Surface, catalytic, and magnetic properties of small iron particles:

 Caren Anderson
 12 days ago
 Views:
Transcription
1 Proc. Ntl. Acd. Sci. USA Vol. 74, No. 3, pp , Mrch 1977 Chemistry Surfce, ctlytic, nd mgnetic properties of smll iron prticles: The effect of chemisorption of hydrogen on mgnetic nisotropy* (superprmgnetism/mgnetic nisotropy/chemisorption/supported ctlysts/mossbuer effect) M. BOUDARTt, J. A. DUMSICt, AND H. TOPS Stuffer Lbortories of Chemistry nd Chemicl ngineering, Stnford University, Stnford, Cliforni 9435 Contributed by Michel Boudrt, November 11, 1976 ABSTRACT The superprmgnetic behvior of very smll prticles of metllic iron (c 1.5 nm), with bout hlf of their toms t the surfce, is chnged reversibly by dsorption nd desorption of hydrogen below the superprmgnetic trnsition temperture. The chnge fter dsorption implies lowering of the nisotropy energy brrier for the mgetic relxtion of iron nd is scribed to chnge in c tl ine shpe. No such chnges re observed for lrger prticles of iron (c 8 nm) with bout 1% of their toms t the surfce. We hve prepred nd chrcterized smll prticles of metllic iron supported on mgnesium oxide (1). The rte of mmoni synthesis on these iron prticles ws shown to increse with increse in their size (2). The behvior of the smller prticles ws scribed to the lower reltive concentrtion of certin surfce toms with low coordintion number; chnges in the mgneticlly split Mossbuer spectr fter nitrogen dsorption indicted tht the surfce concentrtion of these prticulr sites ws pprently incresed by chemisorption of nitrogen (3). But it ws not estblished unmbiguously whether the chnges in superprmgnetic behvior indicted by the Mossbuer effect were due to nitrogen dsorption itself or to chnge in surfce structure brought bout by nitrogen dsorption. The present work ws initited to resolve this question. Hydrogen ws selected s n dsorbte, nd mgnetic susceptibility ws used in ddition to Mossbuer spectroscopy to provide the complementry nd, s it turned out, decisive missing informtion. XPRIMNTAL The Mossbuer spectrometer, the cells, nd the gs hndling systems hve been described elsewhere (1, 4). The essentil feture is the cpbility of collecting Mossbuer spectr with the smple in flowing plldiumdiffused hydrogen or purified helium between 3 nd 8 K within ±1 K. Helium ws used s convenient, noncontminting lterntive to high vcuum Ṫhe mgnetic susceptibility dt were obtined by the Frdy method, with n pprtus described elsewhere (5). In brief, wtercooled electromgnet provided vrible fields up to 3 kam (1 G = 13 Am') nd field grdients up to 3 MAm2 (1 Oe = 79.6 Am2). The smple ws suspended in qurtz bucket from Chn electroblnce enclosed in Abbrevitions: D, dispersion; M, mgnetiztion (ka m'1); HIT, field divided by temperture (AmlK1); TB, temperture t which hlf the metllic iron prticles re superprmgnetic. * This is pper no. IV in series. Ppers nos. I, II, nd III re refs. 1, 2, nd 3, respectively. t To whom queries should be ddressed. t Present ddress: Deprtment of Chemicl ngineering, University of Wisconsin, Mdison, Wisc Present ddress: Hldor Topsoe Reserch Lbortories, Lyngby, Denmrk. multipurpose gshndling vcuum system tht llowed gssing with H2 or He nd evcution to O4 P between 77 nd 72 K. For purifiction, the H2 ws pssed through Deoxo unit, nd the He ws pssed through copper turnings t 5 K. Both gses were subsequently pssed through seprte moleculr sieve (Linde 13X) trps t 77 K. The smples, prepred nd chrcterized s described elsewhere (1), were 1%, 3%, nd 8% iron (wt/wt) supported on mgnesium oxide with metllic iron dispersions of.5,.2, nd.1, respectively (dispersion, D, of the metl is defined s the frction of the iron toms tht re surfce toms). The corresponding surfce verge prticle sizes were 1.5, 4., nd 8. nm, respectively. The frction of the iron present s 57Fe for these three smples ws.26,.32, nd.22, respectively. For convenience these three smples will be referred to s Fe(D =.5), Fe(D.2), nd Fe(D = =.1), respectively. RSULTS Mossbuer Spectroscopy. A known quntity of the smple Fe(D =.5) ws reduced in flowing H2 ccording to the previously described reduction schedule (1). M6ssbuer spectr were then collected in flowing H2 t 298 nd 683 K (Fig. 1) nd in flowing He t 683 K (Fig. 2). The qulittive fetures of these spectr revel two different sttes of iron in the reduced smple: metllic iron giving rise to the mgneticlly split spectrl component, nd Fe2+ in MgO which is responsible for the centrl spectrl doublet (1). In the present study, it is the metllic iron species tht is of interest. It