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Thermal properties of Ti 3SiC 2

M.W.Barsoum a,*,T.El-Raghy a ,C.J.Rawn b ,W.D.Porter b ,H.Wang b ,E.A.Payzant b ,

C.R.Hubbard b

Department of Materials Engineering,Drexel University,Philadelphia,PA 19104,USA

Oak Ridge National Laboratory,Oak Ridge,TN 37831,USA

Received 19August 1998;accepted 7October 1998

Abstract

The thermal properties of polycrystalline Ti 3SiC 2in the 25?C–1000?C temperature range determined by Rietveld re?nement of high temperature neutron diffraction data,show that at all temperatures,the amplitudes of vibration of the Si atoms are higher than those of the Ti and C atoms.Up to 700?C,the vibrations of the Si atoms are quite isotropic but the vibrations of the other atoms are greater along the c -than along the a -axis.The amplitudes of vibration of the Ti atoms adjacent to the Si atoms are higher and more anisotropic than for the other Ti atom sandwiched between the C-layers.Good agreement is obtained between the bulk thermal expansion coef?cients measured by dilatometry,9:1 ^0:2 ×10?6?C ?1,and the values from the neutron diffraction results,8:9 ^0:1 ×10?6?C ?1.The thermal expansion coef?cients along the a -and c -axes are,respectively,8:6 ^0:1 ×10?6?C ?1and 97 0: ×10?6?C ?The heat capacity is 110J/mol K at ambient temperatures and extrapolates to ?155J/mol K at 1200?C.room temperature thermal conductivity is 37W/m K and decreases linearly to 32W/m K at ?C.The thermal conductivity is dominated by delocalized electrons.?Elsevier Science Ltd.All rights reserved.

Keywords:D.Thermal conductivity;D.Thermal expansion;High temperature neutron diffraction

1.Introduction

Recent reports on two structurally related layered ternary carbides and nitrides namely,M 3BX 2and M 2BX,where M is an early transition metal,B is B-group element,and X is either C and/or N have shown them to have an unusual combination of properties [1–12].With electrical and ther-mal conductivities in the range of 2–14×106 V m ?1and 20–40W/m K,respectively,they are good thermal and electrical conductors.In contrast to all binary carbides they are relatively soft (Vickers’hardnesses 3–5GPa),and machinable by a mechanism similar to graphite [1,2,5].As a class,these carbides do not melt but decompose peritectically into the transition metal carbide and the B-group element [6].The decomposition temperatures vary from 850?C for Cr 2GaN,to over 1700?C for Ti 32.

The ternary carbide Ti 3SiC 2was ?rst identi?ed by Brukl [13]as ‘‘Ti 2SiC’’.Bruckl cited the superpositioning of

X-ray diffraction peaks from many of the binary compounds as adding to the dif?culties for prior identi?cation and gives an unindexed powder pattern.Jeitschko and Nowotny [14]determined the structure to be hexagonal,space group P63/

mmc with lattice parameters,a 3:06 A

and c 17:66 A.The structure is comprised of layers of Ti–C interleaved with layers of Si atoms.The carbon atoms occupy all the octahedral sites in the Ti https://www.wendangku.net/doc/b36448191.html,ter,Nickl et al.[15]studied the Ti–Si–C system by synthesizing samples using chemical vapor deposition (CVD)and reported a

unit cell of a 3:066 A

and c 17:646 A.Goto and Hirai [16]also prepared Ti 3SiC 2by CVD and gave an indexed powder diffraction pattern.More recently,Aruna-jatesan and Carim [17]used convergent beam electron diffraction to con?rm the space group.This latter study

obtained lattice parameters of a 3:07 A

and c 17:69 A by powder X-ray diffraction and compared the measured intensities to the intensities calculated from the crystal struc-ture.Discrepancies in peak intensities of the (008)and 1; 1

;12 were attributed to possible contributions from a secondary phase.A recent neutron diffraction study of

Journal of Physics and Chemistry of Solids 60(1999)

429–439

*Corresponding author.Tel.:?1-215-895-2338.

