富山大学水素同位体科学研究センター研究報告26 : 31‑43, 2006.

論文
TiC中の水素の拡散挙動
波多野雄治,野崎天生,本間啓史,松山政夫

富山大学水素同位体科学研究センター〒930‑8555

富山市五福3190

Diffusion of Hydrogen in Tic

Yuji Hatano, Teo Nozaki, Hirofumi Homma and Masao Matsuyama

Hy血ogen lsotope Research Center, University of Tbyama

Gofuku 3190, Toyama 93018555, Japan(Received March I, 2007; accepted June 25, 2007)

Abstract

The difhsion coefrlCient of hydrogen in commercially supplied Tic powder
was measured at 773, 873 and 973 K by hydrogen absorption experiments. The

pre‑exponential factor and activation energy were evaluated to be 1 0‑I I m2･S‑I and 87±1 3

kJ･mo1‑1 , respectively･I. Introduction

Carbides of group 4 and 5 metals have unlque Properties such as reftactoriness,extreme hardness and good resistance against chemical co汀OSion t1,2】. Hence,systematic studies on the interactions between these carbides and hydrogen isotopes

may lead to the development of newfunctional materials f♭r handling of hydrogenisotopes. Indeed, the present authors have found that the intermediate layers of Nb31

波多野雄治･野崎天生･本間啓史･松山政夫

carbides improve hightemperature stability of Pd coating prepared on Nb to form acomposite membrane fわr hydrogen separation [3,4]. Accumulation or data on hydrogen

difRISivity is important for material selection in this application. In addition, ZrC is apotential candidate of coating material for fuel particles used in high temperaturegas‑cooled reactors l5]･ The data on di軌sivity are necessary alsointhis application toevaluate the rate of tritium release &omfuel core to coolant He gas･ The diffusivity ofhydrogen isotopes in the carbides, however, has been scarcely reported･In the present study, the hydrogen absorption of commercially supplied Tic

powder was examined at 773, 873 and 973 K･ The analysュs Or absorptlOn CuⅣeSindicated that the rate of absorption Was COntrOlled by the diffusion process in the bulk･The diffusion coefrlCient evaluated was in a rage from 6×10‑17 to 1 x10‑15 m2･S‑I.

2. Experimental
2.1. Specimen

Specimenused in the present study was powder of Tic supplied by Kojundo

Chemical Laboratory Co･, Japan･ The nominal purity of the specimen was 99%, and theconcentrations of metallic impurities measured by the supplier are summarized inTable 1 I The specimen power was analyzed by X‑ray diffraction (XRD) before and afterhydrogen absorpt10n eXPeriments･ The size distribution of powder particles wereexamined with a scanning electron microscope (SEM).

Table I Concentrations ofmetallic impurities in Tic specimen･

ElementCon°.

32(mass%)

0.3

AI

Cr

0.007

Fe0.005

Mn0.001

Ni0.001

TiC中の水素の拡散挙動

The hydrogen absorpt10n experiments were carried out at 773, 873 and 973 K
using a vacuum apparatus which was similar one used in the previous study 【6]. Thespecimen powder of 2 g was installed in a quartz tube attached to the apparatus andheated in vacuum fわr degasslng. Elevation of specimen temperature resulted insignificant release of gas whose mass number was 28, i. e. CO and/or N2. The specimen
temperature was raised gradually to keep the pressure in the叩paratuS lower than 10‑3Pa. The degasslng Was Stopped when the pressure in the apparatus became lower than

10‑5 pa at 1373 K･ Then, hydrogen absorptlOn Was examined in a closed vacuum system,
in which the hydrogen absorption was indicated by pressure drop 【6】. The initialpressure of H2 gas Was adjusted to be 20‑50 kPa, and the specimen temperature to be773, 873 or 973 K.. The absorptlOn rate Was too Small at temperatures lower than 773 K,
while the pressure change by degasslng fiom the specimen was not negligible attemperatures higher than 973 K even a洗er the degasslng treatment in vacuum at 1373 K.

Hence, lt Was difficult to examine in a wider temperature range.

