The Vapor Pressures Op Alkali Halides by The
THE VAPOR PRESSURES OP ALKALI HALIDES
BY THE METHOD OP SURFACE IONIZATION
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of the Ohio State University
by
Henry Edwin Bridgers, B.S.
The Ohio State University
1953
Approved by i
TABLE OP CONTENTS
Page
List of Figures ii
List of Tables iii
I. Introduction 1
II. The Theory of Surface Ionization 5
III. Apparatus 23
IV. Experimental procedure 33
V. Results 50
VI. Discussion of Errors 65
VII. Summary of Results 68
Appendix 69
Bibliography 7 4
Acknowledgement 77
Autobiography 78
A 0 . 9 9 Q S ii
LIST OP FIGURES Page
1. Schematic diagram of experimental tube 24
2. Detail of Knudsen cell and oven 26
3. Photograph of apparatus 28
4« Rough electrical schematic 30
5. Richardson plot for electron emission 35
0. Calculated- work function vs. filament temperature 36
7. Ion current vs. filament temperature (oil pump) 36
8. Ion current vs. filament temperature (Kl) 41
9. Ion current vs. filament temperature (Ebl) 41
10. Logarithm of ion current vs. residual pressure 51
11. Vapor pressure of KI (this research) 53
12. Vapor pressure of KI (previous measurements) 54
13. Vapor pressure of Rbl 56 iii
LIST OP TABLES Page
1. Hecessary Work Function for 99^> Ionization 12
2. Degree of Conversion of Molecules to Ions 19
3* Variation of Electron Emission with Filament Temperature 38
4. Variation of Ion Current with Filament Temperature for Rbl Using Oil Pump 39
5» Variation of Ion Current with Filament Temperature for KI Using Mercury Pump 42
6. Variation of Ion Current with Filament Temperature for Rbl Using Mercury Pump 43
7. Variation of Ion Current with Pressure of Scattering Gas 50
8. Vapor Pressure of KI 52
9. Vapor Pressure of Rbl 55
10. Molecular Constants of KI and Rbl 58
11. Enthalpy and Entropy cf the Solid Salts 59
12. Heat of Sublimation of KI at the Absolute Zero (this research and data of Zimm and Mayer) 61
13* Heat of Sublimation of KI at the Absolute Zero (data of Cogin and Kimball and of Uiwa) 62
1 4 . Heat of Sublimation of Rbl at the Absolute Zero (this research and data of Niwa) 63 1
I. INTRODUCTION
Prior to 1944 the vapor pressures of the solid alkali halides had been studied by three investigators. Deitz'*', employing an electromagnetic manometer, measured the vapor pressure of Csl 2 3 and of KC1; Niwa , using the method of Knudsen , measured the vapor pressures of LiCl, NaCl, KC1, RbCl, CsCl, NaF, KF, NaBr, KBr,
CsBr, lLlf and Rbl over a limited temperature interval; Mayer 4 and Wintner , who also employed Knudsen's method, determined the vapor pressures of NaCl, KC1, RbCl, NaBr, KBr, and RbBr. 5 Langmuir and Kingdon observed that a tungsten filament heated in the presence of cesium vapor produced cesium ions which could be collected by a suitable electrode. If the filament temperature is raised above a critical value which depends on the pressure of cesium vapor, they found that the ion current is practically independent of the filament temperature. These authors concluded that above this critical temperature every cesium atom which struck the filament was ionized. These same phenomena were observed by Killian^ for potassium and rubidium 7 and by Morgulis for sodium on an oxygen-coated tungsten filament.
Since every atom which strikes the filament is ionized, it is possible to calculate from the observed ion currents the vapor pressures of the alkali metals. The theory of thermal ioniza tion, whicia was first presented by Saha in a series of three papers^’^* ^ and amended for this particular application by 5 I"1 Langmuir , will be developed in the next section. Taylor *■, investigating molecular beams of the alkali metals, used this surface ionization on tungsten as a detector. 12 Eodebush and Henry observed that positive ions of the alkali metals are produced when a beam of alkali halide molecules falls on a hot tungsten filament. They concluded that the alkali halide molecule is first dissociated on the incandescent surface and the alkali metal atom produced is subsequently ionized.
Copley and Phipps‘S and Hendricks‘S continued the investigation of the surface ionization of alkali halide molecules. They found that if the filament is cleaned by flashing to a high temperature in a good vacuum, free of oxygen, the ion current increases as the filament temperature is lowered until a critical value of the temperature is reached where the current decreases rapidly to zero. If the filament is coated with a film of oxygen, the ion current is practically independent of the filament temperature at temperatures above the same lower critical value. If the temperature is raised above 1800 °K, where the oxygen layer begins to strip off, the ion current is observed to decrease gradually.
In this latter case of an oxygen-coated tungsten filament, a plot of ion current versus filament temperature shows a steep increase in ion current, at the critical temperature, to a maximum value which persists over a broad plateau. The plateau is followed by a gradual decrease of ion current upon loss of the oxygen coating. 5 This behavior is analogous to that reported by Langmuir for cesium 3
6 and by Killian for potassium and rubidium on an oxygen-coated filament. In the region of the broad plateau Copley‘S concluded that, not only does every atom of alkali metal produced on the filament surface ionize, but also the extent of dissociation of the alkali halide molecule is effectively complete. When the ion current shows temperature dependence, it is concluded that the work function of the metal is too low for complete ionization of the metal atoms produced. The observations of Copley et a l . ^ ’^ give curves similar to those shown in Figure 7»
Zimm and Mayer15 combined the method of Knudsen 3 and the phenomena observed by Copley^ to measure the vapor pressures of
Had, KOI, KBr, and KI. A suitably collimated beam of alkali halide molecules from a Knudsen oven was allowed to impinge on a tungsten filament whose work function had been increased by adsorption of an oxygen film. The ions produced by dissociation and ionization on the filament wefce collected by a metal cylinder arranged coaxially with the filament and measured by a suitable galvanometer. If the filament conditions, i.e. its temperature and work function, were so adjusted that the ion current was in the region of the afore-mentioned plateau, then every alkali halide molecule which struck the filament produced a positive ion.
From the geometry of the apparatus, the ion current, and the Knudsen cell temperature, the vapor jaessure of the alkali halide at the temperature of the Knudsen cell could be calculated from gas kinetics. Cogin and Kimball'*'*’ employed this method to measure the vapor pressures of CsCl, NaBr, CsBr, Nal, KI, and Csl.
This is an elegant method for the measurement of vapor pressures hut unfortunately it is limited to alkali metal compounds having sufficiently low dissociation energies and probably not including compounds of lithium which has a rather high ioniza tion potential (5*36 v). The method is very sensitive, thus permitting the measurement of low vapor pressures with relative ease. The method affords instantaneous measurements as compared with the conventional Knudsen method, where a single measurement must be made over a prolonged period, during which the cell temperature must remain constant. The rapidity of the method permits more measurements with a given sample and therefore greater reliability. It is possible to measure the vapor pressure at a given temperature several times after repeatedly heating and cooling the charge. In this fashion a guarantee of the constancy of composition of the sample is obtained.
In the present investigation the vapor pressures of KI and
Rbl have been determined by the method of surface ionization over the temperature range TOO - $00 °K. II. THE THEORY OP SURFACE IONIZATION
Consider the ionization of a metal atom, M, effected thermally on an incandescent tungsten filament. Following Langmuir 5 17 and 18 Reimann let us assume that in close proximity to the filament surface, i.e. at the reaction scene, neutral atoms and ions as well as electrons are in equilibrium with the filament and with each other in accordance with the following equation,
M = M + + e(in metal). (l)
This assumption applies even in the presence of an electron retarding or ion collecting field. ¥/e shall further assume that the accommodation coefficients of metal atoms, metal ions, and electrons are all unity. This has been shown to be the case for cesium on tungsten* 19 .
The equilibrium constant for reaction (l) is given by
Kp - (PM+)(Pe ^ (PM) “ e*P(-4F°/RTf) (2 ) where the P's refer to the partial pressures of the reactant and products at the temperature of the filament, ^F° is the standard free energy change of the reaction, R is the gas constant, and T^ is the filament temperature in degrees Kelvin, with the above assumption of unit accommodation coefficient and by application of gas kinetics it is possible to relate the pressure of electrons to the electron current density, as whore ig is the electron current density in amperes per cm ,
M is the molecular weight of electrons in grams per mole, R is the gas constant in ergs per mole per degree, H is the filament temperature in degrees Kelvin, F is the Faraday constant in coulombs per mole, and P 6 is the partial pressure of electrons 2 in dynes per cm . The current density of electrons is given by 18 20 21 the Richardson-Dushman equation ’ ’ as
ie = U-r)AoTf2exp(-0o/kTf), (4) in which r is the reflection coefficient, is the work function, and A q , the thermionic emission coefficient, has the theoretical value
(41) A O = (41tta 6k2e/h3) s 120.1 amp/cm2/deg2.
