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The Influence of the Microstructure of Sintered
Hydroxyapatite on the Properties of Hardness, Fracture

Toughness, Thermal Expansion and the Dielectric Permittivity

presented by

TImothy P. Hoepfner

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601 CJCIRC/DataDuopes-ptis

 

THE INFLUENCE OF THE MICROSTRUCTURE OF SINTERED
HYDROXYAPA'ITTE ON THE PROPERTIES OF HARDNESS, FRACTURE
TOUGHNESS, THERMAL EXPANSION AND THE DIELECTRIC PERMITTIVITY

By

Timothy P. Hoepfner

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Materials Science and Mechanics

April 2001

ABSTRACT
THE INFLUENCE OF THE MICROSTRUCTURE OF SINTERED

HYDROXYAPATITE ON THE PROPERTIES OF HARDNESS, FRACTURE
TOUGHNESS, THERMAL EXPANSION AND THE DIELECTRIC PERMITTIVITY

By

Timothy P. Hoepfner

Sintered hydroxyapatite specimens with a 58-98% relative density range and
average grain sizes between 1.64 um and 7.44 pm were made with a commercial
hydroxyapatite powder. No decomposition of the hydroxyapatite was detected, by x-ray
difli'action, for any specimen. Vickers hardness (Hv) of the Sintered hydroxyapatite
specimens was successfully fit, as a ftmction of the volume fi'action porosity (P), to the
minimum solid area model (MSA): Hv = HVO 6"". The zero porosity hardness value Hv0 =
6.00 :i: 0.79 GPa and the material dependent constant b = 6.03. Fracture toughness (ch0)
of the Sintered hydroxyapatite specimens, measured by indentation methods, diverged
fi'om the MSA model. Fracture toughness increased as the porosity increased. Kw0 a 0.5
MPa m"2 for Sintered hydroxyapatite specimens of 97% relative density increasing to K“,0
22.6 MPa In"2 for specimens of 72% relative density. Thermal expansion coefficients for
Sintered hydroxyapatite, measured by dilatometry = 12.9 x 10" / °C at 100° C , 13.8 x 1045
/ °C at 200° C, 16.3 at 400° C and 19.8 x 1045 / °C at 600° C. The relative dielectric
permittivity was measured for several Sintered hydroxyapatite specimens of varying
porosity and the zero porosity relative dielectric permittivity was calculated using a

dielectric mixing law to k0 = 17.63 :t 0.70.

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

1.0

Introduction

1.1

1.2

1.3

1.4

1.5

Goals of research

Chemistry of sintering

1.2.1 Dehydroxylation and decomposition

1.2.2 Process control of phase purity during sintering
Relevant crystal structures

1 .3.1 Hydroxyapatite

1.3.2 Tricalcium phosphate

1.3.3 Tetracalcium phosphate

Microstructure of Sintered hydroxyapatite

1.4.1 Residual strain energy and microcracking
Microstructure and material Properties

1.5.1 Indentation hardness

1.5.2 Indentation method to determine fi'acture toughness
1.5.3 Hardness and fi'acture toughness studies

1.5.4 Fracture energy and microstructure

1.5.5 Indentation studies of Sintered hydroxyapatite
1.5.6 Summary of hardness and toughness studies

1.5.6.1 Hardness

10

10

10

13

16

17

21

21

2.0

1.6

1.7

1.8

1.5.6.2 Fracture toughness
Material properties and porosity and the minimum solid area
Thermal expansion and microstructure
1.7.1 Thermal expansion and microcracking

Dielectric properties and micro structure

Experimental Procedure

2.1

2.2

2.3

2.4

Starting material

2.1.1 Particle size analysis

2.1.2 Ball milling

Specimen preparation

2.2.1 Die forming

2.2.2 Cold isostatic pressure

2.2.3 Conventional filmace sintering
2.2.4 Microwave sintering

2.2.5 Sectioning the Sintered specimens
2.2.6 Specimen polishing

2.2.7 Surface etching

2.2.8 Specimen mounting for scanning electron microscopy
Microstructure measurements

2.3.1 Mass density

2.3.2 Grain size measurements

2.3.3 X-ray difli'action

Hardness and fi‘acture toughness measurements

iv

21

22

24

25

25

27

27

27

28

28

30

30

37

39

41

43

45

45

45

46

48

50

3.0

2.5

2.6

Thermal expansion

2.5.1 Specimen preparation for thermal expansion measurements

2.5.2 Thermal expansion measurement
Dielectric measurements
2.6.1 Specimen preparation for dielectric measurements

2.6.2 Dielectric apparatus and measurements

Results and Discussion

3.1

3.2

3.3

3.4

3.5

Sintered hydroxyapatite micro structure

3.1.1 Sintered density

3.1.2 Sintered grain size

3.1.3 Etched surface morphology

3.1.4 X-ray diffraction

Indentation measurements

3.2.1 Vickers hardness

3.2.2 Indentation fracture toughness

3.2.2 Thermal expansion

Hardness and microstructure comparisons with literature data

Fracture toughness and microstructure comparisons with
literature data

Further comment on the fracture toughness of Sintered
hydroxyapatite

3.5.1 Indentation toughness model and porosity

3.5.1.1 Efl‘ect of E(Pp) on the fracture toughness
of Sintered hydroxyapatite

51

51

51

52

52

52

56

56

56

56

76

76

81

81

91

98

99

104

3.5.1.2 Indentation fracture toughness of porous
YBa.2Ca3O7_x

3.5.1.3 Porosity dependence of the empirical
constant C

3.5.2 Examples of deviations fiom the MSA model for
fiacture toughness

3.5.3 Possible toughening mechanisms in Sintered
hydroxyapatite

3.6 Thermal expansion
3 .7 Dielectric measurements
3.7.1 Circuit capacitance measurement and correction
3.7.2 The relative permittivity of hydroxyapatite
4.0 Summary and Conclusions
4.1 Further research
Appendix A
Appendix B

References

106

110

114

114

120

128

128

129

135

137

139

147

154

Table 1-1

Table 1-2

Table 2-1

Table 2-2

Table 2-3

Table 2-4

Table 2-5

Table 3-1

Table 3-2

LIST OF TABLES

A survey of secondary phase formation in Sintered hydroxyapatite
under varied sintering conditions for various studies from the
literature.

Ceramic oxides in which the bulk thermal expansion coefficient
was constant for a variety of grain sizes and porosity.

Specific analysis (Ca percentages) and spectro graphic analysis
(impurities) of the hydroxyapatite powder recieved fi'om CERAC
Inc., Milwaukee, WI. The data is copied from the Certificate of
Analysis attached to material.

Processing parameters for Hydroxyapatite disk specimens.
Fired in automatically controlled tube furnace. HAP I is lot
number X16907 from CERAC inc. Milwaukee, WI.

Processing parameters for rectangular HAP Specimens, fired in
C+M box furnace under manual control. HAP II is from lot
number X21949 fiom CERAC. HAP Ia, HAP IIa- hydroxyapatite
powder ball milled with alumina pellets, HAP Iz- hydroxyapatite
powder ball milled with zirconia pellets.

Processing parameters for disk Specimens, fired in C+M box
furnace under manual control

Processing parameters for disk HAP Specimens fired in a
microwave cavity.

Processing parameters, density and grain size data for Sintered
hydroxyapatite.

Lattice parameter data for the as received hydroxyapatite powder
(HAP I) and Sintered hydroxyapatite, calculated using the 3 major
hydroxyapatite peaks fiom Figures 3-13 and 3-14 and Equations

2-2 and 2-3. Data fiom the handbook is included [69].

24

27

31

32

33

34

57

Table 3-3

Table 3-4

Table 3-5

Table 3-6

Table 3-7

Table 3-8

Table 3-9

Density, grain size and the mechanical properties of hardness and
toughness, measured by indentation technique, of Sintered
hydroxyapatite. The standard deviations (0), calculated for the
multiple indentations per specimen, are included. 78

The normalization and statistical parameters fiom the linear

regression analysis of the hardness as a function of volume fi'action
porosity (Equation 3-1: In H = 1n Ho - bP) for this study, Wang

et al. [9], Slosarczyk et al. [11], Best et al. [75], and Lu et al. [74].
Actual hardness data [9,11,74,75] from the literature is included. 88

The normalization and statistical parameters fi'om the linear
regression analysis of toughness as a function of volume fraction
porosity (Equation 3-2: In K,c = 1n K0ic - b P) for this study, DeWith

et al. [54] and Suchanek et al. [56]. Fracture toughness data from
DeWith et al. [54] and Suchanek et al. [56] are included. 92

Porosity dependence of the elastic modulus compared to the

porosity dependence of Poisson’s ratio for experimental data fit

to the MSA model (lnE = in E0 - bEP, lnv = in v0 - va,

Equation 1-8) by Rice [58]. 101

Material dependent coefficients (b,.l and b5) from the MSA

model [57] for A1203, B4C, AIN and SiO2 ceramics calculated

by Rice [58]. The HAP (hydroxyapatite) elastic modulus

attenuation coefficient was calculated for this study using

DeWith et al.’s data [54]. The hardness attenuation

coefficient for HAP has been determined previously in this

study (Table 3-4). 103

Experimental data for YBa¢Cu3O7,x from Tancret et al. [78]

and the fit, for this study, to the MSA model ln(A) = ln(Ao)- bAPP,
where A represents the property (E, Hv, etc.), A0 = the property
at zero porosity (y-intercept for the linear regression), bA is the
slope of the log-linear relation, and Pp is the volume fiaction
porosity. Included for comparison are the fracture toughness
values calculated, for each porosity, using equation 3-3

{ch = C(E/H)"2 P cm}, for this study. Column 6 contains the
fiacture toughness calculated with constant elastic modulus

(E =120 GPa), {K‘candent constant E)}. Fracture toughness
values in column 7 were calculated using the measured specimen
elastic modulus [78], in equation 3-3 {K,c(lndent)}. 108

Comparison of the zero porosity mechanical properties of
YBaQCu3OM and HAP (Calo(PO4)6(OI-I)2). 112

Table 3-10

Table 3-11

Table 3-12

Table 3-13

Table 3-14

Fracture toughness/porosity trends fit to the MSA model
(ln(Kw) = ln(K,c0)- kap) fiom the literature data for a variety
of porous ceramics. The processing method (prc) and fiacture

toughness test method (meth.) are included.

Thermal expansion data for Alumina, fi‘om American Institute
of Physics Handbook 2"” Edition [76].

The averaged thermal expansion coefficients for Sintered

hydroxyapatite specimen numbers 4-8, and 10-12 by dilatometry.

The delta is the diflereme between the cooling data and the
heating data: Delta = a cool - or heat.

Dielectric characteristics for Coors ADS 995 alumina substrate.
Data from Tech Specs, Thin Film Substrates Technical
Specifications 10-3-0897 fiom Coors Ceramics, Golden,

CO [72].

Relative permittivity for Sintered hydroxyapatite fi'om this study
and Fanovich et al. [78] and the fit parameters for the
Maxwell-Garnet equations.

116

120

125

128

130

Figure 1-1

Figure 2-1

Figure 2-2

Figure 2-3

Figure 2-4

Figure 2-5

Figure 2-6

Figure 2-7

Figure 2-8

LIST OF FIGURES

Vickers indentation impression and the characteristic dimensions
used in the hardness calculation and the toughness equation
(Equation 1-6), A) top view left and B) side view. A schematic
of the side view of representative Palmqvist cracks is given in
C) [42].

Particle size analysis from Cerac, Inc.[66] for hydoxyapatite
powder lot numbers X16907T and X21949, used in this study.
Mean values were 10.03 and 8.81 microns with standard
deviations of 6.94 and 7.05 microns for hydroxyapatite powder
lots X16907T and X21949 respectively.

Pressing die for disk specimens, fabricated fiom hardened steel
by the Michigan State University Physics Department Machine
Shop.

Rectangular die press, fabricated fi'om hardened steel by the
Michigan State University Physics Department Machine Shop.
Tolerances set to 0.001 ". Bolted together with 5/ 16" - 18, hex
head bolts before pressing.

Microwave casket assembly. Hydroxyapatite green bodies were
placed on the porous alumina disk. The optical thermometer
measured the temperature by fiom the light emitted through the
hole 1 cm above the alumina.

Microwave fumace power supply, controls and microwave cavity
schematic.

Apparatus for measuring the mass density of the hydroxyapatite
specimens using Archimedes method. The Sintered specimens

were placed into the basket for the suspended mass measurement.

Electrodes and experimental apparatus for the dielectric
measurements. The specimen was placed between the top and
bottom electrodes. The electrodes were pressed onto the
hydroxyapatite surfaces by a 5.09 cm maximum opening
micrometer (not shown).

Parallel circuit for Q-meter measurements.

12

29

35

36

40

42

47

53

55

Figure 3-1

Figure 3-2

Figure 3-3

Figure 3-4

Figure 3-5

Figure 3-6

Figure 3-7

Figure 3-8

Figure 3-9

Density as a firnction of sintering time and different uniaxial die
pressures for hydroxyapatite Sintered in the conventional fumaces
at 1300 °C. The data was taken from a subset of the data
presented in Table 3-1.

Density as a function of die pressure. The data was taken from
Sintered hydroxyapatite specimens Sintered at 13000 C for 15-120
minutes, which are a subset of the data presented in Table 3-1.
Linear fit represents the least squares fit of the data to equation
3-1. Fit parameters are slope = 0.27% relative density per 1 MPa
die pressure, y-intercept = 91% relative density and the coefiicient
of determination r2 = 0.997.

Density as a function of sintering temperature for hydroxyapatite
specimens Sintered for 60 minutes. The data was taken from a
subset of the data presented in Table 3-1.

Average grain size of Sintered hydroxyapatite as a function of
sintering temperature and time for both conventional and
microwave sintering. The data was taken flour a subset of the
data presented in Table 3-1.

Grain size as a function of percent relative density for Sintered
hydroxyapatite. The data was taken from a subset of the data
presented in Table 3-1.

Micrographs of polished and thermally etched surface of Sintered
hydroxyapatite specimen number 15 Sintered at 13000 C for 45
minutes, average grain size = 3.60 microns.

Micrograph of polished and thermally etched surface of Sintered
hydroxyapatite specimen number 45 Sintered at 1350° C for 60
minutes, average grain size = 4.59 microns.

Micrographs of polished and acid etched surface of Sintered
hydroxyapatite (0.1 M HCl for 1 minute), (a) specimen number 3
Sintered at 1300° C for 45 minutes, grain size =1.98 microns, (b)
specimen number 8 Sintered at 1400° C degrees for 240 minutes,
grain size = 7.44 microns.

Polished and thermally etched surfaces of cold isostatically
pressed (250 MPa) and Sintered hydroxyapatite specimen number
22 Sintered at 12000 C for 15 minutes. Average grain size =

1.99 um.

60

61

62

63

65

66

67

68

69

Figure 3-10

Figure 3-11

Figure 3-12

Figure 3-13

Figure 3-14

Figure 3-15

Figure 3-16

Figure 3-17

Figure 3-18

Figure 3-19

Figure 3-20

Figure 3-21

Polished and thermally etched surfaces of cold isostatically
pressed (250 MPa) and Sintered hydroxyapatite specimen number
23 Sintered at 1250° C for 30 minutes. Average grain size =

2.06 um.

Polished and thermally etched surfaces of cold isostatically
pressed (250 MPa) and Sintered hydroxyapatite specimen
number 20 Sintered at 1300° C for 15 minutes. Average grain
size = 2.30 um.

Polished and thermally etched surfaces of cold isostatically
pressed (250 MPa) and Sintered hydroxyapatite specimen number

21 Sintered at 13000 C for 120 minutes, Average grain size =
2.60 um.

X-ray diffraction pattern (Cu K“, radiation) for the as-received
powder and Sintered hydroxyapatite (HAP) specimens numbers
6 thru 9.

Additional x-ray difli'action patterns (Cu K“, radiation) for
Sintered hydroxyapatite specimens numbers 11 and 12.

Vickers indentation Hardness values for Sintered hydroxyapatite
as a function of density. The data was taken fiom Table 3-3.

Vickers Hardness plotted against the average grain size of the
Sintered hydroxyapatite. The data was taken from Table 3-3.

Statistical standard deviation of the Vickers hardness of Sintered
hydroxyapatite plotted against the average grain size. The data
was taken from Table 3-3.

Vickers indentation toughness as a function of density for Sintered
hydroxyapatite. The data was taken from Table 3-3.

Fracture toughness as a function of average grain size of Sintered
hydroxyapatite. The data was taken from Table 3-3.

Standard deviation of the fracture toughness plotted against the

average grain size of the Sintered hydroxyapatite. The data was
taken from Table 3-3.

Ratio of the Vickers indentation crack length and Vickers
indentation diagonal plotted against the % relative density, for all
410 indents on the specimens with known density measured in
this study.

70

71

72

74

75

79

80

82

83

84

85

86

Figure 3-22

Figure 3-23

Figure 3-24

Figure 3-25

Figure 3-26

Figure 3-27

Figure 3-28

Log relative indentation Hardness values for sintered
hydroxyapatite plotted against the volume fraction porosity along
with the solutions for the linear log relative hardness as a function
of volume fraction porosity (Equation 1- 8, Section 1.6). Data
was taken fi'om Table 3-3 for the present study and Table 3.4 for
the literature data.

Fracture toughness values for sintered hydroxyapatite plotted
against the volume fraction porosity. Fracture toughness values
were taken fiom Table 3-3 (present study) and Table 3-5 for the
data from Suchanek et al. [56] and DeWith et al. [54].

Relative fi'acture toughness values for sintered hydroxyapatite
as a fimction of volume fiaction porosity and the calculated
linear fit. Linear fit parameters taken from Table 3-5 for the
data from Table 3-3 (present study) and the fracture toughness
data in Table 3-5 from Suchanek et al. [56] and DeWith et al.
[54].

A section of lower volume fi'action porosity of the relative
fracture toughness values for sintered hydroxyapatite as a
function of volume fiaction porosity and the calculated linear fit.
Linear fit parameters taken from Table 3-5 for the data from
Table 3-3 (present study) and the fracture toughness data in
Table 3-5 from Suchanek et al. [56] and DeWith et al. [54] .

(E/H)“ as a function of the volume fiaction porosities

normalize by (ED/Ho)”, the firlly dense values of the elastic
modulus and hardness respectively. The decay constants bH and
bE are compiled by Rice [58] for A1203, AIN, B4C, and SiO2
(Table 3-6). The bH for HAP was determined in this study, while
bE for HAP was calculated in this study using the MSA model and
DeWith et al.’s data [54] (Table 3-6).

Calculated fi'acture toughness of the hydroxyapatite specimens in
this study using the elastic modulus as function of volume fraction
porosity {K,c (E(P))} (Equation 3-6, material dependent constant
bE = 2.93 [54]).

Crack parameter P/c”2 as a function of the volume fiaction
porosity for hydroxyapatite from this study and for

YBaQCu3O7,x fiom Tancret et al. [78]. The line through the
YBazCu3,O7,x data is fiom the MSA fit (lnP/c3° = ln(P/cmo} bP Pp)
of the crack parameter PIC” [78].

90

96

97

105

107

109

Figure 3-29

Figure 3-30

Figure 3-31

Figure 3-32

Figure 3-33

Figm'e 3-34

Figure 3-35

Figure 3-36

Fracture toughness YBaQCu3O7,x of as a function of the volume
fraction porosity determined by SENB [78] (Table 3-7),
Indentation method Klc = C (Ell-I)“2 P/cm (Equation 3-3) with
the data from Table 3-7, and the indentation method

(Equation 3-3) with constant elastic modulus (E = 114 GPa)

fiom Tancret et al. [78]. 111
The fi'acture toughness of the sintered hydroxyapatite specimens in
this study calculated with C(Pp) (Equation 3-8). 115

Normalized fracture toughness parameters (fracture toughness

for Ricote [48], and fracture energy for Case et al. [81]) studies

in which the fiacture toughness parameters increased or decreased
slightly, over a significant volume fiaction porosity range.
Normalization is done by dividing the fracture toughness by the zero
porosity fi'acture toughness as determined by the intercept of the
linear fit. The linear fit (included in plot) calculated for the entire
range of Ricote et al’s data [48]. The linear fit calculated for the
Case et al. [81] data was done for specimens with < 0.30 volume
fiaction porosity. The ceramics in question are calcium modified
lead titanate for Ricote [48] and gadolinia for Case et al. [81]. 117

Normalized fracture toughness for sintered hydroxyapatite

specimens in this study. Normalization is done by dividing the

fixture toughness by the zero porosity fiacture toughness as
determined by the intercept of the linear fit. The linear fit

(included in plot) was calculated for hydroxyapatite specimens

< 0.20 volume fiaction porosity. 118

Thermal expansion coefficient for high purity alumina determined

by dilatometry, as a function of temperature and compared with

the American Institute of Physics Handbook Value [76]

(Table 3-6). Dilatometry data taken fiom Appendix A. 121

Thermal expansion coefficients, measured by dilatometry on
heating, for sintered hydroxyapatite specimens numbers 4-8 and
10-12. Data taken from Appendix A. 123

Thermal expansion coefficient data for sintered hydroxyapatite,
from cooling dilatometry. The data taken fiom Appendix A. 124

Average thermal expansion coefficient for sintered hydroxyapatite
specimens numbers 4-8 and 10-12 (heating to 6000 C) as a

function of the average grain size. The data was taken from

Appendix A. 126

xiv

Figure 3-37

Figure 3-38

Figure 3-39

Figure 3-40

Difierence in the thermal expansion coefficient for sintered
hydroxyapatite, Delta = or cooling - or Ms , as a function of
temperature. Dilatometry data taken fiom Appendix A.

Relative permittivity data fiom sintered hydroxyapatite and the
fitted Maxwell-Gamet equations MGTl (Equation 1-9) and
MGT2 Equation (1-10). The data was taken from Table 3-9.

Relative permittivity for the sintered hydroxyapatite specimen
numbers 14, 16, 33, 41, 42 and the alumina reference material
ADS995 as a function of frequency. The data was taken fiom
Appendix B.

Relative permittivity for sintered hydroxyapatite specimen
numbers 43-46, 49 and 50 as a function of frequency. The data
was taken from Appendix B.

127

131

132

133

1.0 Introduction

Natural bone is a nano composite of ceramic apatites, principally hydroxyapatite
and carbonate apatite, and polymeric collagen fibrils [1]. Interest in the material
properties of sintered hydroxyapatite is fueled by hydroxyapatite’s applications in
structural bio-implants to replace damaged bone. Natural bone, has strength and resilience
that is difficult to match artificially. Hydroxyapatite is analogous to the natural ceramic in
bone and is bio-active in that hydroxyapatite is non-toxic and an interfacial bond will form
between implanted hydroxyapatite and living tissue [1]. Use of this bio-activity in
processing mechanically functional components, with hydroxyapatite to interface with the
living tissue, requires the study of the material properties of processed hydroxyapatite.
The strict requirements for the material properties and quality of bio-implants are due to
the high cost of replacement in terms of physical suffering and the medical care resulting

fiom the invasive implant procedure.

1.1 Goals of research

The primary goal of this study is to determine the effect of the microstructure of
sintered hydroxyapatite on the mechanical properties of hardness, fracture toughness, and
thermal expansion. The effect of the microstructure of sintered hydroxyapatite on the
dielectric permittivity is also investigated. An additional goal is to catalog the
rnicrostructures of sintered hydroxyapatite produced by compacting and sintering

powdered hydroxyapatite.

1.2 Chemistry of sintering

Sintering of hydroxyapatite allows formation of dense solid shapes, usefiil in
engineering applications, to be formed from hydroxyapatite powder. Sintering requires
mechanical compaction of powder, and firing until difl‘usion combines individual particles.
The compaction and firing process, along with the chemistry and morphology of the

starting powder, determines the microstructure of the solid material.

1.2.1 Dehydroxylation and decomposition

High temperature sintering of hydroxyapatite (HAP) powders, in air will,
depending on the sintering conditions, lead to the thermal decomposition of
hydroxyapatite to tricalcium phosphate (TCP) and tetracalcium phosphate (Tet-CP).
Thermal decomposition of hydroxyapatite is accomplished in two steps, dehydroxylation
and decomposition [2, 3, 4]. The first step, dehydroxylation to oxyhydroxyapatite (OHA)

(equation 1-1) is significant at temperatures greater than 800° C in air [2, 4, 5, 6].

