Crystal Purification Excluding Inclusions
REMOVING INCLUSIONS FROM
CRYSl ALS BY GRADIENT TECHNIQUES WILLIAM R. WlLCOX Gradient techniques for moving inclu-
sions out .of crystals are not only ripe for^ application, but also ‘present op.. and investiportunities for, discovery
gation of. a host of new phenomena rystalline material very frequeqtly ,contains foreign The rem “inclusion” is given to any foreign body-either solid,. liquid, or gas-enclosed within a solid. The presence of inclusions h a niany deleterious effects. It has been stated that the unsu& pected presence of watei i s unquestionably one of the most insididus sources of error in pr&e chemical work (83). The quantity of included selvents may be quite large. For example,’O.O4% internal water was found in high quality cane sugar, and 0.5y0 in large sugar crystals (73). In atomic weight determinationg the p‘ysence of a W c e of water frequently results in a considelably greater error than the same percentage of a common impurity (83). Gaseous incl&ions, in particular, cause errors in specific gravity measurements (73). It has also been suggested that liquid inclusions can contribute to caking problems (23) by seepage of the solvent out of the crystals. Many physical proper& of single crystals are degraded by the presence of inclusions. For example, inclusions cause light wattering, strain effects (82), and shorting of Gmiconductorjunctions. The growth rate of crystals has also been found to be increased by the pre8a c e of inclusions (6, 98). [Thisincrease is probably
C matter.
due to the many additional dislocations typically generated by inclusions (3,40)1. Crystals usually reject impurities during growth. Because of this, 6rtually all of g spec$ic impurity.detected in a reagent may actually be in, the liquid inclvsions. For e x k p l q h k s (73)found that the coloring matter in, cane sugar is &tirely in the inclusions. The inclusions may even be more rich in impurity than the mother liquor, since the impurities rejected during growth are concentrated in the fluid,that.is trapped. In gome products tlk solvent itself may be an impurity, such as water in ammonium perchlorate (23). We see iatei that inclilsions may h e in inany ways. Here, however, we are primarily concerned with inclusions formed during crystallization from solution. This is a, particularly widespread and. tenacious problem, as illustrated by the fact that all of the reagent grade chemicals examined contained inclusions. Liquid inclusions werefoundinNaC1, AgNOa, KCl; KSO4, LiC1,NaSai.5Hs0,N a A O r . 10H~0,Ba(NO&, KIOa, KI, KBrG, K d O a , potwium biphthalate, urea, naphthalene, benzoic acid, oxalic acid, thiourea, and hexamethylenetetramine reagents. Gas bubbles were present in Ba(NOa)t, (NH&),CeNa&Oa. 5H10, NarB4Oi. 10H10, (NOa)a, KIOa, KI, e r O a , KClOa, “anhydrous” NalCO,, benzoic acid, and hexamethylenetetramine reagents. The liquid inclusions in NarSzOa. 5HsO also contained many minute rod-shaped crystals. As will be shown later, isothermal heating to the vicinity of the boiling point of an included solvent is insufficiwt to remove it from the crystal. Indeed, hiating to decrepitation d q not even guarantee elimination of included solvent. The alternativediscussed here is the use of gradient techniques to move the inclusions through h d out of the crystal in a more or less gentle fashion. For the puof discussion we use the concrete exVOL 60
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ample of a temperature gradient, the technique that has been most investigated. Consider a liquid inclusion with a temperature gradient across it. Since the solubility of the crystal depends on temperature, crystalline material will dissolve on the high-solubility side of the inclusion, diffuse across the liquid, and crystallize out on the low-solubility side. The result one sees externally is the movement of the inclusion in the direction of increasing solubility, usually toward the heat source. History of temperature gradient techniques. I n 1926 Whitman (700) was apparently the first to observe that liquid inclusions would move in a temperature gradient. He moved entrapped brine out of ice by means of a temperature gradient and suggested that this is the means by which sea ice eliminates its salt on aging. Temperature gradient techniques received added impetus by the invention of “temperature gradient zone melting” by Pfann in 1955 (70). He suggested use of a sandwich structure of solid-solvent-solid for fabricating semiconductor devices and for growing single crystals. This technique has been extensively employed for crystal growth by workers at Tyco Labs and elsewhere under the names “traveling solvent technique,” “traveling heater technique,” and “thin alloy zone crystallization” (20, 27, 37, 47, 43, 49, 56, 76, 77, 93, 96, 97, 705-108). Pfann also noted that particles which form eutectics with a solid alloy can be melted and moved through the alloy by a temperature gradient (70). I n 1962 he suggested that this mechanism might be utilized to purify sea water (69). Movement of brine droplets in ice under a temperature gradient has been studied by Harrison (37), Hoekstra, Osterkamp, and Weeks (34))and Kingery and Goodnow (42). I n 1966 Chase and Wilcox noted that this technique could be used to remove solvent inclusions from solution-grown single crystals (74). Crystals grown from molten salt solutions by the “flux” technique were studied. Later, inclusions were also removed from single crystals grown from aqueous solutions (704). In this review we cover the literature dealing with the theory and practice of moving inclusions through crystals by several gradient techniques, Emphasis will be on solution-grown single crystals. We begin with a brief consideration of how inclusions are formed.