Equation (4) is suitable for clean "ideal" metals like tungsten but does not represent the electron emission from metals having an adsorbed layer of foreign atoms or ions. In all of the following discussion we shall incorporate into a new parameter 0, called the "calculated work function", any departure of the reflection coefficient from zero and also any departure of the emission constant from the theoretical value A . In accordance with o 15 the above and following Mayer , the electron current density is given by
ie - (4 TTmek2e/h3) Tf2exp(-0/kTf) , (4") where 0, the calculated work function, is dependent on the temperature,, on the surface contaminant, and on the concentration of the oontaminant. This device is used because the resulting expressions are simpler. The important feature for our purposes is that, in reaction (l), the electron partial pressure, which is determined predominately by electron emission from the filament, tends to suppress the ionization of an alkali metal on the filament. it does not matter by what device this electron concentration is 22^26 expressed. The papers of Johnson et al. ” throw considerable light on the true state of affairs on an oxygen-coated tungsten filament.
By an application of statistical thermodynamics, the standard o free energy change, AF may be expressed in terms of the appropriate partition functions as
A F ° - I - HTf ln[(27rmekTf/h2)3/2kTf(f+ £e/fo)], (5) where I is the ionization potential of the alkali metal, mg is the electronic mass, k is Boltzmann's constant, h is Planck's quantum of action, and the f's are the internal partition functions of ions, electrons, and atoms respectively. Two possible spin orientations in a magnetic field resulting in two-fold degeneracy is the only factor in f . The electronic partition function of the 6 atom and of the ion are of the form,
f = + Z . S± exp(- B^kTj), (6) where the g's denote the aegeeeracies and the the energies of the various electronic levels measured with respect to the ground level.
If we neglect any electronic excitation, then the partition functions become simply the degeneracy factors of the ground level.
This approximation is satisfactory for the alkali metals. The
ground level of the alkali metals is doubly degenerate and for
their ions it is non-degenerate. V/ith these considerations
equation (5 ) becomes,
^ P ° - I - RTf ln[(2TrmekTf/h2)3/2(kTf)]. (7)
How by combining equations (2 ), (3 ), (4")» and- (7) one obtains
the following expression for the ratio of the equilibrium pressure
of ions to that of neutral atoms which is had for reaction (l)
at the temperature T^,
PM+ /?M = * ®XP^ " I)/WJf
This is known as the modified Saha equation. Since the mass of
the atom and of the ion may be taken as the same, equation (8) is
also the ratio of the number of ions which leave unit area of the
filament in unit time to that number of atoms. The degree of
ionization may be defined
= .a+/(ao+ z+) = [1 + 2 exp(l - jZO/kT^"1, (9) where the z's are the numbers which leave unit area of the filament
in unit time. The quantity (z q+ Z*.) is the total number of alkali metal atoms which strike unit area of the filament in unit time
and is therefore dependent only on the pressure and temperature
of the metal vapor. Z+ is the number of ions which leave unit
area of the filament in unit time and is proportional to the ion current which would be observed. We may therefore write for the ion current, at constant (Zq + Z+),
i+ = const./[ 1+ 2 exp(l - 0)kTf]. (10)
On taking the logarithm of equation (10) we obtain
In i+ = In const. - ln[l + 2 oxp(l - 0)/kTf]. (ll)
Now let us consider two extreme cases in interpreting this equation.
Case It > I
This is the oase for cesium, rubidium, and potassium on tungsten and for sodium on oxygen-coated tungsten, provided the filament tempera ture is sufficiently high that alkali metal ions do not remain on the .tungsten surface, thereby lowering its work function. We may assume the exponential term in (ll) is small compared to unity and expand the logarithm. Neglecting terms of order higher than the first, one obtains
In i+ = In const. - 2 exp(l - 0)/kTf. (12)
This equation indicates that the logarithm of the ion current increases exponentially with the reciprocal of the filament tempera ture. The greater the difference between the work function and the ionization potential the more rapidly the logarithm approaches its asympototic value. If this difference were so great that the expo nential term might be neglected entirely, one would observe ion currents which are independent of the filament temperature over a wide range of temperature. 10
Case II: 0 < I
If the filament temperature were reduced to the point where the rate of desorption of metal ions is less than the rate at which they are produced, then there will be an accumulation of metal ions on the
surfaoe and a consequent abrupt decrease in the work function. The temperature at whioh this phenomenon occurs is critical ’ and depends on the rate at whioh metal atoms are supplied to the filament. When the rate at which atoms strike the filament exceeds the rate of evaporation of atoms and ions, accumulation on the surfaoe will ooour. The resulting value of the calculated woi?k function is of the order of 1 volt for a layer of alkali metal on tungsten.
This being considerably less than the ionization potentials of the alkali, metals, the exponential term in equation (ll) may be taken as large compared to unity. In this case we write for the logarithm of the ion current
In i+ = In const. - (I - 0)/kTf. (13)
Thus at temperatures less than the critical temperature the logarithm of the ion current decreases linearly with the reciprocal temperature.
Experimental observation of the ion current produced on a tungsten filament immersed in alkali metal vapor has been shown to be in cpmplete agreement with the theory 5 6 • Since at higher temperatures large photoelectric currents are observed and make the ion current measurements difficult, only the asymptote or "plateau" g was observed in the region where Case I applies. Although Killian 11 reported that further inorease in the temperature above the critical ' 27 value led to 100$ ionization, Copley and Phipps , using- a molecular beam technique, were able to extend the temperature range for potassium and verified the theoretical prediction of an exponential decay of In i+ with decreasing l/T^. The change in ji at the critical temperature is so rapid that no intermediate case is observed, i.e. the case where 0 and I might be comparable. In any event equation (ll) for the general case will apply.
In the case of oxygen-coated tungsten, which has a calculated work function, over the temperature range of interest, of from 5 to 6 volts, it has been observed that the oxygen layer strips off the filament over the temperature range 1800-2000 °K. This leads to a gradual reduction in the work function, the lower limit of which is of course the value for clean tungsten, 4 .5 volts. When this occurs 0 is quite temperature dependent and equation (12) is no longer applicable; however, when this stripping begins the logarithm of the ion current should continue to decrease mono- tonioally, but ever more rapidly, with decreasing reciprocal temp erature until a clean tungsten surface is reached, at which point a simple exponential decay is resumed but with the work function for clean tungsten.
In equation (9) one may set a 99$ and solve for the values of 0 required to ionize 99$ of the metal at various temperatures.
This has been done for potassium (X - 4*34 volts) and for rubidium 12
(I = 4*16 volts) and the results are tabulated in Table 1. For filament temperatures in the range 1600-1900 °K, a work function of approximately 5*2 volts is sufficient to ionize 99$ of rubidium or potassium present. This particular range of temperature is pointed out because ion current measurements in this investigation, to be described later, were made in that range.
Table 1.
Necessary Work Function 0, for 99$ Ionization
Filament Work Function Temperature volts o7. K Hb
1000 4 .8O 4 .6 2 1100 4 .8 4 4*66 1200 4.89 4.71 1300 4*93 4-75 1400 4.98 4.80 1500 5.02 4 .8 4 1600 5.07 4.89 1700 5.12 4.94 1800 5 .1 6 4-98 1900 5.21 5.03 2000 5 .2 5 5-07
If the metal atoms, which undergo reaction (l), are products of the dissociation of an alkali halide molecule on the filament, then, in addition to (l), the following dissociation equilibrium must be considered,
MX(g) a M(g) + X(g). (14)
The equilibrium constant for this process in terms of the partial pressures of reactant and products, is 13
Kp = PMPX/PMX = « p ( - A * ,0/ka?f). (15)
It is convenient to discuss this equilibrium in terms of the number of a given species which strike or leave unit area of the filament in unit time. To relate the partial pressures to these numbers we must assume that the accommodation coefficient of each species is unity. This assumption has been shown to be valid for cesium on 19 28 29 tungsten , for hydrogen on tungsten , and for chlorine on tungsten , but it is not valid for hydrocarbons on tungsten 28 . Zimm and
Mayer15 conclude that, in general, one may assume an accommodation coefficient of unity for those vapors which are chemisorbed on the surface. Where only van der Waals forces enter into the binding one observes a small accommodation coefficient. Since the alkali halides are strong dipoles, there are large image forces between the molecule and the metal surface of the filament. On that basis 15 one might expect the accommodation coefficient to be close to unity .
