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Recent progress in understanding ion-beam mixing of metals
104
Nuclear
Instruments
and Methods
in Physics
Research B39 (1989) 104-113 North-Holland, Amsterdam
Section II. Ion beam mixing RECENT PROGRESS L.E. REHN Materials
IN UNDERSTANDING
ION-BEAM
MIXING OF METALS
*
and P.R. OKAMOTO
Science Division, Argonne National Laboratory,
Argonne, Illinois 60439, USA
Recent progress in three fundamental areas related to the ion-beam mixing of metal targets is reviewed: (1) molecular dynamics simulations of the temporal development of energetic displacement cascades; (2) the substantially increased mixing efficiencies that have been reported in many systems at intermediate irradiation temperatures; and (3) amorphization during ion irradiation. Significant advances in our fundamental understanding have occurred in all three of these areas in the past few years. Mass transport at various times during the evolution of energetic displacement cascades in Cu and Ni has been calculated recently using fully dynamic computer simulations. These results, discussed in section 2, strongly support the conclusion drawn from earlier experimental work that a majority of ion-beam mixing occurs at low (l-2 eV) atomic recoil energies during the cascade cooling phase. In section 3, characteristic differences are identified between radiation-enhanced diffusion, that is mass transport due to freely-migrating vacancy and interstitial defects, and the enhanced ion-beam mixing that has been observed in many materials at intermediate temperatures. It is argued here that true radiation-enhanced diffusion should be observable only at substantially higher temperatures. Finally, recent measurements of the shear elastic constant, the lattice parameter, and the long-range order parameter during ion-induced amorphization of highly-ordered intermetallic compounds are summarized in section 4. This new information indicates that ion-induced amorphization is preceded by a first-order phase transformation triggered by an elastic instability, and reveals several parallels between solid-state melting and amorphization phenomena.
1. Introduction Ion-beam energy with
mixing
of ion-beams substrate
potential
[1,2],
materials,
uses of ion beams
ties. Perhaps
no other
which
utilizes
to mix pre-deposited
process
has
greatly
to modify
the
kinetic
surface
layers
expanded materials
is as efficient
the proper-
as ion-beam
for introducing large, nonequilibrium concentrations of alloying elements into a wide variety of hosts under carefully controlled conditions. The list of potential technological applications for ion-beam mixing has expanded further with the more recent development of ion-assisted deposition [3]. By combining ion-beam mixing with simultaneous deposition, ion-assisted deposition removes the limitation on altered layer thickness imposed by finite ion ranges. This innovation has spurred renewed interest in understanding fundamental aspects of the ion-mixing process. New evidence has appeared to support the idea that the high mixing efficiencies achieved during heavy-ion bombardment are a direct result of enhanced mass transport during the “cooling phase” of energetic displacement cascades. Early experimental indications of substantial mass transport at energies of a few eV or less were provided by several examples of the strong influence of thermodynamic variables on relative mixmixing
* Work supported by the US Department of Energy, BESMaterials Sciences, under Contract W-31-109-Eng-38.
0168-583X/89/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
ing efficiencies [4]. Recently, these correlations have been shown to hold even for low irradiation doses [5,6], where the net diffusion distance is of the order of a lattice spacing. The observed correlations clearly demonstrated that the mixing process was dominated by low-energy ( - 1 eV) atomic recoils, and not by higher energy (2 25 eV) “ballistic” events. More recently, molecular dynamics simulations [7,8] of energetic displacement cascades have confirmed many of these ideas. Advances in our understanding of mass transport within energetic displacement cascades, obtained from these computer simulation studies, are reviewed briefly in section 2. With the advances in understanding achieved for low irradiation temperature, attention is now shifting to the additional enhancement in mixing efficiencies observed as a function of temperature in most materials near or slightly above room temperature. This additional increase, first reported by Matteson et al. [9] in 1979, has been attributed to the thermally-activated, long-range migration of individual vacancy and interstitial defects generated by bombardment, i.e. radiationenhanced diffusion. However, as we discuss in section 3, the available data on ion-beam mixing at intermediate temperatures differ substantially from measurements of known radiation-enhanced diffusion effects in largergrained crystalline specimens. New experimental results are discussed concerning the temperature dependence of interdiffusion in the absence of irradiation, which suggest an alternative explanation for the enhanced mixing rates typically observed at intermediate irradiation tem-
L.E. Rehn, P.R. Okamoto / Ion-heum mixing of metals peratures. At past IBMM conferences, much of the interest in the ion-beam mixing of metals has revolved around the production of metastable phases, particularly amorphous materials. Because high concentrations of a wide variety of elements can be alloyed, ion-beam mixing has been used to make a wide variety of amorphous phases. Here too, new ideas have emerged recently concerning fundamental aspects of the phenomenon. In section 4, a brief review is given of experimental data that suggest amorphization during ion bombardment is preceded by a first-order phase transformation induced by an elastic catastrophe.
2. Energetic displacement cascades and ion-beam mixing at low temperatures Energetic displacement cascades are initiated when a few to many keV of energy are transferred from an incoming irradiation particle to a lattice atom. During ion bombardment, energy transfers of this magnitude are typical for all but the lightest (protons) ion and target masses. Because the collisional cross-section is very large at these energies, such transfers result in the rapid displacement from their lattice sites of a large number of atoms in close proximity to each other, called a collisional or displacement cascade. The overwhelming majority of defects created during ion irradiation at energies between some keV and many MeV are generally produced in displacement cascades. Despite sustained research over approximately forty years, the short duration (- 10-‘“-lO~” s) and small size (< 10 nm) of displacement cascades have precluded direct experimental investigations of their dynamics. The importance of mass transport within cascades to the typically high efficiency of ion-beam mixing was recognized several years ago. Early important indirect evidence for the dominance of cascade effects included the very high efficiency itself [lo], the dependence of this efficiency on cascade energy density [11,12], and the strong correlations observed by several investigators between relative mixing efficiencies and various thermodynamic parameters. Much of the relevant information was reviewed by Johnson [4], and by Paine and Averback [13], at the Cornell meeting, and more recently by Averback [14]. No attempt will be made here to provide a comprehensive review of the existing experimental information. The focus of this section is the insight that has emerged through the use of computer simulation. Note that the same characteristics which make cascade dynamics inaccessible to direct experiment, i.e. the extremely short time scale and limited spatial extent, are in fact highly advantageous for computer simulation studies using molecular dynamics (MD). Fully dynamical MD calculations were first performed for high-en-
105
ergy cascades by Guinan and Kinney [15], who followed defect production during displacement events in W. These authors divided the temporal development of an energetic cascade into three phases: A collisional phase, lasting only a few tenths of a picosecond, during which the energy transferred to the primary knock-on atom is dissipated among successive generations of proximate recoils. This collisional phase terminates when none of the recoiling atoms possesses sufficient energy (- 25 eV) to displace it or other atoms from a lattice site. A relaxational phase, lasting the order of half a picosecond, during which many of the defects produced initially in close proximity to each other recombine spontaneously, i.e. athermally, and more isolated defects assume their equilibrium configurations. A cooling or “thermal-spike” phase, lasting a few picoseconds, during which the highly disordered cascade region eventually achieves local thermal equilibrium with its surroundings. Of major interest to our understanding of ion-beam mixing is to identify the relative contributions to the mixing in each of the three phases characteristic of cascade evolution. Experimentally, of course, only the sum of the mixing that has occurred after the termination of all three phases can be determined. The three phases (labelled I, II and III) can be clearly seen in fig. 1, where the Guinan and Kinney results for the calculated defect concentrations in an energetic displacement
TIME
(picosacondt~
Fig. 1. Time development of Frenkel pair concentrations calculated for cascades of two different energies: 600 eV (- - -) and 2.5 keV ( -). II. ION BEAM MIXING
106
L. E. Rehn, P.R. Okamoto
cascade in W are displayed as a function of time after initial transfers of 0.6 and 2.5 keV of energy to a single W atom. Although these authors focussed primarily on defect production and subsequent survival, they did note that the large amount of defect annihilation observed during the final cooling phase resulted in mass transport that was more than an order of magnitude greater than that predicted from equilibrium transport theory. Protasov and Chudinov 1161, and Harrison and Webb [17] introduced approximations to reduce the computing time required for MD calculations of displacement cascades. These two sets of authors both pointed out that radial distribution functions calculated for the cascade atoms at the end of the collisional phase were actually characteristic of a liquid, i.e. that local melting had occurred. The analogy to melting was further supported by calculations of King and Benedek [l&19], who reported Maxwellian-like (thermal) distributions for the kinetic energies of atoms within the cascade region following the collisional phase. These latter authors also reported the existence of “closedchains” of atom replacements, and commented that such chains would imply considerable, intracascade atomic-mixing in alloys. Hence these earlier MD calculations indicated that substantial mass transport does occur within energetic displacement cascades, particularly during the final cooling phase, but they did not directly address either the magnitude of the net atom transport, nor the relative contribution from each of the three phases of cascade evolution. Recently, De la Rubia et al. [7] have investigated mass transport within 3 and 5 keV cascades in Cu using MD. Their results, which represent the highest cascade energies in reduced units yet treated in fully dynamical calculations, confirmed the local melting which was observed in the earlier calculations. Immediately after the collisional phase, regions approximately 4-5 nm in diameter were found to have radial distribution functions indistinguishable from that of a liquid, and this “melting” was found to persist for several picoseconds. Most pertinent to the present discussion, De la Rubia et al. [7] also calculated the amount of atomic mixing at various stages of the cascade evolution. In fig. 2 are plotted their results for the integrated cascade diffusion coefficient
as a function of the distance from the center of the cascade at instants of time corresponding to roughly the end of the collisional phase (0.12 ps; filled circles) and the end of the cooling phase (10 ps; open circles). Here i denotes the i th atom in a coordination shell contain-
/ Ion-beam mixing 0.3-
ofmetals /
I
I
1
I
I
I
5 keV CASCADE CU
RADIUS
Fig. 2. The integrated diffusion tion of distance from the center collisional phase (0.12 ps, filled cooling phase (10.0
km)
coefficient (D( r)t) as a funcof the cascade at the end of the symbols) and at the end of the ps, open symbols).