Formation of Inclusions Specific terms are used in the literature to describe various forms of inclusions (7 70) : (a) Bubbles-bubble-shaped cavities of various sizes filled with vapor or solution (b) Negative crystals-faceted cavities (c) Veils-thin sheets of small inclusions (d) Phantoms or ghosts-oriented veils (an envelope of planar veils each one of which is parallel to some possible crystal face usually, but not always, identical with the final (e) (f)
crystal) Clouds-aggregates of fine bubbles or cavities Solid crystals or crystal fragments
One may also classify inclusions as primary-those inclusions associated with the growth of the crystal, or secondary-those inclusions which form after growth. 14
INDUSTRIAL AND ENGINEERING CHEMISTRY
Primary inclusions. Ideas on the origin of primary inclusions tend to be somewhat speculative since they are usually based on observations made after the crystal is grown. A few recent observations of growth under the microscope have been definitive. If one considers a polyhedral crystal growing from a solution, then a solvent inclusion must begin as a depression in the surface. Alternatively, one may regard this process as the protrusion of the edges and corners of the crystal. There are several possible causes of this. The presence of foreign matter-a bubble, immiscible liquid (44)) or solid particle (78)-can block the solution from the crystal at that point and so initiate an inclusion. Adsorption of impurities or solvent on the crystal surface has been invoked by some as possibly being responsible for inclusion formation (66). Surface depressions can also result from the variation in supersaturation along the surface due to diffusion (4, 7, 8, 77, 18, 35, 36). At low supersaturations (low growth rates) crystals grow from solution by means of growth spirals originating at screw dislocations. The surface must, of necessity, be nearly planar, with the core of the dislocation at the apex of a shallow hillock. Because of diffusion, the solution at the corners and edges of the crystal is more supersaturated than at the center. As the growth rate is increased, the supersaturation increases until eventually it is sufficient at the corners and edges to cause two dimensional nucleation of new growth layers there. The edges now grow faster than the center, which leads to a depression in the center of the face. This in turn increases the supersaturation variation across the face which increases the depth of the depression. I n the extreme case the growth becomes dendritic. Later on if the growth rate slows down the surface can become planar again, thus closing in the inclusion. Likewise, inclusions would be formed by “filling-in” of dendrites by reversion to polyhedral growth (6, 24, 52). Chernov (75) has calculated that there is a certain critical size of crystal beyond which the surface is unstable. The critical size increases with decreasing growth rate. Denbigh and White (79) confirmed this prediction with extensive studies of inclusion formation in hexamethylenetetramine. They also observed microscopically the process of formation of indentations in the crystal surfaces. The sealing-over process has unfortunately never been reported and it does not appear to be well understood. Petrov (68) made detailed microscopic investigations of inclusion formation us. instantaneous growth rate in KN03. He concluded that small oval or round inclusions were rarely associated with an increase in growth rate. Larger flattened inclusions were also not associated with high growth rates, although the growth rate, if previously small, increased when such an inclusion appeared. Funnel-shaped inclusions were always associ-
-~~
R. Wilcox is Manager of the Crystal Technology Section at Aerospace Carp. This work was supported by the U. S. Air Force under Contract No. A F 04(695)AUTHOR William
1001.
ated with high growth rates and suddenly increased growth rates. Strings of inclusions along the edges of crystals invariably seem to be formed by rapid growth of a crystal which was previously rounded by dissolution (79, 68). This may be seen to be a natural consequence of the formation of steps on the rounded edges when growth begins again. Stepped growth also resulted in inclusions during growth of KTaOs-KNbOs mixed crystals (703). The large steps formed during Czochralski growth when the crystal orientation did not correspond to the preferred crystal faces. Dissolution can also produce etch pits on the surface of a crystal. Subsequent growth of the crystal can cover the pits to form minute inclusions (80). Morphological instability due to diffusion can also cause inclusions in crystals grown by directional solidification from melts containing impurities. The freezing interface tends to become cellular under conditions of constitutional supercooling [as recently reviewed ( l o ) ] . Thus, melt enriched in impurities (because of segregation) is trapped in the grooves. The melt eventually freezes to produce impurity-rich inclusions in the form of cells (707) and trails of beads (30, 50, 707). Inclusions were obtained thereby in Sn-Pb alloys containing as little as 0.2 wt. % Pb (50). An impurity rejected by a crystal during growth may, under some conditions, reach a concentration which exceeds its solubility near the crystal surface. If the impurity nucleates to form a second phase, the segregated impurity diffuses to the new phase and causes it to grow. When the new phase sticks to the crystal surface, it may be incorporated. The foregoing process has been studied in detail for the formation of gas bubbles and tubes in ice (9, 7 7 , 78). Incorporation of solid and immiscible-liquid foreign particles by growing crystals has also been studied (76, 33, 44, 94). Faceted bubbles were deliberately introduced in KC1 crystals by bubbling gases into the melt under the crystal during Czochralski crystal growth (65). Dyes are frequently incorporated as microscopic crystals in crystals grown from aqueous solutions (6). The mechanism is thought to be one of adsorption of dye at the crystal surface, since the dye concentrations are far from saturation. An adsorption mechanism is also indicated by the observation that incorporation takes place preferentially on certain crystal faces, leading to hourglass patterns of dye in the grown crystals. Finally, it should be mentioned that solid particles may be incorporated in a crystal in the act of nucleation, which is known to take place, frequently on foreign material in solutions. Processes occurring after growth. Once formed, inclusions frequently undergo many changes. Liquid inclusions may freeze. Other crystals or gases may nucleate from liquid inclusions, giving rise to the simultaneous presence of several phases (87). The shape of the inclusion may change under isothermal conditions as the system tries to minimize the surface energy between crystal and inclusion. Sometimes this leads to rounded
or spherical inclusions (9, 24, 59) or to coalescence of nearly touching inclusions (9). A fluid of elongated or flattened shape has been observed to break up into beads or globules (30, 59, 87). Temperature increases often lead to formation of faceted inclusions-Le., negative crystals (87). Recent evidence indicates that many noncrystallographic veils are due to cracking and rehealing. Powers (74, 75)observed the cracking of a sucrose crystal during growth and the subsequent suck-back of mother liquor into the crack. The present author has witnessed veil formation in aqueous-grown Ba(N03)2 crystals when heated on a microscope hot stage. Cracks began emanating from rounded solvent inclusions at 140” C. Within a few minutes with continued heating, the cracks had healed to leave sheets of tiny droplets-veils. Knight (48) observed similar phenomena with brine inclusions in sea ice upon cooling and during migration in a static temperature gradient (46, 47). Gubelin (29) has noted that veils are associated with cracks or fractures in minerals. Veils and cracks are also found in conjunction in ruby grown hydrothermally (57). Nakaya (59) made detailed observations on vapor bubble formation and behavior in ice. Internal melting (to produce “Tyndall” figures) produced vapor bubbles because of the volume change on melting. When refreezing took place, the bubble was frozen in before all of the liquid solidified. The remaining liquid caused repeated cracking as it froze. The cracks in turn gave rise to void bubble veils. Nakaya has named both types of bubbles “void figures.’’ Negative crystals of water vapor in ice have also been created by inserting a hypodermic needle and connecting it to a vacuum (48). Inclusions can form after growth by precipitation (exsolution) of an impurity present in concentrations exceeding its solid solubility. This is most likely to occur when the temperature of the crystal is lowered following growth (with the solubility of the impurity decreasing with decreasing temperature), Techniques for Removal of Inclusions
