1
Feb., 1053
FIELD EMISSION MICROSCOPE AND FLASH FILAMENT TECHNIQUES
153
FIELD EMISSION MICROSCOPE AND FLASH FILAMENT TECHNIQUES FOR THE STUDY OF STRUCTURE AND ADSORPTION ON METAL SURFACES BY J. A. BECKERAND C. D. HARTMAN Bell Telephone Laboratories, Murray Hill, N . J . Received June .@. I068
IVitli field emission electron microscopes one can see the structure of the surface of a single crystal a t the tip of a metal “point.” The niagnification is about lo6 and the resolution about 20 X 10-8 cm. At 2800’ K., the surface of W point is heniispherioal. Only the 110, 111 and 100 regions consist of small flat planes. In fields of 50 million volts/cm. and at 1200’K. these planes enlarge. The edges of the planes are seen to be in violent agihtion. Hence surface atoms are mobile a t temperatures above one-third of the melting point. Ba atoms show surface mobility a t 400°K. on the 110 and at 800°K. on the 100 planes. With the flash filament technique one can measure the rate a t which Nz is adsorbed on a W ribbon a t low pressures. After NS has been adsorbed for minutes a t a low temperature, the ribbon is flashed a t 2300°K. The sudden rise of pressure is recorded with an ion gage and measures 0, the layers adsorbed. From a family of e us. time curves one calculates s, the sticking probability. For T = 300’K., s = 0.55 from e = 0 to 1.0. Then s decreases from 0.55 to about 4 X for e = 2.0. These data yield an activation energy for the conversion of a molecule to two adatoms of about 100 cal./g. mole for e = 0 to 1.0 and 5000 cal./g. mole at 0 = 2.0. Other experiments yield 100,000 cal./g. mole for the heat of adsorption of 2 adatoms. The heat of adsorption of molecules is much smaller.
In recent times two new tools have been devel- can be greatly increased it is possible to study the oped which should be of considerable interest to the early stages of adsorption where chemical adsorpphysical chemist in the study of adsorption on met- tion is quite likely to be most pronounced and als. The first is the field emission electron micro- where the processes are likely to be simpler. At scope in which the electron emission from a small any time in this process, the ribbon can be ‘Ylashed” hemispherical surface of a single crystal is pro- a t a high temperature: all the adsorbed molecules jected onto a fluorescent screen where it portrays or atoms are suddenly desorbed, and the resulting an image of the surface magnified about a million- rise in pressure can be recorded, From this, the fold. With it one can see that certain crystallo- number of molecules which were adsorbed up to that graphic planes tend to grow more readily than oth- time can be computed. This number can be comers, that the surface atoms are mobile at tempera- pared to the number of molecules which have imtures of about one-third the absolute melting point, pinged upon the surface in the same time. The and that the ease of mobility depends on the crystal ratio is the ‘(condensation coefficient” or “sticking plane. When controlled amounts of a second ma- probability.” In the past this quantity has been terial are adsorbed on this hemispherical surface frequently assumed to be unity and to be independone can ascertain whether they are preferentially ent of the amount adsorbed. In the derivation of adsorbed on certain planes, the directions in which the Langmuir isotherm it is generally assumed that they migrate on different planes, and the tempera- the sticking probability is proportional to the area tures a t which migration and evaporation occur a t of free surface. The experiments with nitrogen on observable rates. For relatively small flat mole- tungsten yield results which differ drastically from cules such as phthalocyanine, the apparent positions either assumption: At room temperature, the of the benzene rings have been observed. For sticking probability is about 0.6 from zero coverage unusually fine ‘(points,” which yield magnifications until the amount adsorbed corresponds to 1 nitroof ten million, it may be possible to see the splitting gen atom for 4 tungsten atoms (call this 6 = 1.0); up of an adsorbed molecule into atoms and how the between 6 = 1 to 2 the sticking probability derate of this process depends on temperature. creases from 0.6 to approximately l X for The second technique employs the recently im- 6 = 2 to 3, the sticking probability lies between proved ionization gage which measures pressures and 5 x 10-6. At higher ribbon temperatures the mm. and permits the recording sticking probability is even lower than it is at room from 10-lO to of pressure changes in about 0.1 second. Because temperature. of the sensitivity and the speed of this gage it is W-e believe that the sticking probability is a measpossible to measure rates of adsorption from metal ure of the probability that an adsorbed molecule surfaces with an area of only one square cm. and at will be converted to two adsorbed atoms before pressures so low that one monolayer is adsorbed in it will be “reflected” from the surface or evaporate minutes or even hours. This means that processes in a time short compared to one second. On this which heretofore have been said to occur “instanta- point of view one can deduce values of the activaneously” can now be studied in considerable detail. tion energy for the conversion of adsorbed moleBecause the surface area can be quite small it is cules to atoms. These are in the range of 0.5 to 4 possible to prepare the metal in the form of a thin rib- kg. tal. per g. mole which compares with 100 kg. cal. bon with a measurable area. Furthermore, the per g. mole for the early stage heat of adsorption. temperature can be changed easily and quickly by Part I. Field Emission Electron Microscope the passage of electric currents; in particular it is The field emission electron microscope was first described possible to heat the metal to such a high temperaby Muller’ in 1936. Two good reviews have been published ture that its surface is really clean. Because the time scale for the adsorption process (1) E. W.Muller, P h y s . Z., 37, 838 (1936).
