- Email: [email protected]
Adsorption of alkali metals on metal surfaces
ADSORPTION OF ALKALI METALS ON METAL SURFACES
III i) A D S O R P T I O N
ENERGY
OF THE
IONS
b y J. H. DE B O E R and C. F. VEENEMANS Natuurkundig Laboratorium der N.V. Philips' Gloeilampenfabrieken Eindhoven/Holland Zusammenfas
s ung
Wenn positive Ionen an eine MetalloberflAche adsorbiert sind, bilden sie m i t i h r e n S p i e g e l b i l d l a d u n g e n e i n e e l e k t r i s c h e D o p p e l s c h i c h t . D i e L a dungen dieser Doppelschicht sind diskret angeordnet und in diesen F~llen m u s s m a n i m m e r b e a c h t e n , d a s s d a s F e l d auch" n a c h A u s s e n d u r c h g r e i f t . D a d u r c h w e r d e n n e u e p o s i t i v e I o n e n s t a r k e r y o n tier M e t a l l o b e r f l A c h e gebunden, wenn schon einige positive Ionen anwesend sind. Aus experirnent e l l e n W e r t e n k a n n die Z u n a h r n e d e r B i n d u n g s e n e r g i e e i n e s C s + - I o n s m i t zunehmender Besetzung berechnet werden. D i e A u s d r f i c k e Itir die E l e k t r o n e n e m i s s i o n y o n d e r I I . M i t t e i l u n g w e t den durch diesen Umstand etwas modifiziert.
§ 1. Introduction In the derivation of the isotherm for the adsorption of alkali metals on metal surfaces in the form of ions (communication II § 4) "¢o n ~ - ape, kT
the adsorption energy Q~ was assumed to be independent of 0. Further in deriving the relation between the electron emission of a Cs covered tungsten surface and the vapour pressure i i log i0 = Cp the constant A in R i c h a r d s o n's emission formula was assumed to be independant of 0. Both assumptions are only approximations; 1) I J . H . de B o e r andC. F. V e e n e m a n s , II J . H . d e B o e r andC. F. V e e n e m a n s ,
Physical, 753, 1934. Physical, 953,1934.
J. H. DE BOER AND C. F. VEENEMANS, ALKALI METALS
96]
we shall now consider what happens if Q~, as well as A, is a function of 0.
§ 2. Increase o/Qi with increasing covering ]raction O. It is known experimentally, from B e c k e r's investigations 1), that with increasing covering fraction of a Cs covered tungsten surface, the heat of evaporation decreases for the atoms, while it increases for the ions. We have shown that the decrease of the heat of evaporation of the adsorbed ions Jrevaporating in the from of atoms could be ascribed to a decrease of the work function, caused by the formation of an electric double layer consisting of adsorbed ions and their images. Now, this double layer causes at the same time, an increase of the heat of adsorption o f the adsorbed Fig. 1. W h e n the c h a r g e s are d i s t r i b u t e d h o m o ions. In order to realise this, we must g e n e o u s l y t h e c h a n g e in remember that the change in potential in p o t e n t i a l in a d o u b l e layer is l i m i t e d to t h e a double layer is only then limited to the region b e t w e e n the region between both charged planes, when c h a r g e d planes. (A fall of p o t e n t i a l in this figure one considers these charges to be dism e a n s a gain of e n e r g y tributed homogeneously (fig. I). When, for an electron, i.e. larger n e g a t i v e v a l u e of pohowever, the atomic structure of such a tential). double layer is taken into consideration, it appears that outside these planes an attractive or repulsive force is perceptible. In fig. 3 ABC gives the potential curve for an electron which passes (along the line ABC in fig. 2) through an electric double layer, bounded by two planes at a distance d and in which single charged particles are evenly distributed at a distance 2d from each other. If we move the electron in such a way that it hits the Fig. 2. W h e n an e l e c t r o n charges, then DE is followed. If we move m o v e s a l o n g t h e line t h e c h a n g e of the electron so that it passes the double .4BC, p o t e n t i a l e n e r g y is g i v e n layer, close to a pair of electric charges, by t h e line A B C i n fig. 3. 1) J.A. B e c k e r , Physica I
Phys. Rev. 28,357, 1926. 61
962
j.H. DE BOER AND C. F. VEENEMANS
the potential line FGH is followed. These lines show that forces come into action already at distances from t h e double layer comparable with the mutual distance of charges in the double layer. +
Potential
t
F ~
i
A
/ ___
B/__
t
Distance
Fig. 3. C h a n g e of p o t e n t i a l e n e r g y , w h e n a n e l e c t r o n is m o v e d t h r o u g h a d o u b l e l a y e r in s e v e r a l , w a y s . T h e c h a r g e s are d i s t r i b u t e d a t a d i s t a n c e 2d f r o m e a c h o t h e r .
