A quantitative atom-probe field-ion microscope study of the compositions of dilute Co(Nb) and Co(Fe) alloys

Surface Science 130 (1983) 63-88 North-Holland ~blishing Company

63

A QUANTITATIVE ATOM-PROBE FIELD-ION MICROSCOPE STUDY OF THE COMPOSITIONS OF DILUTE Co(Nb) AND Co(Fe) ALLOYS Roman

HERSCHITZ

and David N. SEIDMAN

Cornell University, Bard Hal/, Department of Materials Science Center, Ithaca, New York 14853-0121, US.4 Received

7 February

1983; accepted

for publication

Science and Engineering and The Materials

12 April

1983

The compositions of Co-l.Oat%Nb and Co-l.Oat%Fe alloys have been measured using the atom-probe field-ion microscope. The main purpose of this experimental work was to find a set of optimum conditions which gives the correct solute concentrations in these alloys. This information was necessary for measuring the absolute compositions, in our extensive investigations of solute atom segregation effects to individual stacking faults in these alloys. The dependence of each alloy’s composition on the following parameters was investigated: (1) the specimen temperature; (2) the pulse fraction; (3) the field-evaporation rate; (4) the crystallographic plane; (5) the effect of the presence of hydrogen in the atom-probe on the measured Nb composition in a Co- I.Oat%Nb alloy. It is shown that the composition determined by the atom-probe FIM is very sensitive to some of the parameters listed above. The effects of these experimental parameters on the measured Nb and Fe concentrations are discussed in terms of possible freed-evaporation models. Under certain experimental conditions drastically different behavior has been observed in these alloys; preferential field-evaporation of solute atoms in a Co-l.Oat%Fe alloy and preferential retention of solute atoms in a Co-t .Oat%Nb alloy was observed. Correct solute concentrations were obtained by using the following experimental parameters: (I) a specimen temperature of less than or equal to 60 K; (2) a pulse fraction of greater than or equal to 0.10.

1. Introduction It has been shown recently that in atom-probe field-ion microscope (FIM) investigations of alloys, the apparent composition of certain elements can differ from the nominal values expected. For example, Wagner [l] found that the titanium concentration in a MO-l.Oat%Ti alloy is a very sensitive function of the absolute number of atoms detected per field-evaporation pulse, i.e., the instantaneous field-evaporation rate. Also Watts and Ralph [2] have demonstrated that the Ti composition of a Ni-la.Oat%Ti alloy is a function of the pulse fraction. The dependence of the measured alloy composition on the fundamental experimental parameters used in the atom-probe FIM has been investigated recently by Miller and Smith [3] in their detailed study of an Fe-3.0at%Si transformer steel, and by Yamamoto and Seidman [4,5] in their ~39-602g/83/0000-~/$03.00

@ 1983 North-Holland

64

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extensive investigations of ordered Pt,Co and Ni,Mo alloys. In this paper the effects of a number of different important experimental parameters, employed in the atom-probe FIM, on the quantitative chemical analyses of dilute cobalt-based alloys are presented. The main purpose of this work was to find a set of optimum experimental conditions which gives the correct solute concentrations for Co- l.Oat%Nb and Co-l.Oat%Fe alloys. These alloys were used in our extensive investigations of solute atom segregation effects to individual stacking faults - frequently called Suzuki segregation [6,7]. The dependence of an alloy’s composition on the following parameters was investigated: (1) the temperature of the specimen (T,); (2) the pulse fraction (f) - ratio of pulse voltage (V,) to steady-state voltage (VIX); (3) the average field-evaporation rate - average number of ions evaporated per field evaporation pulse; (4) the crystallographic plane examined; (5) the phase of an alloy (fee or hcp); (6) The effect of the presence of hydrogen in the atom-probe FIM on the measured Nb composition in a Co-l.Oat%Nb alloy. It is shown that the compositions determined by atom-probe FIM analyses of Co-l.Oat%Nb and Co-l.Oat%Fe are very sensitive to some of the above listed parameters and a discussion is presented on the effects of these parameters on the measured ~ncentrations.

2. Experimental techniques 2. I. Specimen preparation Wire specimens of Co- l.Oat%Nb and Co-l.Oat%Fe alloys, with a diameter of 0.375 mm and 0.254 mm, respectively, were fabricated at the General Electric Research Laboratory (Schenectady, NY). Atomic absorption spectroscopy analyses were performed on these alloys, and the nomal compositions were found to be Co-0.96at%Nb and Co-0.98at%Fe; the analyses were executed in the laboratory of Professor G.H. Morrison of the Chemistry Department at Cornell University. The wire was cut into 80 cm long specimens, which were encapsulated under vacuum (10M6 Torr), prior to annealing treatments, in quartz capsules. The specimens were annealed at several temperatures in the range 450 to 575OC, for our investigations of solute atom segregation effects to stacking faults in these alloys [6,7]. Sharply-pointed FIM specimens were prepared by a two-step polishing procedure. The first step consisted of electroetching 12 mm long wires of the original diameter in a chromic acid : water solution (3 : 10 by volume) at 6 VAc,

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until the diameter was reduced to - 0.125 mm. Typically it took 6 min of etching for a Co- 1.Oat%Nb and 4 min for a Co- 1.Oat%Fe alloy to reach this diameter; a stainless-steel counter-electrode was employed. Next the thinned wires were inserted in a FIM specimen holder and sharpened to a needle-like FIM tip (an initial radius of - 50-100 A) by electroetching in a freshly-made hydrochloric acid : water solution (1 : 10 by volume) at room temperature at a a stainless steel counter-electrode. potential of 3.2 V,, - also employing Normally a tip having the desired radius was obtained by dipping a 6 mm length of the specimen into the solution and then electroetching away a 3 mm length of the specimen. Occasionally, certain specimens could not be polished to the desired radius by this technique. In order to overcome this problem the electroetching procedure was continued with the application of short (- 0.5 s) sharpness was voltage pulses of magnitude 1.0-5.0 VA,-, until a satisfactory achieved. A good specimen had the appearance of a well-sharpened pencil when examined with an optical microscope at a magnification of 400 x . The initial end form of the electroetched tip was extremely rough on an atomic scale. An atomically smooth end form was obtained by a combination of DC and pulse-field evaporation in the atom probe. 2.2. Experimental

procedure

(1) Atom probe analyses of the basal (0002) plane of the hcp phase were performed at 35, 45, 60 and 90 K for the Co-l.Oat%Nb alloy, and at 45, 60 and 90 K for the Co-l.Oat%Fe alloy. The uncertainty in the measured T, was 0.01 K. (2) At a given specimen temperature the value off was systematically varied from 0.05 to 0.20. The quantity f is given by the ratio VP/V,,,-, where I’,, is the value of a steady-state voltage and VP is the value of the pulse voltage used for the pulse field-evaporation process; VP corresponds to the voltage generated by the pulser. As the value of f is increased V,, decreases, i.e., the smallest value of f corresponds to the largest value of I’,,. The pulse frequency was kept constant at 60 Hz. During each analysis a cylinder of alloy containing 3,000 to 8,000 Co plus Nb or Co plus Fe atoms was examined. (3) The average field-evaporation rate is proportional to Ni,,/NpUISe; where Nion is the total number of either Co and Nb atoms, or Co and Fe atoms detected, and Npulse is the number of field-evaporation pulses applied to the specimen to evaporate these atoms. The vast majority of the data were taken at a ratio of Nion/NpUISe equal to - 0.02 ion pulse-‘. (4) In order to elucidate the effect of field-evaporation rate on the quantitative chemical analyses in a Co- l.Oat%Nb alloy at T, = 45 K and f= 0.15 the was gradually varied from 0.01 to 0.05 ion pulse- ’ during value of N;,“/Nr”i,, the atom-probe analysis. In case of the Co-l.Oat%Fe alloy three separate runs with the value of Ni,JNpUISe equal to 0.01, 0.02 and 0.03 ion pulse- ’ were

