Accelerated kinetics and mechanism of growth of boride layers on titanium under isothermal and cyclic diffusion

The tendency of titanium (Ti) and its alloys to wear, gall and seize during high contact stresses between sliding surfaces severely limits their applications in bearings, gears etc. One way to mitigate these problems is to modify their surfaces by applying hard and wear resistant surface coatings. Boriding, which involves solid state diffusion of boron (B) into Ti, thereby forming hard surface layers consisting of TiB2 and TiB compounds has been shown to produce extremely high wear resistant surfaces in Ti and its alloys. The growth kinetics of these layers are, however, limited by the low diffusivities of B in the high melting TiB2 and TiB compounds. On the basis of the fact that HCP metals such as Ti show enhanced (anomalous) self-diffusion near the phase transition temperature, the first hypothesis of this work has been that the diffusivity enhancement should cause rapid ingress of B atoms, thereby accelerating the growth of the hard boride layers. Isothermal boriding experiments were performed close to phase transition temperature (890, 910, and 915°C) for time periods ranging from 3 to 24 hours. It was found that indeed a much deeper growth of TiB into the Ti substrate (~75 ?m) occurred at temperatures very close to the transition temperature (910°C), compared to that obtained at 1050°C. A diffusion model based on error-function solutions of Fick's second law was developed to quantitatively illustrate the combined effects of the normal B diffusion in the TiB phase and the anomalous B diffusion in Ti phase in accelerating TiB layer growth. Furthermore, isothermal boriding experiments close to transition temperature (900°C) for a period of 71 hours resulted in coating thickness well above 100 ?m, while at 1050°C, the layer growth saturated after about 24 hours of treatment time. In the second part of this work, a novel approach named "cyclic-phase-changediffusion, (CPCD)," to create deeper TiB2 and TiB coating layers on CP-Ti by cyclic thermal processing, has been investigated. It was found that thermal cyclic B diffusion in Ti across the alpha(?)-beta(?) phase transition temperature led to highly hardened surface layers enriched with TiB whiskers that grow to depths exceeding 120 ?m. By solving the transient heat transport problem for cyclic changes in surface temperatures, it was found that there is a "heat-packet" that travels back and forth from the surface to the interior of the material. This heat-packet appears to transport B dissolved in ?-Ti into interior causing increased coating depths.

ACCELERATED KINETICS AND MECHANISM OF GROWTH OF BORIDE LAYERS ON TITANIUM UNDER ISOTHERMAL AND CYCLIC DIFFUSION by Biplab Sarma A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Metallurgical Engineering University of Utah May 2011 Copyright Biplab Sarma © 2011 All Rights Reserved The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of Biplab Sarma has been approved by the following supervisory committee members: Ravi Chandran , Chair 1/7/2011 Date Approved Sivaraman Guruswamy , Member 1/7/2011 Date Approved Zhigang Zak Fang , Member 1/7/2011 Date Approved Michael L. Free , Member 1/7/2011 Date Approved Anthony Sanders , Member 1/7/2011 Date Approved and by Jan D. Miller , Chair of the Department of Metallurgical Engineering and by Charles A. Wight, Dean of The Graduate School. ABSTRACT The tendency of titanium (Ti) and its alloys to wear, gall and seize during high contact stresses between sliding surfaces severely limits their applications in bearings, gears etc. One way to mitigate these problems is to modify their surfaces by applying hard and wear resistant surface coatings. Boriding, which involves solid state diffusion of boron (B) into Ti, thereby forming hard surface layers consisting of TiB2 and TiB compounds has been shown to produce extremely high wear resistant surfaces in Ti and its alloys. The growth kinetics of these layers are, however, limited by the low diffusivities of B in the high melting TiB2 and TiB compounds. On the basis of the fact that HCP metals such as Ti show enhanced (anomalous) self-diffusion near the phase transition temperature, the first hypothesis of this work has been that the diffusivity enhancement should cause rapid ingress of B atoms, thereby accelerating the growth of the hard boride layers. Isothermal boriding experiments were performed close to phase transition temperature (890, 910, and 915°C) for time periods ranging from 3 to 24 hours. It was found that indeed a much deeper growth of TiB into the Ti substrate (~75 μm) occurred at temperatures very close to the transition temperature (910°C), compared to that obtained at 1050°C. A diffusion model based on error-function solutions of Fick's second law was developed to quantitatively illustrate the combined effects of the normal B diffusion in the TiB phase and the anomalous B diffusion in Ti phase in accelerating TiB layer growth. Furthermore, isothermal boriding iv experiments close to transition temperature (900°C) for a period of 71 hours resulted in coating thickness well above 100 μm, while at 1050°C, the layer growth saturated after about 24 hours of treatment time. In the second part of this work, a novel approach named "cyclic-phase-change-diffusion, (CPCD)," to create deeper TiB2 and TiB coating layers on CP-Ti by cyclic thermal processing, has been investigated. It was found that thermal cyclic B diffusion in Ti across the alpha(α)-beta(β) phase transition temperature led to highly hardened surface layers enriched with TiB whiskers that grow to depths exceeding 120 μm. By solving the transient heat transport problem for cyclic changes in surface temperatures, it was found that there is a "heat-packet" that travels back and forth from the surface to the interior of the material. This heat-packet appears to transport B dissolved in β-Ti into interior causing increased coating depths. CONTENTS ABSTRACT...................................................................................................................... iii LIST OF TABLES.......................................................................................................... vii LIST OF FIGURES....................................................................................................... viii ACKNOWLEDGMENTS............................................................................................. xiii 1. INTRODUCTION..................................................................................................1 1.1 Background..................................................................................................1 2. LITERATURE REVIEW .....................................................................................5 2.1 Structure and properties of titanium ...........................................................5 2.1.1 α-alloys...................................................................................................9 2.1.2 β-alloys...................................................................................................9 2.1.3 α + β alloys.............................................................................................9 2.2 Surface performance of titanium ...............................................................10 2.2.1 Coatings on titanium............................................................................12 2.2.2 Titanium nitride coatings .....................................................................13 2.2.3 Modeling of kinetics of titanium nitride coatings................................15 2.2.4 Titanium oxide coatings.......................................................................20 2.3 Boriding of metals......................................................................................22 2.3.1 Structure of boride layers on iron/steel................................................25 2.3.2 Modeling of boride growth in iron/steel ..............................................27 2.3.3 Boriding of titanium.............................................................................30 2.3.4 Titanium boride coatings on titanium ..................................................36 2.4 Cyclic thermal treatments on metals..........................................................38 2.4.1 Cyclic surface treatment ......................................................................38 2.4.2 Cyclic heat treatment for microstructure refinement ...........................40 2.4.3 Role of phase transformation in cyclic thermal treatment ...................40 2.5 Diffusion and phase transformation in titanium ........................................42 2.5.1 Mechanism of anomalous diffusion.....................................................48 3. OBJECTIVES ......................................................................................................54 3.1 Objectives of the present research .............................................................54 vi 4. EXPERIMENTAL PROCEDURE.....................................................................56 4.1 Powder mixture for B diffusion process ....................................................56 4.2 Isothermal boriding near transition temperature........................................57 4.3 Isothermal boriding for long hold time......................................................58 4.4 Thermal cyclic boriding.............................................................................58 5. RESULTS AND DISCUSSION ..........................................................................60 5.1 Modeling of layer growth kinetics.............................................................60 5.1.1 Theoretical modeling based on second law of diffusion .....................60 5.1.2 Comparison with experimental data ....................................................68 5.2 Structure and kinetics of growth of boride layers near the phase transition temperature in Ti........................................................................74 5.2.1 Premise.................................................................................................74 5.2.2 Structure and properties of boride coatings .........................................75 5.2.3 Modeling of coating growth kinetics ...................................................88 5.3 Isothermal diffusion saturation of boron in boride layers………………..99 5.3.1 Premise.................................................................................................99 5.3.2 Results and discussion .......................................................................100 5.4 Mechanism and kinetics of growth of titanium boride layers under cyclic-phase-change-diffusion (CPCD).........................................112 5.4.1 Premise...............................................................................................112 5.4.2 Subsurface temperature profiles during CPCD..................................113 5.4.3 Results and discussion .......................................................................121 6. CONCLUSIONS ................................................................................................142 REFERENCES...............................................................................................................145 LIST OF TABLES No. Page 2.1 Friction and wear data for various metals in contact (Adapted from [30]) ...........12 2.2 List of boron powders and their respective surface areas (Adapted from [80]) ……………………………………………………………...24 2.3 Crystal structure, lattice parameter and fractional coordinates in TiB and TiB2 (Adapted from [91]) …………………………………………………..34 2.4 Activation energy and pre-exponential factor for pure Zr, Ti and Ti-alloys (Adapted from [21])…………………………………………………... 45 5.1 Average thickness values of TiB2, TiB and the composite (TiB2 + TiB) coating layers, determined for different B diffusion temperatures and times [104]………………………………………………………………….. 68 5.2 Diffusivity data [97] used in the calculation of kinetics using error function solutions…………………………………………………………………………. 69 5.3 Summary of total (TiB2+TiB) coating thicknesses obtained in varied isothermal treatments…………………………………………………..… 75 5.4 Diffusivity data for various phases………………………………………............ 96 5.5 Comparison of TiB2 and total (TiB2+TiB) coating thicknesses obtained in varied phase fields of Ti during isothermal treatments. The thickness values shown as italics were taken from ref [104] for comparison .....................101 5.6 Summary of total coating thicknesses obtained in varied cyclic thermal treatments………………………………………………………………122 5.7 Summary of TiB coating thicknesses obtained in cyclic thermal treatment as compared with isothermal treatments ……………………….……134 LIST OF FIGURES No. Page 2.1 HCP crystal structure of Ti ......................................................................................6 2.2 Variations in tensile properties of CP-titanium with increasing O, N, and C content (Adapted from [27])..........................................................................6 2.3 The α and β phase fields of Ti as affected by the O content (Adapted from [27]) ..7 2.4 The α and β phase fields of Ti as affected by the C content (Adapted from [27]....7 2.5 The α and β phase fields of Ti as affected by the N content (Adapted from [27]).................................................................................................8 2.6 Various types of wear upon rubbing a flat ended pin on solid surface (Adapted from [32])................................................................................................11 2.7 Ti-N phase diagram (Adapted from [45])...............................................................14 2.8 SEM micrographs of Ti-6Al-4V, plasma nitrided at (a) 900°C for 6 hours and (b) 900°C for 14 hours (Adapted from [49])....................................................16 2.9 The schematic representation of the partial Ti-N phase diagram and the associated diffusion layers formation in Ti-6Al-4V alloy (Adapted from [60]) ....18 2.10 Ti-O phase diagram (Adapted from [70])...............................................................21 2.11 Microstructure of steel boronized at 900°C (200X) (a) Steel St 37 boronized in Ekabor for 10 hours (200X), (b) Steel C15 boronized in Ekabor for 4 hours (Adapted from [75])................................................................................................26 2.12 Variations of boride coating thicknesses obtained in the iron substrate with different proportions of alloying elements (Adapted from [75]) ............................27 2.13 B concentration profile used for the modeling (Adapted from [85])......................29 2.14 Ti-B phase diagram (Adapted from ASM International [90]) ................................31 No. Page 2.15 Crystal structures of TiB2 and TiB (Adapted from [91]).......................................33 2.16 Arrhenius plot (a) of self-diffusivity for CP-Ti showing the upward curvature as the transition temperature is approached [124]. Comparison of experimentally measured self-diffusivities (b) of various normal BCC metals and anomalous metals like Ti, Zr etc. [125]..........................44 2.17 BCC lattice (a) showing the ABC (111) plane with the body-centered atom at O and vacancy at V. Atom at O collapsed at ABC triangle (b) thereby forming ω-embryo or activated complex (Adapted from [126]) ..............49 2.18 Concentrations of ω-embryos vs. temperature (Adapted from [126])...................53 5.1 Schematic of growth of the TiB2 layer and the TiB whisker layer (a). Concentration profile of B across the layers (b) ....................................................62 5.2 Comparison of the predicted and the experimentally measured TiB2 thicknesses, after correcting for the TiB2 layer growth due to 5 minutes exposure...................69 5.3 Comparison of the predicted and the experimentally measured TiB thicknesses, after correcting for the TiB layer growth due to 5 minutes exposure....................71 5.4 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 24 hours at (a) 850 °C and (b) 1050 °C ..........................................72 5.5 Comparison of the predicted and the experimentally measured dual (TiB2 + TiB) coating layer thicknesses, after correcting for the TiB2 and the TiB layer growth due to 5 minutes exposure ............................................74 5.6 Total (TiB2+TiB) coating thicknesses obtained in isothermal diffusion treatments plotted as a function of total isothermal exposure time .......................76 5.7 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 3 hours at (a) 890 °C, (b) 910 °C, and (c) 915 °C ..........................78 5.8 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 12 hours at (a) 890 °C, (b) 910 °C and (c) 915 ºC..........................79 5.9 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 24 hours at (a) 890 °C, (b) 910 °C and (c) 915 ºC..........................81 ix No. Page 5.10 The enhanced growth of boride layers near the phase transition temperature, (a) TiB2 layer thickness and (b) the total (TiB2 + TiB) boride layer thickness at different temperatures. A dotted line approximately indicating the expected normal kinetics for 24 hours (without the anomalous contribution), across the region near the phase transition, is drawn to highlight the deviations…………………………………..84 5.11 Higher magnification SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 24 hours at (a) 900 °C [104], (b) 910 °C..............86 5.12 Higher magnification SEM micrograph showing the TiB precipitates in 900 °C/24 hours boriding condition.......................................................................87 5.13 Knoop hardness profile for the (TiB2 + TiB) coating produced under isothermal treatment at 910 °C for 24 hours ..........................................................87 5.14 Illustration of diffusion growth of TiB whiskers near the phase transition temperature (910 °C) in CP-Ti (a). The B concentration profile in growing boride phases into the depth of the substrate (b).....................................................90 5.15 Schematic of the structure of TiB2 interface of unit area that is in contact with certain fractional area (Af TiB) of TiB phase and remaining fractional area (Af Ti) of Ti phase............................................................................91 5.16 The predicted boride layer thicknesses at 910°C with varying area fraction of TiB and Ti phases (a). Comparison of the predicted boride layer growth in Ti at 910°C with and without the anomalous component, along with the experimental data (b). For reference, the predicted and experimental data for 850°C and without the anomalous part are also included……………….98 5.17 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments at 850 °C for (a) 24 hours, (b) 48 hours, and (c) 71 hours...………... 102 5.18 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments at 1050 °C for (a) 24 hours, (b) 48 hours, and (c) 71 hours……..….. 104 5.19 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments at 900 °C for (a) 24 hours, (b) 48 hours and (c) 71 hours…………... 106 5.20 Coating thicknesses obtained for (a) TiB2 and (b) total (TiB2 + TiB) layers in isothermal diffusion treatments plotted as a function of total time……………. 108 x No. Page 5.21 Schematic of temperature profile for single cycle as employed for cyclic boriding with different heat segments………………………………………….. 115 5.22 Variation of surface temperature with time……………………………………. 119 5.23 The subsurface temperature distributions corresponding to specific period of temperature cycle shown in Figure 5.22…………………………………..… 120 5.24 Optical micrographs of samples thermally cycled between 890-910C during B diffusion with 0 minute hold time for total time of (a) 12 hours (b) 18 hours (c) 24 hours (d) Higher magnification SEM micrographs for 24 hours treated sample………………………………………………………………………….. 123 5.25 Optical micrographs of samples thermally cycled between 890-910C during B diffusion with 30 minutes hold time for total time of (a) 12 hours (b) 18 hours (c) 24 hours (d) Higher magnification SEM micrographs for 24 hours treated sample…………………………………………………………………………. 124 5.26 Optical micrographs of samples thermally cycled between 890-910C during B diffusion with 42 minutes hold time for total time of (a) 12 hours (b) 18 hours (c) 24 hours (d) Higher magnification SEM micrographs for 24 hours treated sample…………………………………………………………………………. 125 5.27 Optical micrographs of samples thermally cycled between 890-910C during B diffusion with 60 minutes hold time for total time of (a) 12 hours (b) 18 hours (c) 24 hours (d) Higher magnification SEM micrographs for 24 hours treated sample…………………………………………………………………………. 126 5.28 Total coating thicknesses obtained in cyclic boriding treatments plotted as a function of total exposure time………………………………………….... 128 5.29 Ti-O phase diagram showing the O wt% of grade 2 CP-Ti and the limit temperatures during thermal cyclic experiments………………………………..129 5.30 The O wt% of grade 2 CP-Ti superimposed in the Ti-O phase diagram and the limit temperatures used for new sets of thermal cyclic experiments………….. 131 5.31 Optical (a) and SEM (b) micrographs of TiB coating produced under thermal cycling between 880-920°C for a total time of 24 hours (17 cycles). Optical (c) micrograph of TiB coating produces under thermal cycling between 880-940C for 24 hours………………………………………………… 133 xi xii No. Page 5.32 Optical (a) and SEM (b) micrographs of TiB coating produced under thermal cycling between 880-920°C for a total time of 48 hours (34 cycles). The SEM montage of micrographs in (b) illustrates the TiB whisker structure as well as the fine structure of the matrix consisting of irregular TiB particles precipitated out of the α matrix ............................................................................136 5.33 Optical (a) and SEM (b) micrographs of TiB coating produced under thermal cycling between 880-920°C for a total time of 71 hours (50 cycles). The SEM montage of micrographs in (b) illustrates the TiB whisker structure as well as the fine structure of the matrix consisting of irregular TiB particles precipitated out of the α matrix........................................137 5.34 Optical micrographs of TiB coating produced under thermal cycling between 880-940C for a total time of (a) 48 hours (30 cycles) and (b) 71 hours (45 cycles)..............................................................................................................138 5.35 TiB coating thicknesses obtained in cyclic as well as isothermal diffusion treatments plotted as a function of total thermal exposure time ...........................139 5.36 Knoop hardness profile for the TiB coating produced under thermal cycling between 880-920C for a total time of 71 hours (50 cycles). In the figure, the hardness of Ti, (~300 Kg/mm2) TiB (~2000 Kg/mm2) and that of the TiB2 (~3500 Kg/mm2) are indicated for reference ........................................................141 ACKNOWLEDGMENTS I would like to express my sincere gratitude towards Dr. K.S. Ravi Chandran for providing me an opportunity to work on this project and for his patient instruction and guidance and in aiding me to grow as a researcher and a writer. I am also grateful to Mr. Anthony Sanders for his advice, help and useful discussions during the course of the work. I am also thankful to Dr. Zhigang Z. Fang, Dr. Michael L. Free and Dr. Sivaraman Guruswamy for serving on my supervisory committee. Special thanks should be given to my friend and colleague Dr. Nishant Tikekar for useful discussions and training me with various equipments in the initial phase of my work. My lab mates, Curtis Lee, Shawn Madtha, Madhu and Paul Chang also deserve a special mention for their constant help in my work. I would also like to thank Karen Haynes and Kay Argyle for administrative support. This work was completed under the financial support provided by the National Science Foundation and Ortho Development Corporation. Finally, I am extremely grateful to my parents for their continued faith in my abilities and all forms of support, of which I have been the fortunate recipient throughout my life. CHAPTER 1 INTRODUCTION 1.1 Background Surface modification techniques are commonly employed to engineering components to enhance surface properties such as hardness, wear resistance, oxidation and corrosion resistance. Many engineering materials are coated to improve their performance in mechanical and biomedical applications.1, 2 By appropriate coating processes, surface properties can be modified to suit a given application while preserving the properties of the core. Coating concepts such as high conductive coating for electrical applications, noncorrosive coatings for corrosion resistance, and wear resistance coating to resist abrasion are now common.3-7 Diffusion surface hardening of metals has emerged as one of the commonly used techniques to create a hard surface layer on metals like steel, aluminum etc.8-11 This is performed by the diffusion of elements such as carbon, nitrogen, oxygen, chromium, aluminum, or boron, and the respective processes are termed as carburizing, nitriding, oxidizing, chromizing, aluminizing, and boronizing/boriding. The substrate to be hardened is surrounded by a source containing the element to be diffused and heated to high temperature (generally > 0.5 Tm of the substrate). The coating thickness obtained is generally determined by diffusivity of the element in the substrate at that temperature. 2 Titanium (Ti) and its alloys have been used extensively in aerospace, chemical and biomedical industries owing to its low density, high stiffness, and excellent corrosion/oxidation resistance. However, its performance in mechanical/contact applications involving wear is poor because of its low strength, low thermal conductivity and high work hardening rate. One way to improve its wear resistance is by the application of a wear resistant coating.12-13 Physical vapor deposition (PVD)14, chemical vapor deposition ( CVD)15, ion implantation16 and laser and electron beam treatments17 are some of the techniques that have been pursued to increase the wear resistance of titanium and its alloys. However, the coating thicknesses obtained by these above mentioned processes are relatively small. For example, titanium nitride (TiN) coatings deposited by PVD are about 10μm thick and hence it is difficult to use in heavy duty applications such as gears, ball bearings, cams and orthopedic implants.18 Given that these applications are demanding and that PVD/CVD processes are expensive, there is a general need to develop simpler and more cost effective coating processes. Diffusion-based processes such as carburizing of steel and nitriding of titanium are relatively more attractive because of the process simplicity, low cost, and applicability to complex component shapes. Phase diagrams of different titanium systems such as Ti-C, Ti-N, Ti-O and Ti-B reveal that hard compounds like TiC, TiN, TiO2 and TiB2 can be formed on the surface of titanium by high temperature diffusion. Among these, Ti-B system is very attractive because of the possibility to form a double layer of titanium diboride (TiB2) and titanium monoboride (TiB).19 Different techniques can be employed for boriding titanium, but solid state boriding, also known as pack boriding, is one of the simplest and most cost effective methods. In our laboratory, pack boriding of 3 titanium and its alloys have been studied extensively and boride coating layer of about 50 μm have been obtained on the surface of Ti.20 In most component finishing and polishing processes after surface treatment, a substantial amount of the hardened surface layer needs to be removed to provide a good surface finish. This necessitates coating depths in excess of 50 μm such that a significant amount of the hardened layer is left to protect the substrate after finishing. New methods that can provide deeper boride layers need to be developed. A unique characteristic of Group IV HCP transition metals like titanium is that they show anomalous diffusion characteristics near the phase transition temperature.21, 22 The phase transition involves transformation from low temperature closed packed hexagonal (HCP) phase to high temperature body centered cubic (BCC) phase. In these metals, near the phase transition temperature, the self diffusivities are anomalous in the sense that they are relatively higher than at other temperatures and thus do not conform to the usual descriptions based on Arrhenius law of diffusion. The Arrhenius plots for these metals are characterized by an upward curvature near the phase transition, although the degree of this curvature or deviation seems to vary between metals. On this basis that Ti shows enhanced (anomalous) self-diffusion near the phase transition temperature, one of the hypotheses of this work is that the diffusivity enhancement should cause rapid ingress of B atoms into Ti, thereby accelerating the growth kinetics of the hard boride surface layers. A theoretical model based on error-function solutions of Fick's second law of diffusion needs to be developed to quantitatively illustrate the combined effects of the normal B diffusion in the TiB phase and the anomalous B diffusion in Ti phase in accelerating TiB layer growth. 4 The second objective of this research is to demonstrate the feasibility of accelerating the boride layer growth in Ti by the application of a novel process called "cyclic-phase-change-diffusion (CPCD)." The hypothesis is that if reversible phase transformations were induced in titanium surface layers during B diffusion, the transformation could effectively "pump" more B into subsurface layers and can lead to increased coating thickness. This should be encouraged by the low solubility of boron in α phase compared to that in β phase of titanium.23 Therefore, cyclic thermal boron diffusion across the phase transition temperature and its effectiveness in accelerating the boride coating growth is also investigated in this work. CHAPTER 2 LITERATURE REVIEW 2.1 Structure and properties of titanium At room temperature the thermodynamically stable structure of titanium is alpha (α) phase which is HCP as shown in Figure 2.1. The measured lattice parameters c and a are 0.466 nm and 0.295 nm, respectively, and the c/a ratio (1.59) is a little less than the ideal value for HCP metals (1.66), thus pure titanium has high room temperature ductility.24 Titanium undergoes polymorphic transformation from HCP (α) phase to BCC (β) phase upon heating through 882.5 °C.25-26 The high temperature BCC phase of titanium is characterized by the lattice parameter ‘a' (0.332 nm at 900 °C). The structure and properties of titanium and its alloys are significantly influenced by the presence of interstitial elements C, O, N and B. These interstitial elements increase the strength and decrease the ductility of titanium even at low concentrations, as shown in Figure 2.2. The strongest effect on yield strength is caused by the presence of oxygen-an increase in O from 0.18 wt.