Isothermal heating. I t is usually assumed in laboratory (55) and industry (62, 7 7 7 ) that heating to the vicinity of the boiling point of the solvent is sufficient to remove it from a solid product. For removal of water this normally entails heating to a maximum of 130” C (55, 83, 84, 7 7 7 ) . Drying to a constant weight (with respect to time and/or temperature) is commonly assumed to be a critical criterion of success in drying (89). However, for material to escape from a crystal it must have a path to the surface. For isothermal heating this escape requires cracking, fracture, or complete breakage of the crystal. This decrepitation is caused by the stress generated by the vapor pressure of the included phase and by the difference in thermal expansion of crystal and inclusion. Surprisingly high temperatures may be required to achieve decrepitation. For example, heating to 180’ C was not sufficient to rupture hexamethylenetetramine (79). If one desires a whole single crystal, then obviously one cannot resort to this sort of treatment. VOL. 6 0
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A.
Before.
B. After.
Water inclusions Figure 7.
NaCl crystal heated at 705" C: 5 X
I n addition, some materials decompose before reaching temperatures sufficient to cause decrepitation (55). Recent experiments by the author have shown, however, that even heating to decrepitation is not always sufficient to remove all liquid inclusions from crystalline material. A natural NaCl crystal was slowly heated on a microscope hot stage. Popping or snapping, denoting breakage of the crystal at separate inclusions, began at 206" C and was not complete until 300" C was reached. However, small inclusions of liquid remained u p to 320" C (the maximum temperature attained). A laboratorygrown NaCl crystal with many inclusions was cleaved down the center and heated to 705" C in a muffle furnace, and slowly cooled. Although the two pieces of the crystal were still whole, they showed cracks, pits, and "frothing" (Figure 1). The large inclusions had blown themselves out. However, the small inclusions had expanded to become vapor spaces. A technique developed by Powers (73, 74) was used to investigate the nature of these vapor bubbles. I n this technique the crystal is dissolved in water under the microscope. When solvent reaches a liquid inclusion, concentration streamers can be seen flowing into the solvent. If the inclusion is air it bobs to the surface. The vapor bubbles in the heated NaCl collapsed, leaving no trace, thus indicating that they were water vapor at low pressure. Therefore the vapor bubbles were formed by expansion and vaporization of liquid inclusions. This is not surprising since NaCl is plastic, particularly at higher temperatures. Smiltens (89) measured the weight losses of Ba(NO3)Z as a function of time and temperature and reported that the weight loss increased with temperature, with a plateau between 350" and 720" C. Little change in weight with time was observed, particularly in the plateau. This author has heated a Ba(NO3)2 crystal on a microscope hot stage. At 142" C, cracking and popping associated with individual inclusions began. 16
Blown out cavities and water vapor inclusions
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
The intermittent "pops" became more violent as the heating progressed. The last occurred at 420" C. Small inclusions converted to gas bubbles which remained upon cooling. Dissolution in water revealed unusual behavior. When the solvent reached the bubbles they drifted into the solution while rapidly diminishing in size. Some bubbles moved slowly up while others moved down. Smilten's results can now be better understood. The temperatures required to blow an inclusion out are variable ; thus more are released as temperature increases until all have either been released or converted to gas. At about 400" C the Ba(NO3)z begins to decompose (as Smiltens also surmised). Thus the gas bubbles probably contain nitrogen oxides as well as water vapor. Movement of liquid inclusions in a temperature gradient. I t is now apparent that isothermal heating has only limited usefulness for removing included solvents from chemicals. We now investigate the theoretical aspects of moving fluid inclusions by means of a temperature gradient. Experimental results and problems will be discussed later. A prime parameter of interest is the rate of movement of the inclusions. Several equations governing inclusion movement have been derived at various levels of sophistication in the literature (38, 97, 99, 709). We give here one at the intermediate level, which illustrates the most important points. The differential equations and boundary conditions which must be solved are the same as those in zone melting (102). I t is assumed that diffusion through the zone is rate controlling (equilibrium at the crystal-inclusion interface), that the process is at steady state, and that there is no solid solubility of the solvent, no convective mixing, constant properties, and no thermal diffusion. The one-dimensional differential equation for diffusion is (102):
in weight fraction. a travel of
where w is the weight fraction of crystalline material at distance z from the crystallizing end of the inclusion, D is the diffusion coefficient, ps and p a are solid and liquid density, and V is the rate of movement of the inclusion. At the crystallizing surface ( z = 0)
The solution to these equations yields
and a liquid concentration profile of
w
and
=
wo
w=wo+
(3)
IG
where wo is the concentration at z = 0 in the liquid. Similarly at the dissolving surface (z = 1)
m[ 1
- exp
(- E)][I
- exp
(- %E)](7)
(5)
Experimentally and theoretically (lV/D)( p , / p z ) Ps GDPZ
1
tion, diffusion, and condensation. The equation derived for liquid movement is valid for this type of bubble movement. If the bubble is in mechanical equilibrium, then its pressure is exactly balanced by surface tension (2, 87) and so is inversely proportional to the bubble radius. The diffusion coefficient for gases is approximately inversely proportional to pressure, and so, from Equation 8, the travel rate increases with increasing bubble radius (87). Experimentally, however, the travel rate of small inert gas bubbles has been found to decrease with increasing radius (2). This fact indicates that the dominant mechanism of movement is one of surface diffusion of crystal material around the bubble (2, 28,87). Another possible mechanism of movement is dissolution of the gas in the solid at one end of the inclusion and diffusion through the solid to the other end. A travel rate independent of bubble size is predicted. This mode of travel has not been reported. The rate of movement of void figures in ice was found to correspond to an evaporation-condensation mechanism with the rate determined primarily by heat transfer (59). The following observation shows that surface diffusion also occurred in these voids (59) : I n an isothermal environment the voids became rounded. Filling the voids with kerosene, silicone oil, and mercury reduced the rate of rounding but did not eliminate it. Movement of solid inclusions in a temperature gradient. Some solid inclusions either melt bel014 the melting point of the crystal or form a low-melting eutectic with the crystal. These inclusions can easily be moved by heating the crystal to a degree sufficient to