With the assumption of unit accommodation coefficients, equation (1 5) becomes
KP = ( V x ^ m ^ ^ T f ) ^ * exp(-AF°/kTf), (16) where the number of metal atoms leaving unit area of the filament in unit time is denoted by z q, the corresponding number of halide atoms and of alkali halide molecules by z and z respectively, and x m 7 the reduced mass of the molecule- by^M. The equilibria stated in equations (l) and (1 4 ) must coexist on the filament, and therefore 14 it followed from equation (8) that
= s+ [2 exp(I - 0)/kTf], (17) where z+ is the number of metal ions leaving unit area of the filament in unit time. From the conservation of mass it follows* that
(18)
A where z is the number of alkali halide molecules that strike unit area of the filament in unit time. This latter number can be related to the pressure and temperature of a solid sample of the alkali halide situated, remote from the filament, in a Knudsen cell from whioh a collimated beam of alkali halide molecules strikes the filament. This number is
z* - g p (27TmmkT)"^, (19) where p is the vapor pressure of the solid salt at the temperature T, m^ is the molecular mass and g is a dimensionless geometric parameter which will be discussed later. From equations (19) and (18) the number flow of halide atoms may be written,
z>x - z+ [1 + 2 exp (I - 0)/kTf] = (z^/o^). (20)
Inserting equations (17) > (l8)» and (20) into equation (16), we obtain for the equilibrium constant,
Kp = z+2 (27r/ikTf)2 2 exp( I - 0)/kTf
a^z - z
- exp(- AF°/kTf), (21) 15 where is the degree of ionization defined as
(9)
From statistical thermodynamics we obtain for the free energy change of the reaction,
^ F ° = D - kTf ln[(2TT/
Further let us assume that the vibrational and rotational degrees of freedom are fully excited over the temperature range. With these assumptions the quotient of internal partition functions becomes
(23) where co is the vibrational wave number of the molecule and r is o the equilibrium internuclear separation. From equations (22) and
(2 3 ) we obtain for the equilibrium constant
= (2c«j/7rr2)(2 7I^ka?f)^ exp(-D/kTf). (24)
Substituting (2 4 ) into (2l), rearranging, and solving for z+, we obtain for the positive root 16
- (cw/277r^)exp(^-I-D)/kTf [-1
+ £l + 2aiz*(23fr^/oa))exp(^-I-D)/kTfj^3* (25)
The term on the right in the curly bracket is very small compared 2 o 6 to unity, being of the order 10“ at 1100 K and only 10“ at
1900 °K. Expanding the square root and neglecting all but the first three terms, we obtain
z+ s z*ai[l - z*di2exp(l-^)/kTf,(^'r^/2c-!o)exp(D/kT:f)]. (26)
Thus the number of alkali metal ions leaving unit area of the filament in unit time is equal to the number of alkali halide molecules which strike unit area of the filament in unit time multiplied by the degree of ionization and by the square bracketted term above. This term can be shown to be approximately equal to the degree of dissociation as defined by
ad = zx/z* = zx/{zx + zm). (2 7)
Remembering the definition of the degree of ionization, (9)> and equations (16) and (2 4 )» the square bracketted term of equation (26) can be put in the form
L1 “ z*(zm/zx2)J* (28)
Using equation (18), the degree of dissociation as defined in (27), can be put in the form
z ii m (29) z {l - (z /z ) - (z /z )2\ _ x * N,m/ x/ vm/x/J The ratio of the number of undissociated molecules leaving the filament to the number of halide atoms leaving is small compared to unity. If we neglect this ratio and its square in the denominator of (2 9) the degree of dissociation may be written approximately as
(30)
Comparison of (28) and (30) indicates that we may write the ion-current density approximately as
i* = ez. a ez a.a,. * + i d ’ (31) where e is the fundamental electronic charge. Using equation (19) Ac for z , this becomes
(32)
To convert this to ion current, we simply multiply by the area of the filament which is struck by the alkali halide molecular beam.
The vapor pressure of the solid alkali halide may be determined by measurement of the ion current and the Knudsen cell temperature, provided the magnitude of the product, (a^a^), is known. Solving
(32) for the vapor pressure and substituting for the value given in (26), we obtain
(27TmmkT)^ i+/eg P • (33)
ai[l - z*a^(Ttr^/2cio)exp(D/kT;p) . 2exp(l-^)/kTf,..
Neglecting powers of z greater than the first, this becomes, 18 on division,
P r (27TmmkT)^ i+/eg [l + 2exp(I-0)/kTp
z*(TTr^/2oo))exp(D/kTf) • 2exp(l-0)/kTf...]. (34)
For the vapor pressure determination, ion-current measurements were made, at constant cell temperature, over a filament tempera ture range of 1600 to 1900 °K. From observed electron emission currents, the calculated work function over this range was always in excess of 5*8 volts. Since the conversion of molecules is £ practically complete, we may replace z , in the last term of (3 4 )> by i+/e — z+ and in particular by the maximum value observed, corresponding to the highest cell temperature investigated. Using this value for z , the minimum value of 5 .8 volts for 0 , and suitable values for rQ and a?, we may calculate the term in square brackets in (34)• The resulting value is the most unfavorable that would be realized under the conditions of the experiment.
This has been done for both KI and Rbl at several filament temperatures and the results are tabulated in Table 2. For KI,
valuear for r 0 and m) are taken from Herzberg^s 0 7 for Rbl, 7 r o is 31 32 taken from Verwey and de Boer and U) is taken from Gordy .
Values for the dissociation energies were taken from Herzberg^.
From an inspection of Table 2, it is apparent that the conversion of molecules to ions is effectively complete. The departure from completion is so slight that within the precision of measurement of the ion—current density, the factor (a^a^) in equation (32) may be neglected. The observed ion current does indeed show an independence of filament temperature over a wide range as can be seen in Figure 8 and 9*
It is of interest to note that at the lower temperatures, where ionization is more nearly complete, the extent of the dissociation is the predominant factor in the departure of the conversion from completion. At the higher temperatures, where dissociation is more nearly complete, the degree of ionization lowers the extent of conversion. Due to these two opposing effect the product which is the degree of conversion of molecules t ions, exhibits a maximum.
Table 2 o T K f l/(aiad)
KI Rbl
1100 1.000037 1.000005 1300 1.000006 1,000001 1500 1.000024 1.000006 1700 1.000092 1.000027 1900 1.000263 1.000087
Assuming that the conversion to ions is complete, the vapor pressure of solid alkali halide is given by,
(35) where I+ is the ion current and A is the plane projected area of the filament on which the molecular beam deposits.
Since the molecular beam suffers some scattering by the 20
residual gases in the system, the observed ion current is corrected
for this loss before its insertion into equation (35)* To make this
correction, the following relation between the observed and the
correct current is assumed,
IQ = 1+ exp(-L/L')« (36)
In this equation Iq is the observed ion current, I + is the ion
current in the absence of gas scattering, L is the path length of
the molecular beam, and L' is the mean free path. Assuming the mean free path proportional to the residual pressure, the corrected
ion current can be written as
1+ = IQ exp(bP). (37)
The constant b, can be determined empirically by plotting the
logarithm of the observed ion current, at a given cell temperature,
versus the residual pressure and obtaining the slope. Equation (37)
is then used to correct observed ion currents for gas scattering.
The variation in ion current with residual pressure is shown in
Figure 10, the data for which is tabulated in Table 7*
The geometric parameter, g, introduced in equation (19)j arises
because the area of the filament, on which the molecular beam deposits,
is remote from the point source of the beam. Knudsen's equation
gives the total number of molecules issuing in all directions and
at all speeds from unit area of the effusion aperture. Of these,
only those molecules whose velocities lie within a small solid angle,
defined by the collimating system, will strike the filament. 21
In the Knudsen cell, with a oiroular aperture of area 2 S - IT r , the following equilibrium is assumed to exist,
MX (solid) = MX (vapor). (38)
Let us assume that the pressure of MX (vapor) external to the oell is negligible and that the aperture radius, r, is sufficiently small compared to the mean free path as to permit undisturbed molecular flow through the aperture. The number of molecules with velocities lying in the range from C to C + dC, which cross an element ds of the aperture area S in time dt, is
