CBr4 vapor growth morphologies near the polymorphic transition point I. single crystals

Journal of Crystal Growth 114 (1991) 53b—548

ou~o

North-Holland

CRYSTAL GROWTH

CBr4 vapor growth morphologies near the polymorphic transition point I. Single crystals Rong-Fu Xiao and Franz Rosenberger Center for Micrograiirv and Materials Research, Uniiersitv otAlahtima in Huntsiille, !luntsii/le, Alabama 35899, liSA Received 22 May 1991; manuscript received

in

bnal form 5 August 1991

The morphology of CBr4 single crystals was investigated during growth from the vapor with high resolution microscopy and image processing We observed the rounding of corners and edges with increasing temperature at fixed supersaturation, on approaching but distinctively below the monoclinic-to-cuhic phase transition. As the supersaturation was increased at fixed crystal temperature, the thermally rounded features resharpened. This rounding and resharpening could successively he induced with Increases Hi temperature and supersaturation, respectively. In addition to the rounding of features formed by prc-existing facets. new facets formed on temperature increase. These findings are interpreted in terms of surface roughening theory and computer simulation results.

1. Introduction and background One of the often revisited problems in surface physics and chemistry is that of equilibrium and growth morphology of crystals. These morphologies are closely related to, among various factors, the atomic roughness of the crystal surface. Atomically rough surfaces or interfaces are typically nonfaceted. The presence of a facet, on the other hand, suggests low atomic roughness of that region of a crystal. Since its conceptual introduction by Burton, Cabrera and Frank (BCF) [1] surface roughening has been studied by many workers (for reviews, see refs. [2,3]). For solid— melt systems, in general, good agreement is obtamed between theoretically predicted and experimentally deduced surface roughness. However, solid—vapor systems typically exhibit transitions to atomically rough surfaces at considerably lower temperatures than predicted (see table 1 of ref. [4]). This is partly due to the assumption, underlying the above models, that the bonds in the surface and the solid hulk are of equal strength. Chen, Ming and Roscnbcrgcr [4] introduced a ()t122-0248/91/$03.5()

199!

—

model in which the bond strength was assumed to vary with the number of nearest neighbors in a form that is expressed in terms of experimentally accessible parameters. With this model they ohtamed good agreement with experimentally ohserved roughening temperatures for select metal—vapor systems. More detailed insight on the mechanism of surface roughening stems from computer simulations with Monte Carlo methods (for an earlier review, see ref. [5]) or molecular dynamics methods [6,7]. By tracing individual growth units, a microscopic picture of the interface dynamics can be obtained. Recently, we have investigated the effect of nutrient bulk diffusion on surface morphology [8—10].We found that for a smooth surface (at low temperature and supersaturation) the influence of nutrient diffusion is negligible. However, as the surface becomes rougher with increases in temperature and/or supersaturation, the anisotropy in interfacial kinetics is reduced. This reduces the stability of the interfacial shape against diffusion-induced interfacial nonunit’ormities in the nutrient concentration. These Monte

Elsevier Science Publishers R.V. All rights reserved

R. -F. Xiao, F. Rosenberger

/

CBr

537

4 Lapor growth ,norphologies near polymorphic transition point. 1

Carlo simulations also showed that at low ternperatures and supersaturations the solid-on-solid approximation [11] is well justified and that the interfacial width expands considerably upon roughening. Although current electron imaging techniques yield surface features with atomic resolution (for references, see ref. [12]), a real time visualization of dynamic surface roughening is still not practical due to limitations of the image scanning rate pf current instrumentation. Hence, numerous indirect approaches have been employed in surface roughening studies [3,12—14]. Perhaps the most commonly used method is visual observation [2,3,15—24]. It has been shown that microscopic surface roughening can be inferred from the presence of macroscopically rounded parts on a (growing) crystal. Under equilibrium conditions, according to Gibbs [25], Herring [26], Taylor [27] and Rottman and Wortis [28], surface free energy and crystal shape are related through Wulff’s construction or a Legendre transformation. As the temperature is increased, i.e. with increasing surface roughness, the surface free energy becomes more and more isotropic and, in turn, an increasing number of the crystallographically different corners or edges become rounded. Of course, in the non-equilibrium situation of crystal growth, the above conventional equilibrium critena for crystal shape are often irrelevant. Both the face-dependent kinetic roughening [29] and nonuniform transport fluxes associated with supersaturation conditions affect the growth habit, The interpretation of growth shapes in terms of interface roughness and kinetics becomes particularly difficult when both temperature and supersaturation are changed in an experiment. Esin et al. [30,31] have shown by Monte Carlo simulation that new facets may appear with increasing ternperature or supersaturation. Some of their resuits, for a face centered cubic (fcc) crystal with inclusion of next nearest neighbor interaction, are reproduced in fig. 1. It is interesting to note the predicted resharpening of surface features of a rounded crystal on increase in supersaturation. This is in contrast to earlier beliefs [32—35]that supersaturation always makes the surface more rough and, hence, the growth habit more rounded,

~o

0.85

~ ~ ~

04

~ 1.21 o.i 0.2 0.4 0.6 NORMALIZED SUPERSATURATION, AWkT .