66

R. Herschitz, D.N. Seidnzan / Quantitative APFIM study

performed. The field evaporation rate was monitored by an audio ratemeter. (5) Pyramidal (7101) and prismatic (7100) planes of the hcp phase and the (111) plane of the fee phase of each alloy, were analyzed at T, = 45 K and f= 0.15. (6) The effect of the presence of hydrogen in the atom-probe FIM on the measured Nb concentration in a Co-I.Oat%Nb alloy was investigated by introducing hydrogen gas into the chamber of the microscope during the analyses - the partial pressure of hydrogen was charged from 3 X lo-” Torr to 2 x IO-’ Torr.

3. Experimental results 3.1. Co-l.Oat %Nb alloy Fig. 1 shows a FIM image of a [0002]-oriented hcp crystal of a Co-l.Oat%Nb alloy, for T, = 45 K. Stable images of this alloy were obtained using neon as an imaging gas. A gauge pressure of - 4 X 10m5 Torr was typically used. Typical mass spectra - number of events versus the mass-to-charge ratio for a Co-l.Oat%Nb alloy are exhibited in figs. 2 and 3; these spectra were recorded with T, = 45 K employing a value of f = 0.15. The background pressure during the analyses was in the range of (4.0-6.0) x lo- ” Torr. At this pressure the main residual gases were hydrogen ( < 5.0 x 10--‘” Torr), carbon monoxide (< 2.0 x 10-l’ Torr) and helium (C 4.0 x lo-‘* Torr); the partial pressures were measured employing a Uthe Technology Inc. (UTI) Model 1OOC residual gas analyzer. Both cobalt and niobium have single naturally occurring isotopes - 59Co and 93Nb. Cobalt appears only in the plus-two ionization state (59C02’) and 93% of the niobium events appear in the plus-three ionization state (93Nb3i), with the remaining 7% appearing in the plus-two ionization state (93Nb2’); this observation was found to be independent of T, during atom-probe analyses at 35, 45, 60 and 90 K, for a constant value of the evaporation field. Fig. 4 shows a typical mass-spectrum for a Co-l.Oat%Nb alloy analyzed at T, = 90 K. Note that in addition to the isotopes of cobalt and niobium there is an additional peak due to niobium hydride - compare with the mass spectrum recorded at 45 K shown in fig. 2. Our atom-probe has a sufficient mass resolution, in the case of these alloys, to allow for the clear distinction between metal ions and their only slightly heavier hydride ions. The cobalt (niobium) alloy appears to be an ideal alloy for the unambiguous identification of metal hydrides, as both components have only one isotope. For elements having several naturally occurring isotopes it may be more difficult to distinguish between the metal and metal hydride ions. The main results obtained in the study of this alloy are shown in fig. 5,

R. Herschitz,

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Fig. 1. A FIM micrograph of a [0002]-oriented hcp crystal of a Co-l.Oat%Nb alloy. This micrograph was recorded with T, = 45 K, employing neon as the imaging gas (4.0X 10m5 Torr gauge pressure).

where the measured Nb concentration is plotted as a function off at different values of T,. Fig. 5 clearly demonstrates the strong dependence of the measured Nb composition on T, and f. Specifically, at 90 K all of the atom-probe determinations of the Nb concentration are greater than the nominal value; at f equal to 0.05 the measured Nb composition is nine times the nominal value. And at T, = 60 K the agreement is good for f equal to 0.10, 0.15 and 0.20, while atf= 0.05 it is 0.50 at% greater than the nomal value. Whereas, at 35 and 45 K the Nb concentration measurements are essentially independent of the values of f used and are in the range of values obtained from the atomic absorption spectroscopy measurements. Fig. 6 is a plot of the cumulative number of Co plus Nb events as a function

68

R. Herschitz,

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MASS-TO-CHARGE

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32

APFIM

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33

RATtO

Fig. 2. The Co2+ and Nb3’ mass spectrum of the Co-.Oat%Nb alloy. The spectrum was recorded at TS=45Kwithf=0.15at4x10lo Torr Cobalt appears only in the plus-two ionization state (59C02+) and 93% of the niobium events appear in the plus-three ionization state (93Nb3+). Both cobalt and niobium are single isotope metals.

of the cumulative number of field-evaporation pulses at different stages of the atom-probe analyses. One can clearly see the step-like behavior in the fieldevaporation process. Each single step corresponds to the removal of one (0002) plane from the surface of the specimen. Initially - fig. 6a - the field-evaporapulses were tion rate was equal to 0.01 ion pulse- ‘; 5 x lo3 field-evaporation

MASS-TO-CHARGE

RATIO

alloy. The spectrum was recorded at r, = 45 K Fig. 3. Nb2+ mass spectrum of the Co-l.Oat%Nb lo Torr. About 7% of all niobium events appear in the plus-two ionization withf=O.lS at4~10state (93Nb2+).

R. Herschitz,

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69

?

SSco2’

r

E

1007

2

“Nb”

b B 3

_I IO:

(NbH?’ I

z II 28

I

1 29

30

31

MASS-TO-CHARGE

32 RATIO

Fig. 4. The Co2+ and Nb3’ mass spectrum of the Co-l.Oat%Nb alloy recorded at T, = 90 K and f = 0.15 at 4 X IO- lo Torr. Note the presence of an additional peak due to Nb hydride.

(-J

2

8.0-

_

I

DETERMINED ABSORPTION

90K

.

90

K (DISREGAR;;;;,;EbS)

0

60

K

0

45K

n

35K

BY ATOMIC SPECTROSCOPY I

I

0.05

0.10

I 0.20

1

0.15

PULSE FRACTION : f = w Fig. 5. The measured Nb concentration for the (0002) plane of an hcp crystal

(at’%) versus pulse fraction of the Co-l.Oat%Nb alloy.

