Defect structure in Al-rich composition region in the β-NiAl intermetallic compound phase

Intermetallics 3 (1995) 129-136 0 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0966-979.5/95/$09.50 ELSEVIER

Defect structure in Al-rich composition region in the P_NiAl intermetallic compound phase M. Kogachi, Y. Takeda & T. Tanahashi Department of Materials Science, Faculty of Integrated Arts and Sciences, University of Osaka Prefecture, Sakai 593, Japun

(Received 2 April 1994; accepted 27 May 1994)

The defect structure in the B2 type P-NiAI phase was investigated in the Al-rich composition region by means of powder X-ray diffractometry. In the analysis, earlier published density data were referred to for estimation of the total vacancy concentration in the alloy. As a result, the main constitutional defect was found to be the vacancy on the Ni-site (Ni-vacancy), supporting the defect structure model proposed previously by Bradley and Taylor. However, in a region of high Al concentration, some Al atoms substituted on the Ni-site, i.e. antistructure defects of Al atoms (Al-ASD), as well as some vacancies on the Al-sites (Al-vacancies), were recognized to exist. Their amounts did not change with increasing temperature up to 1150°C. These defect types of the Al-ASD and Al-vacancy had always been excluded in usual treatments based on the triple defect model. The reliability of the defect structure determined was examined by comparison with the triple defect model. Further, thermodynamic calculations based on the Bragg-Williams approximation were performed in order to reproduce the observations.

Key words: B2 type NiAl phase, X-ray diffractometry, tional vacancy, antistructure defect.

1 INTRODUCTION

site occupancy, constitu-

(Ni-rich side) and Ni-vacancies (Al-rich side) exist in the NiAl P-phase as constitutional defects.‘.2 Hereafter, we call this defect structure the BT model. After Bradley and Taylor’s investigation’, a similar structural defect has been successively found in other B2 intermetallic compounds, NiGa, CoAl, CoGa and FeA13-*, which consist of Group VIII and Group III components. Such interesting behaviour in these VIII-III intermetallic compounds has been well interpreted from the thermodynamic point of view7*9-14,mainly based on the ‘triple defect model’ proposed by Wasilewski.’ The triple defect’ consists of two vacancies on the VIII component atom site and one VIII component atom on the opposite site, which are simultaneously created at stoichiometry because the ratio of VIII to III component atoms must be kept constant. Thus, in all the treatments based on this triple defect model, the defect structure is expressed by the above two types of constitutional defect; for example, in the case of NiAl, only the N&vacancy and Ni-ASD are taken into consideration, so that the contribution of other types, the

The intermetallic compound NiAl P-phase exists over a comparatively wide composition range around the equiatomic ratio of Ni to Al. The crystal structure is of the B2 type and, ideally, all the Ni atoms occupy the cube corner (N&site) and all the Al atoms occupy the cube center (Al-site) in a body-centered cubic lattice. This perfectly ordered atomic arrangement is attained only in the alloy with stoichiometric composition. When the alloy composition deviates from this, some constitutional defects must be formed in the crystal lattice. From X-ray diffraction and density measurements for the NiAl P-phase alloys, Bradley and Taylor’ proposed that, on the Ni-rich side of the stoichiometry, excess of Ni atoms are substituted on Al-sites, (generating ‘antistructure defects’ (ASD) of Ni atoms, or Ni-ASD), while on the Al-rich side the ASD caused by excess of Al atoms, the AlASD, are not formed, thus resulting in a creation of substantial constitutional vacancies on the Ni-sites, i.e. a creation of Ni-vacancies. Namely, Ni-ASD 129

