This dissertation has been microfilmed exactly as received 70-6859

RATLIFF, John Leigh, 1936- RE ACTION-DIFFUSION IN A METAL-NONMETAL BINARY SYSTEM AND THE MULTICOMPONENT SYSTEMS Ti/SiC AND Ti-6Al-4V/SiC.

The Ohio State University, Ph.D., 1969 Engineering, metallurgy

University Microfilms, Inc., Ann Arbor, Michigan REACTION—DIFFUSION IN A METAL-NONMETAL BINARY SYSTEM AND THE MULTICOMPONENT SYSTEMS Ti/SiC AND Ti-6Al-4V/SiC

DISSERTATION

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

By

John Leigh Ratliff, Met.E., M.S.

***********

The Ohio State University 1969

Approved by

Adviser Department of Metallurgical Engineering Dedicated to

Mary Ann ACKNOWLEDGMENTS

First, I would like to acknowledge my adviser, Dr. G. W. Powell, whose continuous interest and willing­ ness to discuss the results of this work as it progressed were most appreciated. Recognition is also extended to Dr. R. A. Rapp whose advice and contribution of time spent in informative discussions were appreciated. Recognition is given to Mr. D. E. Price of the Battelle Memorial Institute for helpful experimental suggestions and for assistance in performing high- temperature, vacuum annealing and sintering operations. Dr. H. D. Colson of The Ohio State University Department of Mathematics is deserving of special thanks for his helpful suggestions pertaining to the numerical solution of differential equations. Appreciation is extended to Mr. R. 0. Slonaker for preparing the computer program which performed the absorption corrections on the electron-microprobe analyses. Appreciation is also extended to Mr. Neal Farrar and Mr. Ross Justus for their excellent suggestions and work which was performed in relation to the design and construction of experimental equipment. Finally, I would like to acknowledge the Metals and Ceramics Division, Air Force Materials Laboratory, Wright-Patterson Air Force Base for their financial support of this work and The Ohio State University Computer Center for the computer time which they contributed. VITA

October 8, 1936 Born - Kansas City, Kansas

1959 ...... B.S. Metallurgical Engineering, University of Missouri - Rolla, Rolla, Missouri 1960 ...... M.S. Metallurgical Engineering, University of Missouri - Rolla, Rolla, Missouri 1960-1965...... Research Metallurgist; Nonferrous Metallurgy Division, Battelle Memorial Institute, Columbus, Ohio, and part-time graduate student at The Ohio State University 1965-1967...... Research Metallurgist; Bar, Plate, and Forged Products Division, United States Steel Applied Research Laboratory, Monroeville, Pennsyl­ vania, and part-time graduate student at the Carnegie-Mellon University 1967-1969...... Research Associate; Department of Metallurgical Engineering, The Ohio' State University, Columbus, Ohio

FIELDS OF STUDY

Major Field: Metallurgical Engineering Studies in Physical Metallurgy; Professors G. W. Powell, J. W. Spretnak, and P. G. Shewmon Studies in Corrosion; Professors M.E. Straumanis and M. G. Fontana Studies in Kinetics; Professors R. O. Sutherland and W. J. James TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS...... iii VITA ...... iv LIST OF FIGURES ...... vii LIST OF TABLES ...... x Chapter

I. INTRODUCTION . 1

II. LITERATURE SURVEY ...... 3

A. The Importance and Principles of Metal-Matrix, Fiber-Reinforced Composite Materials...... 3 B. Reaction Diffusion in Binary Systems . 12 Experimental Observations Phenomenological Theory C. Reaction Diffusion in Multicomponent Systems ...... 24 Phenomenological Theory Phase Rule and Representation of Diffusion Paths Experimental Observations

III. REACTION-DIFFUSION IN A BINARY METAL-NONMETAL SYSTEM ...... 33

A. Problem Statement and Assumptions . . 34

v CONTENTS (Contd.)

Chapter Page

B. Mathematical Formulation ...... 36 Case I: Metal Initially Saturated with Nonmetal Case II: Metal Initially Not Saturated with Nonmetal C. Results and Discussion...... 42 IV. REACTION-DIFFUSION IN THE SYSTEMS Ti/SiC AND Ti-6Al-4V/SiC ...... 49 A. Experimental Procedure ...... 49 Materials Diffusion Couple Preparation Alloy Preparation X-Ray Analysis Metallography Electron-Microprobe Analyses

B. Results and Discussion...... 61 Reaction-Diffusion Kinetics X-Ray Analyses Metallographic and Electron Microprobe Analyses Diffusion Paths in the Ti/SiC System Mechanism of the Ti/SiC Reaction

V. SUMMARY 113 APPENDIXES . . . 117 REFERENCES. . . . 130 FIGURES Figure Page

1. Aerospace Materials Technology Envelope .... 5

2. Schematic Stress-Strain Diagram for a Metal- Matrix, Fiber-Reinforced Composite Material . . 6 3. Theoretical Variation of Composite Strength with Volume Fraction of High-Strength, Brittle Fibers ...... 9 4. Concentration-Penetration Diagrams for Reaction-Diffusion in a Binary System where Three Phases are Involved ...... 19

5. Relationship between the Concentration- Penetration Diagram and the Phase Diagram for Reaction-Diffusion in a Metal-Nonmetal Binary System ...... 37 TiC 6. Arrhenius Plot Comparing the Values of D Obtained by Vansant and Phelps1*0 with the Values Calculated from Equation (54)...... 44

7. Non-Parabolic Growth of the Titanium Carbide Reaction Layer as Numerically Computed from Equation (54) ...... 45 8. Experimentally Observed Non-Parabolic Growth of the y-Phase in Ni/Al Diffusion Couples . . . 47

9. Microstructures of Initial Materials...... *.52 10. Schematic Diagram Illustrating the Molybdenum Bonding Vessel Assembly ...... 53

11. Specimen Holder for Polishing the Mating Diffusion Couple Surfaces ...... 55

12. Technique for Polishing the Mating Diffusion Couple Surfaces ...... 56

vii FIGURES (Contd.)

Figure Page

13. Furnace Facility for Accomplishing Diffusion A n n e a l s ...... -57 14. Reaction-Zone Growth Kinetics for the Ti/SiC Diffusion Couples ...... 65 15. Arrhenius Plots for the Stages I and II Reactions in the Ti/SiC System...... 68 16. Reaction-Zone Growth Kinetics for the Ti-6Al-4V/SiC Diffusion Couples ...... 71 17. Arrhenius Plots for the Stages I and II Reactions in the Ti-6Al-4V/SiC System ...... 73 18. Reaction-Zone Microstructures for Ti/SiC Diffusion Couples (A) Couple 4, Reacted 2.5- Hours at 1200°C (B) Couple 10, Reacted 75- Hours at 1200 °C ...... 77 19. Reaction-Zone Microstructure and Partially Dissolved Tungsten Marker in a Ti/SiC Diffusion Couple Reacted 4-Hours at 1200°C. . . 80

20. Electron Microprobe Analyses for Silicon and Titanium in the Reaction-Zone of Ti/SiC Diffusion Couple 1 0 ...... 81

21. Electron Microprobe Analyses for Silicon and Titanium in the Reaction-Zone of Ti/SiC Diffusion Couple 1 0 ...... 82

22. Reaction-Zone Microstructures for Ti/SiC Diffusion Couples (A) Couple 13, Reacted 4- Hours at 1100°C (B) Couple 22/ Reacted 72- Hours at 1000°C ...... 84 23. Electron Microprobe Analyses for Silicon and Titanium in the Reaction-Zone of Ti/SiC Diffusion Couple 2 2 ...... 86 24. Electron Microprobe. Analyses for Silicon and Titanium in the Reaction-Zone of Ti/SiC Diffusion Couple 2 2 ...... 87

v4.i1 FIGURES (Contd.)

Figure Page

25. Reaction-Zone Microstructures for Ti/SiC Diffusion Couple 8 Reacted 12-Hours at 1200°C . . 88

26. Electron Microprobe Analyses for Silicon and Titanium in the Reaction-Zone of Ti/SiC Diffusion Couple 8...... 90

27. Reaction-Zone Microstructures for Ti-6Al-4V/SiC Diffusion Couples (A) Couple 8A, Reacted 26.5- Hours at 1100°C (B) Couple 5A, Reacted 74-Hours at 1 2 0 0 ° C ...... 91

28. Electron Microprobe Analyses for Aluminum and Vanadium in the Reaction-Zone of Ti-6Al-4V/SiC Diffusion Couple 5 A ...... 93

29. Electron Microprobe Analyses for Silicon and Titanium in the Reaction-Zone of Ti-6Al-4V/SiC Diffusion Couple 5 A ...... 94

30. Ternary Isotherm Proposed by Brukl1*7 for the System Ti-Si-C at 1200°C...... 97 0 31. Revised Ternary Isotherm for the System Ti-Si-C at 1 2 0 0 ° C ...... 99

32. Microstructures of the Ti-SiC Alloys...... 101

33. Alloy Compositions and Electron Microprobe Analyses of the Phases Present in the Ti-Si-C Alloys...... 103 34. Diffusion Paths for the Stages I and II Reactions in the Ti/SiC Diffusion Couples Prepared from Commercially-Pure Titanium and Reacted at 1 2 0 0 ° C ...... 105

35. Diffusion Paths for the Stages I and II Reactions in the Ti/SiC Diffusion Couples Prepared from Commercially-Pure Titanium and Reacted at 1100° and 1 0 0 0 ° C ...... 106 36. Diffusion Path for the Ti/SiC Diffusion Couples Prepared from Carbon Satruated Titanium and Reacted at 1200°C...... 107 TABLES

Table Page

1. Comp^r^son of Numerically Computed Values of D with the Values Obtained by Vansant and Phelps'*0 ...... 41

2. Chemical Analyses of the Materials for Diffusion Couples ...... 51

3. Summary of Reaction-Diffusion in the Ti/SiC S y s t e m ...... 63

4. Summary of Reaction-Diffusion in the Ti-6Al-4V/SiC System ...... 64

5. Reaction-Zone Growth Constants for the Ti/SiC and Ti-6Al-4V/SiC Systems...... 67

6. Summary of X-Ray Analyses of Selected Ti/SiC Diffusion Couples ...... 74

7. Summary of X-Ray Analysis of the Ti-SiC Alloys ...... 100

8. Summary of Electron-Microprobe Analyses of the Ti-SiC Alloys...... 102

x I. INTRODUCTION

The present research is concerned with reaction- diffusion in both binary and multicomponent metallic systems. Reaction-diffusion is a relatively new term in the diffusion literature which makes more brief reference to the subject of multicomponent-multiphase diffusion in solids. Aside from being one of the most interesting of the various diffusion phenomena, reaction- diffusion also is of considerable practical importance to those segments of industry which are based on materi­ als technology. Examples of the latter include: 1) powder metallurgy; 2) metal cladding; 3) brazing, soldering and diffusion bonding; 4) manufacture of integrated electronic circuits; and 5) development of metal-matrix, fiber-rein­ forced composite materials. The impetus for the present research arises from the anticipated importance of reaction-diffusion in present efforts to develop metal-matrix, fiber-reinforced composite materials. This new concept in materials is revealed by a linear law of mixtures which assumes that in the absence of synergistic effects, any given property of a mixture of two or more materials is determined by the respective properties of the con­ stituent materials and the relative amounts of each present in the mixture. Accordingly, a significant improvement in the ultimate tensile strength of exist- 2 ing structural metals is implied through the combination of such metals with fibers or filaments of very high strength materials. Because of the anticipated higher strength levels, it is further expected that metal- matrix, fiber-reinforced composites will find appli­ cation at elevated temperatures. These goals can, however, only be realized provided that the metal/fiber combinations are initially compatible, i.e., provided that excessive chemical reaction does not occur between the metal matrix and its entrained fibers during pro­ duction or subsequent exposure at elevated temperatures. The initial phase of this research was concerned with the development and verification of a new phenomeno­ logical expression for the rate of layer growth in a metal-nonmetal binary system with a single intermediate phase. The metal side of the diffusing system was treated as finite in extent and numerical methods were employed in the solution. The second phase of this research was concerned with experimental reaction-diffusion studies on the Ti/SiC and the Ti-6Al-4V/SiC systems, i.e., three and five component systems, respectively. These systems are presently of interest because of their potential as metal- matrix, fiber-reinforced composite materials. II. LITERATURE SURVEY

A survey of the literature pertinent to the subjects of this research is most conveniently divided into three major catagories as follows: (1) the importance and principles of metal-matrix, fiber-reinforced composite materials; (2) reaction-diffusion in binary systems; and (3) reaction-diffusion in multicomponent systems.

A. The Importance and Principles of Metal-Matrix, Fiber-Reinforced Composite Materials

Although the principles of fiber reinforcement have been applied for many years to materials such as rubber, concrete and plastic, the application of this concept to metals is still in the early stages of research and development. Some of the factors which are contributing to the present interest in metal-matrix composites are as follows: 1) increasing demand for improved mechanical properties of metals; 2) recent development of high strength-high elastic modulus fibers, filaments and whiskers; and 3) technological innovations to enable the fabrication of metal-matrix composites. From a recent review of composite technology by Standifer^ it is evident that the aerospace industry stands to gain the most from this new class of materials. This industry is increasingly in need of the potential mechanical

3 4 property improvements to be offered by metal-matrix composites, i.e., lighter, stronger, stiffer, high temperature materials. The present aerospace guide line^ for the selec­ tion of structural materials for use within certain temperature ranges is shown in Figure 1. The mechanical properties referred to along the ordinate include strength, elastic modulus, creep rate, stress-rupture, fracture toughness, etc. As indicated by the arrow, a significant advance in materials technology would result in a shift of the materials guide line upwards and to the right. In recent years, many attempts have been made to accomplish this objective. Precipitation and/or dispersion strengthening coupled with general microstructural refinement have been popular approaches. At the present time, nearly as much effort is being directed toward the same end by applying the principles of fiber reinforcement. 2 In a commentary on strong solids, Cottrell considers fiber reinforcement to be another form of dispersion strengthening. In the more conventional sense, dispersion strengthening is strictly the result of dislocation- pariticle interactions. Strengthening by fiber reinforce­ ment also involves a dispersed system but is not directly relatable to a specific dislocation strengthening mecha­ nism. The resultant strength of a composite is mainly determined by the law of mixtures. An excellent review of the principles of metal- matrix, fiber-reinforced composite materials is presented 3 by Kelly and Davies. The basic principles are best illustrated through a discussion of a uniaxial stress- strain diagram, Figure 2, for a typical composite. Here, the material being considered is a metal matrix with a Mechanical Properties / Density < Figure 1— Aerospace Materials Technology Envelope Technology Materials Aerospace 1— Figure U L CL h- 00 m 00 a. m Temperature ercoy Metals Refractory 5 6

HE t Fracture)

10v> 05 CO

Elastic Limit

Strain

Figure 2— Schematic Stress-Strain Diagram for a Metal-Matrix, Fiber-Reinforced Composite Material

i 7 dispersed array of continuous uniaxial lengths of high strength-high modulus fibers. The following assumptions are made: 1) the metal matrix is ductile and yields prior to the initiation of fiber failure 2) the fibers all have the same ultimate tensile strength; and 3) the elastic modulus of the fibers is greater than that of the metal. Four stages of deformation, I, II, III and IV, may be observed in the stress-strain diagram. First, both the matrix and fibers respond elastically to the applied load; the elastic modulus in this region is given by the law of mixtures,

where: E = elastic modulus V = volume fraction c,f and m = subscripts referring to the composite, fibers, and matrix, respectively The second stage of deformation is referred to as quasi­ elastic since the fibers continue to deform elastically while the matrix deforms plastically; the modulus in this region is given by

(2)

where is the slope of the stress-strain diagram £ for the metal matrix at a particular strain in the composite. The third stage of deformation results when both the metal matrix and fibers deform plastically and would, of course, not be observed for brittle, high-strength fibers. The fourth and last stage of deformation defines the ultimate tensile strength of the composite and represents failure. This occurs at a strain closely corresponding to the ultimate tensile strain of the fibers. The ultimate tensile strength of a composite is given by another law of mixture relation which has been validated on many occasions 4 ' 5 ' 6 ' 7

a = O-Vr + a' (1-V^)> a (3) c f f m f u where: ac = ultimate tensile strength of the composite = ultimate tensile strength of the fibers o' = stress within the matrix when the ultimate m tensile strain of the fibers is reached ou = ultimate tensile strength of the matrix metal = volume fraction of fibers in the composite

It should be noted that equation (3) applies only for the condition that a > a . This is, after all, the c u impetus for the development of composite materials and therefore is a reasonable limitation. Furthermore, this condition defines a critical volume fraction, vcr;Lt' of fibers that must be exceeded if the composite is to be stronger than the matrix.