(f)

at T, = 35, 45, 60 alid 90 K

70

R. Herschitz,

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1400s

b

NION

_

NPULSE

'*ION

loot- J

~=~ol “PULSE

-

t’--

01 20

’

1 24

1

I 28

1

’ 32

’

’

1

36

I 40

CUMULATIVE NUMBEROF FIELD-EVA~ATI~ PULSES (x 103) Fig. 6. A plot of the cumulative number of Co plus Nb events as a function of the cumulative number of field-evaporation pulses for the (0002) plane of a hcp crystal of the Co-l.Oat%Nb alloy at T,=90 K withf=0.15.

employed to evaporate one (0002) plane containing approximately 70 atoms. Fig. 6b is a plot corresponding to a field-evaporation rate of 0.03 ion pulse- ’ 2 x lo3 field-evaporation pulses were employed to field evaporate a single

R. Herschitr, I)&. Seidman / Quantitative

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plane. Finally, fig. 6c corresponds to the last stages of the analysis for which the field-evaporation rate was equal to 0.05 ion pulse-’ - 1 X IO3 fieldevaporation pulses were needed for the field-evaporation of one plane. The removal of each plane was monitored during the atom-probe analysis by an audio ratemeter. The step-like increase in the field-evaporation rate simultaneously caused a step-function increase in the output of the audio ratemeter. Fig. 7 shows a plot of the cumulative number of Nb events versus the cumulative number of Co plus Nb events - such a plot is called an integral profile - for the case where average field-evaporation rate varies from 0.01 to 0.05 ion pulse-‘. The smallest vertical step corresponds to the detection of one Nb event. The average slope of this plot corresponds to the average Nb composition of the volume analyzed and it is equal to 1.05 rdr0.19 at% Nb; where the uncertainty is equal to the ratio of the square root of the number of Nb events to the total number of Co plus Nb events detected. This measured Nb composition is in good agreement with the atom-probe determinations, of the same quantity, for specimens for which the average field-evaporation rate was kept constant t~ou~out the entire analysis. Furthermore, the fact that there are no radically large local fluctuations in the slope of the integral profile - it is approximately uniform throughout the entire analysis - also indicates that the change in the field-evaporation rate from 0.01 to 0.05 ion pulse-’ at T,= 45 K andf= 0.15 had no major effect on the measured Nb concentration. Table 1 lists the measured Nb concentrations for different crystallographic planes in a Co- l.Oat%Nb alloy obtained by the atom-probe analyses. The pyramidal (7101) and prismatic (ilOO) planes of the hcp phase, as well as the

SLOPE

CUMULATIVE

=1.05 t

0.19

NUMBER OF Co PLUS Nb EVENTS

Fig. 7. The Nb integral profile for a Co- 1.Oat%Nb alloy for the case when the evaporation rate was varied from 0.01 to 0.05 ion pulse- ’ at T, = 45 K withf = 0.15. The average Nb concentration is 1.05 rtO.19 at% Nb. This value is in good agreement with the atom-probe determinations of the same quantity, when the field-evaporation rate was kept constant throughout the entire analysis.

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Table 1 The measured Nb composition of a Co-l.Oat%Nb analyzed at T, = 45 K and f = 0.15

alloy

APFIM

for different

study

crystallographic

Region analyzed

Number co

Nb

(ilOO) plane of hcp phase

5874

56

0.94~0.13

(7101) plane of hcp phase (111) plane of fee phase

2694 3538

24 35

0.88-+0.18 0.9s+o.17

of atoms detected

a) The uncertainty is equal to the ratio of the square number of Co plus Nb atoms.

Niobium concentration (at% Nb)

root of the number

planes

a)

of Nb atoms to the total

(111) plane of the fee phase were examined. It is clear from table 1 that the Nb concentration measurements at T, = 45 K and f = 0.15 are independent within the experimental uncertainty - of the crystallograp~c region analyzed and are in good agreement with the nominal composition. We have not investigated the dependence of the measured composition on T, and f for the above crystallographic planes, i.e., the analyses were performed only at r, = 45 K andf= 0.15. In order to elucidate the effect of the presence of hydrogen, in the atom-probe FIM, on the measured composition at T, = 45 K and f= 0.15 we introduced hydrogen gas into the atom probe during an analysis. Fig. 8 shows the hydrogen integral profile for the entire run. The profile consists of two distinct regimes: (a) hydrogen partial pressure was equal to - 3 X lo-” Torr; (b) hydrogen partial pressure was equal to - 2 x lOUs Torr. Regime a, in turn, can be separated into two regions - a high concentration surface region which

2500

a t

2000 1

I

b

I

tooo500 -

0

2000 CUMULATIVE

HYDROGEN IS INTRODUCED INTO THE ATOM-PROBE

4000 6000 NUMBER OF Co PLUS

6000 Nb EVENTS

Fig. 8. Hydrogen integral profile for a Co- I.Oat%Nb alloy for the case when the partial hydrogen was changed from (a) 3 X lo- ‘“to(b)2X10-BTorratT,=45Kwithf=0.15.

pressure

of

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73

AVERAGE SLOPE = 0.93 Z 0.13 AT % Nb

CUMULATIVE

NUMBER

OF Co PLUS Nb EVENTS

Fig. 9. The Nb integral profile for a Co- 1.OatBNb alloy for the case when the partial pressure of to (b) 2~ IO-’ Torr at T, = 45 K with f= 0.15. The hydrogen was changed from (a) 3 x lo-” measured Nb composition is 0.93 +0.13 at% Nb; this is in good agreement with the nominal value.

is due to field-adsorbed hydrogen during the initial stages of the atom-probe analysis and a low concentration regime in which the electric field was high enough to ionize hydrogen atoms before they reached the tip. In regime b hydrogen ions were detected continuously throughout the entire analysis. At this partial pressure of hydrogen the flux to the surface of the specimen was large enough for gas atoms to reach the tip. Fig. 9 shows the Nb integral profile corresponding to this run. The mea-

HYDROGEN IS INTRODUCED INTO THE ATOM-PROBE FIM

CUMULATIVE

NUMBER

OF Co PLUS

Nb EVENTS

Fig. 10. The Nb” and Nb’+ mtegral profiles for a Co- l.Oat%Nb alloy for the case when the partial pressure of hydrogen was changed from (a) 3 x IO- lo to (b) 2 x 10-s Torr. Note that before admission of hydrogen the dominant evaporating species of Nb is Nb3’, while after admission of hydrogen the dominant evaporating species is Nb*+.