ing n(r) atoms at a distance r from the center of mass of the vacancy distribution generated by the cascade. The total amount of mass transport that has occurred up to the two different stages in cascade evolution can therefore be extracted by integrating over r to find the areas under the curves. Somewhat surprisingly, the total amount of diffusion that occurs during (area under lower curve) and after (area between curves) the collisional phase differs by less than 10%. Also, the same functional dependence of diffusion on distance from the cascade center is observed for both times. Nevertheless, the authors conclude that the “vast majority” of the mixing occurs during the thermal spike, i.e. after the collisional phase. They point out that a substantial portion of the area under the lower curve in fig. 2 is due to the movement of a large number of atoms that are displaced only small amounts from their lattice positions during the collisional phase. These atoms actually return directly back to their original sites at a later stage in the evolution of the cascade, and hence do not contribute to atomic mixing. The conclusion drawn from these MD calculations, namely that the atomic mixing can be largely accounted for by the diffusion calculated to occur in the locally melted cascade region after the collisional phase, when the average kinetic energy is of the order of 1-2 eV per atom, agrees well with the many experimental observations [4,14] showing a strong dependence of mixing efficiencies on thermochemical parameters with energies of this magnitude, e.g., heats of mixing or sublimation energies. Recently, De la Rubia et al. [8] have performed a second MD study, using the Johnson-&&soy potential to stimulate displacement cascades in Ni. Although
L. E. Rehn, P.R. Okamoto
a similar temperature history and liquid-like cascade region were observed for a S-keV primary knock-on event in both Ni and Cu, the duration of the calculated thermal-spike phase in Ni was found to be substantially shorter. The shorter duration of the liquid-like cascade phase results in significantly less ( - 50%) atomic mixing in Ni compared to Cu, again in good agreement with earlier experimental findings. Hence, based upon several experimental indications of the importance of energy differences on the order of l-2 eV to ion-beam mixing rates, and the new evidence provided by the MD simulations, it must be concluded that the dominant contribution to mixing rates at low ambient temperatures is intracascade mass transport initiated during the cascade cooling phase.
3. Ion-beam mixing at intermediate temperatures Thermally-activated, defect migration processes provide additional mechanisms for producing microstructures with novel or improved properties [20]. Hence considerable interest exists in understanding the temperature dependence of ion-beam mixing, and in particular, in determining the temperature range where freely-migrating defects can significantly alter both the amount and depth of the intermixing. Understanding mass transport during irradiation at intermediate temperatures should also provide valuable insight into other technologically important ion implantation phenomena that require substantial mass transport, such as buried layer formation [21], ion-beam-induced grain growth [22], and sputter-induced, subsurface compositional changes [23]. In general, three temperature regimes of ion-beam mixing have been clearly identified: low-temperatures, where only a weak dependence of mixing rates on irradiation temperature is found; intermediate temperatures, typically beginning near or slightly above room temperature, where mixing rates become more strongly dependent on temperature; and high-temperatures, typically above about 0.6 of the absolute melting temperature, where the additional mass transport induced by irradiation is substantially below the rate of thermallyinduced interdiffusion, and therefore where irradiationinduced mixing becomes insignificant relative to thermal processes. Before discussing results on ion-beam mixing of thin, polycrystalline films in more detail, we digress briefly to provide a short summary of experimental results on irradiation-induced mass transport as a function of temperature in well characterized, largegrained and single-crystal samples. At temperatures where the excess vacancy and interstitial defects produced during irradiation become sufficiently mobile, their migration will enhance mass transport. This radiation-enhanced diffusion (RED), and
/ Ion-beam
107
mixing of metals
its dependence on dose, dose-rate, temperature and defect-sink concentrations have been discussed in detail by Sitzmann [24]; many of the theoretical predictions have been verified in recent years [25,26]. An example of experimental measurements of RED in a well-characterized specimen, taken from the work of Mtiller et al. [27], is shown in fig. 3. Here, measurements of the diffusion coefficient, D, for a Ni-isotope marker layer in a single crystal specimen of Ni during irradiation with 300 keV Ni ions at several different temperatures, and two different dose rates, are plotted in Arrhenius fashion. The weak temperature dependence observed below - 600 K is consistent with ion-beam mixing of the isotope marker layer within individual displacement cascades, as discussed above in section 2. We note that although many studies report a flat temperature dependence in the low temperature regime, careful examination of the actual data consistently reveals a small, but statistically significant increase in mixing with increasing temperature, even at the lowest measurement temperatures; such a slight increase can be seen in fig. 3. The pronounced increase in D (fig. 3) which begins at temperatures between 650-700 K exhibits Arrhenius behavior with an apparent activation enthalpy of 0.58 k 0.08 eV. This energy equals one-half the vacancy migration enthalpy for Ni (1.2 eV), which is the expected value for RED when defect annihilation occurs predominantly by mutual recombination of vacancies and interstitials. Furthermore, D (in units of cm2/s) was found to be directly proportional to the square-root of the ion-current density at temperatures >_700 K, confirming that D is proportional to the product of the irradiation-induced concentrations of vacancies and interstitials. At temperatures above - 1000 K, D blends smoothly into the thermal diffusion data (dashed line in T (Kl
300
600
103/T
(K-l)
Fig. 3. Temperature dependence of the Ni self-diffusion coefficient in single-crystal specimens measured during irradiation with 300 keV Ni ions at current densities of 6 x 10” (open symbols) and 6 X 10” (closed symbols) ions/cm’s. The dashed line is an extrapolation of thermal self-diffusion coefficients for Ni measured at high temperatures in the absence of irradiation. II. ION BEAM MIXING
108
L..E. Rehn, P.R. Okamoto / Ion-beam mixing
Fig. 4. Arrhenius plot of the quantity of Si ion-beam mixed with Nb for a dose of 1.2 X10” Si ions/cm2 at several different temperatures. The quantity of Si that can be intermixed without irradiation in the same time interval is shown by the solid line marked thermal. Note the substantial temperature difference between the onset of a strong temperature dependence in the mixing rate. and the occurrence of significant thermal interdiffusion.
fig. 3). as expected for RED. Hence, enhanced diffusion due to the thermally-activated migration of vacancy and interstitial defects (RED) is an experimentally welldocumented, and theoretically well-understood phenomenon in single-crystal Ni specimens. Analogous effects [25] of dose, dose-rate and temperature on mass transport due to the thermally-activated migration of irradiation-induced point defects have also been reported in large-grained, Ni-Si alloys, but again, only at temperatures 2 650 K. We now return to experimental studies of ion-beam mixing in poly~rystalline thin films. The first observation of a substantial change in the temperature dependence of ion-beam mixing rates was that of Matteson et al. [9], who measured the interdiffusion in Nb/Si bilayer specimens during irradiation with 275 keV Si ions. Their results are shown in fig. 4. The sharp increase in mixing efficiency that occurs above - 200 o C appears, at least on the basis of the limited experimental data, to exhibit Arrhenius behavior, with an apparent activation enthalpy of 0.9 eV. Since this value is roughly one-half of the vacancy migration enthalpy reported at that time for Nb, the authors attributed this increase in mixing efficiency above - 200 ’ C to RED. No dose-rate studies were reported. Ion-beam mixing in polycrystalline films of many different materials has subsequently been shown to exhibit a similar temperature dependence. The
ofmetals
two regimes of apparent Arrhenius behavior have become known as Q-curve behavior, and the vast majority of authors have attributed the increase in mixing that occurs in the higher temperature regime as arising from RED [9,28]. Although it is clear that the intermixing in the upper Arrhenius regime is “enhanced” by irration, that is, that the amount of interdiffusion during irradiation is substantially greater during bombardment, we wish to point out certain disparities that exist between ion-beam mixing results obtained for the upper portion of the Q-curve using polycrystalline bilayer and marker specimens, and expected RED behavior as documented by results such as those shown in fig. 3. One obvious disparity has been discussed previously by Shreter et al. [29]. These authors performed a study similar to that of Matteson et al., and found that the apparent activation enthalpy for ion-beam mixing of NbSi bilayers dropped to only 0.2 eV for irradiation with Xe ions. A dependence of the apparent activation enthalpy on ion-species is clearly inconsistent with the assumption of RED in the defectrecombination-limited regime, for which the magnitude is determined only by the migration enthalpy of the slower moving defect [24]. A second discrepancy, which appears consistently throughout the literature, is the low onset temperatures that have been reported for enhanced mass transport in ion-beam mixed, polycrystalline systems. For example, the onset temperature is < 500 K in Nb/Si (fig. 4), but it is - 700 K in the single-crystal Ni study (fig. 3). Although both vacancy and interstitial defects are expected to become mobile at temperatures substantially below 500 K in Ni, the delayed onset of the RED contribution is well understood in the single-crystal results [30]. For temperatures c 600 K, the irradiation-induced sink concentrations are extremely high; electron microscopy studies yield values for the sink annihilation probability of > 10m5 for a defect migrating in this temperature regime [31]. This high annihilation probability means that the average distance a defect will migrate before annihilation at a sink is -z 10 nm. Therefore, no significant mass transport due to thermally-activated, freeiy-~grating defects (RED) is expected until irradiation temperatures near 600 to 700 K, where the irradiation-induced sink concentration drops dramatically. A third disparity involves several unrealistically low values, as low as 0.1 eV (321, reported for the apparent activation enthalpy in the upper portion of the Q-curve. Particularly for concentrated alloys, values 2 0.5 eV would be expected if the enhanced mixing was indeed due to freely-migrating, irradiation-endured vacancies and interstitials. It is clear that RED, that is the therm~ly-activated, free migration of irradiation-induced vacancy and interstitial defects, does not offer a consistent explanation for the upper Arrhenius regime found for ion-beam mixing at intermediate temperatures in a wide variety of
L. E. Rehn, P.R. Okamoto
materials. In particular, the onset temperature is too low, the measured activation enthalpies are frequently not of the expected magnitude, and even the existence of a well understood dose-rate dependence remains uncertain. This latter point will be addressed in more detail shortly. The situation regarding enhanced ion-beam mixing at intermediate temperatures has received increased attention due to recent reports of “RED” in amorphous systems. The results of Priolo et al. [33], who studied the temperature dependence of mixing of a Au marker layer in amorphous Si during irradiation with 2.5 MeV Ar ions, are shown in fig. 5. The three temperature regimes discussed earlier are clearly evident: a weak temperature dependence below - 400 K, a strong temperature dependence between approximately 400 and 700 K which, at their dose-rate, appears to blend smoothly into the thermal diffusion data at temperatures above - 800 K. Although these results are strikingly similar to the known RED behavior in Ni (fig. 3) we note once again that the onset temperature for enhanced mass transport is low, only - 400 K. Furthermore, Priolo et al. report no dependence of D on dose-rate at 493 K. again different from the Ni study. Although irradiation conditions exist for which no dependence of RED on dose-rate is expected, e.g. the regime where defects annihilate predominantly at sinks, the observation of a substantial dependence on temperature near 493 K argues strongly against this interpretation. That is, unless the irradiation-induced sink concentration is strongly temperature dependent, the diffusion coefficient in the sink-annihilation dominant regime is temperature independent, since the same number of defects migrate the same average distance (to a constant number of fixed sinks) at all temperatures. The combined observations of a strong
T (Kl ,o-l’
IO+ ,?