E-mail address:barsoumw@https://www.wendangku.net/doc/b36448191.html, (M.W.Barsoum)

Ti3SiC2[10]con?rmed the original structure[14],and reported bond lengths and angles,similar to those reported by Nickl[15].

Mechanically,Ti3SiC2is damage tolerant and resistant to thermal shock[1,18].It is relatively light(4.5gm/cm3), elastically rigid(previous authors reported the Young’s modulus to be325GPa[1,19,20].Polycrystalline samples of Ti3SiC2fail in a brittle manner at room temperature,but deform plastically at temperatures greater than1200?C[18]. At1300?C in air,the yield stresses are100and500MPa,in ?exure and compression,respectively.When heated in air a protective oxide scale forms in layers,where the inner layer is comprised of SiO2and TiO2and the outer layer is pure TiO2[4].

The Vickers microhardness decreases with an increase of load,stabilizing at higher loads at7.4GPa for bulk samples with TiC inclusions[19,20],4GPa for purer bulk samples [1,3,8],and6GPa for the CVD deposited sample[16]. These values indicate that Ti3SiC2is anomalously soft when compared with most other carbides.Like all the other312’s and211’s,Ti3SiC2is readily machinable[1,3]. Given the hexagonal layered structure it is not surprising that the mechanical properties are anisotropic.For example, the hardness of single crystals varies from3–15GPa paral-lel and normal to the basal planes,respectively[15].More-over,large-grained,oriented,polycrystalline samples of Ti3SiC2loaded in compression at room temperature deform plastically(strains?50%),with yield points that depend on the orientation of the loading direction relative to the basal planes[11].When the basal planes are oriented in such a way that allows for slip,deformation occurs by the forma-tion of shear bands.However,when the slip planes are parallel to the applied load,a situation where ordinary glide is impossible,deformation occurs by a combination of delamination of individual grains,kink and shear band formation.This propensity for delamination and buckling of individual grains is also observed in areas around Vickers [3]and Hertzian indentations[8].Atomistically,basal plane dislocations multiply and are mobile at room temperature; basal plane stacking faults are also present[9].

Little information is available about the thermal proper-ties of Ti3SiC2.An earlier study[21]reported the thermal expansion coef?cient,measured in an Ar atmosphere,as approximately0:02×10?6?C?1in the temperature range 100?C–600?C and0:12×10?6?C?1in the temperature

range700?C–900?C.Above900?C the thermal expansion coef?cient decreases,eventually becoming negative in the temperature range1100?C–1400?C.The contraction stops at approximately1400?C and high thermal expansion is observed above this temperature.No discussion was given to explain this behavior,which is in contrast with the results of other investigations[1,5,22],where the thermal expan-sion coef?cient was measured to be9:1×10?6?C?1in the temperature range25?C–1000?C in Ar.The room tempera-ture thermal and electrical conductivities were previously reported as43W/m K and4:5×106 V m ?1,respectively [1].

As discussed herein,there are many similarities in the thermal properties of TiC and Ti3SiC2,and consequently, a brief review of their structural similarities is useful for further discussion.TiC x forms in a NaCl-type crystal struc-ture where0:?x?0:the C atoms accupy the octahedral similar CTi6octahedral arrangement is found in the Ti–C layers of Ti3SiC2.That similarity is most obvious when their stacking sequences are compared, namely:

AcBaCbAcBaCbAcBaCbAcBaCb…for TiC and AbC a CbAcB a BcAbC a CbAcB a Bc…for Ti3SiC2; The capital and lower case letters represent the locations of the Ti and C atoms,respectively,a denotes Si atoms in the‘‘a’’positions and the underlined blocks represent stack-ing faults vis-a-vis TiC.Mostly because of these similari-ties,the Raman and X-ray photoelectron spectra of TiC and Ti3SiC2are quite similar.For example,all the Raman vibra-tion modes observed in TiC0.67are also seen in Ti3SiC2[12]. In addition,Ti3SiC2has one extra soft mode that was ascribed to a shear mode of the Si planes relative to the TiC layers.The X-ray photoelectron spectra have shown that the Ti and C atoms are even better screened in Ti3SiC2than in TiC[10].