V - (°u - gm) (4) V orit - (c£ - >. This quantity is shown in Figure 3. V . , the volume fraction of fibers below which ItllLXl equation (3) does not apply, is determined from the condition that 9

Q Volume Fraction (Vf)

Figure 3— Theoretical Variation of Composite Strength with Volume Fraction of High-Strength, Brittle Fibers

i 10

This condition is required if the composite ultimately fails at the strain corresponding to the ultimate tensile strain of the fibers. Imposing condition (5) on equation (3) gives

Vrum . (6)

This quantity also is shown in Figure 3. From the above expressions for V .. and V . it should be noted that as ** crit mmin -i m r*i approaches a^/both volume fractions approach zero and the ultimate strength of the composite is given by equation (3) without limitations. This condition would only be realized for a brittle metal-matrix. Interesting analyses and discussions of composite materials produced from discontinuous rather than continuous fibers also are available3.' 8 Fiber reinforcement is accomplished mainly by a transfer of stress from the matrix phase to the fibers during deformation. In the purely elastic range, this transfer of stress is possible because of the greater elastic modulus of the fibers. At higher stress levels, where the matrix deforms plastically, additional stress is transferred to the fibers by the flow of metal adjacent to the fibers. Thus, an implicit assumption to fiber reinforcement strengthening is that continuity is maintained at the interfaces.between the constituents of a composite material. At low stress levels, an interface created by tight mechanical contact is often adequate to maintain continuity. However, at higher stress levels, a stronger interface created by a diffusion bond is undoubtedly required. 9 When consideration is given to the various methods for the experimental or commercial production of metal- 11 matrix composites, it is recognized that for most metal/ fiber combinations sufficient conditions of elevated temperature and pressure will be imposed to accomplish the required diffusion bonding. The problem then is to control or limit the extent of the diffusion reaction so that the composite will have a useful life during subsequent elevated temperature service. This is generally recognized'1' as one of the basic problems in composite materials. The solution is far from obvious and it is likely that metal/fiber compatibility will ultimately determine the service life of composite materials in much the same way that damage experienced during creep determines the service life of conventional high- temperature materials. Another problem area is that of defects incurred in fiber materials by present fiber manufacturing methods. These are often sufficient to result in composite proper­ ties which are less than anticipated. In work on titanium/boron composites, Metcalf'1'0 analyzed the importance of initial fiber quality and reaction-zone thickness in relation to room-temperature tensile test failures of composites. The most signifi­ cant result from this work was the observation that the fracture stress of boron fibers within the composite decreased exponentially from about 400 ksi to a limiting value of 150 ksi as the titanium boride layer thickness O increased in thickness from 100 0 to 5000 A. From the above discussion it should be clear that reaction-diffusion is a most important phenomenon with regard to the manufacture and subsequent performance of metal-matrix composites. Accordingly, the remainder of the literature review is devoted to the subject of reaction-diffusion. 12

B. Reaction-Diffusion in Binary Systems

A considerable volume of literature is available for review on both the experimental and phenomenological aspects of binary reaction-diffusion. No attempt will be made here to review this entire volume of literature; instead, the review will include several classical investigations and selected articles treating those aspects which are of greatest interest to the present research.

Experimental Observations From an early survey by Rhines^ on diffusion coating processes, it is evident that the original aware­ ness of the phenomenon referred to today as reaction- dif fusion arose from studies on "cementation11 processes. The latter term which is seldom used in present technology refers to a variety of diffusion coating processes such as carburizing, galvanizing, chromizing, etc. With regard to these processes, Rhines concluded that the layer structure formed in binary systems during diffusion at constant temperature and pressure correspond with their order of occurrence in the phase diagram. Single­ phase layers appear for each phase separating the initial constituents, and two-phase regions on the phase diagram are represented within the diffusing system as inter­ facial equilibria between the various layers. Rhines further concluded that regardless of the degree of complexity of the diffusing system, layer growth follows a parabolic law

x2 = kt (7) 13

where: x = layer thickness t = reaction time k = growth constant The influence of temperature on the rate of layer growth 12 is introduced by the Arrhenius equation

k = Ae“Q//RT (8) where: k = growth constant A = pre-exponential constant Q = activation energy R — gas constant T = absolute temperature Combining equations (7) and (8) and taking the logarithm of the new expression yields

ln £ - - - h + B- (9> Thus, data from a diffusion reaction which conforms to the parabolic growth law should yield a straight line when plotted as ln (x /t) versus 1/T. Rhines finally suggests the general applicability of equation (9) to layer growth kinetics in diffusing systems. 13 In 1942, Lustman and Mehl conducted the first comprehensive investigation of intermediate phase layer growth in binary systems. From studies on eight binary systems, it was found that layer growth conformed to the general exponential expression,

xn = kt (10) rather than to parabolic growth where n = 2. The latter case is derivable from Fick's first law of diffusion and would therefore be expected for diffusion-controlled reactions. Lustman and Mehl observed values of n which ranged from 1 to 10,and several possibilities were 14

offered as explanations for these unexpected results. First, combined interfacially-controiled and diffusion- controlled mass transport were considered but ruled out since this could apparently only account for values of n between 1 and 2. Rather reluctantly, it finally was proposed that phase transformations within the reaction- zone during diffusion might account for the spectrum of n values. This explanation was considered to be highly unorthodox since it implied the existence of non-equilibrium phases. Nearly simultaneous with the above observations of Lustman and Mehl, Darken 14 considered the phenomenon of diffusion in metals accompanied by internal precipi­ tation or subscale formation. In an introductory discussion to this subject,Darken warned against the unequivocal acceptance of the concept of local equilibri­ um. This concept assumes that equilibrium conditions exist at moving interfaces in diffusing systems, and that.the rate of diffusion through the system is slow compared with the rate of the reaction at interfaces. It is further stated that diffusion is a non-equil-ibrium process and that any reasoning with regard to diffusion which is based on phase equilibria should be approached with caution. Thus, under conditions where local equilibrium is not a valid assumption, the presence of non-equilibrium phases might be expected. As an extension of Darken's remarks, Kirkaldy 15 states that equilibrium interface concentrations in a dynamic . diffusing system are at best a good approximation. He reasons that under isothermal-isobaric conditions, deviations from equilibrium concentrations at moving interfaces constitute the only driving force available to accomplish phase boundary migration. In this 15-

16 connection, Braun and Powell measured phase boundary compositions in dynamic diffusion couples of the Au-In system; this system contains four intermediate phases. The measurements were made by extrapolating the results of electron microprobe analyses for a given phase into the observed inter-phase boundaries. The interface compositions differed from those given by the equilibrium phase diagram by several weight percent. Certain experimental difficulties associated with narrow reaction layers and the limiting spot size of the electron microprobe precluded the firm postulation of non­ equilibrium phase boundary compositions in this system. One of the most recent reports of non-equilibrium phase boundary compositions in dynamic diffusion couples is by Eifert et.al.17 Deviations from equilibrium compositions ranging from 0.8 to 1.8 weight percent were found in a (fee)/8(bcc) Al-Cu diffusion couples. Diffusion in this system requires a phase transformation at the interface, and because aluminum is the faster diffusing component, the a-phase (aluminum rich) is observed to transform to the 8-phase (copper rich). The departure from equilibrium concentrations at the interface during diffusion is taken to represent the supersaturation required to drive the a -»■ 8 transformation. It should be noted that phase boundary motion and reaction layer growth in the respective works of Eifert et.al. 17 and Braun and Powell 16 was parabolic. Thus, it would seem that deviations from equilibrium phase boundary compositions in binary diffusion couples are not a sufficient condition to account for or promote non-parabolic growth as originally suggested by Lustman and Mehl. 13 16,

18 Castleman and Seigle studied reaction-diffusion in the Al-Ni system. This system contains four inter­ mediate phases which are designated with increasing nickel content as 3/ y, 6 and e. The results of this investigation showed that at temperatures below 600°C and for sufficiently long reaction times, i.e., several hundred hours, all phases present in the phase diagram were observable in the reaction-zone. This result was contrary to that reported in prior work by Storchheim et.al. 19 who identified only the 3 and y phases in Al/Ni diffusion couples which were reacted for short times, i.e., several minutes, at 600°C. To these investigators, the absence of 6 and e-phases suggested that nucleation of all intermediate equilibrium phases within a duffusing system may not be instantaneous. Perhaps the most interesting result from Castleman and Seigle*s work was the non-parabolic growth of the y-phase observed during the early stages of reaction- zone growth in the temperature range 400° to 600°C. This was referred to as a transient period of growth and was manifested by curvature in logarithmic plots of layer thickness versus reaction time. Possible factors which may have contributed to this apparently ' anomolous result are suggested as follows: 1) delayed nucleation of all phases within the reaction-zone during the initial stages of reaction; 2) variable or non-equilibrium interface concentrations; and 3) variation of the diffusion coefficients during the initial stages of reaction as might be induced by structural changes in the nucleating phases. 17

The most recent investigation of reaction diffusion in the Ni-Al system was conducted in 196 7 by Janssen 20 and Rieck who determined the growth kinetics and diffusivities for the four intermediate phases. Growth of the 3-phase was studied in y/Al couples, growth of the y-phase was studied in

J 18

Phenomenological Theory Numerous investigators are responsible for develop­ ing the phenomenological theory of binary reaction- diffusion. Primarily, the mathematical expressions which constitute the theory are the result of problem 22 solving exercises which were initiated by Wagner. Wagner approached interface motion and reaction layer growth in binary diffusion couples as boundary value problems. As an example of his method, the problem of an intermediate phase growing between two terminal compositions, Figure 4, will be considered. The assumptions essential -to this problem are as follows: 1) the diffusion coefficient is independent of distance across the intermediate phase, i.e., not equal to a function of con­ centration; 2) local equilibrium is rapidly established and maintained at all interfaces during diffusion? 3) the terminal phases are initially saturated with respect to the intermediate phase; and 4) interface motion is proportional to the square root of time. Fick’s second law of diffusion, subject to certain boundary conditions, is obeyed for diffusion in the intermediate phase, i.e.,

(11)

(12) C6'-0 ~ CII,I

(13) Concentration Binary System where vThree InvolvedarePhases Figure 4— Concentration-Penetration Diagrams for Reaction-Diffusion ina for Reaction-Diffusion Concentration-PenetrationDiagrams 4— Figure Phases m + H Distance o Phases I + E + I C" *■ o c o c o o a> c c Phases + IE + I

hs E Phase Distance t > 0 Phases I + IE + I

20

In addition to the above, continuity relationships and velocity functions for the moving interfaces can be written as

(16)

(17)

Also, it can be shown that a,particular solution to equation (1 1 ) is

(18)

By substituting equations (16), (17) and (18) into equations (12), (13), (14) and (15) it can be shown that

(19)

Thus, from a knowledge of the reaction time, the equilibrium concentrations at the interfaces and experimentally determined values of 6 ' and 6 ", the average interdiffusion coefficient, D-j-j/ for the inter­ mediate phase can be calculated. Equation (19) was employed by Janssen and Rieck 20 in their work on the Al-Ni system. 23 In 1958, Castleman analyzed the problem of reaction-diffusion in a three-phase system where the terminal phases are semi-infinite in extent rather than 21 saturated with respect to the intermediate phase as was assumed in the above analysis; all other assumptions were identical to those listed above. This seemingly small change in boundary conditions complicated the problem tremendously. No attempt will be made here to present the extensive mathematical results and impli­ cations of this work. It is most important, however, to note that all possible combinations of interface motion may be examined in relation to the parameters which define the diffusing system, i.e.,

1 ) composition differences at the interfaces;

2 ) solubility range of the intermediate phase; 3) diffusion coefficients of the respective phases; and 4) rate constants for interface motion. Kidson, in 1961, re-examined reaction-diffusion in binary systems. Through an extension of methods first 25 devised by Heumann, Kidson was able to obtain an ex- th pression for the rate of growth of the j -layer in an n-phase system. The continuity relationships which may be formu­ lated from Fick's first law are.the essential parts of this derivation. The important assumptions with regard to each phase or layer are essentially the same as those made by Wagner except that the terminal phases are treated as semi-infinite in extent and the diffusion coefficients are not necessarily assumed to be constants.

For any interface, i.e., a/ 8 , in the diffusing system, a continuity relationship may be written. The notation used here is the same as that employed by Kidson.

(20)

X = (21) & which enables a change of variable, the following result may be obtained.

- (DK) 3a a3 (22) - >[• (C a3 “ C 6a) ] where: (23) »

In the above expressions, 6 D is the distance the inter- up face moved, t is the reaction time, D„ is the diffu- 3a sivity in the 3 -phase near the interface, is the diffusivity in the a-phase near the interface, is the equilibrium composition of a at the interface and

Co is the equilibrium composition of 3 at the interface, For the j t h -phase in an n-phase system,Kidson considers the possible motion of the bounding inter­ faces and arrives at *N Ji W x - £i (DK)j+u-(b)6jj.» Y d KI j-i - (DK)j-ul • J'I>J Cjjj-I (24) or W . = B . t' 3 3 . th where is the thickness of the j phase and B^ is the growth constant. 23

At this point, the various factors which control interface motion may be examined with regard to their influence on the rate of layer growth. Kidson concluded that the rate constant, B_j, must be positive and finite. Thus, the presence of all equilibrium phases is required although some may be so thin as to escape experimental detection. From equation (24) it is also clear that small composition differences between phases produce rapid interface motion and that relative interface motion establishes the layer thickness. A less exact form of equation (24) can be obtained by assuming constant diffusivities and a linear concen- 4-V\ tration gradient in the j -phase. One of the most recent and interesting approaches to reaction-diffusion is by Roy 26 who treats the problem of layer growth in a binary, metal-interstitial system. Like Kidson, the essential feature of Roy's approach was the application of Fick's first law of diffusion to moving interfaces. Proper materials balance at the interfaces is accounted for through the use of an idealized concentration-penetration diagram. From an initial knowledge of the phase diagram and experimentally- determined layer growth constants, the results provide a convenient method for calculating the average diffusivity for an intermediate phase. It should be pointed out, however, that this approach is subject to rather severe limitations as imposed by an initial set of assumptions. Thus far, all of the discussion pertaining to reaction-diffusion in binary systems has been limited to two boundary conditions where either the terminal phases are saturated with respect to the adjacent intermediate phases or the terminal phases are semi- 24 infinite in extent. No one has attempted to develop the phenomenological theory based on finite terminal phases. This is partly due to the fact that present mathematical methods do not enable closed-form solutions to the problem. Thus, numerical methods with computer assistance are required. A start in this direction was recently made by Tangilli and Heckel.27 They obtained numerical solutions for the two-phase, diffusion- controlled interface motion in finite couples. With this approach, it is not necessary to assume an initial velocity function for interface motion as has been done in all previous work. Without this restriction they show that interface motion is only parabolic so long as the terminal compositions remain semi-infinite..

