Title: Kinetics of TiB formation
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00099261/00001
 Material Information
Title: Kinetics of TiB formation
Physical Description: x, 245 leaves : ill. ; 28 cm.
Language: English
Creator: Walther, George Charles, 1947-
Copyright Date: 1976
Subject: Borides   ( lcsh )
Titanium compounds   ( lcsh )
Titanium alloys   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Statement of Responsibility: by George C. Walther, Jr.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 235-244.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00099261
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000178775
oclc - 03131978
notis - AAU5289


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The author wishes to thank each of his supervisory

committee members for their advice and counsel during the

course of this work. They have contributed solutions to

a variety of problems encountered during this research.

Thanks are due Dr. Frank Gotsama of Union Carbide

Corporation for his gift of ZrO2 fibers.

Financial support provided by Dr. L. L. Hench, the

Department of Materials Science and Engineering, and the

National Science Foundation is also acknowledged.

And, I would like to thank my wife for her enduring

and endearing during thesepast several years.



ACKNOWLEDGMENTS ......................................... ii

LIST OF TABLES.......................................... .. v

LIST OF FIGURES .........................................vi



I INTRODUCTION................................... 1
Statement of Problem........................1
Ti-B System: Phase Relations............... 2
Ti-B System; Chemical Reactions............ 14
Quantitative Microscopy................... .23
Kinetic Models..............................32

II EXPERIMENTAL PROCEDURE ........................45
Sample Preparation.........................46
Quantitative Microscopy Measurements.......52
Quantitative X-Ray Analysis................70

III RESULTS AND DISCUSSION..........................75
Metallographic Examination..................75
Transport Experiment Results ............... 84
Quantitative Microscopy Results ............89
Quantitative X-Ray Results ................137

IV MODEL ANALYSES ............................... 158

V CONCLUSIONS................................... 195
Recommendations on Use of
Quantitative Microscopy ................... 196
General Recommendations for
Future Work............................... 198

Table of Contents continued.


1 Comparison of the X-Ray Lines of
Orthorhombic TiB, Ti2B, and Ti
Superlattice................................ 200

2 List of Qualitative Microstructural
Features for a Four Phase System............202

3 Calculation of Statistical Parameters
for a Random Sample of Size n............... 204

4 Computer Programs ........................... 206

5 Glossary of Computer Variables.............. 212
Quantitative Microscopy Results
for 1200 1500 C ........................ 214

6 Results of Archimedian Porosity.............222

7 Selected X-Ray Data......................... 223

8 X-Ray Data................................... 224
X-Ray Standards Data.....................224
X-Ray Sample Data.........................225

9 Results of Sasaki Model.....................227

10 Quantitative Microscopy Model
Calculations................................ .. 229

11 Quantitative X-Ray Model Calculations.......231

12 Quantitative Microscopy Slope Data: TiB2....233

13 Velocity and Curvature Results ..............234

BIBLIOGRAPHY........................................... 235

BIOGRAPHICAL SKETCH .................................... 245




1 Powder Compact Kinetic Models ....................34

2 Summary of m Values for Nucleation
and Growth Models................................ 39

3 Results of Electrostaining.......................54

4 Data for TiB Standard Material..................104

5 Quantitative Microscopy Data for
Starting Material Compact....................... 134

6 Variability in Quantimet Operating

7 X-ray Error Determinations ......................138

8 X-ray Absorption for TiB and TiB2............... 152

9 Ti Peak Shift Data.............................. 156

L-A4 Quantitative Microscopy Results for
1200C 1500 0C................................ 214-

A5 Results of Archimedean Porosity .................222

A6 X-ray Standards Data.............................224

A7 X-ray Sample Data............................... 225

A8 Results of Sasaki Model .........................227

A9 Quantitative Microscopy Model

A10 Quantitative X-ray Model
Calculations.................................... 231

All Quantitative Microscopy Slope
Data: TiB2 ................ .................. .233

A12 Velocity and Curvature Results..................234



Figure Page

1 Phase diagram of the Ti-B system after
Palty et al...................................... 6

2 Phase diagram of the Ti-B system after
Rudy and St. Windisch ............................9

3 Crystal structures of TiB2 and TiB.............. 13

4 Grid of length L placed on a section
showing particles of A in a matrix of B.........26

5 Model geometries................................36

6 Particle size distribution of reactant
powders........................................ 47

7 Micrograph of Ti particles....................... 48

8 Micrographs of TiB2 particles ...................49

9 Centorr furnace ..................................51

10 Schematic of electrostaining apparatus..........53

11 The Quantimet 720 image analyzing computer......56

12 Effect of nonideal signal on detected
image ...........................................57

13 Effect of sizer on detected image................59

14 Effect of nonuniform background level
on detected image .............................. 59

15 Quantimet display ...............................60

16 Images detected by Quantimet .....................62

17 Schematic of transport experiments..............66

18 Diffusion couple markers ........................ 69

List of Figures continued.

Figure Page

19 X-ray equipment ................................. 71

20 Sequence of reaction............................ 78

21 Large Ti grain and surrounding porosity.........81

22 Polished and electrostained surface.............81

23 Micrographs of fracture surfaces ................82

24 Result for surface diffusion transport

25 Diffusion couple interfaces.....................87

26-29 Quantitative Microscopy volume fraction
results for 1200C 15000C.....................91-

30 Porosity determined by Quantitative
Microscopy...................................... 96

31 Porosity determined by immersion
displacement..................................... 97

32-35 Quantitative Microscopy mole fraction
results for 12000C 15000C. ...................99-

36-39 Quantitative Microscopy surface area
per volume for 1200C 15000C................106-

40-43 Quantitative Microscopy specific
interface area for 1200C 1500C............111-

44 The proximity parameter.........................116

45-48 Quantitative Microscopy total curvature
results for 1200C.............................117-

List of Figures continued.

Figure Page

49-52 The X parameters for 1200C 1500C.......... 122-

53-56 The R parameters for 1200C 15000C..........127-

57 Qualitative x-ray strip chart patterns ........140

58 Internal standard calibration curves ........... 142

59-62 Quantitative x-ray volume fraction
results for 1100C 14000C....................144-

63 Pulverized x-ray sample ........................149

64 Direct comparison calibration curves...........150

65 Peak shift for Ti (011) line...................154

66 Valensi-Carter model as a function of
extent of reaction.............................163

67 Standard curve for Sasaki model................164

68 Extent of reaction for Quantitative
Microscopy data................................ 165

69 Extent of reaction for quantitative
x-ray data.................................... 166

70-79 Model results for Quantitative
Microscopy data.............................. 168-
80-87 Model results for quantitative
x-ray data....................................179-

88 Average interface velocity results .............191

89 Modified average interface velocity
results...................................... 193


Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy



George C. Walther, Jr.

August, 1976

Chairman: Ronald E. Loehman
Major Department: Materials Science and Engineering

The kinetics of forming TiB from Ti and TiB2 was

studied using pressed powder compact and diffusion couple

geometries. Powder samples were heated in an Ar atmo-

sphere at 1100 1500C for 0 120 min. Metallographic

examination showed the reaction initiates at the contact

points between Ti and TiB2 and proceeds rapidly due to

surface diffusion of Ti coating the TiB2 particles.

Weight loss experiments showed negligible vapor transport

of Ti or B occurs. A Kirkendall shift observed on a Ti-

TiB2 diffusion couple indicates Ti is the major diffusing

element; some counter diffusion of B also occurs.

Analyses by Quantitative Microscopy and quantitative x-ray

diffraction suggest the initial reaction is controlled by

the rate of Ti diffusion through the TiB. During the

later stages, the reaction rate changes to an inverse time

dependence due to reduced availability of Ti. The Quanti-

tative Microscopy measurements provided volume fraction,

surface area, and total curvature data for the micro-

structural features. An average velocity for the reacting

interface was obtained from this data. Evidence to ex-

clude rate control by nucleation and growth or interface

reaction mechanisms is presented. The curvature of the

TiB-TiB2 interface does not significantly influence the


A 10 15 volume % expansion of the powder compact

was observed due to the volume increase of TiB2 trans-

forming to TiB. Competing densification from sintering

of TiB or TiB2 is negligible. Fabrication of TiB articles

by sinter-reacting powders thus results in weaker pro-


This study shows the importance of microstructural

geometry on reaction kinetics in powder compacts.


Statement of the Problem

The object of this study is to examine the mechanisms

of transforming TiB2 and Ti to TiB in a mixed powder com-

pact. Titanium diboride is a hard brittle refractory ma-

terial with a high strength to weight ratio at high tem-

peratures which exhibits good resistance to corrosion,

oxidation, and attack by some liquid metals. It shows

promise for use in crucibles, electrodes, hard facing, and

a variety of cermet or alloy applications. The high

strength and light weight, corrosion resistance, and re-

fractoriness of Ti are also well-known. However, during

an x-ray investigation of the reaction between mixed Ti

and B12C3 powders, rapid formation of TiB as one of the

major products was observed, rather than the expected

TiB2. These results suggested the less stable monoboride

was favored kinetically and implied a potential limitation

on the use of Ti or TiB2 in some applications. Therefore,

a study of the kinetics of forming TiB by the simpler re-


Ti + TiB2 2TiB

was begun to determine the mechanism for the rapid TiB

formation. Since x-ray evidence alone was not sufficient,

it was decided to follow the evolution of the reaction

using Quantitative Microscopy to see what influence the

powder compact structure had on the reaction rate. It

appears that the use of Quantitative Microscopy for this

purpose has never been reported.