J. A. BIWKER, AND C. D. HARTMAN
154
,
Vol. 57
by Jenkins2 and Ashworth .a A recent paper by Becker4 describes in detail how I t may be used to study the surface structure of tungsten and the adsorption properties of barium on tungsten. The essential features of such a microscope are shown in Fig. 1. A fine tungsten “point,” similar in shape to the tip of a needle, is attached to a W loop whose temperature can be varied. When a positive potential of 6 to 9 thousand volts is applied to an anode, fields of 30 to 50 million volts per cm. are produced near the surface of the point. Such high fields pull electrons out of the metal even a t room temperature. These elect,rons come out normal to the surface, travel in approximately straight lines, impinge in the fluorescent screen, and produce a visible attern which can be observed by e e or photographed. If the density of electron emission &om various areas on the point are non-uniform, the pattern on the screen will show corresponding variations in brightness. The magnification is the point to screen distance divided by the radius of curvature of the point. Magnifications of a million with resolving powers of about cm.are readily attained. In special cases it may 20 X be possible to obtain magnifications of ten million and resolving powers of 3 to 5 X 10-8 cm. AQUADAG ANODE, FLUORESCENT SCREEN
w
LOOP
Fig. 1.-Schematic
ENLARGED W POINT
of field emission microscope.
The density of field emission currents from a metal point is given by4
in which F is the field in volts/cm. and pis the work function in electron volts or e.v. From this it follows that variations in j can be produced either by changes in F or in p: j will increase by a factor of 2 either if F is increased by about 5% or i f . 9 is decreased by about 3%. Hence the contrast in pattern intensity will usually be even greater than in optical microscojy. If the surface of the point is very smooth near the tip, will be uniform and variations in the pattern are ascribed to variations in p. A tungsten point which has been heated to 2400°K.is sufficiently smooth so that variations in F are quite small for any angle less than 20” off the wire axis. However, variations in are quite large, so that the current densities from different planes of the single crystal may vary by factors of 1000. Since the tip of the point is so small, it is very likely that it will consist of a single crystal and that its hemispherical surface will expose all possible planes. Hence the pattern should show bright and dark regions which, from their symmetry, can be associated with definite crystallographic planes. Figure 2 shows a series of pictures of the screen for clean tungsten in which only the exposure time was varied. The central dark “rectangle” with a central uniform ellipse is a 110 plane. Above and below it are three 211 planes which are nearly circular. The bright region between the 3 upper 211 planes is a 111 plane which necessarily has 3-fold symmetry. The two small circular dark areas are 100 planes which necessarily have 4-fold symmetry. From such a series, one can conclude that the 110 plane in clean tungsten has the least emission, the 211 planes have higher emissions, the 100 still higher, the 111 plane much higher and that the highest emissions come from regiona surrounding the 100 planes at angles near 15”. The ratio of the highest to the lowest emission is at least 1000 to 1. If such a W point is heat treated at 1200 or 1400°K.and a field of about 50 million volts per cm. is ap lied, the surface shape is changed: the 211 planes and 100 pknes enlarge, the 110 plane changes its shape, and more W atoms accumuIate (2) R. 0.Jenkins, Reports o n Progress in Physica, 9, 177 (1942-1943). (3) F. Ashworth, Advances in Electronics, 3, 1 (1951). (4) J. A. Becker, Bell Svstem Tech., Jr.: SO, 907 (1951).