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sured composition is 0.93 $- O.l3at%Nb; which is in good agreement with the nominal value. Also the fact that there are no radically large local flu&&ions in the slope of the integral profile, indicates that the presence of hydrogen in the system did not affect the Nb concentration measurements. However, a very intriguing result was revealed when we examined the Nbzf and Nb3’ integral profiles - see fig. 10. The dominant evaporating species of Nb in regime a was Nb3+. However, after the admission of hydrogen - regime b - the Nb atoms field-evaporated mainly in the form of Nb*+ ions. It is important to note that no Nb hybrides were detected at this value of T, in either regime. 3.2. Co-l.Oat%Fe

alloy

FIM images of this alloy were obtained using the same procedure as for the Co-l.Oat%Nb alloy - imaging was performed at q = 45 K at a gauge pressure of - 4 X lo-5 Torr neon. A mass spectrum for a Co-l.Oat%Fe alloy is displayed in fig. 11; this spectrum was recorded with T, = 45 K employing a value of f = 0.15. The background pressure during the analyses was in the range of (4.0-6.0) X lo- ” Torr. The main residual gases were hydrogen ( < 5 X lo-” Torr), carbon monoxide ( < 2.0 X lo-” Torr) and helium ( < 4.0 X lo-l2 Ton). Both cobalt and iron appear only in the plus-two ionization state. Iron has four naturally occuring isotopes - 54Fe, 56Fe, 57Fe and ‘*Fe; their natural abundances are 5.82% 91.66% 2.19% and 0.33%, respectively. The first three isotopes of Fe can be readily identified in the spectrum. A

MASS -TO-CHARGE

RATIO

Fig. 11. The Co2+ and Fez+ mass spectrum of the Co-l.OatBFe alloy. The spectrum was recorded lo Torr. Both cobalt and iron appear in only the plus-two at T,=45 K withf-0.20 at 4x10ionization state. Note that the single isotope of cobalt (5gCo2+) and three (54Fe2+, %e*+ and “Fe’+) of the four naturally occuring isotopes of iron are clearly resolved. The missing isotope ‘*Fe’+ has a natural abundance of only 0.33%.

R. Herschitz, D.N. Seidman / Quantitative

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comparison of the experimental isotopic abundances for Fe2+ with the handbook values is given in table 2; the agreement between these values is reasonably good. The isotope 58Fe was not detected as its natural isotopic abundance is very small compared to the other isotopes of Fe. Since Fe atoms represent only lat% of the total number of atoms detected - both Co and Fe one would have to collect 30,000 atoms in order to detect a single atom of the 58Fe isotope. Fig. 12 shows the main results obtained for the Co-l.Oat%Fe alloy. At 90 K the measured Fe concentration is less than the nominal value for f equal to 0.05 and 0.10 - at f= 0.05 no Fe atoms were detected. For T, = 60 K, at f equal to 0.05, the measured Fe composition is 0.35 at% less than the nominal value; while at f values of 0.10, 0.15 and 0.20 the agreement between the measured and expected values is good. At T, = 45 K the Fe concentration measurements are independent - within the experimental uncertainty - of the values off used and are in good agreement with the nominal composition. Table 3 lists Fe concentrations measured at field-evaporation rates of 0.01, 0.03 and 0.05 ion pulse-’ at T, = 45 K and f = 0.15. These concentrations are in good agreement with one another as well as with the nominal value. Therefore, we conclude that the field-evaporation rate does not have an effect on the measured Fe composition, for the range of values employed. Table 4 lists the measured Fe concentrations for different crystallographic planes in a Co-l.Oat%Fe alloy, obtained by an analysis at T, = 45 K and f= 0.15. It is clear that the measured Fe compositions for the pyramidal (ilO1) and prismatic (1100) planes of the hcp phase, as well as the (111) plane of the fee phase are in good agreement with the expected value. The crystallographic dependence of the Fe composition on different values of T, and f was not investigated.

Table 2 Comparison of the experimental the actual isotopic abundances Isotope

s4Fe s6Fe s7Fe 5sFe Total Fe s9co

Fe’+ and Co2’ Isotopic

Number of atoms detected 3 70 5

78 7289

abundances

Experimental

in a Co-l.Oat&Fe

a)

(Xi 3.85 f 2.22 89.74 + 10.73 6.41_+ 2.87

100+ 11.33 100

a) The uncertainty is equal to the ratio of the square root of the number particular isotope to the total number of Fe atoms detected.

alloy with

Actual (W) 5.82 91.66 2.19 0.33 100 100 of Fe atoms

of a

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1.8 1.6 c]

z!

90K

AVERAGE BULK COMPOSITION

I 0. IO

0.05 PULSE

I 0.20

I 0.15

FRACTION

f = -

:

VPULSE

kSc Fig. 12. The measured Fe concentration (at%) versus pulse fraction the (0002) plane of an hcp crystal of a Co- 1.Oat%Fe alloy. Table 3 The measured Fe composition at T,=45 Kandf=0.15

of a Co- I.Oat%Fe alloy at different

The average fieldevaporation rate (ion pulse-. ‘)

Number co

of atoms detected Fe

0.0 1 0.03 0.05

3094 3392 1487

30 35 14

(f)

at T, = 45, 60 and 90 K for

average

Iron concentration (at% Fe)

a)

alloy

for different

of atoms detected

of Fe atoms

Number co

Fe

Iron concentration (at% Fe)

(ilOO) plane of hcp phase

4273

44

1.02kO.15

(ilO1) plane of hcp phase (I 11) plane of fee phase

4867 3407

47 32

0.96+0.14 0.93 kO.15

root of the number

to the total

crystallographic

Region analyzed

af The uncertainty is equal to the ratio of the square number of Co plus Fe atoms.

rates

0.96*0.18 1.02kO.17 0.93 i 0.25

a) The uncertainty is equal to the ratio of the square root of the number number of Co plus Fe atoms. Table 4 The measured Fe composition of a Co- l.Oat%Fe analyzed at T, = 45 K and f = 0.15

field-evaporation

of Fe atoms

planes

a)

to the total

R. Herschitz, D. N. Seidman / Quantitative A PFIM study

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4. Discussion The most dramatic results of our experiments are: (i) For f= 0.05 and T, = 60 and 90 K the measured Nb concentration in a Co- l.Oat%Nb alloy is significantly greater than the nominal composition, whereas in a Co-l.Oat%Fe alloy the measured Fe composition is less than the expected value. Thus, drastically different behavior is seen in these two dilute cobalt-based alloys. (ii) At q = 90 K a sig~fic~t number of Nb hydrides was detected at all values off. No Nb hydrides were observed at 30, 45 and 60 K. If one disregards the Nb hydrides in the calculation of the niobium concentration we obtain the correct value for the Nb composition in a Co-l.Oat%Nb alloy at f values of 0.10, 0.15 and 0.20 - although for f = 0.05 the Nb composition is still greater than the nominal concentration. (iii) As the partial pressure of hydrogen was changed from 3 X lo-” to 2 x lo-’ Torr the charge state of the field-evaporated Nb changed from Nb3’ to Nb2+ at Ts = 45 K. However, the overall Nb composition was not affected by the presence of hydrogen in the atom-probe at this temperature. We now discuss these distinct observations by first presenting a discussion of the physical processes that may have a major effect on the atom-probe measurements of solute concentrations in dilute cobalt-based metal alloys at small values of f. Then we consider the possible mechanisms that affect our concentration measurements in a Co- l.Oat%Nb alloy at 90 K. And, finally, possible mechanisms that lead to the change in a charge state of Nb are considered. 4. I. The effect of pulse fraction on the measured solute concentration While there are many different mechanisms that may affect the measured solute concentration [4] we believe that result (i) above can be explained on the basis of a selective field-evaporation model. At small values off the value of Vn, is large and the concomitant electric field is also large. If this electric field is equal to or greater than the evaporation field (E,) of a metal atom, then field evaporation will occur in the time interval between the application of the high voltage pulses; i.e., when the specimen is at Vo,. In the case of alloys, the local electric field due to V,, may be greater than E, for one of the constituents and yet smaller than the E, value of the other component - this will lead to a deficiency of the component which has the lower I?,. When a field-evaporation pulse is subsequently applied to the tip, the surface will be deficient in the composition with the smaller E, and, hence, the measured alloy composition will be incorrect. Clearly, if both alloy components have exactly the same value of E, there will be no effect on the measured solute composition.