% to 0.4 wt. % increases the yield strength from about 170 MPa to about 480 MPa. As shown in Figures 2.3-2.5,27 presence of O, N and C in titanium also increases the α to β phase transition temperature. In particular, a small increase in O and N can impart a noticeable increase in transition temperature, 6 Figure 2.1 HCP crystal structure of Ti Figure 2.2 Variations in tensile properties of CP-titanium with increasing O, N and C content (Adapted from [27]). (1010 − (1011 − − ) ) 7 600 700 800 900 1000 1100 1200 0 0.2 0.4 0.6 0.8 1 α+β to β phase boundary α to α+β phase boundary α field α+β field β field Oxygen( wt. % ) Figure 2.3 The α and β phase fields of Ti as affected by the O content (Adapted from [27]) 700 800 900 1000 1100 0 0.2 0.4 0.6 0.8 1 Carbon (wt. %) β+TiC β α α+TiC Figure 2.4 The α and β phase fields of Ti as affected by the C content (Adapted from [27]) 8 600 700 800 900 1000 1100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Nitrogen (wt. %) β α+β α Figure 2.5 The α and β phase fields of Ti as affected by the N content (Adapted from [27]) broadening the α + β phase field. The phase diagrams shown indicate this broadening in terms of two solvus lines. The transition from the complete α phase to the α + β phase field is demarcated by the α → α + β solvus line and the subsequent transition from the α + β phase to complete β phase is marked by the α + β→ β solvus line. In addition to the interstitial alloying elements discussed above, many alloying elements form substitutional alloys with titanium. Depending on the alloying element added, it can either increase or decrease the α/β phase transition temperature. Elements such as Sn, Al and O increase the transformation temperature and hence are known as α- stabilizers.25, 28 On the other hand elements such as Fe, Mo, V decrease the transition temperature and hence are known as β-stabilizers.29 Depending on the elements added, commercially available titanium and its alloys are classified as α, β and α + β alloys. A brief discussion of these different types of Ti-alloys is presented below. 9 2.1.1 α-alloys Unalloyed as well as alloys of titanium which retain the HCP structure at room temperature are called α alloys. These alloys can contain substitutional elements like Al, Sn, and interstitial elements like O, C and N. These alloying elements are soluble in the α-matrix and stabilize the HCP phase. The strength and ductility of these alloys are influenced by grain size, interstitial contents and any dislocation state caused by hot/cold working. 2.1.2 β-alloys Upon addition of transition elements like Fe, Mo, V, Nb, Ta etc., the BCC phase of Ti is either partially or fully stabilized at room temperature depending on the total amount of β-stabilizing elements. These alloys can be further classified into two categories: metastable β-alloys and stable β-alloys. In metastable β-alloys, alloying additions do not stabilize the β-phase completely in the matrix at the room temperature. In stable β-alloys, the microstructure is completely stabilized with β phase at room temperature. 2.1.3 α + β alloys Most of the commercial alloys of titanium have alloying elements that stabilize both α and β phases, with the relative proportions of the phases being determined by the total content of each group of α or β-stabilizing elements. Further, there are two subdivisions of these α + β alloys, near α alloys and near β alloys. In near α alloys, a relatively higher amount of α-stabilizing alloying elements is present and the microstructure is predominantly α phase with negligible or very small amount of β phase. 10 In the case of near β alloys, the microstructure is made of mostly β phase due to a relatively higher amount of β- stabilizing alloying elements. 2.2 Surface performance of titanium It is well known that titanium and its alloys undergo severe wear and surface degradation under contact and/or sliding conditions. In tribology, there are specific terms for each surface degradation process and they include wear, fretting, gouging/galling and seizure. Wear is more of a generic term that refers to removal of material from either surfaces when the surfaces are in contact.30 The ASTM definition31 of galling is " a form of surface damage arising between sliding solids, distinguished by macroscopic, usually localized, roughening and creation of protrusions above the original surface. It often includes plastic flow, material transfer, or both." Care is required to discriminate whether a material has undergone normal wear, galling or seizure.32 Figure 2.6 shows schematically some of the differences among these phenomena.32 Galling is characterized by the formation of excrescence. When the running clearance for the material outgrowth is limited, these excrescences rise above the surface of the materials causing seizure as shown in Figure 2.6. The process and the factors influencing galling have been documented in the literature.33-35 Galling primarily depends on the frictional forces between the surfaces in contact. Low frictional forces between the sliding surfaces lead to lesser galling. In counterformal contact conditions, flow of materials in lateral directions also leads to lesser galling. Other important factors that reduce galling are rapid work hardening,36 high hardness37-39 and low surface energy.40 It has also been witnessed that galling in 11 Figure 2.6 Various types of wear upon rubbing a flat ended pin on solid surface (Adapted from [32]) Burnishing - rubbed area visible, but only after a surface texture change Scaring - macroscopic scratches are visible Wear - can measure material removal Galling - material flows up from the surface forming macroscopic excrescences Transfer - Platelets of material A are adhered to material B A B 12 high hardness37-39 and low surface energy.40 It has also been witnessed that galling in pure metals can occur at low contact stresses.41 Seizure is defined as the sticking of two surfaces upon sliding against each other, due to relative motion between them, under load.42 The relative motion causes interfacial adhesion between the surfaces. Seizure in Ti can cause damage to a component in service in two ways.42 The first one is called the fretting-fatigue where the sliding motions between the surfaces introduce crack nucleation and subsequent crack growth causing failure. The second type of seizure is known as the fretting-wear. It involves loss of material from the sliding surfaces under the influence of external vibrations. Table 2.1 listed some values of the coefficient of friction and the degree of wearing when titanium is in contact with itself and with other metals. 2.2.1 Coatings on titanium Surface modification of Ti and its alloys is often performed to improve their performance during service.43 One such surface modification technique is the creation of some hard, adherent and wear resistant surface coatings by diffusion. This is done by diffusing interstitial elements like O, C, N, or B into the surface of Ti.44 These interstitial Table 2.1 Friction and wear data for various metals in contact (Adapted from [30]) Metals in contact Coefficient of friction Wear (g/cm of wear track) Titanium on titanium 0.47 2.5 E-6 Mild steel on mild steel 0.53 7.5 E-6 Stainless steel on stainless steel - 2.5 E-6 Copper on copper 1.1 10 E-6 Titanium on mild steel 0.25 10 E-7 Titanium on copper - 6 E-7 13 elements, O, C, N or B react with Ti to form oxide, carbide, nitride, or boride layers, respectively, on the surface of Ti.44 These surface layers are hard and impart improved wear resistance. Some of the coating technologies as employed to Ti will be discussed briefly here. 2.2.2 Titanium nitride coatings The Ti-N binary phase diagram is shown in Figure 2.7.45 Nitrogen has ~ 8 % solid solubility in α- titanium at 1050 °C and it enables the formation of nitride layers on the surface to improve its hardness and wear resistance significantly. Hence, nitriding is used often in industry to coat titanium and steel surfaces for various applications needing improved wear resistance.46-49 Some of the major nitriding techniques as applied to titanium are elucidated below. 2.2.2.1 Plasma nitriding. Plasma nitriding is a research and development type process often studied to coat titanium surfaces.47, 48 It is mainly done by submerging the substrate in a bath of nitrogen ions generated by radio-frequency plasma. When a very high negative potential is applied to the substrate, these ions are accelerated towards the target from the plasma. These ions then react with titanium to form the nitrided layers at the surface. It is generally done in a temperature range between 400 to 950 °C and for time periods of a few minutes to several hours. The plasma nitriding process in Ti-6Al- 4V alloy can create a compound layer of about 50 μm in depth with microhardness values in the range of 600-2000 HV. 44 2.2.2.2 Ion-beam nitriding. Ion beam nitriding process involves accelerating nitrogen ions to a very high velocity. The high kinetic energy of the ions enables them to penetrate deeper into the titanium substrate. The process is performed in a temperature 14 Figure 2.7 Ti-N phase diagram (Adapted from [45]) range of 500 to 900 °C for 30 minutes to 20 hours in an Ar atmosphere. A compound titanium nitride layer of about 5-8 μm in thickness and having microhardness values in the range of 800-1200 HV was achieved in Ti-6Al-4V alloy.50-52 2.2.2.3 Laser nitriding. A very high energy focused laser beam is used to melt the surface of the titanium substrate. The molten depth can range from 1-1.5 μm,53-56 to as high as 400 μm44 in order to obtain thick hardened layer for applications needing improved wear resistance. When the melted layer is exposed to a nitrogen gas environment, titanium nitride compound layers are formed with a very good metallurgical bond between the layer and the substrate. Microhardness values in the range of 900-1300 15 HV have been obtained on Ti-6Al-4V alloy. However, this process is expensive and restricted to limited substrate geometries. 2.2.2.4 Gas nitriding. Gas niriding is a relatively easy process to implement, and it is well suited for complicated geometries. Titanium is nitrided with nitrogen gas or a mixture of nitrogen and hydrogen/argon in a vacuum chamber. Hardened coatings of thickness of about 2-15 μm and with microhardness values in the range of 450-1800 HV have been obtained on Ti-6Al-4V alloy. A disadvantage associated with this process is that it reduces the fatigue life of the substrate.49, 57 2.2.2.5 Microstructure of nitrided layers. The ingress of nitrogen in α-Ti substrate leads to the formation of an interstitial solid solution. Diffusion of nitrogen into the Ti leads to the formation of compounds such as Ti2N and TiN. Ti-N phase diagram (Figure 2.7) reveals that above 12.7 wt% N and below 1100 °C, Ti2N is predominantly formed. However, as the N content increases, TiN starts forming. Thus, nitriding of titanium produces a thin layer of TiN on the surface. Below the TiN layer, a thicker compound layer of Ti2N is formed and below which a diffusion zone of nitrogen-strengthened titanium exists. Figures 2.8(a) and (b)49, 57-59 show these layers of TiN, Ti2N and diffusion hardened layer in α-titanium. The coating layer thickness (total added thicknesses of TiN and Ti2N) varies between 1 to 50 μm while the diffusion hardened zone can be up to hundreds of micrometers. 2.2.3 Modeling of kinetics of titanium nitride coatings Several successful attempts have been made to model the growth kinetics of nitride layers in Ti and its alloys.47-49, 60 These models are formulated to extract anyone of the two types of specific information: i) With the known diffusivities of the diffusing 16 (a) (b) Figure 2.8 SEM micrographs of Ti-6Al-4V, plasma nitrided at (a) 900 °C for 6 hours and (b) 900 °C for 14 hours (Adapted from [49]) 17 species in different phases, estimation of coating layer thickness for a fixed treatment temperature and time or ii) estimation of diffusivities of the diffusing species in different phases knowing the coating layer thickness at a fixed temperature and time. The basis of one such model will be briefly described in this section. Taktak et al.60 studied the diffusion kinetics of plasma nitriding in Ti-6Al-4V alloy and modeled the nitride layer growth kinetics using semi-infinite, multiphase, volume diffusion characteristics. Figure 2.9 illustrates the partial Ti-N phase diagram along with the nitrided layers formed; δ and ε represent the TiN and Ti2N layers, respectively, followed by the α and β matrix of titanium. The corresponding nitrogen concentrations at the interfaces are also indicated in the figure. The change in nitrogen concentration with time is given by Fick's second law as, ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ ∂ ∂ = ∂ ∂ x D C t x C (2.1) where C is the concentration at distance x from the surface and D is the diffusion coefficient. From Fick's first law, diffusion fluxes at each phase boundary are given as: For the δ/ε interface, δε δ δε δ x k x C J D = − ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ = − (2.2) For the ε/α interface, εα ε εα ε x k x J D C = − ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ = − (2.3) 18 Figure 2.9 The schematic representation of the partial Ti-N phase diagram and the associated diffusion layers formation in Ti-6Al-4V alloy (Adapted from [60]). αε α αε α x k x J D C = + ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ = − (2.4) For the α/β interface, αβ α αβ α x k x C J D = − ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ = − (2.5) βα β βα β x k x C J D = + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ ∂ ∂ = − (2.6) 19 Here , and are the respective diffusion coefficients of nitrogen in TiN, Ti2N, and are the fluxes from the negative and positive sides of a particular interface. C is the concentration of a particular phase. In general, the solution of Fick's second law, satisfying Eqn. (2.1) is, δ D α ε D , β α D phases. β D J − and J + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ = + Dt C x t A B erf x i j ( , ) (2.7) Here and are constant associated with each phase. From Figure 2.9, the values of are as follows, , (2.8) , (2.9) , (2.10) , (2.11) Incorporating these boundary conditions as well as the flux equations, the solution for Fick's second law can be modified to get the interface velocities for each interface. The δ/ε interface velocity equation, as derived by the author, is, i A and B j B i A j S A = C δ δ δε B C C S = − ε εδ A = C ε εδ εα B = C − C α αε A = C α αε εβ B = C − C β βα A = C O B = C − C β βα 20 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ D t k erf D t k erf D t k D t k D Z D B D t k erf D t k D t k Z B ε εδ ε εα δ δε ε εα δ δε ε ε δ δε δ δε δ δε δε δ π π 2 2 2 2 exp 2 2 2 exp 2 2 (2.12) where, Similar equations were derived for the ε/α and α/β interfaces. These equations were numerically solved to estimate the diffusivities of nitrogen in TiN, Ti2N and α phases. Also the activation energies for nitrogen diffusion in TiN and Ti2N were determined through this modeling work. The estimated diffusivities of nitrogen agree reasonably well with the experimentally measured diffusivities in the respective phases. 