1552 CANADIAN JOURNAL O F PHYSlCS. VOL. 37. 1959

devient tr&s rapide ensuite entre les lirnites de 40 minutes et 80 ~ninutes de dCveloppement, le diamctre des grains est doublt., rnais leur noircissenlent est d6cuplC.

CONCLUSIONS

En sornrne dans ce premier travail nous avons obtenu quelques rksultats prCcis :

(1) Les grains exposCs sont affect& par le rkvklateur iinmkdiatenlent et leur diarn6tre augrnente relativeinent plus vite que dans le cas des grains non exposCs qui sont aussi dkveloppables apr&s u11 dkveloppernent Cnergique.

(2) Si on dkveloppe les plaques pendant longternps, dans I'espoir de voir les traces au minimum, on n'augrnente pas beaucoup le diain&tre des grains mais on rCduit forteinent la visibilitk des traces parce que le voile augineilte beaucoup plus rapidement. Ainsi les traces des basses Cnergies seront com- pl6tement saturkes. La meilleure visibilitk des traces est obtenue apr&s un dCveloppenlent rnoyen.

(3) Apr&s un certain teinps de di.veloppement, quand les traces sont clairernent visibles, le change~nent dans le noircisseinent des grains est beau- coup plus rapide que celui du diarn&tre des grains, de sorte que l'opacitk des grains augrnente sans que le diam6tre visuel paraisse augrnenter.

Nous reinercions le Professeur Pierre Demers pour son aide et son encou- ragement dans ce travail. Nous remercions I'adrninistration du Plan de Colombo au Pakistan et au Canada, et le Conseil National des Recherches pour leur aide financiPre.

AHMAD, I. 1958. These de doctoral, Universith de Mor~trCal, Montreal, Que. AHMAD, I. et DEMERS, J. 1959. Ann. Acfas (sous presse). ALV~AL, C. G. 1954. Nuovo cirnento, 12, 351. BERMOND, J. 1959. Phot. Corp. 11 (sous presse, Les I'resses universitaires de MontrGal). BERMOND, J. et SCHERER, h1. 1958. Phot. C0rp. I , 375. DEYEKS, P. 1958. Ionographie (Les I'resses Universitaires de MontrCal). DEMEKS, J. et DEMEKS, P. 1958. Ann. Acfas, 24.

1959. Phot. Corp. I1 (SOLIS presse).

DRIFT MOBILITY O F ELECTRONS I N ATOMIC HYDROGEN*

Considering the scattering of electrons by neutral hydrogen atoms to be spherical, Erginsoy (1950) has show11 that the time of relaxation T is given by

*Work supported by Armour Research Foundation, Chicago, Illinois, U.S.A. tArmour Research Foundation, Chicago 16, Illinois, U.S.A. $Physics Department, Allahabad University, Allahabad, U.P., India.

Can. J. Phys. Vol. 37 (1959)

Can

. J. P

hys.

Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

McM

aste

r U

nive

rsity

on

12/1

7/14

For

pers

onal

use

onl

y.

NOTES 1553

where Nn is the number of hydrogen atoms per unit volume, v is the velocity of the electron,

and Qo is the zero order partial cross section. If we introduce two new symbols,

and

( 3 QL = ~oln: ,

where a0 = h2/4.rr2mq2 is the first Bohr radius of bound electron, h is Planck's constant, q is the electronic charge,

and m the electronic mass,

we can express eq. ( 1 ) as

(4 7 = C/Y Q L , where

c = 8.rr3q%z2/1V,,h3.

Erginsoy (1950) noticed that for slow electrons ( y < 0.5)

and hence 7 = 6/20.

I t has been found that the expression

( 5 ) QL = 105/(344+2440y +7200y3)

adequately represents the variation of QL with y, theoreticallyTand numeri- cally obtained by Massey and Moiseiwitsch (1951). The fit isjillustrated in Table I. The last column also indicates the limits ofjvalidityzof Erginsoy's approximation.