Ti-B System: Phase Relations

Understanding of the phase relations in the Ti-B sys-

tem has been hindered by the refractory nature of the ti-

tanium borides, problems with impurities, limitations of

early x-ray techniques, and difficulties of metallographi-

cally preparing these hard materials. The borides that

have so far been proposed for this system include Ti2B,

TiB (cubic or orthorhombic forms), Ti3B4, TiB2, Ti2B5, and

TiBx x 10). The most reliable evidence supports only

TiB2 andorthorhombicTiB as stable equilibrium phases, al-

though uncertainty concerning the nature of Ti3B4 is not

completely resolved at this time. The development of cur-

rent understanding is presented below.

The preparation of TiB2 was first reported by
Andrieux, utilizing electrolysis of TiO2 dissolved in a

fused boric acid metal fluoride bath. The product was

not very pure. Agte and Moers3 produced purer TiB2 by

vapor deposition reaction of TiCI4 and BBr3 on a heated W

filament. Ehrlich4 performed the first systematic study

of the Ti-B system by x-ray investigation of sinter-re-'

acted Ti and B powders. He reported finding the compounds

TiB (zinc blend structure) and TiB2 (hexagonal A1B2 type).

The Ti lattice parameters increased with B additions up to

44 atomic % without an observed phase break. This sug-

gested a large solubility of B in Ti and that no phases

intermediate in B between Ti and TiB existed. From

samples at both the Ti-rich and B-rich end of his compo-

sitional range, Ehrlich obtained additional x-ray lines

that could not be indexed. From this evidence he proposed

a Ti superlattice and a boride phase higher in B than
5 6
TiB2. Norton et al. and Zachariasen confirmed Ehrlich's

structural interpretation of TiB2. Most of Ehrlich's

other results were contradicted by later workers, who

cited the presence of impurities, non-equilibrium condi-

tions, and inadequate x-ray sensitivity as reasons for the


Except for TiB2, the evidence reported by other early

workers provided little clarification of Ehrlich's re-

sults. From considerations of B atomic radii, Andersson

and Kiessling7 suggested that TiB is fee (NaCl type),

stable only at high temperatures, and that it decomposes

to a-Ti and TiB2 at lower temperatures. Brewer et al.8

did a study on sinter-reacted Ti and B powders similar to

Ehrlich's. They were confident only of the existence of

TiB2 (with a narrow homogeneity range) and found no evi-

dence for higher B phases. The additional weak lines of a

fcc phase were explained as TiN due to N contamination

rather than TiB. Although they also found a continuous

increase in Ti lattice parameters with B additions up to

50 atomic %, in agreement with Ehrlich, the presence of

more lines than required made a Ti superlattice interpre-

tation difficult. Greenhouse et al.9 were the only

workers to claim the existence of a TiB (x = 10) phase
as one of the products of reaction between TiC and B12C3'

Ogden and Jaffeel0 arc melted pure Ti and B powders to

produce Ti-rich alloys for x-ray analysis; they found no

shift in the a-Ti lines, but did observe definite lines

from a second phase, corresponding to Ehrlich's Ti super-

lattice. Following a suggestion of Hansen,1 they pro-

posed these were due to a Ti2B hexagonal phase almost

identical in structure to a-Ti. Utiliting hot pressing
techniques on Ti and B powders, Glaser2 and Post and

Glaser3 reported several new phases: a tetragonal Ti2B, a

hexagonal Ti2B5, and a fee TiB that was stable at low

temperatures. They admitted equilibrium conditions were

not always achieved during their experiments, but felt

their results were stable phases because chemical analyses

showed very low C and N contents in their samples. They

determined the melting point of TiB2 to be 27900C, but

later reported a value of 2920C (Post et al.14).

The first Ti-B phase diagram was presented by Palty

et al.15 (Figure 1). Their results were not definitive

since they noted that three or more phases often coexisted

and hence equilibrium was not always attained. Their pow-

der samples were arc melted and heat treated and then ex-

amined with metallographic, x-ray, and melting point tech-

niques. They noted that etching was required to distin-

guish boride phases and Ti2B detected by x-ray was not

always seen metallographically. After elimination of the

x-ray lines for Ti, TiB, and TiB2 presented by Ehrlich,4

the remainder was assumed to be the pattern for Ti2B.

However, they interpreted their x-ray results for Ti2B and

TiB as being in better agreement with the results of

Glaser.12 No evidence for Ti2B5 was given since the com-

positional range they studied did not extend to that B

level. In spite of problems achieving equilibrium, dis-

crepancies between x-ray and metallographic detection,

and questions concerning interpretation of x-ray data

based on the combined Ehrlich -Glaser12 patterns, this

0 20 40 60 80

Atomic % Boron

Figure 1. Phase diagram of the Ti-B system after Palty
et al.15

diagram due to Palty et al.15 was accepted in later work

by Samsonov and Umanskiy6 and by Hansen.7

Subsequent investigations began to clarify the ques-

tions of extended solubility, presence or absence of Ti

superlattice, Ti2B and TiB structures, and the existence

of high B phases. The early studies did not produce any

doubts about the existence or structural interpretation of
TiB2. Metallographic results of Craighead et al. showed

the B solubility in Ti to be much lower than previously

thought (less than 0.43 atomic %). Decker and Kasperl9

obtained single crystal needles of TiB (1 mm long and 0.1

mm diameter) by arc melting a 23 atomic % B alloy and dis-

solving the excess Ti with acid. From the results of

their x-ray analysis, they described an orthorhombic FeB

type crystal structure based on B chains with the b axis

as the needle axis. Although this structural interpreta-

tion of TiB was initially resisted by Samsonov and

Umanskiy16 in favor of the results of Post and Glaser,13

it gained greater acceptance when Aronsson20 pointed out
that the "Ti2B" x-ray data of Palty et al. were es-

sentially equivalent to the orthorhombic TiB data of

Decker and Kasper.19 A comparison of these two patterns
is given in Appendix 1. In addition, Aronsson20 felt the

cubic form of TiB resulted from a ternary solid solution

with 0, N or C since three coexisting phases had been re-

ported,4,15 and smaller 0 or N atoms replacing B would ex-

plain the smaller lattice parameter of cubic TiB compared

with TiC. Although Nowotny21 reported cubic and ortho-

rhombic TiB phases coexisting in a study of silicide and

boride cermets, he and his coworkers (Nowotny et al.22 and

Wittmann et al.23) later agreed with Aronsson20 that cubic

TiB was not a stable phase in the binary Ti-B system.

These same workers21-23 also found no evidence for the

existence of Ti2B5. Seybolt24 restricted his investiga-

tion to the high B alloys and found only TiB2 no Ti2B5

was seen. Thus, these several workers showed that only

orthorhombic TiB and TiB2 are recognized as stable equi-

librium phases and that Ti2B, cubic TiB, and Ti2B5 were

due to previous experimental artifacts.

These features were all confirmed by Rudy and

St. Windisch.25 They re-examined the Ti-B binary phase

diagram to reconcile their results for several boride

ternary systems with previously reported data. Using high

purity Ti and B powders and sinter-reacting, hot pressing,

or arc melting their samples, they examined them using

melting point determinations, x-ray diffraction, metallo-

graphy, and high temperature DTA. Their resultant diagram

is shown in Figure 2. As can be seen, they found no evi-

Ti TiB
35 -- - - -TIB2I I I



2 -" ~2100

0, 1668
E 1540
15 F

10 880 TB2


5 I
0 20 40 60 80 100

Atomic% Boron

Figure 2. Phase diagram of the
St. Windisch.25

Ti-B system after Rudy and

dence for Ti2B, cubic TiB, or Ti2B5; only orthorhombic TiB

and TiB2 were observed. These two phases are present with

narrow homogeneity ranges. They also remarked on the dif-

ferent etching characteristics of TiB on each side of the

peritectic composition (42 atomic % B), which could ex-

plain the metallographic observance of "Ti2B" by earlier

workers. Two features of Figure 1 may be compared with

the more recent results of Figure 2. The TiB eutectic

temperature (1670C) shown by Palty et al.15 is almost

identical to the melting point of Ti (16680C), shown on

the diagram of Rudy and St. Windisch.25 The peritectic

reaction temperature of "Ti2B" (2200C) in Figure 1 is

also very close to the peritectic reaction temperature of

orthorhombic TiB (2190C) in Figure 2. This suggests the

experimental results obtained in developing both versions

of the diagram were similar, but that the interpretation

of metallographic observations made by Palty et al.15 was

incorrect. The TiB eutectic temperature (1540C) of Fig-
ure 2 is also confirmed by Garfinkle and Davis, who ob-

served the contact reaction between liquid Ti and TiB2 to

be a eutectic reaction at 1550C. Rudy and St. Windisch25

also determined the melting point of TiB2 to be 3225C, in

contrast to the earlier results of Post et al.14 (29200C)

or Latva27 (29800C), and suggest this discrepancy is due
to C contamination.
to C contamination.

In a theoretical consideration of electron concentra-

tions in alloys, Engel28 hypothesized that a stable con-

figuration for a Ti3B4 phase existed. Later, Fenish29

reported fabricating an orthorhombic Ti3B4 compound by

sinter-reacting mixed Ti and B powders in a 3:4 stoichio-

metric ratio. It required several cycles of crushing, re-

mixing, and reheating this product in a TiB2 crucible (at

20200C for 16 20 hrs.) to obtain near completion of the
reaction.30 Residual TiB was removed by dissolving in

hydrofluoric and sulfuric acids. The resultant material

was claimed to be structurally related by several M3B4

borides29 and to undergo a peritectic reaction at

2010C.30 Although Rudy and St. Windisch25 reported no

evidence of another phase intermediate in B between TiB

and TiB2, Walther and Whitneyl found x-ray lines fitting

the Ti3B4 pattern of Fenish in their preliminary study of

Ti and B12C3. Walther also obtained strong Ti3B4 x-ray

intensities (in addition to TiB and TiB2) from Ti and B

powders mixed in a 3:4 molar ratio and hot pressed at

1600 18000C for several hours in BN-lined graphite dies.