(9)
where q is the heat transfer rate per unit area, and k is the thermal conductivity of the crystal. Assuming that the temperature gradient in the inclusion is the same as in the crystal, we find that the heat required per unit mass is
which is independent of the temperature gradient G and the dimensions of the crystal, An estimate of this quantity is also shown in Table I for a variety of materials, and was found to range from 7 X lo3 to 3 X l o 6 cal/g. At a power rate of l$/kWh this amounts to from 0.008 to 3.5$/g and represents an approximate minimum cost to remove inclusions this way. Experimental data and problems associated with temperature gradient techniques are described later. Movement of gas bubbles in a temperature gradient. If the crystal is volatile, then gas bubbles can move in a temperature gradient by a process of evapora18
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Figure 2. Inclusions in A D P crystal after 67.8 hr on 63' C hot plate: 21 X (Bottom surface rested onjilter paper on hot plate)
.
Figure 3. Inclusions in Pb(NO& crystal after 67.8 hr on 63’ Chat plate: 27X
melt them and by applying a temperature gradient, just as with inclusions liquid at room temperature. Inclusions that cannot be liquefied might still be mobile if the crystal can undergo surface diffusion around them, as just noted for gaseous inclusions. Hoekstra and Miller (33)observed movement of glass particles in ice held in a temperature gradient. The rate of movement increased with increasing temperature and decreasing particle size. Solid KC1 was similarly observed to move through ice in a temperature gradient (34). The presence of a thin film of water between particle and ice was hypothesized to explain these results. Other driving forces for inclusion migration. Any treatment leading to a gradient in chemical potential of the crystalline material and/or to different migration rates of solute and solvent in the inclusion should cause movement of the inclusion through the crystal. A temperature gradient is only one means of accomplishing this, although it is presently the most popular. A gradient in electric potential has also been found to move liquid in germanium (77) and gallium arsenide (56). The prime mechanism for movement appears to be preferential electromigration, although the temperature gradients caused by the Peltier and Thomson effects also have an influence (38, 63). Analytical expressions for travel rate in an electric field have been derived and have been found to be independent of the size of the inclusion (38). Tiller has taken finite interface kinetics into account (92). I t is predicted that inclusion movement by an electric field would be more rapid than by a temperature gradient for a number of alloy systems (38)* It is suggested that a centrifugal field would also be useful for moving fluid inclusions. Considerable preferential migration has been found to take place in an ultracentrifuge (39, 67). Shlichta (88) has utilized this phenomenon to grow crystals of Pb(NO3)z and KBr, Only 8 to 10 hr were required to reach equilibrium (complete the growth) at 40,000 rpm, thus indicating sub-
stantial growth rates. With movement of inclusions in an ultracentrifuge one might encounter additional effects due to surface diffusion, plastic flow of the crystal, and the dependence of solubility on pressure. Experimental work is needed. Because the elastic properties of inclusions differ from those of the crystal, gradients in stress provide a driving force for inclusion movement (22). The direction of movement is such as to reduce the elastic energy of the system. Of course, inclusions themselves can be sources of stress in the crystal. (Indeed there is only one temperature at which an inclusion generates no stress, and this is usually the temperature at which it was formed.) Thus they exert a force on one another and are attracted to the crystal surface (58). The magnitude of these forces increases rapidly as the distance approaches zero. I t has also been proposed that “a suitable driving force for bubble movement could be the line tension of dislocations if they are caused to bow out between bubbles by either slip or climb” (90). As noted earlier fracturing may also result from inclusion-generated stresses. Thus Knight (47) has proposed that brine bubbles work their way downward in sea ice by repeatedly cracking the ice below and flowing into the fractures as the ice above becomes cooler. Experimental Observations
The vast majority of experimental work on gradient techniques has been devoted to temperature gradient effects on solvent inclusions and layers. This section is devoted primarily to this subject. Nevertheless many of the phenomena described would be expected to occur in other situations. Kinetics of inclusion movement. Published data on the rate of movement of irlclusions in a temperature gradient are summarized in Table 11. Comparison with the predicted rates of Table I shows that the simple Equation 8 for diffusion-controlled movement is not far from reality for liquid inclusions. The travel rate of void figures in ice has been found to correspond to heat transfer control, which is not surprising since only water vapor is present in the voids, thus eliminating the need for diffusion (59). The rate appeared to be sensitive to slight deviations in ‘‘thermal and crystallographic conditions.” Introduction of air into the voids caused the cavity to fill with hoar ice and greatly reduced the migration rate. Similarly a temperature difference of 0.1 O C across an air bubble in ice caused the cold end of the bubble to become rough in appearance with ill-defined outlines (9). The travel rate in many systems has been found to be independent of inclusion size (37, 34, 46) and crystallographic orientation (34, 56, 708), both observations indicating no influence of interfacial kinetics. O n the VOL 6 0
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other hand, travel rates decreasing rapidly with decreasing size have been noted for gold and aluminum inclusions in germanium (86, 99), for sodium tungstate inclusions in calcium tungstate (77), and for voids in ice (59). Facet formation in the dissolving side, but not on the crystallizing side, of inclusions strongly indicates that interfacial kinetics is only important on the dissolving side (86). Such facet formation has also been observed in moving liquid inclusions in ThOz (74) and voids in ice (59). Figures 2 and 3 show faceted dissolving surfaces on inclusions in NHdHzP04 (ADP) and Pb(NO3)Z crystals after sitting on a hot plate for 67.8 hr (704). I t is worthwhile to consider for a moment the larger significance of these observations (86). When a crystal grows it becomes faceted because initiation of new growth steps is difficult on certain planes, thus making them the slow-growing planes which bound the crystal-Le., the faces. O n the other hand, dissolution can proceed from the edges with ease, thus leading to rounded forms. Interfacial kinetics is much more important, and slow, for growth than for solution. Because of geometry one would expect the situation to be reversed in an inclusion. Growth proceeds easily since the corners now provide easy sites for initiation of new growth layers, and in fact so many layers are present that the surface is rounded. Dissolution, however, requires initiation of steps in the center of the faces, which results in slow "growth" and facets. I n a sense the inclusion behaves as a negative crystal, although the correspondence is not perfect (6).
