Evaluated Material Properties for a Sintered �-Alumina

Ronald G. Munro*

Ceramics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899

Results of a data evaluation exercise are presented for aparticular specification of sintered �-alumina (mass frac-tion of Al2O3, �0.995; relative density (�/�theoretical), �0.98;and nominal grain size, 5 µm). A comprehensive set ofmaterial property data is established based on publishedphysical, mechanical, and thermal properties of aluminaspecimens that conform to the constraints of the materialspecification. The criteria imposed on the properties arethat the values should be derived from independent experi-mental studies, that the values for physically related prop-erties should be mutually self-consistent, and that the setsof values should be compatible with established materialproperty relations. The properties assessed in this mannerinclude crystallography, thermal expansion, density, soundvelocity, elastic modulus, shear modulus, Poisson’s ratio,bulk modulus, compressive strength, flexural strength,Weibull characteristic strength, Weibull modulus, tensilestrength, hardness, fracture toughness, creep rate, creeprate stress exponent, creep activation energy, friction coef-ficient, wear coefficient, melting point, specific heat, ther-mal conductivity, and thermal diffusivity.

I. Introduction

ALUMINA is one of the more widely used and studied ad-vanced ceramic materials. The relative abundance and low

cost of the material resource is advantageous for commercialapplications, while the availability of the material in highlypurified grades makes it well suited to fundamental studies inmaterials research. Among its desirable features, aluminashares with other advanced ceramics the characteristics ofhigh-temperature stability and the retention of strength at hightemperatures. These characteristics often are cited as the mostimportant attributes of structural ceramics. Ironically, property

data for alumina at elevated temperature often are not readilyaccessible in the literature, and the data that are available usu-ally pertain to disparate material specifications. This paper ad-dresses that situation for �-alumina as part of a broader studyon the issues of data evaluation and the need for temperature-dependent property data for advanced ceramics.

The widespread use of alumina has prompted several previ-ous property reviews and data compilations to provide generalsurveys of the properties of all grades of alumina.1–7 Becausemany of the important properties and characteristics of aluminavary considerably with composition, density, and grain size,those reviews were focused on the immense task of determin-ing ranges of values that have been observed for the variousproperties. Those substantial efforts have provided an invalu-able guide to the understanding and application of sinteredalumina.

The present work seeks to build upon those efforts in tworespects while narrowing the application focus. First, therehave been some rather significant results published since theprevious reviews were done, and those newer results are in-corporated in the present assessment. Second, the present workis directed toward deriving a single set of data from diverseindependent efforts, rather than describing the distribution ofthe values across the numerous studies. The objective, then, isto derive a coherent, self-consistent, and comprehensive set ofproperty values for a single specification of alumina. The con-straint on the material specification is significant because manyproperties critical to the application of ceramics (particularlyflexural strength, tensile strength, hardness, fracture toughness,and creep) are known to be sensitive to variations in the mi-crostructure of the material.8 In the present work, that con-straint is imposed by means of some relatively simple criteriapertaining to the composition, densification, and grain size ofthe material. These criteria are discussed in the followingsection.

Evaluated data have an increasingly important role to play inboth manufacturing and materials science applications. Thecurrent trends toward concurrent engineering practices9 inmanufacturing and the growing use of the evolving Standardfor the Exchange of Product Data (STEP) for communicatingproduct specification data10 require a wide range of propertiesapplicable to a wide range of temperature. These applications

M. P. Harmer—contributing editor

Manuscript No. 191842. Received May 6, 1996; approved April 28, 1997.*Member, American Ceramic Society.

J. Am. Ceram. Soc., 80 [8] 1919–28 (1997)Journal

1919

can benefit from the comprehensive scope of properties and theexplicit interpolation formulas for temperature dependence thatresult from the present approach to data evaluation. Efforts toestablish and understand correlations of properties and perfor-mance results also should benefit particularly from the self-consistent relations and the coherent nature of the collection ofproperties, i.e., that the entire set of properties pertains to asingle material specification.

