Fluence and temperature dependence of swelling in irradiated molybdenum

JOURNAL OF NUCLEAR MATERIALS 48 (1973) 339-350.0

NORTH-HOLLAND

PUBLISHINGCOMPANY

FLUENCE AND TEMPERATURE DEPENDENCE OF SWELLING IN IRRADIATED MOLYBDENUM J.L. BRIMHALL, E.P. SIMONEN and H.E. KISSINGER Bat&l/e Memorial Institute, Pacific Northwest Laboratory, Richland, Washington99352, USA

Received 25 June 1973

Volume changes have been analyzed in molybdenum which has been neutron irradiated to various fluences over the temperature range 50 to 1300°C. This data together with all previously reported data has been compiled into a three-dimensional plot of swelling versus temperature versus fluence. Significant low temperature swelling, < 4OO”C, is observed and is consistent with the presence of isolated immobile vacancies. Void swelling only becomes significant at temperatures ? 400°C. The nature of the dislocation and void microstructure at high irradiation temperatures are analyzed quantitatively as a function of irradiation temperature and the results are reasonably consistent with a recent model of Brailsford and Bullough. The same model is also consistent with an observed trend towards saturation in the void swelling at high fluences at the low temperature end of the void region. Les variations de volume du molybdene irradii aux neutrons ‘adiff~rents flux sur le domaine de temperature de 50 fi 1300°C ont etd d&ermi&es. Ces don&es jointes a toutes celles publiees ant~rieurement ont eti: compilees dans un diagramme a trois dimensions gontlement en fonction de la temp&ature et de la fluence. Un gonflement important a et6 observe i basse temphrature (< 400°C) qui est attribuable a des lacunes isolees et immobiles. Le gonflement dfi i des cavitds devient seulement important aux temperatures superieures ‘a4OO’C. La nature de la microstructure de dislocations et de cavites observables aux temperatures d’irradiation dlevees est analyse’e quantitativement comme &ant fonction de la temperature d’irradiation et les resultats obtenus sont en accord satisfaisant avec un modble recent propose par Brailsford et Bullough. Le m&me moddle est aussi en accord avec le fait qu’on observe une tendance a la saturation dans le gonflement par cavite’s sous flux &ves dans le domaine inferieur de temperatures ou se forment des cavitks. In Molybdln, das mit verschiedenen Neutronendosen zwischen 50 und 1300°C bestrahlt wurde, wurden irnderungen des Volumens beobachtet. Diese Ergebnisse werden zusammen mit allen frtiher veriiffentlichten Daten in einem dreidimensionalen Diagramm des Schwellens ah Funktion der Temperatur und der Dosis dargestellt. Ein ausgepragtes Tieftemperaturschwellen wird unterhalb 400°C beobachtet, es ist mit der Gegenwart von isolierten, unbeweglichen Leerstellen vereinbar. Das Porenschwe~en ist nur oberhalb 400°C bedeutend. Das Wesen der Versetzungs- und Porenstruktur bei hohen Bestrahlungstemperaturen wurde in Abhangigkeit von der Bestrahlungstemperatur quantitativ untersucht, die Ergebnisse stimmen mit einem kiirzlich verb’ffentlichten Model1 von Brailsford und Bullough iiberein. Dasselbe Model1 ist ebenfalls mit der beobachteten Tendenz der Slttigung des Porenschwellens bei hohen Dosen und dem unteren Temperaturbereich des Porenschwellens konsistent.

1. Introduction The study of void formation in metals during irradiation has continued at a brisk pace for approximately five years. Within this time, considerable data have been accumulated for several materials. In the bee metals, most work has been directed towards molybdenum. Sufficient data have been generated that more detailed analysis of the swelling in molybdenum as a function of dose and temperature can be initiated.

This report attempts to describe the swelling in molybdenum in terms of basic models over a wide spectrum of dose and temperature. Single crystal and polycrystalline molybdenum have been irradiated in several different reactors over a wide temperature range and the resultant swelling has been evaluated by length change measurements and transmission electron microscopy. This swelling data together with previously reported data have been plotted on a three-dimensional representation

340

J.L. Brimhall et al., Swelling in irradiated molybdenum

of swelling, fluence and temperature. The swelling behavior within the various fluence-temperature regimes is then described in terms of known atomic behavior and models. This is a first attempt at a large over-view of swelling, and refinements are expected as more data are acquired.

