Diffusion of tritium in rutile (TiO2)

Materials Science and Engineering, 14 (1974) 109--114

© Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

Diffusion of Tritium in Rutile (TiO2)*

G.R. CASKEY, JR. Savannah River Laboratory, E.I. du Pont de Nemours and Co., Aiken, South Carolina 29801 (U.S.A.) ( R e c e i v e d March 6, 1973; in revised form May 15, 1973)

Summary Tritium diffusion in single crystals of rutile (TiO 2) was measured at temperatures between 155 ° and 300°C. Diffusivities were calculated from concentration profiles obtained from microdensitometer traces o f autoradiographs generated by the [J-decay of the tritium. Diffusivity is anisotropic with estimated diffusion equations of: D c = 7.5 × 10 - 6 exp(--9040/ RT), and D a = 2. 7 × 10 - 6 exp(--13,100/RT).

tronic semiconductor concurrent with hydrogen absorption 9. This study was undertaken to measure hydrogen diffusivity in rutile single crystals between 150 ° and 300°C to provide the basis for a rationalization of the observed inhibition of hydrogen absorption by the oxide film and the variability in the susceptibility of titanium to reaction with hydrogen reported elesewhere 2 - 5

BACKGROUND INTRODUCTION

Investigation of hot-salt stress corrosion cracking of titanium--aluminum alloys at Savannah River Laboratory showed that the presence of an oxide film on the alloy inhibited hydrogen absorption I . This observation is generally supported by other low-temperature studies 2 - 5 of the behavior of titanium and its alloys in h y d r o g e n atmospheres and is explicable if a stable oxide film of low hydrogen permeability protects the alloys. Rutile is the crystalline form of titanium oxide observed on titanium and m a n y of its alloys at temperatures below ~ 300 ° C 6. This oxide is thermodynamically stable in hydrogen gas at low temperature 7, but will dissolve hydrogen in the ionized state, H ÷ , as shown by infrared absorption studies s The oxide changes from an insulator to an n-type elec-

The rutile form of TiO 2 is the only oxide detected by X-ray or electron diffraction dur-

," ..... ~.............

,

i

i

1

,

I i C -2.95,9 A

,--

i

i

Ii

~-.-\/

i/

!

/ \ ~U :

a 14.594 A

:

l

I(~o

0 Ion Ti Ion

chaln~------

-

ben channel c -~axls

___/" a

*The information contained in this article was deveLo p e d during the course of work under Contract AT

Fig. 1. Crystal structure of rutile. Ti06 o c t a h e d r a

(07-2)-1 with the U.S. Atomic Energy Commission.

stacked to form open channels along e-axis.

110

ing the early stages of oxidation of titanium at temperatures below 1200°C s. There is, however, an accompanying solution of oxygen in the base metal up to a limiting composition of 26 at.%, which is easily detectable at temperatures of > 8 0 0 ° C 1 o. Some solution of oxygen may also occur at lower temperatures. At higher temperatures and long exposure times, suboxides (Ti2Oa, for e x a m p l e ) m a y form, followed by spalling of the oxide and rapid oxidation of the metal i 1 The rutile crystal structure is a tetragonal lattice with two T i O 2 molecules per unit cell. The titanium ions are arranged on a bodycentered lattice at the center of oxygen octahedra. These octahedra are stacked in such a way that relatively open channels exist along the c-axis as shown in Fig. 1. Lattice parameters for pure, stoichiometric TiO 2 are a o = 4.594 A and c o = 2.959 A 12. For oxygen-deficient titanium dioxide, ~TiO i .992, the lattice is slightly expanded, especially along the a-axis, and the lattice parameters are a o = 4.603 A and c o = 2 . 9 6 0 A i3. For still lower oxygen contents (O/Ti < 1.99), phases are formed that retain the same basic octahedra but are differently arranged ~4 Diffusion in futile is known to be anisotropic, a natural consequence of the tetragonal s y m m e t r y of the lattice 15. The most extreme case noted is for interstitial diffusion of lithium where D c / D a = 1 0 s 16. Pron o u n c e d , but less extreme, anisotropy has also been observed for oxygen and boron diffusion 17. i s Two studies of hydrogen (protium) diffusion in rutile have been made previously. Chester and Bradhurst i 9 attempted to evaluate hydrogen diffusivity at room temperature by electrical conductance measurements on the surface of a crystal cathodically charged in a sodium sulfate solution. Their results were interpreted to indicate a diffusivity of 10-11 to 1 0 - i 3 c m 2 / s e c near the surface. Hill 20 evaluated hydrogen diffusivity in futile single crystals at 450 ° to 780°C by measuring the decay in the O-H infrared absorption peak during outgassing. A small temperature-dependent anisotropy noted in hydrogen diffusivity was also dependent on the aluminum impurity content of the crystals. Both of these studies used indirect techniques that require several assumptions and ancillary data to relate the measured quantities to hydrogen concentrations.