Fig. 1. Equilibrium and growth habits of a fcc crystal as a function of normalized bond strength (~/kT) and supersaturation (~.r/kT. where ~s is the chemical potential) for second nearest neighbor bond strength ~2 0.3 ~. After refs. 130,311.

Until recently, surface roughening was generally thought of only as a precursor to bulk melting. Solid—solid (polymorphic) phase transitions, on the other hand, are also associated with bond weakening and discontinuous changes in entropy. Hence, one can expect that a surface roughening transition can also occur as a precursor to a polymorphic transition. This has indeed been demonstrated, for the first time, in our group [19]. During vapor growth experiments with CBr4, Ming, Chen and Rosenberger (MCR) [19] found surface roughening to occur on approaching but distinctly below the transition from the monoclinic to the fcc phase. Most importantly, they found that this surface roughening transition is reversible (i.e. rounded corners resharpened on temperature lowering) and occurred within mmutes of temperature changes as low as 0.02°C. This rapid response is likely due to the “plastic crystal” nature of the high temperature (fcc) phase of CBr4 [36—38].The molecules in fcc CBr4 can readily rotate about their transiationally fixed positions. Although this orientational disorder in the monoclinic, low temperature phase is largely frozen-in, the mobility (self- or surface-diffusion) of molecules can still be expected to be high, particularly on approaching the polymorphic phase transition, which is associated with a rela-

538

R.-F. Xjao, F. Rosenberger

/

(‘Br

4

Iapor growth rnorp/iologie,s near polymorphic transition point.

tively small change of entropy and volume [39]. This special property of CBr4, and of plastic

3

2

________

1

1

12

15

_____

14

________

crystals in general, is very important for in-situ studies of morphological transitions within reasonable experiment times, and for the interpretation of observations in terms of quasi-equilibrium forms. We have continued the work of MCR using more sophisticated equipment (described in the next section), we have better quantified the mor phological changes associated with temperature changes and, furthermore, have investigated the dependence of the growth morphology on supersaturation. In this paper we present our work on crystals that are free of large-angle grain boundaries and other macro-defects. The role of macro-defects in the polymorphic phase transition is investigated in a sequel to this paper [40]. In section 2 we describe the experimental setup and procedures. This is followed by a summary of the relevant thermo-physical and crystallographic properties of CBr4 in section 3. The experimental results are presented and discussed in section 4.

2. Experimental setup and procedures 2.1. Growth cell The growth cell (fig. 2) was designed for in-situ observations of crystal morphology during growth from the vapor under well-defined conditions of temperature, pressure and supersaturation. The vapor chamber (1) is formed by two microscope cover glasses (2) that sandwich a Teflon-coated 0-ring (3). The solid source material (4) is placed at the periphery of this vapor chamber. The crystal (5) grows in the central part. The vapor pressure of the source material is adjusted via the temperature of a copper block (6), which is controlled by a precision temperature controller (Tronac, model 40) through the resistance heater (7) and measured through a thermistor (8). The temperature of the crystal is adjusted via a miniature Peltier heat pump (9) (Marlow, model MIIO21T-O2AC) and another copper block (10), the temperature of which is monitored through another thermistor (11). The thermistors are cali-

________

_________________

11

8

18

-________

_________________________________________ 3 cm Fig. 2. Cross-section of the vapor crystal growth cell: (I) growth (2)crystal. cover (6) glasses, (3) 0-ring. (4)(7)sourcc material.chamber. (5) growing isothermal Cu block, main heater, (8) thermistors for source temperature reading and control. (9) Peltier heat pump. (10) isothermal Cu block. (II) thermistors for substrate temperature reading and control. (12) isothermal partial window cover, (13) window heater. (14) valve, (15) opening to inert gas tank and vacuum system, (16) legs to support the growth chamber. (17) stainless steel hcmisphere, (18) support ring.

brated against mercury-in-glass thermometers with a traceable accuracy of 0.1°C. The upper window is heated by an auxiliary heater (13) to a temperature slightly above that of the source, to prevent condensation in this region. Note that in this arrangement the thermistors (8) and (11) give temperature readings that are closely related, but not identical, to the respective temperatures of the source 1~and crystal T~.We have estimated that the systematic errors (including the thermistor calibration) resulting from these indirect measurements do not exceed 0.2°C. Hence, in the following we will refer to the readouts of the two thermistors as T, and 1~.,respectively. Temperature changes are, however, accurate to within the 0.01°Cresolution of the digital thermometer used (Omega, model 4l2B-THC). Furthermore, systematic errors in ..IT = were corrected for in each run through the determination of the combination of T,, and J~.that resulted in neither growth nor etching of a crystal. Thus, statements of iT can also be considered to be accurate within ±0.01°C. The temperature stability in both crystal and source regions —