E 0 D
16'5
103/T
(K-‘1
Fig. 5. Diffusion coefficients of Au in amorphous Si measured at the indicated temperatures after irradiation with 2.5 MeV Ar ions at a dose-rate of 7X10” ions cm-’ SC’. Open data points represent total diffusion coefficients, and closed data points represent thermal interdiffusion data.
/ Ion-beam mixing
of metds
109 T IK)
IO4
500
,
400
300
I
I
Ni/Zr
i02=3.5e~
,I
2
3 1000/T
(K-l)
Fig. 6. Mean square diffusion distances measured during ion-beam mixing of Ni/Zr bilayer specimens by I-MeV ions at several temperatures.
the Kr
temperature dependence of D but no dose-rate dependence in amorphous Si suggest that the enhancement in mixing that begins above - 400 K is due to an intracascade mechanism. A similar Q-curve dependence for ion-beam mixing has recently been reported in Ni/Zr bilayer specimens. for which the mixed layer goes amorphous very early in the irradiation. These results. by Ding et al. [34], are displayed in fig. 6. Again, we note a relatively sharp increase in the mixing rate at a temperature just below 500 K. In contrast to the amorphous Si results. however. a pronounced dose-rate dependence of the mixing rate in amorphous Ni/Zr was reported at an irradiation temperature of 523 K. In the absence of beam heating effects, the observation of a dose-rate dependence indicates an intercascade process, i.e. that the effects produced by one ion interact dynamically with those produced by other ions. Ding et al. were able to fit their diffusion data to an inverse square-root of dose-rate dependence, in agreement with the Ni study discussed above, and therefore concluded that the enhanced mixing observed above - 480 K in Ni/Zr was due to RED. Unfortunately. the fit of their data to an inverse square-root dependence depends sensitively on the choice of a low-temperature mixing-rate. In the absence of a firm value for this quantity. equally good fits are obtained with exponents between roughly - 0.2 and - 1 [35]. Hence the conclusions that have recently been drawn regarding evidence for well-defined point-defect configurations in amorphous systems. based upon the interpretation that RED is causing the increased II. ION BEAM MIXING
L. E. Rehn, P.R. Okamoto
110 T (K1
300
400
500
’
It’
i
1000/T
temperature
dependence
are changing, since a parallel change is observed even in the absence of ion bombardment. This parallel change suggests that the “thermal-like” cascade cooling phase becomes more efficient at promoting interdiffusion at higher temperatures simply because the underlying thermal processes themselves become more efficient. It should be pointed out that this interpretation, which postulates the same intracascade mechanism in both Arrhenius regions, predicts no direct dependence on ion dose-rate. Hence it is in agreement with the amorphous Si results discussed above, but does not explain the dose-rate dependence found in Ni/Zr. A possible alternative explanation to RED for the dose-rate dependence observed in Ni/Zr is that the irradiation-induced sink structure is in fact dose-rate dependent. More detailed investigations of the effect of dose-rate on interdiffusion during ion bombardment can be expected to clarify this matter. One simple approach, which we are currently exploring in our own laboratory, is to search for an additional increase in ion-beam mixing efficiency at yet higher temperatures, e.g. 1650 K, where true RED can be expected.
(K-‘1
Fig. 7. Diffusion coefficients measured during ion-beam mixing (upper curves) and thermal interdiffusion (lower curves) of Au/Zr and Ni/Zr bilayer specimens. Note that the break in the temperature dependence occurs at approximately the same temperature both with and without irradiation.
ered
/ Ion -beam mixing of metals
of the mixing,
must
be consid-
speculative.
An alternative explanation for the enhanced mixing at intermediate temperatures is suggested by yet unpublished results of Ding et al. [36], who studied interdiffusion in Au/Zr and in Ni/Zr bilayer specimens during, and in the absence of, ion bombardment. These results are displayed in fig. 7. Note that although irradiation greatly enhances the rate of interdiffusion in both alloy systems, the diffusion in the absence of irradiation also exhibits two regions of Arrhenius behavior, with the higher temperature regime having the stronger temperature dependence in both cases. Furthermore, the onset of the higher temperature regime occurs at approximately the same temperature in the thermal annealing, as well as in the irradiation case. The MD evidence discussed in section 2 indicates that the high efficiency of ion-beam mixing in the lower part of the Q-curve, and its dependence upon thermodynamic variables such as the heat of mixing or cohesive energy, are direct manifestations of the fact that the majority of the mass transport induced within individual displacement cascades occurs during a “thermal-like” cooling phase. The results in fig. 7 suggest that the same explanation remains valid for the upper Arrhenius portion of the Q-curve. It is apparently not the irradiation effects that
4. Solid-state amorphization The formation of metastable phases, particularly amorphous materials, has been the subject of several review presentations at previous IBMM conferences. Because of the large variety of elements which can be intermixed to high concentration levels, a large number of amorphous phases have been produced by ion-beam mixing. The focus of previous presentations has been on identifying parameters such as ion mass and irradiation temperature that are critical to amorphization, and formulating generic rules to predict which classes of materials can be made amorphous by ion-beam mixing [37]. Here we focus on the crystalline-to-amorphous (c-a) transformation per se, and in particular on recent experimental evidence [38] that this is preceded by a first-order phase transformation driven by an elastic instability. We are investigating ion-beam induced amorphization in several ordered intermetallic compounds using Brillouin scattering to determine changes in a shear elastic constant, and transmission electron microscopy (TEM) to measure changes in long-range chemical order and lattice dilation. Measurements in Zr,Al of the sound velocity, which is directly proportional to the square-root of the shear elastic constant, are shown in fig. 8 as a function of dose during irradiation with l-MeV Kr ions. The data reveal that a large, almost 50% decrease occurs in the Zr,Al shear constant during disordering, which TEM shows is occurring up to a dose of - 6 x 1013 cm-*. The decrease in shear constant during disordering is substantially larger than the typi-
L. E. Rehn, P.R. Okamoto
DOSE
(Ions/cm2)
Fig. 8. Measurements of the shear sound velocity, which is proportional to the square root of the shear elastic constant, in Zr,Al as a function of ion dose. Open and filled circles denote respectively broad (due to the polycrystalline specimen) and narrow peaks in the Brillouin spectra.
cal 5 10% reported [39] for alloys such as Cu,Au that undergo an order-disorder transformation below their melting point, but does agree with previous measurements of large elastic softening due to disordering of Nb,Ir [40], another intermetallic that in the absence of irradiation, remains ordered up to its melting point. At a dose between 4-8 x lOI cme2, an abrupt increase is seen in the Zr,Al sound velocity (fig. 8). After this abrupt increase, no additional change occurs in the sound velocity upon further irradiation. The discontinuity in the sound velocity demonstrates that the c-a transformation is not a continuous function of irradiation, but rather that a relatively abrupt phase transformation occurs first. For Zr,Al, TEM reveals a simultaneous discontinuity in the long-range order parameter, S, indicating that the phase transformation is first-order [41]. An abrupt phase transformation is also seen in the in situ lattice parameter measurements, which show that the lattice parameter expands monotonically by - 0.8% during disordering, drops abruptly to - 0.6% at a dose of - 5 X lOI cmm2, then remains unchanged up to the highest doses (- lOI cmP2) where diffraction spots can still be observed. The large elastic softening which precedes the phase transformation suggests, in analogy with the martensitic transformation [42], that an elastic instability triggers the transformation. Based upon a similar increase in lattice parameter observed during amorphization of Zr,Al by hydrogen charging [43], we believe that the elastic softening is a direct manifestation of lattice dilation, regardless of whether the dilation results from disordering, heating, or from hydrogen absorption.