EXPERIMENTAL DETAILS

Tritium diffusion in TiO 2 was measured on specimens cut from a single crystal of rutile grown by the Verneuil flame-fusion technique at Materials Research Corp. The boule was cut into four specimens 3 X 3 X 12 m m and one specimen 12 X 12 X 3 mm. Crystal orientations were within 4 ° of nominal, with the caxis either parallel to or at right angles to the length of the specimen. Chemical analysis by spark source mass spectroscopy showed the major impurities to be A1 80, Si < 3 0 , Mg < 7 0 and Na < 4 0 p.p.m., with minor amounts of Zn, Ca and Sr. Transition metal impurities were ~<1 p.p.m. The oxygen--titanium ratio was probably slightly less than 2.00 as indicated by lattice parameter measurements, a o = 4.601 A and c o = 2.952 A. Mass densities of the individual specimens ranged from 4.2477 + 0.0001 to 4.2506 + 0.0004 g/cm 3, compared with an X-ray density of 4.250 g/cm~; these values also indicate slight deviations from stoichiometry. Crystals grown by the Verneuil technique may show a lineage structure that could affect the diffusion measurement by introducing high diffusivity paths parallel to the c-axis. However, there was no indication of sufficient lineage structure to affect the diffusion results significantly, as observed in a rocking curve of the 110 peak on one specimen. The peak shown i n Fig. 2 is asymmetric as a consequence of using both K a i - - K a 2 peaks of the incident copper radiation. Specimens were sealed in stainless steel containers, which were then evacuated and backfilled with tritium. Exposure times, tern-

90

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I

I

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20 I0 I

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Fig. 2. Rocking curve of 110 peak of rutile. Single crystal grown by Verneuil technique. Unfiltered Cu Ka radiation.

111

TABLE 1 Experimental conditions for exposure of futile specimens to tritium Specimen No.

5 2 4a 6

Exposure

Dimensions (cm) t

w

l

0.3 0.3 0.3 0.3

0.3 1.2 0.3 0.3

1.2 1.2 1.2 1.2

Crystal Temp. orientation (° C)

Time (h)

Pressure b (atm)

C C C C

623 983 1630 1098

1.94 1.77 1.57 1.49

II w II ~ I] ~ ]l w

300 250 194 155

a Specimen cracked d u r i n g c h e m i c a l polishing. b T o t a l gas p r e s s u r e a t i n d i c a t e d t e m p e r a t u r e .

peratures and pressures are indicated in Table 1. Diffusivities were calculated from concentration profiles obtained by autoradiography. One face of each specimen was ground to a depth below the limit of tritium penetration in that direction, cleaned and dried. Autoradiographs were made by exposing the specimens to " K o d a k " * Nuclear Track Emulsion plates, Type NTB-2, which have 10-micron emulsion thickness and 0.25-micron grain size, for six to seven days. Optical density of the emulsion darkened by the beta particles emitted by decay of the tritium was assumed to be directly proportional to the concentration of tritium 21. Optical transmittance (T) of the emulsion along a path parallel to the diffusion path was measured with a Grant microdensitometer adjusted to give T = 0.8 for a standard filter of 0.1 optical density. The background density was subtracted from the readings. Because the tritium concentration is assumed proportional to the optical density, the concentration profile is C/C~ = log (1/T)/log (1/T~). With a stage speed of 2 × 10 - 4 cm/min and a recorder chart speed of 8 in./min, the resolution was 0.0025 cm/chart division of 0.1 inch. A typical autoradiograph and the concentration profiles are shown in Figs. 3 and 4. The profiles were not corrected for diffusion of the tritium either along the gradient or out of the specimen to the film during exposure because tritium diffusivity at room temperature is

Registered tradename of Eastman K o d a k Co.

