Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf ·...

13
Appendix: Experimental procedures 139 Appendix: Experimental procedures This section deals with the main experimental procedures used in this study for the elaboration and characterization of the ZTA composites. The composite powder was obtained through the modification of a commercial α-alumina powder, by exploiting a novel technique described in the Chapter II. The characterization of the composite powder required the study of its thermal behaviour, the identification of the zirconia polymorphism, the investigation of the influence of each procedure steps, on the phase evolution, as well as on the crystalline zirconia amount, size and distribution and homogeneity. This analyses were fundamental to set up the right procedure and the proper treatments, in order to obtain a powder with the desired features, suitable to produce homogeneous and reliable components. Starting from the produced AZ composite powder, two former methods were exploited to obtain dense samples: slip casting and cold isostatic pressing. The former was performed to obtain samples for a preliminary characterization, while the latter was exploited to produce femoral heads prototypes. Slip casting consists in pouring a suspension into a porous mould. Dry pressing requires spray dried powders, with desired flowability and compressive behaviour, so that, even if indirectly, also pressing passes through the preparation of a ceramic powder suspension. Consequently, both these forming methods need a careful suspension formulation, in fact the slurries have to fulfill several requirements, concerning the rheological behaviour, the solid content, the particle agglomeration level. The consolidation of ceramic powder into dense bodies occurs during the sintering step. In this thesis, both pressurless sintering and hot isostatic pressing were performed. The characterization of the fired samples was carried out, in term of microstructural features, density and mechanical properties. 1.1 Elaboration 1.1.1 Powder elaboration A commercial α-alumina powder (TM-DAR TAIMICRON, supplied by Taimei Chemicals Co., Japan) was used to develop the alumina - zirconia composite powder. First, the alumina powder was dispersed in distilled water by ball milling, for 3 hrs, by using α-alumina spheres (solid content 50 wt%, powder/spheres weight ratio of 1/5). During dispersion, an almost constant pH value of about 6.5 was reached. Then, a zirconium chloride aqueous solution was added to the alumina slurries, in a suitable amount to develop the desired composition after thermal treatment. The aqueous salt solutions (0.38 M) were prepared with ZrCl 4 and ammonium citrate tribasic, as complexing agent, which allows to modify the pH without zirconium hydroxide precipitation.

Transcript of Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf ·...

Page 1: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

139

Appendix: Experimental procedures

This section deals with the main experimental procedures used in this study for the elaboration and characterization of the ZTA composites.

The composite powder was obtained through the modification of a commercial α-alumina powder, by exploiting a novel technique described in the Chapter II. The characterization of the composite powder required the study of its thermal behaviour, the identification of the zirconia polymorphism, the investigation of the influence of each procedure steps, on the phase evolution, as well as on the crystalline zirconia amount, size and distribution and homogeneity. This analyses were fundamental to set up the right procedure and the proper treatments, in order to obtain a powder with the desired features, suitable to produce homogeneous and reliable components.

Starting from the produced AZ composite powder, two former methods were exploited to obtain dense samples: slip casting and cold isostatic pressing. The former was performed to obtain samples for a preliminary characterization, while the latter was exploited to produce femoral heads prototypes. Slip casting consists in pouring a suspension into a porous mould. Dry pressing requires spray dried powders, with desired flowability and compressive behaviour, so that, even if indirectly, also pressing passes through the preparation of a ceramic powder suspension. Consequently, both these forming methods need a careful suspension formulation, in fact the slurries have to fulfill several requirements, concerning the rheological behaviour, the solid content, the particle agglomeration level.

The consolidation of ceramic powder into dense bodies occurs during the sintering step. In this thesis, both pressurless sintering and hot isostatic pressing were performed. The characterization of the fired samples was carried out, in term of microstructural features, density and mechanical properties.

1.1 Elaboration

1.1.1 Powder elaboration

A commercial α-alumina powder (TM-DAR TAIMICRON, supplied by Taimei Chemicals Co., Japan) was used to develop the alumina - zirconia composite powder.