(33109006 (0le -> C310(P04)6 (OH)2-2x Ox + tzO gas (1'1)

Dehydroxylation is firlly reversible in the presence of water vapor and elevated
temperatures as shown by x-ray difii‘action [4], thermogravimetric analysis [7], and by
proton electrical conductivity [8]. Other experiments have shown that dehydrated
hydroxyapatite, a hexagonal apatite called oxyapatite (OAP) Caw(PO4)60 E] (where E]
denotes a vacancy), undergoes little or no rehydroxyalation of oxyapatite at room

temperature [4,5,6].

Decomposition to tricalcium phosphate and tetracalcium phosphate occurs at

temperatures > 1000 °C (equation 1-2) afier significant loss of hydroxl groups [2,3,4].

caio(PO4)6 (OH)2 ’> 2C3} (P002 + C34P209 + H20 gas (1'2)

Decomposition temperature of hydroxyapatite can be lowered significantly by reduction of
the water partial pressure in the sintering atmosphere [2,3,4,9, 1 0], lowering the calcium
phosphate ratio [2,11,12], and by sintering with particulate additives [10,13].

At temperatures above 1120° C, dehydrated hydroxyapatite decomposes into the
a-form of tricalcium phosphate and tetracalcium phosphate [14]. B-tricalcium phosphate
formed at lower temperatures will also transform into (at-tricalcium phosphate at
temperatures above 11200 C. The or-form of tricalcium phosphate is metastable at room
temperature, the low-temperature B-forrn of tricalcium phosphate is the stable phase

below 1120°c [14].

1.2.2 Process control of phase purity during sintering

Both the dehydroxylation and decomposition reactions, 1-1 and 1-2, have H20 as
a product. The driving force for reactions 1-1 and 1-2 depends, in part, on the partial
pressure of H20 in the furnace. The starting temperatures of the decomposition reaction
as a function of water partial pressure are; 13250 C, 1426° C, 1477° C , 1485° C, 1520° C
and 1565°C at water partial pressures of 0.61 kPa, 4.25 kPa, 9.81 kPa, 12.3 kPa, 33.3
kPa and 101.3 kPa, respectively [3].

The Ca/P ratio of a hydroxyapatite powder is an indicator of the high temperature

stability of hydroxyapatite. A thermogravimetric study of stoichiometric hydroxyapatite
(Ca/P ratio = 1.67) determined that the hexagonal structure of hydroxyapatite is stable
after losing up to 75% of the hydroxyl ions in the form of water [2]. Hydroxyapatite
powders, with low Ca/P ratios, show higher rates of decomposition under the same high
temperature conditions than do hydroxyapatite powders with Ca/P ratios 1.67 or greater
[11]. Experimental data from the literature gives a wide range of secondary phase
composition of sintered hydroxyapatite, for a variety of starting powders and sintering

conditions (Table 1-1).

1.3 Relevant crystal structures

Crystalline phases of hydroxyapatite (HAP) and HAP decomposition products;
tricalcium phosphate and tetra calcium phosphate frequently coexist in the microstructure
of the sintered solid body. Interactions between phases effect the material properties of

sintered hydroxyapatite solid.

1.3.1 Hydroxyapatite

Hydroxyapatite is a member of a class of minerals known as apatites, the general
apatite formula is Ca,(PO4)3X where X denotes (0H),, F2. or Cl [15]. Apatites have a
hexagonal crystal structure with space group P63/m [15,16,17,l8]. Hydroxyapatite in
the hexagonal (apatitic) structure, P63/m has room temperature lattice parameters a0 =
0.9423 nm, and co = 0.6875 nm [18]. The theoretical density of hydroxyapatite is 3.156
g/cm3 [1 5].

Under a strict calcium phosphate ratio of GNP = 1.67, high purity hydroxyapatite

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 1-1 A survey of secondary phase formation in sintered hydroxyapatite, under
varied sintering conditions from the literature.
Starting Temperature Time Atmosphere (1 - B - Tetra- Reference
Powder (°C) (min) TCP TCP TCP
Solution 1050-1350 180 Air 0 O 0 [19]
grown
Solution 1450 180 Air Trace 0 0 [19]
grown
Filter 1150-1300 180 Air 0 0 0 [20]
Cake
Filter 800-1000 120 HIP in Air 0 0 0 [21]
Cake
Comm." 1200 60 Air 0 0 0 [10]
Comm." 120 60 Moisture 0 0 0 [10]
ppt." 1200 600 Air 0 0 O [22]
HAP 1150 1 Microwave Trace 0 0 [23]
whiskers in air
HAP 1200 1 Microwave 0 0 0 [23]
in air
ppt." 1 100 240 air 0 Trace 0 [9]
ppt." 1300 240 air 0 Trace Trace [9]
ppt." 1350 240 air Trace Trace Trace [9]
ppt." 1100-1300 240 Vacuum Trace ----- Trace [9]
Ca/P 1250 120 air 10% 75% n/a [1 1]
=1.55
CW 1250 120 air 5% 35% n/a [1 1]
=1 .61
Ca/P 1250 120 air 3% 0 n/a [1 1]
=1.64
Ca/P 1250 120 air 0 0 0 [11]
=1.67
Ca/P 1250 120 air 0 0 0 [11]
=1.73

 

‘- Commercial powder

" — Precipitate fi'om solution.

5

 

precipitates into a monoclinic structure with space group P2lfb [24,25,26]. Room
temperature hydroxyapatite monoclinic (P2,/b) lattice parameters are; a0 = 0.94214 nm, bo
= 2a,, co = 0.68814 nm and y = 120° [24]. Monoclinic hydroxyapatite has been prepared
hydrotherrnally [25], by a dry method [27], and by heating a single crystal of chloroapatite
to 1200° C in steam [24].

A fully reversible phase change from the monoclinic structure to the hexagonal
structure has been shown by disappearance of birefiingence at 211.5° C [25], dielectric
measurements at 207° C [26], x-ray difli’action analysis and differential scanning
calorimetry, with transition temperature between 2000 C and 210° C [27]. The
subsequent discussion of hydroxyapatite, in this thesis, assumes the hexagonal crystalline
structure, unless specifically noted otherwise.

Thermal expansion coefficients along the crystallographic axes, of hydroxyapatite,
reported in the literature include: a(ao) = 13.6 x1045 /° C , a(co) = 12.6 x10" /°C, varying
linearly with temperature from room temperature to 850° C Trombe et al. [4]; or(a,,) =
13.1 x10“’ /°C , a(co) = 21.7 x10‘° /°C, from 22° C to 1002° C Fischer et al. [28]; and
a(ao)= 12.2 x10‘° /°C , and a(co) = 11.5 x10‘6 /°C fiom 20° C to 576° C Perdok et al.
[29]. The difference (Act ) in the coefficient of thermal expansion along the
crystallographic axes a0 and co, from the three studies are varied: Aa = 1.0 x10"’ /°C [4],
7.4 x1045 /°C [28], 0.7 x10‘6 /°C [29].

Room temperature x-ray diffraction studies of sintered hydroxyapatite reveal the
shrinking of the lattice parameter 30 as a function of sintering temperature. Lattice
parameter ao decreases from 0.9416 nm, for sintering at 900° C, to 0.9411 nm, for

sintering at 1450°C [19], and a0 = 0.9428 nm, for sintering at 1050° C and a, decreases to

below 0.9425 nm for sintering at 1250° C [7]. The lattice parameter a0 reduction is due
to the loss of (OH‘) [7,19].

The hydroxyapatite used by Trombe et al. [4] for crystallographic thermal
expansion measurements was synthesized from tricalcium phosphate and calcium
carbonate by heating for approximately one month at 1000° C-1100° C in a nitrogen/water
vapor atmosphere. The hydroxyapatite material used in the study by Fischer et al. [28] was
extensively heat treated at1200° C for 4 hours before x-ray analysis of the crystallographic
thermal expansion coefficients. Perdok et al. [29] prepared stoichiometric (Ca/P ratio =
1.659 d: 0.03) hydroxyapatite crystals at 70° C. The differences in the concentration of
thermal vacancies between the hydroxyapatite formed in the three studies may explain the
variance in the thermal expansion along the crystallographic axes [29].

For a hexagonal crystal structure equation 1-3 is used to calculate the average
linear thermal expansion coefficient (a) from the measured crystallographic therml
expansion coefficients.

a = [2a(a.)+ a(¢.)] / 3 (1-3)
The average linear thermal expansion coefficient for polycrystalline hydroxyapatite
calculated from the above lattice thermal expansion data are: 13.24 x10‘6 /°C [4], 15.97
x10“ /°C [28], and 11.95 x10‘6 /°C [29].

Jarcho et al. recorded 11 x106 /°C for the average linear thermal expansion
coefficient for hydroxyapatite, at temperatures between 25° C to 225° C [30], the average
linear thermal expansion coefficient for hydroxyapatite measured by dilatometry, by Choi

et al. equals 16.9 x1045 /°C [31].

1.3.2 Tricalcium phosphate

The high terrrperature a-tricalcium phosphate crystallizes in a monoclinic structure

with space group P2,/a, and room temperature lattice parameters a0 = 1.2887 nm, and b0
2.7280, co = 1.5219 nm, with [3 = 126.20°[32]. The theoretical density for a -tricalcium
phosphate is 2.863 g/cm3[32].

The B-form of tricalcium phosphate is a rhombohedral with space group R3c,
room temperature lattice parameters a0 = 1.0439 nm, and co = 3.7375 nm [33]. The

theoretical density for [3 -tricalcium phosphate is 3.067 g/cm3 [33].

1.3.3 Tetracalcium phosphate

Tetracalcium phosphate has a monoclinic crystal structure with space group P2,.
Room temperature lattice parameters are a0 = 0.7023 nm, and b0 = 1.1986, c() = 0.9473
nm, with [3 = 90.90°[34]. Theoretical density for tetracalcium phosphate is 3.051 g/cm3

[34].

1.4 Microstructure of sintered hydroxyapatite

The microstructure of sintered hydroxyapatite consists, in part, of directly
measurable characteristics as porosity, grain size, impurity levels, and the presence of
secondary phases. The porosity, grain size, impurity levels, and secondary phase
relationships are controlled to engineer the processing of hydroxyapatite. Other
microstructural features that can only be measured indirectly include residual stress levels
in grains and microcracking between the grains. Interactions between different solid

phases and pores are also integral to the description of the sintered microstructure of a

solid body.

1.4.1 Residual strain energy and microcracking

Thermal expansion mismatch between phases and thermal expansion anisotropy
among individual grains create rnicrostresses in sintered ceramics during cooling fiom the
sintering temperature [35]. Stresses induced by thermal expansion mismatch and thermal
expansion anisotropy may generate internal microcracks between grains in brittle materials
[3 5]. A microcrack is a separation between grains with a large aspect ratio (length to
width ratio). Anisotropic crystals exhibit thermal expansion anisotropy in which the
thermal expansion varies along different crystallographic axes [3 5]. Thermal expansion
anisotropy of hydroxyapatite has been measured directly with varying results (section
1.3.1). The decomposition products of hydroxyapatite are all noncubic and exhibit some
degree of thermal expansion anisotropy (TEA).

The maximum elastic strain energy Ust stored in a single grain in a material subject

to thermal expansion mismatch or TEA may be expressed as equation 1-4 [36].

Ust=1/8(E ATzAamz) (1.4)

where the maximum thermal expansion difference between two adjacent grains is Aer"m ,
the modulus of elasticity is E, and the temperature change is AT.

Equation 1-5 is an energy criterion for nricrocracking which relates grain size,
grain geometries, material properties, and thermal history and is written in terms of the

maximum strain energy, equation 1-4, and a critical grain size, 8e. [36]:

gc,=kyf/E( ATzAamz) (1-5)
where k is a constant based on the grain’s geometry and 7f is the fracture surface energy.
The quantities E, AT, and Au are as defined following equation 1-4.

The or to B tricalcium phosphate transformation results in a 6.7% volume decrease
which contributes strain energy to the sintered solid body [32,33]. The magnitude of the
strain energy for [3 tricalcium phosphate grains transformed in a hydroxyapatite matrix is a
function of grain volume and the quantity and distribution of B tricalcium phosphate

crystals [7,9].

1.5 Microstructure and mechanical properties

1.5.] Indentation hardness

Vickers indentation hardness is measured by the size of the permanent deformation
of the surface of the tested material and the load required to produce the impression
(Figure 1-1). Vickers indentation hardness can qualitatively measure the relationships
between plastic deformation mechanisms, such as slip and twinning found in alumina at

room temperature [37], and microstructure.

1.5.2 Indentation method to determine fracture toughness

Fracture toughness is a measure of a materials resistance to crack growth [35].
Lawn and Wilshaw [3 8] reviewed the principles of indentation fracture and considered the
applications to fracture toughness evaluation. Due to the complex indentation stress field

considerable uncertainties exist in the absolute fiacture parameters. However,

10

determinations of the relative fiacture toughness for a material can be determined with an
accuracy that is comparable to most other fracture techniques [3 8].

For indentation fracture toughness measurements sharp indenters create an intense
elastic stress field about the point of indentation [3 8]. Shear and hydrostatic compression
near the indenter point account for the residual impression and microfracture initiation
[3 8]. Subsequent cracking is caused by tensile stress acting on the initial microfiacture
[38]. Toughness is measured by the extent of the subsequent cracking[38].

Evans and Charles [39] did a pioneering study of ceramic materials with a large
range of hardness, toughness and Poisson’s ratios. Evans and Charles compared fi'acture
toughness values (Kc) determined by the double torsion technique with the Vickers
indentation parameter (c/a), where c is the indentation crack length and a is the Vickers
indent diagonal[39]. A relationship between (KC (1)) / (H I a [H/(D E]°“) and (c/a) was
found for well behaved halfpenny cracks created by Vickers indentation, (Figure 1-1),
where (I) is a constraint factor, H is Vickers Hardness (Pa), and E is the elastic modulus
(Pa).

Anstis et al. [40] further quantified the indentation toughness technique using
fi'acture toughness data from traditional techniques (double torsion and double cantilever
bend) compiled from a variety of ceramics with a large range of hardness, toughness and
elastic modulus. Comparing toughness data measured by double torsion and double
cantilever bend methods to Vickers indentation parameters leads to an equation for the
fixture toughness as a function of the Vickers indentation crack length in which accuracy

better than 30-40% is readily attainable (Equation 1-6) [40].

11

A) B)

 

 

 

 

 

 

I 2a 1 l 23 |
\/
'<—— 2c —>'
K 2c > I

Vickers Indentation and fully developed half penny cracks
C) l 2a I

w/k/
|< >|

Vickers Indentation and Pahnqvist cracks

 

 

 

 

2c

Figure 1-1 Vickers indentation impression and the characteristic dimensions used in
the hardness calculation and the toughness equation (Equation 1-6), A) top
view left and B) side view. A schematic of the side view of representative
Palmqvist cracks is given in C) [42].

12

E
H.

 

, P
K.=§( )"‘;a-e- (M)

where H, is Vickers Hardness, E is the elastic modulus, P is the indentation load and
indentation crack length is c. The value of the non-dimensional empirically determined
constant Q is equal to 0.016 d: 0.004 [40]. Other researchers [41,42] have successfully
extended the Evans and Charles/Anstis model to the low load regime where Palmqvist

cracks (Figure 1-1) are encountered.

1.5.3 Hardness and fracture toughness studies

Hardness and fi‘acture toughness measurements of sintered ceramics have been
used to determine the influence of microstructural features such as grain size, porosity,
crystallographic phase changes, grain morphology, degree of crystallinity in glass
ceramics, and the elastic and plastic anisotropy.

The inverse trend of hardness as a function of grain size (g.s) (Hv °< [g.s]"") for a
variety of dense oxide and non-oxide materials has been studied by Rice et al. [43].
Several ceramic materials show a distinct Vickers hardness (H,) dependence on grain
size[43]. A 10 fold increase in grain sizes produces; ~70% decrease in Vickers hardness
(I-L) for MgO, ~30% decrease in H, for BeO, ~10% decrease in H, for A1203, and a ~5%
decrease in H, for MgA1204 and B4C[43]. ZrO2 shows very little grain size dependence on
H\, over the grain size range 0.5 pm to 50 um[43]. Other materials such as TiBz, SiC, TiC
and Si3N4 show little effect of a grain size hardness relationship over the grain size ranges

studied (10 rim-140 urn for TiB2 and SiC, 20 rim-140 am for TiC and Si3N4)[43].

13

Krell et al. [44] investigated the hardness versus grain size relationships of high
purity sintered alumina of 99.2% relative density . High purity submicron alumina powder
(Taimicron-DAR) was used to sinter six specimens, with grain sizes ranging from 0.4 ,um
to 4 am, to 99.2% :i:0.4% relative density [44]. Vickers hardness testing (10 N load)
measured a continuous decrease in Vickers hardness as the grain size increased (H, = 22
GPa at grain size = 0.4 pm to Hv= 15 GPa at grain size = 4 um[44]). The increase in
hardness as the grain size decreased for sintered alumina was attributed to the reduction of
dislocation mobility as the grain size decreases [44].

Hardness and toughness measurements of sintered Y203, processed by either hot
isostatic pressing (HIP) or vacuum sintering (VS), were compared using indentation
hardness techniques with indentation loads ranging fiom 25-200 N [45]. Microstructural
comparison showed that HIPed Y203 was denser than vacuum sintered Y203 (99.7%
versus 98.8% theoretical density) with HIPed Y203 having much smaller average grain
size than vacuum sintered Y203 (0.7 pm --HIP versus 15 um "vacuum sintered) [45].
HIP Y203 was ~16% harder than vacuum sintered Y2O3 (H, = 7-7.5 GPa --HIPed Y203
versus 6-6.5 GPa «vacuum sintered Y203 [45]). Direct crack measurements of the
Vickers indentation cracks (indentation toughness technique) of HIP and vacuum sintered
Y203 were used to calculate fi'acture toughness. The calculated fi'acture toughness of
HIPed Y203 was ~9% greater than vacuum sintered Y2O3 [45].

Nano indentation of nano crystalline ZnO and nano phase TiO2 shows a decrease in
hardness as the porosity of the specimen increases [46,47]. Nam-crystalline ZnO and
nano-phase TiO2 exhibited an almost linear increase in hardness as a function of sintering

temperature, regardless of the grain sizes[46,47]. The average grain sizes for nanophase

14

TiO2 were estimated from previous sintering studies of nanophase TiO2 from 12 nm as
compacted (no sintering) to 243 nm for TiO2 sintered at 900° C [47]. The average grain
sizes for ZnO is 7.4 nm (unsintered) to 140 nm for ZnO sintered at 700° C, determined by
dark field TEM [46]. Relative densities of TiO2 were estimated from previous sintering
studies of nanophase TiO2 and increase with increasing sintering temperatures. Relative
density equals ~ 75% for the as compacted TiO2 and reaches a maximum of ~ 90% at
900° C [47]. The relative density of nanocrystalline ZnO, estimated from elastic modulus
measurements, increased as the sintering temperature increased, for specimens sintered at
the maximum temperature of 900° C the relative density was estimated to be 90-95% [46].
Hardness decreases as porosity increases from 1.8 GPa at 15% relative porosity to 4.0
GPa at 5 - 10% relative porosity for ZnO [46] and fi'om 1.3 GPa at 25% relative porosity
to 9.0 GPa at 10% relative porosity for TiO2 [47].

Indentation hardness and indentation toughness measurements of calcium-modified
lead titanate ceramics show the influence of porosity, grain size and tetragonal distortion
[48]. Calcium-modified lead titanate specimens were sintered with relative porosities
ranging 2% to 30%, grain sizes between 2.4 pm to 6.0 um, and three Ca/Pb ratios; 24/76,
26/74, and 35/65. Hardness decreased as porosity increased, from 3.3 GPa at 4-7%
relative porosity to 2.3 GPa at 17.5% relative porosity for specimens with Ca/Pb ratio of
26/74, regardless of grain size (2.99-5.95 pm) [48]. The slopes of the hardness versus
porosity curves were significantly different for the different Pb/Ca ratios signifying the
effect of tetragonal distortion [48].

The quantity, morphology and distribution of fluorine containing mica embedded in

a glass matrix influenced the hardness of a glass ceramic composite, due to the weakly

15

bonded cleavage planes of the mica [49]. Vickers hardness decreased as the mica crystals
increased in number and the aspect ratio increases [49]. A precipitous decline in hardness
is measured as the growth of mica crystals caused them to interlock [49].

Elastic and plastic anisotropy of highly textured (Bi, Pb)2 SrZCaQCu3Ox
superconductor has been studied by indentation hardness measurements as a fimction of
the relative orientation of the indent [50]. Maximum hardness (H, = 45-50 MPa) is
measured when the Vickers indent diagonal is parallel to the grain texture and a rrrinirnum
hardness (H, = 35-40 MPa) is measured when the indent diagonal is 45 degrees ofi‘ of the
grain texture [50].

The fiacture toughness of dense [3 Si2N4 (98.9% :t 0.2% relative density) measured
by the single-edge precracked beam (SEPB) method, is a function of the grain size and
morphology [51]. Intermediate sintering times (4 hours at 2000° C) for [3 Si2N4 produces
an optimal number and distribution of large grains (2-20 pm diameter and 10-300 pm in
length), in a matrix of srmll grains (0.2-2 um diameter and 1-5 am long) to produce the
greatest fracture toughness (ch = 10.3 MPa m'”)[51]. Specimens sintered for 2 hours at
2000° C had a microstructure with fewer large grains distributed evenly in the matrix of
small grains and measured the lowest fiacturc toughness (K,C = 8.5 MPa mm)[51].
Specimens sintered for 8 hours at 2000° C exhibited an increase in the number and
clustering of large grains which decreased the measured fiacture toughness to Km = 8.8

MPa m"2 possibly due to an increase in microcrack density [51].

1.5.4 Fracture energy and microstructure

In studying the apparent fiacture energy 7 as a function of flaw size Rice et al [52]

16

found that ceramics with microstresses exhibit a significant decrease in the apparent
fiacture energy as the flaw sizes decrease to the scale of the intergranular microstresses
(i.e. grain size) [52]. Microstresses are defined to be stresses between neighboring grains
and are due to thermal expansion anisotropy (TEA), volumetric phase changes and
thermal expansion mismatch between phases. As the grain size increases the critical flaw
size increases and the apparent fi'acture energy decreases. Since the fiacture energy 7 is
related to fiacture toughness by Kc E(E y)” [53] the fracture toughness decreases for
materials with microstresses between grains as the grain size increases [52,53].

A review of fiacture energy data for several dense ceramics [53] showed a
pronounced maxima in the fiacture energy versus grain size relationship with a subsequent
substantial decrease in fiacture energy as the grain size increased firrther. The rnaxima in
fi'acture energy at a particular grain size, were most pronounced in non-cubic materials
such as A1203 at ~ 80 um, TiO2 at ~ 16 am and NbIOS at ~ 6 um [53]. The rnaxima in the
fracture energy and the continued decrease in fracture energy as the grain size increased
beyond the critical values has been correlated with the onset of microcracking by other

measurements, including the elastic modulus as a function of grain size [53].

1.5.5 Indentation studies of sintered hydroxyapatite

Vickers hardness values, fiom Kijima et al. [19] (indentation load 0.98 N), for
monophase, dehydrated hydroxyapatite (OHAP) ranged between 6.3 GPa and 6.5 GPa for
specimens with grain sizes between 1.6 pm and 6.5 pm and a narrow range of density
(99.0-99.4% theoretical density).

A steady increase in the fiacture toughness, measured by three point bend test, as a

17

function of density is recorded for sintered hydroxyapatite made fiom a commercial
powder (Merck A.G.) [54]. The fiacture toughness values ranged from K,C = 0.6 MPa
in"2 at ~73% theoretical density to KC = 1.0 MPa in“2 at ~97% theoretical density [54].
As the sintering temperature increased the density, grain size and amount of HAP
decomposition increased [54]. Tricalcium phosphate was detected, by x-ray diffraction,
for the four densest specimens sintered at temperatures greater than 1150° C (out of six
total specimens) [54]. The average grain size of the sintered hydroxyapatite ranges from
1.7 pm to 4 um [54].