2.2.4 Titanium oxide coatings Titanium has the general tendency to form an oxide layer at surface, even at room temperature.61 Although an oxide layer in titanium imparts improved tribological properties,44 it makes it more difficult to create titanium coatings with other elements such as nitrogen or boron. In the bulk, oxygen increases the strength level of α-titanium by solid solution strengthening. The oxidation kinetics have been extensively studied in the past.61-69 It was reported that oxidation of titanium below the phase transition temperature, i.e., in the α field, produced very limited coating growth. When oxidation was done in the β field, noticeable hardening and coating growth were observed. However, the high temperature in the β field also caused severe embrittlement of the oxide layer. Hence, the challenge has always been to form an appreciable oxide coating δε δε εδ Z = C −C 21 on the surface without causing embrittlement and degradation of the oxide layer. Ti-O phase diagram indicates about 3.5% solid solubility of oxygen in α-titanium at 400°C as shown in Figure 2.10.70 Oxygen atoms occupy the interstitial sites in α- titanium. However, upon exposure to high temperature, the titanium surface will form a porous, poorly adherent and thick oxide scale with a solution hardened diffused layer below the oxide layer. Generally, oxide coatings in titanium surface are grown in the temperature range of 850-1000 °C in air at a pressure range of 10-3 to 10-2 mm of Hg.63 At such high process temperature, a hardened surface layer is formed together with a considerable amount of scaling.63 The scale reduces the coefficient of friction.63 To avoid Figure 2.10 Ti-O phase diagram (Adapted from [70]) 22 severe scaling, controlled oxidation of Ti in molten salts was attempted at a lower temperature range.44 For example, titanium pistons are oxidized in controlled, molten salt atmosphere and in a temperature range of 600-900 °C for 2 to 4 hours to avoid excessive oxide layer formation.68 Several other α-Ti, α + β-Ti and β-Ti alloys had been oxidized and tested for wear and biomedical applications.61-69 Ti-22V-4Al alloy, upon oxidation, produced better wear resistant coating than nitriding or carburizing.67 Oxidation of Ti- 6Al-7Nb alloys resulted in maximum surface hardness of 900 HV with hardened subsurface layer up to 50 μm in depth.44 A novel gas based technique developed for treating Ti-6Al-4V alloys is the tifran∗ process.66 Reduction in the wear rate in gears treated with this process has been reported.66 However, the maximum hardness obtainable through titanium oxide coatings (1000 HV) is significantly less than the maximum hardness achievable in titanium nitride (Ti2N) coatings (1500 HV).44 2.3 Boriding of metals Conventional surface hardening treatments where elements are diffused atomistically into a substrate, for example carburizing, nitriding, or carbo-nitriding usually result in a surface hardness level of 800-1100 HK in steels. However, applications requiring very hard surfaces demand hardness as high as 1800-2000 HK. Boride layers can yield hardness levels of this order.71-75 Boron can readily diffuse in metals such as iron/steel and nickel and can produce a much harder surface than that of a carburized surface. In steels, however, thick boride layers are not reliable as the diffused ∗ Tifran is a gaseous oxidation process employed to Ti and its alloys at a temperature in the range of 500 to 725°C for 0.5 to 100 hours of treatment time. The treatment temperature and time are adjusted to get an adherent surface compound layer of atleast 50% by weight of oxides of Ti to a depth of about 0.2 to 2 μm on a solid solution strengthened diffused zone of diffusing element oxygen penetrating to a depth of 5 to 50 μm. This is a patented process and the brief detail obtained from the website : http://www.freepatentsonline.com/6210807.html 23 coating layer of FeB formed during boriding has a different coefficient of thermal expansion from that of the Fe substrate which can eventually lead to cracking of the coating. When controlled boriding is performed, hard and durable Fe2B layers of about 100 μm in thickness can be created. Boriding can be done in gas phase, molten salt, or solid state pack medium. Gaseous boriding agents like KBF, NaB, Na2B4O7, B2H6, and BCl3 are commonly employed for boriding.76 In these processes, the boron source gas is mixed with some reducing agents to use as a boriding medium. Gas boriding produces a very uniform boride layer on the substrate in relatively lesser time. The boriding agents are, however, hazardous and expensive. Liquid phase boriding is done normally in Na2B4O7, HBO2 and NaBF4 salts. In a study by Belyaeva et al.,77 liquid phase boriding on steel was done in a liquid melt containing 60-80% borax and a 20-40% boron containing substance like boron carbide, ferroboron, or calcium hexaboride. It was found that a liquid melt containing 70% borax and 30% boron carbide produces a boride coating of about 150 μm deep into a steel substrate at 1000° C for 6 hours. Liquid phase boriding can be beneficial over solid state because of the higher chemical activity of the boron source in the liquid melt.78 But the main disadvantages associated with these processes are to achieve good fluidity in the liquid bath and very high operating cost.78 The solid state boriding substances include amorphous boron, ferroboron, and B4C with theoretical boron content 95-97 wt%, 17-19 wt% and 77.28 wt%, respectively. Amorphous boron proves to be a more effective boriding medium than crystalline boron.79 This may be due to the greater surface area of amorphous boron as determined 24 by Haag,80 and listed in Table 2.2. Generally, solid state boriding is relatively easy to implement and somewhat less expensive. Solid state boriding had been performed in vacuum as well as inert atmosphere. Minkevic81 argued that such atmosphere is necessary for boriding, but this suggestion was disputed by Kunst and Schaaber (quoted in [82]). The authors reported higher coating thicknesses of the boride layers when boriding was done with amorphous boron in the absence of vacuum. For example, boriding of Armco iron at 1000 °C for 3 hours resulted in a coating thickness of about 200 μm at atmospheric pressure, whereas at a vacuum of 10-5 Torr, the coating thickness was limited to 30-40 μm. A great variation in coating thicknesses has also been observed with varying compositions of the powder mixture employed in solid state boriding.75 A mixture of 33% amorphous boron, 65% Al2O3, and 2% NH4Cl resulted in layer thickness of about one-fourth of the thickness obtained by pure amorphous boron. Optimized power composition is necessary for enhanced coating growth in solid state boriding. Table 2.2 List of boron powders and their respective surface areas Powder Purity (%) Surface area (m2/g) Crystalline boron 99 < 1 Amorphous boron 95-97 12-15 Amorphous boron 99.9 24 25 2.3.1 Structure of boride layers on iron/steel When steel is borided, it forms a whisker layer of Fe2B on the surface. FeB, although a thermodynamically feasible phase, has the tendency to crack because of thermal coefficient mismatch. Diffusion of B in steels exhibits a parabolic relationship with time suggesting that it is diffusion controlled process.75 Figure 2.11 (a) and (b) shows the microstructures of steels borided at different temperature and time. The effect of alloying elements on the thickness of boride layers on steel has been studied.75 It has been found that steels having a smaller amount of alloying elements exhibit a relatively higher coating thickness.75 Figure 2.12 shows the effect of different alloying elements on the boride coating thicknesses in steel. It is evident from the figure that as the alloying content increases the coating thicknesses of the boride layers decreases. There are some exceptions to this general trend, for example, up to around 7% addition of Mn in steel did not affect the coating thickness.83 Blanter and Basedin84 did boriding experiments in alloyed steels in a mixture of 60% borax and 40% boron carbide for 5 hours at 1100 °C. The authors reported relatively lesser boride coating thicknesses in alloyed steel compared to that of unalloyed steels. Lachtin and Peelkina83 reported that high alloyed steel borided in a diborane hydrogen mixture in a ratio of 1:25 imparted a lesser coating thickness with small amount of Cr (2%) and Ni (2%) whereas chrome steel exhibited increased boride layer thickness even after addition of 2.2% W. So, boride coating thickness level achievable in steel surface depends on type of alloying elements present as well as the quantities of such elements. 26 (a) (b) Figure 2.11 Microstructure of steels boronized at 900 °C (200X) (a) Steel St 37 boronized in Ekabor for 10 hours (200X), (b) Steel C15 boronized in Ekabor for 4 hours (Adapted from [75]) 27 Figure 2.12 Variation of boride coating thicknesses obtained in the iron substrate with different proportions of alloying elements (Adapted from [75]). 2.3.2 Modeling of boride growth in iron/steel The FeB/Fe2B layer growth kinetics during boriding of Fe or steel has been modeled in a number of studies.85, 86 In one such study by Yu et al.,85 the dual boride layer formation in mild steel was modeled based on six elementary physico-chemical processes: 1. B (free)→ B (adsorption) 2. B (adsorption) + Fe → FeB if >0.5 B (adsorption) + 2Fe → Fe2B if 0.33< <0.5 B ads C B ads C 28 B/ Fe2B interface; 3. B atoms jump through FeB or Fe2B lattice from high to low chemical potential side 4. Fe2B +B → 2FeB at FeB/ Fe2B interface; 5. 2Fe + B → Fe2B at Fe2B/Fe interface; 6. 2FeB → Fe2B + B phase transformation. For boride layer growth, one or several of these above mentioned steps can be the rate-determining steps. In this model, however, the growth simulation was done with the following assumptions: (i) the interface reactions are sufficiently fast so that the B diffusion in step 3 is the rate determining one, (ii) concentration of B in steel matrix is negligible, and (iii) the B diffusion co-efficient is constant within the diffusion layer. The total boride layer growth is dominated by the B diffusion through three phases: FeB phase, Fe2B phase and the Fe phase. In general, Fick's second law can be applied for the diffusion of B through these phases as, 2 2 x D C t C i ∂ ∂ = ∂ ∂ (i = 1 for 0<x<u and i = 2 for u<x<v) (2.13) where and are the diffusion coefficients of B in FeB and Fe2B phases. The variables u and v are the locations of the FeB/Fe2B and Fe2B/Fe interfaces. Before the start of boriding, at x = 0 and t < 0. (2.14) The B concentration profile from the surface to the depth of the steel sample is illustrated in Figure 2.13. The upper and lower limit of B concentrations in FeB and Fe2B phases are 1 D 2 D 0 2 = Fe B C , =0 FeB C 29 Figure 2.13 B concentration profile used for the modeling (Adapted from [85]) designated as and respectively. From Figure 2.13, the boundary conditions are as follows, for >0.5 at x = 0, (2.15) for >0.5 and with FeB phase at x = u - 0, (2.16) for 0.33< <0.5 and without FeB phase at x = u + 0, (2.17) FeB up C , FeB Clow , Fe B up C 2 Fe B low C 2 FeB up C = C B ads C FeB low C = C B ads C Fe B up C = C 2 B ads C 30 for <0.33 at x = v - 0, (2.18) at x = v + 0 (2.19) In an infinitesimally small time interval ‘dt', the growth of FeB and Fe2B layers will occur by simultaneous consumption of Fe2B and Fe at FeB/Fe2B and Fe2B/Fe interfaces, respectively. Considering that ‘du' and ‘dv' are the respective extensions of FeB and Fe2B layers in time interval ‘dt' and since B should be conserved at the FeB/Fe2B and Fe2B/Fe interfaces, ) du = Fe B low C = C 2 B ads C C = 0 ( FeB low C - Fe B up C 2 dt x D C x D C u u ⎥⎦ ⎤ ⎢⎣ ⎡ ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ + ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ − −ε +ε 1 2 , (2.20) Fe B dv = low C 2 dt x D C v ⎥⎦ ⎤ ⎢⎣ ⎡ ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ − −δ 2 (2.21) Numerically solving Eqns. (2.20) and (2.21), the depth to which coating layers, FeB/Fe2B, penetrated were calculated. Numerically calculated values were in reasonable agreement with the experimentally found ones. 2.3.3 Boriding of titanium Boriding of titanium and its alloys has been studied in our research group for the last couple of years 87-89 in an effort to create hard TiB2/TiB layers on the surface of Ti. According to the Ti-B phase diagram90 shown in Figure 2.14, three hard compounds exist: TiB at 18-18.5 wt%, Ti3B4 at 22.4 wt% and TiB2 at 30.1-31.1 wt% boron compositions. These compounds are characterized by very high hardness (>20 GPa in 31 Figure 2.14 Ti-B phase diagram (Adapted from ASM International [90]) HV for TiB and >30 GPa in HV for TiB2) and their crystal structures are B27, D7b, and C32, respectively.91 The Ti-B phase diagram also reveals that TiB forms by peritectiod reaction, TiB2 by congruent melting, and Ti3B4 by peritectic reaction. A substantial amount of research has been performed to study the morphologies, crystallographic structures, and mechanical properties of these borides.92-95 Sahay et al.92 studied the formation and morphology of TiB whiskers that are formed by hot iso-static pressing of different proportions of Ti and TiB2 powders. It was found that at low volume fraction of TiB (0.3), the whiskers are randomly oriented thin needle shaped ones with high aspect ratios. As the volume fractions are increased (0.92), the TiB whiskers became 32 even finer with whisker diameters approaching 10 nm. The crystal structures of the two titanium borides, TiB and TiB2, are based on the same building block which is a trigonal prism.91 A boron atom lies at the center of the trigonal prism having six titanium atoms at the corners, as shown in Figure 2.15 (a). The B27 structure of TiB consists of columnar arrays of triangular prisms sharing only two of their three rectangular faces with the neighboring prisms, as illustrated in Figure 2.15 (c). This stacking leads to the formation of a zig-zag chain of boron atoms along the [010] direction as shown in the Figure 2.15 (c). The rhomboid shaped cross sectional area in the figure is the boron-free pipe of titanium formed when these prisms of TiB are connected at the edges. The projection of TiB structure on the (010) plane is shown in Figure 2.15 (e). On the other hand, the C32 structure of TiB2 is formed by the vertical stacking of prisms in a closed packed array. Here the alternate planes of Ti and B are formed by stacking the trigonal prism in such a way that the prisms are sharing all their faces with the neighboring prisms as depicted in Figure 2.15 (b). The (0001) projection of the C32 structure is shown in Figure 2.15 (d). Table 2.3 summarizes the crystal structures, lattice parameters and fractional co-ordinates of atoms in TiB and TiB2. Previous research has documented the orientation relationship between TiB and α-Ti, β-Ti and TiB2. Hyman et al.96 reported the following two orientation relationships between TiB and α-Ti, ; 001 [1011]α − − TiB ( ) α 010 {1210} − TiB ( ) α 010 {1120} − TiB ; α 001 [0001] TiB 33 TiB2 (AlB2) (a) TiB (FeB) Figure 2.15 Crystal structures of TiB2 and TiB (Adapted from [91]) (b) (c) (d) Ti (e) B 1/2 0, 1 Ti 3/4 1/4 B 3/4 1/4 34 Table 2.3 Crystal structure, lattice parameter and fractional coordinates in TiB and TiB2 (Adapted from [91]) Phase Structure / Space group Unit Cell Atomic positions TiB Orthorhombic / Pnma a = 6.12, b = 3.06, c = 4.56 Ti: 4c,m, x = 0.177, y = 1/4, z = 0.123 B: 4c,m, x = 0.029, y = ¼, z = 0.603 TiB2 Hexagonal / P6/mmm a = 3.03, c = 3.23 Ti:1a, 6/mmm, x = 0, y = 0, z = 0 B: 2d, 6m2, x = 1/3, y = 2/3, z = 1/2 Fan et al.97 also reported that the same orientation