First, the alumina powder was dispersed in distilled water by ball milling, for 3 hrs, by using α-alumina spheres (solid content 50 wt%, powder/spheres weight ratio of 1/5). During dispersion, an almost constant pH value of about 6.5 was reached.

Then, a zirconium chloride aqueous solution was added to the alumina slurries, in a suitable amount to develop the desired composition after thermal treatment. The aqueous salt solutions (0.38 M) were prepared with ZrCl4 and ammonium citrate tribasic, as complexing agent, which allows to modify the pH without zirconium hydroxide precipitation.

Page 2: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

140

After homogenization under stirring for 1 h, the suspensions were diluted down to 4 wt% and spray dried in order to avoid the salt segregation, as experienced during slow drying in a oven, performed as preliminary tests. This drying step was performed in a Mini Spray Dried Büchi B-290, a drying system equipped with a conventional two-fluid nozzle, where a air jet disperses the liquid into fine droplets, which are quickly dried. The principle of the spray drying will be discussed for the second spray drier used in this work, since the basic concepts are similar, even if different types of nozzles are employed.

In this drying step, the inlet temperature was 140°C, and the outlet temperature was about 75-80°C. This equipment is able to produce spherical granules with a mean size of few microns. Moreover, with this system the alumina primary particles and the zirconia precursor are homogeneously mixed, at the scale of the granules, avoiding any segregation.

The composite powders were pre-treated at 600°C for 1h in a furnace, to promote by-product burn out.

Figure 1 Mini Spray Dried Büchi B-290

1.1.2 Slip casting

The slip casting method is a common procedure in the ceramic field. Precisely, the aqueous suspensions were prepared with 65 wt% solid content, and dispersed by ball milling, using α-alumina spheres. For such a concentrated suspension, the proper spheres quantity for ball milling is better express as a function of the liquid in the suspension, rather than on the basis of the powder content, for instance the liquid/sphere ratio was 1/5.

After dispersion, 1 wt% of PEG 4000 was added, to impart a higher strength to the green bodies, and limit the distortion and cracks during drying.

Page 3: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

141

The slips were poured into moulds made of a porous alumina basis and PVC walls. The drying was performed in a humidity-controlled chamber, at 20°C.

1.1.3 Spray drying

The atomization step was required to obtain a powder suitable for pressing. For this purpose the powder suspensions were dried in a ultrasonic atomizer. In this case the liquid is atomized into droplets by the vibration of an ultrasonic probe.

The main features of a spray drier system are the following: the suspension is pumped to the atomizing device, for instance in this case the ultrasonic probe, or the conventional nozzle for the previously described system, and here it is broken into small droplets. These droplets meet a stream of hot air, loosing their moisture very rapidly. The dry powder is separated from the moist air by centrifugal action in a cyclone, where the moist air is directed through the exhaust pipes and the dry powder settles to the bottom of the cyclone where it is collected in a vessel.

The Sodeva ATSELAB spray dryer was used, its schematic representation is reported in Figure 2. The frequency of the ultrasonic probe, which determines the droplet size, was fixed at 20 kHz, and the inlet temperature was 180°C, the measured temperature at the outlet of the dry chamber was about 80°C. these working condition were chosen on the basis of a previous work performed by Gutknecht 1. These parameters allow to produce granules of the order of about 100 µm.

Figure 2 Schematic representation of the Sodeva ATSELAB spray dryer : 1) drying column, 2) cyclone separator, 3) product vessel, 4) fan, 5) flowmeter, 6) air or inert gas heating, 7) hot

air entrance, 8) ultrasonic nozzle, 9) feed pump

1.1.4 Pressing

The shaping of spherical components can be performed by cold isostatic pressing (CIP), during which a uniform pressure is applied in every direction on the samples.