TABLE I Fit of equation (7)

Q6

y Theor. Calc. eq. 7 YQ A

0.1 168 168 16.8 .15 138 136.1 20.7 .2 112 112.4 22.4

Can

. J. P

hys.

Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

McM

aste

r U

nive

rsity

on

12/1

7/14

For

pers

onal

use

onl

y.

1554 CANADIAN JOURNAL OF PHYSICS. VOL. 37. 1959

If we introduce a dimensionless variable

(6)

we obtain

(7) y = (h/2nq"(2koT/rn)*x = 2 . 5 1 6 6 ~ 1 0 - ~ ~ ~ x = Xx,

where ko is the Boltzmann constant, and T the temperature of the gas.

Now eqs. (4) and (5) give

The velocity distribution of electrons in weak electric fields is essentially Max\vellian given by

The drift mobility is given by

Fro111 eqs. (8), (9), and (10) we obtain

I t is seen that a t high temperatures p~ varies almost linearly with T. Table I also sho\vs the product yQ;. I t will be observed that up to y = 0.5 Erginsoy's relation yQb =: 20 is a good approximation.

The scattering due to ions and other electrons can be talcen into account by the approximate relation

P-l = Pgl+P;;

where p1.n is the illobility due to scattering by ions and other electrons, discussed by Sodha and Varshni (1958).

At high temperatures, contributions due to inelastic collisions of electrons with H atoins need also be taken into account. However, this will be a minor improvement because theoretical results (Massey 1956) show that the cross section for excitatioil of the 2s state of hydrogen is much smaller than the elastic cross section a t the saille energy.

ACKNOWLEDGMENTS

One of the authors (M. S. Sodha) is grateful to Dr. L. Reiffel and Dr. J. J. Brophy for ltiild encouragement.

Can

. J. P

hys.

Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

McM

aste

r U

nive

rsity

on

12/1

7/14

For

pers

onal

use

onl

y.

NOTES 1555

ERGINSOY, C. 1950. Phys. IZev. 79, 1013. MASSEY, I-I. S. W. and I \ ~ O I S E I ~ I T S C H , R. L. 1951. Proc. Iiov. Soc. (Lo~ldoli), A. 205. 48'3. MASSEY, H. S. W. 1956. Revs. Modern Phys. 28, 199. SODHA, M. S. and VARSIINI, Y. P. 1958. Phys. Rev. 111, 1203.

CELLULAR GROWTH IN TIN ALLOYS

Tiller et al. (1953), from a theoretical treatment of the distribution of solute ahead of a plane solid-liquid interface, predicted that cellular growth should occur when the following relationship was satisfied:

where G is the temperature gradient in the liquicl aheacl of a solid-licluicl interface,

X is the rate of growth, Co is the solute concentration, D is the diffusion coefficient in the liquicl, nz is the slope of the liquidus line,

and ko is the distribiltion coefficient.

The validity of the equation was established for face-centered cubic lead alloys by Tiller and Rutter (1956). The present investigation was undertalten to determine whether the equation predicted the onset of cellular growth for alloy systems with a solvent material other than face-centered cubic lead. Walt011 et al. (1955) found the equation to hold for lead in tin alloys, but these experiments alone were not considered sufficient to establish the effect of crystal structure. I t was also desirecl to determine whether the equation applied when ko was greater than unity.

The alloys investigated were made from zo~le-refilled tin with additio~ls of lead, bismuth, or allti~nony. The ko and m values for each solute in tin were obtained from published phase diagrams and are listecl in Table I.

TABLE 1 -

Alloying element in t ~ n k~ ni, "C/at.%

*I)eparttnent of hletallurgical Engineering, University of Toronto, 'I'oronto, Ontario.

Can. J. Phys. Vol. 37 (1959)

Can

. J. P

hys.

Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

McM

aste

r U

nive

rsity

on

12/1

7/14

For

pers

onal

use

onl

y.