Fenish believed his use of very pure starting materials

(Ti:99.98%; B:99.8%30) explained his observation of Ti3B4,
in contrast to the work of Rudy and St. Windisch,2 who

used materials of lesser purity (%99.7%). Although it is

possible Fenish experienced contamination of his samples

from the TiB2 crucible or from the grinding apparatus

during crushing, Walther obtained his results with mate-

rial whose purity is comparable to that of Rudy and

St. Windisch.25 The question of the existence and nature of

Ti3B4 as a stable, metastable, or impurity-stabilized

phase in the Ti-B system is not yet resolved.

The above series of investigations have clarified the

phase relations in the binary Ti-B system. The TiB2 and

orthorhombic TiB phases are the only stable borides pres-

ently established with reasonable certainty. The pos-

sibility that Ti3B4 is also a stable equilibrium compound

is not yet firmly established. The suggestion of a Ti

superlattice made by Ehrlich4 was the result of a misin-

terpretation of his x-ray data because of insufficient

number of lines detected. The pattern for "Ti2B" was

shown to be identical to that of orthorhombic TiB. The

cubic TiB, Ti2B5, and TiBx phases were not found by later

investigations and appear to have been present in earlier

studies because of contamination. The comparison of

features between Figures 1 and 2 shows that incorrect in-

terpretation of metallographic results led to further mis-

understandings concerning the true phase relationships.

The crystal structures of TiB2 and TiB are shown in Fig-

ure 3.







Figure 3. Crystal structures of TiB2 and TiB.

Ti-B System: Chemical Reactions

The problems in understanding the phase relations in

the Ti-B system have also contributed to difficulties in-

terpreting some results of chemical reactivity in this

system. Studies of the reaction between Ti and TiB2 and

between Ti and B have been reported.

In studying the chemical stability of dispersed

boride compounds, Antony and Cummings31 heated 2-4 pm

TiB2 particles in an excess Ti powder matrix for 2 hours

at 10000C. X-ray and metallographic examination showed a

product ring of TiB around the TiB2 particles. However,

their conclusion that the diffusion of B into the matrix

material is rate-controlling is not firmly established by

this simple observation. Strashinskaya and Stepanchuk32

studied the interaction between TiB2 and Group IV transi-

tion metals in mixed powder, TiB2 powder-Ti metal, and

solid-solid contact geometries. They heated their samples

in vacuum for 1 and 3 hours at 1000C intervals between

900-1700C. Their powders were -325 mesh mixed in pro-

portions of 50-50 volume %. Metallographic and x-ray ex-

amination showed that the initial formation of a 1-2 pm

product began after 3 hours heating at 9000C for the pow-

dered samples and at 10000C for the solid-solid contacts.

In the mixed powders, this phase was reported as "rhombic"

TiB (FeB orthorhombic type), which increased with in-
creasing time and temperature of reaction, and after 1

hour at 1400C no more TiB2 x-ray lines could be detected

(the initial Ti content was in excess of that required for

a stoichiometric product). The powder-metal contact re-

action layer increased to about 20 um at 13000C, but

microhardness results on the product layer were anoma-

lously low: '1050 kg/mm2 compared to %2700 kg/mm2 reported

for TiB.33 After 1 hour at 1500C, the microhardness of

this layer increased to 1650-1780 kg/mm2, which was still

uncharacteristically low for TiB. The possibility that

this layer was Ti2B or a solid solution of B in Ti was

proposed; however, the previous section has shown that

neither of these mechanisms is credible in the Ti-B sys-

tem. Since no micrographs of this layer or starting mate-

rial purity data were presented, it is difficult to assess

whether poor metallographic preparation, contamination, or

some other factor could have caused this result. The

solid-solid contact reaction appeared to form a surface

fusion zone at 1500C after 1 hour with a microhardness of

\1700 kg/mm2. Pore formation was observed for this re-

action geometry at 1300-1400C and was attributed to dif-

ferences in diffusivities of "various components" and to

volatilization. The authors also claim this product was

not "rhombic" TiB. The possibility of eutectic liquid

formation at 15000C or higher was not mentioned by

Strashinskaya and Stepanchuk.32 Comparing their comments

with the eutectic temperature evidence presented by Rudy

and St. Windisch25 and Garfinkle and Davis26 suggests

contamination may have lowered the eutectic temperature

from 15400C to 15000C. Examination of their micrographs

for this reaction zone also suggest the possibility that

their "pores" are pullout created during polishing. Since

the two studies discussed above were the only ones found

by this writer to deal with the Ti-TiB2 reaction and their

interpretations are based on insufficient or questionable

results, this provides additional justification to examine

this reaction in greater detail.
Investigations of direct Ti and B interaction show

conflicting results, which may be related in part to

kinetics. Epik34 and Samsanov and Epik35 reported the

kinetics of forming TiB2 from the elements is parabolic.

They utilized a mixture of B12C3 and borax as a B source

packed around solid Ti rods, heated this to 1100-1500C

under a dry hydrogen atmosphere for 1 8 hours, and

measured the thickness of product layer formed on the rods

and their weight gain. This layer was a single phase,

TiB2, which was well bonded due to "wedges" of boride

phase formed into the metal along grain boundaries. They

also claimed there was no counter-diffusion of Ti through

the boride because no porosity was seen at the Ti-TiB2

interface. No mention was made of the greater molar vol-

ume of TiB2 compared to Ti, which could expand into this

porosity. Zhunkovskii and Samsonov3 and Zhunkovskii3

continued similar experiments, but heated their samples

under vacuum (,10-3 mm Hg) and used amorphous B instead of

a Bl2C3-borax mixture. They also found an equally ad-

herent product layer, but during metallographic examina-

tion two distinct phases were seen while x-ray showed only

the presence of TiB2. They postulated that a fcc TiB

formed at temperature, it reverted to TiB2 and Ti upon

cooling, and that residual Ti present influenced metallo-

graphic appearance. This proposal shows a misunder-

standing of the phases in the Ti-B system. The discrepan-

cy between metallographic and x-ray results suggests

either inadequate x-ray sensitivity or poor metallographic

preparation. The micrograph provided by Zhunkovskii37 was

not sufficiently clear to judge the latter possibility.

These authors also reported that the kinetics of forming

TiB2 changes with temperature: diffusion controlled growth

became the dominant mechanism at higher temperatures.

Burykina and Evtoshok38 studied the application of protec-

tive boride coatings on graphite crucibles to avoid car-

burization of molten metals. An intermediate step to pro-

duce B12C3 was followed by application of Ti. The subse-

quent boriding of the Ti produced both TiB and TiB2 layers

with a sharp boundary between them, as determined by

microhardness measurements; with increasing time and tem-

perature the TiB2 layer increased at the expense of the

TiB. This result is in contrast to that of Samsonov and

Epik,35 where only TiB2 was reported. The part played by

the B12C3-borax mixture in favoring TiB2 formation over

TiB is not clear. However, the results of Burykina and

Evtushok38 suggest that when the elements are reacted,

their relative diffusion rates through the TiB and TiB2

layers influence the relative rates of boride formation.

This is further supported by the work of Krzyminski,39 who

reacted metal-powder samples under conditions very similar

to Samsonov and Zhunkovskii,36 but got two definite boride

layers. Even though the boride layers appear to form on

the Ti, it is not clear whether B diffuses into the Ti,

Ti diffuses through the boride layer to react at the sur-

face, or both occur simultaneously.

The above experiments utilized a Ti specimen in a B

matrix; several studies have also been conducted on B

fibers in a Ti matrix. The primary aim of these investi-

gations was to assess the degree of chemical interaction

between fibers and matrix: this interaction would reduce

the suitability of these fibers for use as fiber rein-

forcement. Burykina et al.40 used vapor phase decomposi-

tion to prepare B-coated W filaments which were then com-

pacted with Ti powder. They found some W contamination of

the B fibers by this method of preparation. Heating in

vacuum at 9000C produced only a 1 pm reaction layer after

10 hours. At higher temperatures (11000C) another ragged

layer appeared near the Ti and a measured microhardness of

2700 kg/mm2 suggested it was TiB. This layer remained

thin but the rate of TiB2 layer increase appeared to be

controlled by the rate of interface reaction at 900C,

the rate of volume diffusion at 1000-1100C, and in-

fluenced by interphase and grain boundary diffusion at

higher temperatures. After 300 hours at 9000C, only TiB2

was apparent. This change of mechanism with temperature

is similar to that reported by Zhunkovskii and Samsonov36

for Ti samples packed in B powder. In contrast to the

above results, Staudhammer et al.41 obtained only TiB when

they reacted B fibers with a Ti matrix. The main dif-

ference between their work and that of Burykina et al.4

was that the latter had W contaminated fibers. These re-

sults suggest the Ti-B interaction is too great to allow

use of B fiber reinforcement of Ti. However, Schmitz and

Metcalfe42 found that the alloy Ti 1310 (Ti 13V -

10 Mo 5 Zr 2.5% Al) reacted with B fibers at '850C

sufficiently to give a good bond during fabrication of

fiber reinforced samples, but that negligible further re-

action occurred during 10,000 hours use at 600*C. The

studies of Ti-B interaction show conflicting results with

TiB2, TiB2 + TiB, and solely TiB, reported as product

phases. This range of results is caused by differences of

purity, temperature, and method of contact, which alter

the relative diffusion rates of Ti and/or B through the

product layer.