n Taking the outward normal to the area S as the polar direction and the origin at the center of S, equation (39) becomes in spherical polar coordinates c cos© f c sin© d© d0 do dt ds, (4°) where c is the radial speed. At a point, lying on the normal to and at a distance R from the aperture, the number striking unit area, parallel to S, in unit time is obtained by integrating equation (4 0 ) over all radial speeds, over all azimuthal angles 0, over the area S, over unit time, and over the latitudinal angle © from zero to an upper limit set by the distance R. If R is large 22 compared to the dimensions of the filament area on which the beam deposits, then the upper limit on 6 is given approximately by 1 arcsin (I/TT^R). Carrying out the above integration, the following expression is obtained for the number of molecules striking unit area of the filament in unit time, z* = p (277mmkT)“^(r/R)2. (4l) Comparing equations (4 1 ) and. (19) the parameter g is the square of the ratio of the Knudsen cell aperture radius to the distance of the filament from the aperture. 23 III. APPARATUS The experimental tube, illustrated schematically in Figure 1, consisted essentially of two compartments, one housing the source of a molecular beam and the other the filament and collector assembly. The tube was evacuated through a liquid nitrogen cold trap and a ground glass valve by a two-stage mercury diffusion pump. The diffusion pump was backed, through a dry ice cold trap, by a Duo-Seal mechanical pump. The residual gas pressure was measured with a VG-1A ionization gauge, located close to the filament assembly. In order to treat the filament with oxygen or fluorine gas, a suitable gas handling system connected to the experimental tube through a metal needle valve. With the filament and oven operating, the ultimate vacuum attainable was approxi- - 7 mately 3 x 10 mm of mercury. When the oven was operated at higher temperatures the pressure ranged from the above value to approximately 1 x 10”*^mm of mercury. As shown in Figure 1, both the oven assembly and the filament-collector assembly were attached to the experimental tube by standard-taper ground-glass joints, A, which were sealed by Apiezon-W black wax. These waxed joints were water-cooled by turns of Tygon tubing wrapped tightly about the exterior of the joints. A tungsten filament, I, was supported by tungsten wires, N, which entered the tube through a uranium-glass press seal, B. Slack in the filament was taken up by a tungsten spring, M, 24 A Standard taper glass joints B Tungsten to glass seals p _ C Capillary tubing for thermocouple D Quartz tube for oven support E Knudsen cell F Monel heat shield B B G Magnetically actuated glass shutter H Nickel diaphram I Tungsten filament (0.024 cm. diam.) J Cylindrical nickel guard ring K Cylindrical nickel collector L Collector aperture (0.110 cm. diam.) M Coiled tungsten spring N Tungsten electrode supports Y Graded seal: quartz to pyrex EG Thermocouple leads£=> -To heater supply^ H " . r Figure 1. Schematic Diagram of Experimental Tube. To cold trap and pumps I 25 designed after Blodgett and Langmuir^. The filament diameter was measured by weighing a known length and found to be 0.0230 ± 0.0002 cm. A cylindrical nickel collector, K, 0.5 " I.D. and 2 cm. in length, and two nickel guard rings, J, 0.5 ’’ I.D. and 1 cm. long, were supported by tungsten wires, H, which entered the tube through tungsten-pyrex seals, B. The guard rings were connected to an electrical ground and the collector was connected to the input of a D.C. amplifier. The collector was pierced by a circular aperture, L, which permitted the molecular beam from the Knudsen cell to strike the filament. The diameter of this aperture was measured with a traveling microscope and found to be 0.110 ± 0.0005 cm. Situated between the collector and the Knudsen cell were a nickel diaphragm, H, with a 0.125 " circular aperture, and a glass shutter, G, which could be actuated by an external magnet so as to interrupt the molecular beam. The oven assembly was mounted about a quartz tube, D, on the interior of which was located the Knudsen cell, B. The quartz tube was attached to the vacuum wall via a quartz-pyrex graded seal, I. The oven-heater leads were tungsten-pyrex seals, B, while the thermocouple wires were taken out through pyrex capillaries, C, which were sealed with Apiezon-W. Details of the oven and Knudsen cell are shown in Figure 2, approximately to scale. The heat shield consisted of a monel tube, F, with niokel ends, S, and was both held in position by and electrically attached to one of the heater leads, W. This 26 Figure 2. Detail of Knudsen Cell and Oven. TF7 F D Quartz tube for oven support E Knudsen cell F Monel heat shield 0 Nickel plug with tapered thread P Cromel - alum el-P junction imbedded in nickel slug Q Powdered sample of alkali halide R Nichrome ribbon heater winding S Machined nickel supports for heat shield T Quartz anchor posts for heater winding U Pyrex insulating sleeves V Thermocouple wires W Nickel heater leads X Knudsen cell aperture (0.098 cm. diam.) is not shown in Figure 2. The heat shield, the Knudsen cell, and the diaphragm were electrically grounded. The oven heater consisted of nichrome ribbon, R, wound about the quartz tube and anchored at both ends to quartz posts, T. The Knudsen cell, E, was machined from nickel and consisted of a tube closed at one end except for a small aperture, X, and threaded at the other end to accept a nickel plug, 0. The diameter of the cell aperture was measured by traveling microscope and found to be 0.098 ± 0.0005 cm. It was so machined as to have 45 degree knife edges. The tapered plug, 0, was drilled to accept a nickel slug, P, in which was imbedded the hot junction of a Chromel-Alumel-P thermocouple. The thermocouple wires were insulated from each other by pyrex capillary, U. The cold junction was kept in a dewar filled with crushed ice in such a fashion that a head of ice always kept the junction in an intimate mixture of ice and water. Prior to the experimental measurements the thermocouple was compared with a Platinum vs. Platinum-lO^Rhodium thermocouple which had been compared with samples of tin, zinc, aluminum, and copper from the Rational Bureau of Standards. Thermocouple potentials were measured with a Leeds and Northrup Portable Precision Potentiometer. After the vapor pressure measurements were completed, a National Bureau of Standards sample of zinc was placed in the cell and a melting point obtained in situ. A temperature correction, obtained from this melting point, was applied to all observed thermocouple Figure 3. Photograph, of Apparatus. 29 temperatures. This will be discussed at greater length in a later section. A photograph of the complete experimental arrangement is shown in Figure 3» Lead storage batteries, across which a "trickle charge" was maintained by a Tungar battery charger, supplied the oven-heater windings. By means of series resistance, the heater input could be varied from 10 to 60 watts, corresponding approx imately to a temperature range of from 700 to 900 °K. By maintain ing a given input for about one hour, the temperature drift was o less than 0.5 K per hour. The essential features of the filament and collector circuits are shown schematically in Figure 4» Lead storage batteries were used to supply the filament, I, through suitable series resistance. By means of appropriate battery combinations and the variable series resistance, it was possible to vary the filament input from 0.35 "to 140 watts, corresponding approximately to a filament temperature range of from 900 to 2900 °K. The highest temperatures were employed only for cleaning and degassing purposes. The filament was cleaned by flashing and the collector assembly was degassed by electron bombardment. The filament current and voltage were measured by suitable meters and from the power dissipated by the filament, its temperature was determined from the tables of Jones and Langmuir^, in the following way. From the filament current and its diameter an approximate value for the temperature was obtained by graphic interpolation of 30 Figure 4 Hough Electrical Schematic [JH FP-54 12V Electrons 18V Ions Potentiometer 0 - 180 V 31 the Jones-Langmuir function A 1. This value was used to correct the observed filament voltage for cooling at the ends, by employing an empirical equation of Jones and Langmuir 35 . From the corrected filament voltage, the filament current, and the filament length, the Jones-Langmuir function (,V*A' v \ ) was obtained. Interpolation of this function gave a final value for the filament temperature. The accuracy of the filament temperature will be discussed in a later section. As shown in Figure 4 , the collector and guard rings were at ground potential and the filament potential was adjusted such that ions or electrons were recaved by the collector. This potential was always adjusted to insure that saturated ion currents were collected. No extrapolation to zero-collecting potential was made as the saturated ion currents were independent of collecting potential, within the accuracy to which they were measured. Detection of the collector currents was accomplished by means of a null- amplifier employing a General Electric FP-54 tetrode. The amplifier circuit and the method of zeroing were essentially those of DuBridge and Brown^. A bucking potential inserted in the grid circuit was so adjusted, for a given collector current, as to maintain zero galvanometer deflection. This bucking voltage was taken from the E.M.F. terminals of a Rubicon High Precision Type B Potentiometer. The potentials of the control grid, the space charge grid, and the plate, with respect to the negative side of the cathode, as measured by a vacuum-tube voltmeter, were -3 *0 , 4 »3> and 6.1 volts respectively. 