m d
nucleation symposium
nucleation in the atmosphere Horace R. Byers Rain, snow, fog, and hail are the most important examples of nucleation from the vapor. Condensation of water is the result of nucleation by aerosols such as sea salt. Formation of ice, however, is enhanced best by nucleating agents more active than those occurring naturally in the atmosphere the atmosphere is primarily concerned Nucleation with . theinformation of water droplets and ice particles in cloud and fog, but certain aspects of the ~ h l r a and l possible artificial production of rain and snow are related to it. This subject matter forms part of a branch of meteorology known as cloud physics. Homoponoous Nucloation
In the homogeneous nucleation of condensation, the formation of an embryo droplet, assumed spherical, with a surfacerfree energy proportional to its surface area produces an equilibrium vapor pressure higher than that of bulk water. As the embryo is formed from the vapor, its surface free energy goes from 0 to 427’7, where y is the surface free energy per unit area, or surface tension. For pure bulk water a vapor saturation ratio of less than 1 would mean that a free-energy barrier would have to be surmounted for molecules to form liquid fmthe vapor. This may be seen by writing the free-energy differential for g molecules under isothermal conditions as dG = gkTd(1n p ) . A s the molecules go from the vapor at pressure p to the liquid at tension PO,the elevation of the free energy above the equilibrium of Fo would be obtained by integrating to give AGi = gkT In(po/p) = -gkT ln(p/po). The total elevation of the free energy of an embryo droplet above that of a plane surface of pure water is therefore
- gkT In(b/po) = 4mZy- (4/3)nbn,kT In(p/po)
Np = N1 exp (-AG/kT&:F:& l;12*,YhJ&&&
(1 )
where n, is the number of molecules per unit volume of the liquid. INDUSTRIAL A N D ENGINEERING CHEMISTRY
which is the expression originally ’ derived by Lord Kelvin. In the plane of (7, S),with the values of S increasing into the page from Figure 1, the peaks would be connected by a curve l i e the one labeled “pure” in Figure 2. One is naturally doubtful of the applicability of a bulk value of the surface tension to these tiny embryos. In a previous paper (8) evidence was presented that a correction to the surface tension suggested by Tolman (57) produces good agreement with laboratory measurements. The growth of embryos to the critical radius has been treated by Frenkel (79),Becker and Doring (Z), Volmer and Weber (59),Farley (72), McDonald (&), and others. These treatments start with a Boltzmann-type equilibrium distribution of embryos .~ given by
g*,&wq:z
AG = 4 n ’ y
32
The significance of this expression is seen by plotting 7 for several values of p/po = S at constant temperature, as in Figure 1. These curves represent a free-energy barrier to the growth of embryos at the given supersaturations. The free-energy level must be at least as high as the peak, characterized by the critical radius 7 * , for the embryo to grow. The critical radius is expressed by differentiating Equation 1 and obtaining the maximum at
AG against
(3)
where No is the number of embryos containing g molec u l e each and N1 is the total number of molecules in the system, liquid plus vapor. A steady-state rate of forma-
p . . . . _ ..
.
..
.. .
I
I VOL. 5 7
NO. 1 1
tion of droplets of critical radius is developed from the kinetics of a nonequilibrium distribution. This rate of formation per unit volume per unit time is represented in the form
I = K N 1 exp(-AG*/kT)
(4)
whve AG* is at the critical radius. K is the kinetic factor describing the net effect of chance collisions on the aggregation qf the molecules, and is a function of pressure and temperature. Values of I and of N*, the total number of embryos at the critical radius, computed from the theory are shown in Table I for various values of the saturation ratio. The Tolman correction for the surface tension was used
in the computations. The values are in reasonable agreement with experimental data of Powell (48). Large supersaturations with S-values of approximately 5 or 6 are necessary to form a cloud under these circumstances. But all evidence in the atmosphere shows that clouds form with negligible supersaturations. We therefore shall consider particles that can nucleate the condensation near 100% relative humidity, and shall start with the most favorable ones-soluble nuclei. Condensation on Soluble Nuclei
As water collects around a soluble nucleus a solution droplet results. The water-vapor pressure over most aqueous solutions is less than that over pure water.
