sparking as a random process

3. E.S. Zolotovitskaya, A. B. Blank, V. P. Seminozhko, et al., Zh. Prikl. Spektrosk., 50, No. 3, 463-465 (1989).

4. C. Corliss and W. Bosman, Probabilities of Transitions and Oscillator Strengths of 70 Elements [Russian translation], Moscow (1968), p. 16.

5. A.N. Zaidel', V. V. Prokof'ev, S. M. Raiskii, et al., Tables of Spectral Lines [in Russian], Moscow (1977).

6. R.R. Shvangiradze, I. L. Vysokova, and O. A. Grishutina, Zh. Prikl. Spektrosk., 27, No. 2, 201-205 (1977).

7. I.L. Vysokova, O. A. Grishutina, and R. R. Shvangiradze, Zh. Prikl. Spektrosk., 53, No. i, 133-136 (1990).

SPARKING AS A RANDOM PROCESS

E. N. Severin UDC 620.186:537.52

It is common in metal spectral analysis to use a spark between a flat specimen and a rod with its axis perpendicular to the specimen. Various types of spark generator have been tested, and their descriptions can be found in [i]. The IG-3 condensed-spark generator is widely used in the USSR, which is combined with an ISP-30 quartz spectrograph for many pur- poses, including ones that at present cannot be handled by photoelectric systems.

The spark forms a crater. One assumes for simplicity that each such crater is produced by a single oscillatory discharge. If the generator produces k i bursts during a half-cycle of the supply frequency f (Hz), and during each burst there are k 2 individual oscillatory discharges, the number n of craters at the surface arising in 1 sec is

n = 2rk,k2. ( 1 )

The mean crater diameter with a standard spark can [2] be taken as 20 ~m. The craters are randomly distributed, and after a fairly long period, a bounded sparking spot is formed. An optimality condition is that this spot should be regular, which implies a reproducible shape. A typical example is a circle. In general, the spot shape is governed by the shape of the end of the rod electrode, as well as by the surface finish and so on. Regularity is best provided by electrodes with restricted working surfaces, e.g., with the end turned down to a narrow cylinder or cone, sometimes with rounding at the end. The usual preparation [3] results in a circular spot bounded at the edge by a concentric ring coated with oxide. The oxide does not act as a major insulator capable of restricting the discharge zone, as can readily be seen if the sample is displaced slightly, e.g., by half the spot diameter. The oxide directly in the zone of the new spot does not hinder the formation in any way.

The spot diameter D under ordinary conditions increases roughly linearly with the gap h. An ISP-30/IG-3 combination can be used with a copper electrode with the end turned down to a cylinder 1.7 mm in diameter, with rounding (Fig. i), and when h varies from 2 to 7 mm, D varies correspondingly from 1.5 to 4.5 mm and with h = 4 mm is approximately 2 mm.

A stationary state in the spark plasma is important in applied spectroscopy, as the signal, which here is the ratio of the intensities in the line pair, should be independent of time. That state is attained only when the complete spot area has been processed by the discharge [4], i.e., is covered by craters.

A single discharge interacts explosively with the sample, so if a series of discharges falls at the same point, the differences in the signal levels will be largest as between the first discharge, which strikes a fresh point, and the second, which strikes an area af- fected by the first. Then the end of the running-in (and start of the stationary state) can be taken as when the entire spot area is covered with single-layer craters. This is possible only if the craters are uniformly distributed, and that distribution differs from others in providing a stationary state with the minimum number of single discharges which is there-

Ferrous Metallurgy Institute, Dnepropetrovsk. troskopii, Vol. 55, No. i, pp. 47-52, July, 1991. 1990; revision submitted March ii, 1991.

Translated from Zhurnal Prikladnoi Spek- Original article submitted February 27,

0021-9037/91/5501-0657512.50 �9 1991 Plenum Publishing Corporation 657

I

10

9

8

7

6

9

q

7

Z

1

3 2 1 0 1 Z 3 o , . /

Fig. i Fig. 2

Fig. i. Analytical gap scheme.