R.-F. Xiao, F. Rosenberger

/

CBr

4 lapor growl/i morphologies near polymorphic transition point. 1

was about ±0.02°C over an hour. The current through the Peltier heat pump can be controlled so that either iT is automatically kept constant at a preset value during changes in Te, or iT can be changed at a fixed T~. The vapor chamber can be evacuated and back-filled to a desired inert gas pressure through a syringe-type vacuum valve (14) that connects the pumping port (15) with the vapor chamber through a stainless steel injection needle that pierces the 0-ring. For high resolution observations of the morphology across a whole facet, one must be able to orient the facet exactly normal to the axis of observation. In our setup this is facilitated by mounting the copper block (6) through three thermally insulating legs (16) inside a stainless steel hemisphere (17) that can be tilted and rotated on a support ring (18). 2.2. Microscopy and image processing system The crystal morphologies were optically monitored through various long working distance (> 6.8 mm) objectives of a microscope (Leitz Orthoplan). In addition to bright field, polarized light and differential interference contrast observations, we also used double beam interferometry. The Linnik interferometer (Leitz) allows simple adjustments of the fringe contrast, spacing and orientation. The microscopic images were recorded either directly with an automatic 4 inch >< 5 inch camera (Leitz, Vario Orthomat 2) or with a high resolution image storage and processing system (fig. 3). The system’s video camera (Dage-MTI, model 81) has a resolution of 1024 x _______

Automatic Camera ________

~‘—j

Video Came

__________

Microscope (Leiiz)

Video Recorder (Grundig BK224H)

___________

High Resolutioni ____________

(M1~HR2ooo)

Host Computer Frame Grabber Image Processor (Compaq 2B6)

U

_____

Fig. 3. Block diagram of image storage and processing system.

539

1024 pixels with 256 grey scale levels. The captured image can be stored either on an extra-high resolution video recorder (Grundig, model BK 224H) or on a computer (Compaq 286) hard disk using a frame grabber (Tecon DVX 1024). The image is also displayed on a high resolution (1024 >< 1024/256) monitor (Dage-MTI, HR2000). Stored images can be further processed for contrast enhancement, reduction of interference fringe width, geometrical quantification, etc. with a digital image processor (Media Cybernetics, Image-Pro II) that retains the high resolution. Both processed and unprocessed images were photographed directly from the screen of the high resolution monitor. Some of the interference fringe images were also processed with an interferometry and data analysis system (Zygo) to quantify three-dimensional features of the crystal surface. This image storage and post-growth processing approach allows for a more detailed eva!uation and quantification of the observations than is practical during the dynamic growth experiments. 2.3. Experimental procedures Carbon tetrabromide powder (Aldrich, grade A) was purified by multiple vacuum sublimation at )0~ Torr. The sublimation rate was kept very low to maximize purification. En the first stage of the fractionation, considerable amounts of brownish particulates were retained. After three stages of sublimation no further color change occurred. After introduction of the purified source material, the vapor chamber was evacuated and backfilled with nitrogen gas to a pressure between 10—100 Torr. Since vapor diffusivities are inversely proportional to the total pressure, changes in the inert gas pressure are an efficient means of controlling the growth rate at a given supersatu.

ration, presuming that growth is bulk transport limited. Nucleation on the substrate was initiated via a sudden decrease of 1~(increase of supersaturation). Initial growth following the nucleation proceeded typically at an uncontrollably rapid rate. Moreover, due to the large supersaturation re-

540

R. -F. Xiao, F Rosenberger

/ CBr4

lapor growth ,norphologies near polymorphic transition point, 1

quired for nucleation, morphological stability could not be retained, typically resulting in dendritic and/or polycrystalline growth. Individual crystals suitable for surface morphology studies were then obtained through (repeated) thermal etching of these inadequate crystals to sizes of a few ~m, followed by slow growth under reduced supersaturation to a desired size of the order of 100 j.~m.

r\

/

,~—~--—~c~ C

~

—

the text we use iT interchangeably for (7. The two solid structures of CBr4 are so similar that the low temperature (monoclinic) phase can be well approximated by a pseudo-cubic form of the high temperature (fcc) structure. There are eight fcc unit cells [43—45]in a unit cell of monoclinic CBr4. The transform matrix connecting the two structures was once believed [44] to be ((211), (011), (022)). But, a more recent X-ray diffraction study [45] showed that the correct transform matrix is ((211), (011), (211)). The reported equilibrium form of CBr4 ciystals at room temperature [46] is shown in fig. 4a. Growth forms have also been reported [18,19] and are depicted in figs. 4b—4d, together with our own observations. The indices shown are in accordance with the above X-ray study [45]. The habit represented in fig. 4b occurred at high temperatures and low supersaturations. With increasing supersaturation, the habit changed to the forms shown in figs. 4c and 4d. Based on the monoclinic structure of CBr4 crystals, the facets forming these triangular or hexagonal habits can

/P

//‘~~ C

-p

a

a

//

~a)

(b) A PNA~VP’

3. Material properties and crystallographic infor-

—

~.