~10-- 1 5

cm 2/sec,

and

such

corrections

should be negligible 22. Diffusivities along the c-axis were calculated assuming either the solution for a semiinfinite solid (in the case where the c-axis is parallel to the specimen length) or the solution for a plane sheet (in the case where the c-axis was at right angles to the specimen length}. These solutions, for the condition of constant D, constant surface concentration, and zero initial concentration, are C/C s = erfc (x /2~/Dt ) for a semi-infinite solid, and

__c = 1 _ 4 (-1)Cs n -=0 2n + 1 exp(--D(2n + 1)2n2t/412) COS

Areas Tritil

(2n + 1)Irx 21

7

C - Axis

Penetr

Fig. 3. A u t o r a d i o g r a p h t r i t i u m at 250°C.

o f rutile crystal exposed t o

112 t.O

I

TABLE 2 Tritium diffusivity in rutile (TiO 2 )

'

Temp, oC

0.8

Diffusivity, cm2/sec c-axis

~ 0.6

a-axis

300

(2.2--3.3) x 10--9

2.5 X 10-11

I-

250

(1.1--2.0) × 10- 9

(7.2--8.7) × 10- 1 2

._~ 0.4

194

(3.6--5.8) x 10- 1 °

7.7 x 10- 1 3 to 4.3 x 10- 1 2

155

(1.1--2.6) X 10 - 1 0

(Not measurable)

500°C oC

0.2

5c I , I , I , I , 0.040 0.060 0.080 0.100 0.120 ~.140

0.020

Depth of Penetration, Inch

Fig. 4. Concentration profiles, c/c s vs. X , from autoradiographs along c-axis.

for a plane sheet 23 Since tritium penetration in the a-crystallographic direction was shallow, the expression for a semi-infinite solid was used to evaluate D~. F u r t h e r m o r e , the diffusivities were obtained at 300 °, 250 ° and 194°C only, because Temperoture, °C i0-11

300 I

250 I

200 I

150 I

the tritium penetration along the a-axis at 155°C was t o o low to det ect under these experimental conditions. Figure 5 is an Arrhenius plot of the data in Table 2; the corresponding diffusion equations for the two crystal directions are: D e = 7.5 × 10 - 6 exp ( - - 9 0 4 0 / R T ) c m 2 / s e e D~ = 2.7 × 10 - 6 exp ( - - 1 3 , 1 0 0 / R T ) c m

2/sec

T he m a x i m u m possible error in evaluating diffusivities due to misalignment of the crystals arising from cutting (.+4° ) is negligible for De, but n o t for Da. Diffusivity in an arbitrary direction defined by the cosine of the angle between the given direction and the c-axis of a crystal with tetragonal s y m m e t r y is given by15

i0-9

D = D a sin20 + D c cos20.

The relative errors in D~ and D e are

io-iO

(D a - - D ) / D a = cos 20 (1 -- D c/D a ) a n d ( D c - - D ) / D c = sin20 (1 - - D a / D ¢).

"~ iO-II

i5

10-~2 --

io-'3 1.7

1

%%,%

%

I

I

I

I

I

I

1.8

1.9

2.0

2.1

2.2

2.2

IO00/T

%%

2.4

(°K)

Fig. 5. Temperature dependence tritium in rutile single crystals.

of

diffusivity of

For the m a x i m u m misalignment, 0 ~ 86 ° for Da, 0 ~ 4 ° for D c; and with D c / D a . ~ 2 0 0 , this would yield m axi m um relative errors of A D / D a = - - 1 a n d A D / D c = 0.005. Actual error in Da m ay be less than above in any particular case. In every case, however, the true value of D a will be less than or equal to the measured value D because elimination of a cont ri but i on of D c can only make the measured value smaller.

