Contains report on one research project.Joint Services Electronics Program (Contract DA36-039-AMC-03200(E)

Logan, R. M.

Stickney, Robert E.

Sun, P. B.

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VII. PHYSICAL ELECTRONICS AND SURFACE PHYSICSProf. R. E. StickneyP. B. SunA. DEPENDENCE OF PHOTOEMISSION FROM TUNGSTEN ON SURFACETEMPERATURE AND RADIATION FREQUENCYThis report gives a summary of a thesis submitted by P. B. Sun to the Departmentof Mechanical Engineering, M. I. T., May 1965, in partial fulfillment of the requirementsfor the degree of Master of Science.The temperature dependence of photoemission from a polycrystalline tungsten ribbonhas been determined experimentally in the temperature range 300 0K-2200 0 K. Tempera-tures from 1450 0 K to 2200 0K were determined by a micro-optical pyrometer and cor-rected by the emissivity of tungsten at various temperatures. A mercury lamp (Bauschand Lomb HP-100) and sharp cut filters (Corning Glass) were used to obtain radiationat various frequencies and bandwidths. Both thermionic and photoelectric current weremeasured with a Keithley microammeter (Model 150A) with zero suppression capabilitiesof 100 times the total current.The experimental results at low temperatures agree well with the Fowler theory.At temperatures higher than 1900 0 K the photocurrent increases markedly with tempera-ture, the form being exp(const/kT) for all radiation frequencies. Although the Fowlertheory predicts this result for radiation frequencies lower than the threshold frequency,it does not predict the behavior observed here for frequencies higher or equal to thethreshold frequency. The quantum yield at 2200°K is of the order of 10-3 electrons perquantum for all frequencies.We are now attempting to interpret these data theoretically. The experimental pro-gram will continue after we improve the monochromator and tube designs.P. B. Sun, R. E. StickneyReferences1. R. H. Fowler, Phys. Rev. 38, 45 (1931).QPR No. 78

