On the habit plane of γ″-Ni3V precipitates

WI l-6 160!82’05096 i-04303.M310 Copyright D 1931 Pergamon Ptcss Ltd

.ict~ merail. Vol. 30. pp. 961 to 964. 192 Prmvd m Great Ericam. .A11nghrs rewved

ON THE HABIT PLANE OF ;1”-Ni,V PRECIPITATES K-M.CHANG General Electric Company, Corporate Research and Development. Schenectady. NY 12301, U.S.A. (Rrceited

8 October

1981)

Abstract-The crystallographic habit of coherent 7”-NiJV precipitates that have a bet DOzz structure has been investigated. Theoretical calculation based on the elastic energy theory predicts an unusual habit to be close to (102). This calculation is in good agreement with the results of transmission electron microscopy, Four variants of precipitate habit that correspond to a tetragonal direction coexist, leading to an absence of streaking in the diffraction pattern. R&sum&--Nous avons Ctudit le plan d’accolement des prbcipites de Ni,Vq” cohirents de structure quandratique centree DOLI. Un calcui thiorique de I’knergie eiastique privoit un plan d’accoiement inhabituel proche de (102). Ce calcui est en bon accord avec ies rtsuitats de la microscopic klectronique par transmission. Quatre variantes de plans d’accolement du pr6cipitt correspondant Q une direction quandratique coexistent, ce qui conduit B i’absence de train&es dans ies diagrammes de diffraction. Zu~mmenfa~ung-Die kristaliografische Habitebene von koharenten ~“-Ni~V-~ussche~dungen, die eine DO,,-Struktur haben. wurde untersucht. Theoretische Berechnungen auf der Grundlage der Eiastizidtstheorie ergeben eine ungewshniiche Habitebene nahe bei (102). Dieses Ergebnis stimmt gut mit den Ergebnissen der Durchstrahiungs-eiektronenmikroskopie iiberein. Vier Variant-x der Ausscheidung, die einer tetragonalen Richtung entsprechen, bestehen, welches die Abwesenheit von Streifen im Beugungsbild verursacht.

INTRODUCTION Precipitation of coherent, ordered DOz2 phase, desig nated ;“‘, in nickel-based alloy systems has attracted extensive attention since Inconelf 718 was developed, in which niobium replaced titanium and aluminum as the major hardening element [l, 21. Upon aging, remarkable age-hardening associated with the formation of metastable bet Ni,Nb phase is observed. This is due to the large coherency strains that resulted from its tetragonal distortion in the y-f.c.c. matrix [33. The y” precipitates appear in inconel 718 and in similar alloys as ellipsoidal, disc-shaped particles with the cubic-cubic orientation relationship:

(OO1).Y I I(001 ), and [lOO],., j I (lOO),. Streaking of superlattice spots in the electron diffraction patterns, which is characteristic of precipitates having a plate-like morphology, indicates that 7” precipitates have a habit plane normal to the tetragonal direction--c-axis, i.e. [OOlf planes. This habit plane is confirmed with the trace analysis of dark field images taken from the streaking superlattice spot. In contrast to $‘-Ni,Nb, very lit& effort has been given to the y”-NiXV precipitation in the Ni-base systerns, though very interesting phenomena have been reported. Moreen er ni. [4] using transmission electron microscopy (TEM), have discovered that the precipitation phase in binary alloys containing up to 22 at.% V had a DO12 structure with the disk-shape t Trademark of Huntington Alloys, Incorporated.

morphology. The same orientation relationship obtains between the 7” phase and the matrix as that of Nb-bearing alloys. However, the superlattice spots did not exhibit streaking. The form of the superlattice spots remained spherical through the whole range of aging time and temperature. Despite the observation of the disk morphology of 7” precipitates, no attempt has been made to determine the habit plane. The present work explored the mystery regarding superlattice spots of coherent ‘I”-N&V precipitates in N&-V alloys. Theoretical analysis based on the elastic energy consideration was applied to calcutate the habit plane accurately. Experimental investigation employed the detailed TEM examination to determine the actual habit. Excellent agreement was found between the theoretical calculation and the experimental observation.

THEORETICAL

CALCUL.4TIOXS

There exist many studies concerning the elastic strain energy associated with the formation of coherent precipitate particles. Elastic distortions play a dominant role on the characteristic morphology of precipitates, and the preferred habit must accommodate the elastic strain induced by the crystallographic misfit between the precipitate phase and the parent matrix. Khachaturyan’s k-space method [Yj (Fourier transformation of direct space) provides the most direct treatment toward the habit plane of thin-disk precipitates. Recently Morris and his associates [q 961

962

CHANG:

THE

HABIT PLANE OF y”-Ni,V PRECIPITATES

60

0-I Normalized

tetragonohty

Fig. 1. The angle, 0, between the habit normal and the tetragonal axis of a tetragonal precipitate in the cubic matrix, (A < 0) as a function of the normalized tetragonality (q/v,,) of coherency strain.