II. Material Specification

The goal of the present work is not to review the propertiesof all aluminas, but rather to establish a definitive, comprehen-sive set of data for one particular material specification. Theattainment of this goal is dependent on several factors, but thetwo most basic are the availability of the supporting data andthe independence of the various experimental studies. The firstfactor, the availability of the data, strongly influences the speci-fication of the material; it would be unproductive to specify amaterial for which there are few data. The second factor, theindependence of the studies, is essential to establish or verifythe reproducibility of the results.

For ceramics, the insistence on independent studies invari-ably results in no two studies being conducted on exactly thesame material. Initially, the possibility of restricting the studyto one specific commercial material was considered, but thatrestriction in the case of alumina resulted in an insufficientsupply of independent data. Although much data could befound for a few properties, a comprehensive range of propertiescould not be found for any one specific commercial alumina.

Consequently, a more general approach to material specifi-cation was used. It was found that, if three quantities (purity,density, and mean grain size) were constrained, sufficient re-sults for alumina could be found in the literature to establish acomprehensive range of properties, and, at the same time, theindependently measured values for individual properties werereasonably consistent and reproducible.

In general, stoichiometric Al2O3 has a molecular weight of101.96. The most prevalent and stable single phase of the ma-terial is denoted as �-Al2O3 and occurs in the corundum crystalstructure (space group R3c) containing two formula units perunit cell.4 It is common practice, however, to represent thestructure using a larger hexagonal cell containing six formulaunits, and that practice is followed here.11 This structure (seecover illustration) consists of planes of close-packed oxygenions in the A-B-A-B sequence interleaved with planes of alu-minum ions in an a-b-c-a-b-c sequence. In each aluminumplane, the aluminum ions occupy only two-thirds of the avail-able octahedral sites, thereby maintaining charge neutrality(four Al3+ for every six O2−). A hexagonal crystallographic cellis formed from the repeating sequence A-a-B-b-A-c-B-a-A-b-B-c. The melting point12–15 of this phase is 2050° ± 4°C.

Polycrystalline sintered alumina ceramics are typicallyformed by sintering compacted powders at temperatures on theorder of 1700°C. These ceramic alumina materials are usuallyclassified according to the purity of the phase composition, themass density, and the mean grain size of the sintered material.Commonly, additives also are specified to control the rates ofdensification and grain growth; for example, a small amount ofMgO may be added to control the grain size during sintering.Trace amounts of SiO2, CaO, Fe2O3, and Na2O also may occurin the sintered specimen.

The present work is focused on high-purity sintered �-alu-mina in which the mass fraction of the alumina phase is 99.5%or higher. The material is nearly fully densified with a massdensity that is at least 98% of the theoretical density, and thematerial has a nominal grain size of 5 �m.

III. Properties and Characteristics

For each property or characteristic, the experimental valuesobtained from published reports are viewed as raw data that are

to be processed in the context of known material propertyrelations. For convenience, an analytic interpolation formula isgiven for the temperature dependence of each property. Uncer-tainties are assigned to each interpolation formula according toestimates of the combined standard uncertainties appropriate tothe various sets of data.16 These estimates are based on stan-dard deviations or standard errors of the fits, as appropriate.

(1) Crystallography, Density, and Thermal ExpansionThe crystal structure and the temperature dependences of the

lattice parameters have a basic importance to the properties ofpolycrystalline alumina. It is appropriate, therefore, to beginthis study with an examination of the lattice parameters15,17–21

and their anisotropic thermal expansions.22,23 In practice, thelinear coefficient of thermal expansion, �CTE � L−1(�L/�T), ismost commonly represented as a cumulative expansion coef-ficient,

� = L0−1

L�T� − L0

T − T0(1)

where L is either of the lattice parameters of the hexagonal unitcell, a or c; T is the temperature, and the subscript, 0, denotesa reference state, usually 0°C or room temperature. The thermalexpansion of the crystal structure can be determined either bydiffraction methods, which measure the variation of theatomic-scale dimensions of the crystal structure, or by high-resolution dilatometry methods that detect changes in the mac-roscopic dimensions of the material specimen. The two mea-sures of expansion can have a small difference because of thepresence of defects in the macroscopic specimen. In the presentwork, data from both types of methods are considered to de-termine an optimized, self-consistent representation of the lat-tice parameters and the coefficient of thermal expansion. Tofacilitate the optimization process, empirical interpolation for-mulas are used.

