Lattice misfits in four binary Ni-Base γ - Springer Link

Lattice Misfits in Four Binary Ni-Base and Elevated Temperatures

7/3" Alloys at Ambient

A.B. KAMARA, A.J. ARDELL, and C.N.J. WAGNER High-temperature X-ray diffractometry was used to determine the in situlattice parameters, av and av,, and lattice misfits, 6 = ( G ' - av)/av, of the matrix (y) and dispersed 3;-type (Ni3X) phases in polycrystalline binary Ni-A1, Ni-Ga, Ni-Ge, and Ni-Si alloys as functions of temperature, up to about 680 ~ Concentrated alloys containing large volume fractions of the 3; phase (-0.40 to 0.50) were aged at 700 ~ to produce large, elastically unconstrained precipitates. The room-temperature misfits are 0.00474 (Ni-A1), 0.01005 (Ni-Ga), 0.00626 (Ni-Ge), and -0.00226 (Ni-Si), with an estimated error of _ 4 pct. The absolute values of the lattice constants of the y and 3; phases, at compositions corresponding to thermodynamic equilibrium at about 700 ~ are in excellent agreement with data from the literature, with the exception of Ni3Ga, the lattice constant of which is much larger than expected. In Ni-Ge alloys, 6 decreases to 0.00612 at 679 ~ and in Ni-Ga alloys, the decrease is to 0.0097. In Ni-Si and Ni-A1 alloys, 6 exhibits a stronger temperature dependence, changing to -0.00285 at 683 ~ (Ni-Si) and to 0.00424 at 680 ~ (Ni-A1). Since the times required to complete the high-temperature X-ray diffraction (XRD) scans were relatively short (2.5 hours at most), we believe that the changes in 6 observed are attributable to differences between the thermal expansion coefficients of the y and 3; phases, because the compositions of the phases in question reflect the equilibrium compositions at 700 ~ Empirical equations are presented that accurately describe the temperature dependences of a~, av., and 6 over the range of temperatures of this investigation.

I.

INTRODUCTION

IN the absence of tetragonal distortions, the elastic energy of coherent precipitates is governed primarily by the purely dilatational lattice misfit, 6 = ( G - a,,)/am, where a, and am are the lattice constants of the unconstrained precipitate and matrix phases, respectively. Although it is not the only parameter affecting the elastic energy, 6 is the most important, because the elastic self-energy of the precipitates, which influences morphology, and the elastic interaction energy, which is largely responsible for the spatial correlations that lead to rafting, are both proportional to 32. It is now well accepted that misfit-induced elastic strains affect the morphology and spatial correlations during the coarsening of precipitates in Ni-base alloys. Elastic energy can also influence the kinetics of coarsening, though as of this writing it is fair to state that many of the experimental observations and theoretical predictions regarding its role are inconclusive or contradictory. It almost goes without saying that accurate values of 6 as a function of temperature, T, are essential for any comparison between theory and experiment, because the value of 3 at the aging temperature, not room temperature, is what affects microstructural evolution during aging. The variation of 6 with T has been investigated in commercial Nibase superalloys because of their technical importance.lira However, there have been very few determinations of the dependence of ~ on T in two-phase binary Ni-base alloys containing 3;-type precipitates (these have the stoichiometry A B. KAMARA, Engineer, is with International Rectifier, E1 Segundo, CA 90245-4382. A.J. ARDELL, Professor, and C.N.J. WAGNER, Professor Emeritus, are with the Department of Materials Science and Engineering, University of California, Los Angeles, CA 90095-1595. Manuscript submitted March 4, 1996. 2888--VOLUME 27A, OCTOBER 1996

Ni3X, with the L12 crystal structure). The only two investigations of which we are aware are those of Nembach and Neitet51 on Ni-A1 alloys and Bertrand e t a / . I61 on Ni-AI and Ni-Si alloys. In both investigations, the reported temperature dependences of 6 in Ni-AI alloys are small, but the absolute values of 6 measured by the two groups differ substantially. Bertrand et al. measured the lattice constants of the y and 3/phases in an aged two-phase alloy to temperatures exceeding 800 ~ The type of specimen used by Nembach and Neite is not specified, and the maximum temperature in their investigation was only 227 ~ In the context of how variations of 6 influence morphology, spatial correlations, and kinetics of coarsening, it is important to know how 6 varies with composition as well as temperature. Room-temperature data on the variation of both ar and ar, with composition are available for several binary alloys, but the dependences of these parameters on composition at high temperatures are generally unknown. For the purpose of estimating 6, even at room temperature, choosing the correct values of a~ and G' requires knowledge of the equilibrium compositions of the two phases at the aging temperature. Since 6 involves the difference between the lattice constants, which is quite small compared to their magnitudes, 6 can be seriously in error depending on whose data on the individual values of ar and a~, are selected. The present study was undertaken to obtain data on the lattice misfits in binary two-phase Ni-A1, Ni-Ga, Ni-Ge, and Ni-Si alloys; morphological evolution, spatial correlations, and kinetics of coarsening of 3;-type precipitates in these alloys are all under intensive investigation in our laboratory. In this work, the lattice misfits in concentrated twophase binary alloys are evaluated as functions of temperature using X-ray diffraction (XRD). The rationale behind our decision to undertake experiments on specimens containing large volume fractions of the 3' and 3/phases is METALLURGICAL AND MATERIALS TRANSACTIONS A

that measurements of ar and av, in such alloys are subject to identical systematic errors. The difference between a~ and G' is subject only to random errors; hence, uncertainties in the values of 6 derived from them are influenced, in principle, only by errors in the absolute values of av or ar themselves.