E l.m
I
8
,,I
0.m 0.998
IO"
I
2
3 4 5 6 789IO4
2
3 4 5 678910
IWIM UDlUS Im.1
I
Figure 2. C w s of eqdibrium saturation ratio of watn &opbts containing tht stated mass of NaCl compmed with thc Kelmn curw for pure wotn &oplCrs. The inset shows thc WOC for 5 X IO-16 gram of NaCl on a compessed scale extended to tht droplet si= at which thc giwn mount of NaCl would form a satwa&d salt solution in Iha droplet. AN cmputationr are made for a tanpnahrra of EoC.
i
TABLE 1. VALUES OF LOGd AND LOGtaN* FO VARIOUS VALUES OF SATURATION RATIO AND TEMPERATURE-
-
&ha&
Tmp. 2
(O K) 253.2
lcgrd logd*
263.2 273.2 283.2
1
10 is MOM UDM Ir=angdm~~)
a0
25
a
Ratio, s -
lcgxd log,&* log,d lcgd* logd log,&*
- 98.7
~
6
4 ~
~
- 6.6 -29.5 - 0.7 -15.6 4.6 - 4.1 8.7 4.7
-239.8 - 85.0 -208.9 - 71.3 -178.2 - 55.7 -142.7 ~
7.5 3.7 11.4 11.8 14.7 18.7 17.2 23.8 ~
(8).
Figure 7. Total el6wtion, AG, of the free mcrgy of an mbp &lipkt abom tlM wlur for d plom surface o f p w e wotn as afuncrion of & & of tht dmp for wrim uolurs of the saturation ratio, S X @/Po), and mnstant ranpnohrra. The free e w g y koa1 must be ad lursi as high as tht pdnL charactmiBd b~ the rritiC.1 radius r* for tht
Horace R. Byas is a Rofessm in the. Department of Geophysical Scimes at the. Uniuasity of Chicago. The. fiMnciol nrpport of the National Science Foundation is grate-
~bryo~grau
fully achwledged.
54
I N D U S ~ R I A LA N D E N G I N E E R I N G C H E M I S T R Y
AUTHOR
For an electrolyte solution, Robinson and Stokes (50) give the relation
In(po'/po) = --vpmW.10-~
(5)
where po' is the vapor pressure over the solution, p o is the pressure over pure water, v is the number of moles of ions in the solute, (D is the molal osmotic coefficient, m is the molality, and W is the molecular weight of water. Whether one uses the osmotic coefficient or some other coefficient derived, let us say, from the activity coefficient, one can write v q i, an electrolyte factor. The equilibrium vapor pressure over a solution droplet bears a relation to the vapor pressure over bulk solution similar to that of a pure droplet to pure bulk water. For a solution droplet, it is convenient to express the quantities in grams. The increase in potential per gram is given by P'
- bo'
= ( R T / W ) W'/po')
(6)
where the subscript 0 refers to bulk solution and p' to the solution droplet. Suppose that an infinitesimal mass dM =: d(p,'4*rg/3) is added to a spherical droplet, where p,' i s the density of the solution in the droplet. The resulting change in free energy is balanced by the change in surface free energy, d ( 4 r ?'r2), such that
For solution droplets containing any given mass of solute, there are two equilibrium radii for a given supersaturation, one stable and the other in a labile equilibrium which, with an iofinitesimal increase in the surrounding vapor pressure, will become unstable. On the stable side of the curve, the droplet can only adjust to a new equilibrium as the saturation ratio changes, growing to a slightly larger size as the humidity goes up or evaporating to a smaller one as the humidity goes down. The lower limit of the size may be considered as corresponding to a saturated aqueous solution, reached at a saturation ratio of 0.7 in the case of a nucleus of 5 X gram of NaCl as represented in the inset of Figure 2. Nucleation of Ions
The nucleating effect of a charged particle can be derived from basic electrostatic principles (7). . Tohmfor and Volmer (56) pointed out that when 10 to 100 molecules of water go into an ion, the radii of the droplet and the ion both need to be considered, and also the different dielectric constants N~ for air (vapor) and N for water. The total elevation of the free energy above that of a flat surface of pure water is modified from Equation 1 to
AG
=
4 m2y
- 4-3 d n & T l n
and the equilibrium with the vapor is, as before, at the maximum given from the derivative with respect to
or
I n the range of droplet sizes (r = to lo-" cm.) the second term on each side of this equation is at least four orders of magnitude smaller than the fist term. Neglecting them, we find ln(p,'/po')
= (2 Y'W)/P,'RT~
7
6
(9)
In this expression p,'/po' is the ratio of the vapor pressure over a solution droplet to that over bulk solution. What is wanted is an expression combining Equations 5 and 9 to give p,'/po, the vapor saturation ratio for a solution droplet with reference to a plane, pure water surface. We simply write
@,'/Po)
=
@o'/po)(p,'/po')
(10)
and substitute for the two ratios on the right from Equations 5 and 9 to obtain In(p,'/po) = (2 y'W)/(p,'RTr)
- tmW. l o J
3
(11)
Equilibrium curves as a function of radius for droplets containing a given mass of NaCl nucleating material at a given temperature are plotted in Figure 2. The positions of the curves vary only slightly through a wide range of atmospheric temperatures. They are sometimes referred to as Kohler curves after the Swedish atmospheric chemist (32) who fist developed them for atmospheric conditions. For comparison, a portion of the Kelvin curve for a pure water droplet is entered.