The bonding in TiC and substoichiometric TiC,was recently summarized by Cottrell[23],who concluded that in stoichiometric TiC the pd bonds between the C and Ti are at a lower energy than the dd orbitals created between neigh-boring Ti atoms.Consequently,the pd bonding of the Ti–C interaction completely wins the competition for electrons with the dd bonds.Moreover,the pd band is full,with eight electrons per TiC unit,the dd states are completely empty.In other words,the C atoms tend to saturate their bonds with electrons.In substoichiometric carbides, however,the valence electrons that remain after saturating the Ti–C bonds go into the Ti dd bonds.As x drops below one,an initial small lattice expansion is seen,followed by a lattice contraction owing to the increased dd bonding between the Ti atoms.Once C is absent and vacancies appear,Ti–Ti bonds can exist in three different lengths resulting in a distortion of the octahedra.That distortion of the octahedra was?rst pointed out by Jeitschko and Nowotny[14]and recently con?rmed by Kisi et al.[10]. High temperature neutron diffraction studies of TiC0.58, TiC0.63,and TiC0.67samples also con?rm long range order-ing of carbon vacancies and provide critical temperatures for the order–disorder transformations[24].

The objective of this paper is to report on the thermal properties of Ti3SiC2in the25?C–1200?C temperature range and relate them,when possible,to the properties of TiC.To that effect we measured the thermal expansion,heat capacity,and thermal conductivity,and also gathered

M.W.Barsoum et al./Journal of Physics and Chemistry of Solids60(1999)429–439 430

information on the crystal structure using high temperature neutron and X-ray diffraction.

2.Experimental details

2.1.Processing

The polycrystalline samples were fabricated by reactive hot pressing of Ti,SiC,and graphite powders at1600?C for 4h under a pressure of40MPa.Titanium(99.3%,?325mesh,Titanium Specialists,UT),SiC(99.7%, d m 4m m,Atlantic Equipment Engineers,Bergen?eld, N.J.)and C powders(99%,d m 4m m,Aldrich,Milwau-

kee)were weighed and dry mixed in a V-blender for2h to yield the Ti3SiC2stoichiometry.The microstructure of the sintered material consists of large plate-like grains of diameter50–200m m and thickness5–20m m[1,3].Micro-structural analysis(optical and scanning electron micro-scopy)indicated that the volume fraction of the most common impurity phase in Ti3SiC2,namely TiC x,was less than3vol.%.Details of the powder processing and ensuing microstructures have been presented elsewhere[1,5].

2.2.High temperature X-ray and neutron diffraction

High temperature X-ray diffraction(HTXRD)measure-ments were conducted using a Scintag PAD X goniometer equipped with a modi?ed Buehler HDK-2diffraction furnace.The diffractometer utilized CuK a radiation (45kV and40mA)and a Si(Li)Peltier-cooled solid state detector.The data were collected as step scans,with a step size of0.02?2u and a count time of2s/step between9?and 90?2u.All data were collected in one atm of?owing He gas. The sample temperature was monitored with a Pt/Pt–10% Rh thermocouple spot-welded to the Pt–30%Rh heater strip on which a thin layer of Ti3SiC2powder was dispersed.The calibration of the thermocouple was veri?ed using a second-ary thermocouple and an optical pyrometer.Data were collected on heating at27?C,200?C,400?C,600?C,800?C, 1000?C,1200?C and on cooling at900?C,700?C,500?C,and 25?C.