The Knoop Hardness (1.96 N load) of pure and partially decomposed HAP
increased as the density increased for all specimens [9]. The polyphase material (partially
decomposed to a-tricalcium phosphate and tetra-calcium phosphate) exhibited
significantly greater hardness as a function of density [9]. HAP sintered to 78% relative
density yielded a Knoop hardness of Hk = 2.04 GPa for decomposed HAP versus Hk =
1.03 GPa for monophase HAP [9]. HAP sintered to 76% relative density exhibited a
Knoop hardness of H, = 1.63 GPa for the decomposed HAP versus H. = 0.93 GPa for
monophase HAP [9]. The grain size was 90 um for the HAP specimen sintered in air at
1200° C to 77.6% relative density [9].

The effect of decomposition on the hardness of the sintered hydroxyapatite
specimens shown by Wang et al. [9] was explored firrther by Slosarczyk et al. [11]. The
phase composition and Knoop hardness (indentation load not reported) of sintered
hydroxyapatite prepared fiom powders with different Ca/P ratios (Table 1- 1) was
measured [11]. Hydroxyapatite specimens (of similar density 3.06 g/cm3 to 3.11 g/cm’,

and a grain size range of 6-8 pm) exhibited Knoop hardness values of Hk = 4.9 GPa (40%

18

TCP, 60% OHAP), Hk 4.6 GPa (85% TCP, 15% OHAP) and finally Hk = 4.2 GPa for
hydroxyapatite specimens conrposed of 3% TCP, 97% OHAP [11]. Monophase
dehydrated hydroxyapatite specimens gave a Knoop hardness of HR = 2.7 GPa (2.89
g/cm3), Hk = 4.0 GPa (3.10 g/cm’) with a maximum Knoop hardness Hk = 4.6 GPa at a
density of 3. 12 g/cm3 [11]. The theoretical densities of the decomposition phases (a TCP
=2.863 g/cm3 and [3 TCP = 3.067 g/cm3) are 3-9% lower than monophase hydroxyapatite
(HAP = 3.156 g/cm’). The actual relative density of the polyphase sintered specimen will
depend on the percentage of decomposition phases present.

Fracture toughness, measured by the single edge notched bend technique (SENB),
was shown to be a function of grain size for submicron hot pressed hydroxyapatite
specimens [55]. HAP was hot pressed in an argon atmosphere from 1100 C to 1250° C to
98.8% to 99.5% relative density and with grain sizes from 0.2 um (hot pressed at 1100°
C for 30 minutes) to 1.2 pm (hot pressed at 1250° C for 600 minutes) [55]. Fracture
toughness as a firnction of grain size peaked at 0.4 pm average grain size K,C = 1.2 MPa
m"z dropping to Km < 1.0 MPa in"2 at 1.2 um average grain size [55].

Three-point bend fiacture strength measurements on the hot pressed HAP, by
Halouni et al. [55] displayed a more significant peak of the fi'acture strength as a finction
of grain size compared to the fiacture toughness peak. The fi'acture toughness and
fi'acture strength peaks were at the same grain size [55]. The fracture strength of = 137
MPa, at 0.4 pm average grain size, decreased to 0f = 99 MPa at 1.2 pm average grain size
[55]. Maximums in fracture toughness and fracture strength as a function of grain size
were attributed to the start of microcracking at the critical grain size, due to thermal

expansion anisotropy [55]. There was no attempt to determine the presence of

19

decomposition phases in the hot pressed hydroxyapatite [55].

The fracture toughness as a firnction of processing methods and reinforcing
whisker content was determined by Suchanek et al. [56], for hydroxyapatite whiskers in a
hydroxyapatite matrix. Fine grained elongated hydroxyapatite powder (grain size 20-50
nm diameter 100-3 00 nm in length) were reinforced with 0-3 0% hydroxyapatite whiskers
(whiskers of 1-4 mm diameter with aspect ratio of 5-35, average aspect ratio = 15). The
HAP powder and HAP whiskers were mixed, pressed into pellets and sintered via three
methods; pressure-less sintering, hot pressed sintering and HIP sintering. Hot pressing
and HIP sintering were done in an argon atmosphere and lead to traces (< 5%) of
decomposition product [S-TCP [56]. The fi'acture toughness of HAP/(HAP 0-30%
whisker) composites, decreased exponentially as the porosity increased regardless of the
processing method and whisker content [56]. Maximum fracture toughness values (Km =
1.4-2.0 MPa mm) were achieved by hot isostatic pressed HAP/(HAP whisker) composites
with maximum densities (97% to 99.9% relative density) and whisker contents between
20% and 30% [56]. Hot pressed HAP/(HAP whisker) composites exhibited fi'acture
toughness of K.C = 1.35-1.41 MPa in“2 for HAP/(HAP10-30% whisker) composites with
92.5-97% relative density [56]. HAP/(HAP 10% whisker) composites were pressure-less
sintered to 71% to 90% relative density and the resultant fracture toughness values ranged
fi'om ch = 0.8 MPa in“2 (71% relative density) to KIC = 1.1 MPa in”2 (90% relative
density) [56].

HAP/(HAP whisker) composites, produced by Suchanek et al [56], had higher
fracture toughness values, as a function of density, than unreinforced (0% whiskers) HAP.

Hot pressed unreinforced HAP (0%whiskers) exhibited fiacture toughness of K,C = 1.04

20

MPa m"2 at 97% relative density, which increased to K,C = 1.35-1.41 MPa mm for

HAP/(HAP 10-30% whisker) composites (92.5-97% relative density) [56].

1.5.6 Summary of hardness and toughness studies

1.5.6.1 Hardness

Hardness increases as the grain size decreases, for many sintered ceramics
[43 ,44,45]. The hardness of sintered hydroxyapatite is typically unaffected over a grain
size range of 1.6-6.5 pm [1 9] and obscured by porosity and the presence of decomposition
phases [9,11].

Secondary phases in a sintered ceramic have been shown to significantly influence
the hardness. A large decrease in hardness was measured as the amount of mica increased
in a glass ceramic, a further decrease in hardness can be attributed to the morphology of
mica [49]. Decomposition phases in sintered hydroxyapatite increased the hardness
significantly [9,11].

Porosity is the most significant factor in determining the hardness of sintered
ceramics. Hardness decreases as porosity increases in ZnO and TiO2 [46,47], calcium

modified lead titanate [48] and hydroxyapatite [9,11].

1.5.6.2 Fracture toughness
There is a complex relationship between the grain size and the fracture toughness
of sintered ceramics. As the grain size increases for sintered ceramics the fiacture

toughness decreases slightly [48] or increases slightly [45]. For other ceramics the

21

fi'acture toughness reaches a maxirna at a critical grain size then decreases significantly at
larger grain sizes [53,55]. The grain size versus toughness relationship, with a maxima at
the critical grain size, is related to microstresses between grains and microcracking
[53,55]. For Halouni et al. [55], however, no efion was made to detect the presence of
the decomposition of hydroxyapatite when the specimens were sintered in a moisture fiee
atmosphere. The fiacture toughness was compared to grain size and as the grain size
increases, due to the increasing sintering temperature, the likelihood of the decomposition
of hydroxyapatite, in an argon environment, increases [55].

The presence of secondary phases does not seem to influence the fracture
toughness of sintered hydroxyapatite compared to the rrricrostructural features of porosity
and grain size [54], or porosity and whisker reinforcement [56].

Porosity influences the fixture toughness of sintered ceramics various ways.
Fracture toughness increased as porosity increased for calcium modified lead titanate
ceramics [48]. Decreasing fracture toughness with increasing porosity was determined for
hydroxyapatite regardless of secondary phase composition [54] and regardless of the

whisker reinforcement and the presence of secondary phases [56].

1.6 Material properties and porosity and the minimum solid area model
For a wide variety of materials the porosity dependence of hardness, fracture
toughness, elastic modulus, flexural strength, compressive strength and electrical and
thermal conductivity have been successfully modeled by a minimum solid area model
(MSA) [57,58] derived from the minimum solid area ratios. The minimum solid area

ratios were calculated from (1) the idealized stacking of solid spheres, (2) idealized

22

stacking of cylindrical or spherical pores in a solid matrix, and (3) combinations of (1) and
(2), as a function of volume fraction porosity[57]. The minimum solid area model relates
the material property value of a porous material in relation to the fully dense property

value [57] (Equation 1-7).
A = A0 e 'b” (1-7)

where A is the material property of the porous material, A0 is the rmterial property of the
fully dense material, b is a constant derived fi'om the stacking arrangements. Equation l-7

can be linearized (Equation 1-8).
ln(A)=ln(Ao)-bP (1-8)

where b is the slope of the plot of the logarithm of material property (A) versus the
volume fraction porosity (P).

For all possible stacking arrangements of particle and pore used in the MSA
model, there exists a critical volume fiaction porosity (PC) at which the bond area between
pores goes to zero. Hence physical properties dr0p precipitously to zero for volume
fiaction porosities greater than the critical volume fraction porosity (PC) and Equation 1-7
no longer holds [57]. Pc lies between 0.2 and 0.7 [57]. The minimum solid area model
predicts continuous decreases in the physical properties of hardness, and fiacture
toughness as porosity increases for materials.

Fracture toughness depends less on porosity than do hardness and elastic modulus

23

[53]. In some cases an increase in fracture toughness with increasing porosity at low
porosity (< 15 volume percent) occurs or there is little or no change in fiacture toughness
at low and moderate porosity ranges (up to 15 volume percent porosity respectively) [53].
In contrast, strength and elastic modulus decrease continuously as in porosity increases
[53]. Fracture toughness is less sensitive to changes in porosity than is hardness, which
appears to be associated with either crack bridging between pores or with the interaction

between porosity and the test method [53].

1.7 Thermal expansion and microstructure

A study of several ceramic oxides by Nielson and Leipold [59] found the bulk
coeflicient of thermal expansion, measured up to 2200° C in air, was unaffected by the
microstructural features of porosity and grain size (Table 1-2). Coble and Kingery [60]
studied the physical properties of single grain size sintered alumina with variable porosity.
The bulk thermal expansion coeficient, from 25° C to 1200° C, of sintered alumina was
found to be independent of porosity over a wide range of porosity (Table 1-2) [60].

Table 1-2 Ceramic oxides in which the bulk thermal expansion coefficient was
constant for a variety of grain sizes and porosjy.

 

 

 

 

 

 

Oxide Porosity (%) Grain Size Range (um) Reference
A1203 4-49% 23 um" [60]
A1203 2-8% 3-66 um [59]
MgOOAle3 2-9% 36-53 pm [59]
MgO 2-9% 4-161 um [59]
CaO 2-4% 12-111 um [59]

 

 

 

 

 

 

* Single grain size for the entire porosity range.

24

1.7.1 Thermal expansion and microcracking

A polycrystalline solid that contains microcracks exhibits two characteristic
features in thermal expansion analysis; (1) near room temperature, the thermal expansion
of microcracked materials is lower than the thermal expansion of non-microcracked
material, and (2) a large hysteresis in the thermal expansion versus temperature curve
between the heating data and the cooling data from a microcracked specimen [61,62,63].
Both features (1) and (2) have been experimentally documented using dilatometry for
Nb205 [61], MgTi205 [62] and aluminum titanate materials [63].

Thermal expansion hysteresis between the heating and cooling curves in
dilatometry studies of sintered ceramics results fiom microcrack healing at elevated
temperatures as the temperature increases [64]. The microcracks re-open as the
temperature decreases, due to thermal expansion anisotropy and/or thermal expansion
mismatch [64]. The low values of expansion at room temperature are due to expansion of

grains into the microcracks, limiting overall specimen dilation [61].

1.8 Dielectric properties and microstructure

The relative dielectric permittivity of a polycrystalline polyphase ceramic is
dependent on the porosity and phase mixture of the solid [3 5]. The Maxwell-Garnet
theory (MGT) is a commonly used mixing rule derived for spherical inclusions within a
host matrix [65]. The MGT, included in a study by Calarne et al. [65], can be written as
equation 1-9 (MGTl). Equation 1-9 gives the relative dielectric permittivity of a mixture
of spherical pores in a ceramic host matrix as a function of the relative volume density of

the ceramic. When air is considered to be the host matrix with additions of spherical

25

ceramic inclusions, the MGT results in equation MGT2 (Equation 1-10).

k _ kce,[3 - 2R + 2ka] MGTl 1 9
"" iR+ka.(3-R)] H

 

_ [kce,(l + 2R) + 2(1- R)]
"' ‘ [kw(1- R)+ (2+ R)]

 

MGT2 (140)

where kIn and km,r are the relative dielectric permittivity of the mixture and the ceramic

respectively. R is the relative volume density of the ceramic.

26

2.0 Experimental Procedure
2.1 Starting material

The hydroxyapatite specimens for this study were made from 99% pure calcium
hydroxyapatite (HAP) powder from Cerac Inc., Speciality Inorganics, Milwaukee, WI.
Item number C-207l-1, Lot numbers X16907 (designated as HAP I) and X21949 (HAP
II). The certificate of analysis, from Cerac Inc., is reproduced in Table 2-1.
Table 2-1 Specific analysis (Ca percentages) and spectrographic analysis (irrrpurities)

of the hydroxyapatite powder recieved fi'om CERAC Inc., Milwaukee, WI.
The data is copied fiom the Certificate of Analysis attached to material.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Lot number X16907T (HAP I) Lot number X21949 (HAP II)
Element *% MFound “Theoretical *% “Found MTheoretical
% % % %
Ca 37.28 37.00 36.24 39.90
Al < 0.01 \\ <0.01 V
Cr < 0.01 <0.01
Fe < 0.01 <0.01
Mg 0.08 ‘ 0.1 k
Mn < 0.01 N/A
Na < 0.01 ‘ N/A
Si 0.08 .\ 0.1
Sr <0.01 \\ ‘ <0.01 k

 

* Spectrographic assay
” Specific analysis or property
2.1.1 Particle size analysis
Particle size analysis of the hydroxyapatite powder was performed by Cerac inc.
[66] on powder from both lot number X16907T and lot number X21949. The supplied

data entered in a spreadsheet and plotted as the percent change in the amount of particles

passed as a firnction of particle size (Figure 2-1).

2.1.2 Ball Milling

Approximately 120 grams of hydroxyapatite powder was dry ball milled in an
attempt to lower the initial powder particle size before forming and sintering. Rectangular
specimens R1-R5 and disk specimens numbers 13-17 were made from ball milled HAP
powder. Two 250 ml nalgene bottles were each loaded with 40 g of hydroxyapatite
(either HAP I or HAP II) and 130 g of almnina grinding media (HDAL 025). Another
250 ml nalgene bottle was loaded with 220 g of zirconia grinding media (Zircon 025C)
with 60 g of HAP II. The nalgene bottles were tightly sealed with nalgene screw tops.
The nalgene screw tops were secured to the bottle with duct tape. All three nalgene
bottles, loaded with HAP and grinding media, were tumbled at 20-40 rpm in a large rock
tumbler (Thumlers, Tumbler, Model B, Tru-Square Metal Products, Auburn, WA) for 293
hours. The HAP powder in the bottles adhered to the side and formed a solid mass during
tumbling. Squeezing the sides of the bottle and shaking for several seconds freed up most
of the powder fiom the walls. The milling media was filtered fiom the powder using a
small kitchen sieve (~2 mm sieve). The ball milled powders are denoted as HAP Ia, HAP
IIa and HAPIz. The “a” sufix denotes alumina ball milling and the “z” suffix denotes
zirconia ball milling. All other specimens were made from as received hydroxyapatite

powder.

2.2 Specimen preparation

Thin, dense hydroxyapatite disks (specimen numbers 1-50) and rectangular bars

28

 

 

 

 

 

 

+.
4—1-
as»
g X16907T
.l: ..
O _
392 .l-
X21949
1-IH—
0 :e:::: ‘ :::::::: ..
0.1 1 10 100

Particle Size (Microns)

Figure 2-1 Particle size analysis fi'om Cerac, Inc.[66] for hydoxyapatite powder lot
numbers X16907T and X21949, used in this study. Mean values were
10.03 and 8.81 microns with standard deviations of 6.94 and 7.05 microns
for hydroxyapatite powder lots X16907T and X21949 respectively.

29

(specimens R1 -R10) were produced fi‘om powder, by die pressing and firing (Table 2-2,
Table 2-3, Table 2—4, and Table 2-5). Specimens were polished and sectioned to prepare

them for further measurements.

2.2.1 Die forming

Hydroxyapatite powder, with no added binder, was uniaxially pressed (Carver
Laboratory press, Model C, Fred S. Carver Inc., Menominee Falls, WI) in a cylindrical or
rectangular hardened steel die. Applied pressures varied fiom 6.55 MPa to 24.0 MPa.
The disk and rectangular dies were constructed by the Michigan State University Physics
Department machine shop (Figures 2-2 and 2-3 respectively). The cylindrical steel die
produced disks 5.095 cm in diameter. The rectangular die formed bar specimens 8.89 cm
long and 1.27 cm wide. Afteruniaxial pressing, the steel die was cleaned with acetone
and lint fiee paper towels (Kimwipes EX-L, Kimberly Clark, Roswell, GA). No

lubrication was used on the steel dies.

2.2.2 Cold isostatic pressing

Disk specimens numbers 20-23, 31-35 and r8-r11 rectangular bars were cold
isostatically pressed (CIP) in a room temperature isostatic press (180 Spectrum Inc.,
Columbus, Ohio) after initial uniaxial die pressing (6.55 MPa disk specimens and 7.88
MPa for rectangular specimens). The die pressed hydroxyapatite green bodies were
placed in latex condoms to keep them from being contaminated by the water medium in
the isostatic press. The air in the loaded condoms was removed using a 30 cc syringe and

a blunt needle to withdraw the air. Cotton thread, tied around the opening of the condom

30

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2-2 Processing parameters for Hydroxyapatite disk specimens. Fired in
automatically controlled tube fumace. HAP I is lot number X16907 from
CERAC inc. Milwaukee, WI.
Specimen Material Start mass Pressure Sintering Sintering
label (g) (MPa) temperature (° C) time (min.)

1 HAP I 8 6.55 1300 60

2 HAP I 8 6.55 1300 75

3 HAP I 8 6.55 1300 45

4 HAP I 8 6.55 1300 90

5 HAP I 12 6.55 1300 105

6 HAP I 12 6.55 1300 240

7 HAP I 12 6.55 1400 120

8 HAP I 12 6.55 1400 240

9 HAP I 12 6.55 1300 300

10 HAP I 12 6.55 1300 420

11 HAP I 12 6.55 1300 540

12 HAP I 12 6.55 1300 660

 

 

 

 

 

 

 

31

 

Table 2-3

Processing parameters for rectangular HAP Specimens, fired in C+M box
furnace under manual control. HAP II is from lot number X21949 from
CERAC. HAP Ia, HAP IIa- hydroxyapatite powder ball milled with
alumina pellets, HAP Iz- hydroxyapatite powder ball milled with zirconia

 

 

 

 

 

 

 

 

 

 

 

 

pellets.
Specimen Material Start mass Pressure Sintering Sintering

label (g) (MPa) temperature (°C) time (min.)
R1 HAP la 6 23.64 1300 60

R2 HAP 12 6 23.64 1300 45

R3 HAP 113 6 23.64 1300 45

R4 HAP 11a 6 19.70 1300 15
R5 HAP Ila 6 19.70 1250 15

R6 HAP II 6 19.70 1300 15
R7 HAP I 5 19.70 1250 15

R8 HAP II 5 250 (CIP)* 1300 15

R9 HAP II 5 250 (CIP)* 1300 120
R10 HAP 11 '5 250 (CIP)* 1200 15

 

 

 

 

 

 

*

Cold Isostatic Press, 150 Spectrum, Columbus OH.

32

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2-4 Processing parameters for disk HAP Specimens, fired in C+M box furnace
under manual control.
Specimen Material Start mass Pressure Sintering Sintering
label (g) (MPa) temperature (° C) time (min.)

13 HAP 11a 10 24.00 1300 45

14 HAP 12 10 24.00 1300 60

15 HAP 12 10 24.00 1300 45

16 HAP Ila 10 17.46 1300 15

17 HAP Ia 10 17.46 1250 15

18 HAPH 10 17.46 1300 15
19 HAPI 10 17.46 1250 15
20 HAP H 9 250 (CIP)* 1300 15

21 HAP II 9 250 (CIP)* 1300 120
22 HAP H 9 250 (CIP)* 1200 15

23 HAP H ‘9 250 (CIP)"' 1250 30

24 HAP II 9 6.55 1200 15

31 HAP I 6 80 (CIP)" 1200 60

32 HAP I 6 80 (CIP)" 1350 60

33 HAP II 6 80 (CIP)" 1100 60

34 HAP H 6 80 (CIP)" 1250 601
35 HAP II 6 80 (CIP)" 1150/1300i 60/601'
36 HAP I 6 13.09 1100 60

37 HAP I 6 19.64 1100 60

38 HAP II 6 6.55 1100 60

39 HAP II 6 26.18 1200 60

40 HAP II 6 13.09 1200 60

 

 

 

 

 

 

 

it

-+++

Cold Isostatic Press, [50 Spectrum, Columbus OH.
Cold Isostatic Press run to 80 MPa three times.

Furnace run interrupted at ~ 970 ° C, restarted at ~ 440 ° C.
Specimens were cupped after first firmace run at 1150 ° C. Specimens re-fired at
1300 ° C for 60 mor minutes.

33

 

Table 2-4 Continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Material Start mass Pressure Sintering Sintering
label (g) (MPa) temperature (° C) time (min.)

41 HAP II 6 6.55 1200 60
42 HAP H 6 13.09 1250 601
43 HAP H 6 19.64 1250 601
44 HAP II 6 26.18 1250 601
45 HAP II 6 6.55 1350 60
46 HAP H 6 13.09 1350 60
47 HAP 11 7 6 26.18 1350 60
48 HAP II 6 13.09 1 150/13001' 60/60'1‘
49 HAP II 6 19.64 1150/1300? 60/601‘
50 HAP II 6 26.18 1 150/1300'1' 60/601‘

I Furnace run interrupted at ~ 970 ° C, restarted at ~ 440 ° C.

‘1 Specimens were cupped after first furnace run at 1150 ° C. Specimens re-fired at

1300 ° C for 60 mor minutes.
Table 2-5 Processinflarameters for disk HAP S aecimens fired in microwave cavity
Specimen Material Start mass Pressure Sintering Sintering
label (g) (MPa) temperature (°C ) time (min)

25 HAP H 9 6.545 1050 30
26 HAP H 9 6.545 1100 30
27 HAP II 9 6.545 1150 30
28 HAP I 8 6.545 1200 30

 

 

 

 

 

 

 

34

 

 

1— 12.7 cm —1

V - —
sum... é ml...
W |
i 4 —

5.095 cm

 

 

 

 

 

 

Z Plungers 5.095 cm diameter

Top View

1—12.7 cm ——I

Figure 2-2 Pressing die for disk specimens, fabricated from hardened steel by the
Michigan State University Physics Department Machine Shop.

35

I — 8.89cm— I

- V

rut" a,

 

       

 

 

10.16 cm

 

 

 

 

 

 

 

 

 

 

 

Exploded View

Side Plates 16.51 cmx 10.16 cm x 3.81cm
E Plungers 8.89 cm x 6.35 cm x 1.27 cm
............... Spacer Plates 10.16 cmx 3.81 x 1.27 cm

. Bolt Holes for 5/16"-18 hex head bolts

 

Figure 2-3 Rectangular die press, fabricated fi'om hardened steel by the Michigan State
University Physics Department Machine Shop. Tolerances set to 0.001".
Bolted together with 5/ 16" - 18, hex head bolts before pressing.

36

and the needle, was pulled tight as the plunger, on the syringe, was pulled back and the
needle was removed from the condom. A second condom was pulled over the material in
the first condom and again the air was removed by the syringe and needle. The outside
condom was sealed with cotton thread. The double sealed specimens were then secured in
the middle of a steel mesh (~3-5 mm mesh) cylinder (10 cm diameter and ~ 30 cm long),
which was closed at one end, to keep them fiom being sucked in to the relief valve when
the pressure was released. The mesh cylinder, with the HAP specimens tied with cotton
thread to the inside, was placed in the bore of the cold isostatic press, and the specimens
were isostatically pressed at room temperature. The specimens pressed at 250 MPa were
brought up at 50 MPa/minute and the pressure was slowly released after a minute 250
MPa. The specimens pressed at 80 MPa were brought up and down fiom atmospheric
pressure to 80 MPa three times due to equipment failure (the CIP was set to go to 250
MPa but failed). Afier removing the specimens fiom the isostatic press the condoms were
cut with scissors and peeled off the ceramic bodies. The cold isostatically pressed green
bodies were cleaned with acetone and Kimwipes, to remove latex and lubricant fiom the

HAP specimens, before firing.