Investigations into the bonding mechanisms of the

borides have been spurred by the influence of relative

diffusion rates on chemical reactivity and a desire to

understand their refractory properties. However, the

degree to which the Ti-B and B-B bonds are metallic, co-

valent, or ionic has not yet been resolved. Samsonov and

Latysheva43 investigated the diffusion of B, C and N in

transition metals and related this to bonding. They found

the diffusion rate was inversely dependent on atomic

radius, contrary to expectation, and suggested the amount

of chemical interaction or degree of bonding was more im-

portant than size. They formulated this dependence as a

relationship between activation energy and the parameter

1/Nn, where N is the principal quantum number and n the

number of electrons in the incomplete d-shell of the

transition metal. The activation energy decreased mono-

tonically with increasing 1/Nn, supporting their conten-

tion that diffusion was controlled by the availability of

an unfilled d-shell to bond electrons from the non-metal.

An activation energy for B diffusion in Ti of 9.152.80

kcal/mole was reported; an error in calculating these re-

sults was subsequently corrected44 to give a value of

11.2 kcal/mole. Silver and his coworkers45'46 used NMR to

investigate bonding in the borides and from their results

proposed that the metal atoms contributed electrons to the
B. Tyan et al.47 tested a theory of electron transfer

from B to Ti in TiB2 and TiB with low temperature specific

heat measurements. Although the results for TiB2 did not

conflict with the theory, the TiB results were anomalously

low. They suggested this was due to a strong Ti-B bond or

to transfer of additional electrons from the B to the

bonding part of the band structure. They could not choose

between these alternatives from their data. Gillies and

Lewis48 measured strain of ball milled powders by x-ray

line-broadening analysis and demonstrated that the bonding

strength in hexagonal TiB2 is almost isotropic. This fea-

ture is further supported by Philipp who reacted TiB2 in

a variety of acidic solutions and found it was difficult

to selectively dissolve either Ti or B; he obtained both

elemental species in solution in the stoichiometric

ratio, suggesting none of the Ti-Ti, B-B, or Ti-B bonds

are significantly stronger than the others. The pos-

sibility of a mixture of bond types in these borides could

help explain their range of properties; different bond

types become more predominant in different environments.

For example, partial metallic bonding between Ti atoms

contributes to conductivity in an electric field while

ionic and covalent characteristics of the B-B and Ti-B

bonds give these materials their brittle, incompressible

nature under mechanical loading. Such conjecture requires

additional experimental evidence to clearly establish

the nature of this behavior in the titanium borides.

The studies of chemical interaction in the Ti-B sys-

tem have led to a variety of results. Some of these dif-

ferences may be attributed to misunderstandings about the

possible phases in the system. Others may be artifacts

due to contamination or poor metallography. The observ-

ance of TiB2, TiB2 + TiB, or TiB product layers suggests

relative diffusion rates of Ti and/or B through the

borides affect the kinetics of these reactions. These re-

actions are also strongly influenced by temperature and

degree of contact between reactants.

Quantitative Microscopy

The description of a powder compact structure and its

evolution during a solid state chemical reaction is a com-

plex geometric problem. Most powders are irregular in

shape and size and when compacted their geometry becomes

even more complex since elements of porosity are also

present. For the system studied here, a qualitative geo-

metric description includes the initial observance of Ti,

TiB2, and porosity, and as the reaction proceeds, TiB also

appears. Associated with each of these four phases are

their volumes, the areas of contact between two identical

or different phases or particles, the triple lines of con-

tact between three phases, and the quadruple points where

four phases meet. Appendix 2 shows the possible combina-

tions of these features for a four-phase structure and

also for the case where features common to one material

are ignored. For example, there is no porosity-porosity

'interface in a powder compact; for this study when parti-

cles of the same phase were in contact, they were con-

sidered as one element of the structure. Thus, there are

four types of volumes, six types of interfaces, four types

of triple lines, and a single quadruple point for this

case. As the reactants are consumed to form product,

these geometric features may be created or destroyed, thus

changing the qualitative description of the microstructure

with time. Such a description at any given time has been

called a qualitative microstructural state.50 The compact

or its constituents may also be described qualitatively by

terms such as "uniform," "dispersed," "segregated," "web-

like," "coated," "filiamentary," "globular," etc. The im-

precision provided by such language is often sufficient

for many purposes.

In some cases, however, more quantitative information

is necessary, especially if a structure is examined as a

function of reaction time or some other experimental vari-

able. Quantitative information on phase volume can be ob-

tained by quantitative x-ray or chemical analysis, while

BET analysis gives information on surface area. Such

methods do not provide insight into the influence of an

arbitrary compact structure on the process being studied

and may not always detect interior volume or area compo-

nents. Usually additional qualitative examination, for

example by optical or electron microscopy, is necessary to

characterize the structure and to interpret changes

occurring with time.

The principles of Quantitative Microscopy51 provide a

quantitative description of topological and metric proper-

ties of an arbitrary piece-wise smooth and continuous geo-

metric structure. Topological properties measure the

number and connectivity of elements of the structure.

Metric properties include volume fraction, surface area,

triple line length, and surface curvature, among others.

The generality of this method is not restricted to simple

shapes or structures and is admirably suited to describing

complex powder compact microstructures.

To obtain information about a three dimensional

structure, a number of representative two dimensional sec-

tions must be examined. Topological measurements at the

present state of the art require sectioning serially

through the sample structure and counting the number of

elements of interest and also noting their appearance or

disappearance. It can be shown51 that metric information

is obtained by placing a grid of points on a series of

random sections and making several simple counting

measurements from this superposition. The results of this

series are averaged to give structural information. Fig-

ure 4 shows a grid on a section of A particles in a B

matrix. The volume fraction of the ith phase, V is

directly proportional to the average number fraction of

points falling within that phase, P, or

V = r (1)




S_______ r
+ +

+ ++
-??+ 4-




+/ + -'

Figure 4. Grid of length L placed on a section showing
particles of A in a matrix of B.



i th
The surface area per volume, SV, of the i phase is re-

lated to the number of times one of the grid lines inter-

sects the phase boundary per total grid line length, PL,


S =2 PL (2)

If the PL counts are restricted to the i-i or a particular

i-j boundary, only the corresponding interface area is

measured. Similarly, the three-dimensional triple line

length per volume, Lijk, can be related to the number of

triple points per grid area PAj

Lijk = 2 pijk (3)

The total curvature of a phase boundary, M is defined as

the integral over the surface of the local mean surface

curvature, H.

MV = /fHds = (K + K)dS (4)

where K1 and K2 are the principal normal curvatures at the

surface element dS. This may be related to the number of

tangents a sweeping grid line makes with the ith phase

boundary as seen in a two-dimensional section.
i -i (5)
V = Anet

A tangent may be arbitrarily designated positive if the

curvature vector (at the tangent point) points into the

phase (convex perimeter arc) and negative if it points out

(concave perimeter arc). This is the scheme used in Fig-
ure 4. The difference between the number of positive and
negative tangents per unit of swept area is the net tan-
gent count, Tinet. The tangent count can be applied to
specific i-j boundaries if tangents to the edge formed be-
tween two or more partial surfaces (or corners as seen in
a polished section) are also counted.52 Thus, the total
curvature of specific interface or faceted areas may also
be measured if the additional counts are made. Applying
the above relations to Figure 4, for example, gives

V = 1 VB = 8/25 = 0.32

SAB = 2(32)/10L = 6.4/L

M = -MB = (r(19 17))/L2 = 2r/L2

LV = 0

Thus, the metric parameters, VV, SV, LV and MV can be
quantitatively determined for each phase of a complex
microstructure through the simple counting measurements
and application of Equations (1), (2), (3) and (5).
Each parameter provides an independent item to character-
ize the structure. For example, two structures having the
same V1 could have significantly different S and MV val-

ues and would certainly have different microstructural

geometries. The only restrictions on the generality of

the above relations are that the sections must provide a

suitably random sampling of available structural features

and that a sufficient number of grid placements or fields

of view must be measured to assure adequate statistics.

Usually 25 100 placements are made, depending on the

accuracy desired. Most isotropic microstructures are

homogeneously uniform and locally random so a single sec-

tion plane contains all the statistical metric information

of the three dimensional compact. The accuracy of these

determinations improves with increasing number of points

in the grid, but must be compromised with the effort re-

quired to achieve this accuracy. This effort has been

reduced by electronic means, as described in greater de-

tail later.

Several additional Quantitative Microscopy parameters

obtainable from the simple counting measurements have been

developed. One of these is the mean intercept length, X,

the average surface to surface distance in a structure.

It is a measure of scale of the features examined and may

be applied to grain size of a given phase or "phase size"

of a multiphase material. It can be shown that
S--sv (6)

Although I has a definite geometric meaning, its physical
interpretation is not as straightforward in arbitrary

structures since it is not usually numerically equal to an

average grain diameter or edge length, even for features

of regular shape. Such diameters and lengths have little

meaning when applied to a powder compact. Another para-

meter is the average mean surface curvature, I, defined as

ffHdS ff (K1 + K2)dS
S S71 2(
H e rS --S- -S (7)

where KI and K2 are defined as before. It is thus the

local mean curvature averaged over the surface. It is ob-

tained from the counting measurements by the expression

R = (8)

Although H is an average and does not specify the distri-

bution of curvature values, if a phase volume is changing

due to a change in the energy of its surface, changes in

H will indicate an extension or contraction of this

boundary and the magnitude of the net average driving

force. The motion of interfaces is discussed further in

the next section. Another parameter has been proposed by

Dorfler:53 the proximity parameter is defined as the

fraction of a phase area interfaced with another phase, or

P = (9)

This could be used to weight a known surface to that por-

tion which was undergoing reaction, for example, the oxi-

dation of one metal in a mixture of metal powders. The

presence or absence of a particular proximity parameter

may also indicate in what order phases have appeared or

disappeared during a transformation.