Fig. 2. Comparison of observed intensity distribution (I) with the corresponding normal one (2).

fore significant as being the most effective. The available literature carries no informa- tion on the crater distribution, although it is clear that the topic is important for appli- cations and is of some scientific interest.

One can test for a uniform distribution by comparing the measured running-in time with that calculated on that assumption:

s t~ = - - , ( 2 )

So in which S is the spot area and

So = 2ar2n ( 3 )

is the total area of the craters formed in unit time (r and R are the mean radii of a crater and the spot). Then with h = 4 mm, r = 0.02 m_m, k I = 3, k 2 = 20, R = I ram, f = 50 Hz we get

R2 12 t c - - -- = 1.7 sec. ( 4 )

2r2fklk~ 2 .0 .012 .50 .3 .20

When a m e t h o d was b e i n g d e v e l o p e d f o r d e t e r m i n i n g t h e p r o p o r t i o n s o f s i l i c o n a nd m a n g a - n e s e i n g r a y c a s t i r o n , we u s e d C = 0 . 0 1 ~F a nd L = 0 . 0 1 mIt w i t h t h e I G - 3 g e n e r a t o r [ 5 ] , when t h e r u n n i n g - i n l a s t e d a b o u t 30 s e c . T h a t l a r g e d i s c r e p a n c y i n d i c a t e s t h a t t h e h y p e t h - e s i s i s u n s o u n d .

We h a v e e x a m i n e d t h e c r a t e r d i s t r i b u t i o n w i t h t h e a b o v e s p a r k d i s c h a r g e on g r a y c a s t i r o n .

The crater density p is defined as the ratio of the total area of all craters in a given part of the surface to the area of that part. One has to measure p, where direct counting for example from a photograph is inapplicable because the count cannot be performed where craters are superimposed. One can employ the profile taken along the diameter. We used a method based on the one-to-one correspondence between the set of single discharges in a given time and the set of craters formed, where a more powerful single discharge, e.g., in a series of discharges in a given burst, corresponds to a larger crater diameter and higher radiation intensity from the discharge channel. We examined the crater distribution

6 5 8

from the integral intensity along a narrow spatial layer AB (Fig. i) at a short distance h 0 from the plane of the spot. This is justified because the intensities from parts with equal separation in the discharge channel from the surface will be the same, although in general a spark discharge is spatially inhomogeneous [6]. The horizontal gap of 7 mm was imaged by a lens having f = 150 mm on the spectrograph slit, so the slit received a plane parallel to the surface of the sample and 1 mm from it.

The intensity distribution along the section bounded by the slit corresponds to the optical density distribution along a spectral line on the plate. The blackening was measured along a line with suitable resolution with the microphotometer slit perpendicular to the line, which is practicable only if the line image is sufficiently wide. We used a spectrograph slit of 0.i mm, which resulted in closely spaced lines being superimposed as vari- able bands convenient for such blackening measurement.

The blackening was then converted to intensity for the lines in the region of ~280 nm in the spectrum from iron. Figure 2 shows the corresponding intensity distribution. The bell-shaped curve suggests a Gaussian distribution, which was tested as in [7], and the corresponding theoretical distribution is shown. The observed curve fits a Gaussian distribution with fiducial probability greater than 0.95.

This experiment has been reproduced repeatedly with the same result. Significant devi- ations from a normal distribution (skewness, lordosis, etc.) occurred only when there were visible defects in the discharge surface, when the spot ceased to be regular, and also when auxiliary electrodes with extended working surfaces were used. In the latter case, the general picture was that of a superimposed set of point sources, each having a normal distribution.

Each abscissa x = x 0 in Fig. 2 corresponds to an integral probability density along the MH direction (Fig. i) at a distance x 0 from the spot center, so Fig. 2 is a one-dimensional representation of the two-dimensional distribution in the spot plane. If the spot is regular and a normal distribution applies along any section in the plane, the integral distribution will also be normal.