/ Ion-beam
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111
A similar elastic softening with increasing lattice parameter is well known during heating. In fact, at least six parallels between ion-induced amorphization and heating to the melting temperature, T,,, were noted in the above study. These include: (1) a large, - 50% elastic softening occurs (as a function of temperature up to T,,,; as a function of ion dose through disordering); (2) a discontinuity occurs (as a function of temperature at T,; as a function of ion dose at - 6 x lOI cmm2); (3) a linear relationship exists between the lattice parameter and shear elastic constant changes (as a function of ion dose; as a function of temperature), that (4) extrapolates to zero at an additional dilation of - 3%. The discontinuities found in (5) the long-range order parameter and in (6) the interatomic spacing during irradiation also parallel changes observed during melting. To investigate further the idea that irradiation-induced amorphization is triggered by an elastic instability, we have recently performed Brillouin scattering measurements on three more intermetallics as a function of ion dose: NiAl, which cannot be substantially disordered during ion-bombardment at room temperature, FeAl, which can be disordered but does not become amorphous, and FeTi, which first disorders then becomes amorphous. Initial results [44] for the shear elastic constants of these three materials, obtained for irradiation at room temperature with 1.5-MeV Kr ions, are shown in fig. 9 as a function of dose. The shear constant of NiAl, which shows only a small decrease in long-range order under these irradiation conditions, decreases only slightly (- 10%) by a dose of 4 X lOI cm-*. A larger ( - 20%) decrease is seen in FeAl, which is expected to be almost totally disordered, but not amorphous, by the highest dose (2 x lOi cmP2); the initial increase in velocity is currently not understood. A substantially larger decrease ( - 30%) is seen in FeTi by a dose of 1 x 1014cm-2 and a possibly abrupt increase, such as that seen for Zri Al (fig. 7), occurs at a dose of - 2 x lot4 cmm2. Hence the results shown in fig. 8 provide corroborating evidence that disordering of strongly-ordered intermetallics generates a large elastic softening. Although disordering is apparently responsible for the lattice dilation which drives the strongly-ordered intermetallic compounds amorphous, there are several other processes that can produce lattice dilation. For example, ion-beam mixing can generate highly supersaturated solid solutions, which lead to large lattice dilation. Linker et al. [45] observed a similar lattice dilation and apparent strain release during the implantation of B into Nb and MO. The hydrogen results discussed above also indicate that it is the lattice dilation which eventually drives the lattice unstable. Hence amorphization following supersaturation by ion-beam mixing or by direct implantation can also be understood II. ION BEAM MIXING
112
L. E. Rehn, P.R. Okamoto / Ion-beam mixing
ofmetals
proves to be true, beneficial modifications achieved with far lower irradiation/implantation
1
.” A-
-J
I
0
0 2.d rL -31
0
10'5
IO” DOSE (ions/cm21
Fig. 9. Brillouin measurements of the sound velocity as a function of ion dose in three intermetallic specimens: NiAl, which neither disorders nor goes amorphous; FeAl, which disorders but does not become amorphous; and FeTi, which
disorders and subsequently becomes amorphous.
on the basis of an elastic instability, as can amorphization by solid-state reaction. We note that the apparent elastic instability and first-order phase transformation that occur during ion bombardment do not simultaneously drive the entire crystal amorphous. Strong fundamental spots dominate the diffraction patterns of Zr,Al taken at doses of 6-8 X lOI cm-*, indicating that only a small fraction of the crystal is amorphous immediately after the transformation. Complete amorphization requires doses > 2 X lOI cm-*. During this gradual transformation, however, no additional change is seen in either the shear constant or lattice parameter, demonstrating that the elastic properties of the material following the abrupt transformation are very similar to those of the fully amorphous phase. Large decreases in the shear constant can be expected to generate concomitant mechanical property changes. It would be interesting to compare the mechanical properties of highly disordered materials with similar measurements in fully amorphous phases of identical compositions. Perhaps some of the large property changes which have been reported for amorphous layers [46] are actually due to this large change in elastic behavior,
and
not
to the
structural
differences.
If this
could be doses.
We wish to acknowledge many stimulating sions with our ANL colleagues on topics covered presentation. In particular, we wish to thank nedek and H. Wiedersich for critical comments manuscript.
discusin this R. Beon the
References PI D.H. Lee, R.R. Hart, D.A. Kiewit and O.J. Marsh, Phys. Status Solidi (a)15 (1973) 645. PI W.F. van der Weg, D. Sigurd and J.W. Mayer, in: Applications of Ion Beams to Metals, eds. ST. Picraux, E.P. EerNisse and F.L. Vook (Plenum, New York, 1974) p. 209. Nucl. Instr. and Meth. 131 J.J. Cuomo and SM. Rossnagel, B19/20 (1987) 963. Y.T. Cheng, M. VanRossum and M-A. [41 W.L. Johnson, Nicolet, Nucl. Instr. and Meth. B7/8 (1985) 657. [51 M.G. le BoitC, A. Traverse, H. Bernas, C. Janot and J. Chevrier, Mater. Lett. 6 (1988) 173. [cl A. Traverse, M.G. le Boitt, L. NCvot, B. Pardo and J. Corno, Appl. Phys. Lett. 51 (1987) 1901. R. Benedek and W.E. [71 T.D. de la Rubia, R.S. Averback, King, Phys. Rev. Lett. 59(17) (1987) 1930. R. Benedek and I.M. PI T.D. de la Rubia, R.S. Averback, Robertson, Proc. of Fusion Workshop, to be published. [91 S. Matteson, J. Roth and M-A. Nicolet, Radiat. Eff. 42 (1979) 217. [lOI M-A. Nicolet, T.C. Banwell and B.M. Paine, Mater. Res. Sot. Symp. Proc. 27 (1984) 3; S.-J. Kim, M-A. Nicolet, R.S. Averback and D. Peak, Phys. Rev. B37(1) (1988) 38. 1111 R.S. Averback, L.J. Thompson and L.E. Rehn, ibid., p. 25. [=I J. Bottiger, S.K. Nielsen and P.T. Thorsen, Nucl. Instr. and Meth. B7/8 (1985) 707. u31 B. Paine and R.S. Averback, ibid., p. 666. and D.N. Seidman, Mater. Sci. Forum P41 R.S. Averback 15-18 (1987) 963. u51 M.W. Guinan and J.H. Kinney, J. Nucl. Mater. 103/104 (1981) 1319. Radiat. Eff. 66 (1982) [161 V.I. Protasov and V.G. Chudinov, 1. iI71 D.E. Harrison and R.P. Webb, Nucl. Instr. and Meth. 218 (1983) 727. [I81 W.E. King and R. Benedek, J. Nucl. Mater. 117 (1983) 26. [I91 W.E. King and R. Benedek, Phys. Rev. B23 (1981) 6335. PO1 L.E. Rehn and H. Wiedersich, in: Surface Alloying by Ion Electron, and Laser Beams, eds. L.E. Rehn, S.T. Picraux and H. Wiedersich (American Society of Metals, Metals Park, OH, 1987) p. 134. PI A.E. White, K.T. Short, R.C. Dynes, J.M. Gibson and R. Hull, Mater. Res. Sot. Symp. Proc. 100 (1988) 3. and H.I. Smith, ibid., p. PI H.A. Atwater, C.V. Thompson 345 ; J.C. Liu and J.W. Mayer, ibid., p. 357. 1231N.Q. Lam, ibid., p. 29.
L. E. Rehn. P.R. Okamoto [24] R.S. Sizmann, J. Nucl. Mater. 69/70 (1978) 386. [25] R.S. Averback, L.E. Rehn, W. Wagner, H. Wiedersich and P.R. Okamoto. Phys. Rev. B28 (1983) 3100. [26] M.-P. Macht, A. Mtiller, V. Naundorf and H. Wollenberger, Nucl. Instr. and Meth. B16 (1986) 148. [27] A. Mtiller, M.-P. Macht and V. Naundorf, Proc. 14th Int. Symp. on Effects of Radiation on Materials, Andover, MA, USA, to be published. [2X] Y.-T. Cheng, X.-A. Zhao, T. Banwell, T.W. Workman, M-A. Nicolet and W. L. Johnson, J. Appl. Phys. 60(7) (1986) 2615. [29] U. Shreter, F.C.T. So, B.M. Paine and M-A. Nicolet, Mater. Res. Sot. Symp. Proc. 27 (1984) 31. [30] A. Mtiller, V. Naundorf and M.-P. Macht, Mater. Sci. Forum 15-1X (1987) 1081. [31] J.E. Westmoreland, J.A. Sprague, F.A. Smidt, Jr. and P.R. Malmberg, Radiat. Eff. 26 (1975) 1. [32] See, for example, E. Ma, A.J. Brunner, T.W. Workman, C.W. Nieh, X.-A. Zhao and M-A. Nicolet. Mater. Res. Sot. Symp. Proc. 100 (1988) 75. [33] F. Priolo, J.M. Poate, D.C. Jacobson, J. Linnros, J.L. Batstone and S.U. Campisano, ibid., p. 87. [34] F.-R. Ding, R.S. Averback and H. Hahn, J. Appl. Phys. 64 (1988) 1785. [35] U. Scheuer, ANL, private communication.
/ Ion-beam mxing
of metals
113
[36] F.-R. Ding, L.E. Rehn and P.R. Okamoto, to be published. [37] See, e.g., D.M. Follstaedt, Nucl. Instr. and Meth. B7/8 (1985) 11; J.L. Brimhall, ibid., p. 27; C.H. Hewett, S.S. Lau, I. Suni and D.B. Poker, ibid., p. 597. [3X] L.E. Rehn. P.R. Okamoto, J. Pearson, R. Bhadra and M. Grimsditch, Phys. Rev. Lett. 59 (1987) 2987. [39] P.A. Flinn, G.M. McManus and J.A. Rayne, J. Phys. Chem. Solids 15 (1960) 189. [40] M. Grimsditch, K.E. Gray, R. Bhadra, R.T. Kampwirth and L.E. Rehn, Phys. Rev. B35 (1987) 883. [41] S. Strlssler and C. Kittel, Phys. Rev. Al39 (1965) 758. [42] N.G. Pace and G.A. Saunders, Philos. Mag. 22 (1970) 73. [43] W.J. Meng, P.R. Okamoto, B. Kestel, L.J. Thompson and L.E. Rehn, Appl. Phys. Lett. (Nov, 1988) in press. [44] J. Koike, P.R. Okamoto, L.E. Rehn, R. Bhadra and M. Grimsditch, unpublished. [45] G. Linker, Nucl. Instr. and Meth. B19/20 (1987) 526. [46] G.H. Hubler, in: Surface Alloying by Ion, Electron, and Laser Beams, eds. L.E. Rehn, ST. Picraux and H. Wiedersich (American Society of Metals, Metals Park, OH, 1987) p. 287.