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stud>>

We have used the ionic field-evaporation model [8-141 to calculate E, of pure Co, Nb and Fe as well as the evaporation fields of Nb and Fe in the Co(Nb) and Co(Fe) alloys. The expression for E, within the context of this model is given by Ee = (A + CI, - r~#)~/n~e~,

(1)

where A is the sublimation energy of the atom, 1, the n th ionization potential, n the charge state of the field evaporating ion, #J the work function of the plane from which the ions are field evaporated, and e the charge of an electron. In calculating the Ee’s of solute atoms in an alloy, the quantity A is equal to A = A, + h,,

(2)

where A, is the sublimation energy of the pure component and h, the heat of solution of the solute in the alloy [ 131. Values for A, were taken from a compilation assembled by Gschneidner [15], and the values of cp were taken from a tabulation by Michaelson [ 161. For both Nb and Fe the # values for the different crystallographic planes were available. We have used the values of 9 for the (111) plane, as the atoms in the (111) planes of the fee lattice are arranged in a hexagonal pattern just like the atoms in the (0002) planes of hcp lattice. Finally, the values of 1, were taken from the tables compiled by Moore [ 171. All of the relevant values are listed in table 5. The values of A, of Nb in Co and Fe in Co were calculated from the binary phase diagrams of these two alloys ] 181, using the fact that the solvus line is described by [ 191 “lute = A exp( -h,/k,T), c sat

(3)

where the value of h, corresponds to the slope of a In c~~‘“~~versus l/k,r riot, s”‘“‘e is the solubility limit at each temperature (T), k, is Boltzmann’s Csat constant and A is an entropic constant. For the Co-l.Oat%Nb alloy the value whereas for the Co-l.Oat%Fe the value of h, is 0.14 of h, is 0.22 eV atom-‘, eV atom-‘. Table 6 lists the values of the estimated EC’s for pure Co, Nb and Fe, as well

Table 5 Values of the heat of sublimation (A), work function (+), and ionization potentials (I,) niobium, and iron EIement

Cobalt Niobium Iron

Heat of sublimation A 0 (eV atom- ‘)

Work function tp

4.42 7.58 4.33

5.00 4.36 4.8 1

(eV)

for cobalt,

Ionization potentials I, (eV) 1,

12

13

7.86 6.88 7.87

17.06 14.32 16.18

33.50 25.04 30.65

R. Herschitz,

Table 6 Values of the calculated

evaporation

D.N. Seidman

/ Quantitative

fields for different

APFIM

ionic charge

79

study

states of cobalt,

niobium

and

iron Evaporating species

Calculated evaporation field of pure elements, &(Vk’)

Calculated evaporation field of elements in a solid solution

with cobalt,

E,(VA_‘) Nb’ + Nb*+ Nd+

7.08 3.49 4.27

7.39 3.58 4.32

Fe’+ Fe*+ Fe3+

3.79 3.06 5.11

3.94 3.10 5.15

co’ + co*+ Co3’

3.68 3.24 5.88

as of the Nb or Fe in a solid solution with Co. Note that the values of E, of these solutes are not appreciably different from the E,‘s of the pure elements. This is due to the fact that the values of h, are an order of magnitude smaller than the A,‘s of the elements. The ionic field-evaporation model predicts correctly the charge state for Co and Fe - Co*’ and Fe*+. This model also predicts the charge state of Nb to the Nb *+. However, only a small percentage of Nb*+ ions were actually detected - the charge state of the dominant ion species is Nb 3+. It is important to note that according to the ionic model field evaporation should occur in the form of ions of just one ionization state, *whereas numerous atom probe investigations have unambiguously shown that many metals field-evaporate simult~eously in the form of ions of different charge states [20-231. A field-evaporation model based on the post-ionization of field-evaporated ions has been recently proposed by Haydock and Kingham [24]. If post-ionization processes play a significant role in determining the final charge state of field-evaporated Nb, then it would explain the existence of Nb3+. The fieldevaporation process of Nb may consist of two steps - initial field evaporation as Nb”, followed by post-ionization to Nb3’ (i.e., Nb2’--+ Nb3+). However, the exact ionic potential curves are needed to predict theoretically the possibility of post-ionization. The values given in table 6 help to explain the drastic differences in the field-evaporation behavior, at f equal to 0.05, between the Co-l.Oat%Nb and Co- 1.Oat%Fe alloys. In the Co- 1.Oat%Nb system the value of E, both Nb3* Nb” is than that Co . And thus steady-state electric is enough to field evaporate atoms, while Nb atoms

80

R. Herschitr,

D.N. Seidman / Quantitative

APFIM

study

~refere~f~a~i~.retained on the surface during the time interval when the specimen is at Vn,. The surface is, therefore, deficient in Co atoms and when a field-evaporation pulse is subsequently applied the measured Nb composition is greater than it should be. The opposite effect is observed for the Co-l.Oat%Fe alloy. The value of E, 0 for Fe2+ is less than that of Co*’ - 3.10 V A-’ for Fe’+ and 3.24 V A- ’ for CO*+ _ and this leads to the selective field-evaporation of Fe atoms by Vi,,, while Co atoms are preferentially retained in the surface. In this case the surface is deficient in Fe atoms and this leads to an Fe concentration measurement which is less than the nominal composition. As f is increased the value of l’uc decreases and when the electric field due to Vu, is less than the Ee’s of both elements the correct solute concentrations are obtained. Thus, we have shown that at certain temperatures - 60 and 90 K - the solute concentration measurements, at small values off, for dilute cobalt-based alloys depend strongly on the E,‘s of the solute and solvent atoms. We believe that the observed results should not be limited to only cobalt-based alloys. In general, for any alloy under consideration, when the solute atoms have a greater E, than the solvent atoms - as in the Co-l.Oat%Nb alloy - the solute concentration measurements should be greater than the nominal value. Conversely, if the E, of a solute atom is less than that of a solvent - as in the Co-l.Oat%Fe alloy - the measured solute composition should be less than the expected value. The fact that at f= 0.05 the difference in the absolute values of the nominal and measured solute concentrations for both alloys increases as T, increases is, most likely, due to the temperature dependence of the E, of the ionic species. The field-evaporation mechanism was originally envisaged to be a thermally activated process [8] given by the equation K, = y exp( where surface