130

M. Kogachi, Y. Takeda, T. Tanahashi

Al-vacancy and the AI-ASD, is neglected. However, almost all the experimental work performed relating to this problem to date was concerned with estimation of the vacancy concentration from density and/or thermal expansion measurements. We can then know the total vacancy concentration contained in the alloy, but this total cannot be separated into two portions corresponding to the vacancies located in the respective sites. This will be well understandable by supposing that, in the NiAl case, the Al-ASD and also the Al-vacancy can be arbitrarily created as a compensation for removing some Ni-vacancies, so as to keep the total vacancy concentration constant. Therefore, in order to understand the origin of the defect structure in the B2 type VIII-III intermetallic compounds, it is very important to clarify experimentally the nature of their detailed defect structure. In pursuit of the aim mentioned above, Kogachi et al.,” previously studied the site occupancies of constituent atoms, including vacancies, for the NiAl P-phase alloys by means of the powder Xray diffractometry. However, as pointed out by (Kim, S. M., pers. comm). it was later found that their results for vacancy concentration did not give a unique solution for individual samples. Further, their data were obtained only from the samples quenched from 1000°C. Thus, it is worthwhile to examine the same problem again. The present aim is to determine the constitutional defect appearing on the Al-rich side of the NiAl P-phase as a function of composition as well as of temperature, using X-ray diffraction measurements.

where x is the vacancy concentration. There exist generally four types of constitutional defect: Nivacancy, Al-vacancy, Ni-ASD and AI-ASD; these are respectively estimated from the site occupancies w]/Ni, [VI/Al, Ni/Al and Al/Ni in eqn (1). When the defect structure in the alloy is correctly expressed by the BT model, then [VI/Al = Ni/Al = Al/N1 = 0 and the vacancy concentration becomes X =

1)/2C

(2)

N/N, = l-x

(3)

2.2 The least-squares calculation The integrated intensity of hkl reflection in the powder X-ray diffraction pattern may be written*5 by I + KM.LP.

T.lf12 = KQ lf’1’

(4)

where K, M, LP and T are the scale factor, the multiplicity, the Lorentz polarization factor and the temperature factor, respectively. The structure factor, F, can be expressed in terms of the ‘average scattering factors’, f(Ni) and f(Al), for the Ni and Al sites as f(Ni) = f(A1) when h+k+l=2n(n=O +1,+2,. . .i5)

F=

when h+k+l=2n+ 1

where f(Ni) and f(A1) are obtained by using eqn (1) as f(Ni) = (l-x){(l-cfii + c&1 + (S&i - G.&Y2 = (l-x)+ + (1/2)Af @a)

2.1 Site occupancies In the B2 type Ni,,,Al, alloy the constitutional vacancy is formed on the Al-rich side (O.%c
(2C -

There are two ways to define the vacancy concentration. Here, this is given by the ratio NJN,, where N, and N, are the total number of vacancies and of Ni and Al sites, respectively; this is often7,“,‘3 given by N,IN, where N is the total number of Ni and Al atoms. Since Ns = N + N,:

i f(Ni) -f(Al)

2 X-RAY ANALYSIS PROCEDURE

XBT =

[VI/AI = x + (S,-SJ2,

f(A1) = (l-x)+

- (1/2)Af

(6b)

where fNi and fAl are the atomic scattering factors of Ni and Al, respectively. The resulting intensity is classified into two categories, IF for fundamental reflections and 1, for superlattice reflections: IF = ~(I-x)~ KQ II”

(7)

I, = KQ IAA2

(8)

and

In order to determine the LRO parameters, S, and S,, we follow the same procedure as done in our earlier work,‘5m17that is, the least-squares fitting calculation based on the profile-fitting method,

131

Defect structure in Al-rich region in the P-NiAl phase

which was successfully applied to site preference determination for P-NiAl” and for the Ll, type ternary compounds A13Ti-X.‘6,‘7 The optimum values are then obtained so as to minimize the reliability factor, R, defined as

R = EubJs)(~obs - L,)2mlJ,11'2

(9)

when Zobsis an observed intensity which is evaluated by the profile-fitting method’*, and, Zcalis calculated intensity which corresponds to either eqn(7) or (8). In the calculations by Kogachi et al.“, the vacancy concentration, x, was also included among the variables to be refined. However, as is seen from eqns (5)-(g), we cannot determine x as a unique solution from this procedure. This will be understood by postulating two defect structure models; one is a given defect structure without any Al-vacancies, the other assumes that an arbitrary, but equal, number of vacancies is added to both Ni and Al sites of the first structure. These models correctly give the same value of R (eqn (9)) in spite of an obvious difference in total vacancy concentration, x, between them. Thus, we cannot determine which is the suitable model, as long as x is unknown. Instead of doing this, we here adopted the observed values of x, referring to the density data measured by Taylor and Doyle.2 Their results are plotted in Fig. 1 by solid circles, where the solid line indicates the relation x = xsr (eqn (2)). From this, the data points are found to lie close to this line. Further, according to the thermal expansion measurements by Fukuchi and

