IN MOLYBDENJM*tarc.nucapt.northwestern.edu/refbase/files/Seidman-1974_6815.pdf · an 8 hr anneal at approx 2200°C in a partial pressure of oxygen of 5 x 10-j Torr; and (4) an 3 hr

FIELD ION MICROSCOPE OBSERVATIONS OF THE THREE-FOLD

SYMMETRIC DISSOCIATION OF +a(lll) SCREW DISLOCATIONS IN MOLYBDENJM*t

DAVID N. SEIDMMAX: and JOHN J. BURKE;9

A field ion microscope (FIM) study has been performed of the dislocation structure which exists in the (222) planes and environs of molybdenum specimens. The dislocation structure always consisted of three-fold symmetric dissociated &(I 11) screw dislocations which emerged normal to the {222) planes. Employing the pulsed field evaporation technique it was shown that the dissociated dislocation structure consisted of a kn(ll1) type partial screw dislocation (There k is a constant) which emerged normal to the (212) planes and three stacking faults on t.he (110) planes that intersected one another along a (111) type direction. The three stacking faults exhibited three-fold symmetry about the (111) type vector. This represents the first experimental observation of a three-fold symmetric dissociated $z(lll) screw dislocation in any body-centered cubic metal. The dislocation structure w-as produced LI& situ in the FIM specimen at a specimen temperature of less than 50 K as a result of the molybdenum specimen yielding to electric field induced shear stresses. It is pointed out that the observations are so far typical to the FIJI and that the exact role played by the electric field induced stresses, surface image effect and the small tip size on dislocation geometry remain to be determined.

OBSERT_1TIOS AI.7 JIICROSCOPE -1 EMISSIOS D’IOSS DE L-1 DISSOCL~TIOS TERSAIRE DE DISLOCATIOSS %-IS +a(lll) DARS LE JIOLTBDESE

Le microscope ionique a emission de champ (FIJI) a permis d’etudier la structure des dislocations dans les plans ,:1_, “‘*\ et a leur voiainage dans les echantillons de molybdene. Les dislocations etaient toujours cles dislocations vis $a(1 11) dissocieus energeant normalement aus plans (222 j. En utilisant la technique d’evaporation en champ pulse, nous avons montr6 que la structure d’une dislocation dissociee consistait en une dislocation vis partielle de type ka(ll1) (ou k est une constante) emergeant normalement aus plans {222; et en trois d6fauts d’empilement dans les plans {llO} qui se coupent selon une direction de type (111). Lea trois defauts d’empilement presentent un axe de symetrie d’ordre trois suivant le vecteur de type (111). Ceci est la premiere observation experimentale de la dissociation ternaire cl‘une dislocation vis +a(lll) dans un metal cubique centre. La structure des dislocations Qtait procluite irl sit/~ clans l’echantillon FIJI B une temperature inferieure a 50 K par suite de s cissions induitea par le champ Clectrique. 11 faut remarquer que ces observations sont caracteristiques du FIJI et qu’il reste Q determiner le role exact joue clans la geometric cles dislocations par les deformations induites par le champ electrique, les effeta superficiels et la petite taille de la pointe.

FELDIOSESJIIKROSKOPISCHE BEOBhCHTUSG EISER DREIZXHLIGES SYXMETRIE DER DISSOZIATIOX VOX +x(11 I)-SCHRAUBEWERSETZUNGES IS MOLTBD&

Die Versetzunqsstruktur in den ( 122)-Ebenen von Molybditnproben wurde mit Hilfe der Feldionen- mikroskopie (FIX) untersucht. Die Versetzungsanordnung besteht immer aus dreizlhlig symmetrischen dissoziierten @a(1 1 l)-Schraubenversetzungen, die die {222}- Ebenen senkrecht durchstoBen. JIit der Feldverdampfungsmethode wurde gezeigt, da13 die dissoziierten Versetzungen aus partiellen Schrsuben- versetzungen (vom Typ lia (ill), Iz ist eine Konstante), die die { 222}-Ebenen senkrecht durchstonen und aus drei Stapelfehlern auf {llO}-Ebenen, die sich in (Ill)-Geraden treffen, bestehen. Die drei Stapelfehler zeigen eine dreiziihlige Symmetrie mit (Ill)-Vektoren als Symmetrieachse. Dies ist die erste esperimentelle Beobachtung einer dissoziierten +u(lll)-Schraubenversetzung mit dreiziihliger Symmetrie in einem kubisch-raumzentrierten Metall. Die Versetzungsstruktur wurcle ia-ails in der FIJI-Probe bei Probentemperaturen van weniger als 50 K als Folge einer durch das elektrische Feld induzierten Schubspannung erzeugt. Es wird darauf hingewiesen, dall die Beobachtungen typiach ftir die FIJI sincl uncl da13 die genaue Rolle der durch das elektrische Feld induzierten Schubspannungen, der Oberfliicheneffekte und der kleinen FIJI-Probenspitzen auf die Versetzungsgeometrie noch untersucht werden mu13.

The plastic centered cubic

thought to be

1. ISTRODUCTION Recently there has been a good deal of emphasis on deformat’ion behavior of body- detailed computer calculations of the atom positions

(b.c.c.) metals at low temperatures is in and around the core of $a(lll! screw dislocations/l controlled bv the mobility of screw (Chang,(a) Gehlen et al.,(‘) Vitek et uZ.‘~) and Basin&i

dislocations (see Hirsch(l) and Christian’2) for reriews). et .1.(e)) employin g different interatomic potentials that describe stable b.c.c. lattices. The emphasis has

* Received July 26. 1973; revised March 2.5, 1974. been placed on the discrete atomic nature of the dis- t This rrork was supported by the United States Atomic

Energy Commission. ddditional support =-as received from location core in b.c.c. metals, because it is believed

the Advanced Research Projects Agency and the Sational that the mobility of screw dislocations is determined Science Foundation through the use of the technical facilities of the Materials Science Center at Cornell. by an inherent lattice friction stress (t.he so-called

2 Cornell University, Bard Hall, Department of Materials Peierls stress) that is a result of the dislocation core Science and Engineering and The Materials Science Center, Ithaca, Sew York 14S50, U.S.A.

structure. The computer calculations indicate that

u \ yrn at: TRW Metals Division, Minerva, Ohio 44657, . ,_ . ~I The quantity a is the lattice parameter of molybdenum.