2.2.3 Conventional furnace sintering

Specimens numbersl-12 were fired in a conventional electric tube firmace
(Thermtec, Lenton Thermal Designs). The green bodies were placed on a 30 cm long
alumina semicircular hollow platen which fit into the 8 cm diameter horizontally aligned
alumina furnace tube. A light, dusting (100-200 mg) of alumina powder (AKP-SO,

Sumitoma, Chemical America Inc, New York, NY) was spread beneath the green bodies

37

on the alumina platen. The alumina powder was used to prevent the bonding of the
hydroxyapatite specimen to the alumina platen at high temperatures. The alumina platen
and HAP specimens were centered horizontally in the firmace tube near the furnace
control thermocouple. The maximum temperature, dwell and ramp rate were input into
the process control unit (Model BS4937, type R Eurotherm). Heating and cooling rates
were programmed for 10°C/minute to and from room temperature.

Additional HAP specimens (numbersl3-20, and numbers 26-50) were fired in a
box furnace C + M Inc., High Temperature Furnaces, Bloomfield, NJ). Pressed
hydroxyapatite specimens were set upon a 10 cm diameter alumina platens (3 mm thick)
and placed in the center of the floor in the box fumace. A light dusting (100-200 mg) of
alumina powder (AKP-SO, Sumitoma) was spread between the HAP specimens and the
platen. The box furnace temperature was controlled manually by adjusting the element
current and using a type R (platinum/platinum-l 3% rhodium, Omega Engineering,
Stamford CT) thermocouple for feedback. The thermocouple bead was placed in the
center of the interior of the box furnace at floor level. Ceramic bead insulators, 80%
mullite 20% glass from, Omega Engineering (Omegatite 200), insulated the thermocouple
wire to the cold junction compensator box (Type R, Omega Engineering). The
thermocouple leads and insulation exited the firmace interior through grooves ground into
the refiactory at the fumace door. The heating rate averaged 10-20°C/minute fiom room
temperature. The cooling rates were manually controlled to less than 20 °C/mir1ute down
to 500 °C. Below 500 °C, the furnace interior was convectively cooled to room
temperature. A Fluke 77 multimeter was used to read the voltage from the cold junction

corrrpensator box output, on the millivolt scale. Millivolt to temperature conversion was

38

achieved using the “Revised Thermocouple Reference Tables” for type R (N .I.S.T.

Monograph 175 Revised to ITS-90), published by Omega Engineering [67].

2.2.4 Microwave sintering

Microwave sintered specimens (numbers 25-28) were placed on 5 mm thick
porous alurrrino-silicate refiactory disk 7.4 cm in diameter (Zircar Fibrous Ceramics,
Zircar Products, Florida, NY). The specimen and almnina disk were then placed on the
bottom of a cylindrical microwave sintering casket, Figure 2-4. The ends of the cylindrical
casket were made up of 2 cm thick top and bottom alumino-silicate insulating board ,
SALI type (Zircar Fibrous Ceramics), cut into disks 10.5-11 cm in diameter. The body of
the refiactory casket was made fiom 1.25 cm thick x 3 cm tall cylinder of low density
yttria stabilized zirconia (ZYC', Zircar Fibrous Ceramics). A 5 mm diameter circular view
hole was bored through the zirconia cylinder body centered 8 mm fi'om the bottom edge
of the low density stabilized zirconia cylinder. The cylindrical casket was centered in the
microwave cavity (model CMP-250, Wavemate Inc., Plymouth, MI), with the view hole
facing the center of the microwave cavity viewport.

The microwave cavity was powered by a 2kW, 2.45GHz power supply (Sairem,
microwave power supply, Vaux-en-Velin, France), in the resonant mode. Microwave
power was controlled manually, with a ranrp rate of 20—100 watts every 3 minutes. The
temperature of the specimen was unknown below 500 ° C. The temperature of the
specimen was measured by an optical thermometer (Accufiber Model 10 Optical Fiber
Temperature Control System, Accufiber Division, Luxtron Corporation, Beaverton, OR)

when the temperature was greater than 500 ° C.

39

 

Sali refiactory board 2 cm

 

 

 

 

 

 

Low Density Zirconia cylinder I
3 cm
0.5 cm diameter
T . 0 . I
1 gm] View hole for Optical Thermometer
Porous L____J+-3.2-0.3 cm thigk specimen

  

Alumina iESi!!EEEiii:§§§§§§§§§§§§§§!!!! 0,5 cm

 

Sali refractory board 2 cm

 

Exploded Side View

 

Sali refractory

 

 

11cm

Top View

Figure 2-4 Microwave casket assembly. Hydroxyapatite green bodies were placed on
the porous alumina disk. The optical thermometer measured the
temperature by from the light emitted through the hole 1 cm above the
alumina

4o

Microwave forward power was adjusted and tuned to bring the specimen to the
desired temperature (between 1050-1200 ° C). The microwave cavity was manually tuned
by minimizing the reflected power, accomplished by adjusting the locations of the cavity
short and launch probe in the microwave cavity (Figure 2-5). Tuning the cavity short and
the launch probe was done when the reflected power increased more than 20% of the
previous value. The reflected power was measured at the directional coupler in the
microwave transmission line (Microlab/FXR) by a power meter (Model 432A, Hewlett-
Packard, Palo Alto, CA). Stepper motors controlled by an IBM XT computer moved the
launch probe and the cavity short. Temperature measurements were made using the
optical pyrometer measuring the light radiating from the heated specimen through the view
hole bored in the side of the microwave casket and passing through the microwave cavity
viewport. After sintering, cool down was achieved manually at 10°C/minute to 500°C by
manipulating the microwave power. Below 500°C cooling was convective. Tables 2-2, 2-
3, 2-4, 2-5 and 2-6 list the forming and sintering data for all the specimens included in this

study.

2.2.5 Sectioning the sintered specimens

Sintered HAP and alumina specimens were sectioned with a slow speed cutting
saw (Leco Corporation, St. Joseph, MI) using a 10.16 cm diameter 0.3 mm thick diamond
saw (Superabrasive grinding wheel-M4D220-N75M, Norton Company, Worcester, MA),
with an oil based lubricant (VC-50, Leco Corporation). The HAP and alumina specimens
were then cleaned, by hand, with a liquid detergent (Liquinox, Liquinox Co., Orange, CA)

diluted ~10:1 with tap water, then rinsed with copious amounts of tap water. All HAP

41

    
   
   
 
   
  
 
     

Transmission Line

Microwave Cavity

Microwave Viewport Probe

Directional Coupler

— Water Cooled

Reflected Power Meter

0.1
2450 Mhz

   
  

2000W

  
 

 

=

IBM XT Computer Power Supply

Figure 2-5 Microwave furnace power supply, controls and microwave cavity schematic.

42

sintered sections were further cleaned with Kimwipes and acetone.

2.2.6 Specimen polishing

Hydroxyapatite specimens and parts of specimens were polished in batches that
included 3-10 specimens or parts of specimens of similar thickness (within 20%). The
specimens were glued to a flat 1.91 cm thick 19.2 cm diameter aluminum disk with
thermoplastic (thermoplastic cement, number 40-8100, Buehler LTD, Lake Bluff IL). The
aluminum disk was placed on a hot plate (Cole-Parmer Model number 465 8) and heated
to melt a 1-3 mm thick layer of thermoplastic. Next the specimens were placed on the
liquid plastic and the assembly removed from the heat. An identical aluminum disk was
placed on top of the specimens, to press the specimens against the lower aluminum plate
until the thermoplastic set.

The polishing machine (Vari-Pol VP-50, LECO Corporation, St. Joseph, MI),
used two rotations and a swinging motion (random orbit) to polish the specimens. Size
graded diamond grit (Warren Diamond powder company, Olyphant, PA) was applied to
grit size specific polishing cloth (LECO Corporation) affixed to a rigid metal disk. The
cloth covered disk and the aluminum disk, with which the specimens were glued, were
loaded into the polishing machine. The polishing cloth was lubricated with 10-20ml of
Ethylene Glycol solution (Microid diamond compound extender, LECO Corporation).
The pressure applied on the hydroxyapatite specimens, set by an allen wrench, was set by
1/4 turn tightening of the wrench

The cloth covered metal disk rotation rate was set to 150 rpm. Seven or eight

diamond grit sizes on separate cloth covered metal disks were used, sequentially from the

43

largest grit to the smallest grit, to polish the specimens. Polishing paste containing
diamond grit was graded for 67, 35, 25, 17, 15, 10, 6, and 1 micron sizes.

Initial polishing at grit sizes of 67 or 35 micron polishing evens the surfaces, and
for hydroxyapatite specimens required 40-120 minutes. For the intermediate grit sizes
(25, 17, 15, and 10 micron) polishing took 15-30 minutes for each size grit. Final
polishing of the hydroxyapatite specimen surface was done for 20-30 minutes with 6
micron diamond grit and 30-40 minutes with 1 micron diamond grit. Between grit size
changes and after final polishing the aluminum disk with the aflixed specimens was
removed fiom the polishing machine, and the specimen surfaces were cleaned with
liquinox soap and a soft bristle brush. The disk and the specimens were then rinsed

thoroughly with tap water and dried with paper towels.

2.2.7 Surface etching

Thermal etching, in order to measure the average grain size, was performed on
hydroxyapatite specimens (numbers 6 - 10 and 12 - 23). Small sections (approximately
3mm x 3mm) of polished hydroxyapatite were arranged on the alumina platen with a light
dusting of alumina powder (AKP-SO, Sumitoma), to keep the specimens fi'om bonding to
the alumina plate at high temperature. The specimens were placed in the box fumace and
brought to 1300° C for 1 hour. Heating and cooling rates were approximately 10
°C/minute to and fi'om 13000 C. Sketches of the specimen shapes and arrangements on
the plate were made for specimen identification upon retrieval from the furnace.

Acid etching, for grain size measurements, was done on hydroxyapatite specimens

(numbers 1-5, and 11), using 0.1 M hydrochloric acid at room temperature. Small

polished sections (approximately 3mm x 3mm) were set in a 50 ml glass beaker containing
15-20 ml of 0.1 M HCl, with nalgene tweezers, for 1 minute. The specimens were

removed from the acid with nalgene tweezers, placed in a 100 ml nalgene beaker full of

tap water and rinsed with a large volume of tap water.

2.2.8 Specimen mounting for scanning electron microscopy

Prepared hydroxyapatite specimens (sectioned and polished and either etched or
indented) were attached to an aluminum disk (SEM specimen mount) with carbon tape
(Structure Probe Inc., West Chester, PA) with the specimen surface of interest facing
upwards. The surface of interest of the specimens was coated with ~ 21 nm of gold by a
plasma coating machine (Emscope, SC500). Coating parameters set for the Emscope
plasma coating machine were 3 minutes coating time (plasma on), with a current of 20
mA. The deposition rate was 7 nm/minute, at 20 mA, according to the manufacturer’s

specifications [68].

2.3 Microstucture measurements

The sintered specimens were initially characterized for density, grain size, and
crystalline structure, which are grouped as process variables. Further measurements of
hardness, toughness, thermal expansion, and dielectric properties were made on the

specimens and related to the process variables.

2.3.1 Mass density

Density measurements were made by Archimedes method on whole or sectioned

45

sintered hydroxyapatite specimens. The mass of the specimen dry, wet (by distilled
water), and suspended in distilled water were measured three times, and these
measurements are averaged. Dry specimens were measured, to 0.1 mg precision, on a
electronic laboratory scale (Accutron, Denver Instrument Co. Arvada, CO). Suspended
measurements were made by measuring the mass of the specimen minus the weight of the
distilled water displaced by the specimen (Figure 2-6). The wet specimens were measured
after the suspended measurement, the surface water was wiped off with damp Kimwipes
before measuring. The difference in the mass of the wet specimen and the suspended
specimen is the mass of the displaced distilled water and can be converted into a volume
using 1 g = 1 cm’. The dry mass was then divided by the volume of the displaced water to

determine the specimen density (Equation 2-1).

density = (dry mass) / [(wet mass - suspended mass)/(l g/cm3)] (2-1)

The specimen density was then divided by the theoretical density of the
hydroxyapatite (theoretical density of hydroxyapatite = 3.156 g/cm’), then multiplied by

100 to obtain the relative density as a percent of theoretical density.

2.3.2 Grain size measurements

Grain sizes were calculated from scanning electron microscope (Hitachi S-2500C)
micrographs of polished, etched and gold plated surfaces of sintered hydroxyapatite
specimens. One or more images were taken at magnifications of 2000X or greater with

Polaroid 55 fihn (Polaroid Corporation, Cambridge, MA). Twenty to thirty more lines of

46

SAMPLE

Figure 2-6

BALANCE PAN

\

DISTH.LED
WATER

 

 

 

Apparatus for measuring the mass density of the hydroxyapatite specimens
using Archimedes method. The sintered specimens were placed into the
basket for the suspended mass measurement.

47

5 cm were superimposed on the rrricrographs and the grain boundary intercepts along
these lines were counted. The total length of the superimposed lines was divided by the
number of intercepts multiplied by the magnification in order to determine the average

grain size of the specimen (Equation 2-2).

L,
. = ' 0X 2-2
gs NIOM ( )

 

where g.s. = Grain size (meters), Ln = Total length of the drawn test line(s) (meters), NI =
Total number of grain boundary intercepts, M = Magnification of image, X = Geometric
constant (1.0 was used for HAP). An excess of 200 intercepts/image were used in the

calculations.

2.3.3 X-ray diffraction

Unsintered hydroxyapatite powder (HAP I fiom Cerac Inc.) and sintered
hydroxyapatite powder were pressed into a ~ 3/16 “ diameter ground out depression in a
glass microscope slide. The glass microscope slide was ground out with a coarse SiC grit
impregnated 1/ " diameter brass ball on the end of a 5 - 3000 rpm variable speed rotary
tool (Sears and Roebuck and Co., Hoflinan Estates, IL) . The sintered powder was
obtained fiom the sintered specimens numbers 6-9, 11 and 12 by crushing and grinding a
small (approximately 4 mm x 4 mm) section using a Coors porcelain mortar and pestle
(mortar number 60316, pestle number 522-4, Coors Ceramics Company, Golden, CO).
The grinding was done until the powder was very fine and adhered to the side of the

mortar. About 10-20 turns of the pestle were required to produce appropriate powders

48

once the specimen was broken up. The glass slide with the hydroxyapatite powder sample
was installed into the target holder in the SCINTAG 2000 x-ray machine (Model number
XDS 008, serial number 091, Scintag USA inc.). The powder sample was then irradiated
with a parallel beam of CuKal. radiation (A = 15.405nm) collimated from the x-ray source
by 2mm and 2mm slits ( 40 mm apart) and then a nosepiece 54 mm long with a 1.5 mm
diameter hole. The x-rays were collimated after the sample by 0.5m and 0.3rmn slits 40
mm apart before the x-ray detector. A step scan program was run at 0.2 min/degree with
a step of 0.02 degrees. The counts versus dim‘action data were stored in the controlling
computer (various PC’s, with proprietary software fiom Scintag). A Scintag program
converted the binary data into ASCII which was then downloaded into a spreadsheet
(Quattro Pro 8, Corel Corporation, Ottawa, Ontario, Canada) for analysis and plotting.

The plane spacings for each specimen were calculated using the wavelength fiom
CchrL, the 20 peak from the three major difl'raction peaks on the difli‘action curve, and
the Bragg law (Equation 2-3).

A = 2 d sinO (2-3)

From the plane spacing the lattice parameters (a and c) were calculated using the
plane index for the three major difli'action peaks, from the ASTM powder diffraction files
for inorganic phases [69], and the {plane spacing equation for the hexagonal lattice fiom

appendix 3 in Cullity [70] (Equation 2-4).

d2‘3

 

1 4 h2 + hk + k2 I2
02 + 67 (2'4)

49

2.4 Hardness and fracture toughness measurements

Hardness and toughness measurements were made by measuring Vickers
indentations on the polished faces of the hydroxyapatite specimens (V ickers micro
hardness tester, Buehler LTD, Lake Blufi‘ IL). Loads of 2.94 N, 4.90 N, and 9.81 N were
used with a 10 second loading time and a head speed of 70 uni/s. To guarantee 7 tolO
recordable indents, 10 to 20 indentations per specimen were made. Indentations with
surface spalling were rejected. For the hardness calculation the diagonal lengths of the
indent (2a), in meters, were recorded (Figure 2-7). The total length of the radial cracks
plus the diagonal lengths of the indent, (2c), were measured and recorded for the
toughness calculation.

The hardness and toughness of the sintered HAP specimens were calculated using
Equations (2-5) and (2-6) and‘the Vickers indentation measurements. These equations
and the empirical constant C were from Antsis et al. [40] presented by Wachtrnan [71].

The hardness H is calculated in GPa by Equation 2-5.

H = P / 232 (2-5)

where P is the load in Newtons, a is 1/2 the length of the indent diagonal in meters.

Fracture toughness K,C was calculated using Equation 2-6.

Kic = C (E/HY'ZP 0-3/2 (2-6)

where C = 0.016, E is the elastic modulus (115 Gpa [12]), H is the hardness calculated in

50

(2-4), P is the load in Newtons and c is 1/2 the indent crack length in meters.

2.5 Thermal expansion

2.5.1 Specimen preparation for thermal expansion measurements

Thermal expansion measurements used hydroxyapatite specimens numbers 4-8,
10-12 and a sintered alumina reference specimen (starting powder AKP 30-4 Sumitoma)
microwave sintered at 15000 C for 30 minutes by KiYong Lee, a colleague in the Material
Science Department at Michigan State University. The specimens were cut into rectangles
approximately 10mm x 5mm x 3m with the slow speed diamond saw. The long axis
opposing faces were ground parallel by hand sanding with wet 320, 400 and 600 grit
wet/dry silicon carbide paper (3M corp. Minneapolis MN). Final surface polishing of the
opposing faces was done by hand on the Vari-Pol polishing machine at 150 rpm with grit
sizes starting at 17 um, then 15 um and finally 10 pm, for 2-3 minutes at each grit size.
Hydroxyapatite specimens numbers 4-8, 10-12, and the alumina specimen were then
annealed at 9000 C in a box furnace (Type 59344, Lindbergh Blue, Asheville, NC) for 13

hours.

2.5.2 Thermal expansion measurement

Hydroxyapatite and alumina specimens were placed one at a time in the specimen
well of the thermomechanical analyzer (DuPont Instruments, Model 943) so that the
measurement was to be made on the long axis. The thermomechanical analyzer was

programed to heat the specimen at 10°C/minute to 800° C, hold at 8000 C for 0, 10, 20,

51

30, or 60 minutes. Thermal expansion data were recorded continuously during heating to
8000 C and the cooling to room temperature. Thermal expansion coefficients were

calculated, in uni/m ° C, at 25° C intervals and the data was inserted into a spreadsheet.

2.6 Dielectric measurements

2.6.1 Specimen preparation for dielectric measurements
Disk specimens with both surfaces parallel and polished to 1 micron (see section
2.2.6) and at least a 2.22 cm diameter continuous surface were used for the dielectric

measurements.

2.6.2 Dielectric apparatus and measurements

Quality factor (Q), and parallel capacitance (Cp), measurements of sintered
hydroxyapatite specimens (numbers 14, 16, 33, 36, 41-46, 49, 50) and an alumina
substrate material (ADS 995, Coors Ceramics Company, Golden CO) were made with a
Q-Meter (Model 4342A,Hewlett-Packard, Palo Alto, CA). The alumina substrate
material (ADS 995) was used as a reference material since the dielectric properties are
well documented [72]. A guarded electrode system (similar to the ASTM standard- D
150-95 [73]) was constructed fiom rigid copper and copper pipe (Figure 2-7). The
copper electrodes, copper guard ring and the G10 (Glass fabric and epoxy resin system)
were cut on a lathe. The contact surfaces of the copper electrodes and guard ring were
polished with 25 um diamond paste on the Leco random orbit polishing machine, using a

specimen holder designed to polish parallel surfaces. The rigid copper electrodes were

52

 

Top

 

G-10

 

 

 

 

[ 2.22 cm Cu l 2.22 cm

 

|__2.22cm _|

—“l 1.905 cm Cu “I Bottom
G-10 \

Side View 0.16 cm air gap
Electrode surface for both Electrodes

I
FIND Q- Meter l

 

 

 

 

 

 

 

 

 

 

 

Figure 2-7 Electrodes and experimental apperatus for the dielectric measurements.
The specimen was placed between the top and bottom electrodes. The
electrodes were pressed onto the hydroxyapatite surfaces by a 5.09 cm
maximum opening micrometer (not shown).

53

held in place and compressed on the ceramic specimen by a 2 inch micrometer (China).

The dielectric measurements were made using the “Parallel Connection” for high
impedance components using reference inductors for each frequency range (reference
inductors 16471A through 16490A, Hewlett-Packard). The parallel connection circuit
was used (Figure 2-8). Resonance was first established in the circuit without the unknown
Z. The Q (Q,) and the capacitance (C,) are recorded. The unknown Z (specimen in the
electrode apparatus) is then connected and a new resonance established in the circuit. The
new Q (Q) and capacitance (C2) were recorded. The effective Q, and the effective

parallel capacitance Cp were then calculated (Equations 2-7 and 2-8).

Q = Q1Q2 (C1 ‘ C2) /(AQ C1) (2'7)

C. = (C. - C.) (2-8)

Three capacitance measurements and three Q measurements were taken at 45 kHz
for the hydroxyapatite specimens and the ADS995 alumina substrate. The averages of the
three capacitance measurements and three Q measurements taken at 45 kHz were then
used to correct for the capacitance of the circuit using the calculated capacitance of the
ADS995 alumina substrate. Additional measurements were taken at 8 higher frequencies,
from 72.2 kHz to 7.3 MHz (one measurement per fiequency) at room temperature for the

hydroxyapatite specimens and the Coors alumina substrate ADS 995.

54

Hi Hi

STABLE COIL

 

nknown
Q-meter

Q

 

 

 

 

Low

 

Figure 2-8 Parallel circuit for Q-meter measurements.

55

3 Results and Discussion
3.1 Sintered hydroxyapatite microstructure
Processing parameters for sintered hydroxyapatite were varied to allow for a wide

range of density and grain size of the sintered microstructure (Table 3-1).

3.1.1 Sintered density

For the uniaxially die pressed conventionally sintered hydroxyapatite specimens,
die pressure has the most significant influence on the final density (Figure 3-1). A linear
relation between die pressure and final sintered density was calculated. The relative
density for sintered hydroxyapatite specimens sintered at 13000 C for less than 120 minutes
(numbers 1-5, 13-16 and 18, see Table 3-1) were linear when plotted as a function of the
applied uniaxial die pressure (Figure 3-2). Linear regression analysis (Quattro Pro, Corel ,
Ontario, Canada) determined a SIOpe of 0.27% relative density for every 1 MPa of applied
pressure. The coefficient of determination r2 = 0.997 for the regression analysis.

The densification rate for hydroxyapatite sintered for 60 minutes was significantly

enhanced at temperatures greater than 11000 C (Figure 3-3).