//

~

The polymorphic transition temperature 1ç for CBr4 is about 47°C; the two solid phases are monoclinic at low temperature and fcc at high temperature [39,41]. The temperature dependence of the equilibrium vapor pressure of monoclinic CBr4 is [42] log 0P(Torr) = 9.3867 2841.4/T. Thus, the supersaturation o’ = [P(L,) P(T~)]/P(T~) depends on the temperature difference between the source material and growing crystal the at form + cr) = 2841 o’iT/[7T/T~ + iT)],inand lowlog111(.l supersaturations iT. In

a’

,

\

—~—

a

B _______________

0

(c) .

.

(d) .

Fig. 4. Habits of monoclinic CBr4 crystals. (a) equilibrium form at room temperature [46]. (h)—(d) most frequently occurring growth habits. see text [18,19,43,45].The faces~~iree(001}, a{lOO), r{101}, m(1 ID), 0(1 I IL k{l 12), p{l Ii). ~{l 12), with indices based on ref. [451.

o-{l

IS)

—

be indexed as c{0Ol), m{lsym10), 1! 1), E(1a{100), 12), u(lr{l0l}, 13). The o{1 11), k{1 12), Pt metry group in monoclinic CBr 4 is C71~which contains a mirror plane perpendicular to the rotation axis b <010), that bisects the corner A which is formed by (c, p, p’) facets. Note that both corners B and C are formed by {c, a, p} facets (see fig. 4d) and are, thus, crystallographically identical. In the experiments, we have identified the index of these facets through measurements of the dihedral angles between adjacent faces with a precision protractor in the microscope eyepiece, and also using the relative shadow width resulting from the inclined boundary faces in the microscopic projection. According to the transform matrix of More et a!. [45], the above monoclinic facets correspond to low index faces of the fcc structure as listed in table 1. included in this table are the two-dimensional packing fractions or densities [47] that we have calculated for these fcc faces. This correspondence between the monoclinic and fcc features is, of course, only an approximation. Hence, it is not surprising, as will be reported below, that faces which seem crystallographically equivalent can show different kinetic responses.

R. -F. Xiao, F. Rosenherger

/

CBr

4 i apor growth ,norpho/ogies near polymorphic transition point. 1

4. Results and discussion

4.1. Different rounding temperatures for different corners In our earlier studies on monoclinic CBr4 [19] we found that the rounding of B-corners (fig. 4d) set in a 46.24°C.In this study we succeeded in obtaining the roughening temperatures for all corners (A—C) of the triangular habit. The supersaturation was kept constant in this case (iT 0.08°C) resulting in growth rates of about 100 A/s. As can be seen in fig. 5a, at T~ 46.44°C corners B and C both became rounded but corner A remained sharp. The discrepancy in the roughening temperature for corner B between ref. [19] and the current value is probably due to a systematic error in the thermistor calibration and differences in the thermal resistance between the location of measurement and crystal surface. The corner A remained sharp until T~reached 46.65°C (fig. Sb). Thus, there is a 0.21°C temperature difference for the onset of rounding between corners A and B/C. From fig. Sb, one can see that corners andalso C were furtherof rounded 0C, Band the radius corners at B T~ C 46.65 and was different from that of corner A. Note also that, to the extent that corners B and C rounded at the same temperature (±0.01°C),horizontal temperature nonuniformities within the crystal must be minimal, =

=

=

=

541

Table 1 Index relations of monoclinic to fee faces and their packing densities in CBr4 Monoclinic

fcc

Packing density

c(00l) a(100) p(lll) o(l11) r(lOl) m(l10)

(111) (lii) (111) (010) (100) (131)

0.9069 0.9069 0.9069 0.7854 0.7854 0.2484

k(112) ~(112) u(l13)

(151) (313) (101)

0.1089 0.1851 0.5554

The different rounding temperature for corners A and B/C can be understood in terms of the surface roughening concepts [1—3]discussed above, which predict different roughening temperatures for faces with different indices. In general, high index planes, i.e. planes in which the molecules or atoms are less densely packed, will roughen first. Most simply, one might expect that the rounding of a corner is associated with the roughening the faces that form TheC faces forming theof(sharp) corners A, B it.and are, respectively (c, p, p’), (c, a, p) and (c, a, p’) (see fig. 4d). According to table 1 these faces have the same packing densities within the accuracy of the lattice transformation matrix. Therefore, the rounding of the corners is apparently not associ-

200 ~im

(a)

1(b).

Fig. 5. Different rounding temperatures for different corners at fixed supersaturation iT = 0.08°C.(a) T~= 46.44°C: corners B and C are rounded but corner A is still sharp; (b) T~= 46.65°C: corner A begins to round, corners B and C are further rounded.