&*
OMlm UDlUI ir =anpmUnr1
Ftgwe 3. Epurhbrium M M S for sphaical droplet embryos carrying unit electronic charge for vm'ow values of thc dte1ech.c coaskznl, X , at Oo C. Thc dashed line is thc KelUin c u m for unchmged embryos V O L 57
NO. 1 1
NOVEMBER 1 9 6 5
35
radius equated to zero, a condition which is satisfied by
In@/#,) = (2 y/nLkTr)
-
(q'/8 nLkTr')(l
- 1-9
(13)
where the dielectric constant K~ is taken as 1. The dielectric constant of bulk water is in the range 75 to 100 at atmospheric temperatures, so the K-1 factor often is ignored. However, in the collection of some tens of molecules forming the nucleating mass in a shong field around the ion, K may approach values of lea than 10 as suggested by refraction and other optical dects. Tohmfor and Volmer (56)proposed a value of 1.85, which produces agreement with measured rates offormation of droplets in cloud chambers. Curves of the equilibrium saturation ratio over ionized droplets are shown in Figure 3 for different assumed values of the dielectric constant of the water embryos. While the curves look similar to those for soluble hygroscopic nuclei, the scale of representation is vastly different from that ofFigure 2. Droplets condensing on ions can be carried to the critical radius at saturation ratios less than those at the peaks of the curves of Figure 3 by the same process that prevails in homogeneous nucleation, except that the growth starts at the radius on the stable side of the curve. An expression of the form of Equation 3 is used, with N representing the number of ions per cubic centimeter. Tohmfor and Vohner ascribed a value of 10' to the kinetic factor at 265' K., and to make these values fit the observation of S* of about 4, they intr0d u d a K of 1.85 into AG*. The theoretical treatment fails to account for a r e p larly abed difference in &'* for negative as against positive ions. C. T.R. Wilson noticed thin d e c t in his 1899 experiments, finding that at about -6' C. the S* was about 4 for the negative ions while, for positive ions at about the same temperature, it was about 6. The difference is usually explained qualitatively on the basis of evidence that the dipole of the water molecule has its negative oxygen end oriented outward at the surface, and in the first two or three molecular layers. With an cxtra negative ion the energy of these dipoles is red u d and, consequently, there is a lowering of the surface free energy. Positive ions have the o p p i t e effect. NuclwHon on Insoluble ParHcler
If an insoluble particle is wettable, it forms a base on which a small amount of water can present a large radius of curvature and thus satisfy the Kelvin equilibrium at a much lower supersaturation than would be the ease if the same number of molecules wa8 aggregated without a particulate core. The wettableness is ex@ in terms of the contact angle q between the embryo and the particle surface. The size of the basic particle is a critical factor. A direct physical treatment of the problem is not available, but Fletcher (74) developed a factor involving cos p and the radius of the insoluble particle, assumed to be spherical, which produced a result that seems to be reasonably valid. Figure 4 shows his result based on a nucleating rate of 36
INDUSTRIAL AND ENGINEERING CHEMISTRY
lo'
10"
I'0
10IO' D M m WlUI (mJ
IO'
Figwe 4. Critical saturation ratio as a function of thc radius of rm inmlublc particle, assuming that thc partic& is spherical. Whcn cos 9 = 1 (9 is the contact angle), thc parricle can be comp&tcly u t t e d by a thin j l m m that a liquid sphnicol wfwe with a radius ess&'czlly that of tha po&& is exposcd to thc wpm
\ 9 10"
1'0
10-1
1.o
IO
UDlUI OF fTIUE Immml
Figure 5. S i u distribution of atmosphcrir ocrorolr in thc vicinity of Frankfurt/Main, Germany, measured by Junge (29). Extmn'on of the CUTWin lo- s i n rang6S shows the chnngcd distribution that would rssult frmn thc conplation in thc stated pniods of time, a s m ' n g M 1uu)supply a f t a time zero
one droplet per second for each particle radius. The radius of the insoluble particle is the abscissa in the figure. When cos cp = 1, the particle can be completely wetted by a thin film so that a liquid spherical surface with radius essentially that of the particle is exposed to the vapor. The equilibrium then is just that of a droplet of pure water having the radius shown-in other words, the Kelvin equilibrium at the radius of the particle. Completely wettable, approximately spherical particles, of radii greater than 1 micron or so, when covered with a film of water are theoretically at the critical radius at less than 0.1% supersaturation. Condensation Nuclei in Atmosphere