K,

Q/k&),

(4)

is the field-evaporation rate and Y the vibrational atom, The temperature dependence of E, is given by

E, = [A + CZ,, - n+ + k,T, ln( K,/v)]/n3e3.

frequency

of a

(5)

We now consider the temperature dependence of all the terms in eq. (5). The heat of sublimation as a function of temperature is given by Kirchhoff’s equation 1251, A,=,4,-

J0

‘cP dT+j?,

dT, 0

(6)

where A, is the heat of sublimation at temperature T, cp the heat capacity of a solid at constant pressure and CL the heat capacity of a monatomic gas at constant pressure. The temperature dependence of cP at low values of T is given by 1251 cP = ( 12n4k,/503)T3

+ yT,

(7)

R. Herschitz,

D.N. Seidman

/ Quantitative

APFIM

study

81

where 8 is the Debye temperature and y the electronic constant. Their values for cobalt are equal to 385 K and 5.2 X lo-’ eV atom KP2, respectively; ck is equal to 5/2k,. Using these values we obtain 4.43 eV atom-’ for A at 90 K; i.e. it is only 0.2% greater than A,. Both 1, and 4 are temperature independent quantities. In order to estimate an upper bound to the last term in the numerator of eq. (5) we have used the fact that to a first approximation v is independent of temperature and is equal to lOI s-t; the value of K, was taken to a value of 1.2 ions s- ‘. It should to be 0.02 ion pulse-‘, which corresponds be noted that it has been shown experimentally that the value of v depends strongly on temperature [26]. Using the above values of K, and v we obtain -0.21 eV and -0.08 eV for the k,Tln(K,/v) term at 90 and 35 K, respectively. These values are less than 1% of Q, and, therefore, the temperature dependence of E, should be negligible. However, Burke [27] has measured the temperature dependence of E, of molybdenum between 10 and 110 K and has shown that the theoretical temperature dependence is more than an order of magnitude less than the experimental dependence. Different authors have considered various modifications to the simple ionic field-evaporation model [28-331. Recently, Chibane and Forbes [33] have proposed a model which explains the temperature dependence of E,, over a limited temperature range, for some molybdenum and tungsten data. Further theoretical and experimental work is needed to clarify the temperature dependence of E, for a large number of metals and alloys over a wide range of temperature.

4.2. Formation

of Nb hydrides in a Co-l.Oat

%Nb alloy at T, = 90 K

The existence of metal hydrides was a result of the interaction of hydrogen gas present in the atom-probe during the analysis, with the FIM specimen. Three possible mechanisms are now considered to explain how the formation of Nb hydrides may lead to erroneous solute concentration measurements at 90 K. The possible mechanisms are: (i) formation of a bulk Nb hydride complex in the Co-l.Oat%Nb alloy; (ii) the pulse field-evaporation of metal hydride complexes followed by their dissociation into charged and uncharged species; (iii) the selective field-evaporation of metal hydrides by Voc. When hydrogen reacts with the surface of a specimen the gas may dissolve in the alloy, diffuse into it and, because of a strong interaction with a solute atom, react with it to form a solute-hydride complex beneath the tip’s surface. Alternatively, the solute atoms may migrate to the surface and react with the adsorbed hydrogen gas. Clearly both phenomena may lead to Nb concentration values which are different from the nominal value. It has been shown by a number of authors that hydrogen interacts strongly with niobium [34-381. First, we consider the possibility of hydrogen dissolving in a Co(Nb) alloy. The

R. Herschitr,

82

D.N. Seidman

/ Quantitative

solubility

of a gas in a metal for dilute solutions

c, = afi

exp(A_?/k,)

APFIM

study

is given by Sievert’s law 1391,

exp( -Ah/k,Z’),

(8)

where c, is the concentration (at%) of gas in the solution, LYa constant, p the gas pressure (in Torr), and AS and Ah are the partial molar entropy and enthalpy of solution. AS and A6 are assumed to be independent of the concentration or the gas pressure. The constant (Yis given by fX= (760) - ‘/2 ~~/~~, MS and Ms are the atomic weights of the solid and gas, respectively. The values of AL and A$ for a solution of H, in Co are equal to 0.67 eV atom-’ and - 9.5 x lop4 eV atom-’ K-‘, respectively [40]. Using the above values, c, is Torr hydrogen. equal to - 5 x 1O-4g at% hydrogen at T, = 90 K and lo-” These calculations show that the solubility of hydrogen in cobalt is extremely small under our experimental conditions and, therefore, the probability of formation of a Nb hydride complex as a result of this mechanism is nil. Next, we consider the possibility of the migration of Nb to the surface. The root-mean-square diffusion distance at T, = 90 K is equal to 1O-72 A - which implies that it is physically impossible for Nb to segregate to the surface and react with hydrogen at 90 K. In the absence of diffusion data on the Co(Nb) system we used the tracer diffusivity of Fe in Co [41]. Fig. 13 exhibits the Nb hydride integral profile at T, = 90 K andf= 0.10. If Nb hydride complexes were present in our alloy, then a change in the slope of the integral profile could be a consequence of a local composition variation

1

260,

CU~ULATJVE

NUMBER

OF Co PLUS NbH EVENTS

Fig. 13. The Nb hybride integral profile for a Co- I.Oat%Nb alloy at T, = 90 K and f = 0.10. The fact that the Nb hydride integral profile is approximately uniform indicates that Nb hydrides were detected continuously during the entire analysis and that there was no major redistribution of Nb atoms as a result of their interaction with hydrogen.

R. Hwschitz, D.iV. Seidman / Quanti~ari~ APFlM

study

83

produced by a complex. The fact that the Nb hydride integral profile is reasonably uniform within the analyzed volume indicates that Nb hydrides were detected continuously during the entire analysis and that there was no major redistribution of solute atoms as a result of their interaction with hydrogen. Also, no visual evidence of any Nb hydride precipitates was seen in the FIM images. Thus, we conclude that our results cannot be explained on the basis of the first mechanism proposed above. In the case of mechanism (ii) the following reactions must be considered: (1)

(CoH) i++Co+H’+,

(2)

(COH)~+ --, Co*++ H,

(3)

(COH)~+ + Co*++ Hi+,

(4) (NbH)‘+-+Nb+H’+, (5)

(NbH)‘+

-+ Nb’++

H,

(6)

(NbH)3+

--, Nb3++

H,

(7)

(NbH)3+

-+ Nb*‘+

HI+.