542

R.-F. Xiao, F. Rosenherger

/

CBr

4 Iapor growth rnorpho/ogies near f,olVmorphic transition point. I

ated with the thermal roughening of these low index faces but, rather, of some higher index faces which form a microscopic polyhedral approximation of the smooth macro-shape of the corners. Although the exact indices of these newly

exposed faces are not known, the higher rounding temperature of corner A suggests that somewhat lower index faces are involved in the rounding of corner A than those involved in the rounding of corners B and C.

f)

4i’oo ~u~n

Fig. 6. Rounding and resharpening of corner (‘ and edges on successive increases in crystal temperature and supersaturation. (a) T~= 46.45°C, iT = 0.05°C, corner and edge’~ are sharp as indicated by the equally spaced straight interference fringes: (10 = 46.50°C. iT = 0.05°C. corner is rounded: t~t1 4o.~n( . iT. 0.10°C. corner resharpens: (d) Tn = 46.69°C. iT = corner is rounded again; (e) 7~= 46.70°C. ii = 11.111 C. corner. edges and top face are rounded as indicated by curved interference fringes. (f) Tn = 46.7ti C. ii — (I l~C. corner and edges resharpen.

R.-F. Xiao, F. Rosenherger

/

CBr

4.2. Dependence of corner rounding / reshaipening on temperature and supersaturation The experiments described above were performed at a fixed relatively low supersaturation. Hence, the rounding of corners is likely due to thermal roughening. In order to study the collective effect of temperature and supersaturation on crystal growth morphology, we have also performed experiments in which the temperature and supersaturation were successively increased in alternating steps. In this series we concentrated on corner C. First we increased the temperature at a constant supersaturation of iT 0.05°C. As can be seen from fig. 6a, at 46.45°C the corner and crystal edges were sharp. The equally spaced and straight interference fringes reveal that the c(001) top facet was very flat. When T~was increased to 46.50°C the corner became rounded (fig. 6b). However, when the supersaturation was increased to iT= 0.10°Cwithout changing T~,the rounded corner became sharp again (fig. 6c). This finding might appear contrary to current crystal growth theories [1—3,29]and earlier experimental results [32—35], which suggest corner rounding on supersaturation increases due to kinetic roughening, rather than the observed sharpening. However, on careful inspection, our observations appear to reflect the collective effect of surface roughening and anisotropic growth kinetics on growth habit. At T~ 46.50°C,some higher index faces have already been roughened, but the low index faces are still atomically smooth. Since higher atomic roughness results in higher growth rates, the increase in supersaturation leads to rapid growth on these thermally exposed high index faces. This anisotropic growth, as schernatically indicated in fig. 7 by three successive contours of the growing corner region, leads to a macroscopic resharpening of the corner. In the earlier studies of growth morphologies in solution and melt systems [32—35],however, increases in supersaturation and undercooling, respectively, have resulted in corner rounding rather than the resharpening observed here. One reason for this different behavior could be that in these earlier studies only one temperature was controlled and, =

=

543

4 Lapor growth morphologies near polymorphic transition point. 1

V1

V2

/

,~

v3 / / / / // j/

//

V2

—

I

~ \\

‘~\

\~ v3 \\ \\ \\ \\

,/ \\ \\

/ /

\

Fig. 7. Schematic illustration of resharpening of a corner with increasing supersaturation. The i’s are the normal growth rates in different crystallographic directions.

thus, the supersaturation changes were coupled with changes in the interfacial temperature. This makes it difficult to separate the effects of temperature and supersaturation on the morphology of the crystal. In our vapor growth experiments, however, the supersaturation and crystal temperatures are controlled separately. Furthermore, one must take into account that impurities are less readily removed from liquid phases than from vapors, adding another uncertainty to the interpretation of the earlier experiments. The resharpened corner (fig. 6c) became rounded again when the temperature was further increased at a constant supersaturation (iT= 0.1°C) (fig. 6d: T~ 46.69°C, and fig. 6e: 1~ 46.70°C).At this point, not only were the corner and edges rounded, but, as revealed by the curvature and unequal spacing of the interference fringes, the c(001) top facet became curved near the corner. Finally, as can be seen in fig. 6f, the rounded corner resharpened when the supersaturation was further increased (iT= 0.18°C). As before, we interpret this resharpening in terms of the anisotropy in growth rate (fig. 7). For a coarse quantification of the corner rounding, the apparent horizontal corner radii were determined for different temperatures T~ and supersaturations iT, taking advantage of the image enlargement capability of the high resolu=

=

R.-F. Xiao. F. Ro.senherger / (‘Br

544

4 apor growth morp/iologies near polymorphic transition point. 1

\46700c

__

0650

46.55

‘

46.60

46.65

46.70

TEMPERATURE [°C]

0.08

0.11

0.14

‘

0.17

‘

0.20

SUPERSATURATION ~T

Fig. 8. Radius of rounded corner C as a function of crystal temperature Tn. at constant supersaturation iT = 0.1°C.