Page 4: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

142

For instance, silicone rubber moulds were filled by the atomized powder and immersed in a liquid (oil) which transmitted the pressure uniformly to the mould. The pressure was set at 350 MPa.

The density of the green part was obtained by geometric measurements.

1.1.5 Sintering

1.1.5.1 Natural sintering

The samples obtained by slip casting and that obtained by CIP were sintered in high temperature electrical furnace, in air, at 1500°C, following the thermal cycle set up by dilatometric analyses.

1.1.5.2 Post Hot Isostatic Pressing

The Hot Isostatic Pressing (HIP) is often performed after natural sintering, in order to improve the microstructure, particularly the density, and consequently the mechanical properties. Actually, the bioceramics used in orthopaedic applications must be submitted to post-HIP before being commercialized. This treatment employs pressurized heated gas for consolidation and densification reducing the closed porosity, in fact it is performed on samples having a density higher than 96 % TD.

The press used in this study was a laboratory type (Avure Technologie). The selected post-HIP treatment was the following: heating rate 10°C/min, up to 1520°C for 2 h, cooling rate 10°C/min, the argon pressure was 190 MPa.

1.2 Characterization

In the following sections the main characterization techniques are reported. In some cases, the same investigations were performed using different equipments, because this thesis was carried out in two laboratories, Lince Lab. at Politecnico di Torino and MATEIS, at INSA in Lyon.

1.2.1 X-Ray diffraction (XRD)

The X-ray diffraction technique allows to detect the phase composition of the sample: in fact, each phase presents specific diffractions peaks, on the basis of the lattice structure and atom position. Moreover, this experimental method is employed to evaluate the structure of the crystalline materials and to measure the crystallite size.

X-ray diffraction analyses were carried out by using the conventional diffractometer Philips PW 1710, with a Cu Kα radiation (λ=1.5405600 Å) and a Bruker diffractometer equipped with a furnace allowing the samples to be heated up to 1200°C.

A schematic representation of the instrument is shown in Figure 3.

Page 5: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

143

Figure 3 Scheme of the XRD diffractometer

The X-ray source consists of a filament that heats the cathode, inducing electrons emission. The presence of two metallic electrodes, with a different potential, implies the acceleration of the electrons toward the anode (in this case, made of copper), which emits the X-ray beam having a specific wavelength range, on the basis of the metallic component and the applied tension.

The power employed in X-rays production is only 0.1%, whereas the leftover one is converted into heat, which could induce anode melting. To avoid it, a water cooling system is present.

X-rays pass through a monochrometer (in this case, made of nickel), which selects the Kα radiation of copper. This radiation is then collimated upon the sample.

The instrument presents a goniometer having a Bragg-Brentano geometry, that operates in the θ – 2θ scanning regime, in which the detector (D) and the sample (S) move with respect to the X-rays source (X) in a synchronized way, as schematically presented in Figure 4.

Figure 4 Mechanism of the goniometer in the diffractometer Philips PW 1710

Page 6: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

144

In this way, the incident and the diffracted beams form the same angle θ with the flat surface of the sample, whereas the diffracted beam form a 2θ angle with the incident one (Figure 5).

Figure 5 The Bragg – Brentano geometry

This particular geometry is related to the Bragg equation, employed to evaluate the inter-planar distance in the crystalline lattice. In fact, when the X-rays hit the sample surface, they can interact with the lattice atoms, being their wavelength and the inter-atomic distance similar. The lattice atoms are then able to diffract the X-rays beam and a signal is recorded when a positive interference occurs, according to the Bragg equation:

θλ sendn ⋅⋅=⋅ 2 (1)

where θ is the incident angle, d is the inter-atomic distance, λ is the wavelength of the X-rays beam and n is a number.

On the basis of the inter-atomic distances it is possible to evaluate the geometry and the dimensions of the elementary cell; the whole diffraction pattern allows the identification of the phases through the comparison with the ICDD (International Centre for Diffraction Data) files. In addition, the peak intensity depends on the atom position in the elementary cell: more intense are the signals, more crystalline is the sample.