High temperature neutron diffraction(HTND)measure-ments were conducted at the High Flux Isotope Reactor (HFIR)on the HB-4,high resolution neutron powder diffractometer.HB-4is equipped with a Ge(115)monochro-mator and32equally spaced3He detectors.The powder sample was contained in a cylindrical V can suspended in a vacuum furnace.The furnace heating element was cali-brated using MgO expansion data collected in the same sample can geometry.Data were collected on heating to 27?C,355?C,531?C,714?C,and906?C with a minimum scan time of8h at each temperature.After the room temperature data were collected,the sample was heated to 355?C and held at that temperature for approximately74h before collection of the355?C data.

For the Rietveld re?nements the General Structure Analysis System(GSAS)software package was used[25]. The Nb(110)re?ection from the furnace was observed between37?and38?2u,so this region was excluded from the re?nements.Often,layered hexagonal structures exhibit preferred orientation but attempts to include preferred orien-tation into the structure model did not result in signi?cantly improved?ts and sometimes resulted in negative atomic displacement parameters.To explore the possibility of defects(vacancies and substitutions)occurring at higher temperatures,the occupancies of the Ti,Si,and C sites were re?ned.These re?nements showed a trend of a small amount of Si vacancies as the temperature increased, however,these results were within4s of full occupation. Re?nement of the data collected at714?C suggested a small amount of Si occupying the Ti

sites(within3s of full Ti I occupation).Consequently,the results of the re?nements (lattice parameters,bond-lengths,and atomic displacement parameters)reported in this study were conducted with the sites fully occupied and all atoms re?ning anisotropically.

2.3.Bulk thermal expansion

The thermal expansion of bulk polycrystalline samples of Ti3SiC2was measured under?owing Ar in the25?C–1200?C temperature range in a dilatometer(Unitherm, Anter Corp.,Pitt.,PA).The measurements were carried out on heating and cooling using a ramp and soak cycle. The heating rate was2?C/min,and at every200?C on both heating and cooling the sample was allowed to equilibrate with the furnace for15min before resuming the heating. The data were collected every minute,and over1500indi-vidual data points were collected.The dilatometer was cali-brated using a single crystal sapphire rod.The accuracy of the results is estimated to be^2%.A Ti foil was loosely wrapped around the sample to getter any oxygen present in the system.

2.4.Thermal conductivity and heat capacity

The samples for the constant pressure molar heat capa-city,c p,and thermal conductivity,k total,measurements were electron discharge machined into the appropriate size disks. The thermal diffusivity measurements were carried out using a Flashline?5000thermal diffusivity system(Anter Co.,Pittsburgh,PA).The system uses a Nd:Glass laser to deliver a short heat pulse to the front surface of the speci-men.An infrared detector was used to monitor the tempera-ture rise at the back surface[26].Knowing the specimen thickness,the software calculates the thermal diffusivity using an algorithm developed by Taylor and Clark[27]. The thermal diffusivity of Ti3SiC2was measured from 100?C–500?C in an aluminum block furnace,and from 600?C–1000?C in a graphite furnace under positive nitrogen pressure.An InSb detector was used for the low temperature furnace and a silicon detector was used for the graphite furnace.Five measurements were taken at each temperature.

M.W.Barsoum et al./Journal of Physics and Chemistry of Solids60(1999)429–439431

The thermal diffusivity results were converted to thermal conductivities using the heat capacity results (see below)and the measured density,4.5g/cm 3,of the Ti 3SiC 2sample used for the experiments.

A Stanton Redcroft DSC 1500differential scanning calorimeter (DSC)was used to determine c p ,in the range of 100?C–1000?C using the ratio method of ASTM E1269-95.The DSC runs were made using platinum pans and lids and a heating rate of 20?C/min.A purge of 50ml/min tita-nium-gettered argon was used during the runs.The Ti 3SiC 2sample used was a disk-shaped specimen 4mm in diameter and about 2mm thick which weighed 125mg.This

M.W.Barsoum et al./Journal of Physics and Chemistry of Solids 60(1999)429–439

432Fig.1.Thermal ellipsoids (99%probability)of Ti 3SiC 2at;(a)27?C,(b)355?C,(c)531?C,(d)714?C and (e)906?C.These ?gures were drawn using atoms [28].