ACTA METALLURGICA, VOL. 22, OCTOBER 19i4 1301

130” -1CT.I METALLURGIC.~, VOL. 42, 19;;

TABLE 1. Spark source mass spzctrometric analysis of a molybdenum specimen wirh d equal to :;:I

Concentration: 0.1-i I). l-l 0.1-l l- 1- I- l- l- l- 4- IO- IO- IO- 10- 10(& ..: I.000 3.953 Y ( IiJ-@ at.fr.) 10 IO 10 10 10 10 40 100 100 IO0 lC)lJ l,cil)l)

f Standards were not available for molybdenum. SO the concentrations reported were estimated assumine chat all species were ionized to the same degree by the ionizing spark. Generally, this procedure produces result 3 that are &curate to within a factor of two to three.

: This concentration is reported as an upper limit, due to a possible interference in its determination. S A value of 3,975 ppm for oxygen was obtainecl via a wet chemical test after the spark source spectrome:ric anal?;& was

performed for the other elements.

the core structure of &~<lll) type screw dislocations in a b.c.c. lattice consists of three intersecting generalized faults on (110) planes terminated by fractional dislocations.? It is emphasized that within

the context of the computer models the stacking faults are not stable on the (110) planes, so that a stacking

fault with a constant shear vector (R) is not formed. For a discussion of the theory of generalized dis-

sociations with unstable stacking faults see Vitek

and Kroupa.‘*) The important physical result of the computer calculations is that they all show that the $a( 1111~ dislocat’ion cores have three-fold symmetry

about the (111) direction. To date there has been no experimental verification of this prediction of the

computer calculations, so that the subject has been

essentially a theoretical one. In this paper we present field ion microscope

observations$ of the three-fold symmetric dissociation

of $~(lll) screw dislocations in b.c.c. molybdenum.

The molybdenum specimens were deformed at cryogenic temperatures (<50 K) as a result of the high

stresses (approx 4.5 x lOlo dyne cm-*) produced by

t,he imaging and/or evaporation electric fields. The basic dislocation structure observed was always a

three-fold symmetric dissociated &~(lll) type screw dislocation which emerged normal to the (222) planes.

Employing the pulsed field evaporation technique it was shown that the dissociated dislocation structure consisted of a ka(ll1) type partial screw dislocation

(where k is a constant) which emerged normal to the (222) planes and three stacking faults on the (110)

planes that intersected one another along a (111) type direction. The three stacking faults exhibited three-

t A recent summary and discussion of the computer calculations is given by Duesbery et al. (7). The dislocations terminating unstable stacking faults are termed fractional dislocations and should not be confused Kith partial dislocations. The authors also consider the effect of shear stresses on the dislocation core structure in great detail.

$ The observations reported in this paper mere made during the course of an FIN studycD’ of the temperature dependence of the ionization and field evaporation charac- teristics of molybdenum. This study was also aimed at understanding the contrast effects detected in molybdenum images, so that the contrast effects produced by point defects induced by either irradiation or quenching could be properly interpreted.

fold symmetry about the (111) type vecror. Each of

the three stacking faults was bounded bv a partial dislocation. The experiments were performed on both low purity (approx 1.2 x 1O-3 at. fr. impurity content) and high purity (approx 1.7 10-j at. fr.

impurity content) molybdenum: it is argued that the

observed dissociation effects are not caused by Suzuki

segregation of impurity atoms to the stacking faults.

It is emphasized that our observations are so far

peculiar to the FI>I situation and that the exact role

played by the electric field induced stresses, surface image effects and the small tip size on dislocation

geometry remain to be ascertained.

2. EXPERIMENTAL TECHNIQUES

2.1 Specimen preparation

The experiments were performed on W-O different,

grades of molybdenum. The first grade was Sylvania 0.25 mm dia polycrystalline wire with a resistivity

ratio, W(W = RZ88k’/RJ.2k’) of 33. The results of a

spark source mass spectrometric analysis of this material are shown in Table 1. The sum of all the

maximum values of the concentrations listed is

approx 6.5 x 10m3 at. fr. If it is assumed that an average value for the resistivity of an impurity atom

is 1.5 x 1O-4 ohm cm (at. fr.)-‘, then the value W = 33 implies a total impurity atom concentration of approx 1.2 x 10-a at. fr. Hence, the jpectrometric

analysis and the residual resistivity measurements at 4.2 K yielded impurity concentrations that were in

agreement with one another lvithin a factor of about 5. It is noted that the major impuritie in this com-

mercial grade molybdenum were oxygen, nitrogen and iron.

The second type of specimen employed was prepared by zone refining a 1 mm dia rod of Sylvania 99.9 wt. % pure molybdenum. The processing treatment consisted of the following four steps : (1) two pass zone-refining in a background pressure of 5 x 10-e Torr; (2) a 6 hr anneal at about 22OO’C in a

background pressure of less than 5 x lWs Torr; (3) an 8 hr anneal at approx 2200°C in a partial pressure of oxygen of 5 x 10-j Torr; and (4) an 3 hr anneal at

~.-- -~ L Standards were not available for molybdenum, so the concentrations reported were estimated asuming that.

all the species were ionized to the same degree by the ionizing spark. Generally, this procedure proclnct~s results which are accurate to within a factor of two to three.

: These concentrations were reported as upper hmits due to H. possible interference in their determination. $ The F. Sa, Ti and Hg coneent~ation~ were unavailable due to interference. ‘: _?i vsiue of :;I? UDI~ fo!-osvzen ~-as obtainedvisa, wet chemica1 test after the spark aourcespectrometrie nnialv& . z “...

xas matlc for the other elements.

