Angular scattering from irregularly shaped particles with application to astronom

Donn, B.

Powell, R. S.

English

NASA Technical Reports Server

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ANGULAR SCATTERING FROM IRREGULARLY 
SHAPED PARTICLES WITH APPLICATION TO 
ASTRONOMY 
bY 
B. Do" AND R. S. POWELL 
'" 
. -- - 
Reprinted from 
I. C.E.S. 
PERGAMON PRESS 
OXFORD. LONDON. NEW YORK . PARIS 
1963 
https://ntrs.nasa.gov/search.jsp?R=19640000422 2020-03-24T05:33:08+00:00Z
ANGULAR SCATTERING FROM IRREGULARLY 
SHAPED PARTICLES WITH APPLICATION TO 
ASTRONOMY /- 
BERTRAM Do" and ROBERT S .  POWELL $ y ~ , - . / - .  J ('. L 5/", 
j . .  . -1 k'&8* Goddard Space Flight Center, - . . . - $-.----- .--....- *. -* -.- , - 
/ 
_ _  
(- />& I> f ,  L5,'- / 5  J 
-Fr 1. I N T R O D U C T I O N  
Small, solid particles play an important role in current theories of star for- 
mation (Burbidge and Burbidge, 1958) and the origin of the solar system 
(Urey, 1957). It also appears that the accumulation of the planets can only 
be explained by the coagulation of small particles whose shapes are irregular 
rather than spherical (Donn and Sears, 1962). 
Some information concerning the mass and momentum of particles near 
the earth has recently been obtained from rockets, satellites and probes 
(Alexander et al., 1962). Information about the composition and size of dust 
particles collected on earth is summarized by Fireman and Kistner (1961), 
but the relation of these particles to cosmic grains is not clearly established. 
Until rocket techniques become more sophisticated, most of our knowledge 
concerning the specific nature of the particulate matter in space will be based 
upon observations of the angular scattering from the zodiacal light particles, 
comet grains, and the F corona of the sun; and upon the extinction charac- 
teristics of the interstellar medium. 
The usual procedure in astronomy is to compare observed scattering data 
with theoretical computations for a distribution of spheres in order to obtain 
three characteristics of the particle cloud: (1) effective size and size distribu- 
tion; (2) index of refraction and (3) space density (van de Hulst, 1949; 
Liller, 1960). That distribution of spheres showing the best fit to the ob- 
served data is adopted as representing the scattering material. 
Three major uncertainties affect the conclusions. These are: (1) the assump- 
tion of spherical scatterers ; (2) the incompleteness of astronomical observa- 
tions, i.e. small range of angle and wavelength and (3) the incompleteness of 
scattering calculations for a large range of spherical particle sizes and indices 
of refraction. The analysis is further handicapped by the labor necessary to 
carry out a large number of comparisons for many different size distributions. 
In order to alleviate the incompleteness of the present tables for spheres 
151 
152 BERTRAM DONN AND ROBERT S. POWELL 
and reduce the labor in making comparisons with many size distributions, 
we have prepared a table of scattering intensities and an integrated function 
F(a, 8, m) for the following intervals in the index of refraction, the scattering 
angle measured from the forward direction, and the size parameter: 
L 
m = 1.2(0.2)2.4 
a = 2741 = 0.1(0.1)100 
e = oo(5o)isoo 
The integrated function is given by: 
This function permits quick and simple comparison of the scattering from 
many size distributions. The method will be discussed further in this paper 
and in more detail elsewhere. 
Our primary objective in this investigation is to study the scattering proper- 
ties of irregularly shaped particles in order to evaluate the consequences of 
comparing the observed data with spheres and, thereby, gain a better under- 
standing of which scattering parameters are most definitive from the view- 
point of gathering optimal astronomical data. 
