Vacancy trapping in plastically deformed metals studied by hyperfine interactions

Volume 84A, numberS

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3 August 1981

VACANCY TRAPPING IN PLASTiCALLY DEFORMED METALS STUDIED BY HYPERFINE INTERACTIONS ~ Gary SCOTT COLLINS, Gil P. STERN

and Christoph HOHENEMSER

Department of Physics, Clark University, Worcester, MA 01610, USA Received 6 April 1981

Site populations of ~ In probes in Ni and Cu with vacancy defects trapped after plastic deformation were measured by time differential perturbed angular correlations. Isochional annealing studies show the same defect hyperfine interaction frequencies observed after quenching, irradiation, and ion implantation. Measurements on Ni as a function of deformation yield “dose” curves which are closely correlated with the three stages of mechanical hardening.

In recent years hyperfine interactions detected by nuclear radiation have been widely applied to study the formation, migration and trapping of point defects and small point defect clusters in cubic metals. Typical experiments involve Mbssbauer effect and perturbed angular correlations of gamma rays (PAC). The principal observed effect is formation of bound states between defects and radioactive probe atoms that are present in extreme dilution. The first Mnssbauer experiments, done by de Waard and collaborators more than 10 years ago [I], showed that Fe exhibits unique magnetic hyperfine splittings associated with vacancy-type defects trapped on oversized, implanted probe atoms such as 1311 and 131Xe. The first reproducable PAC experiment, done by Andreeffet a!. in 1974 [2] showed that implantation of 1~4ninto Ni leads to a unique hyperfine field associated with a defect trapped on the ~~1n probe. In addition it has been shown both by Mossbauer spectroscopy [3] and PAC [4] that trapping of defects is followed by subsequent detrapping at a higher temperature; and that in addition to magnetic hyperuine interactions in magnetic metals, electric quadrupole interactions in non-magnetic metals offer a powerful tool for “flagging” trapped lattice defects [5]. FinalResearch supported by National Science Foundation grants DMR 77-01250 and DMR 80-02443. Undergraduate research participant.

ly it has become clear that trapped states may be efficiently formed not only following ion implantation of probe atoms (for which defects are strongly correlated with probe position), but also for quenched and irradiated samples (for which probe and defect position are uncorrelated). A particularly extensive demonstration of this fact has been given by the Konstanz group [6]. For fcc metals 111 hi PAC data are now sufficiently extensive to permit systematic classification of the observed defect structures, using such experimentally derived parameters as the quadrupole interaction strength, the electric field gradient symmetry, and the manner of trap formation (thermal versus athermal). For example, in a forthcoming review of the available literature, Pleiter and Hohenemser [7] identify 19 WIn-vacancy traps in Ag, Al, Cu, Ni, Pd, Pt and Au, and provide a structural classification that includes the nearest-neighbor monovacancy, divacancies (or faulted loops in the {l I 1} plane), and tetrahedral clusters of cubic symmetry. A comparable systematic interpretationis given in a forthcoming paper by Wichert and Recknagel [8]. While implantation, irradiation and quenching all yield essentially the same defect states, there are some significant differences between the methods. Thus, implantation leads to athermal trapping of vacancies below normal vacancy migration temperatures, and pro. duces the largest fractional populations of thermally 289

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activated multi-vacancy defects. Both effectsare presumably related to the correlation of probe atom and defect location as well as the high local concentration of defects around the probe. In contrast, irradiation

To extract interaction frequencics from the PAC spectra, reduced data were fitted to sums of the form ~ G,(w~,t), with population fractions t~and frequencies w1 free, and the appropriate form of G2 for

and quenching result in less complex initial states, exhibit variation of the trapped fraction with dose, and can be interpreted more easily in terms of migration enthalpies. In recent experiments at Clark University we have applied a fourth method plastic deformation to introduce lattice defectssamples into metals. results, 1111n doped of Ni Our and Cu, can obbe tamed for directly compared totthe three other methods of defect production, and help characterize the concentration of trapped defects as a function of deformation dose.

pure magnetic or pure quadrupole interaction. (No attempt was made here to fit combined interactions in Ni.)