23)O’C in it background pressure of less t’han :! X lo-’ Torr. The Aue of 28’ for this second type of specimen lx-as 2.2 ‘*: l(p, ztncorrectecl for an>- possible specimen

size effect (1 mix] specimen dia). The residual resistkit? at 4.2 K corresponds to an

average total impwit> concentration of appros l.i N 1W5 at. fr. employing an average impuritv atom resistivity of 1.5 ‘X 10-A ohm cm (at. fr.)-l.

It is important to note that all the single crystal specimens had a [ill] fiber axis. A comparison of Tables 1 and 2 shows that in the A% = 2.1 x lo3 specimen the elements cobalt, rubidium, niobium:

arsenic, sulfur, copper and potassium were undetected whereas they were detected in bhe 22 = 33 specimen. Presumabl>- these elements were removed by a

combination of the zone refining and annealing treatments described abore. It is aIso noted that the concentration ranges for both tungsten and silicon

were identical for the 2% = 33 and 2.2 x 103 speci-

mens. The segregation coefficient of tungsten in mofybdenum is nearly unity”*) and therefore it cannot

be removed by zone refining. Since the segregation coefficient of silicon in molybdenum is less than unitv(ll) it should, in principle, be removed by zone

refining. The sum of the ~~~~~~121~~. values of the impurity

concentrations listed in Table 2 is approx 1.6 x 10e3 at. fr. Hence, the total impurity atom concentration

determined by spectroxnetric anal>-sis differed from the average impurity atom concentration determined b>- the -1-Z II; resistkit- by a factor of about 10’.

This differencet is most likely due to the fact that the high temperature anneal in the presence of a partial pressure of oxygen caused the formation of metai

oside precipitates which were distributed on a rather

r Eyre. Maher and Bsrtlett”” have conducted a more detailed chemical analysis stud? of zone refkxl molgbdenum than the one performed by us. Although they, also, found that the total impwit>* concentration (see Tables I-3 in Eyre el 02.) 8s measured chemically exceecl~ that predicted by the residutxl resistivity at 1._ ‘) Ii if one employs an average impurity atom resistivlty of 1.5 x 10-J ohm cm (at.fr.)-‘. Their results gives credence to our argument that some of the purification occurs via the mechankm described in this paragreph.

coarse scale throughout the specimen. A coarse distribution of metal oside precipitates Tt.ill result in a low value of the 4.2 I< resistivity, whereas the mass

spectrometric analysis does not clistixx~@h betneen

impurity atoms in solid solution 1-s ones in precipitates.

2.2 Electropnlishing procedure

The specimens were prepared by the standard drop-off techniqne(i3i in a volumetric solution of seven parts methanol to one part sulfuric acid at 5-13 Vdc. Each specimen was transferred imme-

diately to an FIN after a sharp tip was obtained. The FIJI was eracuated to lo-” Torr within less than 1 hr

from the time of completion of the e~ectropolishin~ procedure. This rapicl transfer reduced the number of

tips that flashed prematurely-. The flashing of tips was attributed to the formation of either a heavy

layer of an oside or a nitride of molybdenum on the tip’s surface.

The experiments were performed in two different

types of FIM’s. The first type was an all stainless steel diffusion pumped FIM which was baffled with a

Granville-Phillips liquid nitrogen cold trap. The pressure in this FIX prior to backfilling with helium gas, was always in the range 0.7-Z :x: 10-s Torr. This

F131 v-as used to examine the specimens with .z = 33,

The second type of FIJI was the one described pre- riously b?- Chen and Seidman’xJ) and Berger et uZ.(xj’

The background pressure attained in this FIX prior to backtiling \I-ith helium gas (2.5 x 1.W4 Torr) ii-as

6 x 10-x@ Torr. This FIM was used to esamine the .9 = 2.2 )< lo3 specimen. The FIJI liquid helium cryostat,, the temperature measurement problem, and photographic recording system hare been described by Seidman et cL(x6)~ Seidman and ScanIan and Scanlan et &.(x8) The image was intensified 115th an internal image intensification system based on a i6 mm clia channel electron multiplier array (Turner et &.[19’ ancl Brenner and JIcI<inneyCZo)). The intensified image was recorded on 33 mm ci& film

130-i ACT.1 METALLURGIC_A, VOL. 22, 1954

(Kodak Plus-S) wilth an Automax cin6 camera. The shutter of the camera was synchronized with the output of a zero to 5 kV pulse amplifier (Robertson and Seidmanc21)), so that the specimen nas alternately pulsed for 100 psec to remove 1 or 2 atoms from a typical high index plane and then photographed at best image field between the pulses. The 35 mm cinB film was analyzed with a Vanguard motion analyzer(l8) which handled the 1000 ft rolls of film employed. The photographic recording and analyzing techniques were similar to those employed in our laboratory for the study of point defects in irradiated or quenched metals (see Seidman(22) for a review of this research). A total of approx 1000 ft (15,000 frames) of 35 mm cint5 were recorded and analyzed in the present study.

3. ANALYSIS OF DISLOCATION

CONTRAST

In this section we review briefly the analytical concepts necessary to understand the dislocation contrast? effects which are produced b- perfect dislocations, stacking faults and partial dislocations.

3.1 Perfect dislocations

Any perfect dislocation line in a crystal lattice converts a set of initially parallel atomic planes into a helical ramp (Cottrell’23)). The Burgers vector and the unit line vector of the perfect dislocation are denoted

by b and irespectively, and the unit normal to a set of rational lattice planes by a. This geometric property is valid for all dislocations provided that

ri - b and ii - f do not equal zero. Consider the case where a dislocation line emerges in

a single pole of an FIN surface and the Burgers circuit is drawn in the plane of 6. A circle sketched in the plane of A in “good crystal” (Readt2’)) is transformed into one turn of a helix of pitch Aa b (see Fig. 1 ~IJ Smith et aZ.(25)). The value of 4. l b is given by

6-b =pdhrl (1)

where

p = hu f kv f 110. (2)

Since b is a lattice vector for a perfect dislocation and 4. is the unit normal to a set of rational planes, the pitch will always be equal to an integral number of interplanar spacings: (d,,,‘s). If p = 1 the contrast

t The reader is referred to Bowkett and Smith,(**) Smith et aZ.‘*5j and Smith(‘6’ for more details concerning the geometric theory of FIX contrast effects from dislocations. In this paper we employ the notation of Smith and co-workers.