2. Experimental

procedures

2.1. Material condition The specimen material used in the work newly reported was either triple-pass zone-refined single crystals, polycrystalline rods, or high purity polycrystalline foil. The single crystals and polycrystalline rods were used for determining length changes, and the foils were used for transmission electron microscopy studies at high irradiation temperatures. The purity of the single crystals was better than 99.99%, and that of the polycrystalline foils was approximately 99.95%. The purities of molybdenum used by the other investigators ranged from commercial purity to zone-refined, high purity material. Although it is expected that purity would have some effect on void formation, there was no way to take it into account in any systematic manner. Therefore, all data are considered without any regard to metal purity. All material has been reported to be irradiated in the annealed condition. 2.2. Irradiation conditions Data reported here for the first time were obtained from irradiations in the ETR, EBR-II, and one of the Hanford Reactors. The particular irradiating conditions are described for each reactor. 2.2.1. ETR Most of the high temperature irradiations were pep formed in ETR. Only foil specimens were irradiated at the high temperatures, > 6OO”C, and these were placed in a helium-filled molybdenum capsule. The foils were in intimate contact with the capsule ends. This molybdenum capsule was placed in a larger capsule in which the temperature was maintained by gamma heating and controlled by adjusting the thermal conductivity of an argon gas gap. The thermo-

couple was at some distance from the specimens so the actual temperature had to be estimated based on expected heat transfer and gamma heating. Several capsules had the thermocouples in contact with the small molybdenum capsule which provided a much more accurate indication of the specimen temperature. From these specimens, the width of the grain boundary zone which was denuded of voids was plotted as a function of reciprocal temperature. The denuded zone width from material for which the temperature was not known accurately was plotted on the same curve. Based on the criteria of denuded zone width as a measure of temperature, a more confident estimate could be made. Some of the single crystals were irradiated in the ETR in the cold and hot water test loops. The temperatures were 5O’C and 28O”C, respectively, for the test loops. The crystals were in helium filled, aluminum capsules encased in stainless steel, and depended upon intimate contact between the crystal and capsule wall for thermal conduction. 2.2.2. Hanford reactor Irradiation in the Hanford reactor was either at reactor ambient temperature (40-6O’C) or at elevated temperatures > 350°C. The irradiation conditions have been described in previous publications [ 1,2]. The length change data reported here were for irradiations in the temperature range 60°C to 45O”C, and polycrystalline foil specimens were irradiated at elevated temperatures, )i 450°C. Specimens irradiated in the range 350 to 450°C were in a capsule in which the temperature was controlled to + 5°C. At the high temperatures, 650-8OO”C, the temperature is only known to f 20°C. 2.2.3. EBR-II Irradiations in EBR-II were performed in sodium or NaK filled capsules. There was no temperature control and the temperature corresponded to the temperature of the reactor coolant. This temperature was in the range 450-480°C. For the details of the irradiation from other investigators which are reported here, the reader is referred to the original references. All the neutron fluences are corrected to correspond to neutron energies greater than 0.1 MeV. There are no adjustments for differences in neutron energy

J.L. BrimhaN et al., Swelling in irradiated molybdenum

spectra. A temperature correction is made to account for the differences in neutron flux. The relationship first proposed by Bullough and Perrin [3 ] is used and is given by