II.

Table I. Alloy Compositions and Volume Fractions, fr', at 700 ~ Calculated from the Phase Diagram and from the Integrated Intensities of the X-ray Peaks, fr,x

Alloy Ni-Si N1-A| N1-Ge Ni-Ga

Wt Pct 8.07 9.00 19.38 21.52

At. Pct 18.47 17.70 16.27 18.12

f~, 0.38 0.51 0.43 0.37

.f~c 0.32 0.52 0.54 0.42

EXPERIMENTAL

Four alloys were investigated, the compositions of which are reported in Table I. The Ni-Ga, Ni-Ge, and Ni-Si alloys were prepared by arc melting, while the Ni-A1 alloy was obtained from Pratt and Whitney Aircraft (Middletown, CT) in the form of sheet, 0.5-ram thick. The volume fractions of the 3,' phase, f~,, at 700 ~ are shown in Table I; these were calculated using published solubility limits for the ~/phase, taken from a recent summary, tT~in conjunction with published data on the equilibrium solute concentrations in the 7' phases (Ni-Al,t81 Ni-Ga,tgJ Ni-Ge,t'o~ and NiSir J~). The elemental components were 99.999 pct pure, and consisted of Ni powder and Ga, Ge, and Si chunks. The arc-melted buttons weighed 16.5 g on average, and in all cases the weight losses during melting were less than 0.2 pct. Each button was cut in half parallel to its base (i.e., parallel to the surface in contact with the water-cooled hearth of the arc melter during solidification) using a lowspeed diamond-wheel saw. The lower halves of the buttons were investigated, since they readily yielded flat specimens 2- to 4-mm thick. The Ni-Ga and Ni-Ge alloys were homogenized for 30 minutes at 1000 ~ and the Ni-Si alloy for 30 minutes at 1115 ~ then quenched into iced brine and lightly cold-rolled. The three alloys were then rehomogenized at 1095 ~ for 82 hours, fumace cooled under vacuum, then aged at 700 ~ for 26 hours and quenched into iced brine. The Ni-A1 sample was homogenized at 1000 ~ for 30 minutes and furnace cooled under a protective argon atmosphere, before being aged at 700 ~ for 168 hours and quenched into iced brine. All the alloys contained two phases at both the homogenizing and aging temperatures. We carried out a preliminary evaluation of the lattice constants after homogenizing the alloys at 1000 ~ for 30 minutes and furnace cooling in argon, followed by aging at 700 ~ for 36 hours and quenching into iced brine. The room-temperature lattice constants obtained from the Ni-A1 alloy were in good agreement with the data in the literature. However, the results obtained from the two sides of the arc-melted alloys (referred to as the middle and base) were inconsistent, suggesting that for these alloys the two sides had not yet reached their equilibrium compositions. For this reason, the samples were homogenized again and aged at the temperatures and times indicated previously, after which the data from the Ni-Ga, Ni-Ge, and Ni-Si samples were self-consistent. Elevated-temperature XRD was done using a furnace consisting of a split graphite heating element that surrounded the specimen holder; the heating element contained a gap to allow for the passage of the incident and diffracted X-rays. The specimens and graphite element were protected from oxidation during heating using a reducing gas mixture of 20 pct H2 and 80 pct He. A gas-tight water-cooled shell surrounded the fumace (and several concentric radiation METALLURGICAL AND MATERIALS TRANSACTIONS A

shields as well), all of which contained gaps to allow passage of the X-rays; the gap in the innermost radiation shield was actually fitted with a 9-/zm-thick A1 foil to aid reflectivity and reduce the temperature gradient at the specimen. The gap in the water-cooled shell contained a 0.75-mmthick beryllium window, attached to the shell using a gastight adhesive. The beam intensity at the detector was reduced to about two-thirds of its original value by the AI and Be windows. A Leeds and Northrup (North Wales, PA) controller was used in conjunction with a type-K thermocouple to control the temperature of the diffractometer furnace to within + 1.5 ~ Since the control thermocouple was placed near the heating element, a second type-K thermocouple, located about 2.5 mm from the top of the specimen, was used to monitor the temperature during the diffraction experiments. To ensure flatness of the surfaces examined during XRD, all the samples were metallographically polished to a mirror finish. All room-temperature data were obtained with the furnace in a fixed, raised position. When the furnace is raised, a torque is introduced into the assembly; this torque is absent when the furnace is lowered. Consequently, it was necessary to calibrate the diffractometer in both positions in order to account for the resulting systematic instrumental errors. With the fumace raised, a diffraction pattern was obtained from pure annealed tungsten powder, providing a calibration curve of interplanar spacing, dh~, vs scattering angle, 20. A similar method was used to calibrate the diffractometer with the furnace lowered, but in this case the diffractometer was calibrated using an annealed high-purity polycrystalline copper standard. The values of dh~ for the 3' and 7, phases in the specimens were obtained by referring the measured values of 20 for their diffraction peaks to the relevant calibration curves. The calibration procedures are described in greater detail elsewhere,V21 where further details conceming the other experimental procedures can also be found. The diffractometer fumace was thermally calibrated using the same high-purity annealed copper standard, which was heated to four different temperatures for calibration purposes. At each temperature, the lattice parameter of the Cu standard was determined using the position of the {331 } peak, which was the strongest high-angle peak observed. After taking the systematic errors into account to calculate ac, from d331, the temperature of the standard was determined using the thermal-expansion data of Hume-Rothery and Andrews, t~31corrected for the errors discussed by Pearson.t'41 At each temperature setting, the temperature of the monitoring thermocouple was recorded, providing a calibration curve of specimen temperature vs temperature of the monitoring thermocouple. The amount by which the monitoring temperature exceeded that of the specimen was - 2 0 ~ at - 3 0 0 ~ and - 3 5 ~ at - 7 0 0 ~ VOLUME 27A, OCTOBER 1996~2889