C. Reaction Diffusion in Multicomponent Systems

The experimental and phenomenological aspects of reaction-diffusion in multicomponent systems are con­ siderably more complex than those for binary systems. As will be made apparent in the subsequent review, this additional complexity generally arises from a combination of the following factors:

1 ) interaction effects among the various diffusing species;

2 ) additional degrees of freedom as deduced from the phase rule; and 3) limited amount of accurate information on multicomponent phase equilibria. Regardless of the above, significant progress is being made on the subject of multicomponent diffusion. Furthermore, this progress'is certain to continue when it is realized that most commercially important alloy systems are multicomponent, and that the increasing 25 tendency to design products containing a variety of materials will certainly present increasing problems pertaining to materials compatibility.

Phenomenological Theory 28 In 19 45 Onsager proposed that the diffusional flux of a given component in a multicomponent aqueous electrolyte may be expressed by a linear combination of all concc. -ration gradients in the system, i.e.

n _ /dC,\ Ji = - D,ik\dST7 (x = 1 '2 '**-n) (25) where D* are intrinsic diffusion coefficients. Thus, th the diffusional flux of the i -component is influenced by concentration gradients other than its own. Both 29 30 Bardeen and Herring and Kirkaldy have extended Onsager*s original proposals. According to Kirkaldy,30 the number of independent concentrations in equation (25) may be reduced from the knowledge that

«— 7 C. = constant, (26) i = l 1 provided that the concentration, C^, is expressed in proper units. Substitution of equation (26) into (25) gives

. n - 1 /dcA = - g : where: D., = (D* - D*. ) (28) ik rk m 26

Combination of equation (27) with nonsteady state continuity relationships,

aj . a c . s r + atr - - (29) gives the generalized expression for Fick's second law of diffusion in multicomponent systems.

dC. n-1 , / dCv\

dt~ = 2 1 dx(^DiJc d~ J (l = i/2 /**-11) <3°)

The diffusivities in equation (30) may be thought of as interdiffusion coefficients. These coefficients consti- 2 tute a matrix with (n-1 ) terms where, as discussed by Guy et.al.^ for ternary solid solutions, the on- diagonal terms (D^) are values from the appropriate binaries and are always positive. For example, in a 3 three component system, would refer to the diffusivity in the 1-3 binary. The off-diagonal terms

(D^j, i 7^ k) express the intensity of diffusion inter­ actions within the system and accordingly may be either positive or negative. The above interpretations are not nearly as clear when one considers diffusion in a multicomponent system with intermediate phases in the n-component phase space, 32 Fujita and Gosting present a rigorous solution, of equation (30) for the case n = 3. They assume = C(X) where

X - (31) Thus, their solution for the implied semi-infinite boundary conditions is 27

ci = ci + *t 4 ( V ^ + x) + Ki Y) (32)

c 2 = C 2 + *( Y) + K~ { *) (33) where the a's are functions of the K's are functions of both and the initial concentrations of the components in the diffusion couple and

2 r v $ (q> = erf (q) = y f I e q dq (34)

Kirkaldy^ generalized the solution obtained by Fujita and Gosting by showing that the solution to equation (30) for an n-component system is a linear combination of error functions,

ci = aio + Sk=l a±k erf(rsnrV (35) where: n- 1 a.

= ^ {36) Thus, to obtain C.(x,t) in a single-phase couple subject 1 2 to semi-infinite boundary conditions, the (n-1 ) -(n-1 ) expressions for u, are combined with the 2 (n-1 ) 2 expressions for boundary conditions to obtain the (n-1 ) + (n-1) a-coefficients. An example for n=3 is given in Appendix A. From the above, the additional complexity introduced by cross-term interactions in multicomponent diffusing systems is evident. Whereas only one interdiffusion coefficient per phase is required in a binary system, four diffusion coefficients must be determined for each phase in a ternary system or even nine for a four component 28 system. Experimentally, this is not a simple task and as a consequence not many investigations have been conducted with this objective. Furthermore, from a practical point of view it seems apparent that the information gained is generally not worth the effort. 33 34 35 Kirkaldy ' ' has, however, shown one important scientific reason for the experimental determination of off-diagonal diffusion coefficients; they may be compared with values which are predicted on the basis of assumed thermodynamic models for solid solutions. In this way, the experimental determination of off- diagonal coefficients serves not only to test an assumed solid-solution model but also helps to bridge the gap between thermodynamics and kinetics. 36 Kirkaldy outlined a method which was subsequently applied by Dayonanda and Grace 37 to determine inter­ diffusion coefficients in Cu-Zn-Mn alloys. By intro­ ducing the new variable, X, of equation (31), equation (30) was reduced to the ordinary differential equation

(37)

Equation (37) may be integrated to obtain r*. (38)

. th where C . is the initial concentration of the i 3. component in one side of the diffusion couple. To determine the four D!^s in a ternary system, two diffusion couples must be prepared so that their diffusion paths intersect at the common concentration, C^. The areas under C^-X plots, i.e., the left side of 29 equation (38) , as well as the concentration gradients are graphically evaluated from this plot and the re­ sultant set of simultaneous equations is solved for the coefficients. This only provides information at one point within the ternary diagram, and a complete mapping of the would indeed be a formidable task.

The Phase Rule and Representation of Diffusion Paths The phase rule, upon which subsequent discussion in this section is based, is given as

F = C - P + 2 (39) where: F = thermodynamic degrees of freedom C = total number of components P = total number of phases

2 = temperature and pressure Since temperature and pressure are usually constant during diffusion experiments, equation (39) reduces to

F = C - P (40) Prior to applying the phase rule to multicomponent systems, its relationship to diffusion in binary systems (C=2) will be discussed. A single phase layer in a binary couple has one degree of freedom (independent variable) which is manifested by a concentration gradient across that phase. Two phase equilibria in two-component systems have no degrees of freedom; provided that the diffusion process is unidimensional|this stipulates the existence of a planar interface between the phases. Structural anisotropy and the presence of defect structure can, however, transform a unidimensional diffusion process into a three dimensional process thereby stabilizing slight irregularities along an advancing interface. 30

The restraint on structural morphology and composition in the reaction-zone of binary couples is relaxed considerably by the-addition of one more com­ ponent to the system. To demonstrate this point the phase rule will be discussed in a manner similar to that presented by Clark and Rhines 3 8 for one, two and three phase equilibria in ternary diffusion couples. Two degrees of freedom exist in ternary, single­ phase layers; this implies that two concentrations may vary independently during diffusion. Thus, the diffusion path is not restricted to a straight line in the ternary isotherm. The single degree of freedom which exists in ternary, two-phase equilibria presents the possibility of a two- phase layer rather than the separation of phases by a simple planar interface as would be observed in a binary system. The single degree of freedom means that the concentration of one component is free to vary which is only possible by a change in the relative proportions of the phases participating in the equilibrium. It is sometimes noted that two-phase, ternary equilibria relinquish their one degree of freedom. In this case, the phases are in equilibrium along a tie line and are separated in the reaction-zone by a planar interface. Three-phase equilibria in ternary systems have no degrees of freedom and consequently must be separated in the reaction-zone by a planar interface. 34 . . Kirkaldy has stated seventeen theorems pertaining to the representation of diffusion paths in ternary systems. It should be noted that diffusion path constructions on equilibrium isotherms are commonly used to represent ternary diffusion data. Such con- 31 ' structions, however, provide no information about the reaction-diffusion kinetics. The significant char­ acteristics of ternary diffusion paths may be briefly summarized from the theorems proposed by Kirkaldy: According to Theorem I, diffusion paths are time in­ variant, and as a consequence of mass balance criteria (Theorems IV, V and VI) a path must either be a straight line connecting the terminal compositions of the couple or must intersect this line at least once. The latter 39 conclusion is due to Meijering. Theorem VII states that S-shaped diffusion paths are generally expected in single-phase fields and that this results from the fact that different species have different mobilities in a given phase. Theorems XIII, XIV and XV allow that the diffusion path in two-phase regions may be either a curved or a straight line, while Theorem XVII states that paths connecting three-phase equilibria must be a straight line across a three-phase triangle. In summary, it should be noted that the diffusion path for a given couple is determined mainly by the mobilities of the various species while the phase diagram essentially serves to provide the framework for the path.

Experimental Observations Perhaps the most extensive experimental investi­ gation of reaction diffusion in ternary systems was conducted by Clark and Rhines.38 They studied the sequence of layer structure which developed at 335°C in the reaction-zone of Al-Mg-Zn diffusion couples. The terminal phases were pure A1 and a series of Mg-Zn binary alloys. The results of this study were in fact the main basis for the seventeen theorems proposed by 32-

Kirkaldy. Parabolic growth of the reaction-zones was noted in all of the Al-Mg-Zn couples. Numerous other investigations pertaining to the determination of both intrinsic and interdiffusion coefficients in ternary solid solutions also have been conducted. Reference was made to several such investigations in the previous section which dealt with the phenomenological theory of multicomponent diffusion. Little or no experimental work has been done on systems containing more than three components. III. REACTION-DIFFUSION IN A BINARY METAL- NONMETAL SYSTEM

The current interest which is being shown in the literature for reaction-diffusion has arisen mainly out of concern for materials compatibility problems; Some of the more common problems of this type are experienced in the nuclear industry, during the fabrication of solid-state electronic devices and, as previously discussed, in present efforts to develop fiber-reinforced, metal-matrix composite materials. As indicated from a survey of the literature, the phenomenological approaches to reaction-diffusion problems by most previous investigators may be placed into one of two catagories depending on the conditions stipulated for the terminal compositions of the diffusion couple. These conditions are as follows:

1 ) terminal phases are semi-infinite in . .22,23,24 extent ' • '

2 ) terminal phases are saturated with 22 26 respect to adjacent intermediate phases ' Most previous investigators also have assumed an initial velocity function expressing parabolic inter­ face motion during reaction-diffusion, i.e.,

x^ = kt (41) where: x = reaction layer thickness k = layer growth constant t = reaction time

33 34

The assumption of parabolic growth is logical first because it is so often observed experimentally, and second because, at least in its simplest form, it is directly derivable from Fick's first law of diffusion. In accordance with the above assumptions, the basic 23 24 objective of previous phenomenological treatments ' of binary reaction-diffusion has been to obtain expressions which relate the equilibrium phase boundary concentrations, the diffusivities, and the parabolic growth constants. Thus, from the experimental measurement of reaction-zone growth constants, the mean diffusivities for intermediate phases may be calculated provided that the phase equilibria are known. The present investigation also constitutes a phenomenological treatment of a reaction-diffusion problem. However, rather than initially assuming a velocity function for interface motion, it was the objective of the present work to Calculate the actual dependence of reaction layer thickness on time. The terminal phases of the diffusing systems are considered to be finite in extent and therefore are not restricted in the degree to which they are saturated with respect to adjacent phases. Experimental data which were employed to test .this new analysis were taken from recent work by Vansant and Phelps^® on reaction-diffusion in the Ti-C system.

A. Problem Statement and Assumptions

The analysis to be developed is based on the integration of continuity relationships which may be formulated at an advancing interface from Fick's first law. This method is an extension of that which was 41 originally employed by Fromm and more recently by Roy.26 The binary system being considered is limited to a single intermediate phase, thus, isothermal reaction- diffusion of the terminal phases should produce a . uniform layer of the intermediate phase. The important assumptions necessary for this analysis are as follows:

1 ) the growth of the intermediate phase (MN) occurs only by the advance of the interface adjacent to the metal (M). Accordingly, the nonmetal (N) must diffuse much more rapidly in the intermediate phase than the metal;

2 ) the concentration gradient in the inter­ mediate phase is assumed to be independent of distance, thus,the concentration profile is assumed to be linear for specimens of slab geometry; 3) the diffusion coefficients for the non- metal are assumed to be independent of concentration; 4) local equilibrium is instantaneously established and maintained at all inter­ faces; and

5 ) the nonmetal diffuses interstitially in the metal. Although the above set of assumptions may seem somewhat restrictive, they have been shown to be valid in previous investigations of reaction-diffusion 42 43 44 involving the formation of carbides ' and silicides. ' It should be noted that assumptions 2 and 3 constitute an assumption of quasi-steady state, i.e., the flux is independent of distance. *

36 '

B. Mathematical Formulation

A schematic representation of the diffusion problem with the associated phase diagram is shown in Figure 5.

Case I; Metal Initially Saturated with Nonmetal The reaction-diffusion kinetics for the case where the metal is initially saturated with the nonmetal is formulated first. This is done merely for the sake of subsequent comparison with the more general case where the metal is treated as an unsaturated, finite phase (Case XI). As noted in Figure 5, the range of composition for the MN reaction layer at the temperature, TR , is given by while the constant K 2 represents the concentration difference at the MN/M interface. All concentrations are expressed in g/cm? Since the metal side of the diffusion couple is initially saturated with respect to the nonmetal, only nonmetal diffusion through the intermediate phase is involved in the process of layer growth. In an incre­ ment of time, dt, the MN/N interface advances by an increment, dX^. This requires the accumulation in the reaction layer of an amount, A, of nonmetal which is shown in Figure 5 as an increase in the area of the concentration-penetration plot.

A = l/2K1 dX1 + K 2 dX 1 (42) The accumulation of nonmetal also can be expressed in a continuity relation from Fick's first law,

A = 1/2K-dX. + K-dX. = J. dt (43) 1 1 2 1 in

0 ro Nonmetal Concentration (G /C M the Phase Diagram for Reaction-Diffusion inSystem forBinary a Metal-Nonmetal thePhaseReaction-Diffusion Diagram X(CM) Figure 5— Relationship between the Concentration-Penetration Diagram Diagram and the Concentration-Penetration between Relationship Figure5— MN M+

-j u> 38 • where J. represents the flux of nonmetal into the m reaction layer at x = 0. In accordance with the initial assumptions, can be written as

,m n /k iN (44) in \l lx l, MN where is the average diffusion coefficient of the N nonmetal in the intermediate phase. Substitution of equation (44) into equation (43) gives .

I/2 V * ! + *2-3*! = C @ dt <4 5 > Equation (45) can be integrated to yield

2 K N 1 x, ° L N-,~ (46) or

= kt (47)

Equation (4 6 ) is an approximate formulation of the parabolic growth law where it is obvious that the growth constant, k, includes information from the equilibrium phase diagram as well as the diffusion MM coefficient, . Thus, the growth constant can be obtained from experimental measurements of X- and t MN which further enables the calculation of DN .