R,/D, =K,/D, , where K, and K2 are the defect generation rates (flux) and D, and D, are the diffusion coefficients at temperatures T, and T2. The flux in ETR, 2 X 1014 n/cm2*sec, is used as a standard since most fluxes were near this value. This temperature shift is only applied in the temperature regime of void formation. The difference in flux among the different reactors is not great and the maximum calculated temperature shift is only about 50°C. Typically, the calculated shift is within the accuracy of the temperature measurement. Some ion bombardment data is also included for comparison purposes and the temperature shift is much greater due to the much higher dose rates used in heavy ion bombardment. 2.3. Determination

of volume

change

At temperatures < 45O”C, the volume change was determined by measuring the length change of single crystals and polycrystalline rods after irradiation. Details of the technique have been in a previous publication [4]. The accuracy of the technique is estimated at 1 part in lo5 or of + 0.001% AL/L (0.003% AV/v). At temperatures > 45O”C, the volume change was determined by measuring void size and concentration using transmission electron microscopy. For small void sizes of Q 70A, the voids were measured in the over-focused condition. For larger void sizes, the diameter was measured to the inside of the black ring in the underfocused condition. Some data previously reported have been recalculated in light of advances in image contrast theory in electron microscopy. Although polyhedral shapes were observed for the larger voids, only spherical shapes were assumed when calculating void volume. This procedure was adopted so as to be consistent with that reported by other investigators. The foil thickness was calculated by stereo determination or estimated from the number of thickness fringes The estimated accuracy varied depending on the particular specimen, but could be as great as f 50% in the calculation of the total void volume. In a number of the foils, the dislocation density

341

was also calculated. The line intersect method was used in which the dislocation density pd is given by pd = 2N/Lt, where N is the number of intersections with dislocation made by random lines of length L, and t is the foil thickness.

3. Results Table 1 lists the volume change in molybdenum calculated from the irradiation induced length change of single crystals. Some of the work has been reported previously and is duly referenced. Included also are some data on bulk density changes due to irradiation. Table 2 lists the void parameters and volume changes for molybdenum calculated from transmission electron micrographs. Data from other sources are also listed and are referenced. When a temperature correction was applied due to differences in neutron flux, the corrected temperature is also given. An example of the void microstructure as a function of temperature is shown in fig. 1. At a temperature of 45O”C, it was possible to compare the volume change calculated by length change and that calculated from void measurements. At a low fluence of 7 X 10lg n/cm2, the AVIV was 0.010% and 0.0 15 % from length change and TEM measurement, respectively. At 8 X 1021 n/cm2, the corresponding values were 0.90% and 0.75 %. The agreement is within 30% which is quite reasonable when considering the inaccuracies in determining volume changes by TEM, particularly at the very small void sizes. No voids were positively identified at irradiation temperatures i 400°C. It is possible some voids were present below the resolution limit of the electron microscope. The available ion bombardment data on void microstructures are listed in table 3. The details of the bombardment are given in the appropriate references. A value of 80 dpa was assumed to be equivalent to the damage produced by 1 X 1O23 n/cm2 for the purposes of comparing ion bombardment and neutron data. The swelling data listed in tables l-3 are plotted on a three-dimensional plot of log dose versus temperature versus log swelling, fig. 2. The swelling values are plotted on the vertical axis. The base represents a swelling

342

J.L. Brimhall et ai., Swelling in irradiated molybdenum

Table I Volume changes in molybdenum neutron irradiated in the temperature range 50 to 450°C. Sample

Reactor

Temp. eo

Fluence X 10s21 n/cm2) (E > 0.1 MeV)

AV/V(%)

A B C D E F G H I .I K L

Hanford Hanford Hanford NRX ETR ETR ETR ETR Hanford Hanford Hanford EBR-II

40 40 40 50 100 100 280 280 350 400 450 450

0.03 0.15 0.3 0.07 0.15 0.5 OS.5 0.5 0.07 0.07 0.07 8.0

0.08

-

Ref.

-_ ~____

0.14 0.15 0.08a) 0.07 0.15 0.06 0.11 0.025 0.012 0.010 0.9

I51 ]51 [51 ]61 This work ,t 2, .I Yf $9 ,, 11

a) Measured bulk density change Table 2 Void parameters and void volume in molybdenum neutron irradiated in temperature range 450-I 300°C. Sample

Reactor

Temp. ( Tcbrr) (“C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1.5 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Hanford EBR-II HFR (Bel) EBR-II HFR (Bel) SILOE DFR Hanford ETR ETR ETR ETR ETR Hanford HFR (Bel) ETR EBR-II SILOE Hanford ETR SILOE ETR ETR ETR ETR ETR SILOE ETR ETR ETR

450 460 440 585 600 600 640 650 665 700 708 725 755 750 760 785 790 800 800 900 900 970 985 1000 1050 1150 1200 1230 -1300 -1380

(440) (45 0) (560)

(613) (703)

(815) (780) (755) (870)

Fluence Void (X lo-’ n/cm2) diameter (E > 0.1 MeV) (A)

Void concentration tx lo-l5 cm3)

AV/V (%)

Ref.