TABLE I I .
Figure 4. Percentage decrease in weight of crystals sitting on hot plate held at 63" C
Other interesting observations have also been made on inclusion movement kinetics. Travel rates were observed to increase with increasing temperature for brine pockets in ice (37, 34) and for A1 and Au in Ge (99). Temperature had a particularly striking effect on inclusion movement in NaCl crystals (704). Over 300 hr on an open hot plate at 63" C produced no detectable inclusion movement or change in weight of natural NaCl crystals. At 130' C very slow movement was noted. The inclusions moved rapidly, however, when the crystals were placed on a microscope hot stage at 320" C, even though the temperature gradient was much lower. Temperature increases the travel rate of liquid inclusions by a combination of increasing the diffusion coefficient, D,decreasing the slope of the liquidus, m , increasing the solubility, w o , and by increasing the interface kinetics. Since the temperature changes throughout the crystal, this means that
MEASURED TRAVEL RATES OF INCLUSIONS I N A TEMPERATURE GRADIENT
Gradient Crystal
Inclusion
ThOz GaAs GaP Sic InAs Ge Ge
Ice Ice Ice Ice
~ 0 . 2 - m minclusion of 167, Bi208-64y0 PbFz a t 1200' C 0,025-mm layer of Ga a t 900' C 0.025-mm layer of Ga a t 2850' C 0.25-mm layer of Cr-12 wtyo Si a t 1760' C 0.015-mm layer of I n a t 800' C 0.15-mm diameter Al-rich liquid cylinder Molten A1 wires a t 667' C, originally 0.05- to 0.13-mm diameter NaCl brine droplets a t -13" to -7' C KC1 brine droplets a t -12' to -8" C 0,014 to 0.062 mm KF, NaCl and K I brine droplets a t -5 to -0.5' C 0.05-mm glass bead at -0 .06' C 0.05-mm glass bead at --O.005' C Solid KC1 a t -16" to -12' C Void figure
Ice cu
Void figure H e bubbles -3.5
Ice Ice Ice
20
X 10-6-mm radius
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
(" Clem)
Rate (mmlhr)
-400 -750 N 80 -500 500 -100 31
0.1 0.46 -0.5 0.13 0.7 -1.5 0.76 to 1.8
1 1 11 to 15.7
Ref.
0.007 to 0.03 0.03 to 0.04 0.01 to 0 . 5
1 1 1
0.0016 0.004 0.008 to 0.02 0.62
1.35 -106
0.12 to 0.25 N O . 36
(59) ( 21
the travel rate will vary for inclusions in different locations. Harrison (37) noted that brine droplet migration rates in ice increased as the droplets approached the surface. Although the increasing temperature near the surface accounts for part of this effect, the stress around each droplet acts to force it more rapidly toward the surface (as noted in the preceding section). Wernick (99) observed free convection effects with molten A1 in Ge when the diameter of the wire (from which the strips were formed by heating) was 0.127 mm or larger. For strips of this size, the travel rate averaged 70y0higher when the temperature decreased with height than when it increased with height. Thus free convection can act to increase the travel rate for larger inclusions. Weight changes due to inclusion removal have also been measured for several crystals sitting on a hot plate (704) (Figure 4). Six weeks after removal of the crystals from the hot plate, the weight of the ADP and Pb(NO3)2 crystals showed a further slight decrease. The AgN03 crystal increased very slightly in weight and became a n increasingly darker grey (due to light), Shape stability of inclusions. We have already noted that moving inclusions frequently develop facets on the dissolving side. Brine droplets in ice increased in size as the reciprocal cube root of the distance from the surface-to be expected from the increased “solubility” of ice in brine with increasing temperature (37). Brine droplets also elongated in the migration direction just before penetrating the surface in about one ice grain in 10 (37). Nakamura (59) observed changes in shape and size of moving void figures in ice. The void figures started as disks or hexagonal platelets perpendicular to the C direction. When the temperature gradient was in the C direction, the shape of the voids approached a regular hexagon with pointed corners. As migration proceeded, the hexagons enlarged in width but decreased in thickness. When they became very thin they degenerated into many smaller void figures. O n the other hand, veils of voids sometimes coalesced during migration. Sometimes voids developed a bundle of threadlike trails dragging behind them. Trails were favored by the presence of initial stress in the crystal and by reversal of the temperature gradient. When the temperature gradient was normal to the C direction, a slight deformation occurred. As migration proceeded, the condensing side showed a tendency to split into a system of columns. Breakup of inclusions into smaller droplets has been observed for brine in ice ( 3 4 , Au in Ge (86),sodium tungstate in calcium tungstate (77), and chromium alloys in S i c (708). Breakup occurred more readily for larger inclusions (34, 708), for higher temperature gradients (77, 86),and for higher impurity contents in the
Figure 5. Exit pits on bottom of ADP crystal after 67.8 hr: 27 X