In this w a y a double layer consisting of positive ions and their images exerts an attraction on other positive ions, thereby causing an increase of the binding energy Qi to an amount AQi (see fig. 4), in accordance with experiment. Thus (Q3o ~ Qi + AQi. The value of (Q~)0 can be derived from T a y 1 o r and L a n gm u i r's z) measurements on I I the heat of evaporation in the form of atoms. For this calculation their original S__s..4 . . . . . . . . . -.J___ experimental values have I I been used and not the tabuI lated values, as these have been altered in accordance Fig. 4. W h e n a p o s i t i v e ion is b o u n d t o with their hypothesis of a m e t a l , t h e b i n d i n g e n e r g y Qi is r a i s e d b y an a m o u n t AQi w h e n o t h e r p o s i t i v e ~,active spots" (compare our ions f o r m i n g a d o u b l e l a y e r w i t h t h e i r second communication, § 2) i m a g e s are a l r e a d y p r e s e n t . In table I the values for the heat of evaporation in the form of atoms, ),a are given. According to our second paper § 3
cp
1) J . B . T a y l o r
andI. L a n g m u i r ,
Phys. Rev. 44,433,1933, fig. 9.
A D S O R P T I O N OF ALKALI METALS ON METAL SURFACES. I I I
963
(Xa)o = (Qi)o - - I + *~o where
By means of the values of 0 given in the first column of table I and the effective dipole m o m e n t per adsorbed ion ~z = 6.8 × 10-18 e.s.u., as calculated in communication II § 1 the value of zA~0 can be calculated. These values are given in the third column. W i t h I = 3.88 electron volts and q0o = 4.52 volts, (Q~)ois obtained (4th co.lumn). TABLE I Evaporation of Cs from tungsten. Heat of evaporation in the form of atoms O,a) and in the form of ions (Qi) in electron volts 0
Xa
~A~#
0 0.002 0.004 0.007 0.010 0.022 0.042 0.10
3.00 2.96 2.93 2.89 2.86
0 0.02 0.04 0.06 0.09 0.20 0.38 0.91
2.82 2.74
2.66
Qi
'
2.36 2.34
2.33 2.31 2.31 2.38 2.48 2.93
We see t h a t for small values of 0 (up to 0 = 0.02) Q~ is practically constant and equal to 2.3 electron volts, in complete agreement with the value calculated in communication I § 3. For higher values of 0, however, (0 > 0.02) the positive ions are a t t r a c t e d more strongly, with the result t h a t Q; increases.