II. ION BEAM MIXING
Nuclear
Instruments
and Methods
in Physics
Research B39 (1989) 104-113 North-Holland, Amsterdam
Section II. Ion beam mixing RECENT PROGRESS L.E. REHN Materials
IN UNDERSTANDING
ION-BEAM
MIXING OF METALS
*
and P.R. OKAMOTO
Science Division, Argonne National Laboratory,
Argonne, Illinois 60439, USA
Recent progress in three fundamental areas related to the ion-beam mixing of metal targets is reviewed: (1) molecular dynamics simulations of the temporal development of energetic displacement cascades; (2) the substantially increased mixing efficiencies that have been reported in many systems at intermediate irradiation temperatures; and (3) amorphization during ion irradiation. Significant advances in our fundamental understanding have occurred in all three of these areas in the past few years. Mass transport at various times during the evolution of energetic displacement cascades in Cu and Ni has been calculated recently using fully dynamic computer simulations. These results, discussed in section 2, strongly support the conclusion drawn from earlier experimental work that a majority of ion-beam mixing occurs at low (l-2 eV) atomic recoil energies during the cascade cooling phase. In section 3, characteristic differences are identified between radiation-enhanced diffusion, that is mass transport due to freely-migrating vacancy and interstitial defects, and the enhanced ion-beam mixing that has been observed in many materials at intermediate temperatures. It is argued here that true radiation-enhanced diffusion should be observable only at substantially higher temperatures. Finally, recent measurements of the shear elastic constant, the lattice parameter, and the long-range order parameter during ion-induced amorphization of highly-ordered intermetallic compounds are summarized in section 4. This new information indicates that ion-induced amorphization is preceded by a first-order phase transformation triggered by an elastic instability, and reveals several parallels between solid-state melting and amorphization phenomena.
1. Introduction Ion-beam energy with
mixing
of ion-beams substrate
potential
[1,2],
materials,
uses of ion beams
ties. Perhaps
no other
which
utilizes
to mix pre-deposited
process
has
greatly
to modify
the
kinetic
surface
layers
expanded materials
is as efficient
the proper-
as ion-beam
for introducing large, nonequilibrium concentrations of alloying elements into a wide variety of hosts under carefully controlled conditions. The list of potential technological applications for ion-beam mixing has expanded further with the more recent development of ion-assisted deposition [3]. By combining ion-beam mixing with simultaneous deposition, ion-assisted deposition removes the limitation on altered layer thickness imposed by finite ion ranges. This innovation has spurred renewed interest in understanding fundamental aspects of the ion-mixing process. New evidence has appeared to support the idea that the high mixing efficiencies achieved during heavy-ion bombardment are a direct result of enhanced mass transport during the “cooling phase” of energetic displacement cascades. Early experimental indications of substantial mass transport at energies of a few eV or less were provided by several examples of the strong influence of thermodynamic variables on relative mixmixing
* Work supported by the US Department of Energy, BESMaterials Sciences, under Contract W-31-109-Eng-38.
0168-583X/89/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
ing efficiencies [4]. Recently, these correlations have been shown to hold even for low irradiation doses [5,6], where the net diffusion distance is of the order of a lattice spacing. The observed correlations clearly demonstrated that the mixing process was dominated by low-energy ( - 1 eV) atomic recoils, and not by higher energy (2 25 eV) “ballistic” events. More recently, molecular dynamics simulations [7,8] of energetic displacement cascades have confirmed many of these ideas. Advances in our understanding of mass transport within energetic displacement cascades, obtained from these computer simulation studies, are reviewed briefly in section 2. With the advances in understanding achieved for low irradiation temperature, attention is now shifting to the additional enhancement in mixing efficiencies observed as a function of temperature in most materials near or slightly above room temperature. This additional increase, first reported by Matteson et al. [9] in 1979, has been attributed to the thermally-activated, long-range migration of individual vacancy and interstitial defects generated by bombardment, i.e. radiationenhanced diffusion. However, as we discuss in section 3, the available data on ion-beam mixing at intermediate temperatures differ substantially from measurements of known radiation-enhanced diffusion effects in largergrained crystalline specimens. New experimental results are discussed concerning the temperature dependence of interdiffusion in the absence of irradiation, which suggest an alternative explanation for the enhanced mixing rates typically observed at intermediate irradiation tem-
L.E. Rehn, P.R. Okamoto / Ion-heum mixing of metals peratures. At past IBMM conferences, much of the interest in the ion-beam mixing of metals has revolved around the production of metastable phases, particularly amorphous materials. Because high concentrations of a wide variety of elements can be alloyed, ion-beam mixing has been used to make a wide variety of amorphous phases. Here too, new ideas have emerged recently concerning fundamental aspects of the phenomenon. In section 4, a brief review is given of experimental data that suggest amorphization during ion bombardment is preceded by a first-order phase transformation induced by an elastic catastrophe.
2. Energetic displacement cascades and ion-beam mixing at low temperatures Energetic displacement cascades are initiated when a few to many keV of energy are transferred from an incoming irradiation particle to a lattice atom. During ion bombardment, energy transfers of this magnitude are typical for all but the lightest (protons) ion and target masses. Because the collisional cross-section is very large at these energies, such transfers result in the rapid displacement from their lattice sites of a large number of atoms in close proximity to each other, called a collisional or displacement cascade. The overwhelming majority of defects created during ion irradiation at energies between some keV and many MeV are generally produced in displacement cascades. Despite sustained research over approximately forty years, the short duration (- 10-‘“-lO~” s) and small size (< 10 nm) of displacement cascades have precluded direct experimental investigations of their dynamics. The importance of mass transport within cascades to the typically high efficiency of ion-beam mixing was recognized several years ago. Early important indirect evidence for the dominance of cascade effects included the very high efficiency itself [lo], the dependence of this efficiency on cascade energy density [11,12], and the strong correlations observed by several investigators between relative mixing efficiencies and various thermodynamic parameters. Much of the relevant information was reviewed by Johnson [4], and by Paine and Averback [13], at the Cornell meeting, and more recently by Averback [14]. No attempt will be made here to provide a comprehensive review of the existing experimental information. The focus of this section is the insight that has emerged through the use of computer simulation. Note that the same characteristics which make cascade dynamics inaccessible to direct experiment, i.e. the extremely short time scale and limited spatial extent, are in fact highly advantageous for computer simulation studies using molecular dynamics (MD). Fully dynamical MD calculations were first performed for high-en-
105
ergy cascades by Guinan and Kinney [15], who followed defect production during displacement events in W. These authors divided the temporal development of an energetic cascade into three phases: A collisional phase, lasting only a few tenths of a picosecond, during which the energy transferred to the primary knock-on atom is dissipated among successive generations of proximate recoils. This collisional phase terminates when none of the recoiling atoms possesses sufficient energy (- 25 eV) to displace it or other atoms from a lattice site. A relaxational phase, lasting the order of half a picosecond, during which many of the defects produced initially in close proximity to each other recombine spontaneously, i.e. athermally, and more isolated defects assume their equilibrium configurations. A cooling or “thermal-spike” phase, lasting a few picoseconds, during which the highly disordered cascade region eventually achieves local thermal equilibrium with its surroundings. Of major interest to our understanding of ion-beam mixing is to identify the relative contributions to the mixing in each of the three phases characteristic of cascade evolution. Experimentally, of course, only the sum of the mixing that has occurred after the termination of all three phases can be determined. The three phases (labelled I, II and III) can be clearly seen in fig. 1, where the Guinan and Kinney results for the calculated defect concentrations in an energetic displacement
TIME
(picosacondt~
Fig. 1. Time development of Frenkel pair concentrations calculated for cascades of two different energies: 600 eV (- - -) and 2.5 keV ( -). II. ION BEAM MIXING
106
L. E. Rehn, P.R. Okamoto
cascade in W are displayed as a function of time after initial transfers of 0.6 and 2.5 keV of energy to a single W atom. Although these authors focussed primarily on defect production and subsequent survival, they did note that the large amount of defect annihilation observed during the final cooling phase resulted in mass transport that was more than an order of magnitude greater than that predicted from equilibrium transport theory. Protasov and Chudinov 1161, and Harrison and Webb [17] introduced approximations to reduce the computing time required for MD calculations of displacement cascades. These two sets of authors both pointed out that radial distribution functions calculated for the cascade atoms at the end of the collisional phase were actually characteristic of a liquid, i.e. that local melting had occurred. The analogy to melting was further supported by calculations of King and Benedek [l&19], who reported Maxwellian-like (thermal) distributions for the kinetic energies of atoms within the cascade region following the collisional phase. These latter authors also reported the existence of “closedchains” of atom replacements, and commented that such chains would imply considerable, intracascade atomic-mixing in alloys. Hence these earlier MD calculations indicated that substantial mass transport does occur within energetic displacement cascades, particularly during the final cooling phase, but they did not directly address either the magnitude of the net atom transport, nor the relative contribution from each of the three phases of cascade evolution. Recently, De la Rubia et al. [7] have investigated mass transport within 3 and 5 keV cascades in Cu using MD. Their results, which represent the highest cascade energies in reduced units yet treated in fully dynamical calculations, confirmed the local melting which was observed in the earlier calculations. Immediately after the collisional phase, regions approximately 4-5 nm in diameter were found to have radial distribution functions indistinguishable from that of a liquid, and this “melting” was found to persist for several picoseconds. Most pertinent to the present discussion, De la Rubia et al. [7] also calculated the amount of atomic mixing at various stages of the cascade evolution. In fig. 2 are plotted their results for the integrated cascade diffusion coefficient
as a function of the distance from the center of the cascade at instants of time corresponding to roughly the end of the collisional phase (0.12 ps; filled circles) and the end of the cooling phase (10 ps; open circles). Here i denotes the i th atom in a coordination shell contain-
/ Ion-beam mixing 0.3-
ofmetals /
I
I
1
I
I
I
5 keV CASCADE CU
RADIUS
Fig. 2. The integrated diffusion tion of distance from the center collisional phase (0.12 ps, filled cooling phase (10.0
km)
coefficient (D( r)t) as a funcof the cascade at the end of the symbols) and at the end of the ps, open symbols).