inclusion (77). Breakup for larger inclusions (37, 85) and higher gradients (86) has been predicted theoretically. Likewise sluggish interface kinetics contribute to instability (77, 97), unless the temperature gradient is normal to the most stable (slowest dissolving) face of the inclusion (97). Seidensticker (85) made a stability analysis of the movement of planar solvent layers. For a higher thermal conductivity in the liquid than in the crystal, he found that the crystallizing surface was stable while the dissolving surface was unstable. For a higher thermal conductivity in the solid than in the liquid, either interface was predicted to be unstable under certain conditions. Direction of travel. One expects that the inclusions will move along the vector of the temperature gradient in the direction of increasing solubility. Generally this expectation is borne out by experimental results. However, interface kinetics can cause the travel direction to deviate somewhat from this. For example, diagonal migration of brine droplets was observed in about one ice grain in twenty (37). “All the droplets in such grains would migrate toward the ice water interface, but parallel to the C axis of the grain, even though this might be inclined to the heat flow direction, the principal migration direction.” This author has obtained unmistakable evidence of inclusion travel in the “wrong” direction in ADP and AgN03 crystals on a hot plate. Normally inclusions traveled down toward the hot plate and produced exit pits on the bottom of the crystal where they emerged VOL. 6 0 NO. 3
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21
Figure 6. Exit Pits on top surface Of ADP crystal after 405.3 hr: (Edges of pit have been broken of to expose interior) 71x
.
Figure 7. Exit pits on top surface of A g N 0 8 crystal after 337.5 hr: 89 X
(Figure 5). However several exit pits were found on the top of the ADP crystal (Figure 6) and the AgKO, crystal (Figure 7). I t is proposed that movement of inclusions toward the cooler (top) surface occurred by means of a reflux-extraction mechanism (Figure 8). This hypothesis is based on the fact that many inclusions were observed to contain both a liquid and a vapor phase (Figure 9). We would expect the solvent to evaporate from the hotter (bottom) portion of such inclusions, leaving behind solute which crystallizes out. The vapor would condense in the cooler upper portion of the inclusion, dissolved fresh solute, and run back down the wall around the bubble. In this way we would expect the inclusion to extract its way upward through the crystal. The observations of Roedder (79) on rapid movement of gas bubbles in liquid inclusions in a temperature gradient mav also be Dertinent. A solid meek on one of these bubbles allowed him to observe violent convection of the liquid. Further investigations to elucidate the mechanism are under way (80). Crystal perfection. O n first thought, a temperature gradient might be expected to generate thermal stress in a crystal. However the theory of thermal stresses shows that linear temperature gradients induce no stress in a homogeneous solid (5). That a temperature gradient does not necessarily lead to defect formation is shown by the observation that movement of a planar Ga layer through GaAs produced material with a lower dislocation density (56). Of course we have seen earlier that nonplanar inclusions generate their own stress field even in an isothermal solid. When such inclusions move in a static temperature gradient it is improbable that stress will not occur in some region of the crystal. We have already seen that when this results in a positive pressure, cracking of the crystal can occur. Knight has noted subboundary formation in ice thereby (46). Hopefully the over-all temperature level can be adjusted to eliminate these effects, but experimental investigation is needed.
t
Crystallizing
Figure 8. Diagram of proposed mechanism for movement of inclusions upward. (Temperature decreases with height) 22
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
Figure 9. A D P inclusions containing both liquid and vapor after 405.3 hr: 8 7 X . (Bottom war nearer hot plate)
I t is apparent that heating crystals which contain water of crystallization will usually destroy them. If destruction is to be avoided, refrigeration rather than heating must be employed to generate the temperature gradient. Discussion and Conclusions
We have seen that isothermal heating, even to decrepitation, is inadequate to remove all inclusions from a crystal. Fortunately gradient techniques can be used to move liquid, gas, and sometimes even solid inclusions through crystals. Of these, the effect of a temperature gradient has been most investigated. Even so, several questions remain to be answered-such as the effect on crystal perfection and the cause of occasional inclusion movement in the wrong direction. Most rapid inclusion movement in a temperature gradient is accomplished at higher temperature. These conditions are also likely to result in crystal damage, but this is permissible for removal of solvent from reagents. An additional need is for a technique to remove the inclusion from the vicinity of the crystal after it emerges. Otherwise the impurities in the inclusion remain on the crystal surface as the solvent evaporates.