Topological information requires serial sectioning of

the microstructure; other information obtainable by

Quantitative Microscopy, such as particle size distribu-

tion, requires measurements not made in this study.50,51

A discussion of these topics is beyond the scope of this


The principles of Quantitative Microscopy have been

discovered and rediscovered by workers in many fields,
including geology, metallurgy, biology and medicine. In

spite'of their generality, they have not been applied to

materials science problems to any great extent,55 pri-

marily because of the manual effort involved and the

availability of presumably adequate alternatives, such as

x-ray, density determinations, TGA, etc. However, some

applications of Quantitative Microscopy have been re-

ported. A few examples include studies of the kinetics of

transformations in metals,56 sintering of metals57 and

ceramics,58,59 and the effect of microstucture on

mechanical60 and electrical properties.61 The advent of

automated electronic equipment permits its use as a means

of quality control of slag includions in steel.62 How-

ever, no previous attempt to follow the evolution of a

solid state reaction in a powder compact by this means

could be found by this writer.

Kinetic Models

One viewpoint of solid state kinetic studies is that

only by studying the reaction between single crystal

couples can any meaningful information be gained about the

rates of reaction. This is done by measuring the change

in the composition profile with time or the geometric ex-

tent of product and determining the direction and dif-

fusion rate of various atomic species. This ideal is

often difficult to achieve experimentally and is usually

not representative of technological practice. Because of

this, many reactions are studied between mixed and com-

pacted powders.

Several models of solid state reactions in powders

have been proposed; and these have been reviewed by

Hulbert.63 These models assume spherical particles of one

phase are completely coated by the other matrix phase.

These models are formulated mathematically as

Kt = f(x) (10)

where K is the reaction constant, t is time, and f(x) is

some function of the extent of reaction, x. In these

cases, x is usually the volume fraction of spherical

reactant phase transformed. Expressions for the various

models are summarized in Table 1.

For diffusion controlled growth, Jander64 proposed a

spherical product shell whose thickness, y, increases at a

parabolic rate, i.e.,

SDk (11)

where D is the diffusion coefficient. Ginstling and

Brounshtein65 used the same geometry, Figure 5a, but modi-

fied the relationship to account for the decrease in

interface area as the reaction proceeds. The model was

further modified by Valensi66 and (apparently indepen-

dently) by Carter67 to allow for any volume change that

occurs during the transformation (Figure 5b). Thus, Z is

the ratio of volume of product formed per unit volume of

reactant consumed. Carter68 later learned about the

existence of the Ginstling-Brounshtein model and noted the

difference between the Ginstling-Brounshtein and the

Valensi-Carter models was small when Z<2. Clark et al.69

I 0





N 4N

+o '-4-1

E4 N 0N1
9 w -I X

C '-
o I I I I ^

c- 4 N
o4 C IS o
I -4 CM I -4

4.I a) 4

(W U C
0 1 I a)

0 1 -4 N j

.1 E- 0M c

r U 0

I 4- ") -4







0 4-2

-4 P
-4 to

:i -



2 t
1 r


Figure 5. Model geometries: a) Jander and Ginstling-
Brounshtein, b) Valensi-Carter, c) interface
displacement of arbitrary surface element.

disagreed with Carter concerning Z<2. They introduced the

effect of thermal expansion into the Valensi-Carter model

and noted that deviations from the true value of Z can

have a significant influence on the accuracy of f(x) and

of K determined from it, especially in the early stages of

reaction. The desirability of high temperature data to

accurately determine Z was also mentioned by Hulbert.63

Tammann70 assumed the diffusion coefficient is not

constant but varies inversely with time.

S= t (15)

This may occur due to changes in defect concentration or

because the matrix is a decreasing source of reactant, for

example. Kroger and Ziegler71 applied this to the Jander

geometry [Equation (16)], while Hulbert et al.72 claimed

the Tammann relation and Valensi-Carter geometry gave good

results for the kinetics of forming some spinels.

Zhuravlev et al.73 assumed the activity of the re-

acting phase depended on the fraction of unreacted mate-

rial in developing their kinetic equation.

d = k((l x) (18)

This reduces the reaction rate with time. To introduce

local concentration gradients, Serin and Ellickson74

altered Dunwald and Wagner's75 solution of Fick's second

law for spheres to incorporate the extent of reaction

The above relations present geometric and diffusion

coefficient modifications into shrinking spherical shell

particle models for diffusion controlled reactions.

If one phase is partially miscible in another, re-

actions in powders may follow nucleation and growth

models. Although the probability of a transformation ini-

tiating at nuclei in the interior of one phase is greater

in a cast material, this phenomenon is possible in powder

compacts. When several possible nucleation and growth

rates and nuclei geometries (sphere, plates or rods) are

considered, the equation in Table 1 provides a general

expression;63 where the parameter m may take on the values

given in Table 2, and is a function of reaction mechanism,

nucleation rate, and nuclei geometry. Table 2 shows that

obtaining the value of m does not unequivocally establish

the conditions and geometry of the reaction.

If the interface reaction controls the overall re-

action rate, this rate is directly proportional to the

available interface area
-- = k S(t) (22)

For uniform size spheres, the relation in Table 1 holds.63

Table 2

Summary of m Values for Nucleation
and Growth Models

Phase boundary Diffusion
controlled controlled

Three dimensional growth
Constant nucleation rate 4 2.5
Zero nucleation rate 3 1.5
(saturation of point sites)
Decreasing nucleation rate 3-4 1.5-2.5

Two dimensional growth
Constant nucleation rate 3 2
Zero nucleation rate 2 1
(saturation of point sites)
Decreasing nucleation rate 2-3 1-2

One dimensional growth
Constant nucleation rate 2 1.5
Zero nucleation rate 1 0.5
(saturation of point sites)
Decreasing nucleation rate 1-2 0.5-1.5

Several Quantitative Microscopy relationships have

been developed that permit the average velocity of an

interface (or the average growth rate of the phase it

bounds) to be determined from the counting measurements.

These are not restricted to a particular shape, but do re-

quire a continuously smooth (arbitrary) surface.. If an

element of this surface dS moves a distance n (Figure 5c)

with velocity
v = d (24)

the surface sweeps out a volume at the rate
= ffvdS (25)

It can be shown50 the corresponding changes in area and

total curvature are

S = 2ffv HdS (26)
dS S

dM = ffv K*dS (27)

where H is defined in Equation (4) and K* = K K2, the

Gaussian curvature. If the velocity integral [Equation

(25)] is normalized to the area of interest, an average

velocity, VS may be defined that is obtainable from

Quantitative Microscopy parameters.76
S 1 dV 1 dVv
vs T = s- Sv (28)

Similarly, the other weighted velocities may be averaged
to give

S 1 dS 1 dSv (29)
vH fTHdSH dt M I (29)
S 1 dM 1 dM
K = K77Kd 4 N-G) E 4 (NV-Gv) t (30)
where N and G are the topological parameters number and
genus (connectivity) of the structure, fIKdS is the Inte-

gral Curvature, and the unsubscripted symbols in the terms
second from the right are for unit mass or moles. The
parameters N and G, and hence VK, require serial sec-
tioning to be determined.
If the weighted velocity expressions Equations (25)
through (27) are normalized to the rate of volume change,
two additional curvature averages may be defined. Also
recall that

= g (7,8)
/fvHdS 1
vHdS (dS/dt) 1 dS 1 dSV
HG =TTvd (dV/dt) =2 ~7 7 (31)2
S dM/dt dM V
KG 7v9-3 V7 t 3V -V (32)

The average mean surface curvature, H, has already been

mentioned: HG is the growth rate average mean surface

curvature; and KG is the growth rate average Gaussian

curvature. The latter two parameters were first proposed

by Cahn77 and DeHoff,50'78 respectively. DeHoff notes

these parameters "provide some insight into the distribu-

tion of interface velocities in the system, and, in parti-

cular, into any correlations that may exist between velo-

city and curvature."50 If the interface velocity does not

vary much with position, then from Equations (28) through

(30), vS = VH = vK = v, or from Equations (7) and (31),

H t HG. In this special case, Equations (28) and (30)

also imply

NV G = V V (33)

or that some topological information may be obtained from

metric quantities. If HG < H or HG > H, it suggests that

curvature decreases or increases interface motion, re-


Thus, metric measurements of VV, SV, and MV provide

potentially useful information about the kinetics of a re-

action in terms of an interface velocity. Analogously

with Equation (22), an average growth rate, G(t), may be


vs = --- v = (t) (34)

If U(t) = K, the reaction is controlled by the boundary
reaction; if C(t) = K/t, a Tammann dependence is indi-

cated; and if C(t) = K/E, diffusion through the product

layer limits the reaction rate. A comparison of weighted

velocities or curvatures helps interpret these velocities.

The lack of geometric restrictions suggests this velocity

is a useful extension of kinetic models based on spheres.

However, the range of velocities occurring during a re-

action cannot be too great for the average to be represen-

tative of a particular mechanism.
The studies of phase relations in the Ti-B system2-29

have shown an evolutionary understanding of these re-

fractory materials. Some of the misunderstandings re-

sulting from this work have contributed to misinterpreta-

tions of the chemical interactions occurring in the Ti-B

system. The investigations of the Ti-TiB2 inter-

action31'32 were inconclusive and provided little informa-

tion about the rates or mechanisms involved. The related

work on direct Ti-B reactions34-44 resulted in a range of

boride products and suggested the kinetics of these re-

actions influenced what products were observed. Although

B-TiB2-TiB-Ti layers were reported,only the advance of

TiB2 was measured. Why TiB was kinetically favored over

the more stable TiB2 during the reaction1 between Ti and

B12C3 has not been answered. This evidence of rapid de-

gradation of a potentially useful refractory material also

merits attention. The ability of Quantitative Microscopy

to describe a complex powder microstructure suggests a

means to examine this problem. Thus, the aim of this

study is to investigate the kinetics and mechanisms in-

volved in the reaction between Ti and TiB2 in a mixed

powder compact.