relationship exists between TiB and α-Ti. The direction of the TiB whisker along the B-chain, [010], is always parallel to the closed-packed direction of α-Ti, , in the basal plane. However, the TiB whisker can grow parallel to any of the three directions, thereby giving rise to three possible variant directions of TiB in α-Ti matrix. The orientation relationships between TiB and β-Ti are,94 (100)TiB || (100)β-Ti; [010]TiB || [010]β-Ti (100)TiB || (110)β-Ti; [010]TiB || [001]β-Ti (100)TiB || (112)β−Ti ; [010]TiB || [111]β-Ti TiB exhibits three specific orientation relationships with β-Ti. Li et al.98 showed that the TiB/β-Ti interface along [010]TiB || [111]β-Ti is parallel to (100)TiB || (112)β-Ti. The ⟨ ⟩α − 1120 ⟨ α ⟩ − 1120 35 TiB/β-Ti interface is smooth, sharp, and free from any interfacial phase. Prangnell et al.99 reported orientation relationships between TiB and TiB2 as: 2 [001] 1120 TiB TiB − and 2 [100] [0001]TiB TiB The long, needle shaped morphology of TiB whiskers is considered to be the result of B diffusion along the [010]TiB direction.97 The relatively faster diffusion along the [010]TiB direction is attributed to the continuous B-B bond in this direction. It has also been reported that the diffusion along the [010] longitudinal direction of TiB is about 10 times higher than the other transverse direction leading to a needle shaped morphology of the TiB whiskers.97 Although no detailed B diffusion studies have been performed in TiB, Schmidt et al.100 have performed isotropic diffusion studies using 10B isotope in TiB2. They reported that the B self-diffusivities in TiB2 were of the order of 10-19 - 10-23 m2 /s in the temperature range 800-1200 °C. The author also pointed out the possibility of large error (60-80%) associated with the B diffusivities in this study which may be for two reasons. First, a relatively rough incoherent surface makes it difficult to make precise diffusivity measurements. Second, because of the small penetration depth of the diffusion profile (<500 nm), large error might have resulted in the diffusivity calculations when the diffusion profile is compared with the tracer isotope distribution prior to the diffusion anneal. From the perspective of boride coatings growth on titanium, diffusivities of B in TiB and TiB2 at a particular temperature would determine the overall coating thickness obtainable at that temperature. Fan et al.97 reported the approximate diffusion coefficients of B in TiB and TiB2 at 870 °C and 970 °C as 87.59×10−16 m2 /s, 438.8×10−16 m2 /s and 36 1.91×10−16 et al., ar may be due to th 2.3.4 Several and pack cem al.101 used h substrates.10 above me existence of equipment com m2 /s, m2 /s, respectively. B diffusivities in TiB2, reported by Fan e a few or gnitude higher than those reported by Schmidt et al. This ciated with the diffusivity calculations by Schmidt, as pointed out by the author. Titanium b gs on titanium as high energy electron beam irradiation, laser boriding, e create boride layers on titanium. Kwangjun et i irradiation to create TiB rich surface layers on Ti- 6Al-4V alloy using MoB and TiB2 powders. Laser boronizing technique has also been ers of CP-Ti, Ti-6Al-4V and Ti-4Al-2Sn-4Mo 2 ed both laser and pack boriding experiments on the parison of these two processes. The laser boriding in these alloys produced TiB layer thickness in excess of 150 μm while pack boriding created only about 70 μm of boride layer thickness. There are some interesting observations that can be m de from this research. It was reported that the laser boriding of Ti alloys produced only the TiB2 layer, and no TiB layer formation was observed. But lly produces a dual layer consisting of TiB2 depending on the powder composition. Also the 2 layer was also witnessed in this research. ith high capital cost requiring sophisticated p ing where capital investment is minimal. Aich et al. d experiments to grow titanium boride coatings on titanium using the pack cementation method. The coating formed was mainly of TiB; no TiB2 was 9.31×10−16 ders of ma e error asso oride coatin techniques such ntation have been used to gh energy electron beam used to modify the surface lay The author perform ntioned alloys for com 2 a the conventional pack boriding process genera and TiB or a single layer of TiB TiN layer next to the TiB Generally, laser boriding is associated w ared to that of pack borid 103 performe 37 observed. The powder mixture used consisted of boron, sodium carbonate, and carbon. In this study, the TiB coating thickness obtained was ~30 μm for 24 hours treatment time at 800 °C. Tikekar et al.104 used similar pack cementation method for boriding CP-Ti and Ti-6Al-4V alloy, but with a different composition of the powder mixture involving boron, sodium borate, and calcium powders. The results obtained are different from that of Aich et al. in the sense that a dual layer of TiB and TiB2 formed on the titanium substrate. Boriding was done in both α-phase field (850 °C) and β-phase field (950 and 1050 °C). It was reported that when borided in β-phase field, the TiB2 coating thickness (≈ 6.4 μm at 950 °C and 17 μm at 1050 °C) was more than that in the α-phase field (≈ 3.9 μm at 850 °C). The total coating thickness (TiB + TiB2) obtained was maximum at 1050 °C when borided for 24 hours (≈ 54 μm). A very interesting observation was that upon boriding titanium very close to the α to β transition temperature (900 °C) for 24 hours, the coating thickness obtained was the highest (≈ 60μm) relative to all other treatment conditions. This suggested that the diffusion of boron in titanium at temperatures close to the transition temperature may help to increase the depth of penetration of TiB whiskers. Theoretically, CP-Ti (grade-2) undergoes α to β phase transition at around 913 °C. It is intriguing if there is an enhancement of boron diffusion in titanium or in TiB near the transition temperature akin to the enhancement of Ti self-diffusion near the phase transition temperature. If so, then this could be useful in maximizing the coating thickness. One of the major objectives of this research is to see if we can obtain a deeper boride coating in titanium on the basis of this unusual self-diffusion in titanium. 38 2.4 Cyclic thermal treatments on metals Cyclic thermal treatment (CTT), Chemicothermocycling treatments (CTCT) and Thermo mechanical treatments (TMT) are some unusual treatments that have been employed to alter the microstructure and enhance the mechanical properties of various metals and alloys. All such processes are termed nonisothermal processes because the treatment temperature varies with time. The variation of temperatures with time is mostly periodic. A nonisothermal process is characterized by four important parameters: i) the choice of upper and lower hold temperature (generally termed as terminal temperatures), ii) hold times at the terminal temperatures, iii) the heating and cooling rates during cycling, and iv) the total exposure time. Each of these parameters has a key role in achieving the final properties in the material. In the following, a brief account of the applicability of the nonisothermal processes as employed in various fields of metallurgy as well as the role of phase transformation on such processes is presented. 2.4.1 Cyclic surface treatment CTT processes are employed in metals and alloys to alter both surface and bulk properties. Previous research demonstrated that compared to isothermal processes, cyclic thermal processes are much faster.105, 106 For example, Gyulikhandanov et al.105 performed cyclic as well as isothermal carburizing experiments on steels and reported that the thickness of the carburized layer achieved by cycling is more than twice that achieved by isothermal treatment for the same saturation time. It was also reported that the growth kinetics of the carburized layer during the cyclic treatment was enhanced by increasing the hold time at the upper terminal temperature of the thermal cycle and the number of thermal cycles. A long duration hold at the lower terminal temperature of the 39 cycle did not bring about any appreciable increase in coating growth. This may be partly due to higher solubility of carbon in γ-iron than in α-iron. Nesbitt et al.106 studied diffusional transport of aluminum during cyclic oxidation of Ni-Cr-Al alloy. The author reported a higher oxidation rate in this alloy during cyclic oxidation, forming a protective Al2O3 coating. Rolinski 107 conducted cyclic plasma nitriding in titanium alloys across 930 and 730 °C with a hold time of 1 hour at both terminal temperatures for a total exposure time of 9 hours. Isothermal nitriding treatments were also done at 730 and 930 °C for 9 hours to compare with the results of the cyclic thermal treatments. The nitride coating thicknesses in isothermal hold at 730 and 930 °C were about 1 and 5 μm, respectively. The cyclic treatments resulted in coating thickness of 3-4 μm, slightly lesser than that of isothermal condition at 930 °C. The reason for obtaining lesser coating thickness during cyclic nitriding may be because of the choice of the upper terminal temperature. The upper limit temperature (930 °C) lies in the α+β phase field for the alloys that were used for this study. Hence, a hold at this temperature does not ensure complete phase reversal upon thermal cycling which seems to be important for such processes. Solubility of interstitial elements like N is more in β-Ti than in α-Ti.108 So, ingress of N will be more in β-Ti phase at the upper terminal temperature and the dissolved N will precipitate out and will form nitride compound (TiN or Ti2N) during cooling to the α-Ti phase due to the solubility difference. Haanappel et al.109 conducted cyclic oxidation experiments on Ti-48Al-2Cr alloy and reported a faster oxidation rate in cyclic conditions compared to the isothermal one. 40 2.4.2 Cyclic heat treatment for microstructure refinement Cyclic heat treatments have also been explored in other areas of materials science, for example to accelerate sintering of powders or to refine grain size in metals and alloys. Grain size refinements by cyclic heat treatments have been reported in a number of research studies.110-112 Prior austenitic grain size was refined by cycle heating treatment across austenite and martensite phase fields in Fe-15Ni-5-30Cr-5-10Mo-0-2Ti alloy.113 Reduction of grain size from 1 mm to about 50 μm was achieved by thermal cycling across the austenite and ferrite phase fields. Ramesh et al.114 carried out cyclic grain refinement treatments in Fe-0.2C-10Cr-1Mn alloy steel and reported the average grain size as 80 μm after cycling compared to the 150 μm grain size before cycling. When this alloy was subjected to thermo-mechanical treatments at or slightly above recrystallization temperature, dynamic recrystallization brought about a substantial refinement in grain size to about 48 μm. Wang et al.115 showed that a very coarse lamellar structure (1-3 mm) in Ti-Al alloys can be reduced to a fine one (10-20 μm) by cyclic heat treatment. 2.4.3 Role of phase transformation in cyclic thermal treatment Solid state phase transformation is commonly exploited to control the microstructural and mechanical properties of metals and alloys. Solid state transformations during CCT have shown improved kinetics in many metallurgical processes, like recrystallization, grain growth, and grain refinement116-119 over isothermal conditions. Sista et al.119 investigated the effect of cyclic processing on austempering kinetics of 1080 steel as against the conventional (isothermal) processing. It was reported that when the isothermal austempering was done at 260 and 300 °C, it took 160 and 140 minutes, respectively, for complete bainitic transformations. But when austempering was 41 done cyclically between 260 and 300 °C, the bainitic transformation was completed in 32 ± 4 minutes. Sahay et al.116 observed accelerated grain growth during cyclic annealing of cold rolled steel (0.05% C, 0.05% Al, 45ppm N, Al-killed). The average grain size of this steel obtained when cyclically annealed between 650 and 725 °C for a total of 6 hours (~19 μm) was larger than that obtained by isothermal holds at both the terminal temperatures (~14 μm at 650 °C and ~16 μm at 725 °C) for the same amount of hold time. The authors suggested that the enhanced grain growth kinetics in cyclic treatment is due to reduction of the activation energy for atom movements. Nonisothermal excitation increases the free energy of the atoms in the grains and thus reduces the activation barrier increasing the probability of atomic jumps. A significant increase in the densification rate in metal powders was achieved by cyclic phase transformations.117, 120-123 Schuh et al.117 conducted experiments on compaction of zinc powders, under both isothermal and cyclic thermal conditions. The densification during cycling occurred much more rapidly than during the isothermal process, despite the fact that the average temperature during cycling was almost 150 °C lower than that of the isothermal treatment. Hausner120 found that when electrolytic iron powder is cyclically sintered through the α-γ phase transition temperature, there was a considerable shrinkage in the diameter of the material. Choi et al.121 also reported an enhanced sintering rate of Fe-Ni alloy powder when cycled through the α-γ phase transformation temperature. Kohara122 investigated sintering of iron powder under repeated allotropic transformation through α-γ phase under small compressive load and reported substantial improvement in the sintering rate. Misra et al.123 also witnessed an activated sintering rate in aluminum powder under thermal cycling conditions. It was 42 observed that cyclic sintering of aluminum powder in vacuum ( Torr) between 600-660 °C with a cycle period of 3 minutes resulted in complete densification within 1 hour of treatment. On the other hand, isothermal sintering at 660 °C took more than 1 hour for partial sintering of powders. 