Case II: Metal Initially Not Saturated with Nonmetal The differential equation for reaction layer growth when the metal is finite in extent and not saturated with the nonmetal may be written as

A = 1 / a K ^ + K 2 dX 1 = (Jin - J o u t) dt (48) 39 . where JQUt represents the flux of nonmetal out of the reaction layer into the metal. This is given by

j - _d m (49) out [fix) Q

The concentration gradient evaluated at x = 0 may be obtained from the solution to Fick’s second law subject to certain boundary conditions:

< x < L; t > 0 (50)

C(0 ,t) C 2 t > 0

C (x#0) " C3 0 < x < L

( ^ L . t = ° The solution to this boundary value problem for the metal side of the diffusion couple is given as sin fen-lTiTX 2L (51)

The required concentration gradient may be evaluated from equation (51) to give

(Sir ^5 (52) It should be noted that equation (52) is true provided that X^<

Unlike the problem in Case I, Case II does not lend itself to a closed form solution. Accordingly, numerical methods must be employed to obtain a solution. To do so, equation (53) is rewritten in finite difference form as

MN M — fit X1AX1 " W1DN - W2DNX1 2_,e (54) n=i where W^, W^ and 8 are collected constants. Depending on the information available, equation (5 4) may be employed in one of two ways. First, if and are known, the reaction time required to produce a layer of assumed thickness may be calculated. Second, if only one of the diffusion coefficients is known and experimental measurements of and t are available, the unknown diffusion coefficient may be calculated. This is, in fact, the approach that was taken to test the validity of equation (54). Reaction-diffusion data for the Ti/C system, 40 Table 1, are available from Vansant and Phelps and Ti the diffusion coefficient for carbon in titanium, D , 46 is available from Wagner, et.al. The required phase boundary compositions for the Ti-C system were obtained from references (47) and (48). Accordingly, values of DcTiC were determined and compared with the values reported by Vansant and Phelps. TlC Table 1 - Comparison of Numerically Computed Values of with the Values Obtained

by Vansant and Phelps1*0

D ^ C (cm2/hr) Couple Reaction Conditions Tie Layer

Number Temp.(°C) Time(hrs) Thickness x 104 (cm) Ref.40(a) From Eq.(54)

1 1090 4 1 . 0 4.14 x 10~ 8 2.74 x 10“ 8 mim 2 1288 2 12.7 4.52 x 10 ' 1.19 x 10 0

3 1288 4 18.0 7.52 x 10~ 7 8.15 x 10“ 7

4 1288 . 4 15.4 7.52 x 10” 7 6.08 x 1 0 “ 7

5 1288 4 1 0 . 2 7.52 x 10~ 7 2.74 x 10^ 7

6 1288 8 26.4 7.52 x 10" 7 7.27 x 10" 7

.7 1305 ' 8 . 29.5 9.33 x 10~ 7 8.89 x 10“ 7 - 6 - 6 8 1488 1 24.9 7.28 x 10 0 7.63 x 10 0

9 1488 2 37.6 7.28 x 10" 6 6.49 x 10“ 6

1 0 1488 2 37.0 7.28 x 10" 6 6.28 x 1 0 " 6

1 1 1488 2 28.2 7.28 x 10" 6 3.69 x 10~ 6

1 2 1488 4 61.5 7.28 x 10“ 6 7.56 x 10” 6

13 1488 8 85.0 7.28 x 10~ 6 6.75 x 10" 6

14 1488 1 0 89.2 7.28 x 10“ 6 5.86 x 10~ 6

15 1505 4 6 8 . 6 8.62 x 1 0 “ 6 9.35 x 10" 6

16 1505 4 60.5 8.62 x 1 0 ~ 6 7.29 x 10" 6 TiC •> (a) calculated from Dc = 360 exp (-62,000/RT) cm2/hr 42 •

A computer program, Appendix B, was written for the IBM 7094 computer which assisted in the numerical Tic determination of values of Dc . The essential steps in the computational method were as follows; 1) a given data set (X^, t, T) was matched through equation (54) with an assumed value of diffusivity,

2 ) values of X^ were generated toward the origin

of time, t = 0 , and the compatibility of the match was judged by the extent to

which X^ deviated from zero when t = 0 . 1 0 hours; 3) this process was repeated for an array of diffusivities thereby locating the most TiC compatible value of Dc to four significant digits; 4) the best value of D T i C was subsequently used v to generate reaction layer growth data

for times ranging from 0 . 1 0 to 1 0 0 hours; and 5) the next data.set was selected and the above process repeated. Values of DcT i C which were obtained in this manner were found to be insensitive to time increments, At, in the range 0 . 0 1 to 0 . 1 0 hours. It should also be noted that the mathematical singularity in equation (54) at X^ = 0, t = 0 precluded the possibility of any numerical computation starting with this most obvious data point.

C. Results and Discussion

The diffusion coefficients obtained by Vansant and Phelps are compared in Table 1 with the values obtained 43 by the present method. It should be noted that Vansant and Phelps used Wagner's 22 method for the determination of diffusion coefficients. An Arrhenius plot of these data is shown in Figure 6 . The expression for the TiC temperature dependence of Dc obtained by Vansant and Phelps is

Tic ? = 360 exp (-62,000/RT) cirT/hr , (55) while that calculated by a least-squares analysis of the numerically-determined values is

DC lC = 3 1 6 exp (-62/°°°/RT) cm2/hr (56) The data point shown at 1090°C was not used in either of the least-squares analyses. The excellent agreement between the separate approaches, Figure 6 , confirms the validity of the numerical method according to equation (54) for finite diffusion couples. Also, the close agreement indicates that the titanium sides of the diffusion couples were rapidly saturated with carbon during diffusion. Had this not been the case, Vansant and Phelps might have TiC obtained incorrect values of Dc Figure 7 illustrates the growth of a titanium carbide layer by Ti/C reaction-diffusion at 1288°C. The data obtained by Vansant and Phelps as well as that which was generated by the present numerical method from an experimental data point (X^ = 18.0-microns, t = 4.0-hours) are represented in this figure. Deviation from parabolic growth for reaction times less than 2 0 hours is evident, and it should be noted that several of the experimentally-determined data points lie quite close to the computed non-parabolic line. aus acltd rmEuto (54) Equation from Calculated Values fD Otie yVnat n hls ih the with Phelps and Vansant by Obtained x D of ( ( CM / HR) 10 10 Figure Figure “ -5 -7 “ .0 0.55 0.50 i 1600 6 — Arrhenius Plot Comparing the Values the Comparing Plot Arrhenius — eprtr “ x 0 (K ') (°K )“* 10° x Temperature ( hs Investigation This asn ad helps40 P and Vansant eprtr (°C) Temperature 1400 . 0 0.6 = 000 0 ,0 2 =Q 6 CAL/ MOLE CAL/ 0.65 1200

.0 0.75 0.70

44

TiC Layer Thickness ( Microns) 0 0 1 60 30 Carbide Reaction Layer as Numerically Computed from Computed Numerically as Layer Reaction Carbide qain (54) Equation Tm (Hours) Time 1 eeec LineN Reference Growth Parabolic Figure 7--Non-Parabolic Growth of the Titanium the of Growth 7--Non-Parabolic Figure Vnat n Phelps40 P and Vansant O Nmrcl Solution Numerical © 3

6 trig on For Point Starting h Nmrcl Solution Numerical The 060 30

45 010 0 1

46 ’

Vansant and Phelps probably did not notice the non-parabolic tendency in their short time data since, inorder to obtain reaction layer growth constants for titanium carbide, they plotted versus t 1/2' . At the TiC/Ti interface, two reactions probably compete for the available carbon. First, carbon is converted to titanium carbide by the reaction

Ti + C = TiC , (57) and second, there is a tendency for the titanium side of the diffusion couple to become saturated with carbon by the dissolution reaction

0

TiC - Ti + C . (58)

Since reaction (58) would continue until the titanium is saturated with carbon, it would be expected that Ti/C diffusion couples with more massive (thicker) titanium sides would display even greater deviations from para­ bolic growth. Also, the use of titanium containing an initially lower carbon content would enhance non­ parabolic growth in finite couples. The parabolic growth reference line in Figure 7 was calculated from equation (46) and clearly becomes the limiting law for layer growth as the metal side of the diffusion couple approaches carbon saturation. The computed layer growth data in Figure 7 suggest the same type of deviation from parabolic growth as 18 2 0 was noted in previous reaction-diffusion studies ' on the Al-Ni system. To illustrate this, some of the 18 experimental data obtained by Castleman and Seigle for the y-phase are shown in Figure 8. The y-phase was adjacent to the nickel side of the diffusion couples, _J o o> -24 X t Layer Thickness - - - - 3.6 3.2 2.0 0.8 2.8 1.6

s e l p u o C n o i s u f f i D l A / i N n i e s a h P - y eeec Ln \ Line Reference aaoi Growth Parabolic e h t f o h t w o r G c i l o b a r a P - n o N d e v r e s b O y l l a t n e m i r e p x E — 8 e r u g i F . 1 .6 1.8 2.0 2.2 2.4 2.6 2.6 2.4 2.2 2.0 1.8 1.6

o Time Log ZQ . 32 . 36 . 4.01.2 3.8 3.6 3.4 3.2 3.0 1.4 550 °C 550 500°C

i IV. REAC TION—DIFFUSION IN THE MULTICOMPONENT SYSTEMS Ti/SiC AND Ti-6Al-4V/SiC

Because of the current interest in metal-matrix, fiber-reinforced composite materials and the likelihood that matrix/fiber incompatibility may ultimately limit the service life of these new materials, it is important that research should be conducted on the problem. Although matrix/fiber interaction at elevated temper­ atures is certainly recognized as a problem by those concerned with composite materials, very little effort has been expended to investigate it. The objective of the present research is to investigate reaction- diffusion in the Ti/SiC and Ti-6Al-4V/SiC systems. Both systems offer considerable potential as advanced composite materials which may be capable of service at elevated temperatures.

A. Experimental Procedure

The experimental procedure to be discussed in this section pertains to the multicomponent reaction-diffusion studies which were conducted on the Ti/SiC and Ti-6Al-4V/SiC systems. It includes a description of the initial materials, a presentation of the methods used to prepare the diffusion couples and alloys and a description of the various methods which were employed for the purpose of examination.

49 50

Materials The materials which were used to prepare the diffusion couples are listed in Table 2. The silicon carbide pellets (1/4-inch in diameter by 3/8-inch in length) were a high-density, hot-pressed product which was obtained from the Carborundum Company. As may be noted in Table 2, the pellets contained excess silicon (8.32 weight percent) which was present as a second phase in the microstructure, Figure 9A. Prior to the preparation of any diffusion couples, the as-received pellets were further purified by vacuum annealing for 4-hours at 1350°C. No visible change in microstructure resulted from this heat treatment. Although the pellets may not seem to be the most desirable starting material, it was the best that could be obtained in a shape from which diffusion couples could be conveniently prepared. As will be shown in subsequent discussions, the initial duplex structure of the silicon carbide pellets apparently had no effect on the experimental results of this research. The unalloyed titanium and the Ti-6A1-4V alloy were obtained in the mill-annealed condition from Reactive Metals, Inc. Microstructures of these materi­ als are shown in Figures 9B' and 9C. The Ti-6A1-4V alloy is an alpha-beta alloy where beta is the darker etching phase.

Diffusion Couple Preparation As shown schematically in Figure 10, a diffusion couple was prepared by a pressure-bonding technique which relies on differential-thermal expansion to generate the bonding pressure.49 The vessel, which was Table 2 - Chemical Analyses of the Materials for Diffusion Couples

Materials Nominal Composition,wt.% Purity,W/0 Fe Si Si02 Al V C N 0

Silicon Carbide 87.32 0.30 8.32 1.35 0.20 — 0.89 — — — ~

Titanium 99.0 0.32 0.02 0.01 0.13

Ti-6A1-4V — 0.32 6.2 4.1 0.03 0.01 0.13

(a) two-phase structure consisting of silicon carbide and silicon A

Figure 9— Microstructures of Initial Materials (250X) 53

AUO

SiC

AUO

Figure 10— Schematic Diagram Illustrating the Molybdenum Bonding Vessel Assembly

I

J 54 made of molybdenum, has a lower coefficient of thermal expansion than the central column of materials contained within it. Thus, a pressure is generated on the central column as the assembly is heated to the reaction temperature. The probable pressure produced by this device was not greater than the yield strength of titanium (approximately 2000 psi at 1200°C). Prior to assembly, the mating surfaces of the titanium and silicon carbide were given a fine metallographic polish. The sample holder, Figure 11, and technique shown in Figure 12 were employed to maintain flat surfaces during this preparation. The thickness of the titanium side of all diffusion couples was 0.150-inch. All other mating surfaces in the central column were coated with a methyl alcohol-magnesium oxide slurry; this served as a parting agent and thereby prevented inadvertent reactions or bonding between the various other materials which were in contact under pressure. It should be noted that the entire diffusion anneal was conducted in the bonding vessel. Several diffusion couples were prepared with 0.05-micron aluminum oxide powder markers at the original interface. The markers were deposited on the original interface by dipping the polished titanium surface into a methyl alcohol-aluminum oxide powder slurry. The furnace facility in which the diffusion anneals were conducted is shown in Figure 13. The furnace on the left has a maximum temperature capability of 1300°C and was used for the diffusion anneals while the furnace on the right was used only for the purpose of gas purification. The procedure for conducting a given diffusion anneal was as follows: 55

SAMPLE

Figure 11— Specimen Holder for Polishing the' Mating Diffusion Couple Surfaces 56.

Figure 12— Technique for Polishing the Mating Diffusion Couple Surfaces Figure 13— Furnace Facility for Accomplishing Diffusion Anneals The assembled bonding vessel was placed in the front part of the diffusion furnace where the temperature never exceeded 300°C. The system then was sealed and continuously evacuated to a pressure of about 5 x 10 ^mm Hg as the hot zone of the furnace was heated to the reaction temperature. When the temperature was stabilized, the system was returned to atmospheric pressure under highly-purified argon which flowed continuously through the system during the diffusion anneal. The argon was purified by passage over a strong dessicant, magnesium perchlorate, and finally through the purification furnace which was loaded with titanium turnings and maintained at a temperature of 6 00°C. The latter treatment removed any residual oxygen, nitrogen or hydrocarbons. Next, the assembled bonding vessel was transferred by means of a push-rod fitted through a "Swagelok" seal from the front of the furnace to the hot zone. Time zero for the diffusion anneal was recorded when the temperature of the hot zone was again stabilized; this usually required about 15 minutes. At the conclusion of an anneal, the bonding vessel was withdrawn from the hot zone to a water cooled region in the front of the furnace. In this way the vessel was cooled from the reaction temperature (1000°C - 1200°C) to near ambient temperature in about 15-minutes. During subsequent disassembly of the bonding vessel, the silicon carbide and titanium halves of the diffusion couples invariably separated along a plane through the reaction-zone on the SiC side of the couple. A total of 40 diffusion couples was prepared by the above method; 23 were of the Ti/SiC type and 17 were of the Ti—6Al-4V/SiC type. 59 -

Alloy Preparation Six alloys in the Ti-Si-C system were prepared by powder metallurgical methods to serve as standards for phase identification within the reaction-zones of the diffusion couples. The alloy compositions which were selected are listed in Table 7. The alloys were prepared by blending powder mix­ tures of titanium (325-mesh) and silicon carbide (6 00-mesh). After blending, each powder mixture was pressed at 20,000 psi into a pellet (3/8-inch in diameter by 1/2-inch in length). The pellets were subsequently loaded into a graphite crucible and vacuum sintered for 4-hours at 1500°C. All alloys were finally equilibrated at 1200°C for a period of 8-hours.

X-Ray Analysis X-ray diffraction analyses were conducted on the exposed surfaces (through the reaction zone) of selected Ti/SiC and Ti-6Al-4V/SiC diffusion couples and on the Ti-SiC alloys. This was done by mounting a particular half of a diffusion couple or a polished and etched section of an alloy in a lucite holder and subjecting it to diffraction with a General Electric XRD-5 diffractometer. Copper radiation with a nickel filter was used to obtain the diffraction patterns. The 50 ASTM X-Ray Data File was used as the main reference for phase identification.

Metallography X-ray analyses and metallographic examinations which were conducted on several preliminary Ti/SiC and Ti-6Al-4V/SiC diffusion couples revealed that the reaction-zones were completely confined (except for 60 fragments) to the titanium sides of the couples. Consequently, all subsequent metallographic studies were limited to the titanium sides. To provide mechanical support during grinding and polishing, the titanium side of each diffusion couple 51 was nxckel-plated by using a standard Watts plating bath. After plating, the titanium was mounted in bakelite and sectioned to approximately mid-diameter along a plane parallel to the direction of diffusion. The alloy pellets were prepared for metallographic examination by mounting in bakelite and sectioning along a plane transverse to their length. Standard metallographic practices for titanium were employed to expose the respective microstructures of the alloys and the reaction-zones in the diffusion couples. This involved grinding through 600-grit paper, polishing with 5-micron diamond paste followed by 0.05-micron alumina, and finally etching with 92H20-5HN03-3HF (by volume). Reaction layer thickness measurements were made• from Polaroid photomicrographs which were taken at a t calibrated magnification of 840X. A series of four typical photomicrographs which traversed approximately 10 percent of the total reaction-zone length was employed to determine the mean .reaction-zone thickness; the mean value was calculated from approximately 25 thickness measurements on the photomicrographs.