$ For a b.c.c. lattice h + X: + 1 must be an even number.

effect produced is a spirals with a pitch equal to one dnkl. In general when p is an integer greater than unity then the pitch of the spiral is pd,,,, and the contrast effect is p interleaved spirals (see Smith et aZ.(26) and Sanwald et aZ.@*’ for illustrations of p equal to 2 and 3).

3.2 Stacking faults

Consider the case of a planar stacking fault where the displacement at the fault is given by the vector R, and where the magnitude of R is the same every- where on the fault surface. Denote the unit normal to the fault surface as B and exclude the case where fi x I = 0 from the following discussion. The intersection of the stacking fault with a pole of an FIJI surface results in a step of height ii . R normal to the surface where

and 6 - R = qd,,, (3)

p = hu, + kv, -+ lw I, (4)

since R = [u,v,zuJ. The quantity q need not be an integer in this case since u,, vp and wp are not neces- sarily integers. When the value of q is nonintegral and greater t,han one the step height after field evaporation will be q’d,,, n-here q’ is the nonintegral remainder after an integral number of planes have been removed.

A schematic example of stacking fault contrast is shown in Fig. 1. Figure l(a) is a section through a pole of an FIX specimen prior to the introduction of the fault, while Fig. l(b) shows the same pole after the introduction of a stacking fault. The case drawn is for jql < 1. The contrast expected in the FIM image is shown in Fig. l(c), after the crosshatched piece in Fig. l(b) has been removed by field evaporation. Xote that the “lines of contrast”ll in Fig. l(c) are all parallel to 6he vector I^ x 8. For a schematic illustration of the case where ci is perpendicular to 6 and 1 < (q I< 2 see Smith et aZ.(25)

3.3 Partial dislocations

Since a partial dislocation bounds a stacking fault, the contrast effects observed in a pole of an FIM

5 Pashley’*s’ and Ranganathan’30’ appear to have been the first ones to have realized independently that the helical ramp property of a dislocation would give rise to a spiral type contrast effect in an FIJI image. Ranganathan,‘30’ Sanmald and Hren,‘3l’ and Brandon and PerryfJ*’ have used the condition that in order for a dislocation to be visible in an FIJI image that d - b (where g is the reciprocal lattice vector of the plane involved) be nonzero in analogy with the electron microscope condition for visibility. It is noted that this approach and the approach of Smith and co-workers 8re equivalent.

11 The line which separates the txro halves of the fault and which is parallel to A x 9 is called a “line of contrast.”

c ; iT A ,

^s .‘. & ‘\

\HEADS OF

i;xi

-b-

HEAD OF $7

I

i?xi

-c-

FIG. 1. d schematic illustration of the contrast pro~luced by D stwkinp fault which is charncterized by a constant -hear vrctor R and a unit normal to the plane of the

fa‘alllt d. Figure 1 i- J * cross-dectionitl view of a Angle pole on the surface of an FIN tip n-hich is characterizeri b>- a unit normal il. Figure I(b) is the smnc pole after the stacking fault has been introduced. Tn thk case I ~3 nonintegral and lies between zero and unity. Figure 1 IC) is a top view of Fig. 1 Ib) after the crms-hatched area in Fig. 1 (b) has been removed by field erapwation. The lines of contrast are pnrallcl to the vector A .’ G and these lines shift to the Ieft as field elaporcuion of the crystal proceeds. If the vector R was parallel tu ri thrn the lino of contrast woulcl not shift to the left as field

evaporation proceeded.

specimen are explicable in terms of the analyses presented in Sections 3.1 and 3.2. For a partial dislocation with a Burgers vector b, a spiral with a pitch

equal to 6 - b, will be formed. In terms of d,,, the pitch g is giren by equation (3) with R = b,. If q is

nonintegal then a stepped spiral will be the resulting geometric configuration. An esample of the expected

contrast effect produced ll~- a single partial dislocation bounding a stacking fault and emerging in the center of a pole of an FIJI specimen is shown in Fig. 2 for the

case 0 < [qf < 1. If q is integral for a partial dislocation then a kinked spiral is the resulting geometric configuration. A detailed discussion of this effect and further examples for other ralues of q is giren bl- Bowkett and Smith’“* ad Smith et aZ.(~~l

4. RESULTS

4.1 Pertinent crystallographic it~fi,rrrmtion

The experimental observations which 1x-e will discuss involve the regions of the surface of FIJI

specimens which are centered on (222) planes. The crystallographv relevant to this region is summarized

by the portion of a standard 222 stereographic projection which is shown in Fig. 3. The (hkl} planes

involved in the interpretation of the FIX micrographs are the (22), (2331, (2-k> and jOll> lknes. It is

noted that the (iOl), (ilo) and (Oli) p!anes are all perpendicular to the (22) I1 ) an8 and have a Cl 111 zone axis.

h FIN micrograph of a ~~~olyldt~~um specinlen,

recorcled at a specimen temperature (,I‘=i c.,f 12.7 I< n-ith an 2 value of 1.2 -: 103 and a I1 111 single

crystal orientatiou is showi in Fig. 4. C‘ornpare this micrograph with the 222 stereographic projection shown in Fig. 3.