�L�T� = AL + BLT − CL exp�−DLT� (2a)

L�T� = L0 �1 + �L�T�T� (2b)

where AL, BL, CL, DL, and L0 are adjustable parameters, and thereference temperature is taken as T0 � 0°C. Fitting these ex-pressions to single-crystal data yields the results in Figs. 1 and2 and Table I. The solid curves in Figs. 1 and 2 were producedusing Eqs. (2) and the parameters in Table I. Independent ther-mal expansion data for polycrystalline specimens2,24,25 areshown in Fig. (2b), in which the solid curve is the mean coef-

Fig. 1. Lattice parameters of �-Al2O3 referred to the hexagonal cell.

1920 Journal of the American Ceramic Society—Munro Vol. 80, No. 8

ficient of thermal expansion, �m � (2�a + �c)/3, evaluatedusing Eq. (2a) and the parameters in Table I.

The results for the lattice parameters can be used with themolecular weight to determine the theoretical density of Al2O3from the relation

� =Mz

NAV(3a)

where M is the molar mass, z is the number of formula units perunit cell, NA is Avogadro’s number, and V is the volume of theunit cell. For �-Al2O3 referred to the hexagonal crystallo-graphic cell, M � 101.96 g/mol, z � 6, and V � (31/2/2)a2c.With these values, the theoretical density can be representedconveniently by

��g�cm3� = 3.9853 − 7.158 × 10−5T − 3.035 × 10−8T2

+ 7.232 × 10−12T3 ± 0.05% (3b)

for 20°C � T � 1800°C, which evaluates to 3.984 ± 0.002g/cm3 at T � 20°C.

(2) Elastic PropertiesThe elastic properties of polycrystalline materials are com-

monly considered to be isotropic. Under such conditions, theelastic properties have the well-known relations,

G =E

2�1 + ��(4a)

B =E

3�1 − 2��(4b)

� =E

2G− 1 (4c)

Where E is the elastic modulus, G is the shear modulus, B is thebulk modulus, and � is Poisson’s ratio. These quantities aremost commonly determined by ultrasonic methods, accordingto which the longitudinal velocity (VL) and the shear velocity(VS) are related to the elastic properties and the bulk density(�):

G = �VS2 (5a)

B = ��VL2 −

4

3VS

2� (5b)

� =1

2 �1 −1

�VL�VS�2 − 1� (5c)

Experimental values of the elastic properties of alumina26,27

determined by ultrasonic methods28 are shown in Fig. 3 andcan be represented by the interpolation formulas,

E�GPa� = 417 − 0.0525T ± 7% (6a)

G�GPa� = 169 − 0.0229T ± 6% (6b)

for 20°C � T � 1400°C. For the data sets that are currentlyavailable, the values for the elastic properties of the sinteredproduct are indistinguishable from those obtained for hot-pressed specimens, and the values derived from the single-crystal elasticity tensor also are well within the uncertaintylimits expressed by Eqs. (6).29

(3) Strength and Related PropertiesOne of the more compelling reasons for the interest in struc-

tural ceramics is their retention of strength at high tempera-tures. Under compression,2,25,30 as shown in Fig. 4, the sintered

Fig. 2. Thermal expansion of �-Al2O3: (a) single crystal and (b)sintered polycrystalline.

Table I. Parameters of Eqs. (2)Obtained for the Temperature Interval

0°C � T � 1800°C*

Parameter

Value

a-axis c-axis

A[10−6 K−1] 7.419 8.026B[10−10 K−2] 6.43 8.17C[10−6 K−1] 3.211 3.279D[10−3 K−1] 2.59 2.91L0 (Å) 4.7602 12.9898

*Values obtained from Eqs. (2) using these param-eters have combined standard uncertainties of ±4% forvalues of the thermal expansion and ±0.06% for valuesof the lattice parameters.

Fig. 3. Elastic and shear moduli of high-purity, high-density sintered�-Al2O3.

August 1997 Evaluated Material Properties for a Sintered �-Alumina 1921

�-Al2O3 materials considered here withstand >3000 MPa atroom temperature and have a temperature dependence given by

CS�GPa� = 3.1 − 0.0035T + 1.1 × 10−6T2 ± 15% (7)

for 20°C � T � 1400°C, where CS is the compressive strengthand T is the temperature.