Change in the vacancy concentration, x, with composition in the Ni,_,Al,.. Solid circles indicate the values obtained

Fig. 1.

from the density measurements by Taylor and Doyle.’ The solid line indicates the relation of x = xBT (eqn,(2)) and the broken line the calculated results at T = 300 K.

Watanabe”, concentration of the thermal vacancies created additionally at temperatures above room temperature is much less than 0.1% even at 1000°C for the Al-rich NiAl alloys. Thus, in all the present calculations, we used the relationship given in eqn (2).

3 EXPERIMENTAL

PROCEDURE

Nine alloys of Ni,_,Al, (0.5 5 c ~0.54) were prepared by melting the weighed portions of the metals, Ni with purity of 99.9% and Al with purity of 99.999%, in a plasma jet arc furnace under an argon atmosphere. Each ingot was homogenized at 1000°C for 7 days in a sealed silica tube filled with argon and then water-quenched. Weight losses of the ingot thus prepared were 0.1 to 0.4%. Each ingot was packed into a steel container and crushed by the vibration milling technique to obtain fine powders for X-ray measurements. The particle size of the resulting powders estimated from the transmission electron microscope observation was less than 10 pm, being much less than in earlier work15 (about 30 pm). A portion of each powder sample was annealed in a sealed silica tube filled with argon at 1000°C for 5 min, then cooled to room temperature (RT) at a rate of 2,5”C/min. Other than this treatment, the remaining powders were water-quenched from 950°C after holding them for 20 min. Further, the two samples with the highest Al concentrations were water-quenched from different temperatures; annealing temperature and holding time were 600°C for 15 h, 800°C for 3 h, 1000°C for 15 min, 1100°C for 10 min and 1150°C for 5 min. In addition, to examine the effect of the cooling rate, it was done also at a rate of O.S”C/min for these samples, as an alternative to 2,5”C/min. The X-ray intensity data were collected by a standard type X-ray diffractometer with Cu KQ radiation monochromatized with curved graphite at 40 kV and 30 mA. For 10 or 11 reflections located in the angle range 28 <140”, the measurements were performed by a step-scanning method with 0.02” stepwidth and 20 s fixed time. We have repeated such consecutive measurements two times for each sample. Almost all the slow-cooled samples indicated an existence of appreciable amounts of cu-Al,O, (less than about 2% in volume ratio to the B2 phase), probably due to reaction with silica during the heat treatment of powders. This leads to some deviation in composition of the B2 phase from the

M. Kogachi, Y. Takeda, T. Tanahashi

132

OV

'lb 28

28

Fig. 2. X-ray profiles of 210 superlattice and 222 fundamental reflections for the Ni 46,A&, (slow-cooled). Crosses and solid lines represent the observed data and calcuIated results, respectively.

nominal composition, together with an influence due to weight loss occurring in the homogenizing of the ingots. Thus, their compositions were determined from the values of the lattice constant obtained from 222 reflection, with the aid of the Iattice constant-composition relation given by Taylor and Doyle.’ For some samples, we tried to measure the integrated intensities of a few reflections due to the cw-A&O,in order to estimate the volume ratio. The compositions thus corrected agreed well with those evaluated from the lattice constant. Individual profile fits were made by using the computer program ‘PRO-FIT’ by Toraya.18 The reliability factor.18 R,, extended from 2.3 to 6.4% (in the previous refinement by Kogachi et aLI5 it was in the range 3.1-7.7%). The least-squares calculations were performed in the same way as previously.‘s-17 In the actual calculations, the atomic scattering factors and the anomalous dispersion correction terms for the Ni and Al atoms were evaluated from the tabulated data.20 When the intensity data of (100) reflections were included in the refinement, the resulting reliability factor, R, always became considerably large (about 60% larger). So, we have omitted the (100) data in all the calculations, although the reason for this increase in R is not clear at present.