Our knowledge of atmospheric particles is largely founded on the work of Aitken from 1884 to 1912 ( I ) . Through his portable expansion chamber, still known as the Aitken nuclei counter, he surveyed the particle content of the lower atmosphere. His equipment produced supersaturations at which the most numerous particles, those between 0.01- and 0.1-micron radius, are active. Today these are generally spoken of as Aitken particles. They are capable of serving as condensation nuclei for clouds and fogs, but it is now known that nuclei larger than those measured in the Aitken counter are sufficiently numerous in the lower atmosphere to lay first claim to the available water. Aitken nuclei have radii generally less than 0.1 micron, and at best require supersaturations of 0.5 to 2.0% to carry the water easily through the vapor-to-liquid transition, while large or cloud nuclei with radii from 0.1 to 1.0 micron require supersaturations less than that or even subsaturation in the upper part of their size range, if soluble. A classical representation of the number concentrations of various sizes of aerosols is that of Junge (29) taken from surveys made near Frankfurt a. M., Germany, and shown in Figure 5. In the radius range from 0.01 to 0.5 micron there are between 100 and 10,000 particles per cubic centimeter, with the larger number in the lowest size range, and there are some thousands per cubic centimeter that fall within the range of the socalled cloud nuclei (0.1 < r < 1.0 micron), enough to account for the number concentrations of cloud droplets. The series of curves in the low end of the spectrum in Figure 5 illustrates the cut-off due to coagulation. So-called giant nuclei with radii of several microns are found in the atmosphere. A nucleus of NaCl of l o b 9 gram of dry mass (approximately 5-micron equivalent spherical radius) becomes a water drop of about 25micron radius at a relative humidity of 99%. This is the size of a small drizzle drop with a terminal velocity of about 8 cm. sec.-l A salt particle with a dry mass of lO-*-gram or 10-micron radius would produce a drop of 50-micron radius, which would be a large drizzle drop with terminal velocity of about 30 cm. sec.-l Thus, these giant particles, although small in number, can play a role in precipitation. A complete determination of the sizes, number concentrations, and chemical compositions of the entire
atmospheric particulate aerosol load at any time and place would be a prodigious task involving a multiplicity of techniques, but a large amount of information has been obtained from various parts of the earth and at all altitudes in the appreciable atmosphere. And there is a large amount of literature on the subject. Sea-salt particles become airborne after being ejected from the sea by bursting bubbles; combustion products arise from man-made and lightning-created fires ; dust particles are eroded from the land by the wind or sent into the air by volcanic eruptions or man-made explosions; certain organic materials such as pollens, spores, and the like are carried in the air; certain gas reactions in the atmosphere produce nuclei; and the earth is colliding with dust from interplanetary space. Of the easily recognized chemical components, Junge (29) considers that the continents contribute most of the NH4f, NOS-, NOz-, S04-2, and Caf2, while the oceans are the main source of C1-, Na+, K+, and Mg+'. A useful way of determining the broad distributions, and thereby deducing the sources of these components, is by the analysis of rainwater. One may assume that the rain and snow wash out a representative aerosol
TABLE II. TYPICAL VALUES OF CHEMICAL COMPONENTS I N RAINS I N T H E UNITED STATES Continental Interior Sea Coast Ions ( M g ./Liter) (Mg./Liter)
Naf Ca+2 "4'
c1so4-2
5.0
0.3 3.0
0.3
0.2 0.2 3.0
0.02 9.0 1 .oa
sample of at least the lower half of the troposphere. Some typical values for rains in the United States taken from maps prepared by Junge and Werby (30) are given in Table 11. Homogeneous Nucleation of Ice
In the atmosphere, marked supercooling of water droplets is the rule rather than the exception. One infers from this circumstance that there are nuclei which are active in heterogeneous nucleation of the liquid phase but have much less activity for nucleation of the ice phase. A temperature of approximately -40' C. seems to be fixed as the.temperature of freezing of the purest of small water droplets. The soluble salts that are active in condensation serve to lower the freezing point below this figure, indicating that the nuclei for freezing are not the same as for condensation. Nuclei which cause the formation of ice clouds at temperatures of - 10O to -20 C. are often available in the atmosphere, but they are not the same particles that are active in condensation. The theory of homogeneous nucleation should account for the occurrence of the pure-water phenomena at VOL. 5 7
