P A R T I C L E S I Z E D I S T R I B U T I O N O F C O P P E R

V . I . K u r i n n o i , T . A . K o m a r o v a , N . A . F i g u r o v s k i i , a n d E . N. S e m e n o v a

P O W D E R

UDC 541.182 : 621.762

Elec t ro ly t ic copper powders a r e usual ly s eve re ly aggrega ted [1]. Yet to de te rmine the c h a r a c t e r i s - t ics of e l e m e n t a r y growth p r o c e s s e s , it is n e c e s s a r y to have informat ion on the p r i m a r y par t i c le s ize d i s - t r ibut ion of copper powders . This may be obtained in var ious ways [2], the mos t re l iab le r e su l t s being yielded by the method of d isaggregat ion followed by pa r t i c l e s ize ana lys i s .

The presen t work was under taken with the a im of examining, by the s ed imen tome t r i c and m i c r o s c o p i c techniques, the c h a r a c t e r of the p r i m a r y pa r t i c l e s ize dis t r ibut ion curves of e lec t ro ly t ic copper powders , de te rmin ing the dis t r ibut ion p a r a m e t e r s , and obtaining a s ta t i s t i ca l evaluation of r e su l t s . PM-1 c o m m e r - cial e lec t ro ly t ic copper powder* was chosen for invest igat ion. Sed imentomet r ic analys is was p e r f o r m e d by a weighing method [2] and mic roscop i c analys is by examinat ion under a Deutz polar iz ing mic roscope . The e lec t ro ly t ic copper powder was d i saggrega ted by the technique desc r ibed in [3].

Sed imentomet r ic ana lys i s yielded the following data upon the par t i c le s ize dis t r ibut ion of the copper powder (the data a r e the mean va lues of r e su l t s of t h ree de te rmina t ions , with the weight of each par t i c le f rac t ion conver ted into the pe rcen tage amount of the f rac t ion [2, p. 301]):

Pe rcen tage amounts of pa r t i c l e f rac t ions , #

0,65--1,25 1,,25--2,50 2,50--3,75 3,75--5,00 5,00--625 51,9 36,2 9,3 2,0 0,27

6,25--7,50 7,50--8,75 8,75--10,00 10,00--11,25 11,%--12,50 0,12 0,04 0,03 0,01 0.01

Plotted in s emi loga r i t hmic coordina tes , the re la t ion obtained approx ima tes to a s t ra ight line in the par t i c le radius range f rom 0.65 to 7.5 tt (Fig. 1). Hence it is poss ib le to advance the s ta t i s t i ca l hypothesis that the pa r t i c l e s ize dis t r ibut ion within this range is an exponential one. To ver i fy this hypothes is , use was made of the P ea r s on s ta t i s t i ca l c r i t e r ion of conformi ty (Table 1). F i r s t , using the leas t squa res method, the theore t i ca l dis t r ibut ion p a r a m e t e r s were de te rmined . As a resu l t , the following fo rmula was obtained: f i x ) =160.5 exp [-1.17 ( r -0 .65 ) ] , where r is the par t i c le radius . F r o m the table of P e a r s o n ' s pe rcen tage dis t r ibut ion points [4], the level of s ignif icance was found to be P{%2(r) > 0.45} = 0.025. Thus, our expe r i - men ta l data support the hypothesis of exponential d is t r ibut ion with a probabi l i ty of 97.5%.

Microscop ic m e a s u r e m e n t s were employed for de te rmin ing the l inear s izes of 800 par t i c les of the copper powder. Exponential d is t r ibut ion in this case was found, us ing the Pea r son c r i t e r ion , to be valid with a probabi l i ty of 80%. After normal iza t ion , the f o r m u l a f ( r ) = 160.5 exp [-1.17 ( r -0 .65 ) ] gave the d i s - t r ibut ion function i n t h e form: f ( r ) = l . 1 7 exp [-1.17 ( r -0~ (Fig. 2).

Use of dis t r ibut ion functions has, in the au thor ' s opinion, a number of advantages: The informat ion is ver i f ied , calculat ions can be p e r f o r m e d with compute r s , and dis tr ibut ion p a r a m e t e r s can be de te rmined with l i t t le difficulty. Thus, the mean par t i c le radius and dis t r ibut ion var iab i l i ty a r e found as follows [4]. If the

* 99.5% puri ty - Publ isher .

M. V. Lomonosov Moscow State Univers i ty . T rans la t ed f r o m Poroshkovaya Metal lurgiya , No. 3 (1117, pp. 18-20, March, 1972. Original a r t i c l e submit ted October 8, 1970.