R EFE RENCES (1) Austerman, S. B., J. A m . Ceram. Sot. 46, 6 (1963). (2) Barnes, R. S.,Mazey, D. J., Proc. Roy. Sot. (London) 275,47 (1 963). (3) Belyaev, L. M., Chernov, A. A., Soviet Phys. Cryst. 7, 535 (1963). (4) Berg, W. F.,Proc. Roy. Sot. 164A, 77 (1938). (5) Boley, B. A., Weiner, J. H., “Theory of Thermal Stresses,” p. 95, Wiley, New York, 1760. (6) Buckle H. E “Crystal Growth,” pp. 144, 145, 445; 483, 498, 499; 415, Wiley, d g w Yor;, 1951. (7) Bunn, C. W., Discussions Faraday Sot. 5 , 132 (1949). (8) Carlson, A,, in “Growth and Perfection of Crystals,” R. H. Doremus, B. W. Roberts, and D. Turnbull, Eds., p. 421, Wiley, New York, 1958. (9) Carte, A. E., Proc. Phys. Soc. (London) 77, 757 (1961). (10) Chadwick, G. A. in “Fractional Solidification,” Vol. 1, M. Zief and W. R. Wilcox, Eds., p. 113, Dekker, New York, 1967. (11) Chalmers, B., “Principles of Solidification,” Wiley, New York, 1964. (12) Chase, A. B., Osmer, J. A., Am. MineroIogist49, 1467 (1964). (13) Zbid., 51, 1808 (1966). (14) Chase, A. B., Wilcox, W. R., J. Am. Ceram. Sac. 49, 460 (1966). (15) Chernov, A. A., Souiet Phys. Cryst. 8 , 63 (1963). (16) Corte, A. E., J . Gcophys. Res. 67, 1085 (1962). (17) Denbigh, K. G., Discussions Faraday Sac. 5 , 188 (1949). (18) Zbid., p. 196. (19) Denbigh, K. G., White, E. T., Chem. Eng. Sci. 21, 739 (1966). (20) di Benedetto, B., Wolff, ,G. A., “Single Crystals of Ferrite and Ferroelectric Materials,” Tyco Laboratories, Inc., Waltham, Mass., 1966. (21) Elworthy, P. H., J. Sci. Znstr. 35, 102 (1758). (22) Eshelby, J. D., Phil. Trans. Roy. Sot. London 244, 87 (1951). (23) Garrett, D. E., Chem. Eng. Progr. 62, 74 (December 1966). (24) Georgieva, A., Nenow, D., Phys. Stat. Sol. 22,415 (1967). (25) Giess, E. A., J. Am. Ceram. Sot. 47, 388 (1964). (26) Goldsmith, A,, Hirschhorn, H. J., Waterman, T. E., “Thermophysical Properties of Solid Materials: Vol. 111-Ceramics,’’ Armour Research Foundation, WADC Tech. Refit. 58-476 (1960). (27) Griffiths, L. B., Mlavsky, A. I., J.EIectrochrm. SOC. ill, 805 (1964). (28) Gruber, E. E., J . Appl. Phys. 38, 243 (1967). (29) Gubelin E. J., “Inclusions as a Means of Gemstone Identification,” Gemological Insdtute of America, Los Angeles, 1953. (30) Harrison, J. D., J. Appl. Phys. 35, 326 (1965). (31) Zbid., 36, 3811 (1965). (32) Hodgman C. D. Ed “Handbook of Chemistry and Physics,” 34th ed. Chemical Rdbber, Cievel&d, 1952. (33) Hoektfra P Miller R. D., “Movement of Water in a Film between Glass and Ice, &.’kept. 15h, U. S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1965. (34) Hoekstra, P., Osterkamp, T. E., Weeks, W. F., J. Geophys. Res. 70, 5035 (1965). (35) Humphreys-Owen, S. P. F., Discussions Faraday Sac. 5 , 144 (1949). (36) Humphreys-Owen, S. P. F., Proc. Roy. Soc. 197A, 218 (1949). (37) Hurle, D. T. J., Mullin, J. B., Pike, E. R., J. Mat.Sci. 2, 46 (1967). (38) Hurle, D. T. J., Mullin, J. B., Pike, E. R., Phil. M a g . 9,423 (1964). (37) Ifft, J. B., Voet, D. H., Vinograd, J., J.Phys. Chrm. 65,1138 (1961). (40) Janowski, K. R., Chase, A. B., Stofel, E. J., Trans. A.Z.M.E. 233, 2087 (1965).
(41) Karlina, M. I., Koval’chik, T. L.,Inorg. M a t . 2, 1015 (1966). (42) Kingcry, W. D., Goodnow, W. H., in “Ice and Snow,” W. D. Kingery, Ed., Chap. 19, M. I. T. Press, Cambridge, 1963. (43) Kleinknecht, H. P., J . Appl. Phys. 37, 2116 (1966). (44) Kliia, M. O., Sokolova, I. G., Soviet Phys. Cryst. 3, 217 (1958). (45) Knapp, W. J., J. Am. Ceram. Sac. 26, 48 (1943). (46) Knight, C. A., Can. J . Phys. 40, 1681 (1962). (47) Knight, C. A., J. Geol. 70, 240 (1962). (48) Knight, C. A,, Knight, N. C., Science 150, 1819 (1965). (49) Knippenberg, W. F., Verspui, G., Philips Res. Rept. 21, 113 (1 966). (50) Kramer, J. J., Bolling, G. F., Tiller, W. A., Trans. A.Z.M.E. 227, 374 (1963). (51) Landolt, H. H., Ed., “Landolt-Bornstein Zahlenwerte und Funktionen,” 6th ed., Vol. 2, Springer-Verlag, Berlin, 1962. (52) Laudise, R. A,, “The Art and Science of Growing Crystals,” Chap. 14, Wiley, New York, 1963. (53) Laudise, R. A., Ballman, A. A., J. Phys. Chem. 65,1396 (1961). (54) Lefever, R. A., Chase, A. B., Torpy, J. W., J.Am. Ccram. Sot. 44, 141 (1961). (55) Mitchell J Jr., in “Treatise on Analytical Chemistry ” Part 11, I. M. Kolthoff and P. ?. Elving, Eds., p. 109, Interscience, New York, i961. (56) Mlavsky, A. E., Weinstein, M., J . Appl. Res. 34, 2885 (1 963). (57) Monchamp R. R. Puttbach R. C. “Hydrothermal Growth of Large Ruby Crystals,” AD 807375,’Airtron, Morris hains, N. J., 1966. (58) Moon, F. C., Pav, Y. H., J . Appl. Phys. 38,595 (1967). (59) N a k a p U “Properties of Single Crystals of Ice Revealed by Internal Melting Res.’