X-ray diffraction was carried out using a computer-controlled diffractometer, with unfiltered Cu K~ radiation generated at 40 kV and 20 mA. The X-rays were detected using a proportional counter. Primary slits measuring 1.905 and 3.175 mm were used in conjunction with a 0.3-mm receiving slit. All scans were performed using a 0.01-deg step interval and a minimum counting time of 10 seconds at each step. It was not necessary to use a Ni filter to remove the Cu K0 component, because all the samples are essentially self-filtering. The room-temperature lattice constants of y and 3] in the Ni-A1 alloy were obtained from measurements on a single pair of peaks, but for the Ni-Ga and Ni-Si samples, the data were obtained by averaging the data from two pairs of peaks (one from the middle and the other from the base of the sample). The room-temperature lattice constants for Ni-Ge were obtained from the averages of the data from five sets of peaks. The number of peaks in the arc-melted alloys was undoubtedly limited by their large grain sizes, on the order of 150/zm. In the case of Ni-A1, the grain size was much smaller (~20 ~m). We suspect that the texture of the rolled Ni-A1 sheet limited the number of strong diffraction peaks, but we made no attempt to verify this conjecture. In all cases, the high-temperature data were obtained from measurements on a single pair of peaks for each sample. Each sample was subjected to a single heating cycle, with the temperature being raised incrementally for each scan. The samples were allowed to equilibrate for 30 minutes at each temperature, after which the scans ranged from 0.6 to 2 hours in duration. The fluctuation in temperature during the measurements was + 1.5 ~ as limited by the controller. We used a computer program called XLAB to analyze the data.* This program allowed us to use lower-angle *This program was written by Professor W.A. Dollase, Department of Earth and Space Sciences, University of California, Los Angeles.

peaks without compromising accuracy. The diffraction peaks in the XLAB program are stripped of their Cu K % component using the Rachinger correction."51 Without this correction it can be difficult to resolve the precipitate and matrix peaks, because the precipitate and matrix lattice parameters are so similar, especially in the Ni-Si alloy. The method requires knowledge only of the wavelengths, A, of the Ka~ and K % components of the incident X-rays. We used the data of Deslattes and Henins,t~61 who report Acur~, = 0.1540598 nm. The ratio between Acu K~,/AcuK~ was assumed identical to that reported in Appendix 7 of Cullity,U7J giving Ac~r~ = 0.1544426 nm. The XLAB program was also used to fit the peaks to a least-squares curve of peak intensity vs 20 using the second-derivative method of Savitzky and Golay.t~8~ The program provides a number of parameters defining the quality of the fit. One of the most important of these is called 0-2o, which quantifies the deviation between the stripped raw data and the fitted curve in units of degrees 20. It represents the possible error in precision due to the least-squares fitting process. A perfect fit to the data yields 0"2o = 0 deg; the maximum value of 0"2orecorded in this experiment was + 0.0051 deg. Upon completing the XRD scans, the samples were chemically etched in a solution consisting of nitric acid, 2890---VOLUME 27A, OCTOBER 1996

glacial acetic acid, and water in the ratio 2:1:1, and the microstructures were examined optically and in the scanning electron microscope (SEM).

III.