§ 3. Electron emission and vapour pressure o] caesium This change of Qi + AQi with 0 requires t h a t the a d s o r p t i o n isotherm be written in the form: Qi+ AQi-- x + ~$8 n =
/n Oe
kT
or, considering t h a t Q~ and I are constants and no is proportional to the vapour pressure p: E$O + n ~
ap
d
AQi
kT
In order to derive a relation between the electron emission a n d the vapour pressure of Cs, A (constant of R i c h a r d s o n's equation)
964
J. H. DE BOER AND C. F. VEENEMANS
must be taken to depend on 0. This dependence can be expressed 1) b y A o = A e- ~ 0
where x is a constant. Dividing the emission equation for bare tungsten "~o hT
io = A T 2 e
by i = A oT 2 e
kT
we get, taking logarithms: i A 0 ~A~0 Iog~ =log~ + kT So long as only ions are adsorbed (up to 0 = about 0.13, see communication IV) AV0 is proportional to th~ number of adsorbed ions n, while, according to the expression A o = A e - ~ ° , log A o / A is proportional to 0 (and consequently to n). From this we obtain i log ~ = B ' n
or
*o
i n = B log -:~o
where B and B ' are constant. Substitution in the equation for the adsorption isotherm gives: n -~ B l o g ~0 = a p e h r X e kT
From R i c h a r d s o n's equation i = A oT 2 e
kT
we obtain e ,-V = A o T 2 _ i
A T 2 e - ao i
1) CompareW. S c h o t t k y andH. R o t h e , HandbuchderExperimentalphysik XIII, page 165 (1928). R. S u h r m a r t n aadR. Deponte, Z.f. Physik 861615, 1933.
A D S O R P T I O N OF ALKALI METALS ON METAL SURFACES. I I I
965
Substitution in the expression for n gives i Blogio=
A T 2 - ~0 ap~
i
e
cdO i e
kT
or finally, combining all constants into one: AOi
i
ilogio =Cpe-
aO k---f e
This equation differs from the one derived in communication II by two exponential factors. For small values of 0 these exponential factors are nearly equal to unity; moreover they counteract each other. Thus, for small values of 0, the equation i i log io
= Cp
which was found experimentally by L a n g m U i r and K i n gd o n, remains valid. That for higher values of O, i log i l l o increases more rapidly with p than according to this expression is caused b y the fact that the increase of ezjOi/~r is greater than the decrease of e-~°. Thus the strong increase of the emission is due to the increase of Qi, which is not wholly compensated b y the decrease of A. 28th April 1934.
III i) A D S O R P T I O N
ENERGY
OF THE
IONS
b y J. H. DE B O E R and C. F. VEENEMANS Natuurkundig Laboratorium der N.V. Philips' Gloeilampenfabrieken Eindhoven/Holland Zusammenfas
s ung
Wenn positive Ionen an eine MetalloberflAche adsorbiert sind, bilden sie m i t i h r e n S p i e g e l b i l d l a d u n g e n e i n e e l e k t r i s c h e D o p p e l s c h i c h t . D i e L a dungen dieser Doppelschicht sind diskret angeordnet und in diesen F~llen m u s s m a n i m m e r b e a c h t e n , d a s s d a s F e l d auch" n a c h A u s s e n d u r c h g r e i f t . D a d u r c h w e r d e n n e u e p o s i t i v e I o n e n s t a r k e r y o n tier M e t a l l o b e r f l A c h e gebunden, wenn schon einige positive Ionen anwesend sind. Aus experirnent e l l e n W e r t e n k a n n die Z u n a h r n e d e r B i n d u n g s e n e r g i e e i n e s C s + - I o n s m i t zunehmender Besetzung berechnet werden. D i e A u s d r f i c k e Itir die E l e k t r o n e n e m i s s i o n y o n d e r I I . M i t t e i l u n g w e t den durch diesen Umstand etwas modifiziert.
§ 1. Introduction In the derivation of the isotherm for the adsorption of alkali metals on metal surfaces in the form of ions (communication II § 4) "¢o n ~ - ape, kT
the adsorption energy Q~ was assumed to be independent of 0. Further in deriving the relation between the electron emission of a Cs covered tungsten surface and the vapour pressure i i log i0 = Cp the constant A in R i c h a r d s o n's emission formula was assumed to be independant of 0. Both assumptions are only approximations; 1) I J . H . de B o e r andC. F. V e e n e m a n s , II J . H . d e B o e r andC. F. V e e n e m a n s ,
Physical, 753, 1934. Physical, 953,1934.