Fig. 2.-Field
emission from a single crystal of clean tungsten with varying exposure times.
in the 111 region and the regions surrounding the 110 plane, These accumulations or protrusions above the hemispherical surface, produce extra high local fields; since the emission increases so rapidly with the field, even small protrusions .show up as regions of increased emission. Since such protrusions are robably caused by the movement of W atoms over the surgce, one can conclude that W atoms are mobile on a W surface a t 1200°K.even though W melts at 3600°K. One can also conclude that fields of about 50 million volts per cm. can produce forces on the W surface atoms which are about one fifth as large as the forces which hold these atoms to the underlying W atoms. The experiments of Benjamin and Jenkins2 show that similar conclusions a ply to a number of other metals; they probably apply to afi metals. A second method for modifying the emission pattern is to evaporate a forei n element? such as Ba, onto the W. I n this case, the work function is decreased as 8, the concentration of Ba, increases to a monatomic layer. If the applied voltage V,and hence F , were kept constant, the current densities would attain enormously high values. Hence as the Ba concentration increases it is necessary to decrease F by decreasing V . I n eq. (l),the dominant factors are the exponential ones. The variation of p with 8 can be rather simpIy obtained by observing the value of V required for a constant j as @increases,and substituting in the approximate equation p A p o (V/V0)‘/3 4.4 (V/V0)*/3 (2) Here po and V orcfer to 8 = 0, or clean W. V and POare
FIELDEMISSION MICROSCOPE 'AND FLASH FIT~AMENT TECHNIQUES
Feb., 1053
7
Ba on W.
Fig. 3.-Field
155
Y
Migration a t 400" and 600°K.
Pictures taken a t 300°B., 7.4 kv., -10 p ~ ,1 see. emission for Ba on W: migration of Ba on the 110 plane a t 420 and 600°K., 1 sec.
obtained from the experiment. The value of POaveraged over the various planes i s a proximately 4.4 for clean W. At room temperature, fsa on W remains where it is deposited, since the intensity distribution pattern does not change with time. If, now, the temperature of the surface is raised to about 400"K., it is observed that a bright elliptical ring forms at the edge of the 110 plane. This is interpreted to mean that the Ba atoms which were deposited on t.he 110 plane can migrate over this lane at 400"K., but not a t 300°K. When a particular Ea atom reaches the edge of the plane it is held more fimly and can move no further. As more Ba atoms become attached to the edge, the work function of the edge decreases and its emission increases. If T is raised to 600°K.,the bright ring disappears but a broader bright, ring is formed further out from the 110 plane. This is interpreted to mean that a8 the edges of the successive layers of 110 planes come closer together, the Ba atoms are held more firmly a t these edges than they are on the innermost edge; also that Ba atoms held on the innermost edge can be detached in measurable times at 600°K. but not at 400°K. Figure 3 illustrates this behavior. The interpretation of such observations becomes much more convincing after one makes an atomic model of a hemispherical surface of a body centered cubic crystal. Such a model has been constructed, but it is difficult to represent the essential features in a brief article. The model shows that the 110 planes consist of an innermost layer roughly elliptical in shape resting on top of underlying 110 planes. As the planes extend farther into the crystal the shapes of the edges approach a rectangle. The model also shows that a larger atom than W, such as Ba, can touch only 3 W atoms, or make 3 bonds; in order to move over the surface it needs to break only one bond. At the edge of the first 110 plane, a Ba atom can make 4 bonds and must break two of these. It can do this a t 000°K. The model also shows that in other regions of the surface, a Ba atom can make 5 bonds and must break 3 of these in order to move from such positions. Experiments shows that a t 800 to 900"K., Ba can migrate anywhere on the surface. These deductions can be generalized by saying it requires approximately 300°K. per bond to produce changes which are observable in times of the order of minutes. From this generalization and the model, one would predict that as T is increased, surface migration should f i s t be observed on the 110 plane; then on the 211 plane; next on the 111 and 100 planes; and finally on those regions lying between 100 and 211 planes. At low temperatures, Ba should move off the simple planes and become concentrated on the edges of these planes. At 800-90O0K.,Ba should be able to break 3 bonds and should be able to migrate from one side of the point to the other. Another prediction is that evaporation should begin on the 110 plane at about 900°K. but should require 1200'K. on the 111 and 100 planes and 1500" on higher index planes such as 611. A more general prediction is that in any similar system, surface migration should be observable at temperatures much lower than those required to observe evaporation.