Physical Electronics and Surface Physics

VII. PHYSICAL ELECTRONICS AND SURFACE PHYSICSProf. R. E. StickneyR. M. LoganP. B. SunA. SIMPLE CLASSICAL MODEL FOR THE SCATTERING OF GAS ATOMS FROMSOLID SURFACES1. IntroductionFor the case of gases of extremely low density (i. e. , for free molecule flow), thetransfer of momentum and energy between the gas and a solid surface depends entirelyupon the nature of the collisions of individual gas atoms with surface atoms. A satis-factory theory of this interaction has not yet been established. The principal objectiveof the present study is to formulate a simple model whose behavior agrees qualitativelywith the experimental data for the scattering of a beam of gas particles from a solidsurface.The following symbols are used:u = velocity of gas particleun = component of velocity of gas particle in direction normal to surface planeut = component of velocity of gas particle in direction tangential to surface planev = velocity of surface atom (assumed to be in direction normal to surface plane)M = mass of gas particlem = mass of surface atomj = mass ratio, M/mT = temperature of gas beamgT = temperature of surfaces0 = incident angle (measured from surface normal)01 = outgoing angle (measured from surface normal)= angular deviation of the maximum of the angular distribution of the scatteredparticles from the specular direction.(All angles are measured in the plane containing both the incident beam and thesurface normal.)This work was supported principally by the Joint Services Electronics Program(Contract DA36-039-AMC-03200(E).QPR No. 790 1 00 200 300I / /A905 0oFig. VII-1.Temperature dependenceof scattering patterns.(A) Experimental resultsfor Ar on Pt.I(B) Analytical results.G0 o  In both cases, 0 = 67. 50ann ,. = - O.~800o00and [ = u. 2Curve (i) :Curve (ii):Curve (iii) :Ts/Tg = 1. 24;Ts/Tg = 2. 57;Ts/Tg = 3. 68.0 0o 200 o50T- 100 200 300F B /Fig. VII-2.Mass dependence of scat-tering patterns.(A) Experimental resultsfor He, Ne, and Ar onPt. 1500 (B) Analytical results.In both cases, 0 = 67. 50oand Ts/Tg = 3. 60Curve (i): p. = 0. 02(He on Pt)Curve (ii): 4 = 0. 1(Ne on Pt)Curve (iii):800900. = 0. 2(Ar on Pt).100 200 350/ -- 7 (i ii)i/ (Ii)Fig. VII-3.40 Incident angle dependence ofscattering patterns.(A) Experimental results foro Ar on Pt.I(B) Analytical results.In both cases, p = 0. 2 and,'00 Ts/T = 3. 67Curve (i): 0 = 75 .;00" Curve (ii): O = 600;0Curve (iii): 0 450a80QPR No. 79c-0o'700o90(4.0000F--(VII. PHYSICAL ELECTRONICS AND SURFACE PHYSICS)The experimental results which are relevant to the present study are the lobular scat-tering patterns, examples of which are shown in Figs. VII-1A, VII-2A, and VII-3A.Most of the available experimental results, for a variety of different gases on a varietyof different surfaces, may be described by the following characteristics:1. 8T  is positives2.T is negativeg3. 8M is positive4. 86 may be positive or negativeoCharacteristics 1, 3, and 4 are illustrated in Figs. VII-1A, VII-ZA, and VII-3A, respec-tively. One further characteristic which seems to hold is r1 - 0 as @0 - 0.2. The ModelThe simple classical model which is used is based upon the following principalassumptions: (i) the interaction of a gas atom with a surface atom may be representedl ;unIFig. VII-4. The "Hard-Cube" model.by an impulsive force of repulsion; (ii) the gas-surface intermolecular potential is uni-form in the plane of the surface (hence the interaction does not change the tangentialvelocity of the gas particle); (iii) the surface atoms are represented by independent par-ticles confined by square-well potentials; (iv) the surface atoms have a Maxwellian veloc-ity distribution. The model incorporates many of the same features as that proposedity distribution. The model incorporates many of the same features as that proposedQPR No. 79(VII. PHYSICAL ELECTRONICS AND SURFACE PHYSICS)by Goodman.2 As a result of these assumptions, the model is simplified to the extentthat it contains no adjustable constants. In order to combine assumptions 1 and 2, itis convenient to think of the surface atoms as cubes oriented with one face parallel tothe surface plane and with motion only in the direction normal to the surface plane. Eachgas particle interacts with just one of these cubes (Fig. VII-4).3. Summary of the AnalysisSince the details of the analysis require considerable space, we have chosen to omitthem here. A more complete report has been submitted for publication in the Journal ofChemical Physics.The analysis has been carried out in two stages. In the first stage, the analysis issimplified by representing the velocities of the gas and surface particles by mean valuesinstead of considering the velocity distributions of each. In the second stage, the veloc-ity distributions are considered.The first stage analysis yields only the approximate angular position of the maximumof the scattering pattern, and hence 1, as given by the following expression:1 o + (1)g cos 0An indication of the behavior of Eq. 1 is given in Figs. VII-5 and VII-6.The full analysis involves integration over the distribution functions of the gas andsurface atoms, and this has been done partly by numerical computation. Some of the12- INCIDENT ANGLE,+I0L o = 450 0OR ALL CURVES =+ 6+ -- - L = 0.05LU + 2c( O i i I Ii 1.0 2.0 3.0 4.0-2 Ts/-10-12Fig. VII-5. Characteristics of the approximate analysis: The temperaturedependence of rl, the angular deviation from the specular direc-tion, for several values of the mass ratio ±.QPR No. 79(VII. PHYSICAL ELECTRONICS AND SURFACE PHYSICS)--22--- 20.-ii IL-:-IGL12-io'-,i-iI iMASS RAT:L=0.I FOR ALL 0 = 67.50= 22.50oi- 2- Gi3.0 4.0is / TgFig. VII-6. Characteristics of the approximate analysis: The temperaturedependence of r, the angular deviation from the specular direc-tion, for several values of the angle of incidence, 60.results are shown in Figs. VII-IB, VII-2B, and VII-3B so that they may be comparedwith the corresponding experimental results.4. ConclusionsIt is found that the results for -q given by Eq. 1 are in resonable agreement withthe results from the full analysis. The results from the full analysis are in good qualita-tive agreement with the experimental results as illustrated in Figs. VII-1, VII-2, andVII-3. Significant quantitative results are not expected from such a simplified model.The good qualitative agreement does indicate, however, that this model may contain theprincipal mechanisms of the interaction. The results may also be considered as someindication that the general nature of the experimentally observed scattering patterns isnot dominated by the precise form of the intermolecular potential or by the topographicalform of the atomic surface.R. M. Logan, R. E. StickneyReferences1. J. J. Hinchen and W. M. Foley, "Scattering of Molecular Beams by Metallic Surfaces,"in Rarefied Gas Dynamics, Proceedings of the Fourth International Symposium, editedby J. H. deLeeuw (Academic Press, Inc. , New York, 1965).2. F. O. Goodman, J. Phys. Chem. Solids 26, 85-105 (1965).QPR No. 790i =4 5 0

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Physical Electronics and Surface Physics

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