Electron-Microprobe Analyses Electron microprobe analyses were performed on the Ti-SiC alloys and on the reaction-zones of selected Ti/SiC and Ti-6Al-4V/SiC diffusion couples. The "multiplex1’ mode of recording in conjunction with a 61 2 microns/minute specimen traverse rate was employed for all analyses. By this method, the specimen current and x-ray intensities of up to three elements could be recorded simultaneously. The traverses were started approximately 25-microns away from the reaction-zone and proceeded from the titanium matrix through the reaction-zone and into the nickel plating. Pure samples of those elements involved in the analyses (Ti, Si, V and Al) were used as analytical standards and all analyses were corrected for x-ray absorption according to a reiterative procedure developed 52 by Adler and Goldstein. This procedure is generally applicable to multicomponent systems and the accuracy of the correction is mainly limited by the accuracy and availability of mass absorption coefficients. The mass absorption coefficients recently reported by Smith 53 were employed in the present work. The computer program given in Appendix C was written to facilitate the required multicomponent absorption corrections. It should be noted that the carbon analyses reported herein were calculated by difference on the basis of absorption-corrected analyses for all other elements present.

B. Results and Discussion

The results of this research will be discussed by initially presenting the reaction-diffusion kinetics for both the Ti/SiC and Ti-6Al-4V/SiC systems. This is followed by the experimental results from x-ray ** analyses, metallographic studies, and electron-micro- probe analyses. Finally, diffusion paths are proposed for the Ti/SiC system. 62 -

Reaction-Diffusion Kinetics The reaction conditions and reaction-zone thickness measurements for the Ti/SiC and Ti-6Al-4V/SiC systems are summarized in Tables 3 and 4, respectively. In both systems, the reaction kinetics were determined for temperatures of 1200°, 1100° and 1000°C. Also, titanium with two different carbon levels (commercially- pure and carbon-saturated) was employed to determine the effect of initial carbon content on the Ti/SiC reaction kinetics at 1200°C. The carbon-saturated titanium was prepared by carburizing a 1/4-inch diameter titanium rod in a graphite pack for 24 hours at 1200°C. Metallographic examination of the rod after carburization and slow cooling showed a uniform surface-to-center precipitate of titanium carbide thereby confirming that saturation was achieved. The reaction kinetics for the Ti/SiC system are presented in Figure 14. The most significant obser­ vations are (1) the two stages of parabolic growth at each temperature for the commercially-pure (CP) titanium couples and (2) the appreciably higher parabolic growth rate at 1200°C in the carbon-saturated (CS) titanium couples. Stage I growth is described by the customary parabolic growth law

(59) while Stage II growth is described by

x = kt1^2 + b (60) where k is the reaction-zone growth constant and b is simply an arbitrary constant. Because parabolic growth was observed in all' instances, it is concluded Table 3 - Summary of Reaction-Diffusion in the Ti/SiC System

Couple Type of ^ Reaction Conditions Reaction-Zone Thicknessfju\ Number Titanium Temperature(°C) Time(hrs) Mean Standard Value Deviation 1 CP 1200 1.0 7.1 1.1 2 CS 1200 1.0 11.8 1.8 3 CP 1200 1.5 8.7 1.1 4 CP 1200 2.5 10.6 1.2 5 CP 1200 4.0 10.4 1.9 6 CS 1200 4.0 18.1 1.5 7 CP 1200 12.0 13.6 1.7 8 CS 1200 12.0 28.5 2.6 9 CP 1200 48.0 23.1 2.5 10 CP 1200 75.0 26.8 2.1 11 CP 1175 ‘ 4.0 10.6 1.3 12 CP 1100 1.0 4.6 0.8 13 CP 1100 4.0 8.8 1.1 14 CP 1100 8.0 9.4 0.9 15 CP 1100 12.0 10.7 1.2 16 CP 1100 36.0 15.6 0.9 17 CP 1100 68.0 22.1 3.1 18 CP 1000 4.0 4.4 1.1 19 CP 1000 24.5 10.2 0.8 20 CP 1000 36.0 11.9 1.1 21 CP 1000 50.0 13.6 1.6 22 CP 1000 72.0 ' 15.1 2.3 (a) CP = commercially-pure titanium containing 0.02 weight percent carbon CS = carbon-saturated titanium containing 0.19 weight percent carbon Table 4 - Summary of Reaction-Diffusion in the Ti-6Al-4V/SiC System

Reaction-Zone Thickness Jtl Couple Reaction Conditions Mean Standard Number Temperature(°C) Time(hrs) Value Deviation

1A 1200 4.0 12.6 1.4 2A 1200 10.4 21.3 3.1 3A 1200 24.0 22.4 2.1 4A 1200 48.0 30.1 2.4 5A 1200 74.0 38.7 3.3 6A 1100 - 5.0 7.5 1.0 7A 1100 12.5 9.8 1.2 8A 1100 26.5 15.2 1.5 9A 1100 46.5 15.3 1.8 10A 1100 74.0 18.1 1.9 11A 1100 96.0 • 20.8 2.5 12A 1000 16.0 5.7 0.8 13A 1000 32.0 6.9 1.1 14a 1000 64.0 10.0 1.7 ISA 1000 96.0 10.5 1.6 16A 1000 142.0 12.2 1.4 Mean Reaction - Zone Thickness I Microns ) 25 20 30 Ti/SiC Diffusion Couples Diffusion Ti/SiC a»— Figure 14— Reaction-Zone Growth Kinetics for the for Kinetics Growth Reaction-Zone 14— Figure 2 54 3 \/Time ( Hours) 2 Hours) ( \/Time i SiC Ti /S a bn - auae Titanium CarbonSaturated - omrily- ue Titanium PureCommercially - 6 7 IOOO°C 8 65 9

10

66 that the processes of reaction-zone growth are diffusion- controlled. The transitions from the Stage I to the Stage II reaction kinetics in the CP titanium couples are indicative of changes in the microstructural se­ quence of phases within the reaction-zones during diffusion. It should be noted that the transition at 1000°C is clearly a continuous process, while at ■ 1100° and 1200°C, discrete periods of time were associat­ ed with the transitions. From the la limits of un­ certainty in the reaction-layer thickness measurements, Figure 14, it can only be concluded that no change in the reaction layer thickness occurred during the transi­ tion periods. However, as indicated by the dashed- lines, it is interesting to speculate that the transition at 1100°C and 1200°C also may have been continuous pro­ cesses. Phenomenologically, the dashed-line transitions imply competition between simultaneous processes of reaction-zone dissolution and growth. Further consider­ ation will be given to the exact mode of the transition in a later section where the microstructural aspects of the reaction-zones are discussed. The reaction-zone growth constants which were obtained by least squares analyses of the data shown in Figure 14 are listed in Table 5. "Apparent activation energies" for the diffusion processes which correspond to the two stages of reaction-zone growth were determined from Arrhenius plots, Figure 15. Data obtained by Ashdown54 on the Ti/SiC system are included in this figure, and, as may be seen, these data are in excellent agreement with the Stage I reaction kinetics obtained from the present research. Ashdown studied the com­ patibility of 4-mil-diameter, silicon carbide filaments in commercially-pure titanium over the temperature range Table 5 - Reaction-Zone Growth Constants for the Ti/SiC and Ti-6Al-4V/SiC Systems

1/2 Reaction Growth Constant(p/hr ) System Temperature(°C) Stage I Stage II

Ti/SiC 1200 6.7 2.6

Ti/SiC 1200 — 6.8

Ti-6Al-4V/SiC 1200 6.9 4.3

Ti/SiC 1175 5.3 —

Ti/SiC 1100 4.4 2.1

Ti-6Al-4V/SiC 1100 3.1 1.8

Ti/SiC 1000 2.1 1.4

Ti-6Al-4V/SiC . 1000 1.3 0.8

carbon; all other diffusion couples were prepared from commercially-pure titanium 68

Temperature (°C) 1200 1100 1000 900 800 10.0

Ti / SiC _I2L SZ s Stage I Q = 3 6 ,2 0 0 CAL/ MOLE ISi c a to c o Stage H o Q = 23,400 CAL/M0LE 1.0 p <5 a> c 0 NJ This Investigation 54 1 Ashdown c o o a CD a:

0.1 _ 6.5 70 7.5 8.0 8.5 9.0 9.5 10.0 (Temperature)-1* I03(°K"1)

Figure 15— Arrhenius Plots for the Stages I and II Reactions in the Ti/SiC System 69

650° to 1050°C. The silicon carbide filaments were prepared by chemical-vapor deposition and were pre­ sumably a single-phase material (except for a tungsten core), whereas the silicon carbide used in the present work contained a small amount of free silicon which existed as a separate phase. Because of the excellent agreement between these separate investigations it is concluded that the above mentioned differences, in experimental method or starting materials did not have a significant effect on the experimental results. The Arrhenius plots in Figure 15 conform to equations of the type

In k — — A(tjr) + B (61)

1/2 where k is in units of L/t ' . Since k is known to be directly proportional to the diffusivity in binary systems, and since the units of diffusivity are L /t, it is probably more appropriate to evaluate the "apparent activation energies" in the present work as if k was expressed in these units. Mathematically this may be accomplished by multiplying equation (61) by 2; thus,

2In k =« -2A(^r) + 2B (62)

The "apparent activation energy" is now given by

2A = % <63) ■K- .

where A = slope measured for Arrhenius plot R = universal gas constant, 1.99 cal/mole deg Q = "apparent activation energy", cal/mole 70'

According to this procedure, least-squares analyses gave respective activation energies of 36,200 and 23,400 cal/mole for the Stage I and Stage II reaction- zone growth kinetics in the Ti/SiC system. Although no regular pattern is evident from Figure 14, it seems clear-that the Stage I reaction kinetics persist for longer times as the reaction temperature decreases. Most of Ashdown's work was conducted at relatively low temperatures, thus it is not surprising that he did not observe the Stage II reaction shown in the present research. In this respect it is interesting to note, Figure 15, that Ashdcwn 's data at 1050°C lie considerably below the least squares straight line. It is suspected that the time-temperature conditions for these data carried the diffusion reaction into State II thereby producing the observed departure from linearity. Although it might have been expected, Ashdown failed to observe any difference in the reaction-zone growth constants for either a(hep) or p(bcc) titanium; the equilibrium transformation temperature is 8 82°C. Accordingly, it may be concluded that diffusion processes within the titanium are relatively unimportant with regard to the process of re.action-zone growth. The reaction kinetics for the Ti-6Al-4V/SiC system are presented in Figure 16. Generally, the reaction kinetics in this system are quite similar to those just described for the Ti/SiC reaction. A comparison of the two systems shows that the Stage I reaction as well as the duration of the transition period from Stage I to Stage II persists for somewhat longer times for the Ti-6Al-4V/SiC reaction. Growth Mean Reaction-Zone Thickness ( Microns ) 20 40 30 Ti-6Al-4v/SiC Diffusion CouplesDiffusion Ti-6Al-4v/SiC 0 iue1—Rato-oeGot ieis fortheGrowthKinetics Reaction-Zone 16— Figure T i - 6A1 -4V / SiC Ti / 6A1 - -4V 2 3 4 sj ie {HoursTime 2 ) 7 5 6 8 9 0 II 10

12 72 '

constants which were evaluated from the data in Figure 15 by least-squares analyses are listed in Table 5. The "apparent activation energies" for the two stages of reaction-zone growth in the Ti-6Al-4V/SiC system were evaluated from the Arrhenius plots in Figure 17. Least-squares analysis gave activation energies of 63,200 and 69,700 cal/mole for the Stages I and II reactions, respectively. For comparison, preliminary data from an earlier study on this system 55 by Snide are included in Figure 17. Snide reported an activation energy of 31,300 cal/mole which is almost exactly half of that obtained by the present research. Reasons for this serious discrepancy are not known.

X-Ray Analyses X-ray diffraction analyses were conducted on the reacted surfaces of selected Ti/SiC diffusion couples. The results of analyses of the titanium -sides of the various diffusion couples are summarized in Table 6. Very intense and numerous diffraction peaks which clearly identified the Ti^si^-phase were observed in each diffusion couple. In this respect, it should be noted that many of the diffraction peaks for the Ti^Si^- phase also coincide with those of the ternary phase, T, which is known to exist in the Ti-Si-C system. Diffraction peaks which clearly distinguished the T-phase were not observed, thus, this phase is not reported in Table 5. Because of the thin reaction- zones in couples 1 and 5, strong diffraction peaks from the underlying titanium were observed. Perhaps the most significant result from the x-ray diffraction studies was the identification of the Reaction-Zone Growth Constants [ /t /( h r ) 2] 10.0 0.1 Reactions in the Ti-6Al-4V/SiC System Ti-6Al-4V/SiC the in Reactions . 75 6.5 _ CAL/MOLE _ 69, 0 0 ,7 Q 9 = 6 1200 tg I > IE Stage Snide55 O Investigation This O Pigure 17— Arrhenius Plots for the Stages I and IX and I Stages the for Plots Arrhenius 17— Pigure 7.0 1100

63, CAL/MOLE 0 0 ,2 3 Q= 6 (Temperature)"1 (°K“I) I03 x tg I Stage !000 Temperature (°C)

8.0 i 6AI- SiC / V -4 I A -6 Ti 8.5 0 0 9 S 31,300 P S V v X C A L / MOLE / L A C X v 9.0 0 0 8 t

9.5 73 10.0

* Table 6 - Summary of X-Ray Analyses on Selected Ti/SiC Diffusion Couples

Couple Type of ^ Reaction Conditions Phases Identified,,, Number Titanium Temperature(°C) Time(hrs) by X-Ray Analysis

1 CP 1200 1.0 Ti,Ti5Si3,TiC

5 CP 1200 4.0 Ti,Ti5Si3,TiC

6 CS 1200 4.0 Ti,.Si3/TiSi

7 CP 1200 12.0 Ti5Si3,TiC

8 CS 1200 12.0 TicSi_,TiSi 3 3 9 CP 1200 48.0 Ti5Si3,TiC

17 CP 1100 68.0 Ti5Si3,TiC

22 ■ CP 1000 72.0 TicSi-,TiC 3 3

(a) CP = commercially-pure titanium containing 0.02 weight percent carbon CS = carbon-saturated titanium containing 0.19 weight percent carbon (b) diffraction pattern was obtained from the reacted surface on the titanium, side of each diffusion couple 75

TiSi-phase in couples 6 and 8. The presence of this phase was confirmed by three diffraction peaks which could only have been produced by TiSi. Couples 6 and 8 were prepared from CS titanium which, as previously discussed, showed an appreciably greater rate of reaction-zone growth at 1200°C than similar couples which were prepared from CP titanium. In view of this fact, it is not surprising that the two types of couples differ with regard to the phases which exist in their respective reaction-zones. Diffraction patterns which were obtained from the reacted surfaces of the silicon carbide sides of couples 1, 5, 7 and 9 indicated the presence of only SiC, whereas diffraction patterns taken from a polished silicon carbide surface prior to reaction indicated the presence of both silicon and SiC. This result is highly significant and will be discussed in greater detail in a later section. The results of x-ray diffraction analyses which were conducted on several diffusion couples in the Ti-6Al-4V/SiC system were similar in several respects to those obtained with CP titanium Ti/SiC couples. The Tij-Si^ and TiC-phases were identified in the alloy sides, however other lines which could not be matched within the ASTM X-Ray Data File were also observed in the diffraction patterns. Diffraction patterns from the silicon-carbide sides of these couples were identical to those obtained for the Ti/SiC couples, i.e., only SiC was present.