Figure 4 shows a pattern for Ba on W after approximately half a layer of Ba was deposited in the upper right portion, and this Ba was migrated a t 800°K. for 5 minutes until it had reached all parts of the surface. Below this photograph is a schematic drawing to indicate the locations of a number of planes. It is to be noted that the emission from the 110, 211 and 100 planes i s small as compared with planes of larger index numbers such as 611, 221 or 421. This means that very little Ba is left on the major planes on which Ba can make only 3 or 4 bonds. Only in regions where Ba can make 5 bonds are there comparatively high concentrations. In these regions the Ba is not uniformly distributed but appears to be concentrated in what might be called "clusters" of about 100 X 10-8 cm. in diameter; these are surrounded by neighboring regions having considerably smaller honcentrations. The term "cluster" does not imply that inside the cluster, the concentration is monatomic while outside it, the concentration is zero. To account, for the difference in emission density inside and outside the clusters, the Ba concentrations need only differ by about 10%. The model affords a simple explanation for these clusters. The clusters are formed most readily in regions described by high index numbers. I n such regions the model shows that the surface is composed of small areas or facets consisting of 110, 211 and 100 planes. A small 100 facet might be surrounded by 110 and 211 facets. From the observations on larger 100,110 and 211 planes it is apparent that at a given T near 1000"K., more Ba is left on the 100 plane than on the 110 and 211 planes, presumably because on the 100 plane Ba makes 4 bonds while on the 110 it makes only 3 bonds. One shoulci.ex$ect that the same thing should be true on facets if their size is larger than about 20 to 40 X 10" cm. Consequently, we interpret these clusters as facets of simple planes on which Ba sticks more firmly than it does on neighboring facets consisting of one or more kinds of other simple planes. Recently Dr. Muller has given a number of lectures in which he ha8 disclosed that protons can replace the electrons in producing an ima e on the fluorescent screen. In this case the potential of %e point is positive and fields of about 200 million volts per cm. are used. Hydrogen molecules are made to impinge on the point at room temperature and ions, which presumably are protons, are pulled off. I n this case the resolving power is greater than in the electron case and considerably more structure can be seen. In particular, the edges of the major planes are brought out more clearly. We are inclined to inter ret these results to mean that when Hz molecules strike a dsurface, they break up into H ions which are mobile on the surface a t 300°K. They congregate on the edges of the planes where the can make more bonds with the W. However, on these e&es they are subjected to higher local fields than on the planes and can be pulled off the tungsten. St.il1 another line of work which indicates that it may be possible to observe the breaking up of adsorbed molecules into adsorbed atoms, is that of Ashworth in England.6 (6)Private communication.
.
156
J. A. BECHER AND'C.D. HARTMAN
Vol. 57
about 5 and an extra high resolving power. This postulate does not sound unreasonable.