—

—

Experimental details. Suitable radioactive sources were prepared by plating carrier free 1111n onto 99.999% purity Ni and Cu foils, followed by diffusion for 1 h in vacuum at 1000 and 800°C,respectively, PAC measurements were made after the samples had

been plastically deformed and/or subjected to a vatiety of isochronal annealing cycles, The(daughter PAC spectra for dthe 175—245 obtained keY cascade 111Cd of 2.7 ‘~1n)were withofa standard four-counter, slow—fast coincidence spectrometer, using data reduction methods described elsewhere [9]. For a magnetic dipole interaction 1IWL = !~~~hf/~ and an electric quadrupole interaction h = (3/20)eQ ~ this leads to perturbation factors of the form G 2(w t) = cos(2w t) ,

G2(~,.i0,t) +

10

,

0.2(1

-~-cos2w0t

+

+ ~cos w0t

Observed frequencies. A summary of frequencies observed after cold rolling is shown in table I. Also shown methods are frequencies previously observed usingTable dif- 1 ferent of defect production [4,6,10]. indicates that frequencies previously seen are reproduced in cold rolling experiments, and no new frequendes are seen. This suggests that plastic deformation generally produces the same In-vacancy bound states as other methods. Thermal activation. In some cases our ‘DIn doped samples were subjected to rolling at room temperature, in others at a temperature of~90K (rollers and sampie immersed in liquid N 2). For both cases spectra were subsequently measured at the temperature of deformation, followed by isochronal anneals at higher temperatures In 7~, andway remeasurement at thesite rolling temperature. this we have obtained populations as a function of temperature as shown in fig. 1. In comparison to previous work these data show activation and detrapping behavior as follows. (1) The ~ = 108 Mrad/s and ~ = 169 Mrad/s de-

Table

1

111111 sites in Ni and Cu by method of defect introduction: frequencies and assigned structures.

(1)

~cos 3~0t),

--

—-—----——-———--—-------—-—

plastic

respectively. Here ~zand Q are the nuclear moments of the 245 keV state; Hhf and are the magnetic hyperfine field and the zz component of the electric field gradient; and w~and W~ are the Larmor frequency and the fundamental quadrupole precession frequency, respectively. The form of G 2(cLIL, t) applies to the special case of a source magnetized perpendicular to the plane of the counters, and the form G2(w0 t) is restricted to nuclear spin 1’ 5/2 and an axially symmetnc electric field gradient oriented randomly with respect to the counter plane. 290

—~

Frequencies (Mrad/s) deformation (this work)

quenching irradiation, implantation

98(1) ~ii~h~i ~L 39(1)

WL”98(l) ~L 39(1)

=

‘~‘L=

=

Assigned structure

Refs. previous work

defect-free multivacancy

14,101 (4,10)

53(5)

comb, interaction

[41

171(1) 109(1) 49(1)

divacancy monovacancy faulted loop

(61 [6) [6]

copper u~= 169(1) 108(1) 47(1) ~

c~iç~ to~

w0

=

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80

,-•~•

/ / .k’ =J\J~ \

40

z

0

I

Ni 98

I’i-r-rt

Cu ~

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PHYSICS LETTERS

5

•108

tions. On the one hand the defects in question may be smaller when produced by cold working, and hence “evaporate” more easily. Such variable size of defects

has been previously suggested by the Konstanz group [6] in relation to the w~= 47 Mrad/s state of Cu. Alternatively, we may be seeing the effect of recrystallization, a process which is known to occur in heavily cold worked Cu and Ni at about the temperatures the defects are observed to disappear till.