32 g Using a grid resistor, H , of 1.06 x 10 ohms and a taut suspension §3 Rubicon galvanometer, 0, whose sensitivity was 1.7 x 10 -9 ampere -12 per mm deflection, the amplifier sensitivity was 1.1 x 10 ampere per mm. The advantages of the null method are its independence of galvanometer and amplifier characteristics. By means of a shorting switoh, the amplifier input could be grounded and its balance point, or zero, adjusted prior to each current measurement. In this fashion the accuracy of the observed current is dependent only on the accuracies with which the input resistor and the bucking potential are known, provided, of course, the amplifier sensitivity is sufficient. For measuring larger currents, a smaller grid g resistor, of 1.00 x 10 ohms, was used. The amplifier tube and input resistor were enclosed in a brass tube and situated as close as possible to the collector to minimize "pick-up" and capacitive effects. The amplifier circuitry was carefully shielded and the collector assembly was shielded with wire gauze externally. Leakage paths in shunt with the amplifier input were measured with a source of high voltage and a sensitive galvanometer and found to be in excess of 3 x 10 ^ ohms. A periodic check of the amplifier sensitivity was made to insure that these conditions were maintained. The amplifier was not used to measure the higher electron currents. These were shunted to ground through a 1000 ohm resistor and the potential developed across this resistor was measured with a potentiometer. The entire detector circuit proved to be very stable, it being necessary to rebalance the amplifier zero only occasionally. 33 IV. EXPERIMENTAL PROCEDURE Prior to a discussion of the experimental procedure which led to the vapor pressure results of Section V., it is considered appropriate to devote some attention to experimental observations made before the afore—mentioned procedure was established. These observations have no direct bearing on the final vapor pressure measurement, but they led to modifications in design, without which the final measurements would not have been possible. When the apparatus was first assembled, a three stage oil diffusion pump was used instead of the mercury pump employed in the final design. This was done because a fast mercury pump was not immediately available. It was suspected that decomposition products from the pump fluid (Octoil-S) might diffuse past the liquid nitrogen cold trap and affect electron emission. According to the theory, this could be tolerated, provided that the effect was to reduce the electron emission or, in other words, to raise the calculated work function. A preliminary check indicated that the calculated work function was approximately 5.5 volts when the filament was coated with either fluorine or _7 oxygen. A pressure of 2 x 10 mm of mercury was attainable after a brief pump down. In view of these facts, the oil pump was retained and measurements of the vapor peessure of KI begun. 15 16 At filament temperatures used by earlier investigators , ion currents were measured at several cell temperatures. The vapor pressures obtained from these agreed rather well with the work of Zimm and Mayer15 . No careful observation of the dependence of ion current on filament temperature was made in these initial measure ments on KI, as they were performed chiefly as a check on the apparatus. Without further ado, measurements were begun on Rbl. Since the vapor pressure of Rbl had never been determined by this method an attempt was made to establish the expected ion current independence of filament temperature. The observed behavior was quite to the contrary. The ion current increased steadily with decreasing filament temperature until a critical value of tempera ture was reached, at which point the ion current dropped rapidly to zero. This behavior was much like that reported by Copley 13,14 and Phipps , except that their observations were made with a tungsten filament which was free of oxygen. They explained their results on the basis that the work function was too low to permit complete ionization. Electron emission measurements made con jointly with the above Rbl ion measurements indicated that the degree of ionization should be better than Considerable experimentation was conducted, under a variety of filament conditions, and the above ion current behavior was always observed. The filament conditions, referred to above, dealt with the extent and nature of treatment with both oxygen and fluorine, and with the extent of exposure to vapors from the oil pump, with and without a cold trap. Characteristic observations are shown in Figures 5> 6, and 7 for two extremes of filament treatment. In — Clean tungsten (Jones-L angm uir) o Mercury pump - residual pressure 4xl0~7mm. Hg x Octoil-S pump - residual pressure 4 x IO"7mm Hg - 9 • Octoil-S pump—oxygen pressure I x I0”5 mm. Hg a. e-io = -12 Ll_ H* Q. -15 vjt c+ w -17 - o> 4.5 5 0 5.5 Reciprocal Filament Temperature °K_I x I04 36 7*6-5 Figure 6. Calculated Work Function vs. Filament Temperature o c ^ 60 o £ ■o • Oil pump-oxygen pressure I x 10' 0) mm. Hg oHg pump - residual gas pressure 3 _o 55 4x 10" 7 mm. Hg o x Oil pumpr- residual gas pressure 4xl0"'7 mm. Hg o i I I 1 I I I I L L 1.0 Figure 7« Ion Current vs. Filament Temperature • Oil pump - oxygen pressure I x I0"5 mm. Hg | 08 x Oil pump -residual gas pressure 4xl0'7 mm.Hg 3 o Plateau from mercury pump data c Cell temperature 787° K o 0.6 S 0 . 4 c QJ 3 o § 0.2 1200 1400 1600 1800 2000 Filament Temperature °K / 37 one oase the filament was flashed to a high temperature (approxi mately 2800 °K) for a few minutes, with liquid nitrogen cold traps, and then electron and ion currents measured as a function of filament temperature. In the other case, after cleaning the filament in the same way, it was exposed to an oxygen leak, and the same measurements made in an oxygen atmosphere of 10 -5 mm of mercury. The corresponding behavior, observed after the oil pump was replaced by a mercury pump, is shown in the same figures. Figure 5 is a Dushman plot showing the temperature dependence of electron emission, while Figure 6 shows the corresponding values of the calculated work function. Figure ^ shows the departure of the observed ion currents from values expected, assuming effectively complete dissociation and ioniza tion. The data for these figures are tabulated in Tables 3 and 4 * As is evident in Figure 6 and 7> the conversion to ions was in general greater on a surface of higher warrk function. The fact remains, however, that the calculated work function was always sufficiently high to effect almost complete ionization. The Rbl was replaced by KI, and ion current measured as a function of filament temperature, in order to establish that the aforegoing behavior was not peculiar to Rb. The same incomplete conversion to ions was observed for KI, though the departure from completion was not so marked as with Rbl. On replacing the oil pump with a mercury pump these difficulties were no longer 38 Table 3< Variation of Electron Emission with Filament Temperature 2 Electron Filament -log i/T, 10,000 Calculated Current, Temp., T„ Work Sanction i amps Tf °K volts (Mercury Pump; filament treated by residual gases only, P = 4 x 10” ' mm Hg) 1.28 x 10“ 3 2350 9.635 4.255 5.17 4.44 x 10“ 4 2300 IO.076 4.348 5.26 *.24 2244 10.609 4.456 5.37 2.99 x 10"? 2190 11.206 4.566 5.50 7.36 x 10“ 6 2135 11.792 4.684 5.62 1.78 2080 12.386 4.808 5.72 4.16 x 1 0 - 7O 2020 12.992 4.950 5.81 8.90 x 10“° 1958 13.634 5.107 5.87 1.90 1904 14.281 5.252 5.96 3.08 x 10-9 1844 15.043 5.423 6.05 4.19 x 10“ 10 1785 15.882 5.602 6.16 5.19 x 10-11 1721 16.756 5.811 6.23 (Octoil-S Pump; filament treated by Oxygen leak, P a 1 x io-5 mm Hg; T ■ 787. 6 °K) 8.30 x 1 0 -6 2166 11.750 4.617 5.68 4.22 2136 12.034 4.682 5.72 2.34 2107 12.278 4.746 5.75 1.23 2081 12.547 4.805 5.79 6.20 x 10-7 2049 12.831 4.880 5.82 3«10 2020 13.119 4.950 5.85 i.50 R 1989 13.422 5.028 5.88 8.00 x 10“° 1961 13.682 5.099 5.90 1.34 . 1904 14.433 5.252 6.01 1.98 x 10“9 1843 15.235 5.426 6.12 1.87 x 10“1? 1781 16.229 5.615 6.26 1.10 x 1 0 "!1 1713 17.426 5.838 6.44 (Octoil-S Pump; filament treated by residual gases onlj P - 4 x 10-7 mm Hg; T = 787. 