lines represent respectively the observed intensity data and the calculated profile by PRO-FIT. In Fig. 3, an example of a log[l,,(O)/&,,] - (sin 8/h)2 plot (I,,,(O) = ZIKT, see eqn (4), and A is the wavelength used) is shown for the slow-cooled NiJb.3A153.7; this is useful for examining the degree of agreement between observation and calculation.‘5 Present R-factor values (eqn (9)) extended from 0.7 to 4.2%, indicating a rather good fit compared with the values by Kogachi et al.,” (2.1-10.9%). Considerable decrease in the averaged value of R from 5.4% (previous)15 to 2.5% (present) may reflect some improvement of quality of the samples prepared. The results of site occupancies obtained for the slow-cooled samples are shown in Fig. 4 by the solid circles, triangles and squares, where the occupancies on the Ni-site are given in the upper graph and those on the Al-site in the lower graph. The small vertical line through each data point indicates the error bar estimated irk the same way as that described previously.15,‘6 Error bars for the solid circles are removed where they are within the

4 RESULTS AND DISCUSSIONS 4.1 Experimental results

Figure 2 shows examples of profile-fitting of the 2 10 superlattice and 222 fundamental reflections from the slow-cooled Ni4G,6AlSj.4. Crosses and solid

0.21, 0

’ 0.1

’ 1. 0.2 0.3 (sin8 /I )*

’ 0.4

.I

Fig. 3. log[Z,,,(O)/Z,,J - (sin BiA)2, plot in the Ni,.,A1,37 (slowcooled).

Defect structure in Al-rich region in the P-NiAl phase

corresponding solid circle area. As found from the figure, the number of Ni atoms on the Ni-site (Ni/Ni) decreases rapidly with increase in the Al concentration, c. Simultaneously, the Ni-vacancy

- 95

&a 10 1

Al-site

4

90

oy .5aa .z

[VI/AI

:

54

50

ConIpos~&

c

(%)

Fig. 4. Changes in the site occupancies with composition Ni,.,.AI,.. The data are for the slow-cooled samples.

in

15 HI00

133

concentration ([V]/Ni) increases to compensate for the lack of Ni atoms (i.e. maintained as unoccupied sites). However, this is not complete; the existence of a little Al-ASD (Al/Ni) is recognized. On the other hand, the presence of Al atoms on the Al-site (Al/Al) indicates a gradual decrease, but no Ni-ASD (Ni/Al) appears over the whole composition range concerned. As a result, a few Al-vacancies ([VI/Al) are created. The situation was almost the same in the present samples quenched from 950°C as shown in Fig. 5. Similar results were reported by Kogachi et a1.,15 for the samples quenched from lOOO”C,but both Al-ASD and Alvacancy obtained by them are comparatively larger than present values (Fig. 5). This discrepancy may come partly from a difference in the powder sample quality and from the procedures used for the actual calculations (e.g. vacancy concentration). From the obtained composition dependencies of the site occupancies, we can suggest a creation of the Al-ASD and Al-vacancy as the constitutional defect in the high Al concentration region. These defects are expected to increase with elevating the temperature. We have measured the temperature dependence for the two samples, Ni47.7A151,3 and Ni46,6A15D.4, with high Al concentration in the way described in Section 3. However, as found from Fig 6 and 7, their site occupancies thus obtained did not alter up to 1150°C. In each figure, two data points at RT for respective occupancies represent the results for the samples cooled at a rate of 2.5”Cimin and that of O.S”C/min, indicating no appreciable difference between them.

Composition C (Q)

Fig. 5. Changes in the site occupancies with composition in Ni,.,.AI,.. The data are for the samples quenched from 950°C.

Fig. 6. Changes in the site occupancies with quenching temperature in Ni,, ,Alj2 3.

134

M. Kogachi, Y. Takeda, T. Tanahashi Ni;ASD 3WAl(F’ 0

1

5

6

85

r

t-

loo

m--++-+ AI/Al -

Fig. 7. Changes in the site occupancies with quenching temperature in Ni,, ,A&, 4.