Let the probability density along the diameter (x = 0) be Gaussian:

! z x -i/~ exp(--y~/2~2) (5)

As the spot is regular, the probability distribution of the xOy plane will be a surface ob- tained by rotating the (5) curve around the Oz axis:

! ZxY -- V2-n~ exp ( - - (x z ~- y2)/2~2). ( 6 )

The s e c t i o n by t h e x = xo p l a n e i s

z exp ( - - x~/2~2) exp ( - - yz/2~2), (7 ) ~~ = V ~

which d i f f e r s f rom (5 ) in e s s e n c e o n l y in t h e f a c t o r exp ( - x ~ / 2 a 2) < 1. The t o t a l ( i n t e - g r a l ) p r o b a b i l i t y d e n s i t y a l o n g t h a t s e c t i o n , in v iew o f

1 +~ z - - -V2 -~ ~ exp( - -x~ /2~)dx= I, (8 )

i s

2x. == exp ( - - y2/2~). (9 )

We se e f rom (9 ) t h a t t h e i n t e g r a l d i s t r i b u t i o n i s n o r m a l , as in ( 5 ) , b u t e n l a r g e d by com- p a r i s o n with the latter by a factor of 2~o.

We now consider the running-in for the same conditions but with a normal crater distribution. One naturally assumes that D is bounded by • coordinates, so

~=D/4. (10)

The end o f t h e r u n n i n g - i n t i m e o c c u r s when t h e c r a t e r c o v e r a g e a t t h e s p o t edge c o r r e s p o n d s t o a compact a r r a y (p = 1 ) .

With c o o r d i n a t e s

659

x=x/a (11)

t h e edge o f a c r a t e r i s a t a d i s t a n c e o f 2 f rom t h e c e n t e r , and t h e p r o b a b i l i t y d e n s i t y f o r a no rma l d i s t r i b u t i o n r a t i t i s 0 .0540 [ 8 ] .

The r e l a t i o n be tween t h e c r a t e r d e n s i t y p ( z ) and r i s

p(g) = A ~ ( ~ ) , (12)

in which A is a coefficient of proportionality; A is defined by the boundary conditions

A = P (2)/~ (2) - - 1/0,0540= 18.52. (13)

We derive the integral probability density of the spot as the volume V under the surface of rotation for curve (5) normalized by the (ii) substitution to

z~ = exp (--~B/2)/]/-~-~, (14)

with respect to the Oz axis: 21

V = ~ n~2dz, (15) 22

in which zl, 2 are the integration limits. Equation (14) gives

T 2 = - - 2 in (z ] / ~ ) . ( 16 )

With t h e above c o n s t r a i n t s on t h e s p o t , z l = 2 and ~2 = 0, and c o r r e s p o n d i n g l y z 1 = 0 .0540 and z 2 =_0 .3989 . We s u b s t i t u t e (16) i n t o (15) and i n t e g r a t e t o g e t V = 1 .4938 , so t h e mean density p in the spot for density 1 at the edge is

9 - - A V~- 16.79- 1,4938 = 27.67. (17) The run-in time is found as the ratio of the total number of craters N formed in the spot area to the n of (i) formed in unit time:

The mean density is

t n : N/n.

SO

(18)

We substitute (20) into (18) and use

(19)

N --~ pR2/ r 2. ( 20 )

n---2fklk2-----2.50.3.20---6000, (21)

to get tn =~R2/r2 n 27.67.1.02

= -- 46 s e e , (22) 0.012. 6000

which represents fairly good agreement with the above estimate of 30 sec found by direct experiment.

This confirms that a Gaussian distribution applies for the crater distribution, We used typical spectral equipment at atmospheric pressure with air in the gap. We do not consider sparks in inert gases or the relatively recent spark sources that operate in a dif- ferent way, e.g., the quarter-wave 325 MHz spark source [9], which provides an exceptionally stable discharge. One anticipates that they also will give Gaussian distributions.