3 °K) 9.53 x 10-5 2138 10.681 4.677 5.15 2.04 , 2081 11.327 4.805 5.28 3.90 x 10"b 2024 12.022 4.941 5.41 9 .00 x 10“ 7 1965 12.632 5 .089 5.50 i.70 1905 13.330 5.249 5.60 3.00 x 10“° 1845 14.054 5.420 5.69 4.07 x 10-9 1783 14.893 5-609 5-79 6.88 x 10“1° 1717 15.632 5.824 5.83 7.07 x 10~1J- 1651 16.587 6.057 5.92 39 Table 4 Variation of Ion Current with Filament Temperature (Oil Diffusion Pump) Ion Current Filament o Maximum Ion Current Temperature K Rubidium Iodide 0.041 2138 T = 787*3 °K O.O56 2081 Residual Pressure - 0.081 2024 4 x 10“7 mm Hg 0.104 1965 I = 1.01 x 10 amp max - 8 0.138 1905 0.160 1845 0.168 1783 0.209 1717 0.266 I651 0.305 1582 0.354 1512 O.402 1438 O.438 1364 O.467 1281 0.475 1241 O.490 1196 0.104 1152 0.070 1149 T - 787.6 °K 0.214 1961 Oxygen Pressure 0.263 1904 1 x 10“5 mm Hg 0.298 1843 I - 9.21 x 10-9 amp max 0.350 1781 0-377 1713 0.431 1650 O.47O 1580 O.5O8 1514 0.542 1438 O.568 1362 O.59O 1277 0.621 1196 0.629 1152 40 encountered, as is shown in Figures 8 and 9* an(l the accompanying Tables 5 an As to the anomalous behavior with the oil p\jmp, the following is known about the condition of the filament. The residual pressure rise, observed on flashing the filament, was always higher with the oil pump than with the mercury pump. In absence of a cold trap, the voltage-current characteristic of the filament would change after prolonged (overnight) exposure to pump vapors. This change was such that the voltage for a given current was smaller after exposure by the order of 10$. On flashing, at approximately 2500 °K, for a few minutes, the original characteristic was recovered. The brightness temperature of the filament, as measured by a Leeds and Worthrup Type 8623 Optical Pyrometer, decreased by 5$> after prolonged exposure at a given filament power input. After flashing the filament and adjusting the power input to its original value, it was noted that the brightness temperature had returned to the value observed prior to overnight exposure to the pump oil vapors. These observations suggest the existence of a filament surface phase, or phases, whose constituents are supplied either by the pump oil or by its decomposition products. Recalling, from the theory, that effectively complete ionization may be had by suppressing the electron partial pressure at the filament, and remembering that the observed values of the calculated work function were sufficiently Observed Ion C urrent/ Maximum Ion Current 0.0 O Q 0.5 0.5 LO 1.0 20 40 0 0 0 2 0 0 8 1 0 0 6 1 1400 1200 0 0 0 1 “OTT ia n Tmeaue °K Temperature ent Filam IonCurrent vs. Filament Temperature Ion CurrentIon vs. Filament Temperature 9 8 ' i8— t9— Figure9. Figure8. o Oxygen coated filament filament coated Oxygen o Furn cae filament coated Fluorine • Oxygen coated filament filament coated Oxygen el eprtr 702°K ~ temperature Cell eiul rsue Om. Hg lO^mm. pressure Residual e l eprtr ~ °K 6 0 7 ~ temperature Cell mm.Hg ~I0-6 pressure Residual S^-8r-&-CL^°- ° ^ L C - & - r 8 - ^ JS - § L £ a Rbl 41 Table 5 Variation of Ion Current with Filament Temperature Ion Current Filament Maximum Ion Current Temperature Potassium Iodide 1.000 2085 T - 706 9K 1.000 2029 P = 2 x 10“ 6 mm Hg 1.000 1970 I,D 18> I '* 1 r. 0.993 1912 1.48 X 10-10 amp 1.007 1855 O2 coating 1.007 I852 0.993 1792 1.007 1736 0.986 1732 0.979 1730 1.007 1728 1.010 1676 0.986 1610 0.993 1504 0.978 13tf 0.964 1232 0.928 1143 0.964 1097 0.930 IO42 F2 coating 0.986 1735 1.027 1704 0.973 1671 1.013 I640 0.959 1608 0.993 1575 0.959 1541 0.959 1504 0.966 1467 0.986 1433 0.959 1392 0.946 1356 0.946 1311 0.946 1271 0.946 1232 0.946 1187 0.953 1139 0.959 1093 0.939 1044 0.439 1010 0.088 990 43 Table 6 Variation of Ion Current with Filament Temperature Ion Current Filament o Maximum Ion Current Temperature K Rubidium Iodide 1.000 I867 T - 702 °K 1.020 1805 P - 6 x 10”7 mm Hg 1.000 1745 I*max O.98O 1745 2.15 1 ioi® anip 1.000 1681 O2 coating 1.000 1666 O.98I 1666 0.986 1602 0.980 1600 0.995 1594 1.014 1534 0.996 1532 0.963 1526 1.009 1496 1.006 1458 O.986 1390 O.958 1390 0.967 1384 O.972 1311 O.96I 1311 O.958 1306 0.958 1265 O.963 1223 0.963 1223 0.951 1219 0.967 1135 O.967 1135 0.943 1132 0.958 IO85 0.963 1054 0.953 1031 0.967 1031 0.803 1014 0.437 1000 O.302 990 0.014 974 large to satisfy requirements of the theory, it is difficult to attribute the observed incomplete conversion, from molecules to ions, to the process of ionization. On the other hand, the process of dissociation should be effectively complete at the high tempera tures of the filament, provided the molecules, which strike the filament, remain thereon long enough to reach thermal equilibrium. Oldenberg and Frost 37 indicate that a molecule which is not chemically adsorbed on a hot surface, but merely collides elastically, does not remain sufficiently long to be excited in its vibrational degrees of freedom to the point of dissociation. 38 It has been shown by Schwab and Pietsch for methane and by 28 Doty for methyl chloride, that only about one thousandth of the molecules striking come to thermal equilibrium with a tungsten filament. As a possible explanation for the incomplete conversion observed when using the oil pump, it is suggested that the accommodation coefficient for alkali halide molecules on the peculiar "oil- tungsten" surface phase is quite different from unity. To explain the observed ion current dependence on temperature, it is necessary that this proposed accommodation coefficient exhibit a negative temperature coefficient of the order of 5 x 10 -4 degree -1 . Such a large temperature coefficient might be explained by chemical or phase changes, within the surface film, which occur almost reversibly with changes in the temperature. The condition of reversibility is mentioned because practically the same curves 45 were obtained when the tsnperature was reduced from 2000 °K to 1100 °K as when it was raised from the latter to the former. The dependence of ion current on filament temperature, like that shown in Figure 7» was observed at several cell temperatures. Although it is doubtful that, at a given filament temperature, the surface condition of the filament was exactly duplicated for these various runs, such might be assumed to be approximately the case. Then if the accommodation coefficient, whatever its value, is constant at a given filament temperature, it should be possible to obtain "apparent" vapor pressures corresponding to the various cell temperatures, and from these to determine an "apparent" heat - of sublimation at constant filament temperature. If the proposed accommodation coefficient is compatible with experimental observa tion, then this "apparent" heat should be the same at any particular filament temperature chosen. Further, it should be the same as the heat of sublimation obtained from subsequent vapor pressure measurements with the mercury pump, when the accommodation co efficient is effectively unity. Within the accuracy of the measure ments this proved to be the case. As indicated at the beginning of this section, these phenomena have no bearing on the final vapor pressure measurements, for, after replacement of the oil pump., no further difficulties with the ion current measurement were encountered. Prior to beginning a series of vapor pressure measurements the oven assembly and Knudsen cell were carefully cleaned. The filament-collector assembly was cleaned and a new filament installed. The oven and filament-collector assemblies were mounted on the tube and, with its rear plug removed, the Knudsen cell was inserted in the proper position. Then with filament lit brightly enough to see, and with the waxed joints warmed sufficiently to rotate, the filament was aligned with the collector and cell apertures by sighting through the rear of the Knudsen cell. The cell was charged with about 2 grams of powdered alkali halide, the plug and thermocouple inserted, and the whole assembly positioned in the oven. After a brief pump down, the oven temperature was raised to 300 °G for an extended evacuation. During this initial evacuation the filament and collector were periodically degassed. After several days the residual gas _7 pressure reached about 2 x 10 mm of mercury and vapor pressure measurements were begun. For each sample, vapor pressures were determined at some twenty-five temperatures in the interval 700 - 900 °K. The sequence followed was such that, beginning at about 900 °K, one quarter of the measurements were made as the temperature was reduced in steps to approximately 700 °K, after which another quarter of the measurements were conducted as the cell was heated by integral steps. This cycle was then repeated. This scheme offered a means of detecting any change in the sample with its thermal history. No such trend was observed. A minimum period of one hour elapsed between each observation to insure attainment of thermal equilibrium. The procedure followed for each of the above measurements was as follows. The electron emission and filament temperature were first measured at some point in the range 1700 - I85O °K. If the calculated work function obtained therefrom was sufficiently high, measurement of the ion current proceeded. It was possible to treat the filament at this point with oxygen, or fluorine, at a pressure of 1 x 10 -5 mm of mercury. This was accomplished by isolating the system from the pumps and admitting gas from a small reservoir, whose pressure had been suitably adjusted in accordance with the relative volumes of the system and the reservoir. After an