RESULTS

The precipitate microstructures are shown in the SEM photographs in Figure 1. All the specimens contained bimodal y' particle-size distributions. The larger precipitates in the dispersions range from 1 to 10 p~m in "diameter," while the smaller ones generally varied from 100 to 200 nm. With the possible exception of the Ni-Ge alloy, the larger precipitates in the distributions constituted by far the higher proportion of those present. Examples of the analysis of the X-ray peaks using XLAB are shown in Figure 2 for the {222} peak of Ni-Si, which has the smallest lattice misfit, and the {400} peak of Ni-Ga, which has the largest. In Ni-Si, the Ka~ peak of the precipitate phase overlaps the Ka2 peak of the matrix phase, so that the locations of the peak maxima are imprecise. The individual 7 and ~/ peaks are revealed quite distinctly using XLAB, which in this case yielded fits to the raw data characterized by 0-20= 0.0009 deg for the ~ peak and 0.0017 deg for the 3~ peak. In the other extreme, i.e., the Ni-Ga alloy, the y and ~/peaks are easily resolved without stripping the K % components. The values of 0-20for these peaks were 0.0011 and 0.0017 deg, respectively, and they are shown here because the lattice constant of Ni3Ga was much larger than expected based on data in the literature, as discussed later. The volume fractions of the y and y' phases present in the irradiated volumes of the respective samples are related to the integrated intensities of the precipitate and matrix peaks, tlgj Analysis of the data, taking into account the variation of structure factor with 0 and the Lorentz polarization factor, produced the values offr, shown in the last column of Table I. The agreement is fair for the Ni-Ge alloy and quite good for the others. The absolute values of a~ and G' at room temperature, calculated from the measured values of dhkt after employing the corrections required by the calibration curves, are shown in Table II. The average room-temperature values of at, G', and 6 for the four alloys are shown in Table III (6 for Ni-A1 is not an average value, of course, since only one peak was measured). For Ni-Ge, 6 was evaluated from five diffraction peaks, ranging from the relatively small value of 20 for the {311 } peak ( - 9 2 deg) to the relatively large value of 20 ~- 151 deg for the {420} peak. There is no systematic variation of 6 with 2 0. The standard deviation of these measurements is ___0.00021, which we regard as a random error of _+3.4 pct. In the absence of suitable statistics on the other alloys, it is reasonable to conclude that the error in the reported room-temperature values of 6 for all the alloys is approximately + 4 pct. Figures 3 through 6 show the room-temperature data on ar and a~, from this study compared with selected published data. These include the data of Bertrand et aL,t61 Taylor and Floyd, t81 Bradley and Taylory~ Aoki and Izumi, t2~JNoguchi et aL, I221and Mishima et al., I231on Ni-A1 alloys, Pearson and Rimeky~ Noguchi et al., Mishima et al., Pearson and Thompson,t241 and Feschotte and Eggimannt251 on Ni-Ga alloys, Mishima et aL, Pearson and Thompson, Iz41Klement, t261 Ellner and Predely 71 Brahman et al.,tzs~ Jena and ChaturMETALLURGICAL AND MATERIALS TRANSACTIONS A

(a)

(b)

(c)

(,/)

Fig. 1--SEM micrographs showing the microstructures in the (a) N1-A1, (b) Ni-Ga, (c) Ni-Ge, and (d) Ni-Si alloys. The magnifications of all the images are identical.

vedi,t29] and He and Chaturvedi[3o] on Ni-Ge alloys, and Bertrand et al., Oya and Suzuki,tin and Klement on Ni-Si alloys. The compositions of the two phases in our case were taken as the equilibrium solubilities at 700 ~ which were also used in the calculations offr,. Aside from our datum on the lattice constant of Ni3Ga (Figure 4), the agreement is excellent. The data on the variations of lattice constants with T are shown in Figure 7. The dependences of ar and at, on T are adequately described by quadratic functions of the following form: a~,r, = a + b T + c T 2

[1]

where a, b, and c are constants, the values of which are presented in Table IV, and T is in degrees Celsius. From the definition of 6, i.e., METALLURGICAL AND MATERIALS TRANSACTIONS A

a = a ~ , , - a~,

[2]

we obtain the empirical equation for 6 given by the following: 6=

m + nT + pT 2

[3]

where the coefficients m, n, and p are obtained in straightforward fashion by substitution of Eq. [1] into Eq. [2], expanding the denominator in a power series, and discarding all terms higher than the second order in T. The values of m, n, and p are presented in Table V, and the variation of 6 with T for all four alloys is shown in Figure 8. The curves shown in Figure 8 were obtained using Eq. [3], with the values of m, n, and p reported in Table V. VOLUME 27A, OCTOBER 1996--2891

2500

Table II.

-

Alloy Ni-A1 Ni-Gah Ni-Gam Ni-Geh

~. 2000

:~ 1500 0

v0 9

r

E

{hkl} 331 331 400 311 331 420 311 400 222 331

Ni-Gem looo

Room Temperature Lattice Constants (nm)*

Ni-Si b Ni-Si m

ar, 0.356376 0.359596 0.359608 0.357102 0.357119 0.357068 0.357393 0.357225 0.35101o 0.351014

O'2o 0.0028 0.0009 0.0017 0.0009 0.0049 0.0048 0.0009 0.0030 0.0017 0.0046

a~ 0.354695 0.355979 0.356067 0.354909 0.354817 0.354856 0.35511~ 0.355105 0.351809 0.351803

*The subscripts describe the two sides of the samples (text); b corresponds to the base and m the middle of the arc-melted button. The values of ~2o represent the goodness of the XLAB fit to the raw data and are given in deg 20.

500

0 lllllllll|li,li,i,lilsilslltlltil11111,| 98.5 99.0 98.0

99.5

100

20 (a)

3so

Table III. Average Room Temperature Lattice Constants (nm) and Lattice Misfits (These Are Averages Except for Ni-AI)

Alloy

a~,

a~

6

Ni-A1 Ni-Ga Ni-Ge Ni-Si

0.356376 0.359602 0.35718~ 0.351012

0.354675 0.356023 0.354960 0.351806

0.00474 0.01005 0.00626 - 0.00226

300

0.358 V

o 250

V

'~ 150

fi

s.s'~

0.356

100

.s

e,-

J

o

50-

E o.355 ....

I ....

I ....

I ....

I ....

I ....

I ....

I

116 117 118 119 120 121 122 123

20 (b) Fig. 2--Illustratmg the fitting of the X-ray diffraction peaks (solid curves) by the XLAB program (dotted curves): (a) the (222) peak from the base of the Ni-Si specimen; and (b) the {400} peak from the middle of the NiGa specimen. These are diffraction peaks from scans at ambient temperature. The 3, and 3" peaks are indicated.