Since only Co”, Nb2’, Nb3’ and II’+ ions were detected no other reactions need be considered. Whether or not the dissociation of a hydrogen complex takes place depends on the details of the interatomic potential curves in the presence of the high local electric fields near the (CoH)“+ or (NbH)“+ molecules and also on the bond energies of these molecules. Reaction (1) is the only one which could have produced a deficiency in Co ions and, thus, lead to a Nb concentration which is greater than the nominal value. Reactions (2), (3), (51, (6) and (7) would have no effect on the measured solute composition, while reaction (4) would have produced a deficiency in Nb ions. If reaction (1) had taken place, then hydrogen ions should have been detected continuously throughout the entire atom-probe analysis. Fig. 14 exhibits the hydrogen integral profiles for a Co- 1.Oat%Nb alloy at T, = 90 K for different values off. It is obvious from the data that more hydrogen atoms were adsorbed on the surface at the larger values off. This is due to the fact that at large values off, V,,, is small and hence the electric field due to Yoc is no2 sufficient to ionize a hydrogen atom before it can be adsorbed. By contrast, at low values off the electric field due to V,,, is adequate to ionize. a hydrogen atom before it arrives at the surface, and consequently only a small number of hydrogen atoms were able to reach the surface. The fact that the number of adsorbed hydrogen atoms at f = 0.15 and 0.20 is approximately the same indicates that a saturation coverage was most likely achieved. It is clear that hydrogen ions were not detected at all stages of the analyses - they were present only in the initial stages for all values of f and were due to field-adsorbed hydrogen on the

R. Herschitz, D.N. Seidman / Quantitative

84

FJ

f * 0.20

@

fZ015

@

f:010

@

f = 0.05

APFIM

study

.,

4000

CUMULATIVE

Fig. 14. Hydrogen

integral

NUMBER

profiles

OF Co PLUS Nb EVENTS

for a Co-l.Oat%Nb

alloy at T, = 90 K for different

values off.

surface of the tip. As field-evaporation proceeded the electric field at the surface was high enough to ionize hydrogen atoms before they were able to reach the surface. Therefore, we conclude that reaction (1) did not occur and, consequently, our results cu~~~~ be explained on the basis of this mechanism. Finally, we consider mechanism (iii), which is based on selective fieldevaporation by V,, of metal hydride ions. We have already shown that selective field-evaporation by I/,, of various atoms from the surface may lead to an erroneous solute concentration measurement. Adsorbed gas atoms are known to affect the field-evaporation process by reducing the binding energy of the kink site surface atoms or by forming molecular compounds. It has been shown in the past that the Ee’s of metal ions can be reduced dramatically in the presence of hydrogen gas 142-441. The fact that hydrogen atoms were present only on the surface - fig. 14 - and yet Nb hydrides were detected continuously throu~out the entire analysis - fig. 13 - indicates that hydrogen atoms were able to reach the shank of the specimen, where the electric field is not high enough to ionize them, and then migrate to the end of the tip. Once on the tip the hydrogen interacted with the Co and Nb atoms in two drastically different ways. When a hydrogen atom met a Nb atom a Nb hydride molecular complex was formed which field evaporated in the form of (NbH)3f. Even though no significant number of Co hydrides was detected, Co atoms may have, nevertheless, interacted with hydrogen. Most likely hydrogen reduced the binding energy of the kink site surface Co atoms. This, subsequently, caused a reduction in the E, of either Co or the CoH molecular complex in such a way that the Co atoms were selectively field-evaporated by Vo,. Hence the measured Nb composition at T, = 90 K was greater than the nominal composition at all values of f. The fact that Nb hydride molecular complexes were

observed indicates

only at T, equal to 90 K - none were seen at 35, 45 and (10 K that hydrogen was immobile on the shank at lower T,‘s.

4.3. The effect (?I’the presence mwurcd Nb con~position

of h,ydrogen in the atom-probe

F/M

m

the

It has been shown that the relative abundance of different charge states of the ionic species is a strong function of K,, 7;. EC, (hkl) plane examined. and the type of imaging gas [45-501. The ionic field-evaporation model cannot be used to explain the change in the charge state of field-evaporating Nb as a result of the prsesence of hydrogen in the atom-probe, since it does not always predict satisfactorily the finatly observed charge states of fj~ld-evaporatiilg ions. We now present a qualitative argument, based on a post-ionization field-evaporation model, that explains our results. Haydock and Kingham [24] calculated the probabilities of post-ionization as a function of E, for different metals for “an acceptable model potential”. For most elements a reduction in E, causes an appreciable reduction in the probability of post-ionization. In section 4.1 we suggested the possibility that the post-ionization of NbZt ions, may be responsible for the observation of Nb3’ ions as the dominant field-evaporating species under the ultra-high vacuum conditions - regime a in fig. 10. It is known that the E,‘s of metal ions are reduced drastically in the presence of hydrogen. This, in turn, reduces the probability of post-ionization of Nb2’ ions and, hence, they become the dominant evaporating species when the atom-probe analysis is done in the presence of hydrogen - regime b in fig. 10. Although by no means conclusive - the exact ionic potential curves are necessary for quantitative comparisons with the theory - this mode1 does provide a possible qualitative explanation for the observed phenomena. It is emphasized that although that charge state of the field-evaporating Nb changes from Nb3+ to Nb” the overall Nb composition is not affected by the presence of hydrogen in the atom-probe.

5. Summary

(1) The atom-probe FIM has been used to measure the composjtions of Co- l.Oat~Nb and Co-l.Oat%Fe alloys. This information was necessary for measuring the absolute compositions, in our extensive investigations of solute atom segregation effects to indivjdua1 stacking faults in these alloys [6,7]. (2) It is shown that the measured solute concentration is strongly dependent on both r, and f. (3) Under certain experimental conditions - f= 0.05 and q = 90 and 60 K - drasticaily different behavior was observed for these alloys. The measured

86

R. Herschitz, D.N. Seidman / Quantitative APFIM study

Nb concentration of a Co-l.Oat%Nb alloy is significantly greater than the nominal composition, whereas for a Co- l.Oat%Fe alloy the measured Fe composition is less than the expected value. This phenomenon is explained by the preferential field-evaporation of solute atoms from the Co-l.Oat%Fe alloy and preferential retention of solute atoms in the Co- 1.Oat%Nb alloy. (4) At T, = 45 K and f= 0.15 the measured solute concentration in both alloys is independent of the following parameters: (i) the average fieldevaporation rate; (ii) the crystallographic plane examined; and (iii) the phase of the alloy, i.e., hcp or fee. (5) At c = 90 K the atom-probe determinations of the Nb composition in a Co- 1.Oat%Nb alloy were greater than the nominal value at all values off. This result is explained on the basis of the interaction of hydrogen atoms, present in the atom-probe, with Co and Nb atoms. In case of Nb, a Nb hydride molecular complex is formed which field-evaporates in the form of (NbH)3t. In the case of Co, hydrogen reduces the value of the field-evaporation field of either Co or CoH molecular complexes in such a way that Co atoms are selectively field-evaporated by the I’,,. (6) No Nb hydrides were observed at 35, 45 or 60 K. (7) Correct solute concentrations in both alloys were obtained using the following experimental conditions: (i) a T, of less than or equal to 60 K; (ii) an f of greater than or equal to 0.10. (8) As the partial pressure of hydrogen was increased from 3 X 10P” to 2 x lo-* Torr the field-evaporation charge state of Nb changed from Nb”+ to Nb2+ at T, = 45 K. However, the overall Nb composition was no6 affected by the presence of hydrogen in the atom-probe FIM at this T,. (9) From the results and discussion given in this paper we conclude that using proper experimental conditions it is possible to quantitativp1;. zLleasure the absolute compositions in these dilute cobalt-based alloys. (10) The observed results should not be limited to only cobalt-based alloys. In general, for any alloy under consideration, when the solute atoms have a greater E, than the solvent atoms the solute concentration measurements should be greater than the nominal value. Conversely, if the E, of a solute atom is less than that of a solvent atom the measured solute concentration should be less than the nominal value. Thus, detailed control experiments are needed to establish the proper experimental conditions to quantitatively measure an alloy’s composition.