More importantly for most applications of structural ceram-ics is the strength of the material in flexure or tension. In thesemodes of stress, the strength of a brittle material is limited bythe distribution of flaws in the material specimen.31 Any flawin the material can serve as an origin of failure. Because thedetails of the individual flaws vary from specimen to specimen,tests of large numbers of specimens are required to characterizethe strength behavior statistically.32 The most commonly usedstatistic is the mean value of the strength, termed the flexuralstrength or the tensile strength for materials in flexure or ten-sion, respectively. When the mean value is used as the measureof strength, the standard deviation of the observed values isused as a measure of the spread of values. A more insightfuldescription of the strength values is provided by the use of thetwo-parameter Weibull analysis. In the Weibull model, if PF isthe probability of failure at a strength �, then

PF = 1 − exp�−�V�V0�����0�m� (8a)

where V is the specimen volume, V0 is a volume scale param-eter, and �0 and m are characteristics of the flaw distributionknown, respectively, as the characteristic strength and theWeibull modulus. Larger values of �0 imply greater strength,and larger values of m imply more reliably reproducible speci-mens in the sense of a narrower distribution of values. It isquite common to find Eq. (8a) rearranged into the form

ln ln1

1 − PF= m ln � − m ln �0 + ln

V

V0(8b)

In using Eq. (8b), PF often is estimated from the rank order ofa series of measurements; i.e., if the measured strengths areordered from smallest to largest, then the failure probability ofthe ith value of N results is estimated as PF(i) � (i − 0.5)/N. Inmore recent years, ASTM Committee C-28 has recommendedavoiding the use of this failure probability estimate and thelinear regression method by using a maximum likelihood esti-mation method.33 In either case, the strength at any given fail-ure probability (�(PF)) evaluated from Eq. (8) depends on theeffective fracture volume of the specimen. If the flaw popula-tions are assumed to be the same for two different, but geo-metrically similar, specimen sets, a and b, with volumes Va andVb, respectively, then, from Eq. (8a), the size effect can beexpressed as8,34

�a�PF�

�b�PF�= �Vb

Va�1�m

(9)

Consequently, results from bend tests vary with the details ofthe test configuration. Results also may vary with the stressingrate. The present data are intended to be appropriate for four-point bend tests with 1⁄4-point loading (ASTM C 1211, speci-men configuration B) on a span length of 40 mm and a loadingrate of 0.5 mm/min. A search of the literature for this workfound no high-temperature data meeting the material and mea-surement conditions considered here. In lieu of such data, flex-ural strength results from one round-robin study8 at room tem-perature and two high-temperature studies35,36 on hot-pressedand hot isostatically pressed aluminas with purity, density, andgrain size similar to the prescription of Section II (see Table II)are shown in Fig. 5. Also shown are handbook values over thesame temperature range for a generic polycrystalline alu-mina.25 The agreement among these data sets, although some-what fortuitous, suggests that these values should be a fairrepresentation of the flexural strength in the current context.For temperatures up to ∼1100°C, the flexural strength in Fig. 5has a value of ∼380 MPa with a standard deviation of ∼60 MPa.Above 1100°C, the flexural strength decreases linearly to ∼120MPa at 1500°C. The interpolation formula used in Fig. 5 is

FS�MPa� = 380.5 −1.37 × 105

1 + 1.76 × 105 exp�−0.0039T �(10a)

for 20°C � T � 1500°C. The corresponding results for theWeibull analysis of the data36 for the hot isostatically pressedmaterial are shown in Fig. 6. Because of the limited amount ofdata and the considerable scatter in the values, no trend withrespect to temperature can be discerned reliably for the Weibullmodulus. The Weibull parameters are best expressed as

m = 11 ± 4 (10b)

�0�MPa� = −16.32 + 1.09FS ± 20% (10c)

where FS is given by Eq. (10a) and where 20°C � T �1500°C.

Fig. 4. Compressive strength of high-purity, high-density sintered�-Al2O3.