Part 11. The Flash Filament Technique6 To describe the flash filament techni ue we will (a) describe the ionization gage, ( b ) describe system in whirh the experiments w r e made, (c) outline thc methods used in taking data and how these data are used to calculate sticking probabilities and (d) give a few typical results. (a) The Ionization Gage.7-The ionization gage consists essentially of a tungsten filament cathode to provide a source of electrons, an anode or molybdenum cage to collect the electrons, and a fine tungsten wire in the axis of the cage to collect the ions. The ion collector is a t ground or 0 potential, the anode is +255 volts and the cathode, -45 volts with respect to the ion collector. The electrons are accelerated toward the cage, pass through it, are turned back by the glass walls which take on a potential slightly negative to the cathode, and circulate in and out of the cage before they are eventually collected by the cage. During their passage through the gas, a few electrons ionize the gas and produce positive ions. The ions produced inside the cage can be collected only by the ion collector. This ion current is amplified by a d.c. amplifier and is measured or recorded. The ions produced outside the cage move toward the glass walls and are not measured. The gage is calibrated by establishing a pressure p of nitrogenin the range from 5 X to 2 X 10-4mm.,measuring this pressure with a McLeod gage and measuring the positive ion current, ip for one or more values of the electron currenti,. I t is found that ipis directly proportional to .i and to p so that i, = g i e p (3) For our gage, the gage constant, g, is 25. Hence if .i = amp. and p = lO-Bmm., i, = lO-'amp. At this 4X pressure 25 ions are produced and measured for every million electrons. The speed of response for this gage is very rapid to changes in pressure, but may be limited by the response time of the amplifier or recorder, usually by the recorder. Before the gage is calibrated and used it must be thoroughly degassed by baking the glass a t a temperature just below its yield point for about 1 hour and subsequently heating all metal parts to temperatures of about 1200 to 1400'K. The gage constant g depends on the size of the cage, the number of turns and diameter of the wire of the cage, the cage potential, the ion collector potential and on the nature of the gas. (b) The Experimental System.-A schematic of the experimental system is shown in Fig. 5. A tungsten fibbon cm. thick 15.2 cm. long, 0.102 em. wide, and 1.27 X
&
Fig. 4a.-Field
emission after Ba has migrated over entire surface.
I00
Fig. 4b.-Location
(b) of crystallographic planes as they appear on the screen.
He used unusually fine W points with a radius of curvature cm. and residual pressures of oxygen of of about 3 X about 10+O mm. At this pressure only a small number of molecules of 02 might be expected to strike the 110 plane in one minute. He observes that occasionally a bright spot appears suddenly inside the dark area of the plane. These spots are 2 to 4 mm. in diameter on the screen. Within a fraction of a second or more, such spots split into two smaller spots separated by their own diameter. They appear to rotate in jumps about their common center. In a short time these two spots either disappear completely or else move off independently and at random over the surface. All these processes are speeded up if tbe tungsten surface is heated. The appearance rates of the bright spots are found to depend on the gas pressure. One is strongly tempted t>o interpret these observations as resulting from the adsorption of single molecules, the partial and temporary splitting up into two atoms which either evaporat>eor split completely into two atoms. Hydrogen shows a similar behavior. Argon shows spots which appear and disappear suddenly but are not observed to split into two components. To account for the observed sizes of the spots on the basis of this interpretation it must be postulated that the presence of these adsorbed molecules distorts the fields in their vicinity in such a way as to result in an extra magnification by a factor of
TO PUMPS
f
PG FF PSC CT ESS
Fig. 5.-Schematic
PRESSURECUACE FLASH - F I L A M E N T P U M P SPEED CONTROL COLDTRAP ELECTRO-STATIC SHIELD
of experimental system.
(6) L. Apker, Ind. Eng. Chem , 40, 5, 846 (1948). Preliminary Reports on this Technique were given by J. P. Afolnar and C. D. Hartman a t the M.I.T. Physical Electronics Conference on April 1, 1950; and by J. A. Becker and C. D. Hartman at the Am. Phys. SOC.Meeting in Schenectady, N . Y. on June 15. 1951. (7) The design of this gage follows that developed by Bayard and Alpert,,Reu. SCLInstrumenh. 21, [SI 571 (1950). T h e important new feature of this design is the small surface area of the ion collector. This decreases the spurious ion currents due to light and soft X-rays and permits pressures of about 10-11 mm. to be measured.
4
FIELDEMISSION MICROSCOPE AND FLASH FILAMENT TECHNIQUES
Feb., 1953
(p) (e)
PRESSURE p VS.TlME 8 I N LAYERS VS.TlME (S) STICKING PROBABILITY, 5 VS.TIME
2.0 1.8
Tw= 000' K. 0.16
1.6 1.4
ui
Poz5.08
X 1O"MM.
0.14
k
-I
vi
>.' 0.12
1.26
3
k -I
a
a
1 . O0 a
0.10
m
a
0.8 Z i
0.6
157
n
I!
0.08
(3
0.06
x
u 0.4
E 0.04
0.2
0.02
0 Fig. 6.-Curves
p,
e
0 -
1 0 0.4 0.8 1.2 1.6 0 200 300 400 500 600 TIME I N SECONDS. e IN L A Y E R S . and s show how the pressure, amount adaorbed e, and sticking probability a vary with time; other curve shows s vs. e. Ribbon temperature was 600°K.