4.2 Ob.sermtiot~a of three fold symmetric ,di.s.sociation

of $c~(lll) 8crw dislocation.3

The main result obtained for nil specimens (i.e. both the .9? equal 33 arid 1. ’ 2 Y 103) esamined was that

1

erery (ZE) plane and environs examined showed contrast effects which are characteristic of the three- fold symmetric dissociation of $1,111 type screw dislocations. For ali the dislocation contrast effects

1 we obsen-ed the rector 2 was alwa>-s of the form

<111)[~‘3; that this is the case will be seen from our esplanation of Figs. 5-7. In the b.c.c. lattice a total dislocation which lies along a ,: 111 j direction must be a screw dislocation with b equal to $z, X 1 I:. Ke x-ish to emphasize the point that the dissociated dislocation structures obserred in the (222) planes were identical for both the d = 2.2 x 103 fflll] fiber axis) and the W = 33 ([llO] fiber ask) specimens. For the .2? = 2.2 x lo” specimen the point of emergence of the

central dislocation is at the apes of the specimen and it is noted that in this case this point will not more during field evaporation if the central dislocation Iine is parallel to a .,I11 1; direction. Since the contrast patterns were identical for both the [ill] and [IlO] specimens 11-e concfuded that the line of the central partial dislocation must he the same in the two differently oriented specimens.

The first, contrast effect n-e shali discuss is that caused by the stacking faults on (110t type planes. Figure $ which illustrates this point. is a ten frame pulsed field evaporation sequence. out of a total of IS1 frames of cinC film, that eshibit.+ only the (244) and (133) planes. The other (214; and f133; planes

I I I

Trace of the (Oli) plane.

ACT.4 METALLURGICA, I-OL. 32, 1374

SEIDMAS AND BURKE: +a;1 11) SCREW DLSLOCATIOSS IS MOLTBDESUM

/

1’ ----- 4’

8

\ \ \ \

FIG. 7. A schematic illustration of the three steps detected in the (222) plane shown in Fig. 6. The dashed lines indicate the traces of the three (110) planes which contain the observed stacking faults. _A partial screw dislocation of the form lia[lll], where k is a constant,

lies at the intersection of these three planes.

with a [ill] zone axis also simultaneously exhibited this contrast effect, but we shall discuss this case

first for the purpose of clarity. The line of contrast that runs through the (244) and (233) planes is the trace of the (Oli) plane. Xote that between frame

numbers 17 and 20 the atoms that are imaged in the

(233) plane shift from the right to the left hand side of the line of contrast. This same contrast effect in the

(233) plane repeats itself between the following pairs of frame numbers: 47 and 59 ; 79 and 10.5; and 1%

and 181. The above contrast effect also occurs in the (244) plane as an examination of the following pairs of frame numbers demonstrates : 20 and 4-i ; 39 and

i9; 105 and 114; and 114 and 125 in Fig. 5. The line of contrast seen in Fig. 5 remained in the same position

on the FIJI pattern as approx sixty (22) planes were removed by the pulsed field evaporation

technique and recorded on 4.5 x lo3 frames of film.

This result implies that the plane of the stacking fault

must be an (Oli) plane. Sate that if the plane of the stacking fault was inclined to the surface then the line of contrast, which is parallel to the vector fi x b,

would have shifted parallel to itself across the (233) and (244) planes as successive atomic planes were removed. This parallel shifting motion of t’he line of contrast for a stacking fault which is inclined to a

surface is illustrated schematically in Fig. l(c). X more detailed example of this first contrast

effect is exhibited in Fig. 6. The presence of three lines

of contrast caused by the traces of the three (IlO} planes that are perpendicular to the (222) plane can be seen in this ten frame sequence (out of 224 frames of film). The three lines of contrast caused by the (Oli), (ilO) and (i01) planes in the (?33), (332) and (323) planes respectively can be observed simultaneously by inspecting frame numbers 14, 47, 84 and 129. It

can also be seen that the imaged atoms in the different

planes shift across the line of contrast as successive

(222) planes are removed. (A total of sixty (2-7)

planes were removed and recorded on 4.5 x lo3

frames of tine film.) For example, note the positions of the imaged atoms shifting from one side of t.he line

of contrast to the other side in the (233) plane between the following pairs of frame numbers : 1 and I4 ; 26 and 47 ; 47 and 64; and 154 and 24. It is empha-

sized that the three different lines of contrast seen in Fig. 6 remain in the same position as successive (222)

planes are removed between frame numbers 1 and

114. This means that the three intersect,ing stacking faults which cause the three different lines of con-

trast must lie on the (110) planes. The second contrast effect we wish to discuss is the

stepped spiral effect produced by a partial dislocation (see Section 3.3). Examples of the stepped spiral

effect in the (222) and (332) planes can be seen in both Figs. 5 and 6. The existence of a stepped spiral

appears as a step (or discontinuity) in a ring of atoms in the (233) planes seen in Fig. 5. Some of the steps are indicated by rees in frame numbers 17, 20, 59,

79 and 125 in Fig. 5. The schematic illustration of a

stepped spiral in Fig. 2 should help the reader in confirming the presence of these steps (or discon-

tinuities) in the ring structure. The stepped spiral contrast effect appears in both

the (222) and (331) planes in the FIN micrographs exhibited in Fig. 6. The (222) plane is particularly

interesting in that three different steps are present in

the outermost ring of atoms in this plane. The two vees in frame 1 of Fig. 6 point to two imaged steps in

the (222) plane, Another example of this effect is also seen in frame number 84 where the three rees in

the (222) plane point to the three steps. F@re 7 is a

schematic illustrationt of the three steps observed in

the (222) plane. The third aspect of the contrast which n-e wish to

mention is the presence of a line of contrast through the {144}, but the apparent’ absence of a step or discontinuity in the ring structure through this plane.

This effect is particularly noticeable in frame numbers 17, 20, 79, 105, 12.5 and 181 in Fig. 5.

It is emphasized strongly that n-e were never able

to obtain a perfect crystal in the {Z-32:} planes and environs as a result of continuous and estensive field evaporation. Furthermore, elements of the dislocation contrast effects discussed in this section may be seen in all of the single frame micrographs of

t See Fig. 4 in Smith ‘~1~~) article for an isometric drawing of this contrast effect.