IV.

DISCUSSION

A. Ni-AI Alloys

Our room-temperature lattice misfit of 0.00474 for NiA1 is in excellent agreement with the value of 0.0045 reported by Nembach and NeiteY 1 They also reported that 6 remains approximately constant as a function of temperature to ~225 ~ We observe a small decrease in ~ with T (at 680 ~ the misfit is 0.00424, a reduction of approximately 11 pct), but on the whole the agreement between our results and those of Nembach and Neite is quite satisfactory. Bertrand et al.t61 measured a room-temperature value of 6 = 0.00245 for a single crystal of an Ni-15 at. pct A1 alloy, aged to contain the y and 7' phases. They also found 6 to be essentially independent of T, but their value 2892--VOLUME 27A, OCTOBER 1996

S S

a ''6

0.357

2OO

0

O'2o 0.0042 0.0012 0.0011 0.0006 0.0046 0.0051 0.0007 0.0037 0.0009 0.0022

:0 o 4,

0 o o

s"

.,b

o O.354

?+~

y-

_a

.~' @"

0.353

I"

0.352

0

5

10

15 20 at. % AI

25

30

Fig. 3--Room-temperature lattice constants of the 3' and 3t phases as functions of composition in Ni-AI alloys. The vertical lines indicate the 7 / 7 + ~ and 7 + ~/~' phase boundaries at 700 ~ and the dash-dotted curve represents a least-squares fit to the data on av vs composition for the 3' solid solution only. The plotting symbols represent the data of the following authors: O Bertrand et al., E61 /x Taylor and Floyd, L810 Bradley and Taylor, t2ol [] Aoki and Izumi, ~2~127 Noguchi et al [22] I:~ Mishima et al., Ez3j and 9 present investigation.

of 6 appears to be too small and there is no apparent explanation for the discrepancy. Interestingly, most of the data on the variation of av with composition are in reasonably good agreement (Figure 3), and it can be safely stated that this holds even for data that have been excluded from Figure 3 for reasons of clarity (Figure 2 of Noguchi et aL I221 includes a more complete set METALLURGICAL AND MATERIALS TRANSACTIONS A

0.360

0.353

~

0.359 E 0.358 e..

.s'"

9*" 0.357

7+Y

[]

,-0

, 0.352

s.s, 9

"'~'q--.o

E o.3 0 o

E3~""

0.355

o

o

,/ Y+Y

---.

o

y

~ 0.351 0[]

_o

_a 0.354 0.353 !

[]

0.352 , , , , I , , , , I , , , 5 0

. . . . .

10

15 ot.%Go

l , , , i l

20

....

25

I

30

0.3501 , ; , , , . . . . 0 5

,~ . . . . 10

I .... 15

I . , 20

, i 25

at. %Si

Fig. 4~Room-temperature lattice constants of the y and ~/ phases as functions of composition in N1-Ga alloys. The vertical lines and the dashdotted curve have the same significance as in Fig. 3. The plotting symbols represent the data of the following authors: /~ Pearson and Rimek,tg] V Noguchi et al.,tzz] ,~ Mishima et al.,tz3} [] Pearson and Thompson,t24] o Feschotte and Eggimann,tzs} 9 and present investigation.

Fig. 6--Room-temperature lattice constants of the y and ~/ phases as functions of composition in Ni-Si alloys. The vertical lines and the dashdotted curve have the same significance as in Fig. 3. The plotting symbols represent the data of the following authors: O Bertrand et al.,t61 [] Oya and Suzuki,till ~ Mishima et al,t23} o Klement,t26] and 9 present investigation.

0.358 ues o f ar and av, lie slightly above the empirical curves fitted to the data in Figure 7(a) using Eq. [1]. Since the calculated values o f 6 are quite sensitive to small errors in the individually measured lattice constants, it is possible that the maximum observed in Figure 8 is an artifact.

o.357

.~.~"

E

" 0.356

.0

..~o t-

"~

.,'~

0.355

8 m

o

v'

B. Ni-Ga Alloys

~-(IX

0.354

7+7'

,l~t~ ~

0'353I'~'~t~" v~wn.-a.~9~ . . . .

0

i ....

i .

5

10 15 at. % Ge

. i ....

J .. !..

20

i

25

Fig. 5--Room-temperature lattice constants of the 3' and 3,' phases as functions of composition in Ni-Ge alloys. The vertical lines and the dashdotted curve have the same significance as in Fig. 3. The plotting symbols represent the data of the following authors: ~ Mlshima et aL, t23}[] Pearson and Thompson,(z"] 0 Klement,(26] • Ellner and Predel, [27] Ax Brahman et al.,t28] V Jena and Chaturvedi, [29] O He and Chaturvedl, E3~ and 9 present investigation.

o f data on ar and av, vs composition in Ni-A1 alloys). However, there is a significant variation in the measured values o f av,, as is evident in Figure 3. It is obvious that the error in any calculation o f 6, using a given pair o f values o f ar and ar, taken from the literature, must be large. From the temperature dependence o f 6 shown in Figure 8, it would appear that 6 passes through a slight maximum at approximately 300 ~ We cannot discount the possibility that this maximum is real, but note that the individual valMETALLURGICAL AND MATERIALS TRANSACTIONS A