3.1.2 Sintered grain size

Average grain size as a firnction of sintering temperature and sintering time shows
significant scattering (Figure 3-4). This is partially due to the differences in the ramping
rates and furnace geometries for the two conventional furnaces used in this study. Ramp
rates were electronically controlled in the tube furnace to 10° C/min and manually

controlled in the box furnace to 5-20° C/min. The grain size-sintering temperature Table

56

3-1 Processing parameters, density and grain size data for sintered

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

hydro xyapatite
Specimen Pressure Sintering Sintering Furnace Density Grain size
label (MPa) time (min) temperature type (g/cm’) (microns)
(°C)
1 6.55 60 1300 Tube" 2.88 1.68
2 6.55 75 1300 Tube“ 2.88 1.65
3 6.55 45 1300 Tube“ 2.88 1.98
4 6.55 90 1300 Tube" 2.89 2.07
5 6.55 105 1300 Tube“ 2.88 2.14
6 6.55 240 1300 Tube" 2.92 2.32
7 6.55 120 1400 Tube“ 3.05 5.65
8 6.55 240 1400 Tube“ 3.06 7.44
9 6.55 300 1300 Tube" 2.97 5.93
10 6.55 420 1300 Tube" 2.95 5.93
l 1 6.55 540 1300 Tube“ 2.98 6.73
12 6.55 660 1300 Tube“ 2.79 6.80
13 24.00 45 1300 Box" 3.04 4.37
14 24.00 60 1300 Box" 3.00 3.70
15 24.00 45 1300 Box" 3.05 3.60
16 17.46 15 1300 BoxM 2.96 2.74
17 17.46 15 1250 Box" 2.89 4.09
18 17.46 15 1300 Box" 2.98 5.10
19 17.46 15 1250 Box" 2.84 N/A
20 250 15 1300 Box" 3.09 2.30

 

 

 

 

 

 

 

 

* Tube fumace Thermtec, Lenton Thermal Designs
** Box furnace C+M Inc., High Temperature Furnaces Bloomfield NJ

57

 

Table 3-1 continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Pressure Sintering Sintering Furnace Density Grain size
label (MPa) time temperature type (g/cm’) (microns)
(nrin) (0 C)
21 250 120 1300 Box'" 3.09 2.60
22 250 15 1200 Box“ * 2.92 1.99
23 250 30 1250 Box“ * 3.07 2.06
24 6.55 15 1200 Box‘" 2.47 4.44
25 6.55 30 1050 p-wave* 2.26 2.73
26 6.55 30 l 100 u-wave" 2.65 3.09
27 6.55 30 1 150 u-wave“ 2.95 3.85
28 6.55 30 1200 u-wave" 2.98 4.36
3 l 80 60 1200 Box“ * 3 .02 5 .05
32 80 60 1350 Box" * N/A 4.78
33 so 60 1 100 Box" 1.33 1.48
34 80 60 1250 Box‘MI 3.06 2.54
35 80 60,130 I 150,1300 Box“ "‘ 3.02 2.70
36 13.09 60 1100 Box** 2.08 2.87
37 19.64 60 1100 Box" 2.17 3.92
38 6.55 60 1100 Box'” 1.54 N/A
39 26.18 60 1200 Box* * 2.80 2.54
40 13.09 60 1200 Box“ * 2.59 2.67
41 6.55 60 1200 Box" * 2.43 2.40
42 13.09 60 1250 Box'MI 2.95 2.80
43 19.64 60 1250 Box** 2.99 3.31

 

* Microwave Furnace, Wavemat Cavity, Plymouth, Nfl; Power Supply, Sairem
Vaux-en-Velin, France
** Box firmace C+M Inc., High Temperature Furnaces Bloomfield NJ

58

 

Table 3-1 continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Pressure Sintering Sintering Furnace Density Grain size
label (MPa) time temperature type (g/cm’) (microns)
(min) (°C)

44 26.18 60 1250 Box" 3.00 2.89

45 6.55 60 1350 Box” 2.96 4.59

46 13.09 60 1350 Box" 2.90 3.33

47 26.18 60 1350 Box" 2.98 N/A

48 13.09 60,130 . 1150,1300“ Box" 2.89 N/A

49 19.64 60,130 1 150,1300* Box" 2.92 N/A

50 26.18 60,130 1 150,1300“ Box" 2.94 4.46
" First run at 1150° C for 60 minutes and specimens came out badly cupped, second

run at 1300° C for 130 minutes.

** Box furnace C+M Inc., High Temperature Furnaces Bloomfield NJ

59

 

 

 

98 ~-
.é‘
8 “ i
8 96 --
o
E, -- X
2 C I -
o __
05 94 o - I
Be ..
I
92 ~-
.. II-i'h
90rii‘rii:iriitit
0 100 200 300 400 500 600 700
Sintering Time (minutes)
I 6.6 MPa 0 17.5 MPa 2 24 MPa
Figure 3-1 Density as a function of sintering time and different uniaxial die pressures

for hydroxyapatite sintered in the conventional furnaces at 1300 °C. The
data was taken from a subset of the data presented in Table 3-1.

60

Figure 3-2

‘0

on

J
l

 

 

'i"
I
ea.--
5
o 1' I
394..
E I
d)
a: ..
3292 --
90 . : —: i 4 :
5 10 15 20 25
Die Pressure (MPa)

I Experimental data — Linear Fit

Density as a function of die pressure. The data was taken fiom sintered
hydroxyapatite specimens sintered at 1300° C for 15-120 minutes, which
are a subset of the data presented in Table 3-1. Linear fit represents the
least squares fit of the data to equation 3-1. Fit parameters are slope =
0.27% relative density per 1 MPa die pressure, y-intercept = 91% relative
density and the coefficient of determination r2 = 0.997.

61

100 a

 

 

.. II II II II
I

90 -- .
'3; so -- '
5 .. I
Q
,3 7o -.- -
a i- '-
62 so -- -
e\° ..

50 "ii- -

40 : i i i : i : i 4. : : : : i

1050 1100 1150' 1200 1250 1300 1350 1400
Sintering Temperature (C)

Figure 3-3 Density as a function of sintering temperature for hydroxyapatite specimens
sintered for 60 minutes. The data was taken from a subset of the data
presented in Table 3-1.

62

 

 

-\ -- V I
”’ v
E ' u x
Q 4 h V . x
e ,_ , v v
g I v x I
U) I
t 2 -- I X
E
U) 1’ ‘
0 : i : t : : 4 :
1000 1100 1200 1300 1400
Sintering Temperature (C)
I 15 min 0 Microwave 30 min.
X 45 min. V 60 min.

Figure 3-4 Average grain size of sintered hydroxyapatite as a function of sintering
temperature and time for both conventional and microwave sintering. The
data was taken fi'om a subset of the data presented in Table 3-1.

63

relationship for microwave sintered hydroxyapatite samples is linear for the small sample
size of 4 specimens (Figure 3-4). The grain size was decoupled from the density for

sintered hydroxyapatite specimens with densities greater than 2.90 g/cm3 (Figure 3-5).

3.1.3 Etched surface morphology

Uniaxially pressed sintered hydroxyapatite specimens were polished and thermally
etched for the grain size measurements. The thermally etched surfaces of the uniaxially
pressed sintered HAP specimens were composed of polygonal grain shapes (Figure 3-6
and Figure 3-7). Polished surfaces of the hydroxyapatite surfaces were also acid etched to
delineate the grain boundaries and measure the grain size. Acid etching (HAP specimens
numbers 1-5, 11) resulted in severe changes in the surface due to over etching (Figure 3-
8).

Polished and thermally etched surfaces of the hydroxyapatite specimens cold
isostatically pressed to 250 MPa (numbers 20-23) exhibit significantly different etched
surface morphology. CIPed specimens sintered for 30 minutes or less at temperatures of
1300°C or less had average grain sizes of 1.99 um , 2.06 pm 2.3 um (Figure 3-9, Figure
3-10, Figure 3-11 respectively). Specimen number 21, sintered at 13000 C for 120
minutes, grew the familiar polygonal shaped grains with an average grain size of 2.60

microns (Figure 3-12).

3.1.4 X-ray diffraction
The difli’action scan, using Cu Kerl radiation (A = 15.406 nm), was from 25

degrees to 36 degrees where the most intense peaks from HAP and the decomposition

64

 

 

.. I
7 -u—
.. I
A6 -- I
g .. I
a5 -- '-
3 " I ‘ I
o4 .. . I
.5 I
(D .. .-
5 3 J- I '
g h - I I - I‘
. - r
2 -. fl
. - I
1 _.
0 i . 4 . i . i
55 65 75 85 95
% Relative Density
Figure 3-5 Grain size as a function of percent relative density for sintered

hydroxyapatite. The data was taken from a subset of the data presented in
Table 3-1.

65

 

Figure 3-6 Micrographs of polished and thermally etched surface of sintered
hydroxyapatite specimen number 15 sintered at 13000 C for 45 minutes,
average grain size = 3.60 microns.

66

Figure 3-7

 

V _.__ g;

Micrograph of polished and thermally etched surface of sintered
hydroxyapatite specimen number 45 sintered at 1350° C for 60 minutes,
average grain size = 4.59 microns.

67

 

Figure 3-8

-.
/‘

Tn“ ' 7" I ‘1'»
r.

(”1“ .; “if

.33
. ~,~\.
g} s; *
«w‘ ..

(a) (b)

Micrographs of polished and acid etched surface of sintered hydroxyapatite
(0.1 M HCl for 1 minute), (a) specimen number 3 sintered at 1300°C for
45 minutes, grain size =1 .98 microns, (b) specimen number 8 sintered at
14000 C degrees for 240 minutes, grain size = 7.44 microns.

68

a.

‘1

if} iii ifi if: 1:: E?

 

Figure 3-9 Polished and thermally etched surfaces of cold isostatically pressed (250
MPa) and sintered hydroxyapatite specimen number 22 sintered at 12000 C
for 15 minutes. Average grain size = 1.99 pm

69

 

Figure 3-10 Polished and thermally etched surfaces of cold isostatically pressed (250
MPa) and sintered hydroxyapatite specimen number 23 sintered at 1250° C
for 30 minutes. Average grain size = 2.06 pm

70

<- 10 microns —>

 

Figure 3-11 Polished and thermally etched surfaces of cold isostatically pressed (250
MPa) and sintered hydroxyapatite specimen #20 sintered at 13000 C for 15
minutes. Average grain size = 2.30 mm

71

<— 7.5 microns =>

 

Figure 3-12 Polished and thermally etched surfaces of cold isostatically pressed (250
MPa) and sintered hydroxyapatite specimen number 21 sintered at 1300° C
for 120 minutes, Average grain size = 2.60 um.

72

products of hydroxyapatite exist. According to the Powder Diffraction File for Inorganic
Phases [68] the three main peaks for hydroxyapatite are at 20 = 31.80 for {211}, 20 =
322° for {112} and at 20 = 330° for the {300}. The (Jr-tricalcium phosphate (ct-TCP)
primary peak is located at 20 = 30.7°, the B—tricalcium phosphate (B-TCP), primary peak
is at 20 = 31 .0° and the tetracalcium phosphate primary diffraction peak at 20 = 289°
[68].

The major peaks in the x-ray difli'action patterns, for the as received
hydroxyapatite powder (Raw HAP) and sintered hydroxyapatite specimens numbers 4-12,
are those of hydroxyapatite (Figure 3-13 and 3-14). A faint peak at 20 ~ 29° for
hydroxyapatite specimens (numbers 7, 8, 9, 11, and 12) is associated with tetracalcium
phosphate. Tetracalcium phosphate is the minor product of the decomposition reaction by
a factor of 1:2 compared to tri-calcium phosphate (Equation 1-2). Tri-calcium phosphate
was not detected in the sintered hydroxyapatite specimens by x-ray difli‘action.

A decrease of the lattice parameter co is noted in sintered hydroxyapatite
specimens as the sintering temperature and sintering time increases (Table 3-2). The
lattice parameter were calculated from the angles of the three major x-ray difl‘raetion
peaks of the hydroxyapatite specimens (Figures 3-13 and 3-14) using Equation 2-2 and 2-
3. The lattice parameter CO was determined by averaging the lattice parameter c0
calculated fi'om the diffraction peak for the {211} plane at 20 = 31.8° and the dim-action
peak for the {112} plane at 20 = 322°. The lattice parameter a(, was calculated using the
peak for the {300} plane at 20 = 33.0°.

Sintered hydroxyapatite specimens numbers 4-12 are composed of hydroxyapatite

with no evidence of decomposition.

73

 

 

 

 

#1) . I i , i it—9—HAP

 

.59 ..____.
g #8 HAP
o —-
#7 HAP
#6 HAP
Oriitiiiiiiiiiii++iifiiifi‘ HAPpowder
25 27 29 31 33 35
2-theta (degrees)
Figure 3-13 X-ray difl‘raction pattern (Cu K,ll radiation) for as received (Raw) and

sintered hydroxyapatite (HAP). Specimens number 6 and 9 sintered at
13000 C for 240 and 300 minutes respectively. Specimens number 7 and 8
sintered at 14000 C for 120 and 240 minutes respectively. * Primary
tetra-calcium phosphate diffraction peak.

74

 

 

 

 

Counts

#12 HAP

#11 HAP

 

 

 

 

 

 

 

 

25 27 29 31
2-theta (degrees)

Figure 3-14 Additional x-ray difli'action patterns (Cu K“l radiation) for sintered
hydroxyapatite. Specimen #11 and #12 sintered at 13000 C for 540 and
660 rrrinutes respectively. * Primary and secondary tetra-calcium
phosphate difii’action peaks.

75

 

 

 

 

 

 

 

 

 

 

 

Table 3-2 Lattice parameter data for the as received hydroxyapatite powder (HAP I)
and sintered hydroxyapatite, calculated using the 3 major hydroxyapatite
peaks fi'om Figures 3-13 and 3-14 and Equations 2-2 and 2-3. Data fiom
the handbook is included [69].

Specimen Sintering Sintering a0 c0
label time (min) temperature (°C) (nm) (nm)
HAP I 0 --------------- 0.9389 06943

6 120 1300 0.9406 0.6892
9 300 1300 0.941 1 0.6903
10 420 1300 0.9406 0.6857
1 1 540 1300 0.9384 0.6877
12 660 1300 0.9400 0.6868
7 120 1400 0.9400 0.6860
8 240 1400 0.9400 0.6859
Average ------------------------- 0.9400 0.6882
PDF [69] File #9-432. -------------- 0.9418 0.6884

 

 

 

 

 

 

3.2 Indentation measurements

 

Hardness and fiacture toughness of the sintered hydroxyapatite specimens were

measured by the Vickers indentation method (Table 3-3).

3.2.1 Vickers hardness

Vickers hardness of the sintered hydroxyapatite specimens prepared in this study
are a strong function of the density (Figure 3-15). As a firnction of the average grain size
the hardness values of the sintered hydroxyapatite specimens show no trends indicating
that grain size effects on hardness are significantly weaker than the porosity effects on
hardness, over the range of grain sizes and porosity values for the specimens in this study

(Figure 3-16). There are no discernable patterns in the standard deviation (of the 7-10

76

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3-3 Density, grain size and the mechanical properties of hardness and
toughness, measured by indentation technique, of sintered hydroxyapatite.
The standard deviations (0), calculated for the multiple indentations per
specimen, are included.
Specimen %Relative Grain size Hardness O Fracture (J Fracture
label density x10°m GPa Hardness toughness toughness
GPa MPa(m”2) MPa(m"2)
1 91.4 1.68 3.543 0.274 1.125 0.266
2 91.3 1.65 3.333 0.248 1.233 0.238
3 91.2 1.98 2.792 0.234 1.466 0.231
4 91.5 2.07 3.758 0.432 1.017 0.294
5 91.4 2.14 3.774 0.515 1.006 0.187
6 92.5 2.32 3.326 0.281 1.209 0.204
7 96.6 5.65 4.816 0.551 0.794 0.259
8 97.0 7.44 4.840 0.189 0.479 0.037
9 94.0 5.93 4.145 0.245 0.715 0.140
10 93.6 5.93 3.671 0.150 0.833 0.354
1 1 94.4 6.73 4.197 0.206 0.732 0.104
12 94.2 6.80 4.428 0.351 0.701 0.144
13 96.4 4.37 3.948 0.660 1.017 0.230
14 95.1 3.70 3 .935 0.694 1.027 0.290
15 96.6 3.60 4.446 0.421 0.877 0.149
16 93.6 2.74 3.809 0.165 0.928 0.111
17 91.4 4.09 4.154 0.647 0.789 0.275
18 94.4 5.10 4.347 0.427 0.773 0.182
19 90.0 N/A 3.999 0.229 0.803 0.157
20 97.9 2.30 5.52 0.214 0.450 0.050
21 97.9 2.60 5.42 0.179 0.37 0.066
22 92.6 1.99 3.55 0.471 1.05 0.236

 

 

 

 

 

 

 

 

77

 

Table 3-3 continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen %Relative Grain size Hardness 0 Fracture O Fracture

label density xlof’m GPa Hardness toughness Toughness

GPa MPa(m"2) MPa(m"2)
23 97.3 2.06 5.21 0.191 0.63 0.160
24 78.2 4.44 1.32 0.323 2.11 0.439
25 71.7 2.73 0.91 0.165 2.49 0.259
26 84.0 3.09 2.46 0.379 2.07 0.397
27 93.5 3.85 4.48 0.451 0.76 0.141
28 94.3 4.36 4.07 0.259 0.73 0.089
31 95.7 5.05 5.24 0.222 0.60 0.083
32 N/A 4.79 5.23 0.266 0.38 0.068
34 97.0 2.54 5.54 0.258 0.59 0.070
35 95.6 2.70 5.33 0.237 0.97 0.119
37 68.8 3.92 1.20 0.136 1.84 0.721
39 88.6 2.54 3.68 0.182 1.50 0.161
40 82.2 2.67 1.61 0.106 2.34 0.309
41 76.9 2.40 1.60 0.063 2.67 0.242
42 93.6 2.80 4.15 0.347 0.872 0.166
43 94.7 3.31 4.44 0.336 1.25 0.369
44 95.2 2.89 5.37 0.262 0.695 0.051
45 93.7 4.59 3.77 0.293 0.996 0.152
48 91.4 N/A 4.20 0.176 0.790 0.062
49 92.4 3.21 4.20 0.309 0.868 0.122
50 93.1 4.46 3.08 0.109 1.45 0.319

 

78

 

 

.h
r l
' l
I
'-
I

Hardness (GPa)
(a)
I
1
I

N
L 1
l

 

l
l

65 75 85 95
% Relative Density

0

‘-

Figure 3-15 Vickers indentation Hardness values for sintered hydroxyapatite as a
function of density. The data was taken from Table 3-3.

79

 

 

.. I
54 _ I- _.
' I I
-- III
’64." I. III - I :
CL I
0 .. If '- I
’ -
2 “ "
s2"
.. II I
. I
‘14- .
0 i : i i i : i : i i =1
1 2 3 4 5 6 7 8

Grain Size (microns)

Figure 3-16 Vickers Hardness plotted against the average grain size of the sintered

hydroxyapatite. The data was taken fi‘om Table 3-3.

80

hardness measurements per specimen) as a function of grain size (Figures 3-17).

3.2.2 Indentation fracture toughness

Fracture toughness of the sintered hydroxyapatite specimens were measured to be
0.4 - 0.6 MPa m”2 at ~ 97% relative density. The fracture toughness of the sintered
hydroxyapatite specimens increases markedly, to 2.5-2.7 MPa mm, as the density
decreases to between 72 and 77% relative density (Figure 3-18). A plot of the fracture
toughness as a function of the grain size shows no trend over the grain size range of the
specimens in this study (Figure 3-19). Standard deviation of the fiacture toughness
measurements plotted against the specimen’s average grain size shows no trend (Figure 3-
20).

The ratio between the indentation crack length (c) and the indentation diagonal (a),
as a function of relative density, increases as the density increases for the sintered
hydroxyapatite specimens in this study (Figure 3-21). The trend for the c/a ratio as a
firnction of relative density shows that the cracks barely extend beyond the indent for

percent relative density below 85%.

3.3 Hardness and microstructure comparisons with literature data

All of the Vickers hardness data of the sintered hydroxyapatite specimens fiom this
study (indentation loads of 0.3 kg, 0.5 kg and 1 kg), and selected Vickers hardness data
from Lu et al. (indent load 0.05 kg) [74], and Best et al. (indent load 1 kg) [75] along
with selected Knoop hardness data fi'om Wang et al. (0.2 kg load) [9] and Slosarczyk (no

load specified) [11] all show substantial decreases in hardness as the porosity increases

81

 

 

A07-i- I
E x '-
9.0.6-L
.5 i I
gas-- .-
8 dr- . |-- I
“904* -
a -— I '
503-— : '
co - I
802» ' '
= ' ' 5
E ‘ I
m
:01-- I I
-. I
0 a i . : . i
0 2 4 6 8

Grain Size (microns)

Figure 3-17 Statistical standard deviation of the Vickers hardness of sintered
hydroxyapatite plotted against the average grain size. The data was taken
fiom Table 3-3.

82

w
J
1

l
I

 

 

A O
$2.5 -- o
E .. O
(I!
O
% 2 -- ‘
7; o
m ..
‘c’
§15 -- . . .
.2 " g: '
C) -r-
5 1 .. 9
g .t O O '
LL0.5 -_ ' 2’
0 i : : 4 i
65 75 85 95
% Relative Density
Figure 3-18 Vickers indentation toughness as a fimction of density for sintered

hydroxyapatite. The data was taken from Table 3-3.

83

 

 

A “P .
$2.5 -- o
E __ C
to
C
E 2 -r .
en 0
m -.
3
.§’1.5 "" . . .
a " g . '
g 1-- ~ ‘ .. ..
. o

E "‘ o "O . . 0 Q
LL05 __ . O O .

' ° 0 o

0 x i i L i u i

1 2 3 4 5 6 7

Grain Size (microns)

Figure 3-19 Fracture toughness as a function of average grain size of sintered
hydroxyapatite. The data was taken from Table 3-3.

84

0.8 1"

 

 

g0] -_ ’
2' a-
E0.6 ,_
(U
0.. q-
gas ~-
C
8 *’ 0
£04 -- Q.
a -- . , .
'90-3 7" O . g
g .. O o . o
c . . . O
30.2 -> .0 .
w " . .. .0 o 0
g o
01 "" . . .
.. .c. o
o
0 i l u i
0 2 4 6 8

Grain Size (Microns)

Figure 3-20 Standard deviation of the fracture toughness plotted against the average
grain size of the sintered hydroxyapatite. The data was taken fiom Table
3-3.

85

 

 

 

6 __
5 __
.9
E4 "H-
a -h-
33 -- I
__ I
2 —- _ '
" r
1 a— I I I I I I
0 1 1' , i 4 l i - i . 1‘ 1 l
65 70 75 80 85 90 95 1 00
% Relative Density
Figure 3-21 Ratio of the Vickers indentation crack length and Vickers indentation

diagonal plotted against the % relative density, for all 410 indents on the
specimens with known density measured in this study.

86

(Table 3-4). The selection criteria for the hardness data, fiom the literature, limited the
data to those specimens proved by x-ray difiraction to contain no more than trace amounts
of the decomposition phases of hydroxyapatite.

The hardness data of sintered hydroxyapatite, from this study (Table 3-3) and the
hardness data from the studies by Wang et al. [9], Slosarczyk et al. [11], Best et a1. [75],
and Lu et al. [74] (Table 3-4), were linearized using the model proposed by Rice [57]
(Equation 3-1)

lnH=h1Ho-bP (3'1)
where H is the measured hardness, H0 is the zero porosity hardness, and b is the slope of
the plot of the logarithm of hardness (H) versus volume fraction porosity (P) (see
Equation 1-8 in section 1.6). Linear regression analysis (Quattro pro) of the linearized
data was used to calculate the zero porosity intercept HO and the b value (Table 3-4). The
hardness data and the linear fit of the hardness data was then normalized by dividing the
measured hardness by the zero porosity hardness (Ho). The data for Wang et al. and [9]
Slosarczyk et al. [1 1] were linearized and normalized together due to the conformity of
the two data sets. The normalized data and the normalized linear fit of the hardness data
shows that the data from this study compares favorably to the data fi'om Best et a1. [75],
and Wang et al. [9] Slosarczyk et a]. [11] as a function of the volume fiaction porosity
(Figure 3-22). The hardness values from Lu et al. [74] decreases at a significantly greater
rate as a fimction of the volume fraction porosity then the rest of the plotted data.

Hydroxyapatite powder used in preparing the specimens for Wang et al. [9], and
Slosarczyk et al. [1 1] was synthesized by a wet chemical-method. Lu et al. [74] prepared

two separate hydroxyapatite powders using the wet chemical method by heat drying part

87

Table 3-4

The normalization and statistical parameters from the linear regression
analysis of the hardness as a function of volume fraction porosity (Equation

3-1: In H = 1n Ho - bP) for this study, Wang et al. [9], Slosarczyk et al.
[1 1], Best et al. [70], and Lu et al. [69]. Actual hardness data [9,11,69,70]
from the literature is included.