Table II. Comparison of Material Characteristics of Specimens Used in the Estimate ofFlexural Strength*

Processing condition Sintered Hot pressedHot isostatistically

pressed

Purity (mass fraction %) 99.9 99.9 99.9Relative density (%) >99 >98 >99Grain size range (�m) 1–6 1–2 2–6Specimen dimensions (mm) 3 × 4 × 50 3.81 × 6.35 × 44.45 3 × 4 × 45Outer/inner span (mm/mm) 40/20 38.1/12.7 40/20Loading rate (mm/min) 0.5 0.15 0.5, 1.5Reference 8 33 34

*Equation 10.

1922 Journal of the American Ceramic Society—Munro Vol. 80, No. 8

The flexural strength exhibits steady or monotonically de-creasing values with increasing temperature. When a signifi-cant volume fraction of a polycrystalline ceramic is occupiedby a glassy grain-boundary phase, the material is susceptible tothe onset of a brittle-to-ductile transition at elevated tempera-ture.37,38 The transition appears to be a softening of the glassyphase, which subsequently permits a degree of crack blunting.As a result, it is characteristic of this transition that there is asudden increase in the measured strength of the material and itsfracture toughness.39 The absence of such an increase in eitherproperty in the present case may be attributable to the highmass fraction (99.5%) of the alumina grains in the material,which may preclude the possibility of a substantial glassyphase.

Data on the tensile strength of alumina are very scarce. The

search of the literature found no paper in which material andmeasurement details were reported with the tensile strength.One paper2 gave the tensile strength for an alumina with theAl2O3 mass fraction of 99.9%, relative density of >99%, and agrain size range of 1–6 �m, but no measurement details weregiven. Two other papers25,40 gave results with neither materialnor measurement details. The data from these three sources areshown in Fig. 7. Based on these data, the tensile strength can beexpected to have a value of ∼270 MPa for temperatures up to∼1100°C, whereafter the tensile strength decreases moresharply than the flexural strength, decreasing to a value of <50MPa at 1300°C. The interpolation formula for Fig. 7 is

TS�MPa� =267 − 256�1 + 5.8 × 109 exp�−0.018T��−1�2 ± 10%(11)

for 20°C � T � 1500°C.The results expressed by Eqs. (10) and (11) were obtained

from independent sets of data. Given also the scarcity of thedata, it is desirable to verify the consistency of these two im-portant measures of the strength of the material. If it is assumedthat the flaw systems are the same for the two sets of specimensand that the specimen volumes are the same, then the Weibullanalysis can be used to establish a relation between the meanflexural strength and the mean tensile strength. It is shown inPanel A that the ratio of these strengths should be [4(m + 1)2/(m +2)]1/m � 1.4 when m � 11. Using 380 MPa for the meanflexural strength below 1000°C in Fig. 5 and 270 MPa for themean tensile strength in Fig. 7, the ratio is 380/270 � 1.4, inagreement with the Weibull analysis.

Two other characteristics, hardness and fracture toughness,are commonly discussed in the context of the strength of struc-tural ceramics. Hardness41 is intended to be a measure of theresistance to plastic deformation, which may include effectssuch as material displacement and fracture. Fracture tough-ness42 is intended to be a measure of the resistance to theextension of cracks. Quantitative results for these characteris-tics depend on the procedural details of how the deformation isproduced or the cracks are caused to propagate. In the presentwork, attention is restricted to the Vickers indentation methodfor hardness measurements and the indentation strengthmethod for fracture toughness measurements.

The hardness obtained by the Vickers method43 is

HV = 1.8544P

d2 (12)

Fig. 5. Flexural strength of high-purity, high-density sintered�-Al2O3.

Fig. 6. Weibull parameters of high-purity, high-density sintered�-Al2O3: (a) modulus (m) and (b) characteristic strength (�0).

Fig. 7. Tensile strength of high-purity, high-density sintered�-Al2O3.

August 1997 Evaluated Material Properties for a Sintered �-Alumina 1923

where P is the applied load and d is the mean diagonal lengthof the irreversible impression produced by the indentor. Formost ceramics, the value of HV varies with the load, at least forlower loads. Empirically, the size of the indentation impressionis often related to the load by the expression P � d (some-times called the Meyer law),44,45 where is a constant and isa parameter (sometimes called the indentation size effect indexfor brittle materials).46 Substituting this expression into Eq.(12) shows that HV is independent of load only for the excep-tional case that � 2. For most structural ceramics, < 2under low loads. Consequently, it is prudent to consider thevalue of the hardness with due reference to the load used tomeasure it.