Since a simple additive solid state reaction proceeds

by transport of the reactant phases into contact with each

other and their chemical combination to form a product

phase, several alternative mechanisms were available to

model the various stages of reaction studied here. These


1) Vapor transport, surface diffusion, or volume

diffusion of the Ti with subsequent reaction.

2) A similar transport of B to the Ti.

3) Some combination of the above.

4) Diffusion of Ti or B through a TiB product

layer at a parabolic or a Tammann rate.

5) Interface motion controlled by the rate of

reaction at the boundary.

6) Reaction rate controlled by the rate of

nucleation of TiB.

7) Reaction controlled by the decomposition of

some intermediate metastable or impurity

stabilized phase.

Several experiments were designed and run to demonstrate

the validity of some mechanisms and exclude the others.

Sample Preparation

The starting powders were 99.7% purity Ti produced by

grinding commercial metal (Atomergic Chemetals Corpora-

tion) under a neutral atmosphere and 99.8% purity TiB2

(Ventron, Inc.) made by reducing the oxides of B and Ti

with C. The particle size distribution of these powders

obtained by sieving is shown in Figure 6. The data below

20 pm were obtained using sedimentation methods. The Ti

particles were predominantly 20-50 pm with some particles

as large as 120 pm and had a platelike morphology char-

acteristic of grinding swarf (Figure 7). A negligible

amount was smaller than 20 pm. The TiB2 powder was pri-

marily 20-30 pm with some finer material and some larger

conglomerates 30-80 pm in size (Figure 8). Although

large numbers of small particles (1 pm) were detected in

the SEM and by Coulter Counter measurements, they con-

stituted a very small fraction of the total on a mass or

volume basis; attempts to obtain the complete size dis-

tribution using the Coulter Counter were unsuccessful due

to particle settling problems. The TiB2 particles were

rough but fairly equiaxed. Metallographic examination

showed very small amounts of another phase in the inter-

stices of the conglomerated particles. Electron micro-

probe analysis of these regions suggested the presence of


on N


(N 0




uo!loejj eunlOA\


Figure 7. Micrograph of Ti particles (470 X).



Figure 8. Micrographs of TiB2 particles: a) many small
particles present on larger ones (950 X), b)
large particle conglomerate of several smaller
particles (950 X).

TiC or Ti3B4 residue from the material preparation pro-

cess. Surface area measurement of these powders by BET

analysis gave 66.2 m2/gm for TiB2 and 56.5 m2/gm for Ti.

These powders were mixed in equimolar amounts in a

V-blender for 24 hours and then compacted in a uniaxial

die at 3500 kg/cm2 pressure. The resulting discs (ap-

proximately 6 mm in diameter and 2 mm thick, containing

2.5-3.0 gm of material) were placed in a tungsten element

resistance furnace (Centorr Associates, Inc., Figure 9),

which was evacuated and backfilled with high-purity

gettered Ar three times. Minimal contact between sample

and support was obtained by placing the discs on edge.

A positive pressure of flowing Ar (approximately 860 mm

Hg) was maintained during the heating and cooling cycles.

The furnace temperature was increased at a rate of

100C/min. until the desired temperature of 1100, 1200,

1300, 1400, or 1500C was achieved. This temperature was

maintained for 0, 5, 15, 30, 60, or 120 min. and then the

sample was quenched at 4000C/min. by turning off the fur-

nace. An additional sample was heated to 9000C for 180min.

to obtain a comparison with the results of Strashnskaya and

Stepanchuk.32 To allow for the energy input to the sample

during heat-up, reaction time was considered as holding

time plus heating time above 1100C. Temperatures were

0 )




> 0

*0 *
,4 d





o c


measured using a W-5% Re W-26% Re alloy thermocouple,

positioned approximately 5 mm from the sample :

These sinter-reacted discs were broken into nuggets

for metallographic preparation or pulverized to pass a

325 mesh screen for x-ray diffraction analysis. The nug-

gets were mounted in epoxy and the porosity filled by

vacuum impregnation to improve their strength during

polishing. These were polished using metal-bonded diamond

discs (3M Company) and 0.3 um alumina slurry on nylon

cloths. The solid phases were decorated by electro-
25 30
staining230 in 20 volume % NH40H electrolyte at 18 volts

for 60-80 sec. (current density approximately 100 pamps/

cm ). The anode was a screw placed through the back of

the mount and the apparatus is shown schematically in

Figure 10. Under an optical microscope, the Ti appeared

blue-purple, the TiB was tan, and the TiB2 was white or

light tan. The epoxy-porosity remained gray (Table 3).

Unreacted pressed discs were also mounted, polished and

stained to gain metallographic information about the

initial compact.

Quantitative Microscopy Measurements

Quantitative Microscopy measurements were made using

a combination of manual and electronic counts on an Imanco

Power Supply


Anode /
Anoe Cathode

Mount --

Teflon/ Electrolyte

Figure 10. Schematic of electrostaining apparatus.

Table 3

Results of Electrostaining

Phase Symbol Color Gray-shade

Ti a
TiB2 8
TiB y
porosity 6


light gray
dark gray

Quantimet 720 image analyzing computer. A block diagram

of this instrument is shown in Figure 11. The optical

image of a metallographic microscope is scanned using a

vidicon tube and the image displayed as a series of pic-

ture points of varying intensity on a television screen.

The gray-shade intensities of this representation depend

on the contrast between various phases of the optical

image. The number of picture points of a given intensity

(or voltage pulse) may be detected and separated by

setting suitable threshold windows electronically. Re-

ference to Figure 12 shows a gray (G) and a white (W)

particle in a black (B) matrix. If the phase boundaries

were sharp and the vidicon tube provided an ideal signal,

threshold settings at A and B could unambiguously separate

these phases. All picture points with intensity below A

would be detected as black, all points with intensity

greater than B would be white phase, and the rest would be

detected as gray phase.

Actual vidicon capabilities are not ideal and a

transition range of intensity across a boundary is ob-

tained in practice. For phases separated by a single

threshold, the best agreement between displayed and de-

tected image is usually achieved by setting the threshold

midway in the intensity range. For phases separated by

The Quantimet 720 Image Analyzing Computer:
a) view of instrument, b) block diagram of its

Figure 11.


--- - Scan Line

Ideal Signal


---------------- ----- A

Actual Signal



G- B

Figure 12. Effect of nonideal signal on detected image.

two or more thresholds, as at the black-white boundary,

however, a web or halo of gray phase ("G") is detected

around the white phase since some picture point intensi-

ties fall within the A-B threshold window. This is an

artifact produced by the instrument; although methods

exist to deal with this problem, the required accessories

were not available for this study and an alternative was

found. The sizerr" feature of the Quantimet subtracts a

band of selected picture point width from one side of a

detected particle or region (shown in black on Figure 13).

Since most of the "G" halo was less than 10 picture points

wide, setting the sizer to subtract a 10 picture point

wide band from the edge of the detected gray phase re-

moved most of the artifact. That portion of the true gray

phase (G) also removed was then estimated manually and

added to the reduced picture point count; allowance was

also made for the small portion of "G" that was not sub-

tracted by the sizer. Another problem is uneven illumina-

tion that may cause distortion, as shown in Figure 14.

This was minimized by using only a small central portion

of the available image for analysis. The Quantimet has

three independent threshold settings and can thus separate

four phases. The resulting colors and gray shades are

summarized in Table 3. Figure 15 shows a view observed

-O ~B

Figure 13. Effect of sizer on detected image.


-- ----S----ig





Figure 14. Effect of nonuniform background level on de-
tected image.

Figure 15. Image of microscope view displayed on Quanti-
met screen; grid indicates portion of avail-
able area analyzed for each grid placement.

by the instrument and the grid delineating the analyzed

area. The sequence of black,gray, and white phases de-

tected from it and the "G" halo may also be seen in Fig-

ure 16.

The image analyzing computer calculates the equiv-

alent of the various Quantitative Microscopy counting

measurements by considering each picture point as a point

in a grid. For this study, a grid size of 400 x 400

points (or a total of 160,000) was selected. The actual

size of this area (corresponding.to L in Figure 4) was

measured by a stage micrometer to be 200 pm x 200 pm

or 4 x 10- cm2. The number of points detected for a

phase, QV, divided by the total number of grid points

provides a point count reading, P The computer logic

detects a change from one threshold range to another at

a boundary and counts the number of points, Q on the

boundary between either increasing or decreasing intensi-

ty regions, i.e., on only one side of a particle or phase

region. If the length of grid "line" is known, this gives

a modified intercept count, P Since the point density

in the grid is so high, an approximation to the area

fraction and phase perimeter, respectively, may be ob-

served on the display. A one line memory permits counting

the number of convex and concave tangent points per unit

Images detected by Quantimet: a) black phase,
b) gray phase (note halo around white phase),
c) white phase.