The large discrepancy noted between the previously reported data and our result on the lattice constant o f Ni3Ga is quite difficult to rationalize or explain. Our value o f ar agrees very well with the data from the literature (Figure 4), but at, is much larger than that measured by all the other investigators. Since the data in Table II were obtained from analysis o f peaks from {331} and {400}, we can exclude the influence of tetragonal distortions o f either phase, which would have a strong effect on diffraction from {h00}, as a source o f the discrepancy. We can find no fault with earlier work on the determination o f a~, in Ni3Ga, so it is important to consider other possible sources of error. One likely source o f error is contamination o f the specimen. This was checked by sending a piece o f the alloy used in the X-ray analysis for chemical analysis, which confinned the overall concentration o f the alloy but revealed the presence o f 0.32 wt pet carbon, the only significant impurity. The solubility o f C in either o f the two phases in our alloy is unknown, but 0.32 wt pet C is completely soluble in pure nickel at higher temperatures.t31} If the C present segregated entirely to the Ni3Ga phase and expanded the lattice to the same extent that it does elemental Ni,t3u the lattice constant would increase from its literature average o f - 0 . 3 5 8 nm to - 0 . 3 5 9 nm. This is a significant increase, but a~, ~ 0.359 nm is still smaller than the value o f at, measured. Thus, while we cannot completely discount the possibility that all the carbon in the specimen dissolves VOLUME 27A. OCTOBER 1996--2893

~-

0.361

0.364-

Ni_iI

0.360

Ni-Ga

~" 0.362

0.359

~ 0.358

?

~

0.360

o.357

~ 0.358

~ 0.356 -- 0.355

~ 0.356

0.354

0

'

I , I I I , I , I , I I I 100 200 300 400 500 6[]0 700

,

0.354

I

I00

0

T (~ (a) 0.361

I

,

200

I

,

300

0.356

,

I

600

,

I

700

Ni-Si

?,

U

.~ 0.358

r 0.353 0.357

O O

0.356

.o

0.352

_O 0.351

0.355 0.3540,

I

500

A 0.355 E r v 9,~= 0.354

----~ccE0.359

--

,

T ("C)

0.360

~

I

400

(b)

Ni-Ge f

_~"

,

I , l , I , t , I , I , I I[33 2 0 0 300 4 0 0 500 6 0 0 700

0.350 0

~ I , I , I , i , I , I , I 100 200 300 4 0 0 5 0 0 6 0 0 7 0 0

T (~

T ("C)

(c)

('0

Fig. 7--The temperature dependences of the lattice constants of the y and 3" phases in the four alloys: (a) Ni-A1, (b) Ni-Ga, (c) Ni-Ge, and (d) Ni-Si. The curves are fitted to the data using Eq. [1] and the constants in Table IV.

Table IV. The Coefficients in Equation [ll, Describing the Variations of ay and ay, with Temperature

Alloy Phase Ni-AI Ni-Ga Ni-Ge Ni-Si

3" Y Y' Y 3" 3' 3" 3'

a (nm) 0.356276 0.354590 0.359498 0.355915 0.357081 0.354857 0.350913 0.351703

b x 10~ (nm/~ 6.16199 5.74055 6.65736 6.25751 4.61455 4.75768 4.71791 4.82175

The Coefficients in Equation [3], Describing the Variation of 8 with Temperature

c x 10'~ (nm/~ 2)

Alloy

m x 103

-11.32198 - 1.00986 - 19.05556 -10.66052 11.95170 10.26610 7.58328 10.97854

Ni-A1 Ni-Ga Ni-Ge Ni-Si

4.7551 10.0650 6.2659 -2.2485

exclusively in the Ni3Ga phase, we regard it as an unlikely explanation for the large value of av,. Another possible explanation for the disagreement is that for some unknown reason the Ni3Ga in our alloy contained much more Ga than expected. Microstructural examination 2894--VOLUME 27A, OCTOBER 1996

Table V.

n x 107 (~ 11.1155 9.4648 -4.8734 -2.6435

p x 10'~ (~ -29.2482 -23.4521 4.6342 -9.5473

using SEM revealed the very large, roughly rectangular, particle of what appeared to be Ni3Ga shown in Figure 9; the length of the short edge is - 6 / z m . Energy dispersive X-ray spectroscopy of this particle in the SEM provided a semiquantitative measure of its composition, which was 24.9 at. pct Ga. This is in excellent agreement with the value of 24.1 at. pct Ga reported by Pearson and Rimekt91 for Ni3Ga in equilibrium with the saturated Ni-rich matrix METALLURGICAL AND MATERIALS TRANSACTIONS A

0,012

a slight maximum with T near 300 ~ but the individual values of a~ and av, also deviate from the empirically fitted curve at this temperature.

Ni-Ga t

0.010

C. Ni-Ge Alloys

0.008

To the best of our knowledge, ours are the first measurements of 6 in polycrystalline two-phase Ni-Ge alloys as a function of temperature, though Jena and Chaturvedit291 measured 6 at room temperature in such an alloy. Our room-temperature value of 0.00626 is somewhat smaller than that reported by Jena and Chaturvedi (0.00695) for an alloy aged similarly (at 700 ~ for 160 hours). There is almost no change in 6 in Ni-Ge alloys as a function of temperature, with the misfit decreasing by only 2 pct between room temperature (0.00626) and 679 ~ (0.00612) (Figure 8).