4.2 Examination of defect structure The present analysis revealed that the constitutional defect in the Al-rich NiAl P-phase is mainly the Ni-vacancy. This strongly supports the BT model mentioned in Section 1. However, in addition, we found evidence for the existence of two other types of defect, Al-ASD and Al-vacancy. They are excluded in the triple defect model mentioned in Section 1, which has usually been adopted in many previous studies.3~6~7~9-‘-7 It is thus important to examine the reliability of our analysis results. We here calculated the values of the reliability factor, R (eqn (9)), by supposing two defect structure models: (a) Al-ASD model and (b) triple defect model. The model (a) is that the Ni-ASD does not exist (in eqn (1), Ni/Al=O) and the vacancy concentration is kept constant (x=x~~), which just corresponds to the present results. In this case, the amounts of Ni-vacancy ([V]/Ni) and Al-vacancy ([VI/Al) are uniquely determined when the amount of Al-ASD (Al/Ni) is given. The model (b) is that only the Ni-vacancy and Ni-ASD exist ([VI/Al = Al/Ni=O). In this case, with increase in the Ni-ASD the Ni-vacancy, and consequently the total vacancy, concentration increases (x> xBT). Both models are reduced to the BT model when Al/Ni = 0 for model (a) and Ni/Al = 0 for model (b). The numerical results of R for Ni46.6A153 4 are shown in Fig. 8 as functions of the Al-ASD (model (a)) or of the Ni-ASD (model (b)). Curve (a) for the Al-ASD model has a minimum at an Al-ASD content of about 1.5%.

Fig. 8. Changes in the reliability factor, R, with (a) AI-ASD and (b) Ni-ASD for the Ni4,.,Al,3.4. (quenched from 1OOOT). Curve (a) is for the Al-ASD model and curve (b) for the triple defect model.

On the other hand, curve (b) for the triple defect model indicates a rapid increase with increase in the Ni-ASD and furthermore for curve (b), R values are larger compared with curve (a). Therefore, we can conclude that the triple defect model will not be adequate for explaining the defect structure formed in this alloy. As described in Section 2, another defect structure model having no Al-vacancy, which is constructed by removing the vacancies corresponding to amount of [VI/Al from both Ni and Al sites, gives the same R-factor value as that for the present structure shown in Fig 47. However, this model clearly brings about some decrease in the total vacancy concentration, x, in the alloy from the value of XBT. Further, even if it is the true defect structure, the existence of the Al-ASD cannot be denied. 4.3 Thermodynamic calculation We try here to reproduce the present experimental results by the thermodynamic treatment adopted in all the previous studies.7%‘k’4It is based on the Bragg-Williams approximation of the nearest neighbor interaction. The total free energy, F, of the ‘ternary’ system concerned is then expressed as F = N,U - N,T@

(10)

where the internal energy per site, U, is

u = d’(lk)(l-x)~NiNi

+ 4c(l_x)EAlAl + 4x$,V

+ 4cx( l-x) v,,, 1-x) &iv + s12 v,iv = sz2 VA,,

+ 4c( lLc)( l-x)2I& + 4(l_c)x(

(11)

135

Defect structure in AI-rich region in the P-NiAl phase

and the configurational

entropy per site, @, is

CD= +,/2) [((1-c)(l-x) + S/2} ln((l-c)(l-x) +S,/2} + fc(l-x) - S,/2} ln(c(l-x) - S,/2} + fx - (S,-S,)/2} ln{x - (S,-S,)/2} + {(1-c)(l-x) - S,/2} lnf(l-c)(l-x) - S,/2) + {c(l-x) + S,/2) ln(c(l-x) + S,/2} + {x + (S,-Q/2} ln(x + (S,-S,)/2)] (12) where k, is the Boltzmann constant. lii represents the bond energy between, the i-j atomic pair, including ‘ghost’ bonds between a vacancy and an atom or between a vacancy and a vacancy (ij = Ni, Al or V; V means a vacancy). Vii is given by v,j = 2Ejj- Eii- 4

(13)