Figure 16.

area for each phase, T + or Ti-, by "remembering if the
point is the first or last one of that phase from a pre-
vious scan. This feature detects tangents on only one
side of the phase but if enough counts are obtained, the
statistics remain satisfactory. Fifty placements of the
grid were made to obtain a distribution of values. These
were averaged and the 95% confidence interval and coeffi-

cient of variation calculated (Appendix 3). Using these
averages, the actual grid size (200 um), and the Quantimet
restrictions, the expressions for VV, SV, and MV were
modified as follows:

V = Q /160,000 cm3/cm3 (35)

S (0.50) cm2/cm3 (36)

M 15,708 Qnet cm/cm3 (37)

whbre Q, Q, and Tt(= T+-QT- ) are the averaged in-
strument counts in the area, intercept, and tangent count
modes, respectively. These parameters were determined for
each of the four phases. Manual estimates of Q QS, and
Q were made for TiB in the early stages of the reaction

when it was present in small amounts. The contrast be-
tween the gray epoxy and the blue-purple Ti was not always
great enough to give an unambiguous determination of Ti,

so manual estimates were also made of QS and QT for this
phase. Although individual interface areas can be deter-
mined from PL counts on particular combinations of
boundaries, i.e., Ti-TiB2 interface, the Quantimet could
only determine a QS count for the complete boundary of a
phase. Therefore, QS counts for the (Ti + TiB) and

(TiB + TiB2) phases combined were also measured to make
solution of the following set of equations for six specif-
ic interface areas possible.

SOL = Sao + say + s

S = Sa + SaY + Sad
V v V V

SY = Say + SY + S6

-mea s"s +e a s +me (38)

-fy = Sqo + Sad + saY + qYS

=+Y Sq6+ saY + Sad + qYS

The symbols ca, 8, y, and 6 are for the Ti, TiB2, TiB, and
porosity phases, respectively. Quantitative Microscopy
measurements were also made on the mounted and polished
starting material. The results of the above series of
measurements were used to compute Xi, fi, the proximity
parameter, PX, selected velocity and curvature averages,

and the solutions for the different models presented above

(Table 1). Data reduction was accomplished using several

APL computer programs (Appendix 4).

Typical operation during sample measurements required

that a field of view be selected and the focus and

threshold adjusted. An independent measure of the varia-

bility of each of these steps was found by sixteen trials

on the unstained starting material (this was essentially a

two "phase" sample of solid and porosity). First, the

instrument variability was determined by counting QV, QS,

and QT sixteen times on a single field of view with the

focus and threshold constant. Next, measurements were

made with the focus readjusted after each reading and the

threshold held constant. Finally, the focus adjustment

remained undisturbed for a series of readings where the

threshold was reset each time. Moore79 has discussed many

of the aspects affecting the accuracy of Quantitative

Microscopy measurements.

Transport Experiments

Several additional experiments to determine the

transport species and mechanism were performed. These

are shown schematically in Figure 17. To determine if

vapor transport is responsible for material movement,

pressed powder discs of Ti and TiB2 were placed in a Mo

*2 mm

/'Jq --Epoxy



Ti B2 Ti

Schematic of transport experiments: a) vapor
transport, b) surface or volume diffusion, c)
diffusion couple.

--| -MTo Support

Ti B2

Figure 17.

cylinder, separated by approximately 2 mm. Weight and

dimensional measurements were made on each disc before and

after heating at 15000C for 2 hours, the maximum time and

temperature of this study. Since the Ar gas flow was from

below, this would aid any transport that occurred from the

lower disc; configurations with either Ti or TiB2 as the

lower disc were used. Significant weight changes would

indicate operation of vapor transport from one or both of

the starting materials.

A comparison of surface diffusion to volume diffusion

for material transport was obtained by placing grains of

TiB2 60 70 pm in size on polished solid Ti discs (ob-

tained by hot pressing powder) and Ti grains on TiB2, and

heating to 1500C for 2 hours. These samples were then

polished to remove part of the grains. If surface dif-

fusion was significantly faster than volume diffusion, a

TiB reaction layer on the grains would be revealed by

electrostaining as a ring with unreactedmaterial in the

center, as depicted in Figure 17b. If surface diffusion

was not significant, then the reaction interface would

move up through the grain more uniformly by volume dif-

fusion and no product ring would be observed a rela-

tively sharp change from reactant to product would be seen

polishing through the grains.

To learn which species was diffusing, a Ti-TiB2 dif-

fusion couple was prepared (Figure 17c). This provided a

geometry with minimal porosity and so was a case where

either volume diffusion or grain boundary diffusion might

predominate. Solid discs of Ti and TiB2 were obtained by

hot pressing pressed powder discs. These were polished to

0.3 pm with A1203 slurry. A TiB2 disc was sandwiched be-

tween two Ti discs to provide two different interfaces and

two types of markers were used. One was Th02 powder of

approximately 2 4 pm size, obtained by ultrasonically

dispersing the powder in ethanol, allowing it to settle

for 2 hours, and removing the liquid near the surface.

This was placed on one of the Ti surfaces and allowed to

evaporate. A similar area dispersion on a glass slide is

shown in Figure 18. The other marker was Zr02 fibers

(Union Carbide Corporation), approximately 10 pm in dia-

meter. This sandwich was heated to 13000C for 3 hours in

a vacuum hot press; a light pressure was maintained on the

sample through the heating cycle to insure good contact

between the discs. The result was mounted and polished

perpendicular to the two interfaces to observe the loca-

tion of the reaction layer and the markers.



Figure 18. Diffusion couple markers dispersed on glass
slides: a) Th02 powder (440 X), b) Zr02 fibers
(220 X).

Quantitative X-Ray Analysis

To confirm the results of Quantitative Microscopy, a

quantitative x-ray analysis of the sinter reacted material

was made using the internal standard method.80

A Philips Electronics instrument with a vertical

goniometer was used. Goniometer speed was 1/20 20/min.

An automatic theta compensating divergence slit provided

a constant irradiated sample volume. The 1/20 receiving

slit and graphite crystal monochromator focused the dif-

fracted beam into a Norelco Scintillation detector. The

output pulses were sorted by a pulse height analyzer to

reduce background counts. This signal was recorded on a

strip chart recorder (chart speed 1 in./min.) and the peak

integrated intensity measured using a scaler-timer

counting over the duration of a peak. Excitation voltage

of 45 kv and filament current of 20 ma. were used on the

copper target x-ray tube.

To reduce the effects of particle orientation, the

sample holder was rotated at 20 rpm. The phenolic holder,

Al support, and cable drive are shown in Figure 19. The

disc-shaped sample volume is approximately 1 mm deep and

18 mm in diameter. The irradiated area is rectangular,

12 mm x 15 mm, centered within the disc.



Figure 19. X-ray equipment: a) phenolic sample holder
and Al support, b) cable drive and goniometer
(protective cover not shown).

The sample loading technique consisted of placing the

loose powder on the disc, pressing it with the flat of a

glass slide, and scraping the excess off with the edge of

the slide. An earlier attempt to load samples using the

McCreery technique81 to improve sample packing was made

(on a non-rotating sample holder), but the small improve-

ment obtained for these powders did not justify the extra

effort and the rotating holder was retained.

The sinter-reacted samples were pulverized in a mor-

tar and pestle until they could pass a 325 mesh sieve.

The ductile Ti in the early stage reaction material would

not all pass the screen and so was re-added after sieving

the rest. The mass of these samples was in the range of

0.5 1.5 gm. The internal standard material chosen was

NaC1 as it has strong,sharp peaks that do not signifi-

cantly overlap those of the other materials and can be

ground easily to -325 mesh. Ten weight % of -325 mesh

NaC1 was mixed with each sample. The calibration

standards were made by mixing reactant and product powders

containing 10 weight % NaC1 in the appropriate amounts to

give nominal volume fractions of 0, 10, 25, 50, 70, 90,

and 100% TiB. The reactant powder was obtained by mixing

equimolar amounts of -325 mesh Ti and TiB2 powders with

-325 mesh NaC1. Since commercial TiB was not available,

it was made by reacting several pressed pellets of mixed

Ti and TiB2 at 15000C for 2 hours. These conditions were

chosen to avoid the formation of eutectic liquid and

because longer times did not provide a greater yield of

TiB. The product mixture for standards was made by pul-

verizing this to pass 325 mesh and mixing it with NaC1.

The mass of the standards was 0.5 2.5 gms. and was high

enough to ensure accurate weights.

Prior to analyzing the samples, the experimental de-

viation of several factors was determined. Machine error

was determined by making 10 separate measurements of the

major peak for pure TiB2 and NaCl samples with and without

sample rotation and/or goniometer motion. Next, the de-

viation due to particle orientation and sample loading

technique was determined from 10 measurements of each ma-

terial. Samples were removed and remounted after each

run. The deviation of a single peak indicated the packing

error and the deviation of the ratio between two peaks of

the same material indicated the influence of particle

orientation. The variability due to mixing was found

from 10 runs on mixtures of Ti and TiB2 and of TiB and

NaC1. This effect was determined from the deviation in

peak intensity ratios of the two mixed materials. Cal-

culation of the average, 95% confidence interval (using

Student's t correction), and coefficient of variation were

made for each of the above (Appendix 3).

An internal standard calibration curve was obtained

from 10 runs on each standard. A background count was

measured for 100 sec. at 20 = 50.80 (d = 1.7959 A). The

integrated intensity of the Ti (d = 2.244 A), TiB2 (d =

2.033 A), NaCl (d = 2.821 A), and TiB (d = 2.140 and

2.161 A) peaks was measured from the difference of the

scaler-timer count and background. The angular range of

20 used was 45 300. The two TiB peaks were combined

into one measurement to increase the TiB count and avoid

errors due to peak overlap. The ratios of metal and

boride to NaC1 were averaged and plotted as a function of
known volume fraction. Alexander and Klug80 have shown

this calibration curve should be linear.

A similar technique was used for analyzing the

reacted samples (1100 14000C) except that only four runs

were made on each. The volume fraction for each sample

constituent was found from the calibration curve. The ex-

tent of reaction parameter, x, and various model func-

tions, f(x) (Table 1), were computed.