-0
160
is hung in a litw bulb; to it is connected a similar bulb containing the ion gage; a controllable leak permits nit,rogen gas to flow into the system at a constant rate; the gas in the system is pumped out through a 0.159-cm. diameter hole 0.254 cm. long which leads to a liquid air trap and mercury diffusion pump; and a second ion gage measures the pressure on the pump side of the system. The amount of extraneous metal surfaces exposed to the gas are kept as small as possible to minimize spurious adsorption and desorption. The system is degassed by using the most modern techniques for attaining low pressures of residual gas. The pyrex glass is baked at 500" for about an hour and cooled very slowly. Then all metal parts are heated so hot and so long until the pressure no longer increases when the temperature of the metal is increased still more. The glass ware is rebaked a t about 400" for about one hour. All metal parts are again heat treated. I n this way the residual gas pressure can be reduced to to nini. During these treatments the nitrogen reservoir, whose initial pressure is 1 cm., is separated from the system by a glass tip. This tip is subsequently broken wih a magnetic hammer. The systcm contains no greases of any kind. The controlled leak consists of porous ceramic rods covered to a controlled height with mercury. The nitrogen gas passes through a liquid air trap before it enters the system. The volume V of the system is 2.3 liters. The arca of the tungstcn ribbon is3.1 c m 2 . The pump spced S of thc 0.159diain. hole is 0.11 liters/sec. If the only action in the system is that of pumping, then 1 dp/dl = - ( S / V ) p = - 0 . 0 4 8 ~ =: - p (4) 21 I t is customary to express the pumping speed of a system in terms of a time constanl, T, defined by T = V / S . For our system 7 = 21 seconds. Hence the time required to reduce the pressure by a factor of 10 is 2.3 or 48 seconds. (c) Experimental Procedure.-After the glass tip is broken and the leak rate is set, the pressure, p , as measured by the ion gagc, increases to a steady value p , when the molecules/sec. removed by the pump is the same as that introduced by the leak. The ribbon is then flashed a t 2300°K. which removes all adsorbed gases as evidenced by the fact
that increasing T above this value produces no increase in p . During this flash, the pressure rises and then falls until after about 4 minutes it returns to the same steady state pressure, po, as before. At times t = 0, the heating current is reduced so that the ribbon assumes a "cold" temperature, TO,which may be room temperature or higher. Thereafter the ribbon adsorbs nitrogen and the pressure drops to a much lower value than PO, stays a t this value for an appreciable time and then starts rising; after a longer time the pressure asymptotically approaches PO. Figure 6(p) shows how p varies with t. For this case Towas 600°K.
If at any time t we wish to know how many molecules have been adsorbed, we flash the ribbon a t 2300°K. and observe or record A p , the sudden rise in p . If M represents molecules per then from kinetic theory it follows that AM = K V A p = AMIO
(5)
in which K is the molecules per liter for p = 1 mm. For N2 a t T = 300"K., K = 3.2 X l O I 9 molecules per liter per mm. Instead of reporting the amount adsorbed in term's of M we choose to report it in terms of 0 which is defined as 0 = M / M 1 where M1 is 1.25 X loi4molecules per cmS2. We choose this value for M I because for a 100 plane of tungsten it represents one N atom for 4W surface atoms and because our experiments indicate that the adsorption properties show marked changes when 0 = 1, or 2. In a sense this amounts to defining a monolayer when 0 = 1 or 1N atom for 4W atoms. If the adsorption and the flash off procedures are repeated a t a series of values of t, one obtains a 0 os. t curve such as that shown in the middle plot of Fig. 6 (0). From these two curves one can deduce what fraction of the molecules that strike the surface stick to it, or condense on it, or accumulate on it.
J. A. BECKER AND C. D. HARTMAN
158
Tentatively we shall call this fraction the sticking probability and represent it by s. From this it follows that dB
M I 2 = rate of increase of adsorbed molecules per sec
Y
Vol. 57
is that at that value of p , 8 will grow until it reaches the value corresponding to that straight line. For pressures less than this x intercept and the 8 marked on that line, E is numerically greater than vps and
C I ~ per . ~
. .