3.Results

3･l Characteristics of Specimen Powder
Fig. 1 shows XRD pattems of powder particles before and a洗er hydrogen

absorption tests. All peaks in these pattems could be assigned to Tic (NaCI structure)and Si mixed with the specimen powder as standard refTerence material; nQ Peaks ofother phases such as metallic Ti and Ti oxides were obseⅣed. The lattice parameter of

Tic was evaluated to be 0.4324 mm. This value of lattice parameter is slightly smaller

33

波多野雄治･野崎天生･本間啓史･松山政夫'ロ'■las̲.e;eived

than that fわr high purity

Tic (0･4328 nm)【1,2]. It(.t 't!)Al!Sua)uJ●
105000凵ﾅFロSi0is known that oxygen

ロﾂロ

劍

"

●●

and nitrogen present in:D+a.
Tl.lTpI..⊥冒.⊥

Tic as impurities lowerlllll ●arterH2absorptiom

the lattice parameter [11.
(.n't!)1)!stJa)uI‑1 5 0 5 0 0 0 0 0 0●

Iwithlmo1%hydrogen)+Tic

The specimen used in the●●present study contained●●●●●●
these impurities at total..l｣..i20

concentration or2 at% as406Q

80

100

120

140

2♂/°egFig･ 1 X‑ray diffraction patters of Tic powder befわre (a)described below. Thusand aRer (b) hydrogen absorption experiments.
the slightly small lattice

parameter can be ascribed to the innuence of these impurities･ No noticeable difference

was observed between diffraction pattems before and aRer hydrogen absorpt10nexperiments.

The concentrations or carbon, Oxygen and nitrogen in the specimen powdersubjected to hydrogen absorption experiments were examined in Horiba Co., Japan;

carbon concentration was measured by combustion in 02 gaS flow and that of oxygen

34

TiC中の水素の拡散挙動

and nitrogen by fusion in Ar gas now. The composition of the specimen powder thus

determined was Tic°.958土0 001No.ol 72土0.000200.02 19士0.0002 0r Ti(C,N,0)0.997土0.001. Namely, theTic specimen used was in carbon deficient type non‑stoichiometric composition･

Fig. 2shows SEM

micrograph of the specimen

powder. Majority of particles

was in a range orsize 1 to10 LIm. The size ofca. 200

particles was measured

randomly, and the averageFig. 2

SEM image of TiC specimenpowder.

value of particle size wast!J1 d'J nS JldZH

evaluated to be 4 pm.

J｢'J24 4 43.2

Hydrogen Absorption

by TicTypical example of02000

4000

6000

8000

1 0000Time,∫/sabsorption cuⅣes obtained atFig. 3873 Kis shown in Fig. 3. The

Typical hydrogen absorption curve obtained

at873 K.

initial and equilibrium pressure of H2 in this absorption experiment were 45･3 and 43

35

波多野雄治･野崎天生･本間啓史･松山政夫

kPa, respectively･ This extent of pressure reduction co汀eSpOnded to H concentration in

Tic of 1 mol鞘 ([H】/[TiC] ‑ 0.01).

The rate‑limiting step of hydrogen absorption was evaluated by plottlng(dP/dt)/(dP/dt) l ,‑o against C(t)/Cw where P is the hydrogen pressure, I is time, C(i) isaverage hydrogen concentration in Tic at I, and Cco is the concentration in equilibrium･

If the dissociation at the surfTace is the rate‑limiting step, ‑(dP/dt) is described asfollows:

憲‑‑諾‑〈孟‑AkrC(i,2洋, (1,where n is the amount of gas in the reaction chamber, R is gas constant, T is thetemperature of gas, V is the volume of reaction chamber, A is the total surface area ofTic, k, is the rate constant fわr recombinative release of hydrogen on Tic surface, α isthe sticking coefrlCient, M is the molar mass of hydrogen molecule･ Since the initialconcentration of hydrogen in Tic is negligibly small, ‑(dP/dt) I t=0, can be expressed asA叫RT2Jr.IlRT T

where P. is the initial pressure of H2. In equilibrium, the sticking anddesorpt10n nun are balanced, and hence

A a?.CAkrC的2 where Pのis equilibrium弼同風帖rJ

pressure･ Under the present conditions, the extent of pressure change during absorption

experiment was small･ By assuming P ‑ Pi ‑ Pco, one would obtain from Eq. (1)(芸)′(i)lt=｡ ‑.‑(C(i)/C‑)2 ･36(2)

TiC中の水素の拡散挙動

Ifa first order surface reaction process, such as dissolution ofadatom into subsurface, isthe rate‑limltlng Step, Similar approach easily glVeS(芸)′(=)lt‑̲0 ‑. ‑C(i)/C‑･(3)

Namely, rather simple correlation would be obtained between (dP/dt)/ (dP/dt) l , ‑o andC(t)/Ccc for the surfTace‑limited absorption･ On the other hand, in the case ofdifRISionllimited absorption, ‑(dP/dt) is proportional to the concentration gradient ofhydrogen near the surfaces of Tic particles. Hence, ‑(dP/dt) should decrease sharply in

the initial stage or absorptlOn With increaslng penetration depth or hydrogen, i.e.

increasing C(i)/Cco. According to calculation based on the difRISion model in a sphere atconstant surfTace concentration l71, ‑(dP/dt) should decrease by fTactor 10 when C(t)/Ccoincreases from 0.022 to 0.22. These values of C(i)/G correspond to Dt/a2 ‑ 5×10Jl and5× 10‑2, respectively, where D is the difRISion coefficient and a is the radius of sphere･

The abso叩tlOn CuⅣe Shown in Fig･ 3 is replotted in the above一mentioned manner inFig. 4. The change in (dP/dt)/ (dP/dt) l , =o with C(i)/Cco clearly shows the characteristicsof dimISion‑limited absorptlOn.