 

Linear fit parameters calculated from the hardness data in this study (Table 3-3)

 

b = 6.03

 

r2 = 0.907

 

Standard error" = 0.131

 

Calculated zero porosity hardness Ho = 6.00:1: 0.79 Gpa

 

 

 

Wang et al. [9] and Best et al. [70] Lu et al. [69]
Slosarczyk et al. [11]

Data fiom tables Data fi'om graphs Data from graphs
b = 7.38 b = 4.89 b = 19.4

r2 = 0.892 r2 = 0.947 r2 = 0.969

 

Standard error” = 0.379

Standard error" = 0.244

Standard error" = 0.125

 

Ho = 5.18 :t 1.96 GPa

Ho = 552.9 i 135

Ho = 1218.4 :4: 152

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Volume Knoop Volume Vickers Volume Vickers
fiaction hardness fi'action hardness fiaction hardness
porosity (P) Hk (GPa) porosity (P) H, Unitless porosity (P) IL Unitless
0.40 0.449 0.52 50 0.12 125

0.39 0.155 0.50 50 0.11 128

0.38 0.189 0.49 50 0.05 560

0.35 0.298 0.48 51 0.05 580

0.31 0.85 0.18 145 0.04 605

0.31 0.849 0.16 350 0.04 648

0.24 0.928 0.1 l 205 0.03 660

 

** Standard error of the normalized hardness (H/Ho)

88

 

Table 3-4 continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Wang et al. [W] and Best et al. [B] Lu et al. [L]
Slosarczyk et a]. [S]
Data from tables Data from graphs Data fi'om graphs
Volume Knoop Volume Vickers Volume Vickers
fiaction hardness fraction hardness fiaction hardness
porosity (P) Hk (GPa) porosity (P) PL Unitless porosity (P) H, Unitless
0.23 0.963 0.09 370 0.03 680
0.22 1.025 0.06 425 0.02 758
0.08 2.7* 0.05 410 0.01" 805"
0.02 4.0* 0.03 410 V
0.01 4.6* 4 0.03 450

\ 0.02 700

0.02 670
‘

k 0.01 540 \\

 

 

* Hardness data fi'om Sosarczyk et al. [S]

it

89

Trace of TCP in x-ray difii‘action spectra.

10

 

 

3
0
C
E
m
I
.3 b= 4.9
E
0
m
C
0.01 I i i ; 1L ; 1' ; i ' rf j.
0 0.1 0.2 0.3 0.4 0.5

Volume Fraction Porosity (P)

I Present Study. [9,11] 2 [70] V [69]

Figure 3-22 Log relative indentation Hardness values for sintered hydroxyapatite
plotted against the volume fraction porosity along with the solutions for the
linear log relative hardness as a fimction of volume fiaction porosity
(Equation 1- 8, Section 1.6). Data was taken from Table 3-3 for the
present study and Table 3-4 for the literature data.

90

of the mixture of HAP and water, and freeze drying the rest. Hardness data from
specimens produced from both powders by Lu et al. [74] were lumped together for
analysis (Table 3-4). Three commercial hydroxyapatite powders, used by Best et al. [75],
were characterized by x-ray diffi'action, infrared spectroscopy, inductively coupled plasma
spectroscopy, surface area analysis, particle size analysis and scanning electron
microscopy, before being sintered. The three commercial powders were found to have
significantly different morphologies which influenced the sintered density and grain size of
the sintered specimens [75]. Hardness data fi'om specimens sintered from all three
commercial powders were included in this analysis (Table 3-4).

The resultant microstructures of the sintered hydroxyapatite specimens compiled in
table 3-4 included grain sizes of 2-8 pm this study, 5-10 pm [11,74], to 90 um [9]. Grain
sizes of the final sintered specimens were not specified by Best et al. [75].

The data fi'om this study is in good agreement with the four different studies
[9,11,74,75]. Indentation hardness of sintered hydroxyapatite decreases exponentially as
porosity increases, as modeled by equation 1-8, regardless of the origin and morphology

of the starting powder.

3.4 Fracture toughness and microstructure comparisons with literature data
Fracture toughness studies of sintered hydroxyapatite show a decrease in the
fracture toughness values as the porosity increases when measured by three point bend
[54], and the indentation method [56] (Table 3-5). The fi'acture toughness of sintered
hydroxyapatite specimens, in this study, increased in fracture toughness as the porosity

increases (Figure 3-23). The fi'acture toughness of the whisker reinforced sintered

91

Table 3-5 The normalization and statistical parameters fi'om the linear regression
analysis of toughness as a function of volume fi'action porosity (Equation
3-2: In K, = 1n Koic - b P) for this study, DeWith et al. [54] and Suchanek
et al. [56]. Fracture toughness data fi'om DeWith et al. [54] and Suchanek

et al. [56] are included.

 

Linear fit parameters from the fiacture toughness data in this study (Table 3-1)

 

b=-5.51

 

r2 = 0.657

 

Standard error" = 0.270

 

Calculated zero porosity fracture toughness K,Co = 0.61 :t 0.16 MPa m"2

 

DeWith et al. [54]

Suchanek et al. [56]

 

 

Data from graph Data from graph
b = 2.786 b = 2.812
r2 = 0.630 r'2 = 0.786

 

Standard error” = 0.202

Standard error" = 0.116

 

K.Co = 1.14 :1: 0.23 MPa rn“2

Kn, =1.63 :1: 0.19 MPa :11"2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Volume fiaction Fracture Toughness Volume fraction Fracture Toughness
Porosity (P) (MPa mm) Porosity 0’) (MPa mm)
0.27 0.65 0.29 0.78

0.27 0.6 0.16 1.00

0.22 0.64 0.1 l 1.10

0.22 0.35 0.10 1.05

0.18 0.66 0.08 1.36

0.18 0.81 0.08 1.41

0.1 0.93 0.05 1.32

0.1 0.88 0.04 1.54

0.06 0.98 0.03 1.34

0.06 0.93 0.02 2.00

 

**

Standard error of the normalized fracture toughness (K,C /K.Co)

 

Table 3-5 continued

 

DeWith et al. [54]

Suchanek et al. [56]

 

 

 

 

 

 

 

 

 

 

 

Data fiom graph Data from graph
Volume fiaction Fracture Toughness Volume fraction Fracture Toughness
Porosity (1’) (MPa mm) Porosity (1’) (MPa mm)
0.03 1.08 0.02 1.45
0.03 1.01 0.02 1.65

‘ \V' 0.01 1.48

0.01 1.44

\ 0.01 1.82
k 0.01 1.72

 

93

 

0)
J
l

 

 

 

g25 "’ -
< . -. I
E __ I
d.“ 2..L . - -
3 +3 I
3 O
m1.5"
C
c Ill
0)
3 1- O
O
,_ . x o
a) X X i
50.5
‘6 . x
i!
u. 0 . i 4 i 4 i . i . i t i t i
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Volume Fraction Porosity (P)
I Present Study 0 [56] x [54]

Figure 3-23 Fracture toughness values for sintered hydroxyapatite plotted against the
volume fraction porosity. Fracture toughness values were taken from
Table 3-3 (present study) and Table 3-5 for the data from Suchanek et al.
[56] and DeWith et al. [54].

94

hydroxyapatite, prepared by Suchanek et a1 [56] is greater than the fiacture toughness, as
a function of the porosity, of the over the non-reinforced specimens prepared by DeWith
et al. [54] (Figure 3-23).

The fi'acture toughness data from DeWith et al. [54], Suchanek et a1. [56] and this
study were linearlized and normalized in the same way as the hardness data (section 3.3).

ant=anw-bP (3-2)
where K,c is the measured fracture toughness, Kid, is the zero porosity fracture toughness,
and b is the slope of the plot of the logarithm of fiacture toughness ( Kt) versus volume
fiaction porosity (P) (see Equation 1-8 in section 1.6). The data (Table 3-5) from DeWith
et al.[54] and Suchanek et al [56] have the same functional relationship to the volume
fraction porosity, as determined by the b value (Figure 3-24, and Figure 3-25). The
normalized and linearized data from this study was. not linear and the calculated b value
was negative, deviating from the MSA model (Figure 3-24, and Figure 3-25).

This study and the study by DeWith et al. [54] used commercially available
powders (CERAC Inc., this study, and Merck A. G. [54]). Both studies have similar
microstructures. The sintered grain sizes are 1-6 pm for DeWith [54] and 2-8 pm for this
study. Porosity values were up to 0.30 volume fiaction porosity for both studies. Traces
of decomposition products were detected in specimens sintered at temperatures greater
than 11500 C (relative densities > 85%) for DeWith et al. [54].

The indentation fiacture toughness method used by Suchanek et a1. [56], is similar
to the fracture toughness measurement technique used for this study, however, the
microstructures difler due to the whisker reinforcement in the sintered hydroxyapatite

specimens tested by Suchanek et al. [56].

95

1° b = -5.5

 

 

 

m
3 I
c - I
g, I
D
O
'—
d)
5 1
E x
LL
.8 x
% b=2.8
o:
0.1. : +r::t+::::‘fi:i
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Volume Fraction Porosity (P)
I Present Study 0 [56] x [54]

Figure 3-24 Relative fracture toughness values for sintered hydroxyapatite as a function
of volume fraction porosity and the calculated linear fit. Linear fit
parameters taken from Table 3-5 for the data from Table 3-3 (present
study) and the the toughness data in Table 3-5 fi'om Suchanek et al.
[56] and DeWith et al. [54].

96

.s
O

b = -5.5

 

 

Relative Fracture Toughness

 

b=2.8
0.1 . a i : : 4. i r : : : : :
0 0.025 0.05 0.075 0.1 0.125 0.15
Volume Fraction Porosity (P)
I Present Study 0 [56] x [54]

Figure 3-25 A section of lower volume fi'action porosity of the relative fiacture
toughness values for sintered hydroxyapatite as a function of volume
fi'action porosity and the calculated linear fit. Linear fit parameters taken
from Table 3-5 for the data fi'om Table 3-3 (present study) and the fi‘acture
toughness data in Table 3-5 from Suchanek et al. [56] and DeWith et aL
[54].

97

The studies by DeWith et a1. [54] and Suchanek [56] are linked by the fact that the
fracture toughness measurement techniques and sintered hydroxyapatite microstructure
were vastly different yet the fimctional relationship between fracture toughness and
volume fi'action porosity is nearly identical.

Comparisons between the three studies leads to a three part argument, in which no
conclusion can easily be drawn; 1) the starting HAP powders and sintered HAP
microstructure are similar in this study and the study by DeWith et al. [54], yet the nearly
fully dense (95-97% relative density) fracture toughness and the functional relationship
between fi'acture toughness and porosity are vastly difi‘erent. 2) the studies by DeWith et
al. [54] and Suchanek et al. [56] are linked by a nearly identical b value calculated fi'om
the fiacture toughness versus volume fraction porosity data (Equation 3-2) even with very
different measurement methods and specimen microstructures. 3) the indentation fiacture
toughness techniques are shared by this study and Suchanek et al. [56], however the

measured fimctional relationship between fiacture toughness and porosity are incongruent.

3.5 Further comment on the fracture toughness of porous hydroxyapatite

The significant and steady increase in the fiacture toughness of the sintered
hydroxyapatite specimens in this study as the porosity of hydroxyapatite specimens
increases (Figure 3-18) requires further comment. The lack of evidence of secondary
phase formation, from x-ray difliaction (section 3.1.4), the large sample population (42),
and the increase of the fracture toughness as the density decreases, forces a focus on the
fi'acture toughness as a firnction of porosity for the sintered hydroxyapatite specimens in

this study.

98

The relationship among the microstructure of sintered hydroxyapatite, the
indentation fracture toughness measurement and the measured fi'acture toughness of
sintered hydroxyapatite consists of three major elements: 1) Applications of the
indentation toughness equation (Equation 1-6) to porous commie materials. 2) The
formation and grth of indentation cracks in porous hydroxyapatite specimens 3)
Toughening mechanisms that are unaffected by the grain size, over the grain size range of
the specimens in this study, and are increasingly effective for hydroxyapatite specimens in
which the processing parameters produced higher porosities. The fracture toughness of
near firll density sintered hydroxyapatite, reported in the literature, is between 0.8-1.2 MPa
m"2 [54,56,76], and is comparable to the average of the +90% dense specimens in this

study (ch = 0.77 MPa mm).

3.5.1 Indentation toughness model and porosity

The stress field of the test specimen under indentation loading is a function of the
elastic modulus and Poisson’s ratio of the test specimen, and the load and geometry of the
indenter [3 8]. Indentation fracture toughness is calculated using the indentation stress
field and the resultant indentation crack length (Figure 1-1 [42]) of the indented specimen
[3 8] . The indentation toughness model, derived by fi'acture mechanics fi'om the
indentation stress and the indentation cracks [3 8], has successfully determined the fiacture
toughness for a wide variety of ceramic materials as a function of the hardness, elastic

modulus and the indentation crack length [39,40,41] (Equation 33 [40]).

99

K = 4(3)“? .3. (3-3)
1c H 63/2

V

where C is the empirically determined constant (C = 0.016 [40]), E is the elastic modulus,
HV is the Vickers hardness determined from the size of the indent (Hv = P/2a2, Equation
2-5), P is the indentation load, and c is the indentation crack length (fi'om Figure 1-1,
section 1.5.1). Equation 3—3 was used to calculate Klc for each indent in this study. The
average and standard deviation of the specimen’s K“, were then determined from the 7-10
indents/specimen.

The elastic modulus of ceramics decreases as the porosity increases [35,54,58,60].
The elastic modulus/porosity data has been fit to the MSA model (ln(E) = ln(Eo) - bEPp,
Equation 1-8), where E0 is the fully dense elastic modulus, bE is the material dependent
constant and PI. is the volume fraction porosity [57] (Section 1.6). Poisson’s ratio for
sintered hydroxyapatite also decreases as the porosity increases [53,54]. The porosity
dependence of Poisson’s ratio is much weaker, as determined by the b values, than the
porosity dependence on elastic modulus, for many ceramics (Table 3-6).

The fracture toughness values of the hydroxyapatite specimens in this study
(Tables 3-3, 3-5, Figures 3-18, 3-19, 3-24, and 3-25) were calculated by equation 3-3 with
fixed elastic modulus (E = 115 GPa [56]).

The functional dependence of hardness, as measured by the size and load of the
indent, on the volume fi'action porosity of sintered hydroxyapatite has been measured in
this study and fit to the MSA model [57] (ln(H,) = ln(Hvo) - bH PP Section 3.3). The

relationship between hardness and density indicates deformation processes behave as

100

Table 3-6

Porosity dependence of the elastic modulus compared to the porosity
dependence of Poisson’s ratio for experimental data fit to the MSA model
(lnE = ln E0 - bEP, lnv = in v0 - va, Equation 1-8) by Rice [58].

 

 

 

 

 

 

 

 

 

 

 

Ceramic P range (%) bE bv vo Reference
A1203 15-55 2.8 0 0.27 Coble and Kingery from [58]
B60 0-8 4.0 0 0.155 Petrak et al. from [58]
HAP 3-27 2.9 0.7 0.28 [54] fit in this study
AIN 0-20 5.5 0.9 0.24 Hunter et al. from [58]
Hm 5-15 5.2 0.6 0.26 Desmaison-Brut et al. from
[531
TaN 1-15 4.6 0.6 0.25 “ ”
TIN 1-22 3.0 0.2 0.22 “ ”
ZrN 2-8 3.3 0.8 0.26 “ ”
Graphite 13-32 3.5 1 0.31 Cost et al. from [58]

 

 

 

 

 

 

101

 

expected by the MSA model [57] for sintered hydroxyapatite.
Inserting the MSA functions (modifications of Equation 1-7) for the elastic

modulus and Vickers hardness in equation 3-3 results in equation 3-4.

-bz Pr P

E09 1/2
K,c(E(PP), H(Pp)) = {(H e-bHP,) 03/2 (3'4)
0

where E0 and HW are the fiilly dense values of elastic modulus and hardness, bE and bH are
the material dependent constants (MSA fit [57]) for the elastic modulus and Vickers
hardness respectively, and Pp is the volume fiaction porosity. The material dependent
constants bE and bH are obtained by fitting the modulus-porosity and the hardness-porosity
data to the MSA model (Equation 1-8). Equation 3-4 is simplified by combining the

exponents (Equation 3-5).

(bH‘bIE).

_.__ , E , P
K,C(E(PP),H(P,,))=e 2 ”470123,: (3-5)
0

The efl‘ect of porosity on the elastic modulus/Vickers hardness ratio may be written as
(Eu/Hv0)mexP(1/2(bn - bP))-

Rice [5 8], applying existing literature data to the MSA model, compiled decay
constants for the elastic modulus and hardness for a large variety of porous ceramics
(Table 3-7). The effect of the porosity dependence on the hardness and elastic modulus

(as related by bE and b“), to Equation 3-5 with (P/cm) held constant, ranges from a factor

102

 

 

 

 

 

 

 

 

 

 

 

Table 3-7 Material dependent coefficients (bH and b5) fi'om the MSA model [5 7] for
A1203, B4C, AIN and SiO2 ceramics calculated by Rice [58]. The HAP
(hydroxyapatite) elastic modulus attenuation coefiicient was calculated for
this study using DeWith et al.’s data [54]. The hardness attenuation
coeflicient for HAP has been determined previously in this study (Table 3-
4).

Coeflicient A1203 B4C AIN SiO2 HAP
bE 2.6 4.0 5.5 4.3 2.93“
bH 6.3 5.3 7.7 3.2 6.03"
Ab=bH-bE 3.7 1.3. 2.2 -1.1 3.1
[Reference] Wu & Rice Wu & Rice Boch et al. Park & *[54]
Hench
from [58] from [58] fi‘om [58] from [58] “[this study]

 

103

 

2.10 for alumina (Ab = 3.7) at 0.4 volume fraction porosity to a factor of 0.80 for S102
(Ab = -1.1) at volume fraction porosity of 0.4 (Figure 3-26). The E/H coefficient for
hydroxyapatite = 1.86 (Ab = 3.1) at 0.40 volume percent porosity, was calculated by the
hardness decay constant fi'om the data in this study, bH = 6.03 (Table 3-4), and the elastic
modulus decay constant b5 = 2.93 calculated in this study from the sintered hydroxyapatite

data fiom DeWith et a1 [54] (Table 3-7, Figure 3-26).

3.5.1.1 Effect of E(P) on the fracture toughness of sintered hydroxyapatite

A decrease in hardness with increasing porosity was observed for the sintered
hydroxyapatite specimens in this study. The change in the Vickers hardness as porosity
increases is included in the fracture toughness calculation, due to the hardness and fracture

toughness values being calculated for each individual indent by Equation 3-3. Adding the

elastic modulus-porosity function (E = E0 e"b P” ) with decay constant bE= 2. 93

determined by DeWith et al. [54] to equation 33 results in Equation 3-6.

P
K,C(E(PP)) = 2 ’ Nil—”a 1v)-——"2 c -—2—,2 (3-6)

Recalculation of the fracture toughness of the sintered hydroxyapatite specimens in this
study, using equation 3-6 and bE = 2.93 [54], decreases the fracture toughness relative to
the fracture toughness calculated with equation 3-3. The corrected fracture toughness

values, determined by K,2(E(Pp)) (Equation 3-6), for the sintered hydroxyapatite

104

 

N
I
l

 

 

 

 

z Alumina
o
I
O ~r —
é HAP
351.5 -- _____
E”,
:7 4__ AIN
o d
o —
m ,,,,,,,
9.’ 1 B40
:0
(:7 -
to - Silica
0.5 i : ‘fi : : : :
0 0.1 0.2 0.3 0.4
Volume Fraction Porosity
Figure 3-26 (B "2 as a fimction of the volume fiaction porosities normalized by

(ED/Ho)”, the firlly dense values of the elastic modulus and hardness
respectively. The decay constants bH and b; are compiled by Rice [58] for
A1203, AIN, B4C, and SiO2 (Table 3-6). The b" for HAP was determined
in this study, while b5 for HAP was calculated in this study using the MSA
model and DeWith et al.’s data [54] (Table 3-6).

105

specimens in this study more than double as the volume fraction porosity increases from
0.05 to 0.20 (Figure 3-27).

In addition to the efl‘ect of porosity the elastic modulus can be reduced by
microcracking between grains in a polycrystalline ceramic caused by thermal expansion
anisotropy [36,64,77]. The interactions between porosity and microcracking, and
microcracking and fracture toughness are very complex and will be discussed among the

possible toughening mechanisms in section 3.5.3.

3.5.1.2 Indentation fracture toughness of porous YBa2Cu30.,_,l

Tancret et al. [78] measured the mechanical properties of porous YBa2Cu3O7,,2
high temperature superconductors. The high temperature superconducting specimens
were prepared by cold isostatic pressing and pressureless sintering of commercial
YBa2Cu3O7_x powders [78] . The elastic modulus (E), measured by three-point bending
under quasi-static conditions, the fi'acture toughness (K22), measured by single edged
notched beam (SENB), the Vickers hardness (Hv), and the Vickers indentation crack
parameter (P/c’”) were recorded for specimen porosities between 5 and 31% (0.05-0.31
volume fraction porosity) and average grain sizes between 3 anle um (Table 3-8) [78].

The indentation crack parameter (P/cm) decreases as porosity increases for the
YBa2Cu3OM [78] (Figure 3-28). The indentation crack parameter (P/cm) for the sintered
hydroxyapatite in this study is parabolic in shape peaking at ~ 1.7 MPa m"2 at 0.18 volume
fiaction porosity and falling at volume fraction porosities > 0.25 (Figure 3-28). In this
study, using Tancret et al.’s YBa2Cu3O-,,, data [78], the porosity dependence of the

mechanical properties E, K1c , HV and We”2 were fit to the MSA model [57] (Table 3-8).

106

2.5 —-

...L
01
l
I

ghness (MPa m"1/2)
0
0

p
01
l
I

Fracture Tou

 

 

 

0 1 t : : : 1 : i : i : : 1‘ i
0 0.05 ‘0.1 0.15 0.2 0.25 0.3 0.35
Volume Fraction Porosity

Figure 3-27 Calculated fiacture toughness of the hydroxyapatite specimens in this study

using the elastic modulus as function of volume fi'action porosity (K.c
(E(P))} (Equation 36, material dependent constant bl3 = 2.93 [54]).

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3-8 Experimental data for YBa2Cu3O7,x from Tancret et al. [78] and the fit, for
this study, to the MSA model ln(A) = ln(A0)- bAPP, where A represents the
property (E, Hv, etc.), A0 = the property at zero porosity (y-intercept for
the linear regression), bA is the slope of the log-linear relation, and Pp is the
volume fiaetion porosity. Included for comparison are the fracture
toughness values calculated, for each porosity, using equation 3-3 {Kic =
C(E/H)”2 P cm}, for this study. Column 6 contains the fiacture toughness
calculated with constant elastic modulus (E =120 GPa), {K,2(Indent,
constant E)}. Fracture toughness values in column 7 were calculated using
the measured specimen elastic modulus [78], in equation 3-3 {chandenfl}.

PP E Hv P/c”2 K22 K,c*(Indent, K2, "
Volume [78] [78] [78] [78] constant B) (Indent)
traction (SENB)
porosity (GPa) (GPa) (MPa mm) (MPa mm) (MPa mm) (MPa mm)

0.05 97.2 3.95 15.85 N/A 1.40 1.26
0.06 81.1 4.08 18.03 1.73 1.57 1.29
0.07 62.6 4.09 13.35 1.58 1.16 0.84
0.15 51.4 N/A N/A N/A N/A N/A
0.16 74.4 2.91 12.75 1.09 1.31 1.03
0.25 32 1.09 N/A 0.7 3 N/A N/A
0.29 22 0.64 7.65 0.43 1.68 0.72
0.31 19 0.5 5.05 0.37 1.25 0.50
MSA Fit of the above properties

A0 120 7.08 20.5 2.54 1.34 1.35
b 5.57 7.98 3.89 5.84 -0.180 2.65
r2 0.898 0.953 0.898 0.963 0.023 0.734

 

 

 

 

 

 

 

 

N/A- data not available from Tancret et al. [78]

* Calculated with Equation 33 setting E = 120 GPa, Hv from column 3 and P/c”2 from

column 4.

“Calculated with equation 3-3 using E fi'om column 2, Hv from colurrm 3 and P/c”2 fi'om

column 4.

108

 

N
01

N
O

    

 

 

R? I -

:3 I

<

E15

10 I I

g d [I I

:10 --

2‘2 + '-

O

E. 5J- :- o
0 i a 4. . i

0 ‘0.1 0.2 0.3

Volume Fraction Porosity

I This Study —— [78]

Figure 3-28 Crack parameter P/cm as a function of the volume fraction porosity for
hydroxyapatite from this study and for YBa2Cu3O,,, from Tancret et al.
[78]. The line through the YBa2Cu3O7_,2 data is from the MSA fit (lnP/c”2
= ln(P/cmo)- bP P2,) of the crack parameter P/e”2 [78].