0.075 8.0 0.7 25 0.52 0.5 20 0.15 0.85 0.4 0.6 1.04 1.37 0.15 0.49 0.73 25.0 0.5 0.1 1.61 0.5 1.96 1.26 0.4 0.9 0.9 0.5 1.68 1.98 2.74

20-40 100 50 72 20 80 100 35 20 30 I 6.0 5.0 20 S 3.5 54 10 10 4 3 0.6 0.35 0.5 0.12 0.05 0.1 0.01
.0.015 0.75 0.04 1.10 0.07 0.1 0.55 0.028 0.07 0.1 0.06 0.11 0.11 0.045 0.03 0.08 1.20 0.2 0.045 0.09 0.2-0.4 0.12 0.47 0.19 0.17 0.28 0.2 0.032 co.01

This work I,

20-25 52 25 64 40 20-30 40 25 35 40 55 65 70 35 50 75 72 80 45 65 80-200 140 263 200 290 470 300-600 830 -800 No voids

a) Work previously recorded in ref. [ 131, but more accurate determination

of void sizes is presented in this work.

]71 ]81 ]71 [91 [lOI This worka) 1. ]lll This work ,* ,, *a) l

]7] This work I81 [91 This work a) f, 191 This work 7,

1111 iI21

I121 I91 This work >>

760 _='c @I

I.985 .~- “C (cl

Fig.1. Void structures in molybdenum irradiated to approximately 985“C, (d) 123O’C.

1230'~ Cd) 1 X 10zl n/cm2 (E > 0.1 MeV) at (a) 72O”C, (b) 760°C, (c)

344

J.L. Brimhall et al., Swelling in irradiatedmolybdenum

Table 3 Void parameters and void volume in molybdenum Sample

Ion

31

32

2 MeV N+ 5 MeV Ni++

800

593

33 34 35 36

MeV Ni++ Ni++ 900 66 MeV 1000 7.5 MeV Ta+++ 900 7.5 MeV Ta+++ 900

644 706 632 632

Temp. (“0

870

a) More accurate determination

ion bombarded in temperature range 800-1000°C.

Temp. corr. CC,

dpa

Equivalent fluence (nvt n/cm’)

632

100

5

1.2 x 1oz3 ; ; ;I$

tS”

55 38 113

7x 102’ 5 x 1o22 1.4x 1o23

60 120 55 65

Void Concentration (X lo-l6 cm-j)

AVIV (%)

Ref.

19.0 5.0

0.6

iI41

0.23

[15]a)

4.0 0.5 5.0 6.0

0.43 0.48 0.42 0.8

This work This work

;;$

of the void parameters given in this reference have been made.

value of 0.01%. The ion bombardment data are noted separately by the large square data points. All data are treated equally and there is no attempt to categorize the data from the various investigations. The scatter in the data is quite pronounced and therefore, no attempt was made to draw a smooth curve through the points. The actual curves shown are

Fig. 2. Three-dimensional

Void diameter (A)

representation

based on a theoretical analysis which is discussed in the following section. However, the indicated fit is reasonable within those regions for which there is sufficient data. Except for the temperature region between 450 and 75O”C, there is a lack of data at the high neutron fluences > 1O22 n/cm:!. The extension of the curve to these high fluence regions is based solely on an intuitive extrapolation.

of the temperature and fluence dependence of swelling in irradiated molybdenum.

