Heats of adsorption of sodium, rubidium, and cesium ions on tungsten substrat

Luke, K. P.

Neustadter, H. E.

English

NASA Technical Reports Server

1 
NASA TECHNICAL NOTE N A S A  TN 0-2460 
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LOW-COVERAGE HEATS OF ADSORPTION 
I11 - ALKALI METAL IONS O N  TUNGSTEN; 
ATOM-METAL INTERACTION THEORY 
by Harold E. Neustadter and Keztng P. Luke 
Lewis Research Center 
Cleveland Ohio 
NATIONAL AERONAUTICS A N D  SPACE A D M I N I S T R A T I O N  WASHINGTON,  D. C. AUGUST 1964  
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https://ntrs.nasa.gov/search.jsp?R=19640017828 2020-03-24T06:28:12+00:00Z
TECH LIBRARY KAFB, NM 
I lll11111 lll111 lllll 111 Il1 II 
0079546 
LOW -COVERAGE HEATS OF ADSORPTION 
111 - ALKALI METAL IONS ON TUNGSTEN; 
ATOM-METAL INTERACTION THEORY 
By Harold E. Neustadter and Keung P. Luke 
Lewis Research Center 
Cleveland, Ohio 
NATIONAL AERONAUTICS AND SPACE ADMlN ISTRATION 
For sal. by the Offico of Technical Sorvicor, Departmont of Commorco, 
Woshington, D.C. 20230 -- Prico $0.50 
LOW-COVEF'AGE "SS OF ADSORPTION 
I11 - ALKALI METAL IONS ON "GSTENj 
ATOM-MEW INTERACnON THEORY 
by Harold E. Neustadter and Keung P. Luke 
Lewis Research Center 
SUMMARY 
The heat of adsorption of an ion on a metal ( i n  t h e  l i m i t  of zero cover- 
age) i s  expressed as the  superposit ion of a van der Waals type in te rac t ion  and 
an image charge type in te rac t ion .  The reported experimental values of the  
heat of adsorption of sodium, rubidium, and cesium ions on a tungsten substrate  
a r e  then compared with r e s u l t s  of a t h e o r e t i c a l  evaluation based on t h e  above 
model. 
INTRODUCTION 
Considerable i n t e r e s t  i n  a l k a l i  metal plasma f o r  power generation and 
space propulsion has prompted extensive s tudies  of adsorption of a l k a l i  metals 
on various substrates .  A requirement f o r  a n  
TABLE 1. - EXPERIMENTAL ZERO-COVERAGE 
HEATS OF ADSORPTION 
Source 
Bosworth ( r e f .  1) 
Hughes and Levenstein 
( r e f .  2 )  
de Boer and Veenemans 
( r e f .  3) 
Taylor and Langmuir 
( r e f .  4 )  
Becker ( r e f .  5) 
Scheer and Fine 
( r e f .  6 )  
Sodium I Rubidium 1 Cesium 
Heat of adsorption, cp, ev  
2.50 
1.90 
"2.36 
'2.04 
2.19 
2.04 
aNot measured d i r e c t l y ,  bu t  ca l cu la t ed  from t h e  
assumption t h a t  a l l  cesium adsorbed on tungs ten  
e x i s t s  only as ions .  
adequate adsorption theory i s  the 
spec i f ica t ion  of the  heat of ad- 
sorpt ion i n  the  l i m i t  of zero 
coverage. This report  proposes 
an equation f o r  calculat ing the  
heat of adsorption cp of a.n ion 
on a metal a t  coverages suffi- 
c i e n t l y  low t o  allow neglect of 
in te rac t ions  between neighboring 
adsorbed ions.  Results of calcu- 
l a t i o n s  based on t h i s  equation 
a r e  compared with experimental 
values for sodium, rubidium, and 
cesium ions adsorbed on a tung- 
s t e n  subs t ra te  ( t a b l e  I).  Note 
t h a t  a t t r a c t i v e  energies a re  de- 
noted as posi t ive.  
SYMBOLS 
a. Bohr radius 
e e lectron charge 
k, 
R 
'P 
'PW 
defined by eq. (5) 
f r e e  e lec t ron  densi ty  of m e t a l  ( tungsten) 
distance from metal surface t o  center of ion  
e lec t ronic  p o l a r i z a b i l i t y  
constant, 4 . 3 3  
defined by eq. (3) 
heat of adsorption of ion i n  l i m i t  of zero coverage 
defined by eq. ( 2 )  
defined by eq. (4)  
m Y S I  s 
A model commonly used t o  explain the  adsorptive bond approximates the  ad- 
sorbed ion as a point charge and u t i l i z e s  c l a s s i c a l  image-charge theory. This 
i s  an oversimplification i n  t h a t  (1) it neglects the  contribution of the  elec-  
t r o n i c  d i s t r i b u t i o n  of t h e  ion and ( 2 )  c l a s s i c a l  image-charge theory breaks 
down i n  the  immediate region of t h e  metal surface.  