Noting that N, depends on x (see eqn (3)) the equilibrium state of the system at a given temperature, T, is determined from the next minimum conditions:

afl ax = 0, aF/ as, = 0 aF/ as, = 0 (14) The VaheS of ENjNiand EAIAIwere estimated from the experimental values of heats of melting and vaporization for the pure Ni and Al metals, and for E,, we took lvy = 0. The remaining three bond parameters, Vij were determined so as to give the best fit to the’ observations. The values thus obtained are, in kJ/mol units: ENiNi= -64.9 VNiAl= -23. I VAIV = -0.6

EAIA~ = -50.4 1.4 vNiV =

Numerical results for the vacancy concentration at T = 300 K are shown by the broken line in Fig. 1. The calculated x values lie well on the solid line (x = xsr) on the lower side of the Al concentration, but at higher Al concentrations it deviates somewhat from this line. Figure 9 shows the

400

1200 800 Temperature (K)

1600

Fig. 10. Calculated temperature dependencies of site occupancies

in N&Al,,.

calculated composition dependencies of site occupancies on the Ni-site at T = 300 K. The prediction is found to reproduce the observations (Fig. 4) fairly well. However, the observed existence of the Al-vacancy could not be reproduced by calculation for 300 K even in the high Al concentration region, corresponding to a reduction of the calculated total vacancy concentration (broken line in Fig. 1) in this region. However, the formation of Al-vacancies was made clear by calculation for temperatures higher than 1400 K as seen in Fig. 10, which plots the calculated temperature dependencies of site occupancies for N&Al,,. At much higher temperatures, a considerable number of thermal vacancies are expected from Fig. 10 to be created on the Ni-site as well as on the Al-site. Experimental work at temperatures above 1200°C is to be desired.

REFERENCES

50

54 ComposilEn

C (%)

Fig. 9. Calculated composition dependencies of site occupancies on the Ni-site at T=300 k in Ni,,Al,.

1. Bradley, A. J. & Taylor, A., Proc. R. Sot., Al59 (1937) 56. 2. Taylor, A. & Doyle, N. J., .I. Appl. Cryst., 5 (1972) 201. 3. Wasilewski, R. J., Butler, S. R. & Hanlon, J. E., J. Appl. Phys., 39 (1968) 4234. Ho, K., Quader, M. A., Lin, F. & Dodd, R. A., Scripta Metall., 11 (1977) 1159. Cooper, J., Phil. Mug., 8 (1963) 805. Wachtel, E., Linse, V. & Gerold, V., J. Phys. Chem. Solids, 34 (1973) 1461. Ommen, A. H., van, Waegemaekers, A. A. H. J., Moleman, A. C., Schlatter, H. & Bakker, H., Acta Metall., 29 (1981) 123. 8. Ho, K. & Dodd, R. A., Scripta Metall., 12 (1978) 1055. 9. Wasilewski, R. J., J. Phys. Chem. Solids, 29 (1968) 39. 10. Jacobi, H. & Engel, H. J., Acta Metall., 19 (1971) 701.

136

A4.Kogachi, Y. Takeda, T. Tanahashi

11. Neumann, J. P., Chang, Y. A. & Lee, C. ‘M., Acta Metall., 12. Donaldson, A. T. & Rawlings, R. D., Acta Metall., 24 (1976) 811. 13. Neumann, J. P. & Chang, Y. A., Metafikde, 70 (1979)

118. 14. Kim, S. M., Acta Metall., 40 (1992) 2793. 15. Kogachi, M., Minamigawa, S. & Nakahigashi, Metall., 40 (1992) 1113.

16. Kogachi,

M.,

Minamigawa,

S. & Nakahigashi,

K.,

Scripta Metall., 27 (1992) 407.

24 (1976) 593.

K., Acta

17. Kogachi, M. & Kameyama, A., Scripta Metall., 29 (1993) 1329. 18. Toraya, H., J. Appl. Crys., 2 (1986) 65. 19. Fukuchi, M. & Watanabe, K., J. Japan Inst. Metals, 43 (1979) 1091. 20. International Tab/es for X-ray Crystatfography, Vol. 4, 1974, pp.99 and 149.