J. H. DE BOER AND C. F. VEENEMANS, ALKALI METALS
96]
we shall now consider what happens if Q~, as well as A, is a function of 0.
§ 2. Increase o/Qi with increasing covering ]raction O. It is known experimentally, from B e c k e r's investigations 1), that with increasing covering fraction of a Cs covered tungsten surface, the heat of evaporation decreases for the atoms, while it increases for the ions. We have shown that the decrease of the heat of evaporation of the adsorbed ions Jrevaporating in the from of atoms could be ascribed to a decrease of the work function, caused by the formation of an electric double layer consisting of adsorbed ions and their images. Now, this double layer causes at the same time, an increase of the heat of adsorption o f the adsorbed Fig. 1. W h e n the c h a r g e s are d i s t r i b u t e d h o m o ions. In order to realise this, we must g e n e o u s l y t h e c h a n g e in remember that the change in potential in p o t e n t i a l in a d o u b l e layer is l i m i t e d to t h e a double layer is only then limited to the region b e t w e e n the region between both charged planes, when c h a r g e d planes. (A fall of p o t e n t i a l in this figure one considers these charges to be dism e a n s a gain of e n e r g y tributed homogeneously (fig. I). When, for an electron, i.e. larger n e g a t i v e v a l u e of pohowever, the atomic structure of such a tential). double layer is taken into consideration, it appears that outside these planes an attractive or repulsive force is perceptible. In fig. 3 ABC gives the potential curve for an electron which passes (along the line ABC in fig. 2) through an electric double layer, bounded by two planes at a distance d and in which single charged particles are evenly distributed at a distance 2d from each other. If we move the electron in such a way that it hits the Fig. 2. W h e n an e l e c t r o n charges, then DE is followed. If we move m o v e s a l o n g t h e line t h e c h a n g e of the electron so that it passes the double .4BC, p o t e n t i a l e n e r g y is g i v e n layer, close to a pair of electric charges, by t h e line A B C i n fig. 3. 1) J.A. B e c k e r , Physica I
Phys. Rev. 28,357, 1926. 61
962
j.H. DE BOER AND C. F. VEENEMANS
the potential line FGH is followed. These lines show that forces come into action already at distances from t h e double layer comparable with the mutual distance of charges in the double layer. +
Potential
t
F ~
i
A
/ ___
B/__
t
Distance
Fig. 3. C h a n g e of p o t e n t i a l e n e r g y , w h e n a n e l e c t r o n is m o v e d t h r o u g h a d o u b l e l a y e r in s e v e r a l , w a y s . T h e c h a r g e s are d i s t r i b u t e d a t a d i s t a n c e 2d f r o m e a c h o t h e r .
In this w a y a double layer consisting of positive ions and their images exerts an attraction on other positive ions, thereby causing an increase of the binding energy Qi to an amount AQi (see fig. 4), in accordance with experiment. Thus (Q3o ~ Qi + AQi. The value of (Q~)0 can be derived from T a y 1 o r and L a n gm u i r's z) measurements on I I the heat of evaporation in the form of atoms. For this calculation their original S__s..4 . . . . . . . . . -.J___ experimental values have I I been used and not the tabuI lated values, as these have been altered in accordance Fig. 4. W h e n a p o s i t i v e ion is b o u n d t o with their hypothesis of a m e t a l , t h e b i n d i n g e n e r g y Qi is r a i s e d b y an a m o u n t AQi w h e n o t h e r p o s i t i v e ~,active spots" (compare our ions f o r m i n g a d o u b l e l a y e r w i t h t h e i r second communication, § 2) i m a g e s are a l r e a d y p r e s e n t . In table I the values for the heat of evaporation in the form of atoms, ),a are given. According to our second paper § 3
cp
1) J . B . T a y l o r
andI. L a n g m u i r ,
Phys. Rev. 44,433,1933, fig. 9.