The adsorption energies can be t r e a t e d  as a r i s i n g  from the  superposit ion 
of the  instantaneous dipole moment of the  
of (1) the  in te rac t ion  'pi 
van der Waals type i n t e r a c t i o n  
ion with the metal. Thus , 
of t h e  ne t  ion ic  charge with the  metal and ( 2 )  a 
Cpw 
For 'pi a quantum mechanically corrected image-charge expression m u s t  be 
Sachs and used, s ince the  ions a r e  1 /2  t o  2 angstroms from the  metal surface.  
Dexter ( r e f .  7 )  have proposed such an expression: 
2 e 
4R 4R2 
where R i s  the  distance from the  surface t o  t h e  center of the  ion, p i s  a 
constant , and P 
i n  which no i s  the  f r e e  electron densi ty  of the  metal, and a. i s  t h e  Bohr 
radius. 
2 
The energy a r i s i n g  from the  polar iza t ion  of an adsorbed p a r t i c l e  has been 
s tudied by Prosen and Sachs ( r e f .  8) and is  given by1 
Sodium 
i o n  
I where a is  the  e lec t ronic  dipole p o l a r i z a b i l i t y  of t h e  adsorbed ion 1 
Rubidium C e s i u m  
i o n  i o n  
TABLE 11. - ELECTRONIC POLARIZABILITY 
Source 
Sternheimer ( r e f .  10) 
Fajan  and Joos 
(ref. 11) 
Born and Heisenberg 
( r e f .  12 )  
Pauling ( r e f .  13) 
Tessman, Kahn, and 
Shockley ( r e f .  14)  
Calculated.  a 
aO. 152 
.196 
.210 
.189 
.255 
"2.920 
1.56 
1.81 
1 .41  
1.797 
'5.60 
2.56 
2.79 
2.44 
3.137 
( t ab l e  II), and 
( 5 )  
The complete expres- 
s ion  f o r  t he  heat of ad- 
sorpt ion of ions on a m e t a l  
i n  t he  l i m i t  of zero cover- 
age 5s obtained by adding 
equations ( 2 )  and ( 4 )  : 
Impl ic i t  i n  equation ( 6 )  and the  choice of ion ic  values of po la r i zab i l i t y  
i s  the  assumption t h a t  a p a r t i c l e  t h a t  desorbs as an ion has the  propert ies  of 
an ion p r io r  t o  desorption. Hughes ( r e f .  15) i n  h i s  adsorption-lifetime 
s tudies  has found evidence t o  support t h i s .  
To apply equation (6), it i s  necessary t o  evaluate the  constant p and 
R, t h e  distance f rom t h e  nucleus of t he  ion t o  t he  metal surface.  The locat ion 
of t h i s  "surface" i s  not wel l  defined, however. F'hysically it i s  t h a t  plane on 
which a l l  excess e lectrons would co l l ec t .  The constant p depends on the  
choice of wave function used i n  deriving equation ( 2 ) .  
mated p t o  be 0.46; however, t h e i r  approximations appear t o  make t h i s  an 
upper l i m i t .  That t h i s  value of p i s  too  high h a s  been subs tan t ia ted  by 
others i n  two instances ( r e f .  1 6 ) .  Since p i s  not uniquely determined, this 
I report  evaluates it by matching the  calculated value of cp f o r  sodium adsorp- 
t i o n  t o  the  reported experimental value. I n  the  course of evaluating p ,  R 
* w i l l  a l s o  be determined. The value of cp f o r  sodium w a s  se lec ted  because the  
e lec t ronic  po la r i zab i l i t y  of t h e  sodium ion  is  very s m a l l  ( t a b l e  11). 
Sachs and Dexter e s t i -  
'I 
Thus, 
1The choice of equation (4) t o  express t h e  van der Waals type in t e rac t ion  
i s  based on t h e  r e s u l t s  of an e a r l i e r  study by t h e  authors of this report  
( r e f .  9) .  