This regularity serves to define the electrode processes and assists in developing a quantitative analysis with spark sources, as the following shows. When the edge density attains 1 the density at the center will already be

p (0) ---~ A~ (0) ~--- 18,52- 0.3989-- 7,4, (23)

i . e . , i n c r e a s e d by more t h a n a f a c t o r o f s e v e n , so d u r i n g t h e r u n n i n g - i n p e r i o d , t h e d i s c h a r g e reworks the central part repeatedly, while the edge is processed only partially. That is an unsound distribution as regards quantitative analysis, and it should stimulate research on new designs providing nearly-uniform crater distributions. Further, a certain but small fraction of the discharges will inevitably fall on unaffected parts of the surface outside the visible spot even when the running-in in the spot has long been completed. These ran-

660

dom excursions outside the spot produce undesirable signal fluctuations, and eliminating them would improve the metrological characteristics.

I am indebted to Yu. M. Buravlev for critical comments on the draft.

,

2 .

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5 .

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7 .

8.

.

LITERATURE CITED

Yu. M. Buravlev, Spectral Analysis by Atomic Emission [in Russian], Kiev (1988). Yu. M. Buravlev, Effects of Alloy Composition and Sample Size on Spectral Analysis Re- sults [in Russian], Kiev (1970). Cast Iron, Steel, and Alloys: Sampling Method for Determining Chemical Composition: GOST 7565-81 [in Russian]. I. A. Grikit, Zavod. Lab., 26, No. 5, 577-581 (1960). E. N. Severin, A. A. Kibalov, R. A. Tatarikova, and N. V. Ivchenko, Zavod~ Lab., 55, No. I0, 95-98 (1989). J. P. Walters and S. A. Goldstein, Spectrochim. Acta, 39B, No. 5, 693-699 (1984). A. M. Dlin, Mathematical Statistics in Engineering [in Russian], Moscow (1958). L. N. Bol'shev and N. V. Smirnov, Tables for Mathematical Statistics [in Russian], Moscow (1965). J. R. Rentner, T. Uchida, and J. P. Walters, Spectrochim. Acta, 32B, No. 3/4, 125-154 ( 1 9 7 7 ) .

CONCERNING THE NATURE OF THE DOUBLET AT 2200 cm -I

IN THE VIBRATIONAL SPECTRA OF CYANOGUANIDINE

L. A. Sheludyakova, E. V. Sobolev, and L. I. Kozhevina

UDC 543.422.4

In the IR absorption and Raman spectra of cyanoguanidine C2N4H 4 (CG), in place of a single line in the 2200 cm -I range typical for vibrations of the C~N bond, a doublet having a separation of around 45 cm -I appears (Fig. 1). Sukhorukov and Finkel'shtein [i] attributed the second component to a Fermi resonance [2]. The disappearance of the doublet in the IR absorption spectra of a deuterated sample was similarly explained.

Data we have collected indicates that upon deuteration of CG, the doublet character is preserved in both IR and Raman spectra (Fig. i). Here the low-frequency component maintains its position, while the high-frequency component experiences a shift of 20 cm -I with a conse- quent overall reduction in separation. However, as the frequencies of the lines approach, their relative intensities remain virtually constant both in the IR and Raman spectra. This is in clear disagreement with rules concerning Fermi resonances. A Davidov resonance, quite frequantly observed in the spectra of molecular crystals, could be a second possible explanation for the doublet character of the line. Arguing against this possibility is the fact that the doublet is present in IR spectra of solutions of CG in dimethyl formamide (DMF), Here, a displacement of the high frequency line is observed along with a substantial change in the relative intensity of the doublet (Fig. la-e).

Elimination of various resonance mechanisms as an explanation for the doublet character of the line forces one to seek a reason for the splitting in the chemicostructural particu- lars of the compound, assuming that several structural forms exist [3]. Structural data, it would appear, does not support such a conclusion. In particular, x-ray data records a single form of molecular structure for crystalline CG at both 300 and 80 K [4]. Meanwhile, there is the fact that the single and double bonds in the guanidine fragment are equal in length, which many authors ([4], for example) refer to in terms of mesomerism principles.

We believe that tautomeric conversion takes place in crystalline CG leading to formation of an equilibrium mixture of differing forms, distinguished by the positions of the

Institute of Inorganic Chemistry, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. i, pp. 53-57, July, 1991. Original article submitted July 25, 1990.

0021-9037/91/5501-0661512.50 �9 1 9 9 1 Plenum Publishing Corporation 661

sparking as a random process

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