initial oxygen treatment, residual gases sufficed to maintain a sufficiently high w r k function throughout the course of a series of vapor pressure measurements. After zeroing the amplifier, the ion current observed with the shutter closed was recorded. This background positive current, which actually was predominately photo-emission from the collector, was subsequently subtracted from the ion current observed with open shutter. The ion current with open shutter was observed and the Knudsen cell temperature recorded. These measurements were followed by a record of the filament current and voltage and the residual gas pressure. This procedure was repeated at from three to #ive different filament temperatures in the range 1700 - I85O °K. This completed the necessary measurements for a single vapor pressure determination. The Knudsen cell temperature was changed and, after a suitable period for the re-establishment of equilibrium, the above procedure was repeated. Approximately twenty minutes were required to complete the above measurements at a given cell temperature. During this period the maximum drift in cell tempera ture ever observed was 0.3 degree and this only at the highest temperatures. For most of the observations, no temperature drift was observed and the ion currents were constant to 0.5$). In order to minimize photo-currents, the shutter was closed except when measurements of ion current were made. The background current, which was subtracted from the observed ion current, was never greater than 1$> of the ion current. At constant cell and filament temperatures, the ion current was measured as a function of residual gas pressure. As described in Section II, a gas scattering correction was obtained from these measurements. This correction was applied to the observed ion currents. A correction of 6.6 °K was added to the observed Knudsen cell temperature. As described in Section III, this temperature correction was obtained from a melting point determination in situ. (The temperature scale will be discussed in Section Vi). The plane area of the filament struck by the molecular beam is the product of filament diameter and the length of filament as seen from the Knudsen cell aperture. A tacit assumption in the integration of equation (4 0 ) is that of a point source for the molecular beam. Within the precision of this assumption, the above mentioned length is found by elementary geometric considerations to be given by 49 x = d (R/R - y), (42) where x is the filament length, d is the diameter of the collector aperture, R is the distance from cdl aperture to filament, and (R - y) is the distance from cell aperture to collector aperture. R and (R - y) were measured and found to he 9*50 * 0.03 cm and 8.66 ± 0.03 c® respectively. Using values for the physical constants from Birge 39 , the values listed above and in Section III for the various geometric parameters, and equations (35) ar*d (4l)» "the following expressions are obtained for the vapor pressures in mm of mercury, d £ KI : p s 3.176 x 10* I+Ts A 1 9 (43) Rbls p - 3.592 x 10* I+T22 in which I+ is the corrected ion current in amperes, at the Knudsen cell temperature, T, in degrees Kelvin. 50 V. RESULTS The variation of ion current with residual gas pressure is shown in Table 7j and the log of these data plotted versus gas pressure in Figure 10o Table 7 Variation of Ion Current with Pressure of Scattering Gas Observed Ion log I + 10 Residual Gas Current, IQ Pressure amp.xlO^- mm Hg x 10 Rubidium 2.7 6 O.4425 0.67 Iodide 2.7 6 0.4409 1.0 2.74 0.4378 2.1 T - 723.7 °K 2.72 0.4346 3.0 Tfs 1825 °K 2.67 O.4265 5 .0 2.65 0.4232 6.0 2.57 0.4099 8 .0 2.57 0.4099 10 2.43 0.3856 16 2.27 0.3560 20 potassium 2.07 0.3160 0.30 Iodide 2.07 0.3160 0.70 2.06 0.3139 1 .0 T s 726.1 °K 2.06 0.3139 1 .0 Tf= 1836 °K 2.05 0.3118 1.5 2.05 0.3118 2.0 2.02 0.3054 3.0 2.00 0.3010 5.0 1.99 0.2989 5.0 1.99 0.2989 5.0 1.97 0.2945 7.0 1.94 0.2878 8.0 1.93 0.2856 10 1.90 0.2788 10 In Table 8, the vapor pressure data for KI is recorded, and that for Rbl in Table 9« These includes the observed ion current, corrected for background current; the residual gas pressure; a 51 Figure 10. Logarithm of Ion Current vs. fiesidual Pressure Rb I T = 724.0 °K If* 1825 ° K 0.40 Slope = -3950 mm-1 ift V w. 0) eCL o c a> 3o.35 c o o» o KI T = 7 2 6 .1 ° K Tf * 1836 ° K 0 .3 0 - Slope = —3500 mm.-i 0.5 1.0 1.5 2.0 Residual Gas Pressure (mm. Hg) x I05 52 scattering correction factor^ obtained as outlined in Section II from the appropriate slope in Figure 10; the resulting corrected ion current; the Knudsen cell temperature; and the logarithm of the vapor pressure as obtained from equation (43)* Table 8 Vapor Pressure of KI Observed Residual Scattering Corrected Cell -log p 0 mm Ion Gas Correction Ion Temperature Current Pressure Factor Current °K amp.xlO' mmHgxl07 amp.xlO^ 0.0604 3.0 1.0024 O.O6O5 697.5 4-2945 0.0830 2.8 1.0022 0.0830 706.6 4.1545 0.163 4.0 1.0032 O.I64 719.0 3.8549 0.207 3.0 1.0024 0.207 726.1 3.7515 0.215 3.0 1.0024 0.216 727.3 3.7327 0.478 3.0 1.0024 0.479 745-3 3.3815 O.476 5*0 I.OO4 O O.478 746.2 3.3822 0.611 4.0 1.0032 0.613 749.6 3.2733 1.02 6.0 I.OO48 1.02 762.5 3.0485 1.22 4.0 1.0032 1 .22 768.4 2.9689 1.21 4-5 1.0036 1.21 768.8 2.9724 2.51 16 1.0129 2.54 787.8 2.6450 2.59 6.5 1.0052 2.60 788.4 2.6347 5.24 10 1.0080 5.28 807.0 2.3220 6.19 15 1.0121 6.26 8IO.5 2.2572 9.19 10 1.0080 9.26 819.9 2.0747 14.4 17 1.0137 14.6 832.8 1.8734 20.4 14 1.0113 20.6 842.4 1.7215 24.4 22 1.0177 24.8 850.4 1.6388 37.3 28 1.0225 38.1 861.7 1.4497 36.8 30 1.0242 37.7 864.4 1.4536 52.9 40 1.0322 54.6 872.6 I.2905 49.8 70 1.0563 52.6 873.7 1.3064 63.O 74 1.0596 66.8 883.0 1.2003 82.7 70 1.0563 87.4 891.7 1.0815 The logarithm of the vapor pressure is plotted against the reciprocal of the cell temperature for KI in Figure 11. In Figure 12 is shown the curve of Figure 11 along with the experimental points of CL Q. _ 53 —o ro ® ro OJ CM iO ajnssaid O,6o~i Figure 11 Figure ) (This Research) (This ww Vapor Pressure of KI KI of Pressure Vapor h (6 01- Logic pressure (mm. Hg) -3.0 -4.0 -20 - 1.0 1.15 1.20 eircl eprtr °-x I03 °K-Ix Temperature Reciprocal 1.25 hs research This im n Mayer and Zimm • Cgn n Kimball and Cogin o Niwa x 1.30 1.401.35 M ro M previous investigators. A similar plot for Rbl appears in Figure 13> and in this plot are also included the observations 2 of Niwa . As will be shown, the vapor pressure of these Table 9 Vapor Pressure of Rbl Observed Residual Scattering Corrected Cell -log p ram Ion Gas Correction Ion Temperature Current Pressure Factor Current °K amp.xlO mmHgxlO amp.xlO^ 0.0807 7-5 1.0068 0.0812 696.5 4.H37 0.132 6.0 I.OO55 0.133 707.3 3.8959 0.199 7.6 I.OO69 0.200 716.3 3.7162 0.216 8 .0 1.0073 0.218 716.2 3.6787 0.233 7.8 1.0071 0.235 719.2 3.6452 0.277 6.7 1.0061 0.279 724.0 3.5692 0.539 9.0 1.0082 0.543 739-9 3.2753 0.574 6.0 1.0055 0.577 741.0 3.2485 O.58O 20 1.0181 O.59O 741.5 3.2387 O.582 8.0 1.0073 O.586 742.1 3.2417 I.40 10 1.0091 1.41 763.2 2.8541 1.44 11 1.0100 1.45 763-9 2.8418 I.65 15 1.0136 1.67 767.5 2.7795 3.32 14 1.0127 3.36 785.7 2.4707 3.51 14 1.0127 3.55 787.O 2.4465 3.64 14 1.0127 3.69 788.1 2.4293 7.47 16 I.OI46 7.58 808.0 2.1113 8.63 15 1.0136 8.75 812.3 2.0478 9.02 20 1.0181 9.18 813.3 2.0267 18.2 20 1.0181 18.5 832.4 1.7174 18.1 25 1.0227 18.5 832.5 1.7174 23.0 25 1.0227 23.5 839.8 1.6116 33.5 36 1.0327 34*6 851.5 I.44 O4 45.2 54 1.0491 47.4 859.O 1.3020 44-3 60 I.O546 46.7 860.8 1.3080 46 .O 64 I.O582 48.7 861.6 1.2897 63-5 100 1.0910 69.3 872.4 1.1336 83.4 110 1.1000 91.7 879.7 1.0101 crystalline salts, over the temperature range investigated, can approximately represented by an equation of the form, Logio pressure (mm. Hg) - -4.0 - 2.0 1.0 1.15 1.20 eircl eprtr °- x I03 x °K-1 Temperature Reciprocal 1.25 o This research research This o K. Niwa • 1.30 1.35 1.40 H 57 log p = A - B(1000/t ) + 3/2 log (1000/T), (44) where A and B are positive constants. The latter term arises because of the•difference in heat capacity of vapor and solid. Evaluating these constants numerically, by a "least squares" fit of the experimental data to an equation of the form (44 ), the following expression is obtained for KI, log p = 11.1775 - 10.9875(1000/T) + 1.5 log(lOOO/T) and for Rbl, (45) iog Pmm = 11.1532 - 10.8125(1000/T) + 1.5 log(l000/T). The standard free energy change for the sublimation of a mole of the solid salt is obtained from the observed pressure and temperature by the relation = - HT In K = - RT In p, (46 ) where -4^P^ is the standard molar free energy change at the temperature T, and p is the pressure. The standard state of the vapor shall be taken as 1 mm of mercury, and hence the pressure in (46 ) is expressed in mm of mercury. Prom the definition of free energy, the standard free energy change may also be written (47) where the subscripts, v and s, refer to vapor and solid respectively. The second and fourth terms on the right, involving the enthalpy and entropy of the vapor, may be calculated by the usual methods of statistical mechanics^, if information is available as to the vibrational frequency and. internuclear separation of the molecule. The third and fifth terms for the solid may be determined if heat capacity information is had from the absolute zero to the temperature T. Using this information in conjunction with equation (46 ), it is then possible to obtain a value for the heat of sublimation at the absolute zero, 2\H°, for each of the observed 7 o vapor pressures. The molecular constants used in this calculation are listed in Table 10. The notation is that of Mayer and Mayer^*, Table 10 Salt Vibrational Anharmonieity Equilibrium Frequency Correction Internuclear . , cm"-*- ca x , cm Separation CO 6 6 8 _ ^ Q r x 10° cm o KI 212 30 0.7 30 3.16 30 Rbl 159 32 0.6 * 3.19 31 & estimated value and their equations are used to calculate the heat content and entropy of the vapor. Values for the physical constants are taken 39 o from Birge . The heat capacities of the solids from 10 K to 273 °K are taken from Clusius, Goldmann and Perlick^'*', and Debye's "T3" law used to extrapolate the heat capacity from 10 °K down to 0 °K. For the latter, characteristic temperatures were taken from Clusius et al.