345

J.L. BrimhaN et al,, Swelling in irradiated molybdenum

The shape of the three dimensional plot can be qualitatively described as follows. At low fluences, there is significant swelling at low temperatures which, however, decreases with increasing temperature and reaches a minimum at approximately 400°C. The swelling again increases to a maximum at lOOO1100°C. At low temperatures, the swelling increases slowly with fluence. At higher temperatures, the swelling increases more rapidly with increase in fluence at least up to fluences of ,1021 n/cm2. There is indication of saturation or levelling off of the swelling at higher fluences. The minimum in swelling observed at 400°C at low fluences seems to be erased at high fluences.

4. Discussion and analysis of the data In order to facilitate the analysis, the data are categorized at several groupings. The low temperaturelow fluence region corresponds to temperatures G4OO”C and fluences less than 1021 n/cm2. The high temperature-low fluence region corresponds to temperatures> 4OO’C and fluences < 2 X 1021 n/cm2. The high temperature-high fluence region is restricted to temperatures, 450°C < T < 790°C and to fluences >” 1O22 n/cm2. There is no data at the very high fluence outside of this temperature range. 4.1. Low temperature-low fluence regime At temperatures below 400°C swelling is observed in the absence of visible voids. Swelling in this temperature region is best characterized by an accumulation of isolated immobile vacancies. The rate of accumulation of point defects during irradiation is dependent on three processes: (1) the generation rate K, (2) the recombination rate R, and (3) the rate of diffusion of defects to sinks. The processes are related by the following equation for interstitials: dci x=K-R-Dicipd

(1)

and for vacancies

dC” z=K-R-

(2)

Dvc”Pd ’

Di and D, represent the diffusivities

of interstitials

and

vacancies, respectively, whereas Ci and c, represent their respective concentrations. pd is the density of dislocation sinks including network dislocations, interstitial loops and vacancy loops. The recombination rate,k, is expressed as R = aDicicv,

(3)

where (Y= MZ/a2PN0 ,

(4)

M is the molecular weight, Z the number of nearest neighbor atomic sites, a the lattice parameter, p the mass density, and N, Avogardro’s number. There is experimental evidence that interstitials migrate freely below room temperature in molybdenum [ 161. A rapid interstitial diffusivity insures that a steady state concentration of interstitials is achieved readily, thus eq. (1) should equal zero. The effective generation rate Keff is defined as KeE=K-R.

(9

At steady state eqs. (1) and (5) combine to give

(6)

DiCi = Ke,I Pd .

Eqs. (3), (5), and (6) combined with eq. (2) describe the rate of accumulation of vacancies in terms of the pertinent parameters. Thus,

dC” K -= 1 +cQpd dt

-DvCvPd

*

In the temperature region where the vacancy is essentially immobile, D, g 0, eq. (7) integrates to give CXC’

For small cv, i.e., cv Q 2pd/& the swelling is linear with time but for large c,, i.e., c, 3 2pd/o, the time dependence is c,

z

2pd

llKt.

For the present case of interest Q is 1.26 X 1OW7cm and Pd = 1010/cm2. The swelling has a one-half power dependence on time if the free vacancy concentration is greater than 2 X 1017/cm3 which represents 0.0003% swelling. The experimental swelling values would indicate vacancy concentrations much greater than this and therefore the one-half power dependence is justified.

J.L. Brimhall et al., Swelling in irradiated molybdenum

346

With increasing temperature, the vacancy diffusion term in eq. (7) cannot be neglected. If it is assumed that cv S 2pd/(r, then the integration of eq. (7) gives a more general result in terms of time (fluence) and temperature,

CT,‘=--&[l -exp(-2D,pdt)]

.

”

(10)