specimen shape was chosen to match the 51mg sapphire disk which was used as the reference standard.The results of DSC runs on a similar shaped specimen of platinum indicated that the accuracy of the speci?c heat values deter-mined in this manner was ^4%when compared to literature values for platinum.3.Results

3.1.High temperature diffraction

Figs.1(a)-(e)show the thermal ellipsoids of the structure at 27?C,355?C,531?C,714?C,and 906?C.The Debye–Waller factor (T )is obtained by describing the vibrations of each atom with a symmetrical tensor U having six inde-pendent components.In the general case:T exp ?2p 2 U 11h 2a*2?U 22k 2b*2?U 33l 2c*2

?2U 23klb*c*?2U 13lhc*a*?2U 12hka*b*

However,because of the hexagonal site symmetry,U 23and U 13are both equal to 0simplifying the equation to:T exp ?2p 2 U 11h 2a*2?U 22k 2b*2?U 33l 2c*2

?2U 12hka*c*

where a*,b*,and c*are the edges in the reciprocal unit cell

associated with the x *,y *,and z *axes,respectively.For the hexagonal crystal system anisotropic U ij ’s are converted to U eq by:

U eq 1=3U 11?U 22?U 33?U 12àá

2 The pro?le agreement factors for the Rietveld re?nements are given in Table 1where wR p is the weighted pattern R index and x 2,the goodness of ?t,is the ratio of the weighted

M.W.Barsoum et al./Journal of Physics and Chemistry of Solids 60(1999)429–439

433

Fig.1.(continued

)

Fig.2.Temperature dependence of U eq ?100for the four unique atoms (Ti I ,Ti II ,Si and C)in the structure.The numbers adjacent to the lines represent their slopes.

pattern R to the expected R index.Table 2gives the re?ned fractional coordinates,atomic displacement parameters,and the isotropic equivalent (U eq ).The standard deviation of U eq was calculated as outlined by Schomaker and Marsh [29].Fig.2plots U eq as a function of temperature for the four unique atoms (Ti I ,Ti II ,Si and C,see Table.2)and shows that U eq increases linearly as a function of temperature.The slope of the U eq versus temperature line for the Si atom is approximately three times that of the Ti II atom,which has the second largest slope.The slope of the U eq versus temperature line for the C atom is the smallest but within 6%of the slope for the Ti II atom.The temperature depen-dence of the anisotropic U ij ’s for the Ti I ,Ti II ,Si,and C

M.W.Barsoum et al./Journal of Physics and Chemistry of Solids 60(1999)429–439

434Fig.3.Temperature dependence of anisotropic U ij‘s:(a)Ti II (b)Ti I (c)Si and (d)C atoms.The numbers adjacent to the lines represent their slopes.Note that U 11 U 22 2U 12.

Table 1

Pro?le agreement factors for the Rietveld re?nements.Temperature (?C)wR p (%)x 2

277.73 1.8733009.91 1.3525008.24 1.3817008.99 1.320900

7.27

1.634

Table 2

Summary of crystallographic positions and U eq from the Rietveld re?nements of HTND data.Numbers in parentheses are estimated standard deviations in the last signi?cant ?gure of the re?ned parameter.Atoms and crystallographic positions at 27?C U eq (*100)A ?2Atom Posit.x y z 27?C 355?C 531?C 714?C 906?C Ti I 4f 0.33330.66670.3148(2)0.57(6)

0.76(7)0.99(7) 1.02(7) 1.2(4)Ti II 2a 0000.29(9)0.60(1)0.70(1)0.8(1)0.9(4)Si 2b 0

0.25

0.80(6) 1.52(9) 2.04(8) 2.3(1) 2.72(9)C

0.3333

0.6667

0.5723(1)

0.38(3)

0.67(4)

0.78(3)

0.90(4)

0.98(3)

atoms,is plotted in Figs.3(a)-(d),respectively,and listed in the Appendix.Fig.1and Fig.3(c)show that Ti I ,Ti II ,and C vibrate more along the c -than the a -axis direction.The vibrations of the Si atoms,however,are curious;they are isotropic at all temperatures except at 355?C and 900?C.It should be noted that the atoms all sit on special positions (see Table 2)and that the site symmetry in?uences the vibration directions.