.169

C

I

~VF

~

f/I 50

100

Ii

Cu 47

300 TIK)

Fig. 1. Site populations of ‘11ln observed in 15 m isochronal anneals of cold rolled Ni and Cu. Larmor frequencies WL for Ni and quadrupole precession frequencies “o for Cu are identified in the figure. Filled triangles identify temperatures of deformation and measurement. feet states in Cu are activated and destroyed at the same temperatures observed for irradiation, quenching and implantation in earlier work [6]. (2) The ~L ~ Mradfs defect in Ni is thermally activated arid destroyed at the same temperatures as observed in previous work [4,101, but has a larger maximum population. This indicates that vacancy trapping in cold worked samples can in certain cases be even more effective than using other methods, (3) Recovery of the WL = 98 Mrad/s defect-free fraction in Ni occurs at ~700 K instead of at 900— 1000 K as seen in previous irradiation and implantation experiments [4,10]. This suggests that the w 0= 53 Mrad/s combined interaction state (not directly measured here) breaks up at lower temperature in our cold worked samples. (4) Similarly, the ~ 47 Mrad/s defect in Cu is activated at 300 K as in previous work, but breaks up at ~550 K rather than at 700—800 K. The similarity of activation temperatures in the present and previous work further confirm that we are dealing with the same defects. The fact that detrapping occurs at significantly lower temperatures for the 47 Mrad/s state in Cu and the w0 53 Mrad/s state in Ni may have two quite different interpreta-

A thermal processes. Plastic deformation produces two kinds of athermal processes. Defects may trap on 1~~In during cold rolling at temperatures that do not permit free migration. In addition, plastic deformation may strip previously formed defect traps below their thermal dissociation temperatures. Athermal trapping is illustrated in fig. I by the w~ 108 Mrad/s and 169 Mradfs states of Cu, both of which are formed when Cu is rolled at 90K even though their thermal activation is observed at 250 K. Athermal stripping is illustrated by the fact that after Ni samples are annealed to maximize the population of the WL = 39 Mrad/s site (see fig. I), subsequent rolling at room temperature reduces the population to that observed prior to annealing. Athermai activation of monovacancy and other simple traps may be qualitatively understood from current pictures of cold working [12], according to which plastic deformation of more than about 10% leads to dislocation interactions which release substantial numbers of vacancies. Some vacancies may be released within the capture radius of 1~Inprobe atoms, leading to bound states without thermal activation. Using the same picture, athermal stripping may be visualized as the rupture of many defect traps, accompanied by simultaneous, competing athermal activation of traps on other probes. Site populations as a function of dose. For Ni we investigated site populations as a function of deformation “dose”, defined as e = I t/t0, where t0 and t are the foil thicknesses before and after rolling. Foils were rolled and measured at 295 K, with elongation restricted to less than 5% in each pass. As can be seen from fig. 2, while total deformation varied by a factor of 5 in foil thickness, the ~L = 98 Mrad/s defect-free state and the WL = 39 Mrad/s multivacancy cluster roughly follow logistic population curves. Since the —

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polycrystalline aggregates [15] used in our experiments.

E(%) 0

2 4

0

3 August 1981

20

40

80

oo

If we assume that the observed site populations arise from vacancies that are captured during rolling,

+ \

+

_______

70

60-

____________

____________

-

Ni

only small changes in site populations occur in stage I,

98 .39

in which few vacancies are produced; while large changes in population occur in stage II, where the vacancy concentration is known to increase rapidly. Stage III presents a more difficult problem. An obvious “explanation” of the remarkable constancy of

50 o

o •

•_.-.--•

centration of available vacancies becomes constant,

30

I—

throughout this stage is that trap formation and dissociation are in equilibrium over a wide range of deformation. This might happen if the consite populations

\.

~40.

w

I and II correspond quite well with microscopic models; i.e., then the behavior of the populations for stages

20

and if the density of vacancy sinks and the athermal dissociation rate do not change. It can happen in a number of other ways, however, and a full understanding of the mechanisms will only come from future, more detailed studies.