2.5 Diffusion and phase transformation in titanium Group IV transition metals, specifically Ti, Zr and Hf, have been found to exhibit anomalous diffusion behavior.21, 22 The "anomalous" diffusion here refers to elevated diffusion rates, relative to the normal Arrhenius type behavior. The elevated diffusion rates have been found to occur within a few tens of degrees above the phase transition temperature (β-transus) of HCP metals. Generally, the self diffusion in metals is described by the simple Arrhenius type relationship: D(T) = D0 exp (-Q/RT) (2.22) where, the pre-exponential factor D0 and activation energy Q are assumed to be independent of temperature. R, T are the gas constant and the absolute temperature respectively.21 In general, for metals, the value of D0 is between 0.05 and 5 cm2/s. The magnitude of Q is generally found 21 to be proportional to the melting point of the metal as, Q = 34 Tm (2.23) Since the late 1950s, the existence of anomalous diffusion behavior in some metals, characterized by a strong curvature in their Arrhenius plots (ln D vs 1/T), has 3 − 5×10−3 43 been found.21 In particular, Group IV transition metals, specifically Ti, Zr and Hf, have been found to exhibit the anomalous diffusion behavior. For example, Ti shows normal Arrhenius type temperature dependent diffusion behavior at high temperature, but as the temperature approaches the β to α phase transition temperature, it shows anomalously high self-diffusivity. This is illustrated qualitatively in Figure 2.16 (a), showing the upward curvature of the diffusivity curve as the phase transition temperature is approached.124 Figure 2.16 (b) shows the experimentally measured self-diffusivities in 125 ear the phase nitude higher behavior also present allotropic phase transformation. The anomalous diffusion behavior is also reported to be exhibited by BCC Hafnium,127 γ-uranium,128 ε-plutonium,129 and rare-earth like δ-cerium,130 γ-ytterbium,131 and γ-lanthanum.132 behavior. Claire 21 cited that there could be two or more diffusion mechanisms operating in the anomalous regime (quoted in [21]). Accordingly, the anomalous diffusion behavior was suggested to be of the form: D = A1 exp (-Q1/RT) + A2 exp (-Q2/RT) (2.24) some of the BCC metals plotted as a function of the reduced temperature along with some of the transition metals. The figure clearly shows that in Ti, n transition temperature, the self-diffusivities are about three orders of mag than in normal BCC metals. It is to be noted that all metals that show anomalous diffusion 126 elements Several researchers have tried to explain the anomalous 44 (a) (b) Figure 2.16 Arrhenius plot (a) of self-diffusivity for CP-Ti showing upward curvature as the transition temperature is approached [124]. Comparison of experimentally measured self-diffusivities (b) of various normal BCC metals and anomalous metals like Ti, Zr etc. [125]. Tm(°K)/T(°K) LOG{ D/(cm2s-1)} α, δ-Fe, Mo, Nb, W Cr γ-U β-Ti β-Zr 45 The first term in the right hand side of the Eqn. (2.24) refers to the regular self-diffusion mechanism away from the phase transition temperature. The experimentally determined values for A1, Q1, A2 and Q2 for β-Zr, β-Ti and some Ti-alloys are tabulated in Table 2.4. The A1 values for self diffusion in β-Zr and β-Ti are well inside the commonly encountered range, and the activation energies, Q1 values are also within the limits of melting point correlation. The second term in the right hand side of the equation corresponds to the contribution from the other possible diffusion mechanisms that might be operating in these metals near the phase transformation temperature. The diffusion coefficient arising from this second term is characterized by an activation energy (Q2) that is half of that of the bulk diffusion (Q1) and pre-exponential factor (A2) about two orders of magnitude smaller than that of bulk diffusion (A1). This trend is observed for all the metals listed in Table 2.4. Table 2.4 Activation energy and pre-exponential factor for pure Zr, Ti and Ti-alloys (Adapted from [21]) Metal A1 (cm2/sec) Q1 (Kcal/mol) A2 (cm2/sec) Q2 (Kcal/mol) β-Zr 1.34 65.2 8.5×10-5 27.7 β-Ti 1.09 60.0 3.58×10-4 31.2 Cb in Ti 20 73 5×10-3 39.3 Mo in Ti 20 73 8×10-3 43.0 Cr in Ti 4.9 61 5×10-3 35.3 Mn in Ti 4.3 58 6.1×10-3 33.7 Fe in Ti 2.7 55 7.8×10-3 31.6 Co in Ti 2.0 52.5 1.2×10-3 30.6 Ni in Ti 2.0 52.5 9.2×10-3 29.6 46 Several possibilities have been put forwarded to help explain the second term in Eqn. 2.24, 1. The second term may result from some intrinsic, lattice diffusion mechanisms operating in these metals, such as interstitial diffusion or may be divacancies or some unrecognized mechanisms.22 But this theory was refuted on the grounds that a very small pre-exponential factor was obtained which corresponds to negative activation entropies. Table 2.4 lists those extremely small values of the pre-exponential factor, A2. Normally, diffusion studies in all materials show relatively higher pre-exponential factor corresponding to positive entropy.120 2. The second term may come as a contribution from the grain boundary diffusion. But this hypothesis was rejected on the basis that experiments with these metals were done in polycrystalline samples with fairly large grains. With lesser grain boundary areas, the probability that the contribution to the enhanced diffusivity coming from such diffusivity paths was negligible, as suggested by these authors.133, 134 3. Another possibility is that the second term contribution may come from diffusion through dislocation. However, to justify the anomalous diffusion data, an unrealistic amount of dislocations (1010/cm2) needed to be present in the material. Given that the diffusion experiments were done in well annealed samples, the possibility can be easily ruled out.126 4. Kidson135 proposed anomalous diffusion as an extrinsically-enhanced self diffusion mechanism brought about by impurities. The argument is based on the association 47 of vacancies with some impurities such as O or N present in the metal. At a relatively low temperature, there would be excess vacancy concentrations due to the rapidly diffusing interstitial species bringing about appreciable enhancement in self-diffusion. A high binding energy of the order of 30 Kcal/mol in the impurity-vacancy complex is needed to support this hypothesis. The anomalous diffusion behavior can also be examined from the phase transformation point of view. The significantly low activation energy for diffusion in the HCP metals may arise from the polymorphic transition.22, 136 Group IV transition metals undergo phase transformation from high temperature BCC phase to low temperature HCP phase during cooling. The fact that an anomalous diffusion mechanism is operative in the proximity of the phase transition temperature suggests some influence of phase transformation on diffusion may exist. Also, it is known that there is the formation of a metastable hexagonal (not closed packed) phase, known as ω-phase in Ti, Zr and Hf upon alloying137 or under pressure.138 It is important to note that these ω-structures are observed at room temperature only in alloys of Ti, Zr and Hf, but not in the pure form of these elements. On the other hand, ω-structural fluctuations appeared in Zr-Nb alloy over 1000 °C near the β→α transition temperature where the anomalous diffusion is operative.136, 139, 140 One of the reasons for not being able to observe the ω-phase in pure Ti, Zr and Hf, as argued by the authors, 126 may be the absence of any BCC (β) phase-stabilizing element. It might be necessary to have some β stabilizing element to suppress the HCP (α) phase field to detect the ω-phase fluctuations near the polymorphic transformation temperature by conventional diffraction techniques. 48 2.5.1 Mechanism of anomalous diffusion Sanchez et al.126, 141 proposed a phenomenological model for anomalous diffusion in ω-forming systems. This model is based on the formation of localized ω-like structural fluctuations, near (and above) the transformation temperature. The phenomenological model distinguishes the mechanism of formation of these ω-embryos from those of the activated complexes for diffusion, although the final structures for both are the same. The ω-embryos are formed when two neighboring (111) planes in the BCC lattice collapse to the intermediate position leaving every third (111) plane unaltered. The formation of the ω-embryo involves the co-operative movements of atoms whereas an activated complex does not do so. This can be illustrated with the help of Figure 2.17. The activated complex will form upon displacement of the central atom at O by a distance of a/2√3 (‘a' being the lattice parameter) along the <111> direction of the BCC lattice as shown in Figure 2.17 (a). This displacement will lead to the collapse of the central atom to the nearest (111) BCC plane as indicated by the ABC triad in Figure 2.17 (a). Figure 2.17 (b) shows the structure thus formed by this collapse where the central atom forms trigonal bonding with its neighboring atoms in the collapsed plane. On the other hand, the ω- embryo is formed inside a BCC lattice upon displacing the atom at O by a/4√3 in the <111> direction towards the ABC plane, while the atoms at ABC planes are displaced by the same distance, a/4√3, but in the opposite direction. Such displacements lead to the collapse of those planes into a single plane at the intermediate position of those two planes along the <111> direction. It can be noted that the final structure formed in the collapse plane will be the same as that of the activated complex shown in Figure 2.17(b). 49 (a) (b) Figure 2.17 BCC lattice (a) showing the ABC(111) plane with the body-centered atom at O and vacancy at V. Atom at O collapsed at ABC triangle (b) thereby forming ω-embryo or activated complex (Adapted from [126]). The distinguishing factor between these two structures is the mechanism by which they form. The collapse plane will have the hexagonal (but not closed pack) symmetry and will represent the basal plane for the ω-embryo. When each lattice point of the BCC (β) crystal is displaced by a magnitude either 0, a/4√3 or -a/4√3 (‘a' being the lattice parameter) along a given <111> direction, ω-phase is formed inside the lattice. Since there are three different variants of (111) planes of α, β and γ stacking sequence of BCC lattice, three variants of ω-structure can be obtained.126 The authors pointed out that the collapse of <111> planes to form the ω-structure decreases the free energy of the system and helps the atom in the BCC lattice to migrate to the nearest neighbor vacancy with least expense of energy as illustrated in Figure 2.17 (a). When an atom at O tries to migrate to a neighboring vacancy at V, it has to overcome two successive saddle point configurations. These triangular saddle points are located at one-third and two-thirds of 50 the jumping distance along <111> direction of the BCC lattice. Upon the formation of the ω-embryo by the collapse of the two neighboring (111) planes, i.e., planes through the atom at O and the ABC triad, the diffusing atom O is already at the first saddle point. Hence the probability of the atom at O to complete the jump to the vacant site increases. As the transition temperature is approached, the concentrations of these ω-embryos increase, resulting in an appreciable increase in diffusion coefficient. On the other hand, when the temperature is increased further, random thermal vibrations tend to destroy these ω-embryos and thus diffusion behavior becomes normal as that in other metals. Following an approximate expression incorporating the configuration energy and entropy of BCC system, originally derived by Kikuchi,142 Sanchez 126 showed that the free energy of the system goes down due to the formation of ω-phase close to the transition temperature. Following the Sanchez formulation, the total diffusion coefficient is given by, (2.25) where, D= total diffusion coefficient, D = diffusivity arising from the normal activated comp D = diffusivity arising from ω-embryos. The first term on the right hand side of the above equation can be written as, D D Dω N = + N lexes, the ω ⎟⎠⎞ ⎜⎝ ⎛ − = RT D D Q N exp 0 , (2.26) 51 where, D = pre-exponential factor, Q= activation energy, T = temperature and R= gas constant. The contribution to the total self-diffusivity arising from the ω-embryos can be written as, (2.27) where, 0 ω ω = γ Γ v D a2c γ = numerical constant close to unity, =BCC lattice parameter, = equilibrium concentration of vacancies and = jump frequency. a v c ω Γ ω Γ is defined as, = ω Γ ω υ c 0 (2.28) where 0 υ is the Debye frequency of vibration of atoms (~ 1013 for most metals) and c is the concentration of ω-embryos. The concentration of vacancies can be written in s of the corresponding enthalpy ( H ω term f ) and entropy ( S f Δ Δ ) of formation. Also noting that 0 υ is the same for both ω-em ryos and the norm l activated complex,126 the over ll diffusivity in equation 4 can be written as, b a a exp( ) exp( ) exp( ) 0 0 RT H c R D S RT D D Q m f − Δ − Δ + − = ω (2.29) where, and are given by, 0 D Q ⎥⎦ ⎤ ⎢⎣ ⎡ Δ + Δ = R S S D a m f ( ) exp 0 2 0 γ υ (2.30) 52 m f Q = ΔH + ΔH (2.31) In Eqns. (2.30) and (2.31), H and Sm Δ Δ m are the enthalpy and entropy of vacancy motion, respectively. All other ter s except , in Eqn. (2.29), are classical quantities and hence can be determ or obtained from the literature. The pre-exponential term, D 2/sec, and the activation energy is correlated to the nt (Eqn. 2.23) rather in a straightforward manner.21 The enthalp es of vacancy form H m ined independently me ω c , always appeared to lie between 0.05 to 5 cm lting poi ation ( 0 i f Δ ) and vacancy motion ( ΔH ) are of the order of 21 Δ S m one half of Q. f S and m Δ are the respective vacancy for ation and migration entropies. For most normal metals, (ΔSm/R) is a positive quantity that lies between 1 and 5.21 Sanchez126 formulated the temperature dependence of this non-classical term, Cw, based on the cluster variation (CV) approximation method and thereby predicted the total self-diffusivities of zirconium. A reasonable agreement between the experimental and the predicted values was obtained. Figure 2.18 shows the increase in concentrations of ω-embryos as β → ω transition temperature is reached. It is quite likely that anomalous diffusion behavior in Ti will influence B diffusion in Ti, especially at temperatures very close to the phase transition temperature. If this anomalous diffusion can be exploited to obtain a much deeper coating in titanium, then this would be a very interesting development. Further, any understanding that can be gained with respect to anomalous diffusion near the phase transition temperature can help with respect to thermal cycling of metals and coatings. m 53 Figure 2.18 Concentrations of ω-embryos vs. temperature (Adapted from [126]) CHAPTER 3 OBJECTIVES 3.1 Objectives of the present research The general objective of this research is to develop methods that can result in accelerated kinetics of boride layer growth on the surface of Ti. Two approaches were employed for this process. First, on the basis of anomalous diffusion in HCP metals near the phase transition temperature, the hypothesis is that this anomalous B diffusion can lead to rapid ingress of B and it can lead to increased depths of boride layers. The key objectives are the following. 1. To perform isothermal B diffusion experiments close to the phase transition temperature in Ti. The resulting boride layer coating thicknesses are to be determined using optical and SEM microscopy techniques. The thicknesses are to be compared with the layer thicknesses obtained by isothermal B diffusion away from the transition temperature in order to demonstrate any significant effect. For comparison, the effect of isothermal B diffusion in the α, β and the α + β field for long hold periods on the boride layer growth kinetics are also to be investigated. 2. To identify, if any, the mechanism responsible for the enhanced B diffusion in Ti near the transition temperature. This would result in the accelerated boride layer growth. 55 3. To develop a theoretical model that can explain the growth behavior of boride layers near the transition temperature taking into account of the simultaneous boron diffusion within the boride and Ti-phases. The second hypothesis is that by cyclically changing the surface temperature during B diffusion a heat-packet, which travels back and forth from the surface to interior, can be utilized to transport more B into bulk than is possible by conventional methods. The key objectives to verify this hypothesis are, 4. To carry out thermal cycling B diffusion experiments across the α/β transition temperature in Ti with various hold periods at the limit temperatures and for a varied number of cyclic thermal reversals. 5. To determine the resulting boride layer thicknesses by optical and SEM microscopy techniques and to compare the kinetics of growth with that obtained by the isothermal B diffusion method. 