1310 _%CT_\ JIETALLCRGICA, VOL. 22, 1974

molybdenum published in the literature see: (e.g. Bowkett and Ralph’33’, and Jliiller and Tsong’a)). Thus it is believed that the deformation of a molvb- denum specimen in the stress field caused by the required imaging and/or eraporation electric fields always results in the same basic dislocation structure in the (122] regions of a molybdenum FIM specimen.

The separation between the central partial dis-

location R-hich lies parallel to the i = (11 l)/& vector and the second partial dislocation which must terminate each of the (110) stacking faults was calculated in the following manner. First, the local radii of curvature were calcuIated, using the ring counting method, between the (2%) plane and the {244} planes, employing the equation’3”)

n-here S is the number of rings between the 22 and 244 poles lvhich are separated by the angle 0P+2_2J4. Then the separation between partials (pi) was taken to be given by the maximum radius+ of the ibh (222) ledge constituting a field-ion pole, and this quantity was calculated from the expression’3B)

zz (3r(,,?,_!,,,iid,,,)1’~. (6)

The results for the specimens exhibited in Figs. 5 and 6 are presented in tabular form in Tables 3 and 4. The uncertainty of 124 A in +(212)_-(244) arose from an assumed uncertainty of -&l in the value of N. The uncertainty of k7 A in pr was calculated from dpi/pi assuming a value of &l for the quantity di. It is noted that the specimen (Table 4) with the smaller

values of n222b--(244) . had the smaller values of pi (compare Tables 3 and 4).

TABLE 3. Local tip radii and separation between par&l dislocations for specimen shown in Fig. 6t

Plane in -a-&h Looal tip radii Separation between

second par&I dislocation is

observed (hid}

betweed (222) and {244) planes

rraVzl-(t~J~ (-US

partial dislocations

c_T,*

(244) 193 f 24 (442) 217 ic: 24 (424) 217 f 21

t This specimen had an 1 value of 2.2 x IO*. : CalcuIated from equation (6). 5 Calculated employing equation (6).

l See Fig. I.18 in Bowkett and Smith.(zAj

TIBLE A Local tip radii and separation between pxtia1 dislocations for specimen shown in Fig. 6t

Plane in rvhich second partial dislocation is

observed (h&Z)

(244)

{$

Separation bet xeen partial

dislocations

(his

43 1 i 36 = 7 36 = i

t This specimen had an P value of 33. $ Calculated from equation (5). 3 Calculated employing equation (6).

Another uncertainty that enters into the measurement, of the pi is the determination of the exact position of the second partial dislocation. This was partially taken care of bv assuming an uncertainty of fl in the value of X, but we note that this is not an exact treatment of this error.

5. DISCUSSION

5.1 The dissociated three-fold symmetric dislocation structure

The dislocation structure observed always consisted of three-fold symmetric dissociated screw dislocations which emerged in the (222) planes. This dislocation structure was produced i)a situ in the FIM specimens at a II‘, of less than 50 K as a result of the molybdenum specimens yielding to the electric- field induced shear stresses which were greater than? approx 4.5 x HP* dyne cm-2+ The absence of edge dislocations in our deformed molybdenum FIX specimens is consistent with the electron microscope results(37’ on single crystal molybdenum deformed at less than 0.14 of the melting point. The reason for the presence of only screw dislocations is their low mobility at cryogenic temperatures, whereas the edge dislocations are highIy mobile at these same temperatures and presumably have slipped out of the FIM specimens.

The structure observed in the (222) planes consisted of a partial (111) screw dislocation emerging normal to a (;?22> type plane with stacking faults Iying on the three (110) planes which intersected one another along a (111) type direction (see Figs. 3 and 6). The three stacking faults intersect one another parallel to a (111) type direction and have three-fold s”ymmetry about this vector. A schematic drawing of this dislocation structure is shown in Fig. 8. The stacking faults which lie on the three (110) planes are

t Calculated from the expression +(E*/~z) where E is the evaporation field (38) of molybdenum (4.5 x IO* volt cm-l). This stress is comperable to the shear modulus of molybdenum (12.8 x 10” dyne cm-*) listed by FriedeI.(J*)

SEIDMAS .&SD BCRKE: ;a’1 11, SCREK DISLOCATIOSS IS MOL‘I-BDESTJI 1311

FIG. S. _4 schematic illustration of the dislocation configuration observed in the field-ion micrographs presented in FiTs. 4-H. The partial clidocationa indicated in this diagram are described by a dislocation reaction

of the form given by equation (5).

indicated by crosshatching and the four partial dis-

locations involved by the Burgers vectors b,, b,. b, and b,. The dissociation of the perfect &a[lll] screu- dislocation must involve a reaction of the form:

Qcc[lll] + b, on the (iO1) plane

+ b, on the (ilO) plane

+- b, on the (Oli) plane

+ b, at the intersection. (7

The vector b, is of the form ku[lll] where E is a con-

stant which depends on the type of dislocations employed for b,. b, and b,. Both KroupaQO) ancl Kroupa

and Vitek(-ll) have suggested the following reaction for

the three-fold symmetric dissociation of a fa[lll] screw dislocation :

‘,n[lll] ---f $lIlOll(io~~ f Q4IllOl~i~o~

+ &[Olll(oCj f fa[llll. (S)

Smith’26’ has analyzed the contrast effects expected from equation (8) for the case where all the partia1 dislocations and the stacking faults are imaged in one pole of a field-ion microscope specimen. The contrast, effects we observed involved a number of poles, and

therefore we must discuss our micrographs in more detail. In our case the partial dislocation (fn[lll]) which appears at the intersection of the three stacking fault planes has a q vaIue (see equation 4) of 13. Hence x*e should see a double-stepped spiral: which is intersected b- three lines of contrast caused by the three (110) stacking fault planes. X schematic dran-- ing of the contrast effects we actually observed in the

(22) plane is shown in Fig. i. The presence of these

three steps in the onI)- ring of imaged atoms in the

(222) plane is readily observecl in Fig. 6. The problem

is that we have not been able to observe a second ring

of atoms which we could clearly associate with the

(222) plane as opposed to belonging to the (2331

planes. Thus we could not, verify the presence of a

double stepped spiral contrast effect. The second point n-e wish to make involves the

absence of a step (see Section 4.2) in any of the rings

of atoms imaged in the (244) planes. This result is consistent with the fact that p is equal to unit>- for the three (244) planes and the respective $L \llO\ type Burgers vectors involved, as the contrast theory predicts kinked rings and a line of contrast caused b?- the stacking faults in this case.