Ni-Ge 0.006

,5 0.004 0.002

0 D. Ni-Si Alloys

Ni-Si

-0.002

-0.004

a

7 ?

F 0

100

200

300

400

500

600

700

T (~162 Fig. 8 ~ h e temperature dependences of 3 in the four alloys. The curves are fitted to the data using Eq. [3] and the constants m Table V.

Our value of 6 = -0.00226 at room temperature is almost 25 pct smaller than the widely quoted value of -0.003 reported by Hombogen and Roth. t321However, since 16l increases smoothly from a room-temperature value of 0.00226 to 0.00285 at 683 ~ (an increase o f - 2 6 pct), the value of 3 relevant to investigations of coarsening is not too different after all from that reported by Hornbogen and Roth. The Ni-Si alloy is the only alloy studied having a y' lattice parameter smaller than that of the matrix, and is also the only alloy to show a significant increase in the magnitude of the misfit as a function of temperature. Bertrand et al. B] also reported an increase in 161 in their study of ar and a~, in an Ni-14 at. pct Si single crystal. However, their misfits are much smaller than ours, varying from -0.00185 at room temperature to -0.00225 at 750 ~ (an increase in 16l of - 2 2 pct). Although the fractional increase in the magnitude of 8 is about the same as that observed in the present study, their misfit at 750 ~ is almost identical to the room-temperature misfit reported here. Absent details on the X-ray experiments conducted by Bertrand et al., the discrepancy cannot be resolved. E. General Remarks

Fig. 9--SEM micrograph of a large 3" particle m the Ni-Ga alloy. This particle was subjected to energy dispersive spectroscopy and found to contain - 2 4 at. pct Ga.

at 700 ~ We therefore have no reason to discount our measured value of at,, but are unable to provide a satisfactory explanation for why it is so much larger than all the others. The lattice misfit in the Ni-Ga binary shows a very small temperature dependence, decreasing from 0.01005 at room temperature to 0.0097 at 678 ~ (Figure 8). This is a reduction of only 3.5 pct, the second smallest fractional change observed. As is the case for Ni-A1, 8 passes through METALLURGICAL AND MATERIALS TRANSACTIONSA

It is necessary to address the question of whether we have measured truly unconstrained lattice misfits. In this study, the penetration depth of the X-rays (defined here as the depth into the sample from which the diffracted intensity is 1/e of its value at the surface) is on the order of 8 to 12/zm. The large 3/particles in the bimodal distribution range from 1 to 10/zm in size, suggesting that the majority of the diffraction information comes from precipitates fairly close to the surface. We do not know whether the larger particles in the specimens are coherent, but those intersecting the surface of the sample must be elastically unconstrained, because they are not completely embedded in the matrix. Further evidence for the absence of elastic constraint is provided by the fact that our absolute values of a~ and a~, correlate very well with the measurements made on single-phase specimens (except for Ni3Ga), where coherency stresses are not an issue. It is also important to address the issue of whether changes in the solute concentration of both phases contribVOLUME 27A, OCTOBER 1996--2895

ute to the variation of 6 with T. The times involved in measuring the X-ray peaks in the diffractometer fumace were relatively short (2.5 hours at most), compared to the aging times at 700 ~ Since the kinetics of coarsening are relatively slow at temperatures below 600 ~ and the particle sizes were already quite large, it is unlikely that the compositions of the two phases could have changed significantly during the course of a typical XRD experiment. Therefore, we believe that the variations of 6 with T are attributable primarily to the differences between the thermal-expansion coefficients of the two phases. In closing, it should be noted that there is an inherent error in our high-temperature measurements associated with the fact that our diffractometer was not truly calibrated for the work at high temperatures. As noted, we used the positions of the diffraction peaks from our Cu standard to calibrate the temperature, after having assured alignment of the diffractometer at room temperature using the same standard. There might thus be a systematic error in the values of a . a~., and 6 measured at high temperatures. However, since the variation of 6 with T is small for most of the alloys, it is probable that any systematic error is small as well. We are buoyed in this regard by the comparable temperature dependence of 6 observed in Ni-A1 alloys, as well as the larger one in Ni-Si alloys observed by Bertrand e t al.,[6] even though their absolute values of 6 are systematically smaller than ours.

V.

SUMMARY

The temperature dependence of the 3,/3,' lattice misfits in four binary Ni-base alloys was investigated using XRD. The polycrystalline Ni-A1, Ni-Ga, Ni-Ge, and Ni-Si alloys were aged at 700 ~ and contained high volume fractions of large, elastically unconstrained precipitates of the form Ni3X in a solid-solution matrix. A high-temperature diffractometer was used to determine the in s i t u lattice parameters (a~ and a~,) and lattice misfits 6 = (a~, - a O / a ~ as functions of temperature. The absolute values of the room-temperature lattice constants in all the alloys are in excellent agreement with data reported in the literature, with the exception of av, for Ni3Ga, which is substantially larger than previously measured values. We are unable to account for the discrepancy, but can eliminate contamination and unexpectedly high Ga concentrations in the Ni3Ga phase as probable sources of error. The room-temperature values of 6 are 0.00474 in Ni-A1 alloys, 0.01005 in Ni-Ga alloys, 0.00626 in Ni-Ge alloys, and -0.00226 in Ni-Si alloys, with an estimated error of _+4 pct. In the Ni-Ga alloy, 6 is about 70 pct larger than expected from data in the literature, but this is because of the large value of a~, measured. The temperature dependence of 6 is very small in Ni-Ga and Ni-Ge alloys, decreasing to 0.0097 at 679 ~ in the former, and to 0.00612 in the latter, over the same range of T. In Ni-A1 alloys, decreases about 11 pct to 0.00424 at 680 ~ The temperature dependence of 6 is strongest in Ni-Si alloys, 181 increasing by 26 pct to 0.00285 at 683 ~ We believe that all variations of 6 with T are attributable to differences be-