Acknowledgements This work has been supported by the National Science Foundation through the Materials Science Center at Cornell University. The support of the US Department of Energy is acknowledged for certain technical facilities. We wish

R. Herschitz, D.N. Seidman / Quantitative APFIM

to thank Mr. Robert Whitmarsh for enthusiastic technical Charles Barbour for carefully reading the manuscript.

study

assistance

87

and Mr.

References [I] [2] [3] [4] [5]

A. Wagner, PhD Thesis, Cornell University, Ithaca, NY (1978). A.J. Watts and B. Ralph, Surface Sci. 70 (1978) 459. M.K. Miller and G.D.W. Smith, J. Vacuum Sci. Technol. 19 (1981) 57. M. Yamamoto and D.N. Seidman, Surface Sci. 118 (1982) 535. M. Yamamoto and D.N. Seidman, Cornell University Materials Science Center Report No. 4802 (1982); Surface Sci. 129 (1983) 281. [6] R. Herschitz and D.N. Seidman. Scripta Met. 19 (1982) 849. [7] R. Hers&&z, PhD Thesis, Cornell University, Ithaca, NY (1983); R. Herschitz and D.N. Seidman, Cornell University Materials Science Center Report Nos. 4888 and 4889 (1983); Acta Met., submitted. [8] E.W. Miiller, Phys. Rev. 102 (1956) 618. [9] R. Gomer, J. Chem. Phys. 31 (1959) 341. [IO] R. Gomer and L.W. Swanson, J. Chem. Phys. 38 (1963) 1613. [1 I] L.W. Swanson and R. Gomer, 3. Chem. Phys. 39 (1963) 2813. 1121 D.G. Brandon, Surface Sci. 3 (1964) 1. [13] D.G. Brandon, Surface Sci. 5 (1966) 137. [14] D.G. Brandon, in: Field-Ion Microscopy, Eds. J.J. Hren and S. Ranganathan (Plenum, New York, 1968) ch. 3. [15] K.A. Gschneidner, Solid State Physics. Vol. 16, Eds. F. Seitz and D. Turnbull (Academic Press, New York, 1964) p. 344. [ 161H. Michaelson, J. Appl. Phys. 48 (1977) 4729. (171 C.E. Moore, National Standard Reference Data Series 34 (National Bureau of Standards, US Government Printing Office, Washington, DC, 1970). [ 181 M. Hansen and K. Anderko, Constitution of Binary Alloys (McGraw-Hill, New York, 1958) pp. 472, 484; F.A. Shunk, Constitution of Binary Alloys, Suppl. 2 (McGraw-Hill, New York, 1969) pp. 181, 255. 1191 R.A. Swalin, Thermodynamics of Solids (Wiley, New York, 1972) p. 170. [20] T.M. Hall, A. Wagner and D.N. Seidman, J. Phys. E (Sci. Instr.) 10 (1977) 884. [21] A. Wagner and D.N. Seidman, J. Nucl. Mater. 83 (1979) 48. [22] S.R. Goodman, S.S. Brenner and J.R. Low, Met. Trans. 4 (1973) 2371. [23] E.W. Miiller, S.V. Krishnaswamy and S.B. McLane, Surface Sci. 23 (1970) 112. (241 R. Haydock and D.R. Kingham, Phys. Rev. Letters 44 (1980) 1520. 1251 M.W. Zemansky, Heat and Thermodynamics, 5th ed. (McGraw-Hill, New York, 1968) pp. 353, 327. [26] D.G. Brandon, Phil. Mag. 14 (1966) 803. [27] J.J. Burke, MS Thesis, Cornell University, Ithaca, NY (1974). [28] T.T. Tsong, Surface Sci. 10 (1968) 102. (291 T.T. Tsong. J. Chem. Phys. 54 (1971) 4205. 1301 D. McKinstry, Surface Sci. 29 (1972) 37. [31] R.G. Forbes, Surface Sci. 46 (1974) 577. [32] G.L. Kellogg and T.T. Tsong, Surface Sci. 62 (1977) 343. [33] K. Chibane and R.G. Forbes, Surface Sci. 122 (1982) 191. [34] J.A. Pryde and C.G. Titcomb, Trans. Faraday Sot. 65 (1969) 2758.

88

[35] [36] 1371 [38] [39] [40] [41] [42] (431 (441 145) 1461 f47] 1481 1491 [50]

R. Herschiir, DA.

Seidman / ~uun~ila!ive APFIM study

S.M. Ko and L.D. Schmidt, Surface Sci. 42 (1974) 508. D.I. Hagen and E.E. Donaldson, Surface Sci. 45 (1974) 41. M.A. Pick, J.W. Davenport, M. Strongin and G.J. Dienes, Phys. Rev. Letters 43 (1979) 286. M.A. Pick, Phys. Rev. B24 (1981) 4287. J.D. Fast, Interaction of Metals and Gases (Academic Press, New York, 1965) ch. 7. 0. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry (Pergamon, New York, 1979) p. 47. M. Badia and A. Vignes, Acta Met. 17 (1969) 77. E.W. Mtiller, S. Nakamura, 0. Nishikawa and S.B. McLane, J. Appl. Phys. 36 (1965) 2496. 0. Nishikawa and E.W. Mtiller, Surface Sci. 12 (1968) 247. S. Kapur and E.W. Mutter, Surface Sci. 66 (1977) 45. S.S. Brenner and J.T. MeKinney, Appt. Phys. Letters 13 (1968) 29. E.W. Miilfer and S.V. Krishnaswamy, Phys. Status Solidi 3 (1970) 27. A.R. Waugh and M.J. Southon, Surface Sci. 68 (1977) 79. N. Ernst, Surface Sci. 87 (1979) 469. G.L. Kellogg and T.T. Tsong, J. Appl. Phys. 51 (1980) 1185. G.L. Kellogg, Phys. Rev. B24 (1981) 1848.