= molecules/cm.2/sec. that strike the surface when p = 1
mm
For Na and T = 300”K., Y r= 3.8 X 10” molecules/cm.2/ sec. E = molecules/cm.”sec. which evaporate.
It will be shown below that for T,less than 1000°K. and for 8 less than 1.8,E is negligible compared with ups. Hence s can be calculated for any t by (7)
a
Figure 6(s) shows how s varies with t. Since 0 is known for any t, s can be plotted as a function of 8 and is shown in the adjacent plot. A general method for determining both s and E . from Eq. 6, is to note that de/dt, s and E are functions of t and hence of e; but at a constant 8, d8/dt should vary linearly with p . Hence a plot of dO/dt us. p with 8 as a parameter should yield a straight line whose slope is v / M 1s or 3.04 X lo6 s, while the y intercept should be -E / M 1 which is the evaporation rate expressed in layers/sec. To obtain the necessary data we obtain a family of p us. t and 8 us. t curves for a series of values of the leak rate L . For any 0 we obtain a series of d8/.dt values for different L curves and plot these against the corresponding values of p obtained from the family of p vs. t curves. In Fig. 7 are-plotted such de/dt us. p lines for a range of values of 8. For this figure, T,was 1100°K. The lines for constant 6 are indeed straight and the d8/dt intercepts are 0 or negative. This figure shows that as e increases: the slopes decrease and hence s decreaxes; the d8/dt intercepts become larger and hence the evaporation rates increase. Similar plots for “cold” temperatures less than 1000°K. and sufficiently low pressures, show straight lines all of which pass through the origin. This means that E is negligible compared to vps.
m
>-
c
4
rn
=l
m
Pa
0
z1(
0 c
v1
10-50
0.5
1.0
1.5 2.0 9 IN LAYERS.
2.5
3.0
3.5
Fig. 8.-Log s us. 9 for four values of cold temperature. T AS PARAMETER
1
I
I
1500°K/
/
/
d z
0 10-1. 10-1 U
i ,./’
i
Lu
A‘
v)
a w
a m
20
a
Lu
H
’5
z
ul
a W
u-
VI
Lu
a 10
c Q a
a W
3
c
10-2
5
0’
I
10-3
z
5
0
f *J
+ Q
m
0 10-4
a a
2w PRESSURE, p IN M M OF Hg. Fig. 7.-The variation of adso: tion rate de/dt with presThe slope of any line sure for various e: T, = 1100 determines s; the intercept is the evaporation rate.
k.
One might ask: “What is the significance of the 2 or p intercept for which d0ldt = O?” The ariywer
10-5 0
.
Fig 9.-Log
1.0
1.5 2.0 2.5 0 IN LAYERS, (evaporation rate) us. amount
0.5
several temperatures.
3.0
3.5
adsorbed for
Feb., 1953
MONOXIDE ON IRON:SURFACES ADSORPTION OF HYDROGEN AND CARBON
d8/dt is negative; which means that 8 would decrease. For Fig. 7 we chose conditions such that d8ldt for constant2 was propol‘tional to p . Under some conditions this is no longer true: at low enough values of p , de/dt increases linearly with p but at higher p this rate decreases and d6’/dt may become independent of p . This non-linearity is quite small for 6’ less than 1.0 but becomes more pronounced as 6’ increases from 1 to 2 at temperatures less than 1000°K. I n the third layer, dO/dt again becomes linear with p even a t higher pressures. (d) Sticking Probability and Evaporation Rates as Functions of 0 and T.-In Figs. 8 and 9 we have assembled the available information on s and E obtained by the techniques outlined above. Figure 8 shows how log s varies with 6’ for four values of Tc or the temperature of the ribbon. It is to be noted that a t room temperature, the sticking probability is constant from e = 0 to about 6’ = 1. Beyond this, s decreases exponentially with 8 and drops to a t e = 2. Between 6 = 2 and values of about e = 3, s is comparatively constant. For nearly clean tungsten, the sticking probability decreases rapidly with ribbon temperature. For higher values of 8, the temperature dependence of s is more complicated. In some ranges of 6, s decreases and then increases again as T increases. From extrapolation of these curves to lower temperatures one might expect that a t about T = 2OO0I