In this study, XRD was used to investigate the phases present in the produced composite powders, and, moreover, to study the zirconia crystallization kinetics, by means the evaluation of the zirconia crystallized fraction and size. Some tests were performed in situ, heating the powder samples and following up the evolution of the main zirconia peak, as described in the Chapter II. This latter set of tests was performed in the Bruker diffractometer.

The average crystallite size was calculated by the line-broadening method, using the Scherrer’s equation:

θβλ

cos⋅⋅= k

D (2)

Page 7: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

145

where D is the crystalline size, λ is the wavelength of the CuKα line, k is the Scherrer constant equal to 0.9, and β is the full width at half maximum of the main zirconia peak (2θ≅30.25°), assuming a Gaussian profile.

The weight fraction of monoclinic zirconia was evaluated by the following equation:

( ) ( )( ) ( ) ( )111111111

111111

tmm

mmm III

IIX

+++= (3)

where Ix (hkl) designates the intensity of the peak corresponding to the plane hkl for the phase x (m for monoclinic and t for tetragonal). The volume fraction is obtained as follows 2:

m

mm X

XV

⋅+⋅=

311.01311.1

(4)

1.2.2 Thermal analyses: TG-DTA

The thermal analyses evaluate the behaviour of the sample under controlled temperature changes.

Simultaneous Thermo Gravimetric Analysis - Differential Thermal Analysis (TGA-DTA, SETARAM TG-DTA 92, Caluire, France) were carried out on 115 mg of powder, heated in 20% N2-80%O2 atmosphere at 5°C min-1 up to 1000°C

In the DTA analyses, the difference in temperature between the sample and the reference (α−Al 2O3) is monitored: the same amount of heat energy is added to the sample and the reference (about 150 mg).

TG follows the mass loss of the sample during heating thanks to a microbalance, in order to study decomposition phenomena occurring during the heat treatment of the as-dried AZ powder.

1.2.3 TEM and HR-TEM

The transmission electron microscopy (TEM) is a technique whereby a beam of electrons is transmitted through a thin specimen, interacting with the sample as it passes through. The electron source may be a tungsten filament, which emits electrons either by thermionic and field electron emission. The electrons are then accelerated by an electric potential and focused by electrostatic and electromagnetic lenses, onto the sample. An image, formed by the transmitted beam, is magnified and focused onto an imagining device, such as a fluorescent screen, or can be detected by a sensor such as a CCD camera.

In this PhD thesis, TEM, performed on powders, was use to observe the appearance and growth of zirconia crystallites on alumina grains surface.

The used instrument was the LEO 912, operating at 120 kV accelerating voltage. Specimens were prepared by slow evaporation of a drop of the powder suspension in ethanol, deposited

Page 8: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

146

onto a perforated carbon-covered copper grid. Images were collected both in bright field (BF, Figure 6 a) and dark field (DF, Figure 6 b) mode. In the formed case, the contrast in the image is directly due to the interaction between the electron beam and the sample: thicker regions of the sample, or regions with a higher atomic number, will appear dark, while regions with no samples or lighter atomic number will appear bright. In the latter case, images were obtained with the objective aperture positioned on the first zirconia ring of the diffraction pattern (Figure 6 c), at which the objective aperture only selects the electrons which are in Bragg conditions for zirconia crystallites, so that only zirconia crystallites are illuminated as white dots. Furthermore, a specific feature available on LEO microscope allows performing annular dark field (ADF) images in the TEM mode. This is made possible by rotating the diffraction pattern through the small objective aperture so that the whole selected ring is used to give the DF image. Thus all the zirconia crystallites in Bragg conditions can be imaged in the sample, allowing a more precise determination of their size distribution through numerical analyses performed on DF low magnification images.

