The formation of cosmic grains: An experimental and theoretical study

Surface Science 106 (1981) 576-581 North-Holland Publishing Company

THE FORMATION OF COSMIC GRAINS: AN EXPERIMENTAL AND THEORETICAL STUDY B. DONN and J. HECHT Astrochemishy Branch, Laboratoryfor ExtraterrestrialPhysics, NASAlGoddard Space Flight Center, Greenbelt, Maryland, USA

and R. KHANNA,

J. NUTH and D. STRANZ

Department of Chemistry, Universityof Maryland, College Park, Maryland, USA

and A.B. ANDERSON Department of Chemistry, Case WesternReserve University,Cleveland, Ohio, USA Received 8 September 1980

Current results of a comprehensive theoretical and experimental study of the formation of cosmic grains are described. Grain formation as distinguished from growth takes place in cooling, high temperature clouds at densities between lo8 and 10” cmm3, comprised of all elements in cosmic proportions. This system differs considerably from terrestial conditions and equilibrium nucleation theories cannot be used. A kinetic theory of formation is presented which depends upon the high degree of vibrational disequilibrium. Detailed, quantitative results require molecular parameters and cross-sections which current experimental and theoretical techniques are expected to provide. Experiments on magnesium silicate formation in the vapor and in a low temperature nitrogen matrix are described. The smoke, matrix residue, and cosmic grains show very similar infrared spectra.

1. Introduction

Grains less than a micrometer in size are observed throughout the galaxy and they occur in a variety of astronomical objects including interstellar and circumstellar clouds, novae ejecta and planetary nebulae [1,2]. It is currently believed that grains form in cooling gas expelled from stars [l]. The clearest evidence of grain formation is the simultaneous development of obscuration and infrared emission in novae [3]. Features in the infrared and ultraviolet interstellar extinction curves indicate that silicates, graphitic material and silicon carbide are the likely major consituents of the grains [l]. The variety of elements and molecules present around a star before condensation is 0039-6028/81/0000-0000/$02.50

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B. Dorm et al. I Formation of cosmic grains

Table 1 Molecular equilibrium pressures of condensibles in 0 rich stellar atmospheres Atom

Log pressure

Molecule

Fe Mg S Al Ca Na

-1.21 -1.35 -1.95 -2.44 -2.50 -2.65

Log pressure (dynlcm*)

(dynlcm*) SiO SiS TiO AIOH CaOH AlH

-1.3 -3.4 -4.2 -4.3 -4.5 -4.5

These calculations were made at a temperature of 2000 K and at a total pressure of lo3 dyn/cm*[23]. In C rich systems these abundances may be quite different and it has been estimated that in a carbon rich nova at 2ooO K the ratio of C to Fe is about 10 to 1 [24]. Many more abundant and possibly reactive molecules are also present in both systems [23].

shown in table 1. The regions of probable condensation contain such an array of elements with total densities ranging from about lo8 to 1014cme3. These densities and compositions are very different from those prevailing in terrestial systems which serve as the basis for current theories of nucleation. In those experiments densities of condensibles are greater than 1014cm-3. Only one condensible species is usually present in such experiments, although some recent work has been done on binary [4] and more complex systems [5]. 2. Non-equilibrium effects In the astronomical regions where there is the most direct evidence of grain formation, total densities are below about 10” cme3. In such regions a large degree of vibrational disequilibrium occurs [6] and vibrational temperatures are approximately half of the kinetic temperature. This has a large effect on molecular equilibrium [7] and we show in the following analysis that the disequilibrium has a major direct effect on condensation. A consequence of the complex composition is that the major initial equilibrium condensates [8] are the minerals A&03, CaTi03, Ca2A12Si07, CaMgSi206 and iron. For the complex minerals none of the nominal constituent molecules exist in the gas phase. Current theory does not provide for this circumstance. It is not expected that particles with a well defined mineral composition will form even at higher pressures where thermal equilibrium occurs [9]. The requirement for specific reactions coupled with the low binding energy of small clusters [lo] will prevent the stable macroscopic mineral from forming. Finally, condensation will probably not occur until a large supersaturation has been attained [ll, 121. 3. Kinetic theory of condensation