NO. 1 1
NOVEMBER 1 9 6 5
37
Atmospheric physicists can apply much of the n e w knowledG
procedure as in the liquid case but with geometric factors a and b to account for the probable nonspherical shape, an r* which may he a characteristic length for the crystal, is expressed as
r* = IO"
'OI
10'
IO'
OlWLn UDlUI Icm.1
Figura 6. FIcadng tcrnperntures of wofndrops as a function of thir &. Ths && m e t a h by s e w d inucsfigotors: B = Bigg (3); C = Carte ( 9 ) ; H = Hoffzr (27),L6'M = Langharn and Mason (40); M = Mosrop (46)
-40' C., sometimes referred to as the Schaefer point from the work of V. J. Schaefer (53) who brought it into prominence through demonstrations in a laboratory cold box in the 19405, although Cwilong (77) appears to have been first to publish experimental results. One can conceive of the homogeneous formation of embryo ice crystals directly from the vapor in clouds [Cwilong (77); Bradley ( 4 ) ; Schaefer (54)] or consider that they form by freezing in or on supercooled liquid water droplets [Fisher et al. (73); Lafargue (38): Mason (47, 42)]. From thermodynamic considerations, Krastanow (35) showed that water vapor will condense to supercooled liquid more easily from an energetic point of view than it will go directly to the solid state. He computed that direct vapor-to-ice crystallization would not occur until a temperature of -65' C. or lower was reached. Data from experiments by Sander and Damkohler (52) and Pound et al. (47) have shown a discontinuity at -62'' and -63' C., respectively, which Fletcher (78)interprets as probably marking the sublimation threshold. Because at temperatures above -40' C. it is not possible to create a cloud, at least in the laboratory, without many droplets being present, it is virtually impossible to detect direct deposition even if it should occur. The theory based on the assumption that the ice forms within the liquid has evolved mainly from analyses by Becker and B r i n g (Z),Frenkel(79), Turnbulland Fisher (Si?),Bradley (4,McDonald (45), and Fletcher (77). The rate of acquisition of molecules by embryos cannot be stated in terms of the same kinetic theory as in the vapor case, but Turnbull and Fisher (58) have arrived at the expression (kT/h) exp(-AG'lkT) where h is Planck's constant and AG' is the activation free energy of self-diffusion across the liquid-ice boundary. The rate offormation of ice particles per cubic centimeter per second then becomes
J
sis
(n,kT/h) exp [-(AG'
+ AG,*)/kT]
(14)
where AG.* is the free energy of formation of a n embryonic ice nucleus of equilibrium size. With the same 38
INDUSTRIAL A N D ENGINEERING CHEMISTRY
2 0% W TW J
PJ
where the subscript c refers to ice. Instead of referring the critical size to the ratio ofthe saturation vapor pressures, it is more convenient to express it in terms of supercooling helow the melting temperature To. The expression, originally due to Frenkd (79) but conveniently derived by McDonald
(44) is
where pe is the density of ice and E, is the mean latent heat of fusion between T and To. Putting the value of r* into AG.* one obtains the rate equation. As might be expected, the less the supercooling, the larger the embryo has to be for equilibrium. There are a number of difficulties in computing the rate because some of the factors are unknown or imperfectly known. Pure bulk water cannot be undercooled significantly; but, when it is divided into small d r o p , its freezing temperature becomes much lower. It is not surprising that there should be a volume dependence of the freezing temperature. Even in the purest water some foreign particles might exist to help the nucleation, but the smaller the drop the less the chance that it might contain such a particle. Several investigators [Bigg (3); Mossop (46); Carte (9); Langham and Mason (40); Hoffer (n)] have taken water of the most extreme purity, made it into drops, and studied what appeared to he homogeneous nucleation. The results of some of these findings, which show a decreasing freezing temperature with decreasing size, are given in Figure 6. H.hrogen,n.ous NuclMlion of Ice Crystals