A D S O R P T I O N OF ALKALI METALS ON METAL SURFACES. I I I
963
(Xa)o = (Qi)o - - I + *~o where
By means of the values of 0 given in the first column of table I and the effective dipole m o m e n t per adsorbed ion ~z = 6.8 × 10-18 e.s.u., as calculated in communication II § 1 the value of zA~0 can be calculated. These values are given in the third column. W i t h I = 3.88 electron volts and q0o = 4.52 volts, (Q~)ois obtained (4th co.lumn). TABLE I Evaporation of Cs from tungsten. Heat of evaporation in the form of atoms O,a) and in the form of ions (Qi) in electron volts 0
Xa
~A~#
0 0.002 0.004 0.007 0.010 0.022 0.042 0.10
3.00 2.96 2.93 2.89 2.86
0 0.02 0.04 0.06 0.09 0.20 0.38 0.91
2.82 2.74
2.66
Qi
'
2.36 2.34
2.33 2.31 2.31 2.38 2.48 2.93
We see t h a t for small values of 0 (up to 0 = 0.02) Q~ is practically constant and equal to 2.3 electron volts, in complete agreement with the value calculated in communication I § 3. For higher values of 0, however, (0 > 0.02) the positive ions are a t t r a c t e d more strongly, with the result t h a t Q; increases.
§ 3. Electron emission and vapour pressure o] caesium This change of Qi + AQi with 0 requires t h a t the a d s o r p t i o n isotherm be written in the form: Qi+ AQi-- x + ~$8 n =
/n Oe
kT
or, considering t h a t Q~ and I are constants and no is proportional to the vapour pressure p: E$O + n ~
ap
d
AQi
kT
In order to derive a relation between the electron emission a n d the vapour pressure of Cs, A (constant of R i c h a r d s o n's equation)
964
J. H. DE BOER AND C. F. VEENEMANS
must be taken to depend on 0. This dependence can be expressed 1) b y A o = A e- ~ 0
where x is a constant. Dividing the emission equation for bare tungsten "~o hT
io = A T 2 e
by i = A oT 2 e
kT
we get, taking logarithms: i A 0 ~A~0 Iog~ =log~ + kT So long as only ions are adsorbed (up to 0 = about 0.13, see communication IV) AV0 is proportional to th~ number of adsorbed ions n, while, according to the expression A o = A e - ~ ° , log A o / A is proportional to 0 (and consequently to n). From this we obtain i log ~ = B ' n
or
*o
i n = B log -:~o
where B and B ' are constant. Substitution in the equation for the adsorption isotherm gives: n -~ B l o g ~0 = a p e h r X e kT
From R i c h a r d s o n's equation i = A oT 2 e
kT
we obtain e ,-V = A o T 2 _ i
A T 2 e - ao i
1) CompareW. S c h o t t k y andH. R o t h e , HandbuchderExperimentalphysik XIII, page 165 (1928). R. S u h r m a r t n aadR. Deponte, Z.f. Physik 861615, 1933.
A D S O R P T I O N OF ALKALI METALS ON METAL SURFACES. I I I
965
Substitution in the expression for n gives i Blogio=
A T 2 - ~0 ap~
i
e
cdO i e
kT
or finally, combining all constants into one: AOi
i
ilogio =Cpe-
aO k---f e
This equation differs from the one derived in communication II by two exponential factors. For small values of 0 these exponential factors are nearly equal to unity; moreover they counteract each other. Thus, for small values of 0, the equation i i log io
= Cp
which was found experimentally by L a n g m U i r and K i n gd o n, remains valid. That for higher values of O, i log i l l o increases more rapidly with p than according to this expression is caused b y the fact that the increase of ezjOi/~r is greater than the decrease of e-~°. Thus the strong increase of the emission is due to the increase of Qi, which is not wholly compensated b y the decrease of A. 28th April 1934.