Typical results concerning the scattering from irregularly shaped zinc oxide 
particles are presented and compared with equivalent theoretical results for 
spheres. 
2. F O R M U L A T I O N  OF T H E  PROBLEM 
There are several reasons for suspecting that the particles in space are non- 
spherical in shape. First, light scattered by interstellar dust is polarized in 
the forward direction. Aligned, asymmetric grains would polarize in this 
manner. Secondly, irregular particles, which may be related to the cosmic 
grains, have been collected at high altitudes (Hemenway et al., 1961a, b; 
Fireman and Kistner, 1961). Thirdly, any zodiacal particles produced by 
fragmentation in the asteroid belt (Pietrowski, 1953; Fessenkov, 1959) will 
be angular-not spherical. Finally, experimental and theoretical research on 
crystal growth (Donn and Sears, 1962) indicates that crystals forming in 
space would tend to resemble plates, needles or snowflakes rather than 
spheroids. Cometary grains are expected to fall into this category. 
For our preliminary measurements we picked an irregular particle which 
was easy to grow, whose shape was always the same, with a high, real index 
of refraction, and whose size was easy to control. Zinc oxide crystals fulfill 
these requirements. Also, zinc oxide crystals can easily be made to cluster 
in loose aggregate form so that scattering from porous particles may be 
studied. An electron micrograph of particles collected from one of our 
scattering samples is shown in Fig. 1. 
ANGULAR SCATTERING WITH APPLICATION TO ASTRONOMY 153 
3. EXPERIMENTAL ARRANGEMENT 
The zinc oxide particles are grown by vaporizing zinc in a mixture of dry 
nitrogen and oxygen. The size of the particles is controlled by adjusting the 
temperature of the zinc, the ratio of nitrogen to oxygen, and the flow rates. 
The resulting zinc oxide smoke is diluted and time is allowed for the larger 
particles to settle out. The resulting size distribution is shown in Fig. 2. 
!- 
1160 
lioo iI 
a'- 
Fig. 2 - observed size distribution 
of zinc oxide particles. 
a -  
Fig 30 - computed w e  distribution 
for eauivalenf soheres 
a-  a- 
Fig 3b -computed size distribution Fig 3c- computed size distribution 
for equivalent spheres for equivalent spheres. 
After the smoke has become relatively stable, it is irradiated with a beam 
of unpolarized mercury green or mercury blue light (24360,15468). Angular 
scattering for both polarizations is recorded from 8 = 150" to 8 = 50". 
154 BERTRAM DONN AND ROBERT S. POWELL 
The smoke density is monitored during the entire measurement process. 
After a stable run the smoke is sampled with a standard Cascela thermal pre- 
cipitator modified to accept electron microscope grids. The size distribution 
is then counted from the electron micrographs. A typical scattering diagram 
for the size distribution of Fig. 2 is shown in Fig. 4. 
4. THEORETICAL A N A L Y S I S  O F  Z I N C  O X I D E  S C A T T E R I N G  
D I A G R A M  
The observed scattering diagram shown in Fig. 4 was compared to an 
enormous number of scattering diagrams for spheres in various size dis- 
tributions by using the integrated function of equation (1). Any distribution 
of sizes may be approximated by a horizontal or vertical histogram. The 
scattering which corresponds to each interval, Au = ai - a i - l ,  in the histo- 
gram is then given by F(cti) - F(E~-~) with an appropriate weighting factor. 
In general, then, the scattering from any size distribution, p ,  is given by: 
n 
t = O  
Z ( P ,  8, m) = AiCF(mi> - F(ai- 1)I (2) 
Each interval, ui - ai- l ,  may usually be taken quite large because the 
scattering is relatively insensitive to changes in the shape of continuous dis- 
tributions except at the extreme forward and backward scattering angles. 