Table 3gives the re?ned Ti I –C,Ti II –C,Ti I –Si,Si–Si,and Si–C bond lengths at 27?C,355?C,531?C,714?C,and 906?C.The bond lengths increase linearly with temperature and the largest expansion is seen for the Ti I –Si bond,

followed by the Ti I –C and,lastly the Ti II –C.The difference between the Ti I –C and Ti II –C bond lengths con?rms the prior reports of octahedral distortion [10,14]and indicates that the distortion becomes more severe with increasing temperatures.

X-ray diffraction was carried out to 1200?C and no evidence for any structural transformations was seen.3.2.Thermal expansion

The lattice parameters and unit cell volumes calculated from the HTND data are listed in Table 4.The thermal

M.W.Barsoum et al./Journal of Physics and Chemistry of Solids 60(1999)429–439

435

Table 3

Summary of bond lengths,A ?,from Rietveld re?nements of HTND data a .Temp (?C)Ti I –C Ti II –C Si–Ti I

Si–Si

Refs.

2.085(2)/2.088 2.1814(8)/2.176 2.693(2)/2.681

3.06557(6)/3.0575This work/[10].355 2.089(2) 2.187(1) 2.704(3) 3.07377(8)This work 531 2.092(2) 2.1907(9) 2.708(2) 3.07827(8)This work 714 2.094(2) 2.195(1) 2.715(3) 3.08315(8)This work 906

2.095(2)

2.1983(8)

2.724(2)

3.08895(7)

This work

Numbers in parentheses are estimated standard deviations in the last signi?cant ?gure of the re?ned parameter.

Table 4

Summary of lattice parameters and volume obtained from HTND results a .Temp (?C)a (A ?)c (A ?)volume(A ?)3(V )1/3Volume expansion 27 3.06557(6)17.6300(5)143.485(9)

5.23520.000355 3.07378(8)17.6803(7)144.666(9) 5.24960.00279531 3.07827(7)17.7119(6)145.348(9) 5.25780.004317714 3.08314(8)17.7423(7)14

6.06(1) 5.26640.00595906

3.08896(7)

17.7784(5)

146.908(9)

5.2765

0.00789

Numbers in parentheses are estimated standard deviations in the last signi?cant ?gure of the re?ned

parameter.

Fig.4.Thermal expansion of Ti 3SiC 2as determined from:(a)High temperature neutron (open symbols)and X-ray diffraction (solid symbols)and,(b)Dilatometer,Least square ?ts of the HTND results are depicted by the thin solid lines reproduced in both ?gures.The thermal expansion of TiC is plotted in Fig.4(b)as open triangles [30].

strains,D L /L 0,are plotted against temperature in Fig.4(a).The average thermal expansion coef?cients in the a -direc-tion,the c -direction,and for the volume are,respectively,8:6 ^0:1 ×10?6,9:75 ^0:1 ×10?6,and 8:9 ^0:1 ×10?6?C ?1.The dilatometric thermal expansion of a poly-crystalline sample of Ti 3SiC 2,on both heating and cooling,is plotted in Fig.4(b)as a thick line.Also shown in this ?gure are the HTND data (thin solid lines)and the thermal expansion of stoichiometric TiC (triangles)for comparison.

A least squares ?t of the solid thick line yields a slope of 9:12×10?6?C ?1with an r 2value of 0.997.This expansion value is in excellent agreement with previously reported values [5,22].