^ to be 115 and 102 degrees for KI and Rbl respectively. 42 Following Kelley , it is assumeu that the heat capacity from o 273 K to the melting point can be represented by an equation of 59 the form Cp = a + bT, (48 ) and the constants are determined by using the heat capacity values of Clusius at 272i °K, and the estimated value I4 .O cal./mole degree at the melting points. National Bureau of Standards values 43 were used for the melting points. In this way the following equations are obtained for the heat capacities above 273 °K, KI j C - 11.85 + 0.00225 T P (49) Rbls C - 11.92 + 0.00228 T. P ” o o Integrations from 0 K to 273 K, necessary to compute the enthalpy and entropy of the solids, were performed graphically. The results of these graphical integrations are tabulated in Table 11. The uncertainties are estimates. Table 11 Salt H273 " Ho S273 k.cal./mole cal./deg. mole KI 2.650 ± 0.005 23.84 ± 0.05 Rbl 2.867 ± 0.005 27.18 ± 0.05 Solving equation (47) for the heat of sublimation at the absolute zero, inserting suitable expressions for the enthalpy and entropy of the vapor, and using equation (49 ) and the values of Table 11 to calculate the enthalpy and entropy of the solid, the following is obtained for KI, 60 A H ° = A P j - 365.0 + 69.850 T - 0.0010392 T2 - 8032.9/T - 6.694O T log T, (50) and for Rbl, A H ° = - 243-7 + 69.406 T - 0.0010244 T2 - 4524 .9/T - 6.8575 T log T. (51) Denoting the sum on the right of the standard free energy change by JE. , and using equation (4 6 ) to obtain ^ F°, a value for the heat of sublimation at the absolute zero has been obtained for each of the observed vapor pressures and tabulated in Tables 12, 13, and 1 4 . Tables 12 and 13 include values for KI obtained from the observations of this research as well as those obtained from the data of Cogin and Kimball^, Zimm and Mayer‘S, 2 and Niwa . Table 14 shows the results of this calculation for 2 Rbl, using data of this research and that of Niwa . In the case of KI, the agreement with Oogin and Kimball is very good, as may be seen in Tables 12 and 13 and also in Figure 12. From an inspection of Figure 11, it is apparent that the precision of the measurements is high, there being less scatter in the observed points than in those of previous investigators. It will be observed, in Tables 12 and 13, that the trend in the computed values for the heat is the same for all of the investigations with the exception of Riwa's. Inherent in the calculation of the sum, Si , are various constant errors arising from uncertainty in the heat capacity of the solid above room temperature, and to a lesser extent from uncertainties in the values of the molecular 61 Table 12 Heat of Sublimation of KI at the Absolute Zero, A h ° ’ o 1000 -log p mm L(T) Deviation T cat cal cal from mean (this research) 1.4337 4.2945 13701 34560 48261 135 1.4152 4.1545 13427 34985 48412 286 1.3908 3.8549 12678 35560 48238 112 1.3772 3.7515 12460 35888 48348 222 1.3749 3.7327 12417 35944 48361 245 1.3417 3.3815 11527 36776 48303 177 1.3401 3.3822 11544 36817 48361 235 1.3340 3.2733 11223 36974 48197 71 1.3115 3.0485 10632 37570 48202 76 1.3014 2.9689 10435 37841 48276 150 1.3007 2.9724 10453 37861 48314 188 1.2694 2.6450 9531 38734 48265 139 1.2684 2.6347 9501 38761 48262 136 1.2392 2.3220 8571 39614 48185 59 1.2338 2.2572 8368 39774 48142 16 1.2197 2.0747 7780 40204 47984 -142 1.2008 1.8734 7136 40794 47930 -196 1.1871 1.7215 6633 41233 47866 -260 1.1759 I.6388 6374 41597 47971 -155 1.1605 1.4497 5714 42112 47826 -300 1.1569 1.4536 5747 42235 47982 -144 I.I46 O I.2905 5151 42608 47759 -367 1.1446 I .3064 5221 42658 47879 -247 1.1325 1.2003 4848 43081 47929 -197 1.1215 1.0815 4411 43475 47886 -240 mean 48126 (Zimm and Mayer) 1.617 6.48 18329 30865 49194 251 1.566 5.93 17321 31812 49133 190 1.496 5.24 16020 33207 49227 284 1.429 4.45 14244 34669 48913 - 30 1.399 4.17 13634 35365 48999 56 1.323 3.40 11756 37265 49021 78 1.215 2.28 8583 40346 48929 - 14 1.163 1.73 6804 42026 48830 -113 1.139 1.45 5823 42853 48676 -267 1.120 1.22 4982 43529 48511 -432 mean 48943 62 Table 13 Heat of Sublimation of KI at the Absolute Zero,* «^HCr . 0 1000 -log p AK F.p Deviatii mm111 1H Z(*) T cal cal cal from mei (Gogin and Kimball) 1.386 3.84 12673 35676 48349 232 1.383 3.81 12601 35750 48351 234 1.363 3.55 11913 36241 48I54 37 1-356 3.51 II84O 36415 48255 138 1.344 3.44 11707 36716 48423 306 1.315 3.09 IO748 37477 48225 108 1.302 2.94 10328 37823 48I5I 34 1.301 2.93 1030L 37851 48152 35 1.297 2.95 10403 37961 48364 247 1.297 2.94 10368 37961 48329 212 1.264 2.63 9517 38785 48302 185 1.263 2.56 9271 38917 48I88 71 1.262 2.63 9532 38944 48476 359 1.260 2.51 9112 39004 48 II6 - 1 1.'251 2.43 8885 39266 48151 34 1.237 2.29 8467 39679 48I46 29 1.209 2.00 7566 40534 48IOO - 17 1.209 1.98 7491 40534 48025 - 82 1.207 1.95 7390 40598 47988 -129 1.205 2.02 7668 4O662 48330 213 1.204 2.00 7598 40693 48291 174 1.179 1.69 6557 41497 48054 - 63 1.179 1.67 6479 41497 47976 -141 1.177 1.63 6334 41562 47896 -221 1.162 I.46 5747 42062 47809 -308 1.153 1.39 5514 42367 47881 -236 1.152 1.37 5440 42404 47844 -273 1.144 1.24 4958 42676 47634 -483 1.114 0.90 3695 43747 47442 -675 mean 48117 (Niwa) 1.245 2.491 9149 39431 4858O - 54 1.230 2.355 8757 39889 48646 12 1.215 2.205 8300 40346 48646 12 1.200 2.057 7838 40803 4864 I 7 1.186 1.9H 7369 41261 48630 - 4 1.172 1.768 6898 41716 48614 - 20 1.160 1.651 6510 42127 48637 3 1.145 1.515 6050 42626 4867 6 42 mean 48634 63 ■Table 14 Heat of Sublimation of Ebl at the Absolute Zero, ^ H °0 100,0 a p S Deviat: -l°g llUlimm Cclx 2 (T) T cal cal from me (thi s research) 1.4358 4.1137 13105 34015 47120 266 1.4138 3.8959 12604 34507 47111 257 1.3961 3.7162 12176 34916 47092 248 1.3963 3.6787 12051 34919 46970 116 1.3904 3.6452 11991 35048 47039 I85 1.3812 3.5692 11820 35265 47085 201 1.3515 3.2753 11085 35985 47070 216 1.3495 3.2485 11010 36036 47046 192 1.3486 3.2387 IO984 36058 47042 188 1.3475 3.2417 11003 36084 47087 233 1.3103 2.8541 9963 37037 47000 I 46 1.3091 2.8418 9930 37068 46998 144 1.3029 2.7795 9758 37231 46989 135 1.2728 2.4707 8879 38051 46930 76 I .2706 2.4465 8807 38109 46916 62 1.2689 2.4293 8757 38159 46916 62 1.2376 2.1113 7803 39051 46854 0 1.2311 2.0478 7608 39245 46853 - 1 1.2296 2.0267 7539 39289 46828 - 26 1.2013 1.7174 6539 40145 46684 -170 1.2012 1.7174 6539 40150 46689 -165 1.1908 1.6116 6190 40475 46665 -189 1.1744 I.44O 4 56IO 40998 466O 8 -346 I.I 64I 1.3020 5116 41332 46448 -406 1.1617 1.3080 5150 41412 46562 -292 1.1606 1.2897 5083 41447 46530 -324 1.1463 1.1336 4523 41928 46451 -403 1.1368 1.0101 4O 64 42253 46317 -537 mean 46854 (Niwa) 1.293 2.734 9667 37479 47146 - 50 1.277 2.567 9194 37929 47123 - 73 1.261 2.424 8792 38379 47171 - 25 1.245 2.254 8279 38827 47106 - 90 1.200 1.846 7033 40170 47203 7 1.186 1.712 6601 40618 47219 23 1.172 1.590 6204 4IO 65 47269 73 1.160 1.477 5824 4I 466 47290 94 1.145 1.322 5279 41955 47234 38 mean 47196 64 constants used, tfrom an estimate of these errors the resulting uncertainty in the sum, 2 , is of the order of ± 150 cal./mole. This error may be somewhat larger in the case of Rbl as the molecular constants are not as well known. In addition to the above, calculated values for the heat of sublimation may be in error due to uncertainty in the standard free energy, arising from systematic errors in the vapor pressure and the temperature. These errors, which are discussed in Section VI, lead to an uncertainty in the free energy of the order of * 50 cal./mole. The combined uncertainties, in the sum,2 , and in the free energy, can account for the trend noted in the heat of sublima tion. Since the deviation from the mean is due chiefly to the constant errors discussed above, random errors being much smaller, the uncertainty in the heat of sublimation at the absolute zero is taken as the root-mean—square of the deviations from the mean tabulated in Tables 12, and 14 . Thus for the heat of sublimation at absolute zero for KI is obtained,