High Resolution Transmission Electron Microscopy (HRTEM) was also performed on selected thermally treated powders on JEOL 2010 F Microscope under 200 kV Voltage.

Figure 6 TEM images of the 95 vol% alumina - 5 vol% zirconia powder after treatment at 500°C for 1 h: a) bright field image, b) dark field image obtained with the objective aperture on one ring of zirconia structure as shown by the circle on the respective diffraction pattern

(c)

Page 9: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

147

1.2.4 Laser granulometry

When a laser beam strikes the particles suspended in a inert medium, the produced diffracted rays present intensity and diffraction angle that depend on the size of the impacted particle.

As illustrated in Figure 7, a laser granulometer consists of a laser beam source, at a fixed wavelength, and a series of detectors (multi-diode detector) to measure the diffracted light as a function of the diffraction angle.

The granulometer Malvern Mastersier 2000 was used to evaluate the particle size distribution of the powders (dispersed in water). The Mie theory was used to calculate the particle size distribution. This theory takes into account both the diffraction index and the refractive index of both the sample and the medium.

Figure 7 Schematic representation of a laser granulometer

1.2.5 Viscosimetry

The viscosimetry evaluates the internal friction of a fluid, which is created when a layer of the fluid moves with respect to another layer. The amount of the force required to produce this movement (shear stress) depends on the friction among the layers. The shear rate is the velocity gradient created and it measures the change in speed at which the layer moves with respect to the others. It is measured in reciprocal seconds (s−1). The force required to induce motion, referred to the unit area, is measured in Pascal (Pa).

The viscosity η can be then defined as the ratio between the shear stress and the shear rate; the unit is Pascal· seconds (Pa⋅s) or milli-Pascal· seconds (mPa⋅s).

The rheological behaviour is characterized by the relationship )(γτ &f= , where τ is the shear stress and γ& is the shear rate, previously defined. In this study, the latter relationship was experimentally determined by using a Coulette rheometer (HAAKE VT 501, Villebon, France), which allows the measurement of the shear stress at different shear velocity, from 0 to 1500 s-1. Particularly, the following measurement cycle was exploited:

Page 10: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

148

- the shear velocity increased from 0 to 1500 s-1 in 2 min;

- the suspension was kept at 1500 s-1 for 1 min;

- finally the shear velocity decreased form 1500 s-1 to 0 s-1 in 2 min.

1.2.6 Dilatometry

The dilatometric analysis is an efficient method to investigate the densification of a ceramic body under a controlled thermal cycle, with the aim to set up an optimal sintering treatment so that a high density should be reached, even controlling microstructure features (for instance, limiting grain growth).

The employed instrument (Netzsch 402E) is made of a controllable furnace and a dilatometer, as shown in Figure 8.

Figure 8 Co-axial alumina tubes are part of the dilatometer

An alumina tube acts as sample holder; in addition, it contains a small alumina bar, which is placed in contact with the green sample. Thanks to a piezoelectric sensor, this bar is able to follow the length variations of the sample, allowing to evaluate expansion or shrinkage as a function of temperature.

1.2.7 SEM

The Scanning Electron Microscopy (SEM) is a technique that allows a morphological characterization of powdered and massive samples. It uses the electrons for imaging, reaching higher magnifications and greater depth field than the light microscopy.

Page 11: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

149

A schematic representation of an instrument is reported in Figure 9: from the electron emission source, a heated tungsten filament, the beam is focused on the sample surfaces by a series of electromagnetic lenses. The incident electrons imply electrons emission from the sample surface; the are collected by a suitable detector, during the scanning of a raster pattern, producing a topographical image of the analyzed surface.

Some observations were performed in SE (secondary electrons) modality, while, when a phase contrast was needed BSE (back-scattered electrons) were also detected.

Figure 9 Schematic representation of a SEM instrument

The powders and the microstructure of the composite materials were observed by using SEM Hitachi S2300, and ESEM (FEI, XL30, Eindhoven, Netherlands). exploiting a gold sputtering pre – treatment of all samples in order to increase the sample conductivity.