In practice, one can obtain a closest fit to any scattering diagram by first 
referring to the scattering diagrams of, say, fifty basic functions F(r i )  where 
ai is taken from very small values to arbitrarily large ones in equal steps. 
Each basic function exhibits its own peculiar characteristics. For instance, 
F(2) may exhibit a polarization ratio Zl/(Zl + Z2) < 1/2 whereas F(4) may 
exhibit Zl/(Zl + Z2) =- 1/2. On the basis of these peculiar characteristics most 
of the basic functions may be discarded from further consideration. Those 
which remain may then be weighted and combined by trial and error until 
the desired scattering diagram is constructed. With a little experience one , 
can accomplish this quite easily and, for most distributions, be assured of the 
uniqueness of the fit. 
There are, of course, several different criteria available by which one judges 
which distribution of spheres most nearly fits the observed scattering diagram. 
One choice is to find a distribution of spheres which reproduces only one 
scattering parameter; for instance, the vertical component of the intensity. 
Another distribution can then be found which reproduces the horizontal com- 
ponent and so on until one has several different distributions of spheres, each 
of which accurately portrays one of the characteristic scattering parameters. 
Among the scattering parameters which may be used in this manner are: 
(1) slope of vertical component as a function of angle; (2) same for horizontal 
component; (3) polarization ratio as a function of angle; (4) ratio of forward 
. 
ANGULAR SCATTERING WITH APPLICATION TO ASTRONOMY 155 
to back scattering or ratio at any fixed angles; ( 5 )  ratio of maximum to 
minimum scattering over some angular interval. (All of these should be 
considered as a function of wavelength as well.) The differences between the 
resulting set of "equivalent" sphere distributions may then be used to charac- 
terize the scattering from a particular irregular particle. Various different 
M=2.01 \ 
50 70 90 110 130 150 
0 -  
Fig. 4 -scattering observed 
from zinc oxide pwtitles 
50 T O  90 I10 130 150 
0- 
Fig 5b-scattering computed 
for "equivalent'spheres. 
MiZ.01 
\  \ \ 
" 50 70 90 110 130 Is0 
0 -  
Fig 50 -scattering computrd 
for 'equivalent' spheres 
t 
0- 
Fig 5 c -  scattering computed 
for 'equivalent' spheres. 
irregular particles can then be catalogued by comparing the equivalent sphere 
sets corresponding to each. Under favorable conditions one can then deduce 
the general shape and refractive index of a particle by observing the relative 
dominance of the different scattering parameters. We are in the process of 
investigating the usefulness of this procedure. 
For this paper we have chosen a second criterion by which to judge which 
distribution of spheres is equivalent to the zinc oxide distribution. By using 
the integrated function we have found a single and unique distribution of 
spheres for each index of refraction which roughly reproduces the entire zinc 
oxide scattering diagram. The equivalent scattering diagrams defined on this 
156 BERTRAM DONN AND ROBERT S. POWELL 
0.61 
0.96 
0.66 
0.74 
basis are shown in Fig. 5a, b, c and the corresponding equivalent sue dis- 
tributions are shown in Fig. 3a, b, c. 
0.57 
0.86 
0.62 
0.68 
5. RESULTS 
Using the second criterion mentioned above, we found it impossible to 
match all parameters exactly with one set of “equivalent” spheres. The 
general shape of the vertical and horizontal component curves is most nearly 
reproduced by spheres with index 1.2. The shape of the equivalent horizontal 
component becomes more distorted as we go to higher indices. 
The polarization ratios are shown in Table 1. 
50“ 
90” 
TABLE 1. POLAREATTON RATIOS h/(h + ZZ) 
m = 1.2 rn = 1.6 rn = 2.01 
8.5 4.9 3.9 
8.2 5.8 5.4 
Computed (spheres) 
0.69 -- 