Two applicable papers47,48 were found according to whichthe hardness can be represented as in Fig. 8 when a load of 1

kg is used. Although there is a significant amount of scatter inthe data, the general trends can be represented by the interpo-lation formula

HV�GPa� = 15.5 exp�−0.0012T � ± 15% (13)

where HV is hardness and 20°C � T � 1000°C.Fracture toughness is a more complicated characteristic that

depends quite significantly on the microstructure of the speci-men. Alumina appears to be one of the materials known toexhibit R-curve behavior; i.e., the toughness increases withincreasing crack length. Only one paper discussing both thetemperature and crack-length dependences was found.49 In thatwork, a Vickers indentor was used with loads from 12 to 300N on hot-pressed specimens that measured 2.5 mm × 4 mm ×25 mm. The strength tests were conducted in four-point bend-ing with inner and outer spans of 10 mm and 20 mm, respec-tively, and with a constant crosshead speed of 0.25 mm/min.The fracture toughness, KI, was evaluated as

KI = Y�fδ1�2 (14)

where the geometric factor Y has been determined to be 1.02,�f is the fracture stress, and � is the crack length.

The results for the fracture toughness (Fig. 9) show a lineardependence on the square root of the crack length and a non-linear dependence on temperature. Treating these dependencessimultaneously, a suitable interpolation formula is found to be

KI�MPa�m1�2� = 2775exp�0.0000476T�

T + 1323+ 0.084�1�2 ± 15%

(15)

where 25°C � T � 1300°C and �1/2 is in the range 7–21 �m1/2.The solid curves in Fig. 9 are produced from Eq. (15).

(4) Creep CharacteristicsThe lifetime of a material component operating at high tem-

perature may be limited by the long-term creep deformationcharacteristics of the material.50,51 Ceramics generally exhibit atemperature and stress-dependent steady-state creep rate of theform

Panel A. Flexural versus Tensile Strength

If a single Weibull distribution is assumed to characterizethe flaw system in a test specimen, then a relation betweentwo different test configurations can be developed.64 Forthis purpose, it is preferable to consider Eq. (8a) in a formthat explicitly accounts for the nonuniform stress that occursin bend tests. Using the substitution v � V/V0 for conve-nience,

PF = 1 − exp�−�����0�m dv� (A–1)

Within the nonuniform stress distribution, the maximumstress (�max) that occurs in the specimen is the stress ofprimary relevance to the test result. Dividing � and �0 by�max, Eq. (A–1) can be rewritten as

PF = 1 − exp�− v��max��0�m� (A–2)

where

=1

v �����max�m dv (A–3)

The value of depends on the specific test configuration.For a tensile test with uniform tension, � � �max, and,hence,

t = 1 (A–4)

For a four-point bend test with quarter-point loading,

4-point,1�4 =m + 2

4�m + 1�2 (A–5)

With these relations, the mean fracture strength can be cal-culated using the observation that the number of specimensthat fail at stress � is the difference between the number ofspecimens surviving at stress � − �/2 and � + �/2. Thus,

�mean = � dPF

d�� d� (A–6)

from which it can be found that

�4-point,1�4,mean

�t,mean= �4�m + 1�2

m + 2 �1�m

(A–7)

assuming that the specimen volumes are the same. Usingm � 11 from Eq. (10b), we would expect �4-point,1/4,mean/�t,mean � 1.4 for the present material. For tempera-tures <1000°C, we find in Figs. 5 and 7, respectively,�4-point,1/4,mean ≈ 380 MPa and �t,mean ≈ 270 MPa, whichresults in a ratio of 1.4, in agreement with Eq. (A–7).

Fig. 8. Vickers hardness of high-purity, high-density sintered�-Al2O3.