A comparison of eq. (10) with observed low temperature swelling of molybdenum indicates that the one-half power dependence on time at low temperatures is a reasonable conclusion. The predicted magnib tude of the swelling at the lower experimental temperatures is larger than observed presumably due to the athermal formation of vacancy loops. Vacancy loops have been reported in molybdenum irradiated at low temperatures [ 16,171. These loops account for a fraction of the generated vacancies which are not contributing to swelling. A pronounced reduction in swelling with increasing temperature is predicted by eq. (10) and the experimental results show a reduction in the range 300400°C. This decrease in c, is consistent with an activation energy of 2.0 eV for vacancy migration. An activation energy of 1.5 eV was also considered. However, this lower activation energy predicted a reduction in swelling at 230°C. In this case the observed swelling between 230°C and 400°C would have to result from voids if vacancies are mobile at these temperatures. Attempts were made to observe voids in this temperature region. e.g., at 280°C but none were observed. Furthermore, it is difficult to understand why the void swelling would pass through a minimum at 400°C if voids were present at temperatures as low as 230°C. It is concluded that an assumed activation energy of 2.0 eV for vacancy migration is reasonably consistent with observed swelling in molybdenum. Eq. (10) then properly describes the fluence and temperature dependence in molybdenum below 4OO’C if a correction is made for athermal formation of vacancy loops at temperatures where the vacancy is immobile.

A model of swelling, presented recently by Brailsford and Bullough, was used to test a fit to the data [18]. The model basically uses rate theory as a means of determining a swelling rate and the roles played by the various defect sinks are analyzed in quantitative detail. An approximate swelling formula is presented which includes the role of the defect sinks specifically. The equation for the volume change in percent is given as

‘where F(n) describes the temperature and is given by

F(q)=+{1 +Q}+1 -+nexp

dependence

(-:-

[

(;-$]],(ll)

where

(12)

n=4OOexp[-$J(t-k)],

T, = low temperature at which swelling is - 0.1 of maximum value, T, = high temperature at which swelling terminates, Q = activation energy for self-diffusion, and EA= activation energy for vacancy motion. S is the defect sink term and is given by

S=p,4~r&l [(Pd+4~rsCs)(Pd+4nrsCs+4nrpCp)l ,

4.2. High temperature-Low jluence regime ThiS region is characterized by extensive void formation. Voids were present at the lowest fluence observed, so it is not possible, to establish an incubation period for void nucleation.

0.0

I

400

I

I

600

1

I

800

1

TEMPERATURE

I

1000

I

1

1200

1

1

140

'C

Fig. 3. F(q) as a function of temperature for neutron irradiated molybdenum.

347

J.L. Brimhall et al., Swelling in irradiatedmolybdenum

THH

FLUENCE)

Pd

BOO

600 IRRADIATION

1000

1200

1,

TEHP OC

Fig. 4. The parameters Pd and 4 nrsCs as a function of temperature for neutron irradiated molybdenum. Numbers refer to table 2. where pd = dislocation density, rs = radius of neutral sinks, i.e., voids, C, = concentration of neutral sinks, i.e., voids, and 47rrpCp = sink term for precipitates = 0 for pure molybdenum: Pd 4srsCs ’ z (pd + 4nrsCs>2 .

(13)

F(r)) was calculated for molybdenum using Q = 4.0 eV [19] andE& = 2.0 eV. Based on the experimental data, the value of T, was estimated to be 400°C and

Tf to be 14OO’C. A plot of F(q) as a function of temperature is shown in fig. 3 based on these parameters. In order to calculate S, pd and 4nrsCs are plotted as a function of irradiation temperature in fig. 4. The value of 4nrsCs was computed from the void data given in table 2. The numbers on the plot corresspond to the data number in table 2. The dislocation density pd was determined from the transmission electron micrographs of a number of selected specimens. Again there is much scatter in the data, but there is a definite trend. Smooth curves were drawn through the data and values of pd and 4nr,C, taken from these smooth

348

O.OO

J.L. Brimhall et al., Swelling in irradiated molybdenum

11

400

j

1

600

I

800

I

1

1000

TEMPERATURE

1200

I

I

1400

'C

0.00,

, 400

, 600

,

/ 800

,

j 1000

TEMPERATURE

,

1 1200

,

, 140

'C

Fig. 5. S as a function of temperature in neutron irradiated molybdenum. S computed from data given in fii. 4.