Modern research has produced abundant new knowledge on the nucleation in the melt for a variety of substances. Many of the results are applicable to the water and ice problem. In this respect, atmospheric physicists can barely keep up with developments. In the atmosphere the nucleation problem involves only a few moIecules of water, except in the case of the freezing of drop. Nucleation of ice on a surface, especially that of a particle, is the process to be investigated. It is indicated that the process operates after a thin film of water has been adsorbed on the surface of the nucleus. The film forms ice as a result of nucleation by the particle surface, but the lihn is so thin-about 100 A.-that droplets are
on nucleation in the melt to the water and ice problem
not normally detected and an ice crystal forms as if fmm the vapor. The ice crystals can form selectively on suitable surfaces where epitaxy is present. A small misfit will produce a dislocation or molecules, and it is to be expected that an epitaxy which gives a minimum of such dislocations would produce the lowest interfacial free energy. I n Table I11 are listed, in comparison with ice, some crystals which are known to be active nucleating agents for ice crystals. Silver iodide, for example, is a substance commonly used in artificial nucleation of clouds in the laboratory and in the open atmosphere. The nucleating substances are essentially insoluble in water. Zettlemoyer et al. (67) and Hall and Tompkins (27) have demonstrated that the silver iodide surface is largely hydrophobic, and that only isolated sites representing chemical heterogeneities of oxides or the like or perhaps physical inhomogeneities take up water. It is argued (62) that all of the particularly active nucleating agents possess isolated sites upon which water adsorbs and around which clusters form. Substances which adsorb water in a more or less continuous film are considered by these authors to be much less active. Corrin et al. (70) prepared pure AgI which was inactive, but found a large effect of small amounts of hygroscopic impurities. They infer that the nucleating sites are not related directly to physical defects. The phenomenon of favored growth of ice embryos on irregular features of the nucleating surface can be demonstrated. Among the better known experiments of the growth of ice crystals on crystalline substrates are those of Hallett (22), Hallett and Mason (23), and Bryant et al. (6). Ice crystals were grown on freshly cleaved surfaces of covellite (natural cupric sulfide), and because they were often thin they gave rise to brilliant interference colors in translucent illumination. Color changes accompanying the thickening of the crystals permit a determination of the rate of growth. The first crystals to appear on the covellite invariably grew along those steps in the substrate which exceeded about 0.1 micron in height. Crystals could be found growing on flat areas of the surface when there was a large excess vapor density, substantiating the known compatibility of ice and CuS. A typical hexagonal plate of constant thickness of 0.6 micron grew in diameter TAELE Ill. COMPARISON OF ICE-NUCLEATING CRYSTALS W I T H ICE CRYSTALS
Icc
1 4 . 5 2 1 7 . 3 6 1
... I . . .
-~
1
at a rate of nearly 0.5 micron per second with a vapor excess of 0.39 X 10- gram cm.? at -14' C. Head (24) studied experimentally and theoretically the effects of topography on a compatible s u b s t r a t e AgI-and a poorly nucleating substrate-CdS, contact angle 90°. On the silver iodide, ice grew at ledges formed where the sloping sides of hexagonal etch pits met the base, but no lessening of the undercooling seemed to occur, the ice always showing an onset temperature at the customarily quoted threshold of -4' C. At the lowest temperature of his apparatus, -25' C., Head found no freezing activity on the flat surfaces of cadmium sulfide. With stepped crystals, however, some nucleations occurred, particularly in the smaller steps, in the range - 1 5 O to -ZOO C. If the faces were roughened by etching, nucleations occurred in the range -12' to -18' C. Broken crystals sometimes showed nucleation at fractures, and some fragments produced by crushing showed ice embryos at -10' C. If chemical impurities are directly responsible for the nucleation sites, one then asks why the sires are related to physical defects. A theoretical treatment of nucleation on particles, along the lines of the theory of condensation on insoluble nuclei, has been carried out by Fletcher (75,76). The results are informative, and could be applied to specific situations if such quantities as characteristic dimensions and shape of the crystalline nucleus were known. Artificial Nudealion and Arliflcial Nuclai