The grains size was measured on polished samples, which were thermally etched at a lower temperature than the sintering one, for instance 1350°C for 30 min, or 1450°C for 6 min, depending on the specific SEM instrument used for the observation. This thermal etching allows to reveal grain boundary for SEM observation. The intercept method was used to calculate the alumina and zirconia grains size 3, 4.

1.2.8 Vickers Hardness

The hardness was evaluated by micro-indentation tests, carried out by using two different instruments: a microdurometer Galileo (maximum load 1 kg, objective magnification 10x and 50x,), and a device constituted by a micro-indenter Vickers Testwell FV-700, equipped with

Page 12: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

150

an optical microscope (maximum load 30 kg, magnification 10 x and 80 x). The main feature of the two devices are the same: the machine controls the movement of the indenter into the specimen under the selected test force, and it is equipped with an optical microscope to select the test zone, and measure the size of the produced indentation.

The tests were performed in polished samples, and each indentation was measured three times.

The Vickers hardness, expressed in GPa, is calculated as follows:

( ) 2233 0018544.02sin102101 dPdPAPHv s ⋅=⋅⋅⋅=⋅⋅= α (5)

where P is the force (expressed in N), As is the surface area of the indentation, d is the mean diagonal length (mm), and α is the angle of the indenter (equal to 136° for the Vickers indenter).

1.2.9 Measurements of the threshold for slow crack propagation

The Vickers indentation fracture test is used to estimate the fracture resistance of brittle ceramics, by the direct measurement of Vickers-produced radial cracks. It is worth noting that if the measurements are not carried out in inert atmosphere, for a material susceptible to slow crack growth, as in our case, the cracks go on to grow after the indentation due to sub-critical propagation. Consequently, the intensity factor obtained by this test correspond to the threshold for slow crack propagation, rather than to KIC.

The intensity factor can be expressed by the Anstis’s formula 5:

230

−⋅⋅= cPK I χ (6)

where P is the applied load and c is the crack length, and χ is a constant equal to:

( ) 21HEζχ = (7)

being ζ a material-independent constant, equal to 0.016, E the Young modulus and H the hardness.The load used to produce the indentation was 98.1 N, and the hardness (expressed in GPa) was determined by the eq. (5). The Young modulus, E, for the composite was evaluated by the Rule of Mixture, assuming 400 GPa and 200 GPa for the values of the Young modulus of the alumina and zirconia, respectively.

Page 13: Appendix: Experimental proceduresdocinsa.insa-lyon.fr/these/2010/naglieri/11_appendix.pdf · Appendix: Experimental procedures 140 After homogenization under stirring for 1 h, the

Appendix: Experimental procedures

151

References

1 D. Gutknecht, Elaboration et charactérisation de mico- et nano composites alumine-zircone pour application orthopédique, PhD Thesis, Institut National des Sciences Appliquées de Lyon, 2006.

2 H. Toraya, M. Yoshimura, S. Somiya, Quantitative Analysis of Monoclinic-Stabilized Cubic ZrO2 Systems by X-Ray Diffraction, Journal of the American Ceramic Society, Vol. 67 [9], 1984, pp. C 183-184.

3 J. C. Wurst, J. A. Nelson, Lineal Intercept Technique for measuring grain size in two-phase polycrystalline ceramics, Journal of the American Ceramic Society, Vol. 55 [2], 1972, pp. 109.

4 M. I. Mendelson, Average grain size in polycrystalline ceramics, Journal of the American Ceramic Society, Vol. 52 [8], 1969, pp 443-446.

5 G. R. Anstis, P. Chantikul, B. R. Lawn, D. B. Marshall, A Critical Evaluation of Indentation Technique for Measuring Fracture Toughness : I, Direct Crack Measurements, Journal of the American Ceramic Society, Vol. 64 [9], 1981, pp. 533-538.