6. To formulate the subsurface temperature distribution profiles in Ti as induced by the cyclic temperature fluctuations at the surface during thermal cycling. 7. To investigate the mechanism of B transport into subsurface region by the repeated heat-packet travel caused by the surface temperature fluctuations and its effect on diffusion and supersaturation of B. CHAPTER 4 EXPERIMETAL PROCEDURE 4.1 Powder mixture for B diffusion process The powder mixture used for boriding experiments is comprised of three components: a compound as a boron source, a low melting compound, and a scavenger compound. A solid state boron source can exist either in crystalline or amorphous form. An amorphous boron source was chosen over a crystalline one because of its finer particle size and larger specific surface area (24 m2/g for amorphous vs. <1 m2/g for crystalline boron).80 Finer amorphous boron particles will ensure higher reactivity and larger specific surface area will provide a higher dissolution rate to enhance the diffusion process. The second ingredient of the powder mixture is a low melting compound. Usually, solid state diffusion processes are carried out at temperatures > 0.5Tm, and the second ingredient will be in liquid state at this treatment temperature. The liquid pool will provide easy dissolution and faster diffusion of boron particles within the powder mixture, maintaining a very high boron activity adjacent to the Ti substrate. An appropriate amount of this second ingredient is added to the powder mixture to obtain uniform distribution of the same around the boron source. However, addition of this second ingredient also introduces oxygen to the powder mixture.104 Ti has strong affinity towards oxygen and forms titanium oxide (TiO2) on its surface. Moreover, boron can also 57 react with oxygen to form boric acid (B2O3). Hence, in an oxidizing environment, there will be a reduction of boron activity in the powder mixture. Therefore, a third ingredient is added to the powder mixture to prevent the above mentioned reactions from occurring. This ingredient is a scavenging element that will lock the oxygen in the powder mixture by undergoing preferential oxidation over Ti or boron. The scavenging element was chosen based on two criteria: (i) the Gibbs free energy for this element to form its oxide is lower than that of Ti and boron, and (ii) it does not react with Ti.104 A suitable ratio of these ingredients in the powder mixture (the boron source, the transport medium that forms the liquid pool, and the scavenger element) was used to get the optimum powder pack combination.104 4.2 Isothermal boriding near transition temperature Grade 2 CP-Ti samples (composition in wt. %: 0.3 Fe, 0.17 O, 0.1 C, 0.03 N, 0.015 H, 0.3 max.) were polished using 800 grit SiC paper. A powder mixture,104 composed of a boron source (amorphous boron, composition in wt.%: 95-97 B, 0.89 Mg, 0.12 water soluble, particle size FN 0.694, from SB Boron Corporation, Bellwood, IL), a transporting medium and an activator were prepared by ball milling the powders for 16 hours. The boriding experiments were done using this powder mixture in a sealed stainless steel crucible. The experiments were carried out for 3, 6, 12, 18 and 24 hours at each of the temperatures: 890, 910 and 915 °C. The temperature was controlled within ±3 °C, with a thermocouple that was in contact with the powder pack. After the treatment, the samples were removed, sectioned and metallographically polished. Metallographically etched coating structures were examined in optical and scanning electron microscopes (SEM). Coating thickness measurements were made from the SEM 58 and optical micrographs. The distance from the edge of the sample to the furthest tip of the penetrating TiB whisker is taken as the coating thickness. These measurements were done at 10 equally spaced locations on a micrograph taken at 50X, 100X and 2000X magnifications. Such measurements were done on multiple micrographs and then the average of these measurements was taken as the average coating thickness. 4.3 Isothermal boriding for long hold time Commercially pure titanium (CP-Ti, Grade 2, Composition in wt. %:0.07 Fe, 0.12 O, 0.007 C, 0.006 N, 0.001 H and bal. Ti) samples were used for this study. The samples were polished till 800 grit surface finish before boriding. Similar experimental procedure was followed as discussed in the previous section. Isothermal boriding experiments were performed for 48 and 71 hours at each temperature of 850 and 1050 °C. Boriding at 900 °C was done for 3, 6, 12, 18, 24, 48 and 71 hours. The samples were then sectioned, metallographically polished, etched, and examined under optical and scanning electron microscope (SEM). The thicknesses of the TiB2 and TiB whisker layers were determined by similar method as mentioned in the previous section. 4.4 Thermal cyclic boriding Cyclic thermal diffusion experiments were performed using the same approach as mentioned above. CP-Ti grade 2 samples with chemical composition in wt. %: 0.3 Fe, 0.17 O, 0.1 C, 0.03 N, 0.015 H, 0.3 max. were thermally cycled between 890-910 ºC (with varying hold time at the limit temperatures) for total thermal exposure times of 3, 6, 12, 18 and 24 hours. The hold time at both limit temperatures were varied as 0, 6, 18, 30, 42 and 60 minutes. Furthermore, thermal cyclic experiments with CP-Ti Grade 2 59 samples with a different chemical composition (in wt. %:0.07 Fe, 0.12 O, 0.007 C, 0.006 N, 0.001 H and bal. Ti) were also done for 3, 6, 12, 18, 24, 48 and 71 hours of total exposure times across two sets of limit temperatures (one set: between 880 and 920 °C, other set: between 880 and 940 °C). The reason for conducting these two sets of experiments is discussed in detail in the results and discussion section in Chapter 5. A similar approach to that discussed above was implemented for determining the boride layer thicknesses. CHAPTER 5 RESULTS AND DISCUSSION 5.1 Modeling of layer growth kinetics 5.1.1 Theoretical modeling based on second law of diffusion The mathematical framework to predict the growth kinetics of the boride layers formed at temperatures above and below the beta transus (β-transus) temperature of Ti is very important both from fundamental and application points of view. There is no prior work on quantitative prediction of the growth of boride layers on Ti. For the growth of multiple compound layers by diffusion, error-function based solutions of Fick's second law can be developed to predict the kinetics.151, 152 The growth of FeB/Fe2B layers on Fe during boriding is somewhat similar to the boride layers here. Nearly all the growth of FeB/Fe2B layers can be explained based on the diffusivity of B alone and assuming that the diffusion of metal component is negligible.85, 86 In the present analysis, error-function solutions for the growth of two boride layers during B diffusion are developed. The chemical diffusivity values of B in TiB2 and TiB (determined from the work of Fan et al. [97]) were used to predict the growth of the two boride layers. In the Ti-B system, TiB2 is a stoichiometric line compound and TiB has narrow stoichiometric range. Thus, in practice, diffusional growth of these compounds under B concentration gradient does not involve large concentration gradient 61 within the phases. Nevertheless, the concentration difference between B/TiB2/TiB layers can be considered to represent the average compositional gradients in the phases. The development of the error function solutions will be illustrated on the basis of growth of TiB2/TiB whisker layer on titanium [Figure 5.1(a)]. Three interfaces exist in this system: the B-TiB2 interface, TiB2-TiB interface and the TiB-Ti interface. The B concentration profiles across the layers are schematically shown in Figure 5.1(b). The Fick's second law of diffusion, relating the changes in concentration of B with time and location is, 2 2 x D C t C ∂ ∂ = ∂ ∂ (5.1) where D is the diffusion coefficient and C is the concentration. The development of error function solutions is based on these assumptions: (i) the growth of the dual layer is controlled only by the diffusion of B and the diffusion of Ti in the opposite direction can be ignored, 97 (ii) the diffusion coefficient of B is concentration independent, and (iii) the solubility of B in Ti-matrix is negligible.23 With these assumptions, the initial and boundary conditions can be written as: Initial conditions: (t=0) at x = 0 (5.2) (in TiB2/TiB) = 0 for x > 0 (5.3) Boundary conditions: (t>0) S C = C C 62 Figure 5.1 Schematic of growth of the TiB2 layer and the TiB whisker layer (a). Concentration profile of B across the layers (b). ξ(t) η(t) C2,1 C3,2=0 C1,2 C2,3 x = 0 x C1,1 x = x1 x = x2 CS Bulk Surface 1 2 3 (a) TiB2 TiB Ti Boron concentration, CS (b) 63 = upper limit of B concentration in TiB2 at the surface (5.4) = lower limit of B concentration in TiB2 at the TiB2/TiB interface (5.5) = upper limit of B concentration in TiB at the TiB2/TiB interface (5.6) = lower limit of B concentration in TiB at the TiB/Ti interface (5.7) = B concentration in Ti matrix = 0 (5.8) The general solutions for B concentration in the boride layers and for that in Ti matrix which satisfy Eqn. (5.1) are of the form,151, 152 1,1 C = C 1,2 C = C 2,1 C = C 2,3 C = C 3,2 C = C ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = + D t C x t A B erf x i i i i 2 , (5.9) where and re the concentration and diffusivity of B in the respective phase (TiB2, and are the respective constants for each phase which need to be determined from the initial and boundary conditions. Following Wagner approach, 152 the time-independent boundary position for the TiB2/TiB interface at x1 are, i C TiB or Ti). i D a i A i B x D t 1 1 = 2ξ (5.10) x D t 2 / 1 = 2ξ (5.11) 64 where ξ and are the normalized growth parameter for the TiB2/TiB interface in terms of and , respectively. Since the growth parameters corresponds to the movement of the same interface, one can write,152 ξ / 1 D 2 D x D t D t 2 / 1 1 = 2ξ = 2ξ (5.12) Rearranging Eqn. (5.12) yields, 1 2 ξ / = ξ 1 = ξφ D D (5.13) where 2 1 1 D D φ = Similarly, for the TiB-Ti interface, one can write, x D t 2 2 = 2η (5.14) where η is the normalized growth parameter for the TiB-Ti interface in terms of Using Eqns. (5.10), (5.11), (5.13) and (5.14) and incorporating the initial and boundary conditions [(Eqns. (5.2) to (5.7)] in Eqn. (5.9), the variations of concentrations of B in TiB2 and TiB phases are determined as, 2 D . ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ − = − D t erf x erf C C C x t C S TiB S 1 1,2 2 ( , ) 2 ξ (5.15) 65 ( ) ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = − − ( ) ( ) 2 ( , ) 1 1 2 2,1 2,1 2,3 η φ ξ φ ξ erf erf erf D t erf x C x t C C C TiB (5.16) During the growth of the layers, simultaneous advancement of the TiB2/TiB and TiB/Ti interface boundaries at and in a small time step ( ) will occur because of the accumulation of B atoms at those interfaces driven by the differences in B flux between TiB2, TiB and Ti phases. Hence, applying the rule of mass conservation at the TiB2/TiB and TiB/Ti interfaces, one can write,152 1 x 2 x dt ( ) 1 1 2 1 2 1 1,2 2,1 x x TiB x x TiB x C D x C D dt C C dx = = ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ ∂ ∂ − = ⎟⎠ ⎞ ⎜⎝ − ⎛ (5.17) ( ) x x2 TiB 2 2 2,3 3,2 x C D dt dx C C = ⎟⎠ ⎞ ⎜⎝ ⎛ ∂ ∂ − = ⎟⎠ ⎞ ⎜⎝ − ⎛ (5.18) Differentiation of the concentration terms in Eqns. (5.15) and (5.16) at the interface yields, 1 x ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ − ∂ − = ⎥⎦ ⎤ ⎢⎣ ⎡ ∂ ∂ = Dt erf x erf x C C x C S x x TiB 1 1,2 1 2 1 2 ξ ( ) ( ) ( 2) 1 1,2 exp ξ ξ π − − = − erf D t C C S (5.19) 66 ( ) ( ( )) ( )⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ − − − = ⎥⎦ ⎤ ⎢⎣ ⎡ ∂ ∂ = φ ξ η φ ξ 1 2 1 1 2,1 2,3 2 1 erf D t erf x erf erf x C C x C x x TiB ( ) ( ( )) ( 2 2 ) 1 1 2 2,1 2,3 exp φ ξ η φ ξ π − − − = − erf erf D t C C (5.20) Similarly, differentiating the concentration term in Eqn. (5.16) at interface , 2 x ( ) ( ( )) ( )⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ − − − = ⎥⎦ ⎤ ⎢⎣ ⎡ ∂ ∂ = φ ξ η φ ξ 1 2 2 1 2,1 2,3 2 2 erf D t erf x erf erf x C C x C x x TiB ( ) ( ( )) ( 2) 1 2 2,1 2,3 exp η η φ ξ π − − − = − erf erf D t C C (5.21) Now, plugging in Eqns. (5.19) and (5.20) in Eqn. (5.17), we get, ( ) ( ) ( ) ( ) ( ( )) ( 2 2) 1 1 2 2 2 2,1 2,3 1 1 1 1,2 1,2 2,1 exp exp φ ξ η φ ξ π ξ ξ π ξ − − − − − − − = erf erf D t D C C erf D t D C C t D C C S (5.22) Rearranging Eqn. (5.22), ( ) ( ) ( ) ( ) ( ( )) ( 2 2) 1 1 1 1,2 2 2,1 2,3 1,2 2,1 exp exp φ ξ ξφ π η φ ξ ξ ξ π ξ − − − − − − − = erf erf C C erf C C C C S (5.23) Similarly, plugging in Eqn. (5.21) in Eqn. (5.18), we get, 67 ( ) ( ) ( ( )) ( 2) 1 2 2 2 2,1 2,3 2,3 3,2 exp η η φ ξ π η − − − − = erf erf D t D C C t D C C (5.24) Rearranging Eqn. (5.24), ( ) ( ) ( ( )) ( 2) 1 2,1 2,3 2,3 3,2 exp η η π η φ ξ − − − − = erf erf C C C C (5.25) Eqns. (5.23) and (5.25) are nonlinear and are to be solved for two unknown parameters, ξ and η , which are the growth parameters for the TiB2 and TiB layer, respectively. These equations were solved simultaneously using MATLAB program and ξ and η were determined for the three treatment temperatures (850, 950, and 1050 °C). From the growth parameters, the time-dependent layer thicknesses for the TiB2 and TiB layers can be calculated using Eqns. (5.10) & (5.14), respectively. The experimentally measured coating thicknesses at 850, 950, and 1050 °C, reported by Tikekar et al.,104 are being used to validate the theoretical model. Table 5.1 summarizes the experimental data of boride layer thicknesses at different treatment temperatures. An important aspect needs to be considered in comparing the predicted growth rates of the TiB2 and TiB layers with the experimental data. Because B diffusion occurs during the heating of the samples (10 °C/min) from room temperature to the isothermal treatment temperatures, there will be some pre-existing layer thickness that is not part of growth at the diffusion temperatures. Hence this was subtracted from the experimental data for a meaningful comparison with experiments. 68 Table 5.1 Average thickness values of TiB2, TiB and the composite (TiB2 + TiB) coating layers, determined for different B diffusion temperatures and times [104]. 850°C 950°C 1050°C Time (h) TiB* (μm) TiB2 (μm) Total (μm) TiB (μm) TiB2 (μm) Total (μm) TiB (μm) TiB2 (μm) Total (μm) 0.083 13 0.5 ± 0.1 13.5 ± 3.0 15 1 ± 0.1 16 ± 2.5 15 1.5± 0.1 16.5 ± 1.9 3 21.5 1.5 ± 0.1 23 ± 3.2 22.8 3.2 ± 0.3 26 ± 2.7 26 5 ± 0.3 31 ± 2.5 6 21.3 2.7 ± 0.2 24 ± 3.5 24.2 4.8 ± 0.2 29 ± 3.2 27 10 ± 0.7 37 ± 3.4 12 21.8 3.2 ± 0.2 25 ± 4.2 28.6 5.4 ± 0.3 34 ± 3.3 29 12 ± 0.9 41 ± 3.6 18 22.7 3.3 ± 0.3 26 ± 5.4 39.3 5.7 ± 0.3 45 ± 4.4 35 15 ± 0.9 50 ± 5.7 24 24.1 3.9 ± 0.3 28 ± 6.3 40.6 6.4 ± 0.4 47 ± 5.4 37 17 ± 1.0 54 ± 5.9 * TiB coating thickness was determined by subtracting the average thickness of TiB2 layer from the average total coating thickness. Hence there is no S.D. for these data. 5.1.2. Comparison with experimental data For the present calculations, the B diffusion coefficients were determined from the work of Fan et al.97 and are reported in Table 5.2. The TiB layer growth is predominantly controlled by the diffusion of B in [010] direction, and therefore, the estimated B diffusivity in TiB is specific to this direction. The diffusivities of Ti in TiB2 and TiB are 103 to 104 times lower than that of B in these phases.92, 97 Hence the effect of Ti diffusion on layer growth can be neglected. Figure 5.2 shows the predicted TiB2 thickness development as a function of time, compared against the experimental data. The experimental data have been corrected for the 5 minutes growths ─ the TiB2 thicknesses observed after 5 minutes at the respective temperatures were deducted from the original thicknesses. A reasonable agreement between the predicted data and the experimental data at 850 and 1050 °C can be seen. In 69 Table 5.2 Diffusivity data [97] used in the calculations of kinetics using error function solutions. T (°C) Chemical diffusivity of B in TiB2 (m2/sec) Chemical diffusivity of B in TiB (m2/sec) 850 1.34 X 10-16 6.13 X 10-15 950 6.92 X 10-16 3.25 X 10-14 1050 2.78 X 10-15 1.34 X 10-13 0 2 4 6 8 10 12 14 16 18 2 7 12 17 22 27 Time (hrs.) TiB2 layer depth (μm) 850-exp 950-exp 1050-exp 850-calc 950-calc 1050-calc Figure 5.2 Comparison of the predicted and the experimentally measured TiB2 thicknesses, after correcting for the TiB2 layer growth due to 5 minutes exposure. 