Nucleation of cosmic grains can only be understood in terms of a kinetic theory of condensation. Somewhat similar approaches, for other condensation problems, have been

578

3. Dorm et al. I Formation

of cosmic grains

taken by Buckle [13], Bauer and Frurip [14] and Brady et al. [15]. In these investigations, collisions dominated the process. The general set of kinetic equations of conden~tiou may be written: Ai+Cj%Cf+r

3

(1)

C~+,SCj+l+

hV *

(2)

C?+i+MSCj+i+M

3

(3)

C;+r+M%C,+ArtM,

(4)

CjtMSCi_i+AltM,

(5l

where Ai is a condensible atom or molecule, Cj is a mixed cluster of j atoms or molecules of variable composition, C* is an excited, unstable transient, and M is a non-reactive collision partner. For clouds with densities less than lO”c~rn-~three-body collisions are negligible. The vibrational temperature is also much less than the kinetic [S]. Consequently, collisions can neither stabilize nor dissociate clusters of interest. Such clouds are also optically thin, that is, the ambient flux is significantly less than for a black body at the gas kinetic temperature. In such situations clusters are stabilized by radiative association. In cosmic clouds the general set of equations reduces to: Ai+CjSCT+i

5

cy+1 * Cj+, + /IV s

(1) (24

In eq. (1) we designate the forward rate as kt and the reverse rate as kd. In eq. (2a) the forward rate is taken as k,. Estimates of reaction probabilities, l%, for the fo~ation of transients in eq. (1) can be obtained from chemical kinetics [17] and the probability of radiative stabilization, pi, in eq. (2a), is given by: PR

k k,+k,

z--L-=

-1 rr 7;lf’

where the r’s are lifetimes against radiation or dissociation. Typical radiative lifetimes (rJ for electronic transitions are lo-’ s,and for vibrational transitions are lo-* s. The lifetime of the transient against dissociation is given by unimolecular reaction theory and we use the expression [15]: (7) where Y* is the characteristic vibration frequency - 10’”s-‘, ET+1is the total energy of the transient, ES+, is the critical energy for dissociation and s is the total number of active modes. By using, in eq. (7), E’ - 2 eV, E * = EC+ 3 kT, T = 2000 K and s - 213of the number of vibrational modes, we can estimate the probability Pa. The total probability for cluster growth increases from 10e5for a qua~mer to 10-r for a lo-mer. Thus, larger clusters will

B. Dow et al. I Formation of cosmic grains

519

grow much more rapidly than smaller ones and the rate of growth will be nearly the impingement rate. Because of the vibrational disequilibrium, species with binding energies greater than about 1 eV will not collisionally dissociate once initially stabilized. A large number of binary diatomic clusters of cosmically abundant elements have binding energies of that magnitude [17]. Calculations indicate that a number of metalosilicate compounds also satisfy this criterion. Current experimental and theoretical procedures can provide the molecular parameters and reaction cross-sections needed to obtain quantitive results from the kinetic theory presented here. Quantum chemical calculations of structure and binding have been carried out for (SiO),, n s 10 and for a variety of Mg t Al t SiO systems. Such calculations can provide the data for specific systems of astrophysical interest for which the experimental approach is not feasible.

