partially Reduced Hematite," Trans. AIME, 200. 150 (1954). 64. Johnson, G. and Weyl, W. A., "Influence of Minor Addi­ tions on Color and Electrical Properties of Rutile," J. Am. Cer. Soc., 32. 398 (1949). 65. Johnson, G., "Influence of Impurities on Electrical Conductivity of Rutile," J. Am. Cer. Soc., 36. 100 (1953). 66. Smlgelskas, A. D. and Kirkendall, E. 0., "Zinc Diffu­ sion in Alpha Brass," Trans. AIME. 171. 130 (1947). 67. Darken, L. S., "Diffusion, Mobility, and Their Inter­ relation Through Free Energy in Binary Metallic Sys­ tems," Trans. AIME, 175. 184 (1948). 68. Dunnlngton, B. W., Beck, F. H., and Fontana, M. G. , Corrosion, 8., 2 (1952). 69. Simnad, M. and Spilners, "Kinetics and Mechanism of the Oxidation of Molybdenum," Trans. AIME. 203. 1011 (1955). 70. Jones, E. S., Mosher, J. F., Spelser, &., and Spretnak, J. W., "The Oxidation of Molybdenum," Corrosion. 14. 20 (1958). 71. Carter, R. E. and Richardson, F. D., "An Examination of the Decrease of Surface Activity Method of Measur­ ing Self-Diffusion Coefficients in Wustite and Cobal- tous Oxide," Trans. AIME, 200. 1244 (1954). 92 72. Marshall, P. A., Jr., Enright, Di P., and Weyl, W. A., "On the Mechanism of and Recrystallization of Oxides," International Symposium Reactivity of Solids, Gothenburg 1952, p. 273• 73» Rostoker, W., "Observations on the Lattice Parameters of Alpha and TiO Phases in the Titanium-Oxygen Sys­ tem," Trans. AIME, 194. 981 (1952). 74. Ehrlich, P., Z. anorg. allg. Chem., 242., 5 3 (1941). 75• Forland, K. S., "Photo Oxidation on the Surface of Rutile," International Symposium Reactivity of Solids, Gothenburg, 1952, p. 291. 7 6 . Gulbransen, E. A. and Andrew, K., Trans. Electrochem. Soc., 2£, 364 (1949).

77. Seith and Kell, Z. Electrochem., 22.* 3^° (1933). 78. Schottky, W., Z fur physik. Chem., B, 22., 335 (1935). 79. Ronge, G. and Wagner, C., J. Chem. Physics, 18. 74 (1950). 80. Wasilewskl, R. J. and Kehl, G. L., "Diffusion of Ni­ trogen and Oxygen in Titanium," J. Inst. Metals, 81, 94 (1954). 81. Hall, Z. anorg. allg. Chem., 184. 421 (1929). 82. Rundle, R. E., "A New Interpretation of Interstitial Compounds— Metallic Nitrides and Oxides of Composition MX, Acta Cryst., 1, 180 (1948). 8 3 . Hume-Rothery, W., "Metallic Carbides and Nitrides of the Type MX," Phil. Mag. (7 ), 44, 1154 (1953). 84. Pauling, L., "The Nature of the Chemical Bond," Cor­ nell Univ. Press, 2nd Edition (1940). 85* Barrer, R. M., "Aspects of Gas-Metal Equilibrium, In­ terstitial Solution, and Diffusion," Discussions Faraday Soc., *£, 68 (1948). 8 6 . Secco, E. A. and Moore, W. J., "Diffusion and Exchange of Zinc in Crystalline Zinc Oxide, J. Chem. Physics, 2^,942(1957). 8 7 . Speiser, R., Private communication. AUTOBIOGRAPHY

I, David L. Douglass, was b o m in Newark, New Jersey, September 28, 1931* I was reared in Maplewood, New Jersey, attending the secondary schools in that township. I gradu­ ated from high school in 19^9» and enrolled at the Pennsyl­ vania State University in the metallurgy curriculum, in the Pall of 19^9. I graduated with a B. S. degree in 1953 after having worked as a laboratory assistant in physical metallurgy laboratories as an undergraduate. In addition I worked under Dr. V. P. Zackay in the construction and estab­ lishment of a single crystal laboratory. Upon graduation I accepted employment with the E. I. duPont de Nemours and Co., Inc. at the Savannah River Plant . in Aiken, South Carolina, as a research physical metallur­ gist. I spent 15 months in that laboratory working on the metallurgy of uranium and its application to nuclear fuel elements. In September of 195** I was appointed St. Joseph Lead Fellow at the Pennsylvania State University, where I began.graduate work. I received the degree Master of Science in August 1955* having worked under Dr. R. W. Lindsay and written a thesis on liquid immlscibility rela­ tions in the quaternary system Fe-Cu-S-C. Following the completion of work for the Master*s degree, I became a research metallurgist°at the Battelle 93 • ■ ■ Memorial Institute in Columbus, Ohio. My work there was concerned with the transformations and phase-relations of zirconium-uranium and uranium-titanium, alloys. I en-‘ tered The Ohio State University in September of 1955* a^a. in the Spring of 1956 I enrolled on a part-time basis under the Battelle Educational Program. I was appointed' part-time instructor in September, 1956, in the Department of Metallurgical Engineering at The Ohio State University, and taught courses in extractive metallurgy. I resigned from Battelle Institute in December, 1957» and.worked full time at The Ohio State University while completing requirements for the degree Doctor of Philosdphy. • Upon completion of the work at The Ohio State Uni­ versity for the Ph.D. degree I will be employed as a research metallurgist at the Knolls Atomic Power Labora-; tory, Schenectady, New York. This laboratory is operated for the Atomic Energy Commission by the General Electric Company.