The thermal expansion coef?cients calculated from the HTXRD data were slightly lower than from the HTND (see Fig.4(a)).Note that the X-rays diffract because of the X-ray diffracting from the surface of a thin layer of powder as opposed to a bulk sample in the case of the neutron diffraction data.It is expected that some thermal convection is taking place for the X-ray sample (the temperature at the bottom of the powder in contact with the heater strip is higher than the powder at the top which is exposed to the He atmosphere),while the sample for the neutron diffraction data collection is contained in a V can in the center of a furnace that the neutrons penetrate.3.3.Heat capacity

The temperature dependencies of c p for Ti 3SiC 2and stoi-chiometric TiC (for comparison)are plotted in Fig.5.Curve ?tting of the data yields:c p 164.4?[16419/T (K)].The molar heat capacity at room temperature is 110J/mol K and increases monotonically with temperature,and extrapolates to ?155J/mol K at 1200?C.3.4.Thermal conductivity

The thermal conductivity,k total ,of Ti 3SiC 2is plotted as a function of temperature in Fig.6.In the 25?C–1200?range the thermal conductivity is a weak function of temperature.A least squares ?t of the data yields the following relation-ship.

k total 38:6?:0045 K

with an r 2value of 0.86.The room temperature thermal conductivity is 37W/m K,which is slightly lower than the previously reported value of 43W/m K [1].4.Discussion

The results shown in Tables 2–4are in accord with what is currently known about Ti 3SiC 2.The strongest bonds,and hence smallest amplitudes of vibrations,are those between the Ti and C atoms.The Ti–C bonds,however,are not equal in strength.The central Ti II atoms that are bonded from either side by C-atoms do not vibrate as much as the Ti I atoms that are bonded to the Si and C atoms.The large amplitudes of vibration of the Si atoms are an indication that their bonding to Ti I is relatively weak (as compared to the Ti–C bonds),which is consistent with the fact that the Ti I atoms vibrate more along the c -than along the a -axis.In light of what is currently known about the anisotropy of the mechanical properties of Ti 3SiC 2,one of the more surprising results of this work is the small thermal expansion anisotropy observed.This apparent paradox can be partially

M.W.Barsoum et al./Journal of Physics and Chemistry of Solids 60(1999)429–439

436Fig.5.Temperature dependence of heat capacity,c p of Ti 3SiC 2.Also plotted are the heat capacity results for TiC [31]and three times the latter.

Fig.6.Temperature dependence of the thermal conductivity of Ti 3SiC 2.

explained by the results shown in Table3.According to these data,the lack of anisotropy is not because the Ti–Si bond is as strong as the Ti–C bond,but rather owing to the averaging of the various contributions to the thermal expan-sion.In the25?C–900?C temperature range the Ti II–C,Ti I–C and Ti II–Si bonds expand at5.5,8.8and13ppm?C?1, respectively.The average value of9.1ppm?C?1is almost identical to the bulk thermal expansion of Ti3SiC2(Fig. 4(b)).At900?C the expansion of the Ti II–C,Ti I–C and Ti II–Si bonds contribute,respectively,17%,30%and53% to the overall expansion along the c-axis.That is,the expan-sion along the c-axis is not very different from that along the a-axis because the Ti–Si bond is weaker,and the Ti II–C bond is stronger,than the average Ti–C bond.

Another potential contributing factor to the lower thermal expansion along the c-axis at900?C,is that the Si atoms vibrate preferentially along the a-axis(Fig.1(e)).We suspect that the anisotropy in thermal expansion of the Si atoms at900?C re?ects the formation of Si vacancies during the time it took to collect the data.If that is the case,the vibrations of the Si atoms should be permanently affected. The anisotropy of the Si vibrations at355?C is not under-stood at this time.

The expansion along the a-axis re?ects the expansion of the average Ti-C bond and is thus not too different from that of pure TiC,viz.7.4ppm?C?1.Note that at2.132A?,the mean Ti–C bond distance in Ti3SiC2is slightly lower than that in stoichiometric TiC(2.16A?).The higher expansion rate of the Ti I–C bond relative to Ti II–C is what causes the distortion of the octahedra to increase with increasing temperature.The results plotted in Fig.4and listed in Table4also show that there is good agreement between the thermal expansion calculated from the HTND data and the dilatometric results.For the reasons noted before the HTXRD data were not used in calculating the thermal expansion coef?cients.