Fig. 9. Radius of rounded corner C as a function of supersaturation iT at constant crystal temperature Tn = 46.70°(’.

tion image processing system. The results arc plotted in fig. 8 (r versus T~)and fig. 9 (r versus iT). From fig. 8 one can see that the radius of the rounded corner increased significantly as 1~ approached the polymorphic transition temperature (~ 47°C), indicating a strong increase of surface roughness. Correspondingly, the resharpening of the corner in response to supersaturation increases is reflected in a decrease of the radius of the corner with increasing iT (fig. 9). For a more detailed characterization of a rounded

corner, a fourfold enlargement of the corner region of fig. 6e is given in fig. 10a. Using the Zygo interferometry analysis system, the diffuse interference fringes of this figure were digitized, the centers of the fringes were presented as thin lines (dotted in fig. lob) and analyzed for the three-dimensional features of the corner region. Fig. 11 a represents the resulting three-dimensional surface of fig. 10. In fig. 1 lb we have plotted three sections of the corner surface in vertical planes through the same point P on the c-face. One

(a)

(b)

Fig. 10. (a) Enlarged ttourfold) image of the corner region of fig. Oe. tb) Digiii,ed interference fringes (dotted lines).

R.-F. Xiao, F. Rosenherger / CBr

545

4 iapor growth morphologies near polymorphic transition point. 1

/

reported. As discussed above, such changes originate in different changes of the surface roughness of different faces upon variations in growth conditions. In this final section we present some results on the effects of stepwise changes in temperature and supersaturation on facet formation. As can be seen in fig. 12a, at iT 0.05°C the corners and edges of the hexagonal habit (see fig. 4c) remained sharp up to T~ 46.55°C.As T was increased to 46.67°Cat the same supersaturation, two new facets began to emerge (fig 12b). These two facets situated between the c(00l) and p{lll) faces were identified as o’(113) and u’(113),

P

2%4~Ø~~j ~

=

‘c/k ~

\~k~ ~

=

(a)

1 ~

0

I

‘

-0 5

~

-1.0

-

-1.5

.

1~

-2.0

~ ~

-3.C

-

-

\\

-

-2.5

~

(b)

2

.

-

-

0

20

40

60

80

HORIZONTAL DISTANCE [pm] Fig. II. (a) Three-dimensional corner surface recovered from fig. lob. (b) Profiles of crystal sections along three planes originating from point P. also indicated in (a): curve I: plane bisecting the corner C; curve 2: plane perpendicular to edge BC. and curve 3: plane perpendicular to the edge AC. The wavelength is 5200

A.

plane bisected the corner C (curve 1), and the others were perpendicular to edge BC (curve 2) and AC (curve 3), see fig. 4d. These profiles clearly illustrate the different rounding behavior along these three directions and the asymmetry of the corner surface with respect to the bisecting plane. This asymmetry, which can also be seen in figs. 6b and 6d, reveals an actual crystallographic difference between the a- and p’-faces, that is lost in the approximate lattice transformation (table 1). 4.3. Appearance of new facets The morphological changes of crystals during growth are by no means confined to the corners and edges. Changes of relative sizes of facets and, thus, in the overall growth habit have often been

which, to the transformation matrix of More etaccording al. [45], belong to the same family (101) in the corresponding fcc representation. However, the different size of these two new facets indicates different growth behavior. One may be tempted to interpret this difference in terms of nonuniformities in either the temperature or vapor concentration field. Based on the highly regular shape (parallel edges) of the two new facets, nonuniformities in the transport conditions can hardly be responsible for this difference. Furthermore, an estimate of the concentration boundary layer width (~mass diffusivity/ growth rate) [48] .

at the growing crystal for the experimental conditions shows that concentration non-uniformities would only be significant over distances that largely exceed the dimension of the whole crystal growth chamber. Since the concentration inhomogeneities in our vapor growth experiments should be negligibly small, the size difference between cr(113) and u’(113) faces most likely reflects actual kinetics differences and thus differences in their packing density. As pointed out before, the index correspondences between the monoclinic and fcc structure of CBr4 listed in table 1 are only approximations. The current cxperiment suggests that the u(1 13) face is more closely packed than the a”(l13) face. As the temperature was further increased to T~ 46.68°C, the new facets grew larger, while the edges between c{OO1)/u(113) and o”(l13) faces became more rounded (fig. 12c). Keeping T~ at 46.68°C, we then increased iT to 0.67°C, which caused the u’(113) facet to grow more rapidly and to disappear before the cr(1 13) facet =

546

R. -F. X,ao, F. Ro.senherger

/

C’Br

4 i opor groust/i mnorpliologies near polymorphic transition point. /

(fig. 12d). This can again be understood in terms of the lower packing density and, hence, higher surface roughness and more rapid growth response of the u’(l13) facet. Interestingly, no new facet appeared on the edge between the c{00!} and o(111) faces. This can also be understood in

terms of the low packing density of potential facets through this edge (see, e.g., the value for the equilibrium k(! 12) in table 1) and their resulting high roughness. The rounding of crystal edges with increasing temperature is understood from the theoretical