Metallographic and Electron Microprobe Analyses The results which are presented in this section complement the preceding section on reaction-diffusion 76 kinetics by defining the sequence of microstructure and the composition profiles which characterize the reaction-zones. The culmination of this work is presented in the next section where diffusion paths for the reactions in the Ti/SiC system are proposed. The extreme complexity of the Ti-6Al-4V/SiC reactions (five components) precluded the possibility of establish­ ing diffusion paths within this system. Microstructures which characterize the reaction- zone' in the 1200°C, Ti/SiC diffusion couples (CP titanium) are shown in Figure 18. The most fully develop­ ed microstructure for the Stage I reaction-zone is shown in Figure 18A for couple 4 (reacted 2.5-hours). The discussion of this microstructure and indeed all others will begin from the titanium matrix and proceed toward the nickel plating or silicon carbide side of the reaction-zone. Accordingly, the first feature to be encountered in Figure 18A is a single-phase region adjacent to the titanium matrix. This' single phase extends continuously into a region of two-phase equilib­ rium where isolated precipitates of the second phase increase in proportion as the nickel plating is approach­ ed. Although not clearly shown, the second phase in the reaction-zone was frequently observed to develop into an essentially continuous phase. Presumably, this phase was in contact with SiC during diffusion. The most fully developed microstructure for the Stage II reaction-zone is shown in Figure 18B for couple 10 (reacted 75-hours). Except for the appearance of a new phase, which is very thin but continuous and adjacent to the nickel plating, this microstructure is essentially identical to that shown in Figure 18A. This new phase apparently nucleated and grew during 77

TITANIUM

REACTION-ZONE

NICKEL

A

TITANIUM

REACTION-ZONE

NICKEL

Figure 18— Reaction-Zone Microstructures for Ti/SiC Diffusion Couples (A) Couple 4, Reacted 2.5rHours at 1200°C (B) Couple 10, Reacted 75-Hours at 1200°C (750X) 78 diffusion thereby producing the observed transition from the Stage I to the Stage II reaction-zone growth kinetics. As the growth of the new phase proceeds, the entire reaction zone undergoes a period of re­ adjustment, Figure 14, before again resuming a constant rate of parabolic growth. The readjustment or transition period probably involves the simultaneous growth of the new phase adjacent to the silicon carbide and dissolution of the reaction-zone adjacent to the titanium. Dissolution at the titanium/reaction-zone interface is quite probable since during any period of disrupted reaction-zone growth, the titanium would still continuously act as a "diffusion-sink" for silicon and/or carbon. Thus, the dashed-line transition periods suggested in Figure 14 are reasonable. In order to acquire some knowledge about the mechanism of reaction-zone growth in the Ti/SiC system a diffusion couple was prepared with aluminum oxide powder markers on the original interface and was reacted for 12-hours at 1200°C. Implantation of the markers by the method described in the experimental procedure should have delineated the position of the original interface by an observable trace of particles through the reaction-zone microstructure. Although the reaction-zone in this couple was normal in all respects (thickness and structure), no trace of aluminum oxide particles was observed on either as-polished or polished-and-etched surfaces. Thus, it is concluded that the markers were present in the silicon carbide/ reaction-zone interface which, as previously discussed, corresponds to the plane of fracture in all diffusion couples. The presence of the markers in this location

4 79 would mean that the reaction-zone grows mainly from the reaction-zone/titanium interface, i.e., by the transport of silicon and/or carbon through the reaction- zone rather than by the transport of titanium in the opposite direction. Further evidence that this is the case was the absence of any "Kirkendall effect" porosity in the titanium adjacent to the reaction- zone. An additional marker movement experiment also was conducted with 1-micron tungsten wire placed on the original Ti/SiC interface. During subsequent diffusion for 4-hours at 1200°C, the tungsten wire dissolved into the titanium side of the couple. This is shown in Figure 19. Although no information with regard to marker movement was gained from this experi­ ment, it did indicate that the presence of an additional slow-diffusing metallic species in the titanium had little or no effect on the subsequent growth of the reaction zone. Electron-microprobe analyses for titanium and silicon were conducted on the reaction-zone of couple 10 (reacted 75-hours at 1200°C). The results of these analyses are presented on concentration versus distance plots in Figures 20 and 21. Photomicrographs corres­ ponding to the areas which were analyzed are also shown in each figure. Because of the narrow width of the reaction-zone layers (single and double-phase) with respect to the minimum electron beam diameter (5-microns), the analyses are of quantitative signifi- 0 cance at only those locations where concentration pla­ teaus were established. Three such locations are identified as A, B and C in both Figures 20 and 21. 80

Figure 19— Reaction-Zone Microstructure and Partially Dissolved Tungsten Marker in a Ti/SiC Diffusion Couple Reacted 4-Hours at 1200°C x -Roy Intensity 100 60 80 20 in the Reaction-Zone of Ti/SiC Diffusion Couple 10. Couple Diffusion Ti/SiC of Reaction-Zone the in Figure 20.— -Electron Microprobe Analyses for Silicon and Titanium and Silicon for Analyses Microprobe -Electron 20.— Figure E x p e r i m e n t a■• l ■ O - Corrected 'cx D i s t a n c e{ M i c r o n s ) 9 "—■

20 R e a c t e d75 H o u r s a tI 2 0 0 ° C OOD-O'1 ' O - D O ^O Couple 10

30 750X 81 3525 x ~ Roy Intensity too 40 60 80 20 nteRato-oeo iSCDfuinCul 10. Couple Diffusion Ti/SiC of Reaction-Zone the in Figure 21.— Electron Microprobe Analyses for Silicon and Titanium and Silicon for Analyses Microprobe Electron 21.— Figure 20 5 D i s t a n c e( M i c r o n s ) Reocted 75 Hours at 1200°C Couple 10 25

750X 30 35 82 40 83

Further discussion concerning the placement of the composition plateaus on a ternary isotherm so as to establish the diffusion path for this reaction is deferred until the microstructures and electron-micro- probe analyses of the remaining couples in the Ti/SiC system have been presented. With regard to the electron-microprobe analyses, it should also be noted that there are additional complications which may hinder reaction-zone analyses to the extent that they are no longer quantitative. These include (1) "relief" effects during metallo- graphic polishing (2) cracks and minute porosity in the reaction-zone (3) "rounding-off" of the reaction- zone adjacent to the nickel plating. Microstructures which characterize the reaction- zones in the 1100° and 1000°C, Ti/SiC diffusion couples (CP titanium) are shown in Figure 22. Identical structures, with regard to the sequence of phases, were observed at both temperatures. The microstructure which corresponds to the limit of the Stage I reaction- zone at 1100°C is shown in Figure 22A for couple 13' (reacted 4-hours). This structure consists of a single-phase layer adjacent to the titanium followed by another single-phase layer which eventually blends into a two-phase layer. It should also be noted that the two- phase layer is quite similar tot that which was observed for the Stage I reaction-zone at 1200°C, Figure 18A. The most fully developed microstructure for the Stage II reaction-zone at 1000°C is shown for couple 22 (reacted 72-hours) in Figure 22B. A new single-phase TITANIUM

REACTION-ZONE

] NICKEL }

A

TITANIUM

REACTION-ZONE

NICKEL B

Figure 22— Reaction-Zone Microstructures for Ti/SiC Diffusion Couples (A) Couple 13, Reacted 4-Hours at 1100°C (B) Couple 22, Reacted 72-Hours at 1000°C (750X) 85 '

layer adjacent to the nickel plating may be observed in this structure. Although it could not be confirmed by electron-microprobe analyses, this is presumably the same new phase which nucleated and grew within the reaction-zone of the 1200°C, Ti/SiC couples. As for the reaction at 1200°C, it is felt that the formation of this new phase is responsible for the transitions in the reaction-zone growth kinetics at both 1100° and 1000°C. The results of electron-microprobe analyses with corresponding photomicrographs for couple 22 (reacted 72-hours at 1000°C) are shown in Figures 23 and 24. Two composition plateaus are indicated in each figure. The results of these analyses were not nearly as defini­ tive as those which were obtained for the 1200°C couple with regard to analytical resolution of the respective phases within the reaction-zone. This was undoubtably the result of highly unfavorable ratios of electron beam size to phase widths. Typical reaction-zone microstructures in the 1200°C, Ti/SiC diffusion couples (CS titanium) are shown for couple 8 (reacted 12-hours) in Figure 25. Of all the reaction-zones observed in the present research, these structures were by far the most complex. As shown in Figure 25A, the main features of the reaction-zone are two single-phase layers, a two phase layer, and an outermost single phase layer which was presumably adjacent to the silicon carbide. Figure 25B shows the highly irregular nature of the interface between the two- phase layer and the outermost single phase layer. Although this two-phase layer was present in other diffusion couples of this type (reacted 1 and 4-hours x - Ray Intensity 100 0 4 20 0 6 80 Couple 22. Couple and Titanium in the Reaction-Zone of Ti/SiC Diffusion Ti/SiC of Reaction-Zone the in Titanium and Figure 23.— Electron Microprobe Analyses for Silicon for Analyses Microprobe Electron 23.— Figure orce — Corrected Experimental

itne Microns) ( Distance ece 7 Hus t IOOO°C at Hours 72 Reacted ope 22 Couple 20

750X 25

66

0 3 - Ray Intensity Couple 22. Couple and Titanium in the Reaction-Zone of Ti/SiC Diffusion Ti/SiC of Reaction-Zone the in Titanium and 5 0 5 25 0 2 15 10 5 O Figure 24.--Electron Microprobe Analyses for Silicon for Analyses Microprobe 24.--Electron Figure xeietl ••*<>•• Experimental orce 1 • Corrected itne Microns) M ( Distance

ece 7 Hus t IOOO°C at Hours 72 Reacted ope 22 Couple

75 OX

I

88

TITANIUM

• ^ v . w *4 • ' i A i : 1 REACTION-ZONE

NICKEL

TITANIUM

REACTION-ZONE

Figure 25— Reaction-Zone Microstructures for Ti/SiC Diffusion Couple 8 Reacted 12-Hours at 1200°C (750X) 89 at 1200°C), its irregular nature suggests that it may have nucleated within the reaction-zone a short time, <1-hour, after the reaction was initiated. According to this reasoning, the two-phase layer would have nuclea­ ted adjacent to the second single-phase layer and grown toward the silicon carbide side of the couple. The results of electron-microprobe analyses on couple 8 (reacted 12-hours at 1200°C) with a corres­ ponding photomicrograph is shown in Figure 26. Four composition plateaus are indicated which coincide with the four layers in the reaction-zone. Microstructures of the reaction-zones observed in the Ti-6Al-4V/SiC diffusion couples are shown in Figure 27. Because of the two additional degrees of freedom which exist within a five-component system as compared with a three-component system (Ti/SiC), a greater variety of microstructure might have been expected in the reaction-zone of the former. This, however, was not the case; the Ti-6Al-4V/SiC reaction- zone microstructures were no more complex than those in the Ti/SiC couples. Furthermore, reaction temperatures had no effect on the sequence of phases within the reaction-zone. Figure 27A shows the reaction-zone microstructure for couple 8A (reacted 26.5-hours at 1100°C) which represents the limit of the Stage I reaction. The first feature in the microstructure is a single-phase region adjacent to the titanium. This single phase extends continuously into a two-phase region of coexistence with isolated precipitates. The final microstructural feature is a predominately single-phase layer which is adjacent to the nickel plating. As a manifestation

r x -Roy Intensity 100 60 20 80 nteRato-oeo iScDfuinCul 8. Couple Diffusion Ti/Sic of Reaction-Zone the in Figure 26.— Electron Microprobe Analyses for Silicon and Titanium and Silicon for Analyses Microprobe Electron 26.— Figure CorrectedExperimental "O' -O* C * ‘t>[>OI>C>| D > T ‘Cl* P»QDOK3KD“DCM3KIH3.. Reacted Hours 4 at I200°C 000,,0i*’ #0'< i0t0*0,,0,*0,i0*0’0 D i s t a n c e( M i c r o n s ) 0 25 20 Couple 8

750X 5 040 3530 91

w

T1-6A1-4V

REACTION-ZONE

NICKEL

REACTION-Z ONE

B

Figure 27— Reaction-Zone Microstructures for Ti-6Al-4V/SiC Diffusion Couples (A) Couple 8A, Reacted 26.5-Hours at 1100°C (B) Couple 5A, Reacted 74-Hours at 1200°C (750X) 92 of the additional degrees of freedom in this system, it is interesting to note that the isolated precipi­ tates mentioned above occasionally extend into the outer­ most layer. In a three-component diffusion system, three-phase equilibria are confined to an interface, whereas this restraint would not exist in a system with four or more components. The microstructure in Figure 27B is for couple 5A (reacted 74-hours at 12 00°C). Except for an addi­ tional single-phase layer in this couple which is adjacent to the nickel plating, the sequence of phases is essentially identical to that shown in Figure 27A. Since this new phase was not observed in any of the Stage I reaction-zones, it is concluded that the nucleation and subsequent growth of this phase during diffusion was responsible for the transition periods in the reaction kinetics (Figure 16). The results of electron-microprobe analyses on the reaction-zone of couple 5A (reaction 74-hours at 1200°C) are presented in Figures 28 and 29. Two composition plateaus which coincide with the first two reaction layers were resolved. Due to the presence of considerable porosity in the outer portion of the reaction-zone, the analyses in this region are of only qualitative value. There are several interesting features with regard to the composition profiles presented in Figures 2.8 and 29. First, it should be noted that the aluminum and vanadium contents in the alloy readily participated in the formation of the reaction-zone. In this respect, 55 Snide has shown that aluminum in a Ti-6A1-4V/B composite (reacted 100-hours at 850°C), rather than participating in the reaction-zone, is rejected into the alloy as the X - Roy Intensity (V~O.M.-Oi n>0 in the Reaction-Zone of Ti-6Al-4V/SiC Diffusion Couple 5A. Couple Diffusion Ti-6Al-4V/SiC of Reaction-Zone the in Figure 28.— -Electron Microprobe Analyses for Aluminum and Vanadium and Aluminum for Analyses Microprobe -Electron 28.— Figure »—0 —0 20 " 00 o.,^ "'0-0— J M ^ 050 30 R e o c t e d7 4 H o u r s o f I 2 0 0 ° C D i s t a n c e ( M i c r o n s ) i i ^ _ Couple5A 40

E x p e r i m e n t a l Corrected 60 75 OX 70 93 QO x -Ray Intensity 100 40 20 60 eo nte ecinZn o i6l4/i ifso ope 5A. Couple Diffusion Ti-6Al-4V/SiC of Reaction-Zone the in 10 Figure 29.— Electron Microprobe Analyses for Silicon and Titanium and Silicon for Analyses Microprobe Electron 29.— Figure Corrected E x p e r i m e n t a l«o - 20 040 30 -D*' D i s t a n c(M e i c r o n s ) Reacted Hours 74 at I200°C Couple 5A 50

60 75 OX 94 70 eo 95 reaction-zone advances into the alloy matrix. The evi­ dence for this was the formation of a stabilized alpha-titanium envelope which separated the reaction- zone from the alpha-beta alloy matrix. Aluminum is known to be a strong alpha-titanium stabilizer. In a previous discussion of x-ray diffraction analyses on Ti-6Al-4V/SiC diffusion couples, the Ti^Si^ and TiC-phases were shown to be present in the reaction-zones. In view of the fact that only four phases were observed in the reaction-zone and that aluminum and/or vanadium is probably present in each phase, it is likely that compositional modifications of the Tij-Si^ and TiC-phases are present. That is, the pure binary phases have been extended into fields of five-component phase equilibria.