rn = 1.6 I rn = 2.01 
Observed 
(zno) 
m = 2.01 
0.62 
0.81 
0.74 
0.12 
The spheres with rn = 1.6 match the average observed polarization ratios 
a little better than the other distributions but only the spheres for m = 2.01 
match at 90”. The relative slope characteristic defined by: 
’ 
W )  = [Il@) - ~, (~>l /Vl( lW - I,(l5o0)l 
is matched most closely by the spheres with rn = 2.01 as can be seen in 
Table 2. 
TABLE 2. RELATIVE SLOPE CHARACTERISTIC 
~ ~~~~ 
Computed (spheres) 1 Oks&Gd 
8 
rn = 2.01 
5.4 
3.8 
The shape of the vertical component is matched almost equally well by all 
the distributions. One can, of course, continue to define new characteristics 
ANGULAR SCATTERING WITH APPLICATION TO ASTRONOMY 157 
m 
1.2 
1.6 
2.01 
for purposes of matching, and thus give some sort of rough index of fit to 
each computed curve. For the present, however, let us just point out the 
spheres with m = 1.2 most nearly approximate the actual size distribution 
since they give the largest proportion of big particles. Nevertheless, none of 
the “equivalent” distributions defined by our second criterion show any 
evidence of particles bigger than a = 1.8, whereas 15 per cent of the particles 
in the observed zinc oxide distribution are larger than a’ = 1.8. 
The size parameter, a’, for the zinc oxide particle was arbitrarily computed 
using the length, L, between the tips of two spikes. It is, therefore, not sur- 
prising that the observed size distribution is different than the deduced ones. 
ln order to obtain a distribution function which roughly approximates those 
computed for the equivaient spheres, the size parameter defined by a‘ = 
27cL/I must be multiplied by a scaling factor B. Then 
r 
0.25L 
0.16~5 
0.018L 
--
can be compared directly to the size parameter defined for spheres i.e. 
27cr 
I 
a=- 
and the equivalent zinc oxide radius is then given by : 
r = B L  
The values for B are given in Table 3. 
TABLE 3
I I 
which corresponds to: 
+ the length of one spike + the length of one spike 
roughly the diameter of the central junction 
This is only an estimate of the effective size parameter because we do not 
know the accuracy of our observed size distribution as counted from the 
electron micrographs. 
Nevertheless, it appears probable that irregular zinc oxide particles exhibit 
scattering characteristics like those of much smaller spheres of high index of 
refraction or like only somewhat smaller spheres of low index. Apparently, 
the “equivalent” spheres are always smaller than the longest length of the 
irregular particle for indices of refraction lower than, or equal to, that of the 
irregular particle. 
158 BERTRAM DONN AND ROBERT S. POWELL 
R E F E R E N C E S  
ALEXANDER, W. M., MCCRACKEN, C. W., SECRETAN, L. and BERG, 0. E. (1962) Paper 
presented at Costar meeting, Washington, D.C., May,, 1962. To be published in Pro- 
ceedings of Costar, 1963. 
BURBIDGE, E. M. and BURBIDGE, G. R .  (1958) Handbuch der Physik 51, 134, ed. by S. F. 
Liigge, Springer, Berlin. 
DONN, B. and SEARS, G. W. (1962) to be published. 
FESSENKOV, . G. (1959) Ann. d'Ap. 22, 820. 
FIREMAN, E. L. and KISTNER, G. H. (1961) Geochem. Cosmochem. Acta 24, 10. 
HEMENWAY, C. L., FULLAM. E. F., PHILLIPS, L. (1961a) Nature 190,897. 
HEMENWAY, C. L., SOBERMAN, R. K., FULLAM, E. F., BALSAMO, J. J., COLE, J., HALLGREN, 
D., VEDINAK, P., GOODMAN, A., HOW, G. (1961b) Geo. Res. Directorate Research 
Note No. 71, p. 11. 
VAN DE HULST, H. C. (1949) Recherches Astron. Obs. d'Utrecht 11, part 2. 
LILLER, W. (1960) Ap. J.  132,867. 
PIOTROWSKI, S. L. (1953) Acta. Astr. Ser. A S ,  115. 
UREY, H. C. (1957) Progress in Physics and Chem. of the  Earth, vol. 2. Pergamon Press, 
London, New York, Paris. 


Angular scattering from irregularly shaped particles with application to astronomy

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