-l

100 p.m

Fig. 12. Appearance and disappearance of new facets with incie~isingtemperature and supersaturation. respectively: (a) Tn = 46.55°C. iT = 0.05°C;(h) Tn 46.67 C iT = 0.0~C: new facets nr(1 13) and i’(l 13) appear; (c) T = 46.68 C iT = 0.OS C. new facets grow bigger’ (d) Tn = 46.68 C iT = 0.67°C: r(l 13) face grows out and u’(113) disappears.

R.-F. Xiao, F Rosenherger

/ (‘Br4

Iaporgrowth morphologie.r near polymorphic transition point. 1

work of Wortis et al. [28,49]. They found that for a crystal with attractive next nearest neighbor interaction such as in CBr4 [42], the edges should become rounded at the same temperature as the corners. However, the appearance of new facets with increasing temperature has, to our knowledge, not been predicted by any analytical theory. Only Monte Carlo simulations by Esin et al. [30,31], have predicted such behavior. In studying the growth shape dependence on surface roughening and growth kinetics, taking second nearest neighbor interaction into account, these authors found that the appearance of new facets at dcvated temperatures is possible. As can be seen from fig. I, the crystal shapes in columns two and three show new facet development with increasing temperature in agreement with our observations. However, the appearance of new facets with increasing supersaturation as shown in fig. 1 has not been observed throughout our experiments. Only melt growth studies have yielded such a result [50], yet, as pointed out earlier, a distinction of temperature and supersaturation (undercooling) effects is difficult in such experimen ts.

5. Summary

We have experimentally studied morphological changes of CBr4 crystals during growth from the vapor at various supersaturations and at temperatures below but very close to the compound’s polymorphic phase transition. Fully faceted growth habits were obtained at low temperatures and supersaturations. As the temperature was increased at fixed supersaturations, the corners of the crystals became rounded as a result of thermal roughening. Different rounding temperatures were found for crystallographically different corners. Rounded corners resharpened in response to supersaturation increases at fixed temperature. This resharpening is interpreted as the collective effect of surface roughening and anisotropic growth kinetics. Furthermore, new facets were found, for the first time, to form on temperature increase at low supersaturations, and to grow out on subsequent increase in supersaturation.

547

Acknowledgements The authors are grateful for the support provided by the Microgravity Science and Applications Division of the National Aeronautics and Space Administration under Grant No. NAG1972, and by the State of Alabama through the Center for Microgravity and Materials Research at the University of Alabama in Huntsville. The work has greatly benefited from discussions with N.-B. Ming (Nanjing University, P.R. China) who visited our group with support from the National Science Foundation (Grant INT-8903 173). Valuable help has been provided by Lisa Monaco in the design and assembly of the image storage and processing system and the operation of the Zygo interferometry system. We also want to thank Lynne Carver for graphics support and Melissa Rogers for proofreading.

References [1] W.K. Burton, N. Cabrera and F.C. Frank, Phil. Trans. Roy. Soc. London A 243 (1951) 299. 121 1. Sunagawa, Ed., Morphology of Crystals (Terra, Tokyo, 1987). [31W. Schommers and P. von Blanekenhagen, Eds., Structure and Dynamics of Surfaces II (Springer, Berlin, 1987).

[4] J.-S. N-B. Ming and F. Rosenberger. J. Chem. Phys. Chen. 84 (1986) 2365. [5] H. Miiller-Krumhhaar, in: Monte Carlo Methods in Statistical Physics. Ed. K. Binder (Springer, New York, 1979) p. 261. and references therein. [6] J.Q. Broughton and G.H. Gilmer, J. Chem. Phys. 79 (1983) 5119. [7] Molecular-Dynamics Simulation of Statistical-Mechanical Systems, Proc. Intern. School of Physics, Enrico Fermi Course XCVII, Eds. G. Ciceotti and W.G. Hoover (North-FIolland. Amsterdam, 1986) 181 R.-F. Xiao, J.1.D. Alexander and F. Rosenherger, Phys. Rev. A 38 (1988) 2447. 191 R.-F. Xiao, J.I.D. Alexander and F. Rosenberger, J. Crystal Growth 100 (1990) 313. [10] R.-F. Xiao, J.I.D. Alexander and F. Rosenberger. Phys. Rev. A 43 (1991) 2977. [111D.E. Temkin, in: Crystallization Processes, Ed. N.N. Sito (Consultants Bureau, New York, t969) p. 15. [121 ED. Williams and NC. Bartelt, Science 251 (1991) 393, and references therein. [13] F. Fabre, D. Gorse. B. Salanon and J. Lapujoulade, J. Physique 48 (1987) 1017.