Thus, we can conclude that the dislocation reaction

give11 by equation (S) is not inconsistent n-ith our observations. In orcler to substantiate this &in1

further it might be worthwhile to employ the corn--

puter simulation technique(31*3” of dislocation contrast effects.

5.2 The efect of the electric jield induced stress OIL

the stability of stacking faults

The high electric field used to field evaporate and/ or image an FIN specimen results in a stress distri-

bution which has yet to be calculated esactly; although Smith and Smith(42) have calculated an uveru~e value of Go, (the stress which acts on the z--

plane along the z-axis (the specimen axis)), and hare found that this stress is essentially a constant value for the first 103_1 from the specimen’s surface (for a

specimen with a tip radius of approx 1000 -4). In the

case of molybdenum a negative hydrostatic pressure (p) of 9 . lOlo dyne cme2 (in Section 5.1) till result in a volume increase ((dV/F) . 102)f of approx -3.6 per

cent. YiteP3) has suggested that this large expansion of the crystal n-ill cut off the interaction between

atoms very close to second-nearest neighbors and that this would result in stable stacking faults on the (110) and (211) planes in a b.c.c. crystal. He suggests that this argument may explain the dissociated dislocations observed by Smith and Bowt-kett(44) and Smith and GallotQ5) in tungsten and iron respectively;

although in neither of these b.c.c. metals was there an>- evidence found for the three fold symmetric dissociation of &;lll) screw dislocations reported here. The dislocations observed by Smith and co-rrorkers in tungsten and iron were most likely ,not introduced as a

t Calculated from the expression (46) clY,‘T- = --[:~(I - 2v),‘Ejp where Y is Poisson’s ratio and E is Young’s moclulus.

1312 ACTA NETALLURGICA, VOL. ‘2, 1974

result of the FIJI specimens yielding in situ to the electric field induced stresses at cryogenic temperatures. These metals do not usually deform plastically in the FIX, but instead fail catastrophically after which the resulting FIN image is unusable. Hence, the dislocations they observed were most likely produced at an elevated temperature during the fabrication of the wire specimens.

There are no detailed calculations yet available to predict the effect of the field-induced stresses on a given dislocation configuration in an FIM specimen. We lvish to suggest that it would be very worthwhile to esamine the effects of large negative hydrostatic pressures and shear stresses on the stability of the dislocation core structure of @(ill) screw dislocations that exhibit three-fold symmetric dissociation emplodng discrete lattice calculations. It is certainly possible that the field induced stresses play an important role in stabilizing the three-fold symmetric dissociation of the $z(lll) screw dislocations that we have observed, but it is not clear as to how this stabilization occurs.

5.3 Separation of partial dislocations

In Section 4.3 (also see Tables 3 and 4) it was shown that there was a measurable separation between the central partial dislocation and the three partial dislocations which terminated the (110) st,acking faults. It was noted that the separation between partial dislocations was a function of the local radii and that this separation decreased as the local radii decreased. We now consider the question of the observed separation of partial dislocations at a surface.

Gerers et uZ.(~~) have considered the energetics of the problem of the intersection of a dissociated dislocation with a flat free surface. They have examined four possible situations (see Figs. 1 and 2 in t,he Gevers et uZ.(*~) paper) for the case where a stacking fault bounded by two partial dislocations intersects a flat surface which is assumed to be atomi- cally clean. Their diagrams show that it is possible to have either an expansion or contraction of the distance between the partial dislocations bounding the stacking fault. This expansion or contraction effect varies as a function of distance from the point where the partial dislocations intersect the free surface. The four different possible topologies are determined by the sign and the magnitude of 6 - b, for each of the partial dislocations bounding the stacking fault. Under t he assumption of isotropic elasticity theory they consider the following contributions to the energy of the different configurations : (1) the line energy of the

dislocations; (2) the stacking fault energy; (3) the surface energy (assumed to be a constant for the ledge produced); (4) the interaction betlveen the partial5 bounding the stacking fault; and (3) the interaction between successive stacking faults of a sequence. Their calculations neglected any effects of image forces on the partial dislocations. The final espressions they obtained relate the surface energy and t,he stacking fault energy to a number of measurable geometric properties of the dissociated dislocations.

Our case is considerably more complicated than the sit’uation envisioned by Gevers et al. for the following reasons: (1) the large negative hydrostatic stress acting on the tip may affect the equilibrium separation distance between the partial dislocations; (3) the energy of the ledge produced where the stacking fault intersects the surface is affected by the small radii of curvature of a sharply pointed FIX tip; and (3) the configuration shown in Fig. 8 involves the interaction of three stacking faults and four dislocations.

We have already discussed point (1) in Section 5.2 and will not pursue it any further. Let us now consider point (9). Within the context of a continuum thermodynamic model the chemical potential of an atom (,B,J at. a point on a curved surfacer is given b- the Herring equation(4s)

#&=pQ,+ 1 [Y(;l J a2y 1

‘r_ +-._

2 an=2 rl

Lazy.1 &&yl r2 Q- 1 69

where f& is the atomic volume of an atom, y is the surface tension, rl and tz are the principal radii of curvature of the original surface, and n, and n, are the projections of the variable unit vector 6 into a plane tangent to the surface at the point under considera- tion. The x-axis being chosen in the direction of the principal curvature l/r, and the y-axis in that of l/r,. Equation (9) shows that p, in a ledge in a surface lvith small values of rl and r2 till be greater than that of an atom in a ledge on a surface with larger values of rI and r2. Thus the energy of a ledge: of a fixed length increases as rl and rl decrease. This qualitative argument implies that as r1 and ,ry are decreased the same ledge would decrease its length to help mini- mize the overall free energy of the configuration; i.e.

t 11-e have taken the chemical potential of an atom on a flat surface to be zero.