ing n(r) atoms at a distance r from the center of mass of the vacancy distribution generated by the cascade. The total amount of mass transport that has occurred up to the two different stages in cascade evolution can therefore be extracted by integrating over r to find the areas under the curves. Somewhat surprisingly, the total amount of diffusion that occurs during (area under lower curve) and after (area between curves) the collisional phase differs by less than 10%. Also, the same functional dependence of diffusion on distance from the cascade center is observed for both times. Nevertheless, the authors conclude that the “vast majority” of the mixing occurs during the thermal spike, i.e. after the collisional phase. They point out that a substantial portion of the area under the lower curve in fig. 2 is due to the movement of a large number of atoms that are displaced only small amounts from their lattice positions during the collisional phase. These atoms actually return directly back to their original sites at a later stage in the evolution of the cascade, and hence do not contribute to atomic mixing. The conclusion drawn from these MD calculations, namely that the atomic mixing can be largely accounted for by the diffusion calculated to occur in the locally melted cascade region after the collisional phase, when the average kinetic energy is of the order of 1-2 eV per atom, agrees well with the many experimental observations [4,14] showing a strong dependence of mixing efficiencies on thermochemical parameters with energies of this magnitude, e.g., heats of mixing or sublimation energies. Recently, De la Rubia et al. [8] have performed a second MD study, using the Johnson-&&soy potential to stimulate displacement cascades in Ni. Although
L. E. Rehn, P.R. Okamoto
a similar temperature history and liquid-like cascade region were observed for a S-keV primary knock-on event in both Ni and Cu, the duration of the calculated thermal-spike phase in Ni was found to be substantially shorter. The shorter duration of the liquid-like cascade phase results in significantly less ( - 50%) atomic mixing in Ni compared to Cu, again in good agreement with earlier experimental findings. Hence, based upon several experimental indications of the importance of energy differences on the order of l-2 eV to ion-beam mixing rates, and the new evidence provided by the MD simulations, it must be concluded that the dominant contribution to mixing rates at low ambient temperatures is intracascade mass transport initiated during the cascade cooling phase.
3. Ion-beam mixing at intermediate temperatures Thermally-activated, defect migration processes provide additional mechanisms for producing microstructures with novel or improved properties [20]. Hence considerable interest exists in understanding the temperature dependence of ion-beam mixing, and in particular, in determining the temperature range where freely-migrating defects can significantly alter both the amount and depth of the intermixing. Understanding mass transport during irradiation at intermediate temperatures should also provide valuable insight into other technologically important ion implantation phenomena that require substantial mass transport, such as buried layer formation [21], ion-beam-induced grain growth [22], and sputter-induced, subsurface compositional changes [23]. In general, three temperature regimes of ion-beam mixing have been clearly identified: low-temperatures, where only a weak dependence of mixing rates on irradiation temperature is found; intermediate temperatures, typically beginning near or slightly above room temperature, where mixing rates become more strongly dependent on temperature; and high-temperatures, typically above about 0.6 of the absolute melting temperature, where the additional mass transport induced by irradiation is substantially below the rate of thermallyinduced interdiffusion, and therefore where irradiationinduced mixing becomes insignificant relative to thermal processes. Before discussing results on ion-beam mixing of thin, polycrystalline films in more detail, we digress briefly to provide a short summary of experimental results on irradiation-induced mass transport as a function of temperature in well characterized, largegrained and single-crystal samples. At temperatures where the excess vacancy and interstitial defects produced during irradiation become sufficiently mobile, their migration will enhance mass transport. This radiation-enhanced diffusion (RED), and
/ Ion-beam
107
mixing of metals
its dependence on dose, dose-rate, temperature and defect-sink concentrations have been discussed in detail by Sitzmann [24]; many of the theoretical predictions have been verified in recent years [25,26]. An example of experimental measurements of RED in a well-characterized specimen, taken from the work of Mtiller et al. [27], is shown in fig. 3. Here, measurements of the diffusion coefficient, D, for a Ni-isotope marker layer in a single crystal specimen of Ni during irradiation with 300 keV Ni ions at several different temperatures, and two different dose rates, are plotted in Arrhenius fashion. The weak temperature dependence observed below - 600 K is consistent with ion-beam mixing of the isotope marker layer within individual displacement cascades, as discussed above in section 2. We note that although many studies report a flat temperature dependence in the low temperature regime, careful examination of the actual data consistently reveals a small, but statistically significant increase in mixing with increasing temperature, even at the lowest measurement temperatures; such a slight increase can be seen in fig. 3. The pronounced increase in D (fig. 3) which begins at temperatures between 650-700 K exhibits Arrhenius behavior with an apparent activation enthalpy of 0.58 k 0.08 eV. This energy equals one-half the vacancy migration enthalpy for Ni (1.2 eV), which is the expected value for RED when defect annihilation occurs predominantly by mutual recombination of vacancies and interstitials. Furthermore, D (in units of cm2/s) was found to be directly proportional to the square-root of the ion-current density at temperatures >_700 K, confirming that D is proportional to the product of the irradiation-induced concentrations of vacancies and interstitials. At temperatures above - 1000 K, D blends smoothly into the thermal diffusion data (dashed line in T (Kl
300
600
103/T
(K-l)
Fig. 3. Temperature dependence of the Ni self-diffusion coefficient in single-crystal specimens measured during irradiation with 300 keV Ni ions at current densities of 6 x 10” (open symbols) and 6 X 10” (closed symbols) ions/cm’s. The dashed line is an extrapolation of thermal self-diffusion coefficients for Ni measured at high temperatures in the absence of irradiation. II. ION BEAM MIXING
108
L..E. Rehn, P.R. Okamoto / Ion-beam mixing
Fig. 4. Arrhenius plot of the quantity of Si ion-beam mixed with Nb for a dose of 1.2 X10” Si ions/cm2 at several different temperatures. The quantity of Si that can be intermixed without irradiation in the same time interval is shown by the solid line marked thermal. Note the substantial temperature difference between the onset of a strong temperature dependence in the mixing rate. and the occurrence of significant thermal interdiffusion.
fig. 3). as expected for RED. Hence, enhanced diffusion due to the thermally-activated migration of vacancy and interstitial defects (RED) is an experimentally welldocumented, and theoretically well-understood phenomenon in single-crystal Ni specimens. Analogous effects [25] of dose, dose-rate and temperature on mass transport due to the thermally-activated migration of irradiation-induced point defects have also been reported in large-grained, Ni-Si alloys, but again, only at temperatures 2 650 K. We now return to experimental studies of ion-beam mixing in poly~rystalline thin films. The first observation of a substantial change in the temperature dependence of ion-beam mixing rates was that of Matteson et al. [9], who measured the interdiffusion in Nb/Si bilayer specimens during irradiation with 275 keV Si ions. Their results are shown in fig. 4. The sharp increase in mixing efficiency that occurs above - 200 o C appears, at least on the basis of the limited experimental data, to exhibit Arrhenius behavior, with an apparent activation enthalpy of 0.9 eV. Since this value is roughly one-half of the vacancy migration enthalpy reported at that time for Nb, the authors attributed this increase in mixing efficiency above - 200 ’ C to RED. No dose-rate studies were reported. Ion-beam mixing in polycrystalline films of many different materials has subsequently been shown to exhibit a similar temperature dependence. The
ofmetals
two regimes of apparent Arrhenius behavior have become known as Q-curve behavior, and the vast majority of authors have attributed the increase in mixing that occurs in the higher temperature regime as arising from RED [9,28]. Although it is clear that the intermixing in the upper Arrhenius regime is “enhanced” by irration, that is, that the amount of interdiffusion during irradiation is substantially greater during bombardment, we wish to point out certain disparities that exist between ion-beam mixing results obtained for the upper portion of the Q-curve using polycrystalline bilayer and marker specimens, and expected RED behavior as documented by results such as those shown in fig. 3. One obvious disparity has been discussed previously by Shreter et al. [29]. These authors performed a study similar to that of Matteson et al., and found that the apparent activation enthalpy for ion-beam mixing of NbSi bilayers dropped to only 0.2 eV for irradiation with Xe ions. A dependence of the apparent activation enthalpy on ion-species is clearly inconsistent with the assumption of RED in the defectrecombination-limited regime, for which the magnitude is determined only by the migration enthalpy of the slower moving defect [24]. A second discrepancy, which appears consistently throughout the literature, is the low onset temperatures that have been reported for enhanced mass transport in ion-beam mixed, polycrystalline systems. For example, the onset temperature is < 500 K in Nb/Si (fig. 4), but it is - 700 K in the single-crystal Ni study (fig. 3). Although both vacancy and interstitial defects are expected to become mobile at temperatures substantially below 500 K in Ni, the delayed onset of the RED contribution is well understood in the single-crystal results [30]. For temperatures c 600 K, the irradiation-induced sink concentrations are extremely high; electron microscopy studies yield values for the sink annihilation probability of > 10m5 for a defect migrating in this temperature regime [31]. This high annihilation probability means that the average distance a defect will migrate before annihilation at a sink is -z 10 nm. Therefore, no significant mass transport due to thermally-activated, freeiy-~grating defects (RED) is expected until irradiation temperatures near 600 to 700 K, where the irradiation-induced sink concentration drops dramatically. A third disparity involves several unrealistically low values, as low as 0.1 eV (321, reported for the apparent activation enthalpy in the upper portion of the Q-curve. Particularly for concentrated alloys, values 2 0.5 eV would be expected if the enhanced mixing was indeed due to freely-migrating, irradiation-endured vacancies and interstitials. It is clear that RED, that is the therm~ly-activated, free migration of irradiation-induced vacancy and interstitial defects, does not offer a consistent explanation for the upper Arrhenius regime found for ion-beam mixing at intermediate temperatures in a wide variety of
L. E. Rehn, P.R. Okamoto
materials. In particular, the onset temperature is too low, the measured activation enthalpies are frequently not of the expected magnitude, and even the existence of a well understood dose-rate dependence remains uncertain. This latter point will be addressed in more detail shortly. The situation regarding enhanced ion-beam mixing at intermediate temperatures has received increased attention due to recent reports of “RED” in amorphous systems. The results of Priolo et al. [33], who studied the temperature dependence of mixing of a Au marker layer in amorphous Si during irradiation with 2.5 MeV Ar ions, are shown in fig. 5. The three temperature regimes discussed earlier are clearly evident: a weak temperature dependence below - 400 K, a strong temperature dependence between approximately 400 and 700 K which, at their dose-rate, appears to blend smoothly into the thermal diffusion data at temperatures above - 800 K. Although these results are strikingly similar to the known RED behavior in Ni (fig. 3) we note once again that the onset temperature for enhanced mass transport is low, only - 400 K. Furthermore, Priolo et al. report no dependence of D on dose-rate at 493 K. again different from the Ni study. Although irradiation conditions exist for which no dependence of RED on dose-rate is expected, e.g. the regime where defects annihilate predominantly at sinks, the observation of a substantial dependence on temperature near 493 K argues strongly against this interpretation. That is, unless the irradiation-induced sink concentration is strongly temperature dependent, the diffusion coefficient in the sink-annihilation dominant regime is temperature independent, since the same number of defects migrate the same average distance (to a constant number of fixed sinks) at all temperatures. The combined observations of a strong
T (Kl ,o-l’
IO+ ,?