Diffusion Paths in the Ti/SiC System This section essentially unifies the experimental results obtained by x-ray analyses, metallagraphic observations and electron-microprobe analyses. The unification is accomplished through the construction of schematic diffusion paths for the Stage I and Stage II reactions at 1200°, 1100° and 1000°C. As previously discussed, ternary diffusion paths illustrate the sequence of phase equilibria which connect the terminal phases in a diffusion couple. Although no information pertaining to reaction kinetics can be represented on a diffusion path, it is important to note that the path is primarily determined by the relative mobilities of the diffusing species and the rate at which they accumulate at various locations within the reaction- zone . 96 '

The recent 1200°C ternary isotherm for the.Ti-Si-C 47 system according to Brukl is given in Figure 30. Brukl's . main contributions to the Ti-Si-C system were the discovery of the T and F-phases and the extension of the Ti^Si^-phase into the ternary field. The

composition of the T-phase is close to Ti2 SiC and that of the T-phase is close to Tij-Si^. Assuming that near equilibrium phases exist within the reaction-zones of the Ti/SiC diffusion couples, the ternary diagram, Figure 30, is not consistent with the results of the present research. Accordingly, the ternary diagram was revised as shown in Figure 31. The new diagram differs in several respects from the one given by Brukl. It includes the TiSi_-phase re- Eg cently reported by Schubert and contains a slight rearrangement of the phase equilibria involving the Tit-Si^/ T, T and TiSi-phases. With regard to these revisions, it is interesting to note that Brukl's constructions in the vicinity of the latter group of phases was uncertain. Also, it is known that the chemical properties of titanium are quite similar to zirconium and that a total of at least seven silicide phases exist within the Zr-Si binary system 57 , thus, it is not surprising that additional silicides such as Ti^Si and Ti^Si^ exist within the Ti-Si binary system. Although the diagram in Figure 30 is a 1200°C isotherm, it is likely that the phase boundaries and connected equilibria are rather insensitive to tempera­ ture changes within the range 882° to 1330°C. This speculation is based on the known stability of the binary phases within this temperature range, and the relatively narrow solubility ranges of each phase in the Ti

I200°C T i-S i-C Isotherm

Wm I Phase ^ 8 2 Phases

□ 3 Phases

TiSi

vo SiC si

47 Figure 30.— Ternary Isotherm Proposed by Brukl for the System Ti-Si-C at 1200°C» 98 ternary diagram. Below 8 82°C beta-titanium (bcc) transforms to alpha-titanium (hep) and above 1330°C 58 eutectic melting occurs in the Ti-Si binary. Thus, a single diagram was employed for the subsequent representation of diffusion paths at 1200°, 1100° and 1000°C. Prior to the presentation of diffusion paths, the results of x-ray and electron-microprobe analyses on the five Ti-Si-C alloys will be discussed. The main purpose for preparing the alloys was to verify certain regions of ternary phase equilibria, Figure 31, and to provide massive samples of several of the phases which could be used to verify the present computer- corrected method of electron-microprobe analysis. The nominal alloy compositions and the respective phases which were observed in each alloy by x-ray diffraction are given in Table 7. The microstructure of each alloy is shown in Figure 32. Here, it may be noted that there are four phases in the microstructure of alloy 4. As such, it represents a deviation from equilibrium in a ternary system at constant temperature and pressure. The results of electron-microprobe analyses on the alloys are summarized in Table 8 and Figure 33. Generally, the analyzed composition of each phase corresponds quite closely with the phase diagram value. It is also of interest to note in Figure 33 that, as the result of sintering, the nominal or intended compositions of alloys 3, 4, and 5 were shifted toward the carbon-rich corner of the phase diagram; the final composition of these alloys were approximated by quantitative metallography.

0 Ti

I2 0 0 °C T i-S i-C Isotherm

TiC I Phase 2 Phases

3 Phases

TiSi.

vo C SiC VO

Figure 31.— Revised Ternary Isotherm for the System Ti-Si-C at 120D'C. 100

Table 7 - Summary of X-Ray Analysis on the

Ti-SiC Alloys

Alloy Nominal Phases Identified Number Composition(wt.%) by X-Ray Analysis

1 Ti Ti

2 Ti-3.ISi-l.3C Ti,Ti5Si3 3 Ti-6.6Si-2.8C TiC,Ti5Si3 4 Ti-15.3Si-6.5C T,TiC,SiC

5 Ti-17.9Si-7.6C T,SiC 101

TIC.4,

NO. 3

Figure 32— Microstructures of the Ti-Si-C Alloys (500X) £able 8 - Summary of Electron-Microprobe Analyses of the Ti-SiC Alloys

Alloy Analyzed Chemical Composition, wt.% Number Phase Si Ti C

1 Ti 0 100 0

2 Ti 1 99 0

Ti + Ti5Si3 *a) 7 91 2

3 TiC, 0 87 13. J.-X 24 72 4 Ti5Si3

4 TiC.l-x 0 78 22 T 12 70 18

Ti5Si3 25 73 2

SiC 70 0 30

5 T 70 15 15

SiC 70 30 0 102

(a) duplex microstructure * Nominal Alloy Composition 2 1200°C T i- S i- C Isotherm ■ Approximate Alloy / Composition after i Sintering % I Phase T i3 Si x Phase Composition U 2 Phases Reported in Table 8 □ 3 Phases Ti5Si3 / i^Si^ (D 103

Figure 33,— Alloy Compositions and Electron Microprobe Analyses of the Phases Present in the Ti-si-C Alloys. 104 ‘

Diffusion paths which characterize the Ti/SiC diffusion couples are presented on Ti-Si-C ternary phase diagrams in Figures 34, 35 and 36. These paths are consistent with the x-ray diffraction data, the microstructural sequences within the reaction-zones and the electron-microprobe analyses. With regard to the latter, the composition plateaus {A,B,C and D) which specify the compositions of the various layers are indicated on each diagram. The diffusion paths for the Ti/SiC (CP titanium) reactions at 1200°C are shown in Figure 34. Beginning from the titanium corner, the path for either the Stage I or Stage II reaction connects carbon-silicon saturated titanium with the Ti^Si^-phase. From this point the path passes through a two-phase region of microstructure which consists of the phases Ti^Si^ and Tie (Figure 18). The amount of the TiC-phase increases within this layer as is indicated by the curvature of the diffusion path. For the Stage I reaction, a continuous layer of the TiC-phase ultimately exists in equilibrium with SiC. However, for the Stage II reaction, an additional layer, T-phase, was observed to be in contact with the silicon carbide sides of the diffusion couples. Thus, the diffusion path for the Stage II reaction passes from the TiC-phase through the T-phase. Accordingly, it is concluded that the transition from the Stage I to the Stage II reaction is initiated by the nucleation and growth of the T-phase from a supersaturated version of the TiC-phase. The duration of the transition period would then correspond to that period of time which is necessary for a dynamic balance between the diffusional growth processes within the reaction-zones to be re-established. T i-S i-C Isotherm

1 Phase 2 Phases 3 P h a s e s '5Sl 3

Ti5Si4 ID

Figure 34.— Diffusion Path for the Stages I and II Reactions in the Ti/SiC Diffusion Couples Prepared from Commercially-Pure Titanium and Reacted at 1200°C. Ti

T i-S i-C Isotherm

les I Phase TiC am 2 Phases 3 P h a s e s

TiSi

Stage I Stage IE TiSi 106

C SiC

Figure 35,— Diffusion Path for the Stages I and II Reactions in the Ti/SiC Diffusion Couples Prepared from Comraercially-Pure Titanium and Reacted at 1100°and 1000*C. □ 2 Phases

i I 3 Phases

TiSi 107

C SiC

Figure 36.— Diffusion Path for the Ti/SiC Diffusion Couples Prepared from Carbon-Saturated Titanium and Reacted at 1200*0. 108

As previously discussed, x-ray diffraction analyses from the silicon carbide-side of each diffusion couple indicated the presence of only SiC. From this, it is concluded that, the diffusion paths for both the Stage X and II reactions pass through SiC before reaching the terminal composition, SiC-8Si. The diffusion paths for the Ti/SiC (CP titanium) reactions at 1100° and 1000°C are shown in Figure 35. Except for the addition of the TigSi phase, the paths are essentially identical to those shown in Figure 34. The Ti^Si-phase is the additional single phase layer which was observed (Figure 22) to be adjacent to the titanium. Again, the nucleation and growth of the T-phase from supersaturated Tic is thought to be responsible for the transitions in the reaction kinetics. The diffusion path for the Ti/SiC (CS titanium) reaction at 1200°C is shown in Figure 36. This path differs from the Stage II reaction path shown in Figure 34 only by its involvement with the TiSi-phase. As may be noted from the reaction-zone microstructures (Figure 25), TiSi is apparently the continuous phase in the irregular two-phase layer. The amount of T-phase in this layer increases as the irregular T/Tisi interface is approached. A summary of pertinent crystallographic data for all of the phases and/or compounds which were observed within the reaction-zones of the Ti/SiC diffusion couples is presented in Appendix D.

Mechanism of the Ti/SiC Reaction As shown by the diffusion paths in Figures 32 and 33, the binary silicide phases, Ti^Si and/or Ti^Si^, 109 are concentrated in those portions of the reaction-zones which are adjacent to the titanium side of a diffusion couple. It may also be recalled that a marker movement experiment suggested that the reaction-zones grow by the diffusion of silicon and carbon toward the titanium side rather than by the transport of titanium in the opposite direction. These observations are most significant since they imply that silicon is the most mobile species in the reaction-zone. The carbon-rich phases in the reaction-zone are concentrated adjacent to the silicon carbide side of each couple. Evidently; carbon which is released by the reduction of silicon carbide accumulates within the plane of reaction and subsequently produces several interesting results. An attempt will now be made to relate a logical sequence of events which probably occur within a very short period of time and which serve to initiate the diffusion path for the Ti/SiC (CP titanium) diffusion reaction at 1200°C. Remembering that these couples actually consist of titanium against a two-phase struc­ ture, SiC-8Si, the initial diffusing system must be composed of parallel diffusion couples, i.e., Ti/SiC and Ti/Si. The Ti/Si couples may be active initially, however, as will be shown, it is probably that they ultimately yield to a uniform Ti/SiC reaction. Aside from the localized Ti/Si reactions, the Ti/SiC reactions are initiated by the reduction of silicon carbide under the influence of a nearly finite chemical potential gradient. This releases free silicon and carbon and is followed by the formation of a layer of the Ti^Si^-phase adjacent to the titanium. Simultaneously, carbon from the Ti/SiC reactions begins to participate in the process 110

of reaction-zone growth. Some of the carbon is evidently reconsumed within the plane of the reaction to convert the areas of free silicon (second phase in the SiC-8Si terminal composition) into SiC thereby forming a continuous layer of SiC in the reaction plane. Evidence for this conclusion is based on two factors; first the results of x-ray diffraction analyses on reacted silicon carbide (SiC-8Si) surfaces and second, a comparison of the present work on the Ti/SiC system with that by Ashdown.54 As previously mentioned, only SiC was ob­ served on the silicon carbide surfaces after reaction, whereas prior to reaction, both silicon and SiC were observed. Also, since the reaction-zone microstructures and growth kinetics in the present work were in excellent agreement with those obtained by Ashdown, there is further reason to believe that a continuous layer of silicon carbide is formed in the plane of reaction. Ashdown's data was obtained from reacting pure silicon carbide filaments with titanium. Thus, the probable effect of the excess silicon in the present diffusion couples was simply to reduce the amount of carbon which was free to diffuse toward the tiLanium side of the couples. The carbon which was not consumed by the * formation of a continuous layer of SiC diffuses away from the reaction plane by transport through the Ti^Si.^- phase. Subsequently, the solubility product for Tie in TigSi^ is exceeded and Tic begins to precipitate; this produces the two-phase reaction layer which was observed. Reaction-zone growth proceeds by this process until the continuous layer of TiC adjacent to the silicon carbide becomes sufficiently supersaturated with respect to both silicon and carbon so as to nucleate the Ill

T-phase. This, in turn, gives rise to the transition period which was observed in the reaction-zone growth kinetics. Exactly why the Ti^Si^-phase forms adjacent to the titanium rather than the Ti^Si or TiC-phase in the Ti/SiC (CP titanium) couples which were reacted at 1200°C is not known. Standard free energies of formation are not available for the silicide phases; however, it is.suspected that of the three phases which may exist in equilibrium with titanium, TiC has the most negative standard free energy of formation and would therefore be the most likely phase to form.

Ti + C = TiC ^G1200°C= 'OOOcal/g-atom C In addition to equilibrium thermodynamics, the extent of supersaturation which is required for the nucleation of a phase as well as the relative mobilities of the diffusing species within the reaction-zone may determine the phase which exists in equilibrium with titanium. For instance, if the TiC-phase was the first to form, its continued existence would depend on the ability of an adjacent phase (perhaps a.silicide) to supply carbon at a faster rate than it could be consumed by dissolution of the carbide at the TiC/Ti interface, i.e., carbon must accumulate at this interface. This latter effect was discussed in a previous section of the dissertation which dealt with reaction-diffusion in the binary Ti/C system. If the conditions for carbon accumulation are not met, the carbide, in effect, would be reduced at the TiC/Ti interface under the influence of a chemical potential gradient. Thus, some phase other than TiC.would exist in equilibrium with 112 titanium. The remaining possibilities are Ti^Si and TigSi3,and for the present reaction at 1200°C this phase happens to be Ti^Si^. It should be clear from the above that thermodynamics as well as kinetics de­ termine the observed sequence of microstructure within a reaction-zone. At lower temperatures, 1100° and 1000°C, the Ti^Si-phase rather than Ti^Si^ is in apparent equilibrium with titanium in the Ti/SiC (CP titanium) diffusion couples. Since the transport of any particular species through the reaction-zone is undoubtedly controlled by several thermally activated diffusion processes, it is conceivable that the dynamic balance of silicon flow within the system could have been altered by the reduced temperatures so as to stabilize a new phase, Ti^Si. The remaining reaction-zone microstructure in these diffusion couples resulted from supersaturation and precipitation effects as was previously discussed for the reaction at 1200°C. The Ti^Si-phase was also observed to exist in apparent equilibrium with titanium in the Ti/SiC (CS titanium) couples which were reacted at 1200°C. This suggests that in addition to the kinetic factors mention­ ed above, the presence of carbon in titanium may have increased the activity of silicon so as to stabilize this phase rather than Ti^Si^. In this respect, it should also be noted that because of reciprocity relations the activity of carbon would also have been increased but apparently not to the extent necessary to stabilize the TiC-phase adjacent to titanium. V. SUMMARY

The present research dealt with two aspects of reaction diffusion. First, the problem of reaction- diffusion in a metal-nonmetal binary system, M/N, with a single intermediate phase, MN, was analyzed mathematically. Second, reaction-diffusion in the multicomponent systems Ti/SiC and Ti-6Al-4V/SiC was investigated experimentally. The objective of the mathematical analysis was to calculate the rate of growth of the MN reaction layer in M/N diffusion couples for which the metal sides were treated as finite in extent. This approach differed from previous analyses of similar problems which have always assumed a parabolic growth function for the reaction layer and which treat the metal side of a couple as either semi-infinite in extent or saturated with respect to the nonmetal. Although the set of assumptions which were imposed on the present problem were somewhat restrictive, the results clearly demonstrated that non-parabolic growth of the MN reaction layer is expected for an initial period of time. Subsequently, the parabolic rate law is approach­ ed as the metal side of the diffusion couple becomes saturated with respect to the nonmetal. Experimental data from a reaction-diffusion study on the Ti/C system by Vansant and Phelps 40 were employed for the purpose of this demonstration. The initial period of non-