The difnlSion coefficient of hydrogen D in Tic was evaluated by fitting thesolution of di仇ISion equation to the absorption cuⅣes by assumlng that the powder

particles are spheres whose diameter is 4 pn for simplicity･ The surface concentration

37波多野雄治･野崎天生･本間啓史･松山政夫

of hydrogen was assumed to be constant during the absorptlOn Since the extent ofpressure change was small as mentioned above･ Under such conditions, the amount orabsorbed hydrogen at ∫, 〟t, is described as〟t‑‑.一意ni.乏exp(‑Dn2n21,a2, 【7,I(4)〟∞Fig･ 5 shows the results offitting for absorption curve obtained at 873 K as an example･The experimentally‑obtained absorption curves was well reproduced at D ‑ 2xl0‑16
ノm2･S‑1.

The diffusion coefrlCient thusevaluated was plotted agalnSt reciprocal

temperature in Fig. 6.
1The activation energy

for hydrogen di軌lSion

was derived as

1'一 00‑I(Jp P)I(JPd)0000 ノhV87土13
0 0 4 2

kJ･mol l and thepre‑exponential factor
0.0

0.2

as 10111 m2･S‑).

0.4

0.6

0.8

1.0C(t) / C∞

Fujita and Fig･ 4

Plot of (dP/dt)/(dP/dl) l FO against C(i)/G. Solid

Symbol indicates the experimental data. DashedMasuda[8】

haveand dotted lines co汀eSpOnd to Eqs. (2) and (3),examined

hy血ogenrespectively.

38

TiC中の水素の拡散挙動

absorption of Ti covered
IllfI AA

by Tic and reported thatA∇∇ム∇

the apparent activationenergy△∇for absorption

Awas l14l$Bﾓrﾓvﾕｧ2ﾓ○D‑2.0×10‑16mZs‑I

kJ･mol 1. h

▽D‑2.0×10‑15m2S‑I
l●lcontrast to the present0

2000

4000

6000

8000

10000

Time, t /sobservations, Fujita andFig･5

Masuda [8] concluded

Typical result of fitting of Eq. (4) to absorption

curve obtained at 873 K.

that the rate‑limitlng Step[･ sZ u/qJuaPuJ303tm!SnJ !Gof absorptlOn Was theActi､ration energy
dissolution process of87土13 kJ･mo1‑I

adatoms into Tic layer■and not the dimISion

through Tic because the1.00

1.05

1.10

1.15

1.20

1.25

1.30

1000/ T/KI

value of activation

Fig16

Arrhenius plot of diffusion coefficient ofenergy was slgnificantly

hydrogen in Tic.
higher

than

that

fわr

hydrogen diffusion in TiH2･ These authors believed that the activation energy of39

波多野雄治･野崎大生･本間啓史･松山政夫

hydrogen di爪ISion in Tic is comparable to that in TiH2 because the amngementS OfTi

atoms in these materials are similar to each other･ In TiH2, hydrogen occupleS

letrahedral sites of fcc structure formed by Ti atoms. On the other hand, carbon in TicoccupleS OCtahedral sites. It isknown that stoichiometric Tic does not react withhydrogen l1,9‑11]: the presence of carbon vacancies is essentialfor dissolution ofhydrogen in TiC･ Results of neutron‑di於action analysis on Ti carbohydrides l12] andcombination study of X‑ray and neutron diffraction methods on TiCo.48Do60 [13]showed that majority of hydrogen isotopes in TiCl̲x OCCuPied octahedral sites (carbonvacancy) and only minor portion was fTound in tetrahedral sites. Hence, the activationenergy of hydrogen difRISion in Tic could be significantly different from that in TiH2.

In our opinion, the possi6ility of diffusion‑limited absorption could not beruled out intheir study l8]; the difference between the present value of activation energy ofdifRISion (87土13 kJ.morl) andtheir apparent activation energy (114 kJ･mo1‑I) is notvery large.