Fig. 6. The product F(q) .A’(figs. 3 and 5) as a function of temperature in neutron irradiated molybdenum.

curves were used to compute S. The several high fluence points are considered separately and are discussed in the next section. A plot of S as a function of temperature is shown in fig. 5. The curve demonstrates that the contribution to void growth is greatest when the dislocation and voids are about equally effective as sinks. This occurs at low temperatures where the dislocation density and void density are high and at very high temperatures where the two curves in fig. 4 intersect. Fig. 6 shows a plot of F(Q) .S as a function of temperature. The curve is not symmetrical, but has a shoulder on the low temperature side. A maximum swelling value was estimated from the data at a fluence of 5 X lO*O n/cm*. This value of swelling was used as a scale factor and a curve was drawn to fit the basic shape of fig. 6. The value of S was assumed to be constant between 1 X lO*O n/cm* and 1 X lO*l n/cm* so the swelling is linear with fluence over this range. It is this curve which is shown in the three-dimensional plot (fig. 2) between 1 X lO*O and 1 X lO*l n/cm* and at temperature > 450°C. The trend in the data indicates a reasonable fit to this type of curve in this fluence range. The peak temperature can be altered and the ratio of the peak height to shoulder height can change depending on the exact position of the pd and 4nr,Cs curves in fig. 4. The basic trend of the variation in pd and 4nr,C, with tempera-

ture is intuitively expected. However, even using the outer limits of the experimental data for calculating S, the basic shape of the curve in fig. 6 is not altered. The selection of the temperature limit of void formation, T, and Tf is somewhat critical, but the values chosen are felt to be the best, based on available experimental evidence. Therefore, it is shown that the experimental data on void formation in molybdenum can be fitted quite well to the model of Brailsford and Bullough in the fluence range 1 X lO*O to 1 X lo*] n/cm* and in the temperature range 400-1400°C. 4.3. High temperature-high

jluence

The data at high fluence is restricted to several data points in the temperature range 450-780°C. The value of the void sink term 4nrsCs was significantly higher for these data than for the lower fluence data. There was only one data point for dislocation density and this showed a somewhat lower dislocation density at the higher fluence than at the lower fluence. This is not unexpected as other work has shown a saturation or decrease in the dislocation density with increase in fluence [20]. Therefore, in the calculation of S at the high fluence, pd has the same values as the lower fluence but higher values of 4nr,C, are used. Such a calculation results in lower values of S than are shown in fig. 6. The swelling values are therefore lower than

349

J.L. Brimhall et al., Swelling in irradiated molybdenum

would occur if the value of S were constant. The shape of the curve between 450-800°C in fig. 3 at 2.5 X 1022 is based on this lower value of S. The extrapolations to temperatures lower than 450 or greater than 800°C follow the existing trend of the curves. In essence, the increase in the effectiveness of the void sinks relative to the dislocation sinks at the high fluences causes a net decrease in the void growth since more of both types of point defects are going to the voids. It is this factor which is causing the curve of swelling versus fluence to ‘bend over’ at the higher ffuence. It would be difficult to explain complete saturation by this mechanism since one of the sink effectiveness terms must go to zero. However, the model is actually only valid below saturation. At these high fluences, the void lattice forms and it is the presence of this lattice which influences saturation [ 10, 21,221. At the lower fluences, there was insufficient data at any one temperature to determine if S is decreasing with fluence. There is indication that at the high temperatures the swelling dependence is less than linear at fluences even below 1021 n/cm2. Initially both dislocations and void concentration could be increasing in such a fashion as to keep S nearly constant. Eventually, the dislocation density begins to saturate or decrease causing a decrease in 5’.At the high temperatures, this condition may occur early and therefore the linear portion of the curve can be rather short.

The variation in swelling with temperature is found to be reasonably described by the model of Brailsford and Bullough. A linear dependence of swelling on fluence is postulated up to a fluence of 1 X 1021 although the linear region may be short at the high temperatures. The minimum in the swelling observed near 400°C is less evident at higher fluences since the swelling at the high temperatures, > 4OO”C,increases faster than that at low temperatures. High temperature-high

The swelling levels off at high fluences. This levelling off is compatible with the changes in the void and dislocation sink structure which are observed. Much more data need to be acquired at the very high fluences. The overall fit of the data to the models which have been presented is reasonable considering the scatter in the data, different purities, lack of accurate temperature measurement, etc. As more data become available, particularly in those regions lacking data, the shape of the three-dimensional plot will be modified.