1924 Journal of the American Ceramic Society—Munro Vol. 80, No. 8

d�

dt= A�n exp�−Eact�RT� (16)

where d�/dt is the creep rate, � is the applied stress, n is aparameter known as the creep stress exponent, Eact is the ac-tivation energy, R is the fundamental molar gas constant, and Ais a scale parameter. The parameters A, n, and Eact are deter-mined from least-squares fits to the experimental data. In thepresent case (see Fig. 10) the creep rate under flexural stressconditions52–54 spans 6 orders of magnitude on the temperaturerange from 1200° to 1800°C for applied stresses in the intervalfrom 100 to 200 MPa. For Fig. 10, the solid interpolationcurves are given by Eq. (16) using the parameter values A �3.6 × 1011 s−1, n � 1.08, and Eact � 323 kJ/mol. These curveshave a combined standard uncertainty for log10(d�/dt) of ±8%.

(5) Tribological CharacteristicsIn many applications of advanced ceramics, the durability of

the material under sliding conditions is an important designconsideration, and the sliding friction and wear characteristics

are required for estimates of lifetime, heat generation, and en-ergy consumption. These tribological properties are difficult toassess because they depend on both microscopic and macro-scopic contact conditions and are dependent on the specificmaterial pairs in contact, rather than being intrinsic propertiesof one material.55 The measurements of friction and wear prop-erties vary with the configurations of the apparatus and thespecimens as well as varying with the specifications of thematerial pairs. Consequently, studies of these properties oftenpresent results within the context of a fixed measurement pro-tocol using a single measurement apparatus. Further, to inter-pret the measurement results succinctly, attempts have beenmade to provide maps56 or transition diagrams57 that identifystress and temperature domains of distinguishable friction andwear behaviors. A transition diagram for alumina57 is shown inFig. 11 that shows the coefficient of friction (COF) and adimensionless measure of wear called the wear coefficient:

Kw =VwH

FnDs(17)

where Vw is the wear volume, H is the hardness, Fn is thenormal force, and Ds is the total sliding distance. Regions I, II,and III in Fig. 11 were considered to be regions of relativelymild wear that were distinguished from each other by themechanisms involved in the wear process. In region I, reactionsbetween alumina and water vapor may have formed a protec-tive surface that limited the amount of wear.58 At the highertemperatures of region II, plastic flow made significant contri-butions to the wear process. In region III, protective surfaceformations were found containing silicon, apparently from asilicon impurity in the bulk material. Region IV was consideredto be a region of severe wear in which the wear coefficientswere at least 2 orders of magnitude greater than those of re-gions I, II, and III. Wear in region IV was characterized byintergranular fracture.

(6) Thermal PropertiesTemperature gradients, thermally induced strains, and the

rate of transport of thermal energy are especially significantconcerns in applications of materials at high temperature. The

Fig. 11. Friction and wear transition diagram for high-purity, high-density sintered �-Al2O3 (COF is coefficient of friction and Kw isdimensionless wear coefficient).

FIG. 9. Fracture toughness of high-purity, high-density sintered�-Al2O3.

Fig. 10. Steady-state creep rate of high-purity, high-density sintered�-Al2O3.

August 1997 Evaluated Material Properties for a Sintered �-Alumina 1925

primary properties of interest in this context are specific heat,thermal conductivity, and thermal diffusivity. The specific heatdescribes the increase of temperature when a quantity of heat isadded to a material; the thermal conductivity characterizes thesteady-state heat flow in the material; and the thermal diffu-sivity is related to the transient response of the material to aheat pulse. For isotropic materials, the thermal transport prop-erties are correlated by the relation

� = �CpD (18)

Table III. Selected Property Values for Sintered �-Al2O3*

Property

Temperature (°C)

20 500 1000 1200 1400 1500

Bulk modulus (GPa) 257(50) 247 237 233 229 227Compressive strength (GPa) 3.0(5) 1.6 0.7 0.4 0.3 0.28Creep rate at 150 MPa

(×10−9 s−1) 0 0 4 280 6600 24600Density (g/cm3) 3.984(2) 3.943 3.891 3.868 3.845 3.834Elastic modulus (GPa) 416(30) 390 364 354 343 338Flexural strength (MPa) 380(50) 375 345 300 210 130Fracture toughness for crack

length of 300 �m(MPa � m1/2) 3.5(5) 3.0 2.7 2.6 2.5 2.5

Friction coefficient at 2 GPa 0.40(5) 0.8 0.4Hardness Vickers, 1 kg

(GPa) 15(2) 8.5 4.6 3.7 2.9 2.5Lattice parameter, a (Å) 4.761(3) 4.777 4.797 4.806 4.815 4.820Lattice parameter, c (Å) 12.991(7) 13.040 13.102 13.129 13.156 13.169Poisson’s ratio 0.231(1) 0.237 0.244 0.247 0.250 0.252Shear modulus (GPa) 169(1) 158 146 142 137 135Sound velocity, longitudinal