>aper 13, U.S. Army Snow, Ice, and Pe;mafrost Research Establishmen;. Wilmette., Ill... 1956. (60) Nelson, W. E., Rosengreen, A., Bartlett, R. W Halden, F. A., Muller, R. A., “Growth and Characterization of @-SiliconCarGide Single Crystals,” Stanford Research Institute, AFCRL-66-579 (1966). (61) Nielsen, J. W., Dearborn, E. F., J.Phys. Chem. 64,1762 (1960). (62) Nisson A. H M a c m u r r a h H . ,D., in “Chemical Engineering Practice,” Val. 7, H. W.’Crem;r and S. B. atkins, Eds., p. 269, Academic Press, New York, 1963. (63) O’Connor, J. R., J . Appl. Phys. 31, 169 (1960). (64) O’Connor, J. R., “The Art and Science of Growing Crystals,” Chap. 6, Wiley, New York, 1963. (65) Ohring, M., Tai, K. L., Rev. Sci.Znstr.38, 563 (1967). (66) Panchenkov, G. M., Levina, I. I., Dokl. Akad. Nauk SSSR 86, 585 (1952). (67) Pedersen, K. O., Z . Phyr. Chem. A170,41 (1934). (68) Petrov, T. G., in “Growth of Crystals,” Vol. 3, A. V. Shubnikov and N. N. Sheftal’, Eds., p. 107, Consultants Bureau, New York, 1962. (69) Pfann, W. G., Science 135, 1101 (1962). (70) Pfann, W. G., Trans. A.Z.M.E. 203, 961 (1955). (71) Pfann, W. G., Benson, K. E., Wernick, J. H., J. Electron. Control 2, 597 (1757). (72) Powell, R. L., “American Institute of Physics Handbook,” Chap. 4g, McGrawHill, New York, 1963. (73) Powers, H. E. C., Intern. SugarJ. 6 1 , 17 (1959). (74) Ibid., p. 41. (75) Powers, H. E. C., Nature 182, 715 (1958). (76) Rashkovich, L. N., Shang, W. W., 7th International Congress & Symposium on Crystal Growth, International Union of Crystallography, Moscow, 1966. (77) Robertson, D. S., Cockayne, B., J.A#/. Phys. 37,927 (1966). (78) Rocquet, P., Rossi, J. C., Gironne, J. A., J. Metals 19 (a), 57 (1967). (79) Roedder, E., Kansas City Meeting, Geological Society of America, 1965. (80) Roedder, E., private communication, u. S. Geological Survey, Washington, D. C., 1767. (81) Roedder, E., Sci. Am. 207 (lo), 38 (October 1962). (82) Rosenfeld, J. J., Chase, A. B., Am. J . Sci. 259, 519 (1761). (83) Salutsky, M . L., in “Treatise on Analytical Chemistry ” I M Kolthoff and P. J. Elving, Eds., Vol. 1, Chap. 8, Part 1, Interscience, Ned Yokk, i959. (84) Schwer, F. W., Proc. Ann. Meeting SugarZnd. Technicians 23, 15 (1964). (85) Seidensticker, R. G., in “Crystal Growth,” H. S.Peiser, Ed., p. 733, Pergamon, Oxford, 1967. (86) Seidensticker, R. G., J . Electrochem. Soc. 113, 152 (1966). (87) Shewmon, P. G., Trans. A.Z.M.E. 230, 1134 (1964). 12, 290 (1967). (88) Shlichta, P. J., BnlI. Am. Phys. SOC. (89) Smiltcns, J., Anal. Chim. Acta 30, 403 (1964). (90) Speight, M. V., J . Nucl. M a t . 12, 216 (1964). (91) Tiller, W. A., J . Appl. Phys. 34, 2757 (1963). (92) Zbid., p. 2763. (93) Trumbore, F. A., White, H. G Kowalchik, M., Logan, R. A., Luke, C. L., J . Electrochem. SOC.112, 782 (1965): (94) Uhlmann, D. R., Chalmers, B., Jackson, K. A., J. AppI. Phys. 35,2986 (1964). (95) Walker, A. C., J . Franklin Znrt. 250, 481 (1950). (96) Weinstein, M., LaBelle, H. E., Jr., Mlavsky, A. I., J . Appl. Phys. 37, 2913 (1966). (97) Weinstein, M., Mlavsky, A. I., Zbid., 35, 1892 (1964). (98) Wells, A. F., Discussions Faraday Soc. 5 , 196 (1949). (99) Wernick, J. H., Trans. A.Z.M.E. 209, 1169 (1957). (100) Whitman, W. G., Am. J.Sci. 211,126 (1926). (101) Wilcox, W. R., Corky, R. A,, M a t . Res. Bull. 2, 571 (1767). (102) Wilcox, W. R., in “Fractional Solidification,” Vol. 1, M. Zief and W. R. Wilcox, Eds., Chap. 3, Dekker, New York, 1967. (103) Wilcox, W.R., Fullmer, L.D., J.Am. Ceram. Sot. 49, 415 (1966). (104) Wilcox, W. R “Removal of Liquid Inclusions from Solution-Grown Crystals,’’ TR-1001 (9i50-03)-5, Aerospace Corp., El Segundo, Calif. (105) Wolff, G. A., Das, B. N., J . Electrochem. Sot. 113, 299 (1966). (106) Wolff,G. A., LaBelle, H. E., Jr., J . Am. Ceram. Soc.48,441 (1965). (107) Wolff, G . A Mlavsky A. I Intern. Conf. on “Adsorption et Croissance Cristalline,” NaiGy, France: 1965; (108) Wright, M. A., J . Electrockem. Sac. 112, 1114 (1965). (109) Yue, A. S., in “Fractional Solidification,” Vol. 1, M. Zief and W. R. Wilcoa, Eds., p. 560, Dekker, New York, 1967. (110) Zerfoss, S., Slawson, S. I., Am. Mineral 41, 598 (1956). (111) Zief, M., private communication, J. T. Baker Chemical Co., Phillipsburg, N. J., 1967.
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