E 0 D
16'5
103/T
(K-‘1
Fig. 5. Diffusion coefficients of Au in amorphous Si measured at the indicated temperatures after irradiation with 2.5 MeV Ar ions at a dose-rate of 7X10” ions cm-’ SC’. Open data points represent total diffusion coefficients, and closed data points represent thermal interdiffusion data.
/ Ion-beam mixing
of metds
109 T IK)
IO4
500
,
400
300
I
I
Ni/Zr
i02=3.5e~
,I
2
3 1000/T
(K-l)
Fig. 6. Mean square diffusion distances measured during ion-beam mixing of Ni/Zr bilayer specimens by I-MeV ions at several temperatures.
the Kr
temperature dependence of D but no dose-rate dependence in amorphous Si suggest that the enhancement in mixing that begins above - 400 K is due to an intracascade mechanism. A similar Q-curve dependence for ion-beam mixing has recently been reported in Ni/Zr bilayer specimens. for which the mixed layer goes amorphous very early in the irradiation. These results. by Ding et al. [34], are displayed in fig. 6. Again, we note a relatively sharp increase in the mixing rate at a temperature just below 500 K. In contrast to the amorphous Si results. however. a pronounced dose-rate dependence of the mixing rate in amorphous Ni/Zr was reported at an irradiation temperature of 523 K. In the absence of beam heating effects, the observation of a dose-rate dependence indicates an intercascade process, i.e. that the effects produced by one ion interact dynamically with those produced by other ions. Ding et al. were able to fit their diffusion data to an inverse square-root of dose-rate dependence, in agreement with the Ni study discussed above, and therefore concluded that the enhanced mixing observed above - 480 K in Ni/Zr was due to RED. Unfortunately. the fit of their data to an inverse square-root dependence depends sensitively on the choice of a low-temperature mixing-rate. In the absence of a firm value for this quantity. equally good fits are obtained with exponents between roughly - 0.2 and - 1 [35]. Hence the conclusions that have recently been drawn regarding evidence for well-defined point-defect configurations in amorphous systems. based upon the interpretation that RED is causing the increased II. ION BEAM MIXING
L. E. Rehn, P.R. Okamoto
110 T (K1
300
400
500
’
It’
i
1000/T
temperature
dependence
are changing, since a parallel change is observed even in the absence of ion bombardment. This parallel change suggests that the “thermal-like” cascade cooling phase becomes more efficient at promoting interdiffusion at higher temperatures simply because the underlying thermal processes themselves become more efficient. It should be pointed out that this interpretation, which postulates the same intracascade mechanism in both Arrhenius regions, predicts no direct dependence on ion dose-rate. Hence it is in agreement with the amorphous Si results discussed above, but does not explain the dose-rate dependence found in Ni/Zr. A possible alternative explanation to RED for the dose-rate dependence observed in Ni/Zr is that the irradiation-induced sink structure is in fact dose-rate dependent. More detailed investigations of the effect of dose-rate on interdiffusion during ion bombardment can be expected to clarify this matter. One simple approach, which we are currently exploring in our own laboratory, is to search for an additional increase in ion-beam mixing efficiency at yet higher temperatures, e.g. 1650 K, where true RED can be expected.
(K-‘1
Fig. 7. Diffusion coefficients measured during ion-beam mixing (upper curves) and thermal interdiffusion (lower curves) of Au/Zr and Ni/Zr bilayer specimens. Note that the break in the temperature dependence occurs at approximately the same temperature both with and without irradiation.
ered
/ Ion -beam mixing of metals
of the mixing,
must
be consid-
speculative.
An alternative explanation for the enhanced mixing at intermediate temperatures is suggested by yet unpublished results of Ding et al. [36], who studied interdiffusion in Au/Zr and in Ni/Zr bilayer specimens during, and in the absence of, ion bombardment. These results are displayed in fig. 7. Note that although irradiation greatly enhances the rate of interdiffusion in both alloy systems, the diffusion in the absence of irradiation also exhibits two regions of Arrhenius behavior, with the higher temperature regime having the stronger temperature dependence in both cases. Furthermore, the onset of the higher temperature regime occurs at approximately the same temperature in the thermal annealing, as well as in the irradiation case. The MD evidence discussed in section 2 indicates that the high efficiency of ion-beam mixing in the lower part of the Q-curve, and its dependence upon thermodynamic variables such as the heat of mixing or cohesive energy, are direct manifestations of the fact that the majority of the mass transport induced within individual displacement cascades occurs during a “thermal-like” cooling phase. The results in fig. 7 suggest that the same explanation remains valid for the upper Arrhenius portion of the Q-curve. It is apparently not the irradiation effects that
4. Solid-state amorphization The formation of metastable phases, particularly amorphous materials, has been the subject of several review presentations at previous IBMM conferences. Because of the large variety of elements which can be intermixed to high concentration levels, a large number of amorphous phases have been produced by ion-beam mixing. The focus of previous presentations has been on identifying parameters such as ion mass and irradiation temperature that are critical to amorphization, and formulating generic rules to predict which classes of materials can be made amorphous by ion-beam mixing [37]. Here we focus on the crystalline-to-amorphous (c-a) transformation per se, and in particular on recent experimental evidence [38] that this is preceded by a first-order phase transformation driven by an elastic instability. We are investigating ion-beam induced amorphization in several ordered intermetallic compounds using Brillouin scattering to determine changes in a shear elastic constant, and transmission electron microscopy (TEM) to measure changes in long-range chemical order and lattice dilation. Measurements in Zr,Al of the sound velocity, which is directly proportional to the square-root of the shear elastic constant, are shown in fig. 8 as a function of dose during irradiation with l-MeV Kr ions. The data reveal that a large, almost 50% decrease occurs in the Zr,Al shear constant during disordering, which TEM shows is occurring up to a dose of - 6 x 1013 cm-*. The decrease in shear constant during disordering is substantially larger than the typi-
L. E. Rehn, P.R. Okamoto
DOSE
(Ions/cm2)
Fig. 8. Measurements of the shear sound velocity, which is proportional to the square root of the shear elastic constant, in Zr,Al as a function of ion dose. Open and filled circles denote respectively broad (due to the polycrystalline specimen) and narrow peaks in the Brillouin spectra.
cal 5 10% reported [39] for alloys such as Cu,Au that undergo an order-disorder transformation below their melting point, but does agree with previous measurements of large elastic softening due to disordering of Nb,Ir [40], another intermetallic that in the absence of irradiation, remains ordered up to its melting point. At a dose between 4-8 x lOI cme2, an abrupt increase is seen in the Zr,Al sound velocity (fig. 8). After this abrupt increase, no additional change occurs in the sound velocity upon further irradiation. The discontinuity in the sound velocity demonstrates that the c-a transformation is not a continuous function of irradiation, but rather that a relatively abrupt phase transformation occurs first. For Zr,Al, TEM reveals a simultaneous discontinuity in the long-range order parameter, S, indicating that the phase transformation is first-order [41]. An abrupt phase transformation is also seen in the in situ lattice parameter measurements, which show that the lattice parameter expands monotonically by - 0.8% during disordering, drops abruptly to - 0.6% at a dose of - 5 X lOI cmm2, then remains unchanged up to the highest doses (- lOI cmP2) where diffraction spots can still be observed. The large elastic softening which precedes the phase transformation suggests, in analogy with the martensitic transformation [42], that an elastic instability triggers the transformation. Based upon a similar increase in lattice parameter observed during amorphization of Zr,Al by hydrogen charging [43], we believe that the elastic softening is a direct manifestation of lattice dilation, regardless of whether the dilation results from disordering, heating, or from hydrogen absorption.