4. Experiments on vapor condensation The theoretical analysis of cosmic grain formation is being coordinated with an experimental study. Because magnesium silicates appear to be a major constituent of grains, the simultaneous condensation of magnesium and SiO was investigated [12]. Two independently heated crucibles were placed about 1 cm apart in a bell jar at a total pressure of 5 Tot-r. They were surrounded by a large auxilliary furnace which controlled the temperature of the ambient, usually inert, gas. The Mg crucible was heated to about 700°C and the SiO to 14OO”C,providing comparable vapor concentrations of Mg and SiO. By varying the temperatures of the crucibles the concentration ratio of the condensables could be varied. With the auxilliary furnace unheated, a large amount of smoke was collected. The grains were tan to black and exhibited various degrees of instability. The black material exploded when ignited in air although all of the material produced in this manner would gradually oxidize. Electron microscopy showed the grains to be a few hundred angstroms in diameter and X-ray diffraction indicated that they were amorphous. Mg t SiO vapor condensation was studied as a function of ambient temperature. Copious smoke formation occurred at nominal room temperature of the ambient gas but the yield decreased to zero as the temperature was raised to 500°C unless the crucible temperatures were raised. The usual condensible partial pressures were extimated to be 0.1 Torr. Extrapolation of the Mg and SiO partial pressures over a lunar rock sample [18] yields values less than 10e6Torr at 1400K. This indicates that the supersaturation without condensation in our system at 770 K was much greater than 105. The infrared spectrum showed broad, structureless absorption features at 10 and 20 pm (fig. 1B). These features are quite similar to interstellar absorption or circumastellar emission bands. Annealing of several samples in a vacuum at 1000°Cfor an hour produced an infrared spectrum characteristic of forsterite, Mg,Si04. Preliminary results on the Fe t SiO system indicates it behaves like Mg t SiO. Condensation of SiO [19] by itself

580

B. Dorm et al. I Formation of cosmic grains

IR ABSORBTION

SPECTRA

OF

Mg + SiO

p --!?-_

CONDENSATES

9 IO~.~~ I5 .,_, - 12 , --_‘li.mlr-

20

3op

Fig. 1. IR absorption spectra of Mg + SiO condensates: (A) initial deposit of Mg + SiO condensed in a N2 matrix at 12 K; (8) lower curve, Mg f SiO residue after sublimation of matrix; upper curve. Mg + SiO smoke formed in 5 Torr of Ar at a condensation tem~rature of SCQ’C.

produced grains with an infrared spectrum identical with that of Si203. X-ray microprobe and ESCA analysis confirmed the Siz03 composition and structure of the smoke grains. The same strong temperature dependence was obtained as with Mg + SiO.

5. Matrix isolation experiments Condensation under iaboratory conditions occurs in some tens of microseconds. This is too fast to determine the inte~ediate species for grains whose nominal moIecuIes do not exist in the gas phase. However, matrix isolation techniques have been used to study the gradual growth of metal clusters [20]. The second part of our experimental program has been the matrix isolation study of the systems used for vapor smoke formation, SiO [21] and Mg t SiO. The Mg + SiO system was investigated by co-condensing Mg, SiO and N2 at 12 K. The Mg/SiO ratio was about unity and the (Mgi SiO)/Nz ratio about l/500. The initial deposit (fig. IA) shows four absorption features not found with the SiO alone. The peak at 1197cm-’ completely disappeared after 3 hours at 30 K plus 2 hours at 32 K. The other features showed slight changes and no new absorptions occurred. Upon continued warmup and NZ sublimation a residue remained whose infrared spectrum appears in fig. 1B. This shows broad 10 and 20 pm absorption bands which are very similar to the Mg + SiO smoke spectrum shown in fig. 1B. These are very s~ilar to interstellar absorption features 1221.The IR spectrum of the SiO residue was likewise very similar to that of S&O3smoke particles. A vibrational analysis of the four absorptions that can be attributed to a magnesium silicate compound is being undertaken. Additional structural and analytical determinations of smoke and matrix condensation will be carried out.

B. Dorm et al. I Formationof cosmic grains

581

6. Conclusion The following can be concluded from our investigation of cosmic grain formation. (1) Grains generally form under very non-equilibrium conditions. (2) A kinetic analysis of cosmic grain formation is required. (3) A kinetic theory can be formulated and, in principle, quantitive calculations carried out. (4) Experimental and theoretical techniques appear capable of providing reaction rates and cross-sections for a more detailed analysis. (5) Theory indicates amorphous grains of mixed composition will form. (6) Vapor and matrix condensation experiments can provide data on the condensation mechanism and products applicable to cosmic systems. (7) The preliminary experimental results generally support the theoretical predictions.

References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13] [14] [ls] [16] [17] [18] [19] [20] [21] [22] [23] [24]

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