.

0

_•__•_.,

0~~~~

0

_•/•-

0

0.2

0.4

0.6

,~,g

~

1~Insite populations in Ni on deforFig. 2. Dependence mation dose at 295 of K. Here e is the thickness reduction. A~o indicated are the three stages of work hardening of Ni. = 53 Mrad/s combined interaction state (not directly measured) forms at 7~~270 K, and the “CL = 39 Mrad/s multivacancy cluster forms at 350 K, it follows that defect formation must occur here through

both thermal and athermal processes. As a first step in interpreting the data, we note a

remarkable correlation between the population trends and the three stages of work hardening in Ni, also indicated in fig. 2. These stages have microscopic interpretations as follows [13]: Stage I: easy glide of dislocations, with little or rio point defect production. Stage II: multiple glide, with dislocation multiplication and interaction, and considerable point defect production.

Stage III: continued dislocation production and growing dislocation annihilation.

The specific values of stage boundaries shown in fig. 2 were taken from work on single crystals [14]. We chose boundaries for unfavorably oriented crystals, which are expected to correspond to those of the 292

Conclusion. Our exploratory PAC studies of cold worked Ni and Cu have uncovered a number of interesting phenomena related to vacancy defects that promise, through further work, to shed considerable light

on atomic scale processed involved in plastic deformation. References [11 H. de Waard, R.L. Cohen, S.R. Reintsema and S.A. Drentje, Phys. Rev. (1974)P.3760; SR. Reintsema, S.A.BlO Drentje, Schurer and H. tie Waard, Radiat. Eff. 24 (1975) 145. [2] A. Andreeff, H.-J. Hunger and S. Unterricker, in: Intern, ConL on Hyperfine interactions studied in nuclear reac-

tions and decay, Contributed papers, eds. E. Karisson and R. W~ppIing(Univ. of Uppsala, Uppsala, 1974) p. 68. [3] G. Vogl, W. Manse! and W. Yogi, J. Phys. F4 (1974) 2321. [4] C. Hohenemser, A.R. Arends and H. de Waaxd, Phys. Rev. 1111 (1975) 4522; C. Hohenemser et at, Hyp. lnt. 3 (1977) 87. [5] L. Thomé and H. Bernas, Phys. Rev. Lett. 36 (1976) 1055; see also Hyp. mt. 5 (1978) 361. [6] Th. Wichert, M. Deicher, D. Echt and E. Recknagel, Phys. Rev. Lett. 41(1978) 882; 0. Echt, E. Recknagel, A. Weidinger and Tb. Wichert, Hyp. mt. 4 (1978) 706; see also Z. Phys. B32 (1979) 59, [7] F. Pleiter and C. Hohenemser, to be published.

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[8] Th. Wichert and E. Recknagel, in: Nuclear and electron

resonance spectroscopies applied to materials science, eds. E.N. Kaufmann and G.K. Shenoy (Elsevier NorthHolland, New York), to be published. [9] A.R. Arends et a!., Hyp. tnt. 8 (1981) 191. 110) R.M. Suter, M. Haoui and C. Hohenemser, Hyp. tnt. 4 (1978) 711. [11] A. van den Beukel, in: Vacancies and interstitials in metals, eds. A. Seeger, D. Schumacher, W. Schilling and J. Diehl (North-Holland, Amsterdam, 1970).

3 August 1981

[12] 1.-I. Takamura, in: Physical metallurgy, ed, R.W. Cahn (North-Holland, Amsterdam, 1970).

113) J. Weertman and J.R. Weertman, in: Physical metallurgy, ed. R.W. Cahn (North-Holland, Amsterdam, 1970). [14] P. Haasen, Philos. Mag. 3 (1958) 384. 115) R.W.K. Honeycombe, The plastic deformation of metals (Ainold, London, 1968).

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