The first experiments in changing a supercooled cloud to ice crystals in the atmosphere were accomplished by Schaefer (59, who lowered the temperature by dropping pellets of solid COS into the cloud. Each pellet momentarily cooled a path of droplets to a temperature where freezing would occur homogeneously or otherwise, as the purity of the droplets required. In this way tremendous numbers of ice crystals could be formed with a small quantity of dry ice, and these in turn would infect the cloud by turbulent mixing. Shortly after Schaefer's experiments with dry ice, Vonnegut (60) discovered the usefulness of the epitaxially favorable crystals of silver iodide. They are produced as a smoke from generating system that have undergone improvements over the yean. A common method is to burn acetone containing silver iodide in solution. To prepare the solution, sodium or potassium iodide is used with silver nitrate (AgN08 KI + AgI KN03). While dry ice can produce ice crystals in an undercooled cloud at any subfreezing temperature up to approximately 0' C., silver iodide has a nucleating threshold of -4' C. or lower. In practice, the AgI has the advantage that it can be dispersed in smoke particles fine enough to become aerosols that diffuse
+
+
, ~ ~ ' I ~ U I MVSOM L 5 7 NO. 1 1 -%
N O V E M B E R1 9 6 5
39
with the air currents. Most commercial cloud seeding is attempted from generators located on the ground, whence the particles are supposed to be carried by the wind, turbulent mixing, and updrafts to the undercooled portions of the cloud. Other substances that have been reported by Fukuta (20) to serve as artificial nuclei about as well as AgI are PbI2, CuS, CuO, C u 2 0 , Bi13, and some others, but AgI has received the most attention. Experiments with some organic materials have also been reported by Braham (5), Head (24-26), Komabayasi and Ikebe (33),Krasikov (34),Langer et al. (39),Power and Power (49). Following up ideas concerning the importance of hydrophobic surfaces, Zettlemoyer et al. (62) have experimented with hydrophobed silicates. A most unusual substance tested recently by Knollenberg (37) in the University of Chicago Cloud Physics Laboratory is crystalline urea (NH2CONH2). Although it is hygroscopic and highly soluble, it has an endothermic heat of solution. In this way it takes on a water film, then freezes part of it by absorbing 60.5 calories of heat per gram of solute. I n field tests in natural clouds it proved to be remarkably active. Natural Ice Crystals
While investigation proceeds rapidly in studying artificial ice nuclei, there is considerable activity in the identification of the natural nuclei. The best information concerning the substances which serve as natural ice nuclei in the atmosphere has been obtained by Kumai (36, 37) and Isono (28). Snow crystals precipitating in unpolluted atmospheresparts of Japan, Lake Superior, Greenland-are collected on collodion-coated slides of the electron microscope. To prevent the snow crystals from subliming too rapidly, the collection is made in an igloo with a hole in the roof or, in the case of Greenland, in the entrance to a snow tunnel. During sublimation each crystal is photographed at short time intervals under an optical microscope until the last photograph shows only where the center was. This spot, located with reference to the grid on the slide, is later examined and photographed under the electron microscope. At what was the center of each crystal a particle is found which is considered to be the nucleus. Aerosols located at other points also are found, but they are thought to have been captured by the snow-crystal either within the mother cloud or during fall beneath the cloud. I n the electron microscope the substance of the nucleus is identified by electron diffraction or, in some cases, by its appearance. Of 271 snow crystals from Houghton, Mich., studied in detail, Kumai found that 87y0had clay mineral particles as their nuclei. Of 356 snow crystals collected on the elevated ice cap of northern Greenland in summer, 85% had clay mineral particles at their centers. More than half of the clay minerals were identified as kaolin, the remainder being montmorillonite, illite, attapulgite, and related groups. Of the total number of center particles, only four-two in each geographic locationwere hygroscopic substances. A few combustion par40
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