113

DISCUSSION The composition of the rutile crystals used in this study is comparable with that of Crystal A of Hill, which contained 80 p.p.m. A1. However, the behavior of the crystals is not. Hill found that the temperature dependence of protium diffusivity changed markedly at ~ 6 5 0 ° C , where the activation energy decreased from 3.08 eV to 0.395 eV at higher temperatures. Activation energies calculated in this study for tritium diffusion {0.40 eV and 0.57 eV for the c- and a-crystallographic directions, respectively) are in agreement with Hill's high temperature result, rather than the expected behavior based on the lower temperature results. Hill attributed the change in activation energy at 650°C to the formation of planar regions of faulted structure, possibly Magneli phases, in the crystal at the higher temperatures. Because the hydrogen in Hill's specimens was present naturally in the asgrown crystal as compensation for the trivalent impurities (principally aluminum), the higher activation energy at the lower temperatures may represent the trapping energy of the proton at a n A13 ÷ impurity site, and the lower activation energy (0.40 eV) would be that for diffusion. In the present study, the diffusing tritium is in excess of that required to compensate for any tri- or divalent impurities present in the crystal. The measured activation energies, therefore, may be assumed to represent the diffusion process itself. Tritium diffusivity in rutile is predominantly along the c-axis but with a significant component in the basal plane (along the a-axis). Such behavior is expected in view of the nature of the crystal structure of rutile; fairly open channels of low electron density exist for interstitial diffusion in the c-direction (Fig. 1). These channels are also believed to play a significant role in the diffusion of substitutional impurities, such as iron or chromium, and may even influence diffusion of titanium in the oxide 24.25 The measured anisotropy of D c / D . ~ 200 for tritium is, however, considerably less than the factor of 10 s reported for lithium diffusion between 80 ° and 360°C16. This difference in magnitude of the anisotropy of the t w o diffusants m a y reflect a correspondence between the relative "size" of the diffusants and the barrier to basal plane diffusion. The

barrier to c-axis diffusion of H ÷ is about 0.1 eV according to the calculations of Kingsbury e t al. 2 8 . Although calculations were not made for basal diffusion of H ÷ , the energy barrier should be larger than for c-axis diffusion in analogy with lithium diffusion, where the calculated energy barriers are 0.11 and 3.2 eV for c-axis and basal plane diffusion 26 The measured values for tritium are 0.40 and 0.57 eV, respectively. The relatively small difference between the activation energies for cand a-axis diffusion observed in the case of tritium may be attributed to the smaller size of the diffusant.

CONCLUSIONS

Tritium diffusivity in rutile has several n o t e w o r t h y characteristics: A pronounced anisotropy in both the diffusion coefficient (7.5 × 10 - 6 cm2/sec IJ caxis and 2.7 × 10 - 6 c m 2 / s e c !1 a-axis) and activation energy (9040 cal m o l e - 1 OK-1 II c-axis and 13,100 cal mole - 1 °K - 1 II a-axis). Activation energies of the same magnitude as for hydrogen diffusion in metals. Diffusion rates are 102 to 104 less than for s-titanium at the same temperatures. These results indicate that TiO 2 films should inhibit hydrogen absorption by ~-titanium. ACKNOWLEDGEMENTS

The author wishes to thank M.R. Louthan, Jr., and S.P. Rideout for their interest in and encouragement of this investigation. The spark source emission spectroscopy was provided by B. Tiffany and the mass density measurements by C.W. Krapp of the Savannah River Laboratory.

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17 R. Haul and G. Dumbgen, J. Phys. Chem. Solids, 26 (1965) 1. 18 V.N. Bogomolov, Soy. Phys. Solid State, 5 (1963) 1468. 19 D.F. Chester and D.H. Bradhurst, Nature, 199 (1963) 1056. 20 G.J. Hill, Brit. J. Appl. Phys., 21 (1968) 1151. 21 P.J. Fitzgerald, M.L. Eidinoff, J.E. Knoll and E.B. Simmel, Science, 114 (1951) 494. 22 M.R. Louthan, Jr., D.E. Rawl, Jr. and R.T. Huntoon, Corrosion, 28 (1972) 172. 23 J. Crank, The Mathematics of Diffusion, Oxford, 1956. 24 J.P. Wittke, J. Electrochem. Soc., 113 (1966) 193. 25 H.B. Huntington and G.A. Sullivan, Phys. Rev. Letters, 14 (1965) 177. 26 P.I. Kingsbury, Jr., W.D. Olsen and O.W. Johnson, Phys. Rev., 175 (1968) 1099.