70 most cases, the predicted layer thicknesses of TiB2 are within 10-20% of the experimental data. But the numerical predictions at 950 °C are slightly higher than the experimental trend. Especially for treatment times exceeding 6 hours, the numerical predictions are 20-30% higher than the experimental values. As discussed in the next section of this chapter, the TiB2 layer recedes due to a complex mechanism involving enhanced anomalous diffusion in Ti near the α/β phase transition temperature.21 The temperature region for such anomalous diffusion in Ti can extend up to 950°C. It is therefore suggested that the small difference (20-30%) between the predicted and the experimental TiB2 layer thickness at 950°C, especially at longer boriding times, is due to the TiB2 layer recession. This effect is absent at 850°C and 1050°C. Figure 5.3 is the comparison of the experimentally measured TiB coating thicknesses (after deducting the TiB thicknesses due to 5 minutes exposure) and the predicted growth data. The predictions are in reasonable agreement with the experimental data at 850 and 950 °C. Most of the numerical data are in the range of 20-25% of that of the experimental values. However, there is a large discrepancy between the predicted and the experimental data at 1050 °C by about a factor of two. Actually, the experimental growth data at 1050 °C, being nearly similar to that at 950 °C, is itself quite unusual.104 This may be attributed to the thickening of TiB whiskers at high temperatures. While almost all of the TiB whiskers were relatively thin at 850 and 950 °C; at 1050 °C, many TiB whiskers in the layer were relatively thicker (Figure 5.4 a and b). It was suggested earlier 92 that diffusion in the transverse direction of TiB whiskers is about 10 times slower than that in the [010] direction, which is the axial direction of whiskers. This means that the rates of thickening and lengthening will be about equal when the whisker 71 0 5 10 15 20 25 30 35 40 45 50 2 7 12 17 22 27 Time (hrs.) TiB layer depth (μm) 850-exp 950-exp 1050-exp 850-calc 950-calc 1050-calc Figure 5.3 Comparison of the predicted and the experimentally measured TiB thicknesses, after correcting for the TiB layer growth due to 5 minutes exposure. 72 Figure 5.4 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 24 hours at (a) 850 °C and (b) 1050 °C. a 10 μm b TiB2 layer TiB layer 10 μm 73 aspect ratio reaches 10. Above this aspect ratio, thickening of TiB whiskers provides a faster means of transporting B and reacting with Ti, as opposed to the axial transport and extension of growth along the TiB axial direction. Since the model predictions are based only on diffusivities for growth along the [010] TiB direction, they should not agree with the experimental data of total layer thickness at 1050 °C, if TiB whiskers appear to be much thicker than those at lower temperatures. Indeed, it appeared from the experimental results, that at 1050 °C a significant fraction of TiB is no longer whiskers and they seemed to thicken due to increased B diffusion in the direction transverse to TiB whisker axis. Figure 5.5 shows the comparison of the total (TiB2+TiB) layer thickness predictions with the experimental data. The predictions for the 850 and 950 °C are in reasonable agreement with the experimental data, while at 1050 °C; the predicted thicknesses are relatively higher. This difference arises from the TiB layer growth behavior as discussed above. The diffusion model, described above, seemed to predict the boride layer growth kinetics well-specifically at temperatures away from the phase transition temperature in Ti. The predicted TiB2 layer thicknesses are within 25% of that the experimental values for all three boriding temperatures. The predictions of the TiB layer also show reasonable agreements with that of the experimental data except for the 1050 °C boriding condition. The plausible reason behind the discrepancy has also been described in view of the TiB layer morphology observed at 1050 °C. 74 0 10 20 30 40 50 60 70 2 7 12 17 22 27 Time (hrs.) Total dual layer depth (μm) 850-exp 950-exp 1050-exp 850-calc 950-calc 1050-calc Figure 5.5 Comparison of the predicted and the experimentally measured dual (TiB2+TiB) coating layer thicknesses, after correcting for the TiB2 and the TiB layer growth due to 5 minutes exposure. 5.2 Structure and kinetics of growth of boride layers near the phase transition temperature in Ti 5.2.1 Premise This section focuses on the detailed results obtained during the isothermal boriding experiments conducted near the phase transition temperature of Ti. The obtained boride layer thicknesses, analysis of morphological aspects and the hardness measurements on these layers were documented and reported. Furthermore, a theoretical model is proposed based on Fick's second law of diffusion to explain the boride layer growth kinetics near the transition temperature. 75 5.2.2 Structure and properties of boride coatings The average coating thickness values along with the standard deviations obtained during isothermal boriding close to the transition temperature are presented in Table 5.3. Figure 5.6 shows the plot of the average coating thickness as a function of time at different treatment temperatures. The coating thicknesses increase with increase in treatment time. The coating thicknesses obtained at 900 and 1050 °C in our previous studies 104 are also plotted in the same figure for comparison. The growth behavior of boride layers at all temperatures can be represented by the parabolic kinetics. In Figure 5.6, the treatment temperatures: 900, 910, and 915 °C are the closest to the β transus temperature (913 °C) of the material used in this study. Of these, the temperature 910 °C, within the experimental error of ±3 °C, is the closest to the β transus and it can be seen that the coating growth kinetics at this temperature is the most accelerated, compared to that at 900 and 915 °C. Thus, 910 °C, for all practical purposes can be considered to be right on the α-β transition point. Table 5.3 Summary of total (TiB2+TiB) coating thicknesses obtained in varied isothermal treatments 890°C 900°C 910°C 915°C Time (hr) Total (μm) SD (μm) Total (μm) SD (μm) Total (μm) SD (μm) Total (μm) SD (μm) 3 18 6 39 4 30 5 23 6 6 28 7 40 4 44 8 35 8 12 31 8 45 5 54 9 52 8 18 44 8 54 6 65 10 58 9 24 46 10 60 6 75 11 66 10 76 0 20 40 60 80 100 5 10 15 20 25 910C 915C 890C 900C 1050C Total time of exposure, (hrs.) Figure 5.6 Total (TiB2+TiB) coating thicknesses obtained in isothermal diffusion treatments plotted as a function of total isothermal exposure time. To illustrate the general structure of conventional boride layers on titanium, the SEM micrographs of the boride coating structure obtained at 850 and 1050 °C isothermal treatments are to be referred from Figure 5.4 (a) and (b), respectively.104 These coatings actually consist of two boride layers, a top TiB2 layer and a TiB layer below. The TiB2 is a monolithic layer whereas the TiB layer is made of long, high aspect ratio whiskers that grow nearly perpendicular to the surface. Generally, the relative kinetics of growth of these layers determine the total coating thickness, since the B-TiB2, TiB2-TiB and TiB-Ti interfaces are nearly in equilibrium during the diffusion layer growth.88 It was found that at temperatures in α-phase field (850 °C), the TiB layer growth is relatively faster than that of TiB2 layer. On the other hand, at treatment temperatures > 950 ºC which is well 77 inside the β-phase field, a relatively thicker TiB2 layer is formed. This is evident from coating structure of 1050 °C sample, where a relatively thicker TiB2 layer is obtained compared to that obtained at 850 °C. The total coating depth is, however, controlled by the diffusion of B through the axis of TiB whiskers.92 The reverse rate of diffusion of Ti in TiB toward the surface is about ten times slower than the forward diffusion of B.97 Therefore, the major limiting factor is the diffusion of B through TiB and its reaction with Ti substrate to grow the TiB whisker. Consistent with this, the coating thicknesses at the isothermal diffusion temperatures of 850 and 1050 °C for 24 hours saturates to about 30 and 55 μm, respectively. The structure of boride layer in samples borided at 890, 910, and 915°C for 3 hours are presented in Figure 5.7 (a-c). The coating at this stage is characterized by a very thin TiB2 outer layer (1 to 1.5 μm) and a TiB layer containing distributed TiB whiskers growing into the depth. The thickness of the TiB2 layer does not seem to vary with the temperature. However, the TiB layer beneath the TiB2 layer grew slightly deeper into the substrate at temperatures 910°C compared to that at 890 and 915°C, although the layer itself does not contain a high area density of TiB whiskers. This is probably due to the early stage of B diffusion where the inherent tendency of the formation and growth of TiB into substrate is distributed in nature.103 The SEM micrographs of coating structure in samples borided at 890, 910, and 915 °C for 12 hours are presented in Figure 5.8 (a-c). The only common aspect between the coating structures in these conditions and that obtained at 850 and 1050 °C is that both TiB2 and TiB layers are present. The thicknesses of the TiB2 layers in these samples 78 Figure 5.7 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 3 hours at (a) 890 °C, (b) 910 °C and (c) 915 °C. TiB whiskers a TiB2 5 μm b 5 μm as 5 μm c 79 Figure 5.8 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 12 hours at (a) 890 °C, (b) 910 °C and (c) 915 ºC. 10 μm a TiB whiskers TiB2 10 μm b precipitated TiB 80 Figure 5.8 continued are in the range between 3 to 4 μm. As observed in 3 hours treated sample, the thickness of the TiB2 layers in these samples also do no seem to be affected by the temperature, whereas the TiB layer beneath the TiB2 layer grew relatively deeper into the substrate at temperatures 910 and 915 °C compared to that at 890 °C (Table 5.3). The TiB layers are made of TiB whiskers and precipitated TiB particles as shown in Figure 5.8 (a and b). The SEM micrographs of coating structure in samples borided at 890, 910, and 915 °C for 24 hours are shown in Figure 5.9 (a-c). A very thin layer of TiB2 also formed in these samples, irrespective of the treatment temperature. The TiB2 layers in these samples are relatively thicker than those in 12 hours treated samples but still much thinner than that in the sample treated at 1050 °C for 24 hours. This is expected, because a relatively thicker TiB2 layer is favored at this treatment temperature as it lies c 10 μm 81 Figure 5.9 SEM micrographs of boride coating on grade 2 CP-Ti after isothermal treatments for 24 hours at (a) 890 °C, (b) 910 °C and (c) 915 °C. 10μm a ~ 45 μm b ~ 70 μm TiB whiskers 10μm 82 Figure 5.9 continued completely in the β phase field of Ti. TiB layers in the present samples are characterized by ahigh area density of TiB whiskers penetrating deep into the substrate. In particular, at treatment temperatures of 910 and 915 °C, the area densities of TiB whiskers are relatively higher and the penetration was much deeper, compared to that treated at 890 °C. For the sample borided at 890 °C for 24 hours (Figure 5.9 (a)), a lower average coating thickness (~ 46μm) was obtained compared to that at 910 and 915 °C. This treatment temperature is significantly below the transition temperature (transition temperature for titanium ~ 913°C) and probably only α phase field existed in this condition. To illustrate the influence of proximity to the phase transition temperature the TiB2 and the total layer thicknesses were plotted as a function of temperature in Figure 10μm c ~ 62 μm 83 5.10 (a and b). The thickness of TiB2 layer after 24 hours varied significantly with the temperature while such a variation is not seen at shorter times (3 hours). As shown in Figure 5.10(a), the TiB2 layer thickness, grown in 24 hours of diffusion, goes through a minimum near the phase transition temperature. Assuming that "normal" growth conditions exist at 850°C and 1050°C, a straight line was drawn joining these two data points to show how far the TiB2 growth at temperatures near the phase transition is lagging behind the normal trend. Figure 5.10(b) shows the variation of total boride layer thickness as a function of temperature for various treatment times. It can be seen that near the phase transition temperature, much deeper boride layers are obtained. Again assuming the prevalence of overall normal growth kinetics at 850°C and 1050°C, a straight line was drawn to show how far the growth kinetics is accelerated near the phase transition temperature. It can be seen that the increased TiB growth is more than that required to offset the lag in TiB2 growth near the transition temperature. It is also to be noted that the α-β phase transition temperature is sensitive to alloying elements, especially oxygen. Even the presence of a small amount of oxygen introduces a α+β phase field in Ti.27 For example, for 0.15 wt% of oxygen, α to β transition takes place over a temperature range of 883 to 914°C. Hence, the enhanced TiB layer growth can also be seen at 890°C (Figure 5.10(b)), as the α to β phase transformation must have started at this temperature. The surprising finding of this study is that the TiB whiskers grow deeper at temperatures close to the α-β transition temperature and this growth is significantly higher than that obtainable at a much higher temperature (1050 °C). This is evident from 84 0 2 4 6 8 10 12 14 16 18 20 800 850 900 950 1000 1050 1100 Temperature (oC) TiB2 layer thickness (μm) 24 hrs 12 hrs 3 hrs α/β phase transition temperature Normal kinetics (24 hrs.) (a) 0 10 20 30 40 50 60 70 80 90 100 800 850 900 950 1000 1050 1100 Temperature (oC) Total boride layer thickness (μm) 24 hrs 12 hrs 3 hrs α/β phase transition temperature Normal kinetics (24 hrs.) (b) Figure 5.10 The enhanced growth of boride layers near the phase transition temperature, (a) TiB2 layer thickness and (b) the total (TiB2+TiB) boride layer thickness at different temperatures. A dotted line approximately indicating the expected normal kinetics for 24 hours (without the anomalous contribution), across the region near the phase transition, is drawn to highlight the deviations. 85 Figure 5.6 and 5.9 (b and c), where the average depth of the coating layers exceeded 60 μm. The sample treated at 1050 °C for 24 hours has a maximum coating depth of about 50 μm. Figure 5.11 (a and b) shows the montage of coating morphologies for the samples borided at 900 and 910 °C for 24 hours. Most of the TiB whiskers are in nanometer size range varying between 200 to