/ Ion-beam
mixrng of metals
111
A similar elastic softening with increasing lattice parameter is well known during heating. In fact, at least six parallels between ion-induced amorphization and heating to the melting temperature, T,,, were noted in the above study. These include: (1) a large, - 50% elastic softening occurs (as a function of temperature up to T,,,; as a function of ion dose through disordering); (2) a discontinuity occurs (as a function of temperature at T,; as a function of ion dose at - 6 x lOI cmm2); (3) a linear relationship exists between the lattice parameter and shear elastic constant changes (as a function of ion dose; as a function of temperature), that (4) extrapolates to zero at an additional dilation of - 3%. The discontinuities found in (5) the long-range order parameter and in (6) the interatomic spacing during irradiation also parallel changes observed during melting. To investigate further the idea that irradiation-induced amorphization is triggered by an elastic instability, we have recently performed Brillouin scattering measurements on three more intermetallics as a function of ion dose: NiAl, which cannot be substantially disordered during ion-bombardment at room temperature, FeAl, which can be disordered but does not become amorphous, and FeTi, which first disorders then becomes amorphous. Initial results [44] for the shear elastic constants of these three materials, obtained for irradiation at room temperature with 1.5-MeV Kr ions, are shown in fig. 9 as a function of dose. The shear constant of NiAl, which shows only a small decrease in long-range order under these irradiation conditions, decreases only slightly (- 10%) by a dose of 4 X lOI cm-*. A larger ( - 20%) decrease is seen in FeAl, which is expected to be almost totally disordered, but not amorphous, by the highest dose (2 x lOi cmP2); the initial increase in velocity is currently not understood. A substantially larger decrease ( - 30%) is seen in FeTi by a dose of 1 x 1014cm-2 and a possibly abrupt increase, such as that seen for Zri Al (fig. 7), occurs at a dose of - 2 x lot4 cmm2. Hence the results shown in fig. 8 provide corroborating evidence that disordering of strongly-ordered intermetallics generates a large elastic softening. Although disordering is apparently responsible for the lattice dilation which drives the strongly-ordered intermetallic compounds amorphous, there are several other processes that can produce lattice dilation. For example, ion-beam mixing can generate highly supersaturated solid solutions, which lead to large lattice dilation. Linker et al. [45] observed a similar lattice dilation and apparent strain release during the implantation of B into Nb and MO. The hydrogen results discussed above also indicate that it is the lattice dilation which eventually drives the lattice unstable. Hence amorphization following supersaturation by ion-beam mixing or by direct implantation can also be understood II. ION BEAM MIXING
112
L. E. Rehn, P.R. Okamoto / Ion-beam mixing
ofmetals
proves to be true, beneficial modifications achieved with far lower irradiation/implantation
1
.” A-
-J
I
0
0 2.d rL -31
0
10'5
IO” DOSE (ions/cm21
Fig. 9. Brillouin measurements of the sound velocity as a function of ion dose in three intermetallic specimens: NiAl, which neither disorders nor goes amorphous; FeAl, which disorders but does not become amorphous; and FeTi, which
disorders and subsequently becomes amorphous.
on the basis of an elastic instability, as can amorphization by solid-state reaction. We note that the apparent elastic instability and first-order phase transformation that occur during ion bombardment do not simultaneously drive the entire crystal amorphous. Strong fundamental spots dominate the diffraction patterns of Zr,Al taken at doses of 6-8 X lOI cm-*, indicating that only a small fraction of the crystal is amorphous immediately after the transformation. Complete amorphization requires doses > 2 X lOI cm-*. During this gradual transformation, however, no additional change is seen in either the shear constant or lattice parameter, demonstrating that the elastic properties of the material following the abrupt transformation are very similar to those of the fully amorphous phase. Large decreases in the shear constant can be expected to generate concomitant mechanical property changes. It would be interesting to compare the mechanical properties of highly disordered materials with similar measurements in fully amorphous phases of identical compositions. Perhaps some of the large property changes which have been reported for amorphous layers [46] are actually due to this large change in elastic behavior,
and
not
to the
structural
differences.
If this
could be doses.
We wish to acknowledge many stimulating sions with our ANL colleagues on topics covered presentation. In particular, we wish to thank nedek and H. Wiedersich for critical comments manuscript.
discusin this R. Beon the
References PI D.H. Lee, R.R. Hart, D.A. Kiewit and O.J. Marsh, Phys. Status Solidi (a)15 (1973) 645. PI W.F. van der Weg, D. Sigurd and J.W. Mayer, in: Applications of Ion Beams to Metals, eds. ST. Picraux, E.P. EerNisse and F.L. Vook (Plenum, New York, 1974) p. 209. Nucl. Instr. and Meth. 131 J.J. Cuomo and SM. Rossnagel, B19/20 (1987) 963. Y.T. Cheng, M. VanRossum and M-A. [41 W.L. Johnson, Nicolet, Nucl. Instr. and Meth. B7/8 (1985) 657. [51 M.G. le BoitC, A. Traverse, H. Bernas, C. Janot and J. Chevrier, Mater. Lett. 6 (1988) 173. [cl A. Traverse, M.G. le Boitt, L. NCvot, B. Pardo and J. Corno, Appl. Phys. Lett. 51 (1987) 1901. R. Benedek and W.E. [71 T.D. de la Rubia, R.S. Averback, King, Phys. Rev. Lett. 59(17) (1987) 1930. R. Benedek and I.M. PI T.D. de la Rubia, R.S. Averback, Robertson, Proc. of Fusion Workshop, to be published. [91 S. Matteson, J. Roth and M-A. Nicolet, Radiat. Eff. 42 (1979) 217. [lOI M-A. Nicolet, T.C. Banwell and B.M. Paine, Mater. Res. Sot. Symp. Proc. 27 (1984) 3; S.-J. Kim, M-A. Nicolet, R.S. Averback and D. Peak, Phys. Rev. B37(1) (1988) 38. 1111 R.S. Averback, L.J. Thompson and L.E. Rehn, ibid., p. 25. [=I J. Bottiger, S.K. Nielsen and P.T. Thorsen, Nucl. Instr. and Meth. B7/8 (1985) 707. u31 B. Paine and R.S. Averback, ibid., p. 666. and D.N. Seidman, Mater. Sci. Forum P41 R.S. Averback 15-18 (1987) 963. u51 M.W. Guinan and J.H. Kinney, J. Nucl. Mater. 103/104 (1981) 1319. Radiat. Eff. 66 (1982) [161 V.I. Protasov and V.G. Chudinov, 1. iI71 D.E. Harrison and R.P. Webb, Nucl. Instr. and Meth. 218 (1983) 727. [I81 W.E. King and R. Benedek, J. Nucl. Mater. 117 (1983) 26. [I91 W.E. King and R. Benedek, Phys. Rev. B23 (1981) 6335. PO1 L.E. Rehn and H. Wiedersich, in: Surface Alloying by Ion Electron, and Laser Beams, eds. L.E. Rehn, S.T. Picraux and H. Wiedersich (American Society of Metals, Metals Park, OH, 1987) p. 134. PI A.E. White, K.T. Short, R.C. Dynes, J.M. Gibson and R. Hull, Mater. Res. Sot. Symp. Proc. 100 (1988) 3. and H.I. Smith, ibid., p. PI H.A. Atwater, C.V. Thompson 345 ; J.C. Liu and J.W. Mayer, ibid., p. 357. 1231N.Q. Lam, ibid., p. 29.
L. E. Rehn. P.R. Okamoto [24] R.S. Sizmann, J. Nucl. Mater. 69/70 (1978) 386. [25] R.S. Averback, L.E. Rehn, W. Wagner, H. Wiedersich and P.R. Okamoto. Phys. Rev. B28 (1983) 3100. [26] M.-P. Macht, A. Mtiller, V. Naundorf and H. Wollenberger, Nucl. Instr. and Meth. B16 (1986) 148. [27] A. Mtiller, M.-P. Macht and V. Naundorf, Proc. 14th Int. Symp. on Effects of Radiation on Materials, Andover, MA, USA, to be published. [2X] Y.-T. Cheng, X.-A. Zhao, T. Banwell, T.W. Workman, M-A. Nicolet and W. L. Johnson, J. Appl. Phys. 60(7) (1986) 2615. [29] U. Shreter, F.C.T. So, B.M. Paine and M-A. Nicolet, Mater. Res. Sot. Symp. Proc. 27 (1984) 31. [30] A. Mtiller, V. Naundorf and M.-P. Macht, Mater. Sci. Forum 15-1X (1987) 1081. [31] J.E. Westmoreland, J.A. Sprague, F.A. Smidt, Jr. and P.R. Malmberg, Radiat. Eff. 26 (1975) 1. [32] See, for example, E. Ma, A.J. Brunner, T.W. Workman, C.W. Nieh, X.-A. Zhao and M-A. Nicolet. Mater. Res. Sot. Symp. Proc. 100 (1988) 75. [33] F. Priolo, J.M. Poate, D.C. Jacobson, J. Linnros, J.L. Batstone and S.U. Campisano, ibid., p. 87. [34] F.-R. Ding, R.S. Averback and H. Hahn, J. Appl. Phys. 64 (1988) 1785. [35] U. Scheuer, ANL, private communication.
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[36] F.-R. Ding, L.E. Rehn and P.R. Okamoto, to be published. [37] See, e.g., D.M. Follstaedt, Nucl. Instr. and Meth. B7/8 (1985) 11; J.L. Brimhall, ibid., p. 27; C.H. Hewett, S.S. Lau, I. Suni and D.B. Poker, ibid., p. 597. [3X] L.E. Rehn. P.R. Okamoto, J. Pearson, R. Bhadra and M. Grimsditch, Phys. Rev. Lett. 59 (1987) 2987. [39] P.A. Flinn, G.M. McManus and J.A. Rayne, J. Phys. Chem. Solids 15 (1960) 189. [40] M. Grimsditch, K.E. Gray, R. Bhadra, R.T. Kampwirth and L.E. Rehn, Phys. Rev. B35 (1987) 883. [41] S. Strlssler and C. Kittel, Phys. Rev. Al39 (1965) 758. [42] N.G. Pace and G.A. Saunders, Philos. Mag. 22 (1970) 73. [43] W.J. Meng, P.R. Okamoto, B. Kestel, L.J. Thompson and L.E. Rehn, Appl. Phys. Lett. (Nov, 1988) in press. [44] J. Koike, P.R. Okamoto, L.E. Rehn, R. Bhadra and M. Grimsditch, unpublished. [45] G. Linker, Nucl. Instr. and Meth. B19/20 (1987) 526. [46] G.H. Hubler, in: Surface Alloying by Ion, Electron, and Laser Beams, eds. L.E. Rehn, ST. Picraux and H. Wiedersich (American Society of Metals, Metals Park, OH, 1987) p. 287.
II. ION BEAM MIXING