109

From Equation 3-3, the indentation fracture toughness was calculated using the elastic
modulus, Vickers hardness, and P/c”2 for each YBa2Cu2O7_x specimen. The resulting
indentation fracture toughness values fit to the MSA model exhibited significantly smaller
material dependent constant (bk = 2.65) than the bk value (5.84) determined from the MSA
fit of the fi'acture toughness values determined by SENB [78] (Table 3-8, Figure 3-29).
The fracture toughness values of the YBa.2Cu3O7_x specimens calculated by equation 3-3
with a constant elastic modulus (E, = 120 GPa), along with each specimen’s Vickers
hardness and crack parameter (P/cm) are unvarying over the entire porosity range (Table
3-8, Figure 3-29).

YBa2Cu3O7,x high temperature superconducting ceramic has a orthorhombic
crystal structure [79]. YBa2Cu3O7,x is similar in the mechanical properties of the elastic

modulus and hardness as hydroxyapatite (Table 3-9).

3.5.1.3 Porosity dependence of the empirical constant C

The difference between the fi‘acture toughness of YBa2Cu3O.,,x determined by
SENB and by the indentation method suggests the correction factor, C, may be a function
of the volume fiaction porosity. The constant C had been determined by comparing
indentation crack patterns of a number of ‘er11 behaved” reference ceramics [40] to
fiacture toughness values determined by conventional fiaeture toughness techniques such
as double torsion (DT) [39,40], and double cantilever beam (DCB) [40]. Using the MSA
model for the SENB fi'acture toughness data to serve as the correct fiacture toughness
values, as a function of porosity, and the MSA model fit (ln(Kk) = ln(Kmo) - bx PP,

Equation 1-8) for the indentation fiacture toughness values, as a fiinction of porosity, a

110

._L
o

LllllLlJ A 1-1 rrrrrrl
I '1‘ I III

ghness (mPa m"1/2)

 

 

Fracture Tou

 

0.1 A. 1 4. i 1 : 4 4 4 : : ‘r i
0 . 0.1 0.2 0.3
Volume Fraction Porosity

I SENB o Indent x ConstantE

Figure 3-29 Fracture toughness YBa2Cu3O7_x of as a function of the volume fraction
porosity determined by SENB [78] (Table 3-7), Indentation method Kk = C
(Ell-I)"2 P/c”2 (Equation 3-3) with the data from Table 3-7, and the
indentation method (Equation 3-3) with constant elastic modulus (E = 114
GPa) fiom Tancret et al. [78].

111

Table 3-9 Comparison of the zero porosity mechanical properties of YBa2Cu3O7,x and
HAP (C310(PO4)6(OH)2)-

 

 

 

 

 

 

 

Material E0 Hv0 K120
YBa2Cu3OM“ 114 GPa [78] 5.0 GPa [78] 2.4 MPa In"2 [78]
MSA Fit" 120 GPa [78] 7.1 GPa [78] 2.5 MPa m"2 [78]
Ca.,(Po,),(0H)2 115 GPa [54] 6.0 GPa [This study] 1.1 MPa m"2 [54]
117 GPa [80] 6.4 GPa [22] 1.2 MPa m“2 [76]

 

* YBa2Cu2O2,x data fit by Tancret et al. [78] using power law functions: E = 150(1'Pp)In ;

Hv0 = H\,(,(l-P,,)m and K2, = K,,,,(l-P,,)m where PP is the porosity, and m is a microstructure
dependent exponent.

** YBazCu3O-M data [78] fit to the MSA model (ln(A) = ln(A0)- bAPP), for this study

(fiom Table 3-8)

112

 

correction factor as a function of the volume fraction porosity C(Pp) can be calculated for

porous YBa2Cu3O7_x [78], (Equation 3-7).

K,CO(SENB)e“"‘P” _ 2,2,2 K,CO(SENB)
K,co(1ndent)e’b"P” ’ e K,CO(Indent)

 

 

((102): (3'7)

where the difference between the material dependent parameters bK (Indent) and bK
(SENB) are from the MSA model fit (ln(ch) = ln(cho) - bK Pp, Equation 1-8) of the
YBa2Cu3O7_,2 data, AbK = bK (Indent) - bK (SENB), K220(SENB) is the zero porosity
fracture toughness determined from the SENB data fit to the MSA model, Kmandent) is
the zero porosity fi'acture toughness determined fi'om the indentation fiaeture toughness
data fit to the MSA model. For the data fiom Tancret et al. [78] (Table 3-8) the
correction equation C(Pp) = 1.88 e '3‘”. Adding C(PP) to the indentation fi‘acture
toughness equation (Equation 3-3) relates the calculated fracture toughness from the
indentation method to the fiaeture toughness determined by SENB and results in

(Equation 3-8).

E P
K1. = 4 (Pix-12:6)”2 :372— (3-8)

Application of C(PP) to the indentation fracture toughness of sintered hydroxyapatite
(K,C{E(PP)}) (Equation 3-6) can be used as a first approximation to correct the indentation

fiacture toughness method to porous ceramics (Equation 3-9).

113

l

—-2 . 1 P
K. 8(1),. 1. E112.» = 4(P.)E.e (gem 2“ 13-91

The fi'acture toughness correction (K,2{C(PP),E(P,,)}) of the sintered hydroxyapatite
specimens in this study further lessens the porosity dependence of the fiacture toughness

(Figure 3-30), as compared to the fiacture toughness calculated by equation 3-6

(K..{B(P.>}> (Figure 3-27).

3.5.2 Examples of deviations from the MSA model for fracture toughness

From the 21 examples found in the literature in which the fiacture toughness of
porous ceramics were measured only 4 show the fi'acture toughness increasing slightly or
remaining unchanged as the porosity increases (Table 3-10). The normalized fi’acture
toughness parameter data fiom Ricote et al. [48] and Case et al. [81] (Figure 3-31)
depends less on the specimen porosity than the sintered hydroxyapatite specimens in this
study (Figure 3-32). The critical volume fraction porosity (P,) for which physical
properties drop precipitously is seen for Gd2O3 at Pc ~ 0.30 [81]. At P ~ 0.25 the fiacture
toughness parameter of the sintered hydroxyapatite specimens drops off precipitously and

appears to indicate the critical volume fraction for sintered hydroxyapatite.

3.5.3 Possible toughening mechanisms in sintered hydroxyapatite
Fracture toughness is a measure of the energy needed to extend a crack [82].

Crack deflection by pores may increase the fiacture toughness as the porosity increases

114

2.5 '1-

 

 

‘3 ..
F 2 -— .
E 0
E v- . . .
é o o . .
«01.5 -- ’ .
3 o 0.0 ’
E -I- . . .
32 O
E 1 ‘1' ‘. . .
g .. .0 0
g 0
5.0.5 --
0 4 : : : i : 'r 1r 4. : .L i : :
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Volume Fraction Porosity

Figure 3-30 The fi-acture toughness of the sintered hydroxyapatite specimens in this
study calculated with C(PP) (Equation 3-8).

115

Table 3-10

Fracture toughness/porosity trends fit to the MSA model (ln(Kbo) =

1n(K,,,)- ber) fi'om the literature data for a variety of porous ceramics.
The processing method (prc) and fi'acture toughness test method (meth.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

are included.
Ceramic (prc*) Porosity range % bk (meth.**) Reference
A1203 (HP) 240 2.2 (DCB) Wu and Rice from [53,58]
A1203 (PC) 4-42 3.4 (NB) Lam et al. fi‘om [53]
A1203 (HP) 0-9 2 (WOF) Cappola and Bradt fi'om [53]
A1203 (S) 0.44 3.4 (NB) Pabst from [53]
A1203 (HP/S) 2-46 4.2 (NB) Claussen et a1. fiom [53]
A1203 (S) 5-50 2.5 (N/A) Evans and Tappin fi'om [53]
A1203 (HP) 2-14 no fit (DCB) [53]
MgO (HP) 5-25 no fit (DCB) [53]
Gd203 (CIP/S) 347 no fit (NB) [81]
HAP (CIP/S) 3-27 2.79 (TPB) [54] fit in this study
HAP (HP,S) 1-29 2.81 (Ind) [56] fit in this study
HAP (CIP,S) 2-31 no fit (Ind) [this study]
PZT (S) 2-15 2.4 (DT) Biswas and Fulrath fiom [53]
PCT (N/A) 4-28 no fit (Ind) [48]
YBa2Cu3O7,x 5-31 5.8 (SENB) [78] fit in this study
YBa2Cu3O7,x 5-31 2.7 (Ind) [78] fit in this study
SiC (8) 1-7 1.8 (N/A) Seshardi et al. fi'om [58]
B4C (HP) 0-15 2.3 (DCB) Wu and Rice fiom [58]
34C (HP) 0-15 3.4 (DT) Hollenberg & Walther fi'om [53]
Si3N4 (HP/S) 0-10 5.2 (Ind) Mukhoyadhyay et al. fiom [53]
Si2N4 (HP/S) 0-50 2.4 (N/A) Rice et al. fi'om [53]

 

 

 

 

 

*HP-hot pressed, PC-pressure cast, S-sintered, /S-and sintered, CIP-cold isostatic
pressing, HP,S-hot pressed specimens plus sintered specimens, N/A-data not available.

“DCB-double cantilever beam, NB-notch beam, WOF-work of fi'acture, TPB-three point
bend, Ind-indentation crack measurement, DT-double torsion, SENB-single edge notched
beam, N/A-data not available.

116

 

 

 

 

 

E».
a)
E
S
to
CL 2
0
5 [48]
«3 J 0
U- 81
3 . l 1
.5
E .
I
O . 0
Z
0 i ‘ : l : i 1 1 . l
0 0.1 0.2 0.3 0.4 0.5
Volume Fraction Porosity
Figure 3-31 Norrmlized fracture toughness parameters (fracture toughness for Ricote

[48], and fiacture energy for Case et al. [81]) studies in which the fracture
toughness parameters increased or decreased slightly, over a significant
volmne fraction porosity range. Normalization is done by dividing the
fiacture toughness by the zero porosity fiacture toughness as determined
by the intercept of the linear fit. The linear fit (included in plot) calculated
for the entire range of Ricote et al’s data [48]. The linear fit calculated for
the Case et al. [81] data was done for specimens with < 0.30 volume
fraction porosity. The ceramics in question are calcium modified lead
titanate for Ricote [48] and gadolinia for Case et al. [81].

117

 

 

 

E
a)
E .
E I
as
o.
9 I
3
6 I
9
LL
8 I
I!
'6 I
E
o .-
Z
O : i : l # i 1. i F i
0 0.1 0.2 0.3 0.4 0.5

Volume Fraction Porosity

Figure 3-32 Normalized fracture toughness for sintered hydroxyapatite specimens in
this study. Normalization is done by dividing the fiacture toughness by the
zero porosity fracture toughness as determined by the intercept of the
linear fit. The linear fit (included in plot) was calculated for hydroxyapatite
specimens < 0.20 volume fi'action porosity.

118

[83,84]. For a specific crack-pore geometry the fracture toughness may increase if the
pores cause the direction of crack propagation to deviate from the direction normal to the
applied stress [82] In general, however, the fi'acture tbughness decreases as porosity
increases due to the local applied stress acting over decreasing cross sectional area
[85,82]. Fracture toughness decreases with increasing porosity (Section 3.4) for both
sintered hydroxyapatite [54,56], and YBaQCu;,O7,x [78].

Microcracks induced by thermal expansion anisotropy or thermal expansion
mismatch can decrease the fiacture toughness for many non-cubic ceramics [53]. For
example microcracking due to thermal expansion anisotropy was deemed responsible for a
15% decrease in the fiacture toughness of B-silicon nitride as the average grain size
increased [51].

Chou et al. [77] compared the elastic modulus and fi‘acture toughness of SiC
platelet reinforced alumina for two different SiC platelet sizes. E and Klc for SiC platelet
(24 um average diameter) reinforced alumina decreased 40% and 50% respectively as the
volume fraction of SiC platelets increased from 0.0 to 0.4 [77]. Alumina reinforced by
SiC platelets of 12 um average diameter exhibited a 65% increase in Klc for 0.4 volume
fi'action SiC addition [77]. Thermal expansion mismatch resulted in microcracking
between the large SiC platelets and the alumina matrix [77].

Microcracking due to thermal expansion mismatch and phase transformation
resulted in toughening by crack shielding and a locally reduced elastic modulus for
MoSiz/unstabilized ZrO2 composite [86]. K1c values for 20 volume percent ZrO2 /MoSi2
were over twice that of MoSi2 [86].

The absence of apparent grain size-property trends in the data from the sintered

119

hydroxyapatite specimens in this study implies that either 1) No microcracks exist or 2)

Microcrack damage has saturated for the grain size range included in this study [36].

3.6 Thermal Expansion

Thermal expansion data for a high purity alumina reference specimen collected by
identical methods as the sintered hydroxyapatite specimens prepared for this study, was
compared to the American Institute of Physics Handbook [87] data for alumina (Table 3-
11). The average thermal expansion coefficients from 3 different ms with the alumina
reference specimen were plotted against the handbook data (Figure 3-33). There was
reasonable agreement up to ~ 4000 C, for thermal expansion coefiicient (or) taken on
heating and cooling, with significant divergence between the heating and cooling curves

above 6000 C (Figure 3-33).

Table 3-1 1 Thermal expansion data for Alumina, from American Institute of Physics

 

 

 

 

 

 

Handbook 2"” Edition [87].
Temperature (0 C) Parallel c-axis Perpendicular c-axis Polycrystalline
(x1045/0C) (x10’6/0C) (x 104/OCT“
O 5.5 4.6 4.9
200 7.8 7.1 7.33
400 8.9 8.1 8.37
600 9.4 8.5 8.8
800 9.7 8.8 9.1

 

 

 

 

 

 

* calculated from lattice expansion data and equation 1-3.

Thermal expansion coefficient data for sintered hydroxyapatite specimens numbers

120

.3

h
J
1

 

 

"12 J—
2 . -
e n I I I
810 "8 I'o I...
- . mm ; -°.'x
E 3 _ .0.0.I. x
o _ 00 i-
: I
.9 e —— l'
3 .II
to X
‘>% 4 .-
DJ
E .4.
E 2 -—
a:
': fir-
l—
0 : l : l : 4T . § t l r + t + 4 l
O 100 200 300 400 500 600 700 800
Temperature (C)
I Heating 0 Cooling x Reference data [76]
Figure 3-33 Thermal expansion coeficient for high purity alumina determined by

dilatometry, as a fimction of temperature and compared with the American
Institute of Physics Handbook Value [76] (Table 3-6). Dilatometry data
taken from Appendix A.

121

4-10 and numbersl 1-12 on heating showed much more variability at temperatures greater
than 600° C (Figure 3-34). The thermal expansion coefficients collected during cooling,
for the same experimental runs, exhibit significant scatter at all temperatures and had a
different shape than the heating data (Figure 3-35). The average thermal expansion
coefficient, measured during heating, for all the hydroxyapatite specimens increases from
12.9 ppm at 1000 C to 19.1 ppm at 600° C and the average thermal expansion coefficient
measured during cooling increases very little being 19.1 ppm at 100° C and 20.8 ppm at
600° C (Table 3-12). No correlation between the grain size, and the thermal expansion
coefficients, measured at 400° C, are seen (Figure 3-36).

The difi‘erence, Delta (A), in the thermal expansion coeflicient data, for the
hydroxyapatite specimens, between the heating and cooling curves, for all the runs, is
positive below 500° C and goes negative at temperatures greater than 500° C (Figure 3-

37).

122

N

01
J
l

N
O
l

l

.5
01
l
l

 

_s
o
l
l

 

Thermal Expansion Coefficient (ppm)

01
l
L

l r l A l .r l 1 l
r v I l

0 100 200 300 400 500 600 700 800
Temperature
#4 I#5 x#ss $1116 X#7

v #8 A #10 a #11 x #12 Q Ave.

Figure 3-34 Thermal expansion coefficients, measured by dilatometry on heating, for
sintered hydroxyapatite specimens numbers 4-8 and numbers 10-12. Data
taken from Appendix A.

123

0.)
O
I
I

 

 

E -.
e o
#525 -r- . . .
a: ~~ .0 21. E13 F,
8 XX :3 8‘ 83258]
220 -~ ‘B§§' EEA-e 23% §f§
.9 3:: WEE EVE .0
2 w .7 ¥§E i; 3m:XX:X :33; ‘8
to x6
x

Lg- 15 .. « XxxngX '2 ’fix;
_ E 'xZ XX x
g 24 Zi'
'03 -. o
.C

o
*‘10 - t t . r 4. e : %4 9:55-1—

0 100 200 300 400 500 600 700 800
Temperature
#4 I #5 EB #58 v #6 x #7

A #8 a #10 E #11 X #12

Figure 3-35 Thermal expansion coefficient data for sintered hydroxyapatite, from
cooling dilatometry. The data taken from Appendix A.

124

Table 3-12 The averaged thermal expansion coefficients for sintered hydroxyapatite
specimen numbers 4-8, and 10-12 by dilatometry. The delta is the
difference between the cooling data and the heating data: Delta = a cool -

 

 

 

 

 

 

 

 

 

a heat.
Temperature (°C) Heating data (ppm) Cooling data (ppm) Delta (ppm)
100 12.89 19.07 6.18
200 13.75 18.41 4.66
300 15.12 17.78 2.66
400 16.34 17.42 1.08
500 17.52 18.78 1.26
- 600 19.79 20.77 0.98
700 20.20 17.52 -2.68
750 20.92 16.96 -3.96

 

 

 

 

 

125

 

16.5 ~—

 

 

A I
E
Q. q.-
9;
.3 16 a, I
Q
55 I.
O m-
0 I
8
3315.5“-
C
N
a
x .,
LU
E
g 15 -+- - -
"' .. I
I
14.5 %1 i 4 : + .L : 4 + : :
1 2 3 4 5 6 7 8

Grain Size (Microns)

Figure 3-36 Average thermal expansion coeflicient for sintered hydroxyapatite
specimens #4-8 and #10-12 (heating to 600° C) as a function of the average
grain size. The data was taken from Appendix A.

126

 

 

O 200 400 600 800
Temperature

#4 .#5 E#5$'#6 x#7
A#8 8#1OE#11Z#12

Figure 3-37 Difierence in the thermal expansion coeflicient for sintered hydroxyapatite,
Delta = on m- on ma , as a function of temperature. Dilatometry data
taken from Appendix A.

127

3.7 Dielectric measurements
3.7.1 Circuit capacitance measurement and correction
The circuit used to measure the relative permittivity was calibrated using the
alumina reference specimen (ADS995, Coors) of known dielectric properties [72] (Table
3-13). The average measured capacitance (from three measurements at 45 kHz) of the
circuit (Figure 2-7) with the alumina reference specimen inserted in the electrodes was
46.23 pF at 45 kHz. The capacitance of the alumina reference specimen in the electrodes
(C ADS) was calculated from the known relative permittivity at 45 kHz and the geometry of
the electrodes CADS = 28.89 pF (Equation 3-10) [88].
Cms=(€ode)/d

Where 60 is the permittivity of free space, kd is the relative permittivity, A is the area of the

(3-10)

electrodes (corrected to add the width of the guard gap per ASTM D 150-95 [73]), and d
is the specimen thickness. The circuit capacitance Cc was then established to be the
difference in the measured capacitance Cm and the capacitance calculated for the reference
specimen Cms- The circuit capacitance was determined to be Cc = CIn - CABS = 17.34 pF.
The capacitance for the sintered hydroxyapatite specimens was determined by subtracting
the circuit capacitance (17.34 pF) from the measured circuit capacitance. The circuit

capacitance determined at 45 kHz was used at all frequencies.

 

 

 

Table 3-13 Dielectric characteristics for Coors ADS 995 alumina substrate. Data from
Tech Specs, Thin Film Substrates Technical Specifications 10-3-0897 from
Coors Ceramics, Golden, CO [72].
Frequency Dielectric constant Loss Factor Q = 1/(Loss factor)
1 kHz 9.9 :1 0.003 333
1 MHz 9.9 :1 0.001 1000

 

 

 

 

 

128

 

3.7.2 Relative permittivity of hydroxyapatite

The relative permittivity of the hydroxyapatite specimens was calculated from
corrected capacitance measurements. The geometry of the electrodes and specimen
thickness were used to calculate the relative permittivity of sintered hydroxyapatite by
rearranging equation 3-3 [88] (Equation 3-11).

kd=Cd/eoA (3-11)
where the variables are as defined for equation 3-10.

The fully dense hydroxyapatite relative permittivity (kw), was calculated for
MGTl (Table 3-14) by a simple fit of the data to equation 1-9. For each specimen the
difiemnce of the measured relative permittivity kd and the calculated km, fiom equation 1-
9 was calculated with the specimen’s relative density and the variable km. The differences
were then summed. The fully dense hydroxyapatite relative permittivity (km) was
incremented in equation 1-9 until the sum of the differences was at a minimum. The fiilly
dense hydroxyapatite relative permittivity (kw) was also calculated for MGT2 and
equation 1-10 (Table 3-14).

The relative permittivity of sintered hydroxyapatite at 45 kHz decreased as the
relative density decreased (Figure 3-3 8). As a function of the relative density the data for
the hydroxyapatite specimens more closely matched MGT2 than MGTl (Figure 3-3 8).
The relative permittivity of the sintered hydroxyapatite is stable over the measured
frequency range (45 kHz - 7.3 MHz) (Figure 3-39, Figure 3-40).

The relative permittivity of hydroxyapatite sintered with Mg2+ additives and
partially decomposed, as determined by x-ray dim'action was measured by F anovich et al.

[89]. The relative permittivity of the sintered hydroxyapatite specimens measured by

129

Table 3-14 Relative permittivity for sintered hydroxyapatite fiom this study and
Fanovich et al. [89] and the fit parameters for the Maxwell-Garnet

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

equations.
\\ This study Fanovich et al. [89]
‘ Fit parameters Fit parameters R
k MGTl MGT2 MGTI MGT2 K
kccr 13.01 17.63 15.4 28.3 \
Difierence per 0.831 0.698 1.39 0.696
data point“ k
Specimen Relative km Mg2+ Relative kTn
Label Density weight % Density
44 0.952 11.63 1 0.897 13.62
14 0.951 13.55 0 0.856 12.61
43 0.947 11.62 3 0.846 9.81
45 0.937 12.05 5 0.830 9.45
16 0.936 12.64 \V‘
42 0.936 12.47
50 0.931 11.53
49 0.924 12.02
46 0.918 I 1.63
41 0.769 7.94
36 0.658 5.62
33 0.579 4.93 x
* The sum of the differences between the measured data and the fit equation divided

by the number of total data points.

130

_s
A
l
I

_L
N
l
T

 

J
O
L l

Relative Permittivity
CD
I

 

 

6-
4-
2—1
0.%i::r%*#*%1%r‘.:%‘rui
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Relative Density

I HAP — MGT1 — MGT2

Figure 3-38 Relative permittivity data fiom sintered hydroxyapatite and the fitted
Maxwell-Garnet equations MGT1 (Equation 1-9) and MGT2 Equation (1-
10). The data was taken from Table 3-9.

131

14
a . 5 ..
.3312 - 0 - I
. x .
E10 . - = x
2 Ba x E
z: 8 BE 83
¢_u
i? 6

x I 9 ‘

l 1 i L J 1 l L I A l 1 l
I ' I ' I ' l 1 r 1 l ' T

0 1000 2000 3000 4000 5000 6000 7000
Frequency (kHz)

 

I ADSQQS O #14 x #16 V #33
A #36 E #41 E #42

Figure 3-39 Relative permittivity for the sintered hydroxyapatite specimen numbers 14,
16, 33, 41, 42 and the alumina reference material ADS995 as a function of
fi'equency. The data was taken fi'om Appendix B.

132

13 g

>.

312.5 I

.=_:

E 5 ‘

a, 12 v

(L

a) X

€115

g .. i z E
11 A

E l V
10.5 ¢

1 I l I 1 I l I l I l I l
I I 1 1 l I l v I I l

0 1000 2000 3000 4000 5000 6000 7000
Frequency (KHz)

 

I#43. 1144211457 #46A #498 #50

Figure 3-40 Relative permittivity for sintered hydroxyapatite specimen numbers 43-46,
49 and 50 as a function of frequency. The data was taken from Appendix
B.