Nothing unusual is observed in the heat capacity response of Ti3SiC2in the temperature range explored(Fig.5);the heat capacity increases monotonically with temperature and then reaches a plateau at?155kJ/mol.Once again a comparison with TiC is useful.If the Si atoms are assumed to behave more like C than Ti atoms,then the limiting chemistry of Ti3SiC2would be Ti3C3or3TiC.As shown in Fig.5,there is good agreement between the heat capacity of Ti3SiC2,and three times that of TiC,over the entire temperature range explored.Here again this should not be taken as evidence for the strength of the Ti–Si bond,but rather a re?ection of the averaging of the bond strengths discussed before.

The foregoing conclusions are important,and partially explain why the mechanical properties can be anisotropic at the same time that the thermal properties are not.The modest thermal expansion anisotropy is consistent with, and partially explains,the excellent thermal shock resis-tance of this material[1,18].The results shown here are also in accord with the fact that the B-group elements are relatively weakly bound in the312and211structures. Previously,Barsoum and El-Raghy[5]had postulated, based on the bond length data alone,that electrons from in-between the B-group element and transition metal bonds are transferred into the dd Ti bonds,destabilizing the former and stabilizing the latter.The results of this work reinforce that notion.

The electronic portion of the thermal conductivity,k e,can be calculated from the Wiedmann-Franz Law:

k e L0s T

where s is the electrical conductivity at temperature,T and L0 2:45×10?8W V=K2.The room temperature conduc-tivity of Ti3SiC2is4:5×106V?1m?1[1],and thus at 300K,k e is33W/m K.This value accounts for?90%of k total measured in this work,viz.37W/m K.The Wiedmann-Franz Law is justi?ed in this case because of the excellent shielding of the Ti atoms in Ti3SiC2[10].The room temperature conductivity of TiC is21W/m K and increases with temperature[32].

5.Summary and conclusions

Reitveld analysis of the HTND results have shown that,at all temperatures,the amplitudes of vibration of the Si atoms are substantially higher than those of the Ti and C atoms. The amplitudes of vibrations of the Ti atoms on the two Ti sites are also different;the central Ti atoms that are bonded to6C atoms are more tightly bound to the structure than the Ti atoms that are bonded to3C and3Si atoms.These results indirectly con?rm the relatively weak nature of the Si–Ti bonds as compared to the Ti–C bonds,a conclusion in accord with the known anisotropy in the mechanical proper-ties.The volume expansion calculated from the HTND is 8.9(^0.1)×10?6?C?1;the expansions along the a-and c-axes are8.6(^0.1)and9.75(^0.7)×10?6?C?1,respec-tively.The dilatometric bulk thermal expansion is9.12×10?6?C?1over the range25?T?1200?C and is in excellent agreement with the diffraction results.The room temperature heat capacity is110J/mol K and extrapolates to ?155kJ/mol K at1200?C.The room temperature thermal conductivity is37W/m K and decreases linearly and slightly to32W/m K at1200?C.The thermal conductivity is dominated by delocalized electrons.

Acknowledgements

This research was sponsored by the Assistant Secretary for Energy Ef?ciency and Renewable Energy,Of?ce of Transportation Technologies,as part of the High Tempera-ture Materials Laboratory User Program,Oak Ridge National Laboratory,ORNL,managed by Lockheed Martin Energy Corp.for the US Department of Energy under contract DE-AC05-96-OR22464.This work was also

M.W.Barsoum et al./Journal of Physics and Chemistry of Solids60(1999)429–439437

partially funded by the Division of Materials Research of the National Science Foundation (DMR 9705237).CRJ was supported in part by an appointment to the ORNL Postdoc-toral Research Associates program jointly administered by Oak Ridge Associated Universities and Oak Ridge Institute for Science and Education.The authors would also like to thank Dr.Bryan Chakoumakos for assistance with the neutron powder diffraction data collection and processing.Appendix A See Table 5.

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