3 
t h e  contribution of Cp t o  t h e  heat of adsorption of sodium ions on tungsten 
i s  s m a l l  (qW Z 0.04 evy and one can approximate 
Cp(Na' - W) = 'pi = 2.46 ev ( 7 )  
A t  equilibrium t h e  sodium ion w i l l  be a t  t h a t  R value f o r  which 'pi i s  
a maximum. Taking 
r 
d'pi/dR = 0 
gives the  r e s u l t  
R = 2pic112 ( 9 )  
For tungsten ( l a t t i c e  constant of 3.16 A, one conduction e lec t ron  per 
atom) = 1.1, and from equation ( 9 )  R = 2.2 p .  The constant p can now be 
evaluated by using t h i s  r e s u l t  i n  equations ( 7 )  and ( 2 > ,  the  f i n a l  r e s u l t s 2  
being p E 0.33 and R = 0.73 A. 
The use of a hard sphere model, the  assumption of adsorption taking place 
on t h e  (110) plane of tungsten, and t h e  value 
surface a t  0.93 A from t h e  plane through t h e  centers of the  outermost layer  of 
R = 0.73  A, loca te  the metal 
i_l:94 4 
Na+ ,-R-0.73 
S u rface 
Figure 1. - Sodium ion adsorbed on a (110) plane of tungsten. (Dimensions i n  angstroms.) 
atoms (see  f i g .  1). This i s  71 percent of t h e  distance from t h e  center of the  
surface layer  of atoms t o  t h e  outermost tangent of the  surface layer  of atoms, 
which i s  a physically reasonable r e s u l t .  
Suff ic ient  evidence j u s t i f i e s  the  assumption t h a t  f o r  tungsten emit ters  
the  emitt ing surfaces were e s s e n t i a l l y  (110) planes ( r e f s .  4, 5, a.nd 1 7 ) .  
distance R w a s  a l s o  calculated f o r  rubidium and cesium ions on tungsten by 
using the  same hard sphere model, and assuming the  value of p ,  and the loca- 
t i o n  of the  surface t o  be independent of the  nature of the  adsorbed ion. 
The 
Because a i s  not uniquely determined ( t a b l e  11), the  calculat ion of Cp 
w a s  performed f o r  both the most recent ly  reported calculated values, and the 
average of a l l  reported experimental values of a.  The r e s u l t s  a r e  l i s t e d  i n  
', 
c 
(1 
'This value of p i s  s l i g h t l y  lower than the upper l i m i t  p = 0.46 sug- 
gested by Sachs and Dexter ( r e f .  7 )  and considerably higher than the  value 
p = 0.09 used. by Cutler and Gibbons ( r e f .  1 6 ) ,  which i s  reasonable. 
4 
t ab l e  111. I n  general ,  t h e  calculated values of cp a r e  i n  reasonable agree- 
ment with the  experimental values. Tha t  t h e  calculat ions based on the  calcu- 
l a t e d  values of a show a s l i g h t l y  lower value f o r  t he  cesium ion - tungsten 
TABLE 111. - APPLICA‘EON O F  EQUATION ( 6 )  TO ADSORPTION 
OF ALKALC METAL IONS ON TUNGSTEN 
Ion 
sodium 
Rubidium 
Cesium 
Elec t ronic  
p o l a r i z a b i l i t y ,  
3 
”0.200 
152 
a1.899 
b2. 920 
“3.305 
b5.600 
Distance from 
metal sur face  
t o  center  
of ion,  
RJ 
A 
“0.73 
al. 44 
al. 69 
I n t e r a c t i o n  
energy, 
ev 
(Pi, 
a2. 460 
“1.875 
al. 660 
Heat of adsorption, cp, 
ev  
Calculated 
2 . 5 1  
2.50 
2.13 
2 .27  
2.03 
2.29 
Experiment a1  
2.50 I 
aAverage of value l i s t e d  i n  t a b l e  11. 
bCalculated. 
adsorption than f o r  t h e  rubidium ion - tungsten adsorption i s  pa r t i cu la r ly  in-  
t e r e s t ing .  This i s  i n  agreement with t h e  experimental r e s u l t s .  While t h e  
major  bonding i s  due t o  the  image-force of t h e  ne t  charge of t h e  ion, the  po- 
l a r i z a t i o n  e f f ec t  cannot be neglected. It i s  pr imari ly  the  difference i n  
p o l a r i z a b i l i t i e s  t h a t  accounts f o r  t he  heat  of adsorption of cesium on tungsten 
being lower than t h a t  of rubidium on tungsten when t h e  calculated values of a. 
a re  used. 