113 114 parabolic growth which was predicted from this analysis was compared with that which was experimentally observed by Castleman and Seigle 18 for growth of the y-phase in Ni/Al diffusion couples. Reaction-diffusion in the multicomponent systems Ti/SiC and Ti-6Al-4V/SiC was studied at temperatures in. the range 1000° to 1200°C and for times up to 142 hours'; in all, 40 diffusion couples were prepared. At each temperature investigated, the reaction kinetics in both systems showed two stages of parabolic growth. The transitions from the Stage I to the Stage II growth kinetics were rationalized in terms of simultaneous growth and dissolution processes within the reaction-zone. The influence of initial carbon content on the reaction kinetics in the Ti/SiC system was investigated by reacting several couples at 1200°C which were prepared from carbon-saturated titanium. Carbon saturation markedly increased the rate of reaction-zone growth. For the Ti/SiC system (commercially-pure titanium), "apparent activation energies" of 36.2 and 23.4 kcal/mole were obtained for the Stages I and II reactions, respectively. In this regard, the activation energy for the Stage I reaction was in excellent agreement 54 with previous work by Ashdown who studied the com­ patibility of silicon carbide filaments in commercially- pure titanium at temperatures below 1050°C. Since Ashdown*s reaction conditions were less severe (time and temperature) than those of this investigation, it was not surprising that he did not observe the Stage II reaction. A marker movement experiment which was conducted on the Ti/SiC system at 1200°C suggested that the 115

reaction-zone grows primarily from the reaction-zone/ titanium interface, i.e., by the diffusion of carbon and silicon toward the titanium side of the couple. For the Ti-6Al-4V/SiC system, "apparent activation energies" of 63.2 and 69.7 kcal/mole were obtained for the Stages I and II reactions, respectively. In 55 earlier preliminary studies on this system, Snide reported an activation energy of only 31.3 kcal/mole. X-ray diffraction, metallography, and electron microprobe analyses were employed to study the reaction- zones in both the Ti/SiC and Ti-6Al-4V/SiC diffusion couples. Metallographic examination of the reaction- zones showed that in all instances the microstructures were consistent with the permissible combinations and sequences of phases as governed by the phase rule. Metallographic studies showed that the nucleation and growth of a new phase within the reaction-zone was associated with the transitions in the reaction-kinetics of both the Ti/SiC and Ti-6Al-4V/SiC systems. In the * Ti/SiC couples, the new phase was identified as the ternary phase, T; however, in the Ti-6Al-4V/SiC couples the new phase was not identified. The Stage II reaction-zone microstructure (Ti/SiC couples prepared from commercially-pure titanium) produc­ ed at 1200°C contained the phases Ti^Si^, TiC and T, while the Stage II reaction-zones produced at 1100° and 1000°C contained the phases Ti^Si, Ti^Si^, Tic and T. The additional phase, Ti3Si, produced at the lower temperatures was not represented in the Ti-Si-C phase diagram devised by Bruklf^ however, its existence has been reported by Schubert.5 6 The reaction-zone micro­ structure in the Ti/SiC couples which were prepared from carbon-saturated titanium contained the phases Ti^Si, TigSig, TiSi and T. 116 '

From the above knowledge, diffusion paths were constructed on Ti-Si-C phase diagrams for the various Ti/SiC diffusion reactions. In this regard, since the Ti-Si-C diagram given by Brukl was not consistent with the results of this research, a new phase diagram was proposed and subsequently employed for the representation of the diffusion paths. Because of the inherent complexities in five- component phase equilibria, no diffusion paths were pro­ posed for the Ti-6Al-4V/SiC diffusion reactions. Electron microprobe analyses of these couples showed that vanadium and aluminum as well as titanium and silicon participated in the formation of the reaction- zone microstructure. A mechanism was proposed for the Ti/SiC reactions whereby the relative mobilities of the diffusing species are the primary factors which determine the sequence of phases within the reaction-zones; thermo­ dynamics provides a permissible framework for the reactions. APPENDIX A

The following is an expansion of equations (35) and (36) for a three component (n=3) system with semi- infinite boundary conditions. The result is a system of six equations containing six unknowns which may be solved simultaneously for the respective a-coefficients.

+ C 1 x>0 = a i o a i l e r f ( 2 V >r1) + a12 e r f ( 4 ^ ) (A—1) t=0u v

C 1 = + (A—2) x<0 a i o a i l erf( ^ > a12 e r f ( 2 ^ ) t=0

4* (A-3) q2 x>0 = a20 a21 e r f ( 2 Y u ^ ) + a22 erf( ^ t=0

4* (A—4) C2 = a20 + 6 r f ( 2^ ) x<0 a21 e r f ( 2 V u ^ ) a22 t=0 APPENDIX B

Computer program for performing- the numerical solution to equation (54) .

StAtCUIt ItJJUb SIBJOB $1BF I (. DECK2 C PROGRAM FOR NUMERICAL SOLUTION TO REACTION LAYER GROWTH PROMLEM c flux out of reaction layer is not equal to zero .. .. .

C LIST of varibles c I ^initial value of time to start the calculation*hrs c x -initial value of compound layer thickness to start the calculations C C0=C0NCENTRATI0N in compound layer AT I/C »GMS/CM#*3 C Cl=CONCENTRATlON in COMPOUND at M/C>GMS/CM**3 C C2=CONCENTRATiON in METAL a T M/c»GMS/cM**3 C . C3=CONCENTRATION. in metal when t =o, gms/ cm**3 C K1=C0-C1 C K2-C1-C2 c l ^Thickness of meTal*cm C A2=PRE-EXPONENTIAL IN METAL DIFFUSION COEFFICIENT C Q2=ACTIV a TION ENERGY FOR DIFFUSION IN METAL»CAL C D1=DIFFUSI0N COEFFICIENT in COMPOUND LAY eR»CM**2/HR C ' D2-DIFFUSI ON COEFFICIENT IN METAL*CM**2/HR C GRAD=CONCENTRATION GRADIENT IN METAL AT X=0,GMS/cM**4 C Xi=THICKNESS OF COMPOUND LAYER»CM C DELT1=INCREMENT OF TIME,HRS C DELXl=INCREMENT OF COMPOUND LAYER THICKNESS,CM C Y =INTEGER DENOTING NUMBER OF DIFFUSION COEFFICIENTS( D l) C Z = integer denoting NUMBER OF i n i t i a l conditions c DIMENSION Kl<50)»K2£5°)»C2£5°)»C3£5°>»L(&0)»T2<50)»T(sO},X(50), 1D1(10000), X i (2 500) INTEGER Y,Z REAL K1*K2»L READ<5»20) y *z READ( 5*2l) TMAX*TMIN»A2»02»D»DB READ*5*22) (K K I)*<2**2)))) W3=W2*SEr S GRAD=-tW3/(D2*DELTiJ*tO#5*Kl(I)+K2(i))) DELX1-(W1-W3*X1(N-1) l/X K N -l) X1(N)=X1(N-1)+DELX1 IF(T1 • LT. TCI) .AND. X I (N) *GT, X l(N -l) .AND. K .EQ. 0) GO TO 7 119 IF (T1 *GE* TMAXI) GO TO 4 IFtK .EQ. 1) Wr i Te (6*32) T l * X l(N) *GRAD»DELX1 IF(T1 .LE. TMINJ -GO TO 5 GO TO 3 4 DELTl=-0

W1=-W1 W2=-W2 GO TO 2 5 IF(K .EQ, 1) GO TO 10 IF«ABSCXi(N)) . l T. ABS(XB)) GO TO 6 GO TO 7 6 XB=X1(N) 7 IFlTl .LT. T(I)) DELTi =q IF lT l ,LT. TCI j > W2=-W2 IF (J .EQ. Y) GO To 8 GO TO 9...... 8 D1C J )=DB t m a x i - tmax ...... K=K+1 GO TO 1 9 CONTINUE 10 CONTINUE 20 F0RMAT(2I8) 21 FORMAT(5F8.0»E8.0) 22 FORMAT(8F8.0) 23 FORMAT(10E8.0) 30 FORMAT(1H1»3HD1=*E14.6/1X»3HD2=»E14.6/2X»2HT=*E14.6/2X*2HX=»E14.6/ 120 11X*3H1'2=»E14.6/////) ...... " ------31 FORMAT C//17X*8 h TIME*HRS»1OX»12HTHICKNESS»CM*6X*18HGRADI ENT »GMS/CM* l*4»lOX»8HDELXl,CM//) 32 FORMAT(11X»E1A.6*8X»E1A,6*10X»E14,6*8X»E1A,6) STOP END SDATA - - APPENDIX C

Computer program for performing the x-ray absorption corrections on electron-microprobe analyses.

sexecute IBJOB SIBJOB MAP $IBFTC .DK1 C ITTERAT i VE PROCEDURE FOR PERFORMING THE ABSORPTION CORRECTION ON SIBFTC «DK1 C ELECTRON MICROPROBE ANALYSES

LIST OF INPUT VARIABLES N =NUMBER OF COMPONENTS IN The SYSTEM NO ^NUMBER OF DATA SeTS TO BECORRECTED to to MURO -MASS ABSORPTION COEFFICIENTS SIGEF =SIGMA EFFECTIVE FROM REFERENCE K -RELATIVE INTENSITIES FROM MICROPROBE DATA H =H VALUES FROM REFERENCE Z =ATOMIC NUMBER A -ATOMIC NUMBER

DIMENSION MUROI7.8 ) »SIGEF(10),K(10),H(83)»CHI< 8>• 1 Z<10)»A(10)rC(lO)tCHlO(lO)»FCHI110)»FCHIO(10)» 2 S1900(161*21),52000(161*21)*S2250(81,21)*52500(81*21)* 3 S3000(31*21)*53250(31*21)*S3500(31 *21)»S(161*21> »Sl(161*21) REAL K»MURO integer o »r *p *c x *b COMMON CHI*S20Q0,S2250,S3250/B1/S1900/B3/S2500/B4/S3 /B5/S350 READ I 5 *25 > N*NO M=N-1 C READ IN MAIN MATRICES FOR SIGMA AND CHI READ t 5*19) MS1900( I , jj ,j=l,21) * 1=1*161) READt5*19)((S2000(l,J),J=1,21)*1=1*161) READ(5*19)((S2250(I»J)*J=1*21)*1=1*81) READt5*19)(tS25°u(I*J)*J=1*21)*1=1*81) READt5*19)((S3000(I,J),J=1,21)*I=1* 31) READ(5*19)I (S3250(I»J)»J=1*21)*1=1* 31) READt 5*19)t (S3500( I*J)»J = 1»21)*1=1* 31) C READ IN AUXILLARY MATRICES READ!5 *2 1 )(H (I)*I= 6 *8 2 ) READ<5»21)(IMU ro (I*J )»J=1*N)* 1=1*M ) READt 5 >21)( £ l I ) * I = l»N) READt5*21)tAtl)*I=1»N) READ(5*2l)tSiGErtl)»I=1»M) ' WRITE (6*22) DO 1810=1*NO READt5*21)IK(I)*I=1»N) WRlTEt 6 *2 4 )t < ( I )* 1 = 1»N) DO 11=1*N 1 CCI)=K CI) DO 18 0=1*5 C . COMPUTE CHI(ABSORPTION FACTOR) FOR EACH ELEMENT IN THE ALLOY . DO 4 1 = 1*M C H It I)=0*0 DO 2 J=1*N 2 CHItI)=MUROtI»J)*C(JJ+CHItI) CHItI)=1.26*CHItI) 4 CONTINUE c compute The average atomic number of the a llo y DENOM=0.0 DO 5 1 = 1 *N 5 DENOM=C

IF UFLOA'n lZBARl-lZBAR)/2.0) . gT. FRAXON) GO To 7 ZBAR=FLOAT(IZBAR1) GO To 8 7 ZBAR=FLOAT(IZBAR) 8 DO 9IJ=2»21 J=IJ ...... B=ZBAR IFtSl900(l*U)-H(B).LE* .001) GO To 10 9 CONTINUE c begin search fo r sigma and chi in main matrices 10 DO 16 I =1*M IF (SigOOt 1 * 1 } .LE. SiGEFUj .AND. SlGEFO) .LT. S20 (1»1)) 1 CALL SUBltS.Si»i *IM»CX»S 11J jF tS 2 0 0 0 ti» ij#LE. S ig EF11> .AND. SIGEFcX*$11) IF t S2250 (1 *1 ) .LE. SiG EFdl .AND. S IGEF CI) .LT. S25 (1 *1 )) 1 CALL SUB3(S>S1 , i , Im*cX*5H) IF {S3OOCH 1 * 1 ) .LE. SiGEF( I ) .AND. SlGEF11) .L T. S32 5 0 ( l » l ) ) .1 CALL SUBA(S*Si,I,iM*CX.$ll) 124 IF tS3250 Ci»i ) 4 LE* SiGEF .AND. SiGEF(I) .LT, S35 <1*1)) 1 CALL SUB5(S»Sl»I,lM*CX»$ll) 11 XLO =tSl6EF( I >-S( i*l))/(S K l» l J-S(l»l))*(Sl( IMt J|-SUM*Jn+S(lM»J) xhi =« s ig ef t i )-s

DO 1 N=1*161 DO 1 J=1i21 T(N»J) =SIN»J) 1 TKN»J)=Sl(N*J) DO 10 L=2»161

M=L IF (CHItI)«GE«S(L»1)*AND*S(L+l*1)•GT#C H I(I)) RETURN 1 10 continue RETU R N END SIBFTC *DK3 SUBROUTINE SUB2(T*Tl»l»M*ICX**)

DIMENSION T(161*21)*Tl(161»21) COMMON CHI(8 )*S(161*21).51(81*21).52(31*21) ICX-81 D02N=1»161 DO 2J=1*21 2 T(N*J)=S(N»J)------D03N=1*81 DO 3 J - l *21 3 T1(N*J)=S1(N.J) DO 20 L=2*81 M=L v IF (CHI(I ) .GE.S(l »1).AND. S(L+l*l) . gT. C H K l)) RETURN 1 20 CONTINUE return END SIBFTC.DK4 SUBROUTINE SUB3tT.Tl*1 *M*ICX**) DIMENSION T(16l»21)»TlI161*21) COMMON CHIt8J*S2(161*21).»S(81*21)»S3(31»21)/B3/51(81*21) ICX=81 DO 3 N=1*81 DO 3J=1»21 T(N*J)=S(N*J) 3 Tl(N»J)=SKN»J) DO 30L=2*81 M=L IF(CHI(I).GE*StL»li.AND*S(L+l»l).GT.CHKl)) RETURN 1 30 CONTINUE . RETURN END , • * ...... SIBFTC *DK5 127 'SUBROUTINE SUB4(T,T i *I» m»i c x** j DIMENSION T (i6 1 *2 1 )» t 1 ( 161*21) COMMON CHI(8)*S2tl61*21)*S3(81»21)*Si(31*21)/B4/S(31*21) ICX=31 DO 4N-1*31 - DO 4J=1*21 I(N*J)=S(N»J) 4 TKN»J)=SKN»J] D040 L=2»31 M=L , IFtCHU I).GE. S

T(N*J)=S(N*J) 5 Ti (n »J)=Si (n »J) DO 50 L=2*31 M=L IFICHI • I ) *GE* S(L»1)#AND.S(L+1*1),GT,CHKI)) RETURN 1 . 50 CONTINUE return END SDATA. 128

3

— 4.316 3 . 2 1 2 4.508 4.400 4.911 4.275 4.088 Density,g/cm O — — — ' 4.98 4.683 5.162 5.17 10.079 — — — — — — Constants,A X-Haytb) — a b c Lattice 3.082 4.327 3.307 2.950 7.465 6.53 3.63 10.39 3 APPENDIX"D c /mcm,Mn^-Si /mcm,Mn^-Si /mmc,hep 3111 3

6 6 6 3 Group and Lattice Group Type Crystal System, Crystal System, Space tetragonal,lT, Ni3P tetragonal,lT, orthorhombic,Pnma,FeB hexagonal cubic,Fm3m,NaCl hexagonal, P hexagonal, cubic,Im3m,bcc hexagonal,P * SiC(T) 2 5 s i 3 unit cell The following is The a pertinenttabulation of is following crystallographic data for the compounds 3-Ti a-SiC*a) Ti a-Ti hexagonal,P Ti TiC Compound TiSi - - Ti3Si (b) (b) constants calculated knowledge number molecules/from lattice and a of the of (a) (a) modification polymorphic more data III; all are there in for polymorphs than 90 which were within whichreaction-zones the identified Ti/SiC of the diffusion couples; the referenceswere data obtained from and (47) (59). 129 LIST OF REFERENCES

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