548

R. -F. Xiao, F. Rosenherger

/

CBr

4 lapor growth morp/iologie,s near polymorphic trao.otion point. I

[14] KS. Liang, E.B. Sirota, K.L. D’Amieo, G.J. Hughes and 5K. Sinha, Phys. Rev. Letters 59 (1987) 2447. [15] 1. Sunagawa and P. Bennema, in: Preparation and Properties of Solid State Materials, Vol. 7, Ed. W.R. Wilcox (Dekker, New York. 1982) p. 1. and references therein. [16] D. Nenow, Progr. Crystal Growth Characterization 9 (1984) 185. and references therein. [17] K.A. Jackson and CE. Miller. J. Crystal Growth 40 (1977) 169. [18] A.E. Morgan and W.J. Dunning, J. Crystal Growth 7 (1970) 179. [19] N-B. Ming, J.-S. Chen and F. Rosenberger. J. Crystal Growth 69 (1984) 631.

[20] A. Pavlovska, J. Crystal Growth 46 (1979) 551. [21] J.C. Heyraud and J.J. Metois, J. Crystal Growth 82(1987) 269, and references therein. [22] J.E. Avron, L.S. Balfour, C.G. Kuper, J. Landau, S.G. Lipson and L.S. Schulman, Phys. Rev. Letters 45 (1980) 814. [23] P.E. Wolf. F. Gallet, S. Balibar, F. Rolley and P. Nozières, J. Physique 46 (1985) 1987. [24] F. Gallet, S. Balibar and F. Rolley. J. Physique 48 (1987) 369, and references therein. [25] J.W. Gibbs. Collected Works: On the Equilibrium of Heterogeneous Substances (Green. New York. 1928). [26] C. Herring, in: Structure and Properties of Solid Surfaces, Eds, R. Gomer and C’S. Smith (Univ. of Chicago Press, 1953) p. 5. [27] J.E. Taylor. Bull. Am. Math. Soc. 84 (1978) 568. [28] C. Rottman and M. Wortis, Phys. Rept. 103 (1984) 59. [29] A.A. Chernov. in Modern Crystallography Ill: Crystal Growth, Springer Series in Solid State Sciences, Vol. 36, Eds. M. Cardona, P. Fulde and H.-J. Queisser (Springer. Berlin, 1984). and references therein. [30] V.0. Esin, L.P. Tarabaev, V.N. Porozkov and l.A. Vdovma. J. Crystal Growth 66 (1984) 459. [31] V.0. Esin, V.1. Danukyuk and V.N. Porozkov, Phys. Status Solidi (a) 81(1984)163. [32] H.J. Human. J.P. van der Eerden, L.A.M.J. Jetten and J.G.M. Odekerken, J. Crystal Growth 510980589.

[33] L.A.M.J. Jetten, H.J. Human, P. Bennema and J.P. van der Eerden, J. Crystal Growth 68 (1984) 503. [34] S.D. Peteves and G.J. Ahhaschian. J. Crystal Growth 79 (1986) 775. [35] M. Elwcnspoek and J.P. van Ocr Eerden. J. Phys. A (Math. Gen.) 20 (1987) 669. [36] R.M. Hooper and J.N. Sherwood. in: Surface and Defect Properties of Solids. Vol. 6 (Chemical Soc., London. 1977) p. 308. [37] J. Timmermans, J. Phys. Chem. Solids 18 (1961>1. [38] M. More, J. Lefebvre and R. Fouret. Acta (‘ryst. B 33 (1977) 3862. [39] J.G. Marshall, L.A.K. Staveley and KR. Hart. Trans. Faraday Soc. 52 (19Sf,) 19. [40] R.-F. Xiao and F. Rosenherger. J. Crystal Growth 114 (1991) 549. [41] N.H. llartshorne and P. MeL. Swift, J. Chern. Soc. (1955) 3705. [42] R.S. Bradley and 1. Drury. Trans. Faraday Soc. 55 (1959) 1844. [43] P. Gorth, Chemische Kristallographie Vol. 1 (Fngclmann, Leipzig, 19)16) p. 230. [44] C. Finhack and D. Hassel, Z. Physik. Chem. B 36 (1937> 301. [45] M. More. F. Baert and J. Lefehvre. Aeta Crst. B 33 (1977) 3681. [46] A. Pavlovska and J. Vcsselinov. Kristall Tech. II (1976) 235. [47] NW. Ashcroft and ND. Mermin, Solid State Physics (Saunders College/Holt. Rinehart and Winston. Philadelphia. PA, 976) p. 86. [48] F. Rosenherger. Fundamentals of (‘rystal Growth I (Springer. Berlin. 1979). [49] M. Wortis. in: (‘hcmisiry and Physics of Solid Surfaces. Vol. 7. Eds. R. Vanselow and R. howe (Springer, Berlin. 1988) p. 367. [50] M. Elwcnspoek and W. Boerhof, Phys. Rev. B 36 (1987) 5326.