The results of the above experiments are presented

and related to the several alternative mechanisms pres-

ented earlier.

Metallographic Examination

A qualitative examination of the series of metallo-

graphic samples for each temperature shows the quantities

of Ti and TiB2 decreasing and TiB increasing with time.

The porosity also increases and, at higher temperatures

and longer times, is estimated to be about 50%. Some

pullout due to polishing is observed, especially at the

shorter times or lower temperatures, where less sinter

bonding occurs. Edge rounding of the TiB and TiB2 and

relief polishing of the epoxy is also seen, as would be

expected from samples of this particle size and range of

hardness. In some cases, the boundary between the borides

could also be detected due to differential relief during

polishing. During the grinding stage with 15 pm metal-

bonded diamond discs, the brittle TiB2 often fractured

and left many small pits on the surface. These were

usually removed by the polishing step, but those that re-

mained often became sites of pitting corrosion during the

electrostaining; a compromise between allowing sufficient

staining time to achieve adequate color contrast and yet

avoiding excessive corrosion of Ti or TiB2 at longer times

was required for some specimens. The deterioration of the

decorated colors with time, especially for Ti, occa-

sionally required that samples be repolished and restained

for examination in the Quantimet.

The TiB product first appeared at the contact regions

between Ti and TiB2 and began growing into the TiB2. As

the reaction proceeded, the TiB began extending to the

sides of this region and coating the TiB2 particles. It

took approximately 60, 30, and 15 min. to coat the larger

particles at 1100, 1200, and 1300C, respectively, while

at 1400 and 15000C, most particles had a TiB product layer

surrounding a TiB2 kernel after only 5 8 min. Many

smaller grains were fully converted to TiB by the time

coating of the larger particles was complete. After 2

hours at 1500C, almost all of the TiB2 was consumed, al-

though some of the larger particles had a central core of

unreacted material and uncoated portions of some TiB2

particles could still be seen. In contrast to the results
of Strashinskgyaand Stepanchuk,32 no contact reaction

zones were seen in the sample heated to 900C for 180 min.

This may be due to the smaller particle size or lesser

purity of their samples. Some completely uncoated parti-

cles were found by electron microprobe examination to be

reacted, suggesting these grains had become electrically

insulated from the rest during vacuum impregnation and

hence did not stain. Figure 20a 20e shows a representa-

tive sequence of micrographs for this reaction, while

Figure 20f illustrates this last point.

The Ti phase evolution shows these large platelike

particles decreasing in both length and breadth but main-

taining a non-equiaxed aspect until the reaction is near

completion. At this stage, the particles are usually

observed bonded to the TiB network with large voids

surrounding them; these are presumably the regions

formerly filled with larger Ti grains (center of Figure

20e). In some well-reacted specimens, a few Ti particles

much larger than the rest are seen (Figure 21). During

the course of the reaction, the Ti particle boundaries

seen in section become rounded and smooth at local rough-

ness while the boride boundaries remain ragged.

Figure 22 is an SEM micrograph of a polished and

stained sample. The particle rounding, epoxy relief, and

corrosion pits are readily visible in this view. Figure

23 shows fracture surfaces of the unreacted starting mate-

Figure 20. Sequence of reaction: a) starting material,
b) initial contact reaction (both 440 X).

Figure 20. Sequence of reaction: c) reaction continues,
d) TiB2 particles coated (both 440 X).

Sequence of reaction: e) near completion, f)
unreacted TiB2 (both 440 X).

Figure 20.

eure 21.

Large Ti grain and surrounding porosity
(110 X).

Polished and electrostained surface (540 X).

Figure 22.



Figure 23. Micrographs of fracture surfaces: a) initial
sample (570 X), b) sample reacted at 13000C/
17 min. (1950 X).





~ ~Jrr

Figure 23. Micrographs of fracture surfaces: c) sample
reacted at 1500C/124 min. (1030 X).

rial, a 13000C/17 min. sample, and a 15000C/124 min.

sample. The initial pointed contacts and openness of the

structure may be seen. This open structure is retained

and expanded with the development of projecting and appar-

ently overlapping needles of TiB.

Transport Experiment Results

The metallographic examination suggested that Ti is

the major diffusing species since TiB is seen to cover

the TiB2 and not the Ti. That the reaction proceeds from

a contact region also supports volume or surface diffusion

mechanisms no initial uniform coating of Ti or TiB on

TiB2 was seen, as would be expected for vapor transport.

Vapor transport of Ti or B is not a significant mechanism

in this reaction, even though the Ti vapor pressure at

these temperatures is fairly high (10-4 min. Hg).82 This

is confirmed by the separated discs experiment (Figure

17a); the weight change of either disc was less than 0.5%.

In addition, the Mo support inadvertently touched the Ti

disc and after heating was found with a gold coloration

near the region of contact. Auger analysis of this sur-

face showed the presence of 0, N, Mo, Mg, C, and Ti, pro-

viding more evidence for surface diffusion of Ti. It has
been reported that TiB2 vaporizes congruently83 with a
been reported that TiB2 vaporizes congruently with a

vapor pressure of <10-6 mm Hg at 2200C, so little vapor-
ization from this refractory material would be expected

at the temperatures utilized here.84

Confirmation that surface diffusion is the major

mechanism of Ti transport is provided by the experiment in

which TiB2 grains were placed on Ti. Figure 24 shows the

product ring microstructure expected (Figure 17b) if sur-

face diffusion is significantly faster than volume diffu-

sion. This view also demonstrates the fracture holes

characteristic of grinding TiB2 additional polishing to

remove them was not attempted for fear of polishing

through the grains.

Initial observation of the shrinking TiB2 phase sug-

gested Ti was diffusing through the product layer. How-

ever, it was subsequently recognized that even though Ti

was coating the TiB2 by surface diffusion, product forma-

tion could either occur by reaction of Ti with TiB2 at the

TiB-TiB2 interface or by diffusion of B through TiB to

react with Ti at the particle surface; both mechanisms

might also operate simultaneously. The diffusion couple

results demonstrate that both Ti and B diffuse, but Ti

diffuses at a faster rate. Figure 25 shows the two

couples with Th02 and ZrO2 markers. The reaction layer

is 225 30 pm thick. The markers are at the Ti-TiB

Figure 24. Result for surface diffusion transport experi-
ment (440 X).



Figure 25. Diffusion couple interfaces: a) Th02 markers
(440 X), b) ZrO2 markers (440 X).

interface, demonstrating that Ti diffused into the TiB2

and TiB. This result contradicts the contention of

several previous investigators31,32 that B is the major

diffusing species. However, they did not use markers

and none of the visible observations made here conflicts

with their micrographs or the descriptions of their couples.

Several needles of TiB projecting into the Ti may be seen,

as well as particles of TiB present in the Ti with no

visible connection to the TiB layer. These correspond to

the wedges or teeth of boride phase that have been reported

by earlier researchers. They provide evidence of counter

diffusion of B, which precipitated from solid solution dur-

ing cooling. The distance of these precipitates from the

TiB layer (410 40 um) suggested diffusion occurred along

grain boundaries. However, etching in a very dilute solu-

tion of HF and H202 showed these particles are located at

grain boundaries and within grains. The TiB grain struc-

ture was revealed as moderately columnar with many grains

extending completely across the product layer.

Hot pressing the TiB2 at 19000C for 3 hours gave about

85% dense material. To achieve greater densities, higher

temperatures (%23000C) and/or much higher pressures

(%20,000 atmospheres) are required.85-87 The porosity is

visible in the TiB2 but not in the TiB layer, indicating

it was absorbed during the transformation by expansion of

the TiB. Comparison of the TiB wedges visible on the dif-

fusion couples and the overlapped TiB needles in Figure 23

show a similar morphology. An excess of Ti appears
necessary to form these needles: Decker and Kasper used

an excess of Ti in producing their TiB single crystal

needles for x-ray crystal structure analysis.

The results of metallographic analysis and the trans-

port experiments show the reaction initiates at the con-

tact points between Ti and TiB2 particles and subsequent

reaction proceeds rapidly due to surface diffusion of Ti

over the TiB. The Ti then reacts to form TiB and con-

tinues to react with TiB2 by diffusing through the TiB

reaction layer.

Quantitative Microscopy Results

The Quantitative Microscopy results follow qualita-

tive observations. The Ti and TiB2 volume fractions, sur-

face area per volume, and total curvature per volume all

decrease as the reaction proceeds; the TiB parameters all

increase initially with a slight decrease in surface area

later. The porosity generally increases or holds steady

with time. These results were accelerated with increasing

temperature. They are tabulated in Appendix 5 and shown

graphically in the figures indicated below. Where shown,

the error bars designate the 95% confidence interval.

Data for 1100*C samples were not collected because of

excessive pullout during polishing.

The volume fraction data (Figures 26 through 29) for

the solid phases fit the trends well except for the

1200*C/31 min. reactant point; although this point may re-

flect a real plateau in the volume-time relation, there

is no corresponding plateau in TiB. Since EV = 1, an

equal but opposite shift in porosity fraction gave the re-

sults as drawn. These results also show that at 1400 and

15000C, the reaction goes almost to completion very

quickly but then advances very little. At these tempera-

tures, the value of VTi is very small; during its deter-
mination many fields of view gave QV = 0. Since the

molar volume of Ti is 2/3 that of TiB2, the observed

values for Ti are too low. The metallographic examination

for these times and temperatures suggests that most of the

Ti is isolated in a few large grains. Thus, the sample is

not representative of the true volume fraction of Ti since

it is no longer as homogeneous or uniform as before. A

random sectioning plane could easily miss this portion of

the Ti volume fraction, and many more fields of view

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