(km/s) 11.00(30) 10.77 10.54 10.44 10.35 10.30Sound velocity, shear (km/s) 6.51(20) 6.33 6.14 6.06 5.97 5.93Specific heat (J � kg−1 � K−1) 755(15) 1165 1255 1285 1315 1330Tensile strength (MPa) 267(30) 267 243 140 22 13Thermal conductivity

(W � m−1 � K−1) 33(2) 11.4 7.22 6.67 6.34 6.23Thermal diffusivity (cm2/s) 0.111(20) 0.0251 0.0150 0.0136 0.0127 0.0124Thermal expansion from

0°C (10−6 K−1) 4.6(2) 7.1 8.1 8.3 8.5 8.6Wear coefficient at 2 GPa

(log10) −6(1) −4 −6Weibull modulus 11(4) 11 11 11 11 11Weibull characteristic

strength (MPa) 395(25) 390 360 310 210 125*Alumina mass fraction, �99.5%; mass density, �98% of the theoretical density; and nominal grain size, 5 �m. Numbers in parentheses are representative combined standard

uncertainties of the final digits; i.e., the quantity 3.0(5) is equivalent to 3.0 ± 0.5. Units are given in parentheses.

Fig. 12. Specific heat of high-purity, high-density sintered �-Al2O3.

Fig. 13. Thermal transport properties of high-purity, high-densitysintered �-Al2O3: (a) conductivity and (b) diffusivity.

1926 Journal of the American Ceramic Society—Munro Vol. 80, No. 8

where � is the thermal conductivity, � is the mass density, Cpis the specific heat at constant pressure, and D is the thermaldiffusivity.

Specific-heat data for alumina25,59 are shown in Fig. 12. Thecorresponding interpolation formula is

Cp�J�kg−1�K−1� = 1117 + 0.14T − 411 exp�−0.006T� ± 2%(19)

for 20°C � t � 1800°C. Results from independent studies ofthe thermal conductivity36,60,61 and the thermal diffusiv-ity40,62,63 are shown in Fig. 13. For these data, the interpolationformulas are optimized simultaneously giving

��W�m−1�K−1� = 5.85 +15360 exp�−0.002T�

T + 516± 6% (20)

for 20°C � T � 1800°C, and

D�cm2�s−1� = 0.011 +18.9 exp�−0.0014T �

T + 164± 18% (21)

for 20°C � T � 1400°C.

IV. Conclusion

Property data for a constrained specification of sintered�-alumina have been reviewed to produce a comprehensive setof values for the major material properties as a function oftemperature. The mass fraction of the alumina phase of thematerial is designated to be at least 99.5%, which allows asmall amount of MgO to be added to control the grain size. Themass density is constrained to be at least 98% of the theoreticaldensity, and the nominal grain size is 5 �m. Interpolation for-mulas, contained in Eqs. (1) through (21), have been givenwhenever feasible. Based on these relations, representative val-ues of all the properties on the temperature range from 20° to1500°C are given in Table III.

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Ronald G. Munro is a member of the Ceramics Division of the National Institute ofStandards and Technology. Dr. Munro was awarded a National Research Councilpostdoctoral appointment at NIST in 1976 (when NIST was called the NationalBureau of Standards) and subsequently became a staff member in 1978. His work hasincluded many-body theory, molecular dynamic simulations, physics of materials athigh pressure, multivariate statistics, tribology, and advanced data evaluation meth-odologies. Currently, Dr. Munro is a member of the Data Technologies Group, wherehis research activities include the modeling of materials and their property relations,the development of data evaluation methodologies, and the development of evaluatedmaterials property databases for structural ceramics and high-temperature supercon-ductors. Dr. Munro is a member of the NIST Editorial Review Board, the EditoralBoard of the Journal of Physical and Chemical Referencce Data, the AmericanCeramic Society, the American Physical Society, and the American Society forTesting and Materials.

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