have solved analytically the case of tetragonal precipitates forming in the cubic matrix, using Khachaturyan’s equation for elastic energy. Part of their results applicable to “J”precipitation are refined as follows. Assuming homogeneously elastic constants, a coherent inclusion may relax its elastic energy to a minimum in a thin-disk shape with a definite habit. Consider the case where the matrix has a negative anisotropy factor, A = (Cl, - CL2 - 2C,,)/C,, < 0, such as nickel alloys; let the tetragonal c-axis of the precipitate phase be along [OOl] direction. The tetragonality of transformation strains is defined as q = e3 - e,/el, where e,, e3 are principal strains perpendicular and parallel to the tetragonal axis, respectively. Then, by minimizing the elastic energy, the preferred habit plane is necessarily of type (sine, 0, co@, where 8, the angle between the tetragonal axis and the normal of the habit plane, satisfies the relations 6 = O”, when

9 2 0;

tice reflection in the k space comes from precipitates with the same habit. Therefore, streaking of superlattice spots becomes evident, and the precipitate platelets in the dark field images taken from these superlattice spots would be in edge-on orientation. The author has derived the completed analysis elsewhere [8]. In general, Ie, I > Ie3 I in Case 2. Since the misfit is the least along the tetragonal axis, the habit plane must be the one containing this axis. Elastic energy calculation gives {lOO}-type habit. For each crystallographic correspondence between 7” and 7, two variants of habit plane, (100) and (OlO), coexist because of the crystalline symmetry. However, no such precipitate has ever been found in any alloy system experimentally. In Ni-V binary system, 7”-Ni3V is an equilibrium phase. Figure 2 shows the lattice constants of Ni-V binary solid solution and ordered Ni,V phase as a function of vanadium content [9]. The 7”-Ni,V precipitation is then evidently Case 3, where e, and e3 have the opposite signs. Coherency strains of different signs can compensate for each other if the habit plane lies at a definite angle with the tetragonal axis. According to the Ni-V binary phase diagram, the boundaries of 7 + Ni3V two-phase region are located at 17 and 22 at.% V for the ordinary aging temperature 700°C. The coherency strains of y”-Ni3V precipitates are calculated by extrapolation of Fig. 2: e, = -0.222x, e3 = 1.22% and 7 = -6.49. Employing the elastic constants of nickel [lo] the angle predicted from the equation 0 = COS-’ :l + 40/q is 27.4”, which gives a habit very close to (102) plane (e = 26.6”). Four variants of habit planes corresponding to (102), (iO2), (012) and (Oi2) exist for each tetragonal axis [OOl] of disk-shaped Ni3V precipitates. Depending on the orientation of thin foil, the TEM dark field

(1) 3.65

9 = 90”, 0=

when

cos-’ km,

0 2 q 2 -q,,; when

(2) -qo 2 rl.

(3)

The specified tetragonality q. is a material character, by definition lo = (Cl, + ZC,,)/(C,, + CL2). Figure 1 plots the angle 8 as a function of the normalized tetragonality (q/qo); this characteristic curve fits all alloy systems with A < 0. The above results can be understood easily from the minimum energy point of view-the habit must lie on the crystallographic plane yielding least elastic misfits. The 7” precipitation in Inconel 718 and Nbbearing alloys belongs to Case 1, where e, and e3 have the same sign, and le3 1 > le, 1. Cozar and Pineau [7] using extraction carbon replicas of precipitates, measured that el = 0.89%, and e3 = 3.17%. Since ;~“h misfit concentrates along c-axis, the precipitate particles must prefer a habit of x-y plane, orthogonal to c-axis. Each tetragonal direction has a unique variant of the habit plane, and, each superlat-

1

3.60 d _

1

5 f

5

2

/++-+A(

NI-V I

3.55 -A

s

/ t 3.50

D

’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ I5

Atomic

25

20

percent

30

vanadium

Fig. 2. Lattice parameters of the Ni-V solid solution and the 7”-N&V phase as a function of the vanadium content.

_ f:!3zL 3~5 sup*riartiazspot m3> rzi-saiup to ;o!;r zLo:uos of Sij\ precipitates with the spsdic h&i: ~srim:~. Lack of streaking at the suI&attice spots ~KSS,ZXS 2xphatOry. So Dattei what orienta:ton the thin foil has, there are al\+aGs some variants not in an :dge-on position. Cnsaturated Laue condition of electron diffraction no !onger exists. Furthermar-. the iup2:positiOtl oi rerfrctions from four varir--uit in the 5ymm- iis _^

izyia:~~(&!-

E?X’ERIJlEST.~L

OBSERVATIOS

In order to verify the abate argument. a 100-gm ingot with the nominal composition of X-17.5 V (at.“,) was arc-melted for investigation. After homogenization and hot-rol!ing, the sample was solution annealed at 11oO’C ior 1 h, water quenched, and then aced at 72i’C for 23 h. Thin foi! for TEM xere prepared by the standard jet polishing technique using a solution of 20 pet HClO, in methanol at -SO’C. and were examined under a JOEL-200 STEM electron microscope operated at 200 kV. Electron di5fraction patterns on various reciprocal lattice planes confirmed the precipitation phase as having a DO,.__ structure. In all cases the superlattice spots did not exhibit streaking, as previously reported. Figure 3 consists of the dark field image. the selected arta diffraction, and the (100) stereographic projection of a thin foil oriented along 100 zone. Three variants of the precipitate habit can be clearly