133

Fanovich et al. [89] were greater than the sintered hydroxyapatite specimens in this study
as a function of relative density. Fitting the data fiom Fanovich et al. [89] to MGT1 and
MGT2 produced a closer match to MGT2 (Table 3-14). Sintered monoclinic
hydroxyapatite of 97.6% relative density was determined to have a relative permittivity of

15.4 at 100 kHz by Ikoma et al. [26].

134

4.0 Summary and Conclusions

Commercially available hydroxyapatite powder can be sintered to 96% relative
densities by simple uniaxial die pressing and pressure-less sintering at 13000 C. Final
sintered density is a strong function of the pre-sintering densificatiort A linear relationship
between final sintering density and uniaxial die pressure was determined. The final
sintered density of hydroxyapatite specimens sintered at 1300° C for less than 120 minutes
increased 0.27% in relative density for each additional MPa of pressure applied. An
increase in the relative density of sintered hydroxyapatite to 98% required cold isostatic
pressing before sintering at 13000 C. Average grain sizes for the hydroxyapatite
specimens fell between 1.5 pm and 7.5 um and are a function of sintering time and
temperature.

There were no decomposition phases of hydroxyapatite detected by x-ray
difli’action for hydroxyapatite specimens sintered at 1300° C with sintering times up to 11
hours and at 14000 C for as long as 4 hours. The phase stability of the hydroxyapatite is
attributed to the slightly rich calcium content (36-3 7% by specific analysis) of the
commercial hydroxyapatite powder and from the moisture present in the ambient
atmosphere of the fiimaces used.

The Vickers hardness values measured for the sintered hydroxyapatite specimens
in this study were successfully fit, as a function of the volume fraction porosity (P), to the
exponential decay equation (Hv = Ho e") with the zero porosity hardness value Ho = 6.00
i 0.7 GPa and decay constant b = 6.03.

Fracture toughness of the sintered hydroxyapatite specimens in this study diverged

fi'om the expected exponential decay function as the porosity increased. The measured

135

fi'acture toughness is 0.4-0.6 MPa m“2 for sintered hydroxyapatite specimens of 97%
relative density. The fracture toughness of sintered hydroxyapatite increased to 2.5-2.7
MPa m“2 at 72-75% relative density. Published data fiom other researchers on the
fracture toughness of sintered hydroxyapatite was successfully fit, in this study, to the
exponential decay equation with nearly identical b values of 2.786 [54] and 2.812 [56].
Fracture toughness of specimens at 97% relative density were 1.34-1.5 MPa m”2 for
hydroxyapatite whisker reinforced hydroxyapatite[56] and 1.01-1.2 MPa m"2 for dense
unreinforced sintered hydroxyapatite [54,56,76].

Corrections to the indentation fi'acture toughness equation (Equation 2-6,
Equation 3-3) for the decrease in the elastic modulus as the porosity increased decreased
the calculated fracture toughness over the entire porosity range ( Kk(E(Pp)), Equation 3-
6). The exponential in equation 3-6 decreased K: to a greater degree as the porosity
increased. ch increased as the porosity increased up to a 0.2 volume fiaction then
decreased. KIc peaked at 121.6 MPa m"2 for specimens of 0.225 volume fi'action porosity.

Comparing the fracture toughness measured by SENB to that measured by the
indentation method for YBazCu3O7_x [78] suggested a further correction to the indentation
fi'acture toughness equation K,C(E(Pp)). Assuming the empirical constant is a function of
porosity C(Pp), K1c measured by the indentation method can be equated to Klc measured
by SENB for the YBaQCu3O-,_x specimens. C(Pp) added to K,c(E(Pp)) produced
K,c(C(Pp),E(Pp)) (Equation 3-9). Applying ch(C(Pp),E(Pp)) to the indentation of the
sintered hydroxyapatite specimens prepared for this study increased Klc to 0.6-1.0 MPa
m"2 at low porosity (~ 0.03 volume fiaction porosity). Klc peaked at 1.8-2.0 MPa m"2 for

volume fraction porosities 0.06 to 0.17 before decreasing.

136

Both corrections to the indentation fiacture toughness equation (Equation 3-6, and
3-9) when applied to the sintered hydroxyapatite indentation data produced increasing Klc
at low and moderate porosities (0.02-0.15) before falling off. A small percentage (5 out
of 2 1) of the Kk/Porosity studies found in the literature report other than decreasing K,c as
porosity increases.

The hysteresis seen in the heating and cooling curves of sintered hydroxyapatite
from the dilatometer was determined to be an artifact of the apparatus and not due to
microcracking. The same hysteresis was seen for dilatometry data for the non-
microcracked alumina specimen. The thermal expansion coefficients for sintered
hydroxyapatite, averaged for the heating data for all the hydroxyapatite specimens tested,
equals 12.89 x10‘6/°C at 100° C , 13.75 x10‘/°C at 2000 C, 16.34 at 400° C and 19.79
x 1015/ °C at 600° C. The dilatometer was not accurate above 6000 C based on the
comparison between the handbook data [71] and the dilatometer values for the high purity
alumina specimen above 6000 C.

The maximum relative dielectric permittivity of sintered hydroxyapatite in this
study was k = 13.55 for a specimen of 95.1% relative density. The minimum relative
dielectric permittivity k = 4.93 for a specimen at 58.0% relative density. Maxwell-Garnet
mixing laws were used to determine the zero porosity relative permittivity and the
functional relationship between the relative permittivity and porosity of sintered
hydroxyapatite specimens. The first mixing law (MGT 1) assumes spherical pores in a
ceramic matrix and was the least successful in fitting the data fiom this study. MGT2 in
which spherical ceramic particles are in a matrix of air fit the data more successfully.

MGT1 predicted a zero porosity relative permittivity of 13.01. MGT2 predicted k0 =

137

17.63 fiom the data in this study.

4.1 Further Research

The indentation technique for fracture toughness measurements used in this study,
though used successfully for sintered hydroxyapatite by Suchanek et al. [56] needs fiu'ther
scrutiny. The size of the indentations grew as the sintered hydroxyapatite specimens
became more porous, as expected: The larger indents, however, failed to produce the
increased extent of the half-penny cracks. Possrble mechanisms that would limit the
indentation cracks in porous hydroxyapatite are densification below the indent and crack
bridging between pores. Densification below the indent tip under load would absorb
energy and disrupt the plastic/elastic interface responsible for indentation crack grth
[90]. Crack bridging results in greater surface areas formed from halfpenny cracks of

seemingly the same length.

138

APPENDIX A

Appendix A Thermal expansion data.

The thermal expansion data collected at 25 °C intervals fiom 50 °C to 800 0C for
both the heating and cooling curves. The data was taken for sintered hydroxyapatite
samples numbers (4-8, 10 and 11) along with two sintered alumina specimens.

Table A1 Thermal expansion data for Hydroxyapatite samples number 4, 5 with no
dwell at 800 °C, and 5 with a pause at 800 °C. The data is used in Figures

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3-26 to 3-27.

Temperature 4 (um/m oC ) 5 (um/m 0C ) 5 soak (um/m oC)
(0C) Heat Cool Heat Cool Heat Cool
50 12.2 0 11.4 N/A 12.0 N/A
75 12.7 3 12.7 N/A 13.1 15.8
100 12.6 0 13.0 N/A 13.5 15.4
125 12.6 , 13.7 13.0 N/A 13.9 14.8
150 13.1 16.1 13.4 20.3 14.4 15.1
175 13.4 16.8 13.9 21.9 15.1 16.2
200 14 N/A 14.2 22.4 15.3 15.3
225 13.8 17.8 14.8 23.4 15.6 16.2
250 14.1 18.8 14.6 25.0 14.4 16.6
275 14.5 17.2 15.5 26.5 15.0 15.9
300 14.2 17.7 16.5 18.0 15.9 16.6
325 14.9 17.0 16.3 17.3 15.5 15.5
350 15.0 18.6 16.5 N/A 15.9 15.7
375 15.4 18.5 16.9 21.6 15.9 15.1
400 16.6 19.3 17.5 16.1 17.8 16.5
425 16.1 19.8 17.1 17.1 17.5 17.4
450 16.2 20.7 17.6 23.9 15.8 18.4
475 16.1 20.2 17.2 21.3 17.2 19.1

 

 

 

 

 

 

 

 

 

139

APPENDIX A
Table A1 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature 4 (um/m °C ) 5 (um/m °C ) 5 soak (um/m °C )
(0C) Heat Cool Heat Cool Heat Cool
500 17.0 19.6 18.0 23.8 17.7 19.6
525 17.4 20.2 18.3 20.8 19.2 19.8
550 16.6 21.3 19.2 21.0 19.0 19.8
575 18.1 18.9 20.4 19.0 18.8 20.7
600 18.0 20.4 20.5 18.6 15.9 21.8
625 20.0 20.9 22.6 18.5 21.7 21.5
650 17.0 18.1 21.1 17.6 21.4 19.9
675 18.8 18.2 21.7 15.9 22.1 18.4
700 19.0 15.5 23.2 15.5 20.0 19.7
725 18.2 14.5 24.0 20.9 20.9 19.2
750 17.9 16.3 21.1 10.9 22.1 18.7
775 19.5 15.8 19.7 11.8 22.9 17.2
800 20.7 N/A 20.0 9.64 N/A N/A

 

 

 

 

 

 

 

 

 

Table A2 Thermal expansion data for Hydroxyapatite samples number 7, 8, and 10
fiom Figures 3-26 to 3-27.

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature 6 (um/m °C ) 7 (um/m °C ) 8 (um/m oC)
(0C) Heat Cool Heat Cool Heat Cool
50 12.7 13.7 11.6
75 12.8 13.0 12.5
100 13.0 12.9 12.5
125 12.8 16.9 13.0 15.7 13.2 17.2
150 13.3 17.4 13.6 15.5 13.4 18.2
175 13.9 18.2 13.7 15.8 9.58 18.6
200 13.5 15.6 14.1 16.0 10.4 16.7

 

 

 

 

 

140

Appendix A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table A2 continued
Temperature 6 (um/m °C ) 7 (um/m °C ) 8 (um/m °C )
(0C) Heat Cool Heat Cool Heat Cool
225 14.5 17.9 13.9 16.1 11.6 17.7
250 14.7 18.9 14.3 16.3 13.2 17.5
275 15.4 18.6 14.9 16.3 13.7 13.3
300 14.9 18.5 14.9 16.7 15.3 19.1
325 15.7 17.2 15.1 16.4 15.7 18.5
350 16.6 17.4 14.8 16.7 15.4 N/A
375 17.3 19.2 14.9 16.8 15.9 19.5
400 14.9 15.3 15.4 17.0 15.6 20.3
425 16.5 18.9 14.8 14.2 17.0 19.6
450 17.5 . 18.8 15.6 13.3 16.7 21.1
475 18.4 13.5 15.0 18.4 17.5 21.6
500 18.3 16.2 15.8 17.9 16.9 19.6
525 19.9 21.0 15.7 17.7 18.3 19.7
550 19.6 20.0 17.1 19.5 16.8 19.4
575 17.8 20.6 18.2 19.8 18.1 20.5
600 20.9 20.6 18.9 21.2 19.0 19.8
625 24.0 21.4 23.4 23.4 27.8 17.5
650 21.3 20.0 20.2 19.4 16.8 18.5
675 21.1 18.5 20.1 18.5 23.51 18.3
700 20.0 17.7 22.3 15.6 18.9 18.4
725 19.7 16.4 22.1 15.2 19.6 16.4
750 20.2 15.9 20.5 14.6 18.9 N/A
775 21.6 15.2 20.9 15.4 19.9 18.5
800 27.2 N/A 21.1 14.0 28.9 N/A

 

 

 

 

 

 

 

 

 

141

APPENDIX A

Table A3 Thernml expansion data for Hydroxyapatite samples numbers 10, 11, and
12 from Figures 3-26 to 3-27.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature 10 (um/m oC ) 11 (um/m °C) 12 (um/m °C)

(°C) Heat Cool Heat Cool Heat Cool
50 12.6 N/A 12.8 N/A 11.9 18.8
75 12.8 N/A 13.2 18.3 12.3 23.1
100 13.0 N/A 13.4 19.1 12.1 22.7
125 13.8 19.1 13.4 19.1 11.4 21.2
150 14.4 18.2 13.9 14.3 11.0 21.1
175 14.4 19.4 14.2 17.6 12.0 N/A
200 14.7 20.5 13.2 20.8 13.5 20.0
225 14.4 19.0 13.7 17.3 14.0 19.7
250 15.1 13.3 13.9 16.2 14.4 18.0
275 15.8 18.8 14.1 17.3 14.3 18.6
300 15.6 18.4 15.0 17.4 14.6 17.6
325 15.9 19.8 15.5 18.7 14.9 N/A
350 17.1 21.7 16.1 17.0 14.9 17.1
375 16.9 18.4 16.3 19.1 15.3 17.5
400 17.8 17.8 16.7 16.8 15.4 17.7
425 17.5 18.1 16.2 17.9 16.2 13.3
450 18.7 13.4 17.2 18.2 16.5 14.7
475 16.3 19.1 17.9 19.5 16.8 16.2
500 18.9 N/A 18.0 18.6 16.5 14.9
525 19.6 20.3 18.2 18.7 16.9 16.1
550 19.7 21.3 18.9 19.7 16.7 17.1
575 20.3 20.5 19.9 20.3 18.4 17.7
600 22.1 22.4 18.9 20.9 17.5 21.2

 

 

 

 

 

 

 

142

 

 

APPENDIX A

 

 

 

 

 

 

 

 

Table A3 continued
625 25.0 23.8 22.9 19.8 20.5 19.6
650 21.5 20.7 20.6 19.4 17.6 17.5
675 21.1 22.5 21.5 22.3 17.3 16.7
700 20.7 20.8 19.8 18.3 16.6 16.2
725 20.8 21.1 19.8 21.0 19.5 10.3
750 20.6 21.5 20.1 21.5 17.9 16.3
775 21.2 19.8 22.3 N/A 18.1 10.1
800 26.9 18.5 23.2 N/A 19.6 N/A

 

 

 

 

 

 

 

 

 

Table A4 Thermal expansion data for the alumina sample number 1 with 1 g weight,
alumina number 1 with 5 g weight (denoted 1a) and alumina sample

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

number 2.
Temperature 1 (um/m _°C ) 1a (um/m oC ) 2 (um/m oC )
( C) Heat Cool Heat Cool Heat Cool
50 5.24 4.92 5.27
75 5.66 5.40 5.62
100 5.80 5.84 5.76 5.49
125 6.26 8.77 6.06 6.09
150 6.57 8.38 6.38 6.41
175 6.73 8.78 6.74 6.85
200 7.09 8.24 7.03 7.03 6.76 8.90
225 7.14 8.53 7.38 7.36
250 7.42 8.71 7.28 7.58
275 7.56 8.92 7.77 7.69
300 7.8 8.77 8.12 7.95 8.61 9.20
325 7.86 8.77 8.31 8.21
350 8.35 8.96 8.90 8.39

 

 

 

 

 

 

 

 

 

143

APPENDIX A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table A4 continued
Temperature #1 (1.1an °C ) #1a(um/m °C ) #2 (um/m °C )

(0C) Heat Cool Heat Cool Heat Cool
375 9.36 9.04 8.72 8.73

400 8.9 9.20 9.00 9.09 9.15 9.36
425 9.15 9.57 9.15 9.18

450 9.4 9.25 9.36 9.1

475 9.95 9.58 9.40 8.97

500 9.93 8.95 9.82 9.89 11.0 8.81
525 9.97 9.35 9.95 9.69

550 11.0 8.99 10.4 10.1

575 10.5 9.54 9.66 10.8

600 10.5 q 8.67 9.96 10.3 9.16 9.40
625 10.5 8.62 11.0 11.5

650 10.3 8.32 10.3 10.9

675 11.3 8.48 10.9 10.7

700 10.7 7.31 11.5 11.5 12.2 8.83
725 9.24 7.36 9.99 11.5

750 11.8 5.96 12.3 11.5

775 10.2 7.26 11.1 11.5

 

 

 

 

 

 

 

 

 

144

APPENDEX A

Table A5 The averaged therrml expansion data for sintered hydroxyapatite (from
Tables A1,A2 and A3) and alumina (fiom Table A4).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature HAP (um/m °C ) Alumina (um/m °C )
(0C) Heat Cool Heat Cool
50 12.32 18.8 5.14 5.27
75 12.79 19.07 5.56 5.62
100 12.89 19.07 5.72 5.76
125 13.01 17.21 6.14 7.43
150 13.39 17.36 6.45 7.40
175 13.35 18.06 6.77 7.82
200 13.66 18.41 6.98 8.06
225 14.03 18.34 7.29 7.95
250 14.30 17.84 7.43 8.15
275 14.80 18.06 7.67 8.31
300 15.21 17.78 8.12 8.64
325 15.50 17.55 8.13 8.49
350 15.81 17.74 8.55 8.68
375 16.09 18.41 8.94 8.89
400 16.41 17.42 9.04 9.22
425 16.54 17.37 9.16 9.38
450 16.87 18.06 9.29 9.18
475 16.93 18.77 9.44 9.28
500 17.46 18.78 10.16 9.22
525 18.17 19.37 9.87 9.52
550 18.18 19.90 10.50 9.55
575 18.89 19.78 10.32 10.17
600 19.08 20.77 9.98 9.46

 

 

145

 

 

Table A5 continued

APPENDEX A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature HAP (um/m oC ) Alumina (urn/m °C )
(0C) Heat Cool Heat Cool
650 19.72 19.01 10.5 9.61
675 20.80 18.81 10.97 9.59
700 20.06 17.52 1 1.48 9.21
725 20.51 17.22 10.24 9.43
750 19.92 16.96 1 1.87 8.73
775 20.68 15.48 10.93 9.38
800 23.45 14.05 N/A N/A

 

146

 

 

 

 

APPENDIX B

Appendix B The dielectric data

The calculated relative permittivity and the measured quality factor Q, for the
Alumina substrate (ADS 995) and hydroxyapatite specimens numbers 14, 16, 33, 36, 41-
46, 49, 50. The data was taken in the fi'equency range 45 kHz to 7.3 MHz.

Table B1 Dielectric data for alumina substrate (1.016 mm in thickness).

 

 

 

 

 

 

 

 

 

 

Frequency (kHz) Relative permittivity Q

45.0 9.9 333

72.17 9.3 244
101.62 8.8 268
160.77 10.2 235
307.17 8.7 196
702.20 9.9 309
1641.90 9.9 217
31 12.91 9.6 246
7302.00 1 1.4 195

 

 

 

 

 

147

 

APPENDIX B

Table B1 Dielectric data for hydroxyapatite specimen number 14 (2.845 mm in

 

 

 

 

 

 

 

 

 

 

thickness).

Frequency (kHz) Relative Permittivity Q
45.0 13.6 52.6
72.17 13.3 25.4

101.62 13.2 30.3
160.77 14.1 35.9
307.17 12.2 42.5
702.20 13.1 50.7
1641.90 12.1 55.9
3112.91 10.4 58.1
7302.00 1 1.9 69.2

 

 

 

 

 

Table B1 Dielectric data for hydroxyapatite specimen number 16 (2.969 mm in

 

 

 

 

 

 

 

 

 

 

 

thickness).
Frequency (kHz) Relative Permittivity Q

45.0 12.6 56.2
72.17 12.6 27.0
101.62 10.6 35.8
160.77 12.9 37.1
307.17 12.8 44.4
702.20 13.7 64.4
1641.90 10.7 84.8
3112.91 8.9 80.8
7302.00 9.9 1 15

 

 

 

 

 

148

APPENDIX B

Table B1 Dielectric data for hydroxyapatite specimen number 33 (1.123 mm in

 

 

 

 

 

 

 

 

 

 

thickness).
Frequency (kHz) Relative Permittivity Q

45.0 4.9 185
72.17 4.7 105
101.62 4.1 96.8
160.77 4.7 82.8
307.17 4.3 108
702.20 5.4 93.7
1641.90 5.4 84.4
31 12.91 4.6 104
7302.00 4.5 132

 

 

 

 

 

Table B1 Dielectric data for hydroxyapatite specimen number 36 (1.730 mm in

 

 

 

 

 

 

 

 

 

 

thickness).
Frequency (kHz) Relative Permittivity Q

45.0 5.6 186
72.17 3.9 87.7
101.62 4.8 93.9
160.77 5.5 77.6
307.17 3.8 90.8
702.20 5.2 79.2
1641.90 5.4 65.6
3112.91 5.2 84.6
7302.00 4.6 88.2

 

 

 

 

 

149

APPENDIX B

Table B1 Dielectric data for hydroxyapatite specimen number 41 (0.866 mm in

 

 

 

 

 

 

 

 

 

 

thickness).
Frequency (kHz) Relative Permittivity Q

45.0 7.9 156
72.17 7.8 108
101.62 7.5 l 14
160.77 7.8 95.4
307.17 7.4 101
702.20 7.8 86.3
1641.90 8.3 71.7
3112.91 8.1 61.4
7302.00 8.2 42.4

 

 

 

 

 

Table B1 Dielectric data for hydroxyapatite specimen number 42 (1.113 mm in

 

 

 

 

 

 

 

 

 

 

 

thickness).
Frequency (kHz) Relative Permittivity Q

45.0 12.5 37.2
72.17 12.3 26.3
101.62 11.5 28.7
160.77 11.9 33.1
307.17 11.5 41.8
702.20 1 1.7 49.9
1641.90 12.3 56.3
3112.91 11.6 72.3
7302.00 12.6 72.6

 

 

 

 

 

150

APPENDIX B

Table B1 Dielectric data for hydroxyapatite specimen number 43 (1.336 mm in

 

 

 

 

 

 

 

 

 

 

thickness).

Frequency (kHz) Relative Permittivity Q
45.0 11.6 127
72.17 10.6 70.4

101.62 11.0 92.7
160.77 1 1.0 125
307.17 10.7 87.8
702.20 1 1.0 134
1641.90 10.9 139
3112.91 11.2 133
7302.00 13.0 119

 

 

 

 

 

Table B1 Dielectric data for hydroxyapatite specimen number 44 (1.214 mm in

 

 

 

 

 

 

 

 

 

 

 

thickness).

Frequency (kHz) Relative Permittivity Q
45.0 11.6 110
72.17 11.6 78.6

101.62 11.7 87.2
160.77 11.0 95.8
307.17 10.9 134
702.20 1 1.0 155
1641.90 12.1 165
3112.91 12.2 177
7302.00 12.9 148

 

 

 

 

 

151

APPENDIX B

Table B1 Dielectric data for hydroxyapatite specimen number 45 (1.610 mm in

 

 

 

 

 

 

 

 

 

 

thickness).

Frequency (kHz) Relative Permittivity Q
45.0 12.1 229
72.17 11.3 148

101.62 ’ 10.6 168
160.77 11.6 135
307.17 11.2 152
702.20 11.2 173
1641.90 12.2 164
3112.91 11.7 156
7302.00 12.5 131

 

 

 

 

 

Table B1 Dielectric data for hydroxyapatite specimen number 46 (1.651 mm in

 

 

 

 

 

 

 

 

 

 

thickness).
Frequency (kHz) Relative Permittivity Q

45.0 11.6 184
72.17 1 1.3 97.3
101.62 11.6 106
160.77 11.4 158
307.17 1 1.1 108
702.20 10.4 179
1641.90 1 1.1 1 12
3112.91 10.9 138
7302.00 11.9 11 1

 

 

 

 

 

152

APPENDIX B
Table B1 Dielectric data for hydroxyapatite specimen number 49 (1.580 mm in

 

 

 

 

 

 

 

 

 

 

thickness).
Frequency (kHz) Relative Permittivity Q

45.0 12.0 245
72.17 1 1.1 154
101.62 1 1.4 146
160.77 1 1.3 158
307.17 1 1.2 157
702.20 10.6 199
1641.90 10.8 166
3112.91 11.1 127
7302.00 11.0 157

 

 

 

 

 

Table B1 Dielectric data for hydroxyapatite specimen number 50 (1.595 mm in

 

 

 

 

 

 

 

 

 

 

 

thickness).
Frequency (kHz) Relative Permittivity Q

45.0 11.5 188
72. 17 l 1.2 136
101.62 1 1.2 140
160.77 10.1 93.1
307.17 1 1.0 103
702.20 10.8 132
1641.90 1 1.0 123
3112.91 11.2 106
7302.00 11.2 150

 

 

 

 

 

153

[11

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[5]

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[31

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