ticles were found in the Houghton, Mich., series. About 10yc of the nuclei from both places could not be identified by the available techniques. I n 13 of the Greenland snow crystals no center nucleus could be observed, suggesting the possibility of homogeneous nucleation. Since Kumai’s work, the Chicago group under Rucklidge (57) has examined the nuclei of ice crystals formed from the vapor in a cloud chamber. Although the method still lacks some refinements, the data are sufficient to indicate that the nuclei are the same as those found by Kumai. REFERENCES (1) Aitken, J., “Collected Scientific Papers,” C. G . Knott, ed., Cambridge University Press, Cambridge, 1923. ( 2 ) Becker, R., Doring, W., Ann. Phys. 24, 719 (1935). (3) Bigg, E. K., Proc. Phys. Soc. B66, 688 (1953). (4) Bradley, R. S., Quart. Rev. 5, 315 (1951). (5) Braham, R . R., Jr., J. Atmos. Sci. 20, 563 (1963). (6) Bryant, G. W., Hallett, J., Mason, B. J., J . Phyi. Chem. Solids 12, 189 (1959). (7) Byers, H . R., “Elements of Cloud Physics,” University of Chicago Press, Chicago, 1965. (8) Byers, H. R., Chary, S. K., Zeits. Agnew. Math. Phys. 14, 428 (1963). (9) Carte, A. E., Proc. Phys. SOC.B69, 1028 (1956). (10) Corrin, M . L., Edwards, H. W., Nelson, J. A . , J . Atmos. Sci. 21, 565 (1964). (11) Cwilong, B. M., Proc. Roy. Sac., London A190, 137 (1947). (12) Farley, F. J. M., Zbid., A212, 530 (1952). (13) Fisher, J. C., Holloman, J. H., Turnbull, D., Sci. 109, 168 (1949). (14) Fletcher, N. H., J . Chem. Phys. 29, 572; 31, 1136 (1958). (15) Fletcher, N. H., Ibid., 31, 1136 (1958). (16) Fletcher, N. H., Ibid., 38, 237 (1963). (17) Fletcher, N. H., Phil. Mag. 7, 255 (1962). (18) Fletcher, N. H., “The Physics of Rainclouds,” p. 53, 210, Cambridge University Press, Cambridge, 1962. (19) Frenkel, J., “Kinetic Theory of Liquids,” Clarendon Press, Oxford, 1946. (20) Fukuta, N., J . M e t . 15, 17 (1958). (21) Hall, P. G., Tompkins, F. C., Trans. Faraday Soc. 58, 1734 (1962). (22) Hallett, J., Phil. Mag. 6 , 1073 (1961). (23) Hallett, J., Mason, B. J., Proc. Roy. SOC., London A247, 440 (1958). (24) Head, R . B., Bull. Obs. Puy de Dome 1, 47 (1961). (25) Head, R . B., J . Phys. Chem. Solids 23, 1371 (1962). (26) Head, R. B., Nature 196, 763 (1962). (27) Hoffer, T. E., J . M e t . 18, 766 (1961). (28) Isono, K., Zbid., 12, 456 (1955). (29) Junge, C. E., Advan. Geophys., H. Landsberg and J. Van Mieghem, eds., 4, 1, Academic Press, New York, 1958. (30) Junge, C. E., Werby, R . T., J . Met. 15, 417 (1958). (31) Knollenberg, R . G., L’niv. Chicago Dept. Geophys. Sci., Cloud Phys. Lab., Tech X o t e 29, 1965. (32) Kahler, H., Med. Statens Met.-Hydrogr. Anstalt (Stockholm) 3 ( 8 ) , 1926. (33) Komabayasi, M., Ikebe, Y . , J . M e t . SOC.Japan 39 (Z), 82 (1961). (34) Krasikov, P. N., Tr. Glavnoi Geojz. Obs. 104, 3 (1961). (35) Krartanow, L., Met. Zeits. 58, 37 (1941). (36) Kumai, M,, J . Met. 18, 139 (1961). (37) Kumai, M., Francis, K. E., J . Atmos. Sci. 19, 474 (1962). (38) Lafargue, C., C. R . Acad. Sci. Paris 246, 1894 (1950). (39) Langer, G., Rosinski, G.?Bernsen, S., J. Atmor. Sci. 20, 557 (1963). (40) Langham, E. J., Mason, B. J., Proc. Roy. Sot., London A247, 493 (1958). (4:i5yason, B. J., “The Physics of Clouds,” Oxford University Press, New York, (42) Mason, B. J., Quart. J . Roy. Met. SOC. 78, 22 (1952). (43) McDonald, J. E., Am. J . Phys. 31, 31 (1963). (44) McDonald, J. E., J . Atmos. Sci. 21, 225 (1964). (45) McDonald, J. E., J . Met. 10, 416 (1953). (46) Mossop, S. C., Proc. Phys. Soc. B68, 193 (1955). (47) Pound, G. M., Madonna, L. A,, Sciulli, C., Carnegie Inst. Tech. Metals Res. Lab. Quart. R e p . 5, 1951. (48) Powell, C. F., Proc. Roy. Soc., London A119, 553 (1928). (49) Power, B. A,, Power, R . F., Noture 194, 1170 (1962). (50) Robinson, R. A,, Stokes, R . H., “Electrolyte Solutions,” Butterworth’s, London, 1959. (51) Rucklidge, J., J . Atmos. Sci. 22, 301 (1965). (52) Sander, A , , Damkohler? G., Naturwissensch. 31, 460 (1943). (53) Schaefer, V. J., Chem. Rev. 44, 291 (1949). (54) Schaefer, V. J., Project Cirrus, Gen. Elec. Res. Lab. 33, 1952. (55) Schaefer, V. J., Sci. 104, 457 (1946). (56) Tohmfor, G., Volmer, M., Ann. Phys. (Leipzig) 33, 109 (1938). (57) Tolman, R. C., J . Chem. Phys. 17, 333 (1949). (58) Turnbull, D.: Fisher, J. C., Zbid., p. 71. (59) Volmer, M., Weber, A,, Z . Phys. Chem. 119, 277 (1926). (60) Vonnegut, B., J. Appl. Phys. 18, 593 (1947). (61) Zettlemoyer, A. C., Tcheurekdjian, N., Chessick, J. J., Nature 192,653 (1961). (62) Zettlemover, A. C . , Tcheurekdjian, N.: Hosler, C. L., 2. Angew. Math. PAYS. 14, 496 (1963).