Fig. 3. The dark

;qp from. sn< a-?“F7 in (pie dair;, $dd age. The ang!es bc:wen habit normals and xtragonal axis [OOl] are measured as - 3. O- and - 13.. Trace analysis on the stereographic projection confirms that the habits near to ; 103: planes. Trvo edge-on :ariants sorrespond with (012) and (01% which are ‘ok Z&X.&tion f 35.6’ and -26.6’ away- from the [ !M] axis. respectively. The other two variants corresponding to (102) and iiO2). whose normals do not !ie on (100) plane, are equivaient to each other, as cross-sected on the (113.31plane. Larger cross sections of prrcipitate particles ivex obsened for the Iatter variants in Fig. 3. and their projected habits are normal to [Iti)]. In the 110 orientation, (IO?) is equivalent to (012) and (012) is equivalent to (TO?): therefore. only two variants appear as shoxn in Fig. 3. But nox of the habit normal iies on the (t 10) plane. as ii!usIrated by the large cross sections of precipitate pla:_iets. The measured angle between the tetragonal axis and the projected habit normal is 30.5’. Again. this measurement is x-fry close to the [ 102; projection ti3.5’). The best illustration for the different variants of precipitate habit takes place Lvhen the thin foil has the off-symmztrl; orientation. An example is given in Fig. 5. The dark field image was taken from the (01)) superlattix reflection. instead of (Wl) in Figs 3 and 4. Two variants near to the edge-on orientations show narro\\-er but brighter images. The other tuo variants. having less contrast intensity. lie nearly paralI?l to the thin foil plane, and large cross sections of disk morphologv a:e observed. The stereographic traZe analysis is difiicult to perform in this case since no accurate crystallographic reference exists.

dijtingijhe~

pattex field image and selected area diffraction orisntatlon referring to the (100) standxd

,j

of ;:“-Si;V projection.

i&L.

i.‘bi

precipitates in the l!,I*?:

.I

Yoj

CHAXG:

THE HABIT PLXXE OF T:“-Ni,V PRECIPITATES

Fig. 4. The dark field image and selected selected area diffraction pattern of 7”-Ni,V precipitates in the (1 10):. orientation referring to the (1101standard project.

near :102j-. and four variants of the habit plane exist with respect to each tetragonal direction. The unusual habit is caused by the opposite sign of transformation strains, e, and e,, and the precipitate platelets have the minimum elastic eners on such a habit plane. Because of the coexistence of four habit variants, no streaking appears at the superlattice spots in the ekctron diffraction pattern. Ackno~~ledgemenr-Sincere thanks are due 10 Ann Ritter who performed the excellent TELLIwork.

Fig. 5. The dark field image and selected area diffraction of 7”~Ki,V precipitates in an off-symmetry orientation.

pattern

Another interesting aspect of $‘-NiJV precipitation is the alignment of precipitate disks along the specific crystallographic direction. This so-called ‘tweed’ structure *as observed in Figs 3, 4 and 5. Elastic interaction between precipitate particles results in such a periodic structure. The mutual interaction between precipitates seems to have little effect on the individual precipitate habit and is out of the scope of present work. SUMMARY Coherent

7”~Ni,V precipitate

exhibits

the habit

1. D. F. Pautonir

3. M. Obiak and 0. S. Duval, Trans. Am. Sot. ,Cierais 62, 611 (19691. 7 I. Kirman, f. Iron Steel fnsr. 207, 1612 if969). 3:J. M. Oblak. D. F. Paulonis and D. S. Duvall. :\feraif. Truns. 5, 143 (1974). 4. H. .A. Moreen. R. Taegert and D. H. Patonis. .Cletnlf. Trans. 5, 79 (1974). -5. A. G. Khachaturyan, Smiet Phpics-S&d State. 8, 1163 fi967). 6. S. H. Wen. E. Kostlan, M. Hong, A. G. ~atchatur~an and J. W. hforris Jr. Acra ntzruf[. 29, Q&Y(1981). 7. R. Cozar and A. Pineau, .%f~ciil. Trans. 4. 17 (1973). 8. Ii. M. Charm, PhD. The& Universitr of California. Berkely. California, Lawrence Berkeier Laborator! Report LBL-9208. May (19YY). 9. W. B. Pearson and W. Hums-Rothery. J. Inst. Mrtais 80, 641 (195’1. 10. C. Kittel. htroduction ro S&i State Pjrpics. 4th edn,

p. 149. Wiley. Sew York (19fll.