2896~VOLUME 27A, OCTOBER 1996

tween the thermal-expansion coefficients of the y and 3" phases. Empirical equations are presented that accurately describe the temperature dependences of a~, a~,, and 6 from 20 ~ to 700 ~ ACKNOWLEDGMENTS We are grateful to the National Science Foundation for providing financial assistance for this research under Grant No. DMR-9212536. We also thank Professor W.A. Dollase, Department of Earth and Space Sciences, UCLA, for making the XLAB program available, for assisting us in its use, and for useful discussions. Mrs. J. Fisher of the Department of Materials Science and Engineering also helped with the XLAB program, and we thank her as well. REFERENCES 1. D.A. Grose and G.S. Ansell: Metall. Trans. A, 1981, vol. 12A, pp. 163145. 2. M.V. Nathal, R.A. MacKay, and R.G. Garlick: Mater. Sei. Eng., 1985, vol. 75, pp. 195-205 3 D Bellet and P. Bastie: Phil. Mag. B, 1991, vol. 64, pp. 143-52. 4. L. Miiller, T. Link, and M. Feller-Kniepmeier: Seripta Metall. Mater., 1992, vol. 26, pp. 1297-1302. 5. E. Nembach and G. Nelte: Prog. Mater. Sci., 1985, vol. 29, pp. 177-319. 6. C. Bertrand, J.-P. Dallas, J. Rzepski, N. Sidhom, M.F. Triehet, and M. Comet: Mere. Sci. Rev. Met., 1989, vol. 86, pp. 333-46. 7. A.J. Ardell: m Experimental Methods of Phase Diagram Determination, J E. Mortal, R.S. Schlffman, and S.M. Merchant, eds., TMS, Warrendale, PA, 1994, pp. 57-66. 8 A Taylor and R.W. Floyd: J. Inst. Met., 1952-53, vol. 8, pp. 25-32. 9. W.B. Pearson and D.M. Rimek: Can. J. Phys., 1957, vol. 35, pp. 1228-34. 10. A. Dayer and P. Feschotte: J. Less-Common Met., 1980, vol. 72, pp. 5170. 11. Y. Oya and T. Suzuka: Z Metallkd., 1983, vol. 74, pp. 21-24. 12. A.B. Kamara: Master's Thesis, University of Califomia, Los Angeles, CA, 1995. 13. W. Hume-Rothery and K.W. Andrews: J. Inst Met., 1941, vol. 68, pp. 19-26. 14. W.B. Pearson: Handbook of Lattice Spacings and Structures of Metals, Pergamon Press, Oxford, United Kingdom, 1958. 15. W.A. Rachinger: J. Sci. Inst., 1948, vol. 25, pp. 254-55. 16. R.D. Deslattes and A. Henins: Phys. Rev Left., 1973, vol. 31, pp. 97275. 17. B.D. Cullity: Elements of X-Ray Diffraction, 2nd ed., Addison-Wesley, Reading, MA, 1978, p. 509. 18. A. Savltzky and M.J.E. Golay: Anal Chem., 1964, vol. 36, pp. 1627-39. 19. B.D. Cullity: op. cit., p. 407. 20. A.J. Bradley and A. Taylor: Proc. R. Soc, 1937, vol. A159, pp. 56-72. 21 K Aoki and O. Izumi: Phys. Status Solidi A, 1975, vol. 32, pp. 657-64. 22. O. Noguchi, Y. Oya, and T. Suzuki: Metall. Trans. A, 1981, vol. 12A, pp. 1647-53. 23. Y. Mishima, S. Ochiai, and T. Suzuki: Acta Metall., 1985, vol. 33, pp. 1161-69. 24. W.B. Pearson and L.T. Thompson: Can. J. Phys., 1957, vol. 35, pp. 34957. 25. P. Feschotte and P. Eggimann. J. Less-Common Met., 1979, vol. 63, pp. 15-30. 26. W. Klement, Jr.: Can. J. Phys., 1962, vol. 40, 1397-1400. 27. M. Ellner and B. Predel: J, Less-Common Met., 1980, vol. 76, pp. 181-97. 28. I.R. Brahman, A.K. Jena, and M.C. Chaturvedi: Scripta Metall. Mater., 1989, vol. 23, pp. 1281-84. 29. A.K. Jena and M.C. Chaturvedi: J. Mater. Res., 1989, vol. 4, pp. 141720. 30. Z. He and M.C. Chaturvedi: Mater Scz. Technol, 1993, vol. 9, pp. 106268. 31. M.F. Singleton and P. Nash: m Phase Diagrams of Binary Nickel Alloys, P. Nash, ed., ASM INTERNATIONAL, Materials Park, OH, 1991, p. 50. 32 E. Hombogen and M. Roth: Z. Metallkd., 1967, vol. 58, pp. 842-55.

METALLURGICAL AND MATERIALS TRANSACTIONS A