CONCLUDING REMARKS 
While equation ( 6 )  i s  not exact ( t h e  polar iza t ion  term considers only 
dipole-dipole in t e rac t ions ) ,  t h e  r e s u l t s  obtained ( t a b l e  111) are  general ly  
good. On the  bas i s  of t he  calculat ions performed, t he  theory presented i s  
adequate t o  explain the  phenomena of adsorption of a l k a l i  metal ions on tung- 
s t e n  i n  the  l i m i t  of zero coverage and emphasizes t h a t  t he  e f f e c t  a r i s ing  from 
the  po la r i zab i l i t y  of t h e  adsorbed ion  should not be neglected. 
va r i e ty  of experimental techniques and laboratory conditions of numerous work- 
e r s .  It must a l s o  be recognized t h a t  except f o r  t h e  cesium adsorption the re  i s  
only one reported value of cp f o r  each system. The r e s u l t s  of t h i s  study m u s t  
necessar i ly  be considered within the  framework of these  l imi ta t ions .  
Unfortunately, the  experimental values of cp had t o  be co l lec ted  from a 
Lewis Research Center 
National Aeronautics and Space Administration 
Cleveland, Ohio, May 27, 1964 
5 
1. Bosworth, Richard Charles Leslie: The Mobility of Sodium on Tungsten. 
Proc. Roy. Soc. (London), ser. A, vol. 150, 1935, pp. 58-76. 
2. Hughes, F. L., and Levinstein, H.: Mean Adsorption Lifetime of Rb 
on Etched Tungsten Single Crystals: Ions. Phys. Rev., 113, no. 4, 
Feb. 15, 1959, pp. 1029-1035. 
3. de Boer, J. H. , and Veenemans, C. F. : Adsorption of Alkali Metals on Metal 
Surfaces. Chemical Physica, vol. 1, 1934, pp. 753-762. 
4. Taylor, John Bradshaw, and Langmuir, Irving: The Evaporation of Atoms, 
Ions and Electrons from Caesium Films on Tungsten. Phys. Rev., vol. 44, 
no. 6, Sept. 15, 1933, pp. 423-458. 
5. Becker, J. A.: Adsorption on Metal Surfaces and Its Bearing on Catalysis. 
Advances in Catalysis, vol. 7, Academic Press, 1955. 
+ 6. Sheer, Milton D., and Fine, Joseph: Kinetics of Cs Desorption from Tung- 
sten. Jour. Chem. Phys., vol. 37, no. 1, July 1962, pp. 107-113. 
7. Sachs, R. G., and Dexter, D. L.: Quantum Limits of the Electrostatic 
Image Charge Theory. Jour. Appl. Phys., vol. 21, 1950, pp. 1304-1308. 
8. Prosen, E. J. R., and Sachs, R. G.: The Interaction Between a Molecule 
and a Metal Surface. Phys. Rev., vo l .  61, Jan. 1-15, 1942, pp. 65-73. 
9. Neustadter, Harold E., and Luke, Kueng P. : Low-Coverage Heats of Adsorp- 
tion. 1 - Alkali Metal Atoms on Tungsten; Atom-Metal Interaction 
Theory. NASA TN D-2430, 1964. 
10. Sternheimer, R. M. : Electronic Polarizabilities of Ions. Phys. Rev., 
vol. 115, no. 5, Sept. 1, 1959, pp. 1198-1206. 
11. Fajans, K., and Joos, G.: Molrefraktion von Ionen und Molekclen im Lichte 
der Atomstruktur. 
of the Atomic Structure.) Zs. Physik, bd. 23, 1924, pp. 1-46. 
(Mass Refraction OS Ions and Molecules in the Light 
.. 
12. Born, M., and Heisenberg, W.: Uber den Einfluss der Deformierbarkeit der 
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vol. 114, 1927, pp. 181-211. Chemical Abstracts, vol. 25, June-Oct. 1927. 
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1953, pp. 890-895. 
6 
15. Hughes, F. L . :  Mean Adsorption Lifetime of Rb on Etched Tungsten Single 
Crystals:  Neutrals. Phys. Rev., vol .  113, no. 4, Feb. 15, 1959, 
pp. 1036-1038. 
1 6 .  Cutler,  P. H. , and Gibbons, J. J. : Model f o r  the  Surface Potent ia l  
Barrier and the  Periodic Deviations i n  t h e  Schottky Effec t .  Phys. Rev., 
vol. 111, no. 2,  July 15, 1958, pp. 394-402. 
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Etched Tungsten Single Crystals.  Phys. Rev., vol.  113, no. 4, Feb. 15, 
1959, pp. 1023-1028. 
NASA-Langley, 1964 E-2585 
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Low-coverage heats of adsorption. iii - alkali metal ions on tungsten, atom-metal interaction theory

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