References 111B. Mastel and J.L. Brimhall, Acta. Met. 13 (1965) 1109.

vt J.L. Brimhall

5. Conclusions Data on the swelling in irradiated molybdenum has been compiled for a wide spectrum of temperatures and fluence. Models have been derived or existing models used to explain the behavior. The following conclusions have been made on swelling within certain temperature-fluence regions: Low fe~per~~~e-law

ffuence

Swelling is due to isolated immobile vacancies. The swelling decreases with temperature beyond approximately 300°C as vacancies become mobile and go to sinks. Void formation eventually causes swelling to increase apain. Swelling can be shown to depend on (fluence)? at temperatures where vacancies are immobile.

fluence

and B. Mastel, Rad.Effects 3 (1970) 203. [31 R. Bullough and R.C. Perrin, Irradiation Effects on Structural Alloys for Nuclear Reactor Applications, ASTM-STP484 (1970) p. 317. [41 H.E. Kissinger, J.L. Brimhall and B. Mastel, Materials Research Bulletin 2 (1967) 437. 151 H.E. Kissinger, J.L. BrimhaB, B. Mastel and T.K. Bierlein, Int. Conf. on Vacancies and Interstitials in Metals, ed. J. Diehl, W. &hilling and D. Schumacker (Kernforschungsalage Jiilich, Germany, 1968) p. 681. f61 C.R. Piercy and R.H. Tuxworth, The Effect of Fast Neutron Irradiation on the Density, X-ray Lattice Parameter and the Line Breadth of Metals,CRRM-1010 (1961). f-u J.D. Elen, C. Hamburg and A. Mastenbrock, J. Nucl. Mater. 39 (1971) 194. [81 F.W. Wiffen, Radiation Induced Voids in Metals, ed. J.W. Corbert and L.C. Ianniello (US Atomic Energy Commission, Wash., DC.) p. 386. (91 Y. Adda, ibid, p. 31. [lOI B.L. Eyre and A.F. Bartlett, AERE (Harwell) R-7027 (1972). illI R.C. Rau, R.L. Ladd and J. Moteff, J. Nucl. Mater, 33 (1969) 324.

350

J.L. Brimhall et al., Swelling in irradiated molybdenum

[12] G.L. Kulcinski, B. Mastel and J.L. Brimhall, Rad. Effects

2 (1969) 57. [ 131 J.L. Brimhall, H.E. Kissinger and G.L. Kulcinski, The Effect of Fast Neutron Irradiated on the Density, X-ray lattice Parameter and the Line Breadth of Metals, CRRM1010 (1961) p. 338. [14] J.H. Evans, Rad. Effects 10 (1971) 55. [ 151 G.L. Kulcinski, J.L. Brimhall and H.E. Kissinger, Radiation Induced Voids in Metals, ed. J.W. Corbert and L.C. Ianniello (USAEC, Washington D.C.) p. 449. [16] D.M. Maher, M.H. Loretto and A.F. Bartlett, Phil. Mag. 24 (1971) 181. [ 171 B.L. Eyre, D.M. Maher and A.F. Bartlett, Phil. Mag. 23 (1971) 439.

[ 181 A.O. Brailsford and R. Bullough, J. Nucl. Mater. 44 (1972) 121. [ 191 J. Askill, Diffusion in body-Centered Cubic Metals, ed. J.A. Wheeler and F.P. Winslow (ASM, Metals Park, Ohio, 1965) p. 247. (201 J.A. Hudson, D.J. Mazey and R.S. Nelson, Voids Formed by Irradiation of Reactor Materials, ed. SF. Pugh, M.H. Loretto and D.I.R. Norris (AERE, Harwell, 1971) p. 213. [21] G.L. Kulcinski and J.L. Brimhall, Ordered Defect Structures in Irradiated Metals, 6th Int. Symposium on Effects of Raddiation on Structural Materials, ASTM, STP, in press. [22] J.L. Brimhall and G.L. Kulcinski, Void Formation in Ion Bombarded Niobium, Radiation Effects, to be published.