If majority of hydrogen fわrms cluster with carbon vacancy (occupation ofoctahedral site itself or that of tetrahedral site adjacent to the vacancy), theconcentration of hydrogen possible to be accommodated in Tic should have an upper

limit detemined by the concentration of carbon vacancy. indeed, the equilibrium

40TiC中の水素の拡散挙動

Concentration of hydrogen in the present Tic specimen showed very weak dependence

on H2 Pressure (lH]/lTiC] ∝ Pl/4 ‑ pl/5 )･ Namely, the increase of lH]/lTiC] with P＼tended‑to cease at the value around 1 xlO12･ This value of lH]/lTiC] is comparable to but

slightly higher than the concentration of carbon vacancy evaluated by the chemicalanalysis (2‑4× 1 0‑3)･ The concentrations or oxygen and nitrogen may be overestimateddue to pick up of these impurities during the transportation of specimen in air. The

mechanism underlying this discrepancy'however, has not been fully understood. The

details of pressure dependence will be reported as a separate paper･The activation energy for the self‑di軌sion of carbon in Tic has been reported

to be 208 ‑ 460 kJ･mol‑tl14]･ Namely, the presently obtained value ofactivation energy

for hydrogen di凪lSion is radically smaller thanthat of carbon. This clear differenceindicates that hydrogen does not mlgrate aS a Cluster with carbon vacancy･ Theexperiments fわr the specimen with larger extent of carbon deficiency (i.e. large x inTiCl‑･r) is currently under preparation to get better understanding of the mechanism ofhydrogen di爪lSion.

4. Conclusions
The difRISion coefficient of hydrogen in commercially supplied Tic powder

was measured at 773, 873 and 973 K･ The value obtained was expressed as41

波多野雄治･野崎天生･本間啓史･松山政夫

10‑Ilxexp(‑87j=13 kJ.mo1‑I/RT) lm2･S‑1]･ Although carbon vacancies appeared to play akey role in hydrogen accommodation in Tic, the presently obtained value or activationIenergy f♭r hydrogen di軌sion was radically smaller than that of carbon in Tic.

Acknowledgements
This study was supported in part by a Granトin‑Aid f♭r Scientists Research (C)of Ministry of Education, Culture, Sports, Science and Teclmology of Japan, Nol
17560613･ The authors express their sincere thanks to Professor A. Pisarev for his
indispensable advice in the evaluation orrate limiting step ofhy血ogen abso叩hon･Referen cesll]

E･ K･ Storms, The RefractoりノCarbides, Academic Press, New York, NY, USA,1967.

[2]

H･ 0･ Pierson, Handbook of RejTractofy Carbides and Nitrides, Noyes

Publications, Westwood, NJ, USA, 1996.
[3]

Y･ Hatano, K Ishiyama, H･ Homma and K. Watanabe, Int. J. Hydrogen Energy,

32 (2007) 615‑619.

[4】Y Hatano, K･ Ishiyama, H･ Homma and K. Watanabe, ∫. Alloys & Compounds,

inpress.

[5】

K. Minato, T. Ogawa, K. Fukuda, H. Nabielek, H. Sekino, Y Nozawa and i.

Takahashi, J. Nucl. Mater., 224 (1995) 85‑92.

[6] JR･ Hayakawa, Y･ Hatano, A･ Pisa,ev, K･ Watanabe, Phys. Sc,., TIO8 (2004)
38‑41.

[7] J･ Crank, The Mathematics of DIHusion, 2nd ed., Oxfわrd University Press,42

TiC中の水素の拡散挙動

Oxfbrd, UK, 1975, p. 89‑93.
[8]Y･ Fujitaand K/Masuda, Z. Metallkde., Bd. 74 (1983) 434‑439.

[9]H･ Goretzki, H･ BittnerandH･ Nowotny, Mh. Chem., Bd. 95 (1964) 1521‑1526.

[10] K･ Yvon, H･ Nowotnyand R･KiefrTer, Mh. Chem., Bd. 98 (1967) 2165‑2172.
[11] G･ W･ SamsonowandW･W. Morosow,Mh. Chem., Bd. 102 (1971) 1667‑1678.
[12] I･ S･ Latergaus, V. T.畠m, I. Karimov, D. Ya. Khvatinskaya and D. K.

Dolukhanyan, Inorg. Mater. 20 (10) (1984) 1420‑1423.
[13] G･ Renaudin, KI Yvon, S･ K･ Dolukhanyan, N. N. Aghajanyan, V. Sh. Shekhtman,

J･Alloys & Compounds, 356‑357 (2003) 120‑127.
[14] G VI Samsonov and I･ M･ Vinitskii, Handbook of Rej:ractoFy Compounds(English Ed･), IFl/Plenum, New York, NY, USA, 1980, p. 222.

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