$ The actual energy of the ledge should be obtained from an atomistic model that involves the details of the atom positions in a specific ledge on a highly curved surface. In this paper we are using a continuum thermodmamic model which is embodied in equation (9) as a first order treatment of this problem.

SEIDM_IS .%3-D BCRKE: &a,1 11; SCREW DISLOCATIOSS IS JIOLTBDESUJL 13 13

the separation between the partial dislocations would

be smaller in the specimen with the smaller values of

T(~~~)_~~,,~. This conclusion is not meant to imply that

in an unstressed bulk specimen the equilibrium

spacing between the partial dislocations would be

greater than the values reported in Table 3> rather it is

intended to explain our specific FINS observations.

In view of the complexity of the present situation it

does not seem reasonable to try to extract a value of the stacl;ing fault energy from our measurements of the separation between the partial dislocations. Smith et al.(49) have used a simple expression (derived by Gilman( for the contraction of a dissociated screw dislocation which emerges normal to a free surface, to calculate the stacl;ing fault energy for a dissociated dislocation they observed in an iridium FIJI specimen.

We do not feel that their calculation is warranted at

the present time because of the problems discussed in this section and in Section 5.1.

.5.4 Possible Suzuki segregatiotb of ittlpurity atom

to stacking faulta

It is felt that Suzuki impurity segregation effecW1) are not the cause of the measured separation distances

between the partial dislocations, i.e. the measured distances are not caused by the preferential adsorption or desorption of solute atoms on or from the stacking

fault ribbons, which results in a decrease of the stacking fault energy and a subsequent increase in

rl,,,,_C,4,j. There are two points which we wish to

make to substantiate the above statement. The first point is that the FIJI specimens were deformed by the

electric field induced stresses at T,‘s of approximately less than 50 IL This implies that the solute atoms which were adsorbed or desorbed on or from the stacking faults would have had to be mobile at a T, of

less than 50 K. This requirement does not seem highly probable. The second point concerns an estimate of the tmxinuttt value of the degree of

coverage of the stacking fault ribbons by adsorbed impurity atoms. For the .2 equal 2.2 x 10” specimen

(see Table 3) the degree of coverage \Fould be appros

3 x 10e3 of a monolayer, if all the impurity atoms in the FIJI tip (ZOO _\ average radius) were adsorbed on the three stacking fault ribbons associated with the dissociated ?a ,, 1 ‘111’) screw dislocation. A similar calculation for the .% equal 33 specimen (see Table 4) yielded a mn.ximum value of the degree of coverage of 0.07 of a monolayer. If Suzuki segregation effects were important in our specimens then we would

$ It is noted that the specimen with the snaller \-dues of riI??j - :2rr! (see Table 4) was alsr, the mare impure one. i.e the one with .A = 33.

9

expect the separation distance between the partial

dislocations to be larger in the J? equal 33 specimen

as opposed to the .B equal 7.2 x 103 specimen. In

fact just the opposite effect was obserl~ed (compare

the values in Tables 3 and 4).

6. SUMM_‘.RY AND CONCLUSIOSS

1. The first observation of a three-fold synmetric

dissociated screw dislocation structure in any b.c.c. metal has been detected in molybdenum specimens which were deformed by the electric field induced stresses, that must. act on the tip region of all FIJI specimens, at a specimen temperature of less than 50 IL

2. The structure n-as always observed in the {2??}

planes and consisted of a partial (11 l! type screw dislocation emerging normal to a {2X} type plane with

stacking faults lying on the three (110) planes which intersected one another along a (111) type direction

(see Fig. 8). The central partial dislocation was of the form kalll) where k is a constant. The three (110) stacking faults exhibited three-fold symmetry about

the central ku(ll1) type partial screw dislocation.

3. The separation distance between the central partial dislocation (ka(ll1)) and each partial clis- location which bounded the stacking faults on the (110) planes was a function of the local radii of

curvature of the tip (see Tables 3 and 4). A first order model was presented to explain this effect.

4. The observed three-fold symmetric dislocation

structure was present in both low purity (approx 1.2 x 10e3 at. fr. impuritv content) and high purity

(appros 1.5 x 10--j at. fry impurity content) molybdenum specimens. Simple arguments were presented to show that the observed dislocation dissociations

could not have been caused by Suzuk.i segregation effects.

5. The basic three-fold symmetric dissociated clis-

location structure persisted through continuous and extensive field evaporation of the specimens. In

addition, elements of the contrast effects reported in this paper can be seen in the {Z?} planes and en-

virons of all of the single frame micrographs of molybdenum published in the literature.

6. It is suggested that the effects of large negative

hydrostatic pressures and shear stresses (greater than and equal to 9 x 10 lo dvne cm-l) on the stability I of the dislocation core structure or Ja 111) screw dislocations, near a free surface: be examined employing discrete lattice calculations.

7. It is stressed that our observations are so far characteristic of FIJI conditions and that the exact role played by the electric field induced stresses,

1314 ACTA METALLCRGICA, VOL. 22, 1974

surface image effects and the small tip size on dis-

location geometry remain to be determined.

ACKNOWLEDGEMENTS

The authors wish to thank Xr. B. F. Addis for growing the high purity single crystals of molyb-

denum, Xrs. Karen Pratt for photographic work, and Robert Whitmarsh for enthusiastic technical assist- ance. D. S. Seidman wishes to thank the John Simon

Guggenheim Memorial Foundation for support funds

during the performance of this research.

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Documents

IN MOLYBDENJM*tarc.nucapt.northwestern.edu/refbase/files/Seidman-1974_6815.pdf · an 8 hr anneal at approx 2200°C in a partial pressure of oxygen of 5 x 10-j Torr; and (4) an 3 hr