�9 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West I7th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

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: f }

2 4 5 8 p

i

0 2 3 4 5 ~r. g

Fig. 1 Fig. 2

Fig. 1. Distribution function in semilogar i thmic coordinates . An= number of par t ic les in fraction, r =par t ic le radius.

Fig. 2. Normal ized distribution function and corresponding exper i - mental points.

TABLE I. Correlation between Experimental and Theoretical Data with Assumed Exponential Distribution

Range Fraction Exptl. Theor. frequen- frequen- limit% p cies M i cies E i

0,65-- 1,25 1,25--2,50 2,50--3,75 3,75--5,00 5,00--6,25 6,25--7,50

I08,1 36,2 9,3 2,0 0,27 0,12

113 38,4 8,9 1,99 0,48 0,108

distribution function is given in the general form f ( r ) = a exp [ - a ( r - b ) ] , then r m e a n = b + l / a and o'2=1/a 2. In our case, rmean =0.65+ 1/1 .17=1.50 # and (~2=1/1.172=0.73.

6 X2 2 (M~:-- El)2 = E~ ~ 0.45.

i=l By means of re la t ively simple calculations, it is possible to obtain fur ther information regarding the cha rac t e r of par t ic le size

distribution. Let us determine, for example, the amount of par t ic les having radii not exceeding 2 #. For this determination, it is convenient to employ the integral distribution function, which is of the following form: F ( r ) = l - e -1"I7 (r-~ giving

P(r ~< 2) = F(2) ---- 1 - - e - 1.17 (~-0.65) ~_-- 0.80.

According to data yielded by sedimentometr ic analysis, the copper powder has 0.1% of part icles with radii g r ea t e r than 7 #, which is slightly more than would be expected f rom exponential distribution. This is probably due to incomplete disaggregat ion of the powder.

On the basis of the resul ts obtained, one conclusion may be drawn regarding the charac te r of the p r i m a r y par t ic le sys tem in the electrolyt ic copper powder. As the radii of the p r imary powder par t ic les a re distributed according to an exponential law, it is reasonable to assume that the sys tem is c h a r a c t e r - ized by the "absence of an af tereffect" [5] with regard to their l inear dimensions.

The resul tant mean par t ic le radius and distribution variabi l i ty are stable part icle size distribution charac te r i s t i c s of a powder. Their stabili ty is ensured by the part icle measurement method em- ployed, which involves determinat ions of p r ima ry powder par t ic le s izes . On the other hand, the mean radius and variabi l i ty meet the n e c e s s a r y requirements of mathemat ica l s tat is t ics for the evaluation of these pa rame te r s in the case of a general assemblage. Mathema- t ical s tat is t ics , too, test i fy to the exceptional stabili ty of mean values. In view of this, the mean radius and size distribution variabi l i ty de- termined by the technique descr ibed here may be recommended as stable technical cha rac te r i s t i c s of electrolyt ic copper powders.

C O N C L U S I O N S

1. It is demonstra ted that the p r imary par t ic le radius distribution of PM-1 electrolyt ic copper powder is an exponential one. The par t ic le size distr ibution of e lectrolyt ic copper powders can conveniently be charac te r i zed by means of a distr ibution function of the t y p e f ( r } =a exp [ - a ( r - b ) ] , where a and b a re ex- per imental ly determined constants.

2. The mean radius and distribution variabi l i ty may be recommended as stable technical c h a r a c t e r - is t ics of e lectrolyt ic copper powders.

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3. The p r i m a r y pa r t i c les of the e lec t ro ly t ic copper powder const i tute a s y s t e m cha rac t e r i z ed by the "absence of an a f te re f fec t" with re la t ion to the i r l inear d imens ions .

LITERATURE CITED

I. V.I. Kurinnoi and T. A. Komarova, "Aggregation of electrolytic copper powders," Sb. Tr. VZPI, No. 39, 80 (1967).

2. N. A Fi~rovskii, Sedimentometrie Analysis [in Russian], Izd-vo AN SSSR, Moscow-Leningrad (1948). 3. T.A. Komarova, V. I. Kurirmoi, and IN. A. Figurovskii, Poroshkovaya Met., No. I, 6 (1970). 4. G. Khan andS. Shapiro, Statistical Models in Engineering Problems [Russian translation], Mir, Mos-

cow (1969). 5. V. Feller, Introduction to the Theory of Probability and Its Applications [Russian translation], Vol. 2,

Mir, Moscow (1967), p. 21.

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