represents bout hlf of the totl iron in ll the reduced smples. The prticle size dependence on the bove effect of the gseous tmosphere over the smple ws studied by obtining spectr of smple Fe(D =.2). This smple ws reduced, nd spectrum ws tken t 39 K in flowing H2 with the velocity offset method, which llows the scnning of the two metllic iron peks tht re locted the furthest from the zero of velocity (6). This method provides greter sensitivity to chnge in the metllic iron spectrum thn tht possible with the constnt ccelertion mode used to collect the dt of Figs. 1 nd 2. The smple ws then heted to 683 K in flowing H2 followed by switching to flowing He. After 1 h t 683 K in flowing He, the smple ws gin cooled to 39 K nd second spectrum ws tken t this temperture in flowing He. The two spectr re shown in Fig. 3. For smple Fe(D =.5), the constnt ccelertion velocity mode ws used in order to record simultneously the chnges in the different iron spectrl components. Since this method does not hve the sensitivity of the offset method, computer nlysis of the spectr shown in Figs. 1 nd 2 ws undertken. The mechnics nd rtionle of the computer nlysis hve been described elsewhere (1), but the essentil fetures of the computer fitting will be outlined here. The mgneticlly split metllic iron component ws fitted with six peks, the two peks 86
2 Chemistry: ry ( b VLOCITY, mm s' FIG. 1. M6ssbuer spectr of 1% Fe/MgO smple in H2. () t 673 K; (b) t 298 K. closest to the zero of velocity being constrined to be equl. The Fe2+ component ws fitted with two peks of equl dip nd width, nd the superprmgnetic metllic iron component, hidden by the Fe2+ spectrum, ws tenttively given single, unconstrined pek. From the position nd temperturedependence of the unconstrined pek, this spectrl component cn be ssigned to superprmgnetic metllic iron (1). It should be noted here tht the superprmgnetic spectrl component could hve been fitted with more thn one peke.g., n symmetry doublet (6). However, the ddition of more peks to the lredy complex centrl region of the spectrum is not wrrnted. The results of the computer nlysis for the spectr shown in Figs. 1 nd 2 re presented in Tble 1. The spectrl res hve been corrected for the nonresonnt bckground count rte ccording to the procedure described by Housley et l. (7), the vrition in these corrections not exceeding 1% from spectrum to spectrum. The spectr of Fig. 3 showed 6% increse in the mgneticlly split re with the switch from H2 to He. Additionl experiments showed tht this chnge disppered completely with the switch bck, from He to H2. The sme remrk pplies to chnges recorded in Tble 1. In other words, ll chnges in spectr cused by switching from H2 to He re reversible. As to smple Fe(D =.1), the metllic iron spectrl prmeters remined unchnged to within 1% s the gs flowing over the smple ws switched from H2 to He between 3 nd 683 K Z CO Q88  Q86 (.1) 1. Q98 _ Q Boudrt et l _ VLOCITY, mmsi FIG. 2. M6ssbuer spectr of 1% Fe/MgO smple t 683 K. () in H2; (b) in He. f i '11'i.' V I.I4.tPor". ; 1 P. ** VI1%, T % I, '11. '\ ra. '. ; A: i :i I :. b 4 Proc. Ntl. Acd. Sci. USA 74 (1977) 87 Tble 1. Metllic iron spectrl prmeters of Fe(D =.5) In H2 In H2 In He Prmeter t 298 K t 683 K t 683 K Mgneticlly split re (mms'), ± Superprmgnetic re (mms), ± Totl re (mms1), ± Frctionl superprmgnetic re, ± Internl mgnetic field* (MAm), ± Isomer shiftt for mgneticlly split line (mms1), +± * Compred to tht of NBS Fe foil: I.2 MAm1 t 298 K. t Isomer shifts reported with respect to metllic iron t 298 K. Mgnetic Susceptibility. Smple Fe(D =.5) ws reduced in flowing H2, fter which mgnetic susceptibility dt were collected t tempertures of 71, 74, 65, 49, 386, 299, nd 77 K in sttic H2 (Fig. 4A). A density equl to 3.58 gcm3 for the smples ws used in the clcultion of the mgnetiztion (M). Above 299 K, the metllic iron prticles behved superprmgneticlly, s evidenced by the superposition of curves showing M versus field divided by temperture (HIT) (8). The minor devition from complete superposition (in the low mgnetiztion direction) s the temperture is incresed is due to the temperturedependence of the spontneous mgnetiztion nd does not represent devition from superprmgnetic behvior. Quite clerly, however, the mgnetic behvior t 77 K does not fll in superposition with the MversusH/T curves obtined t higher tempertures, nd this devition must be ttributed to deprture from complete superprmgnetic behvior. An dditionl experiment, with results not shown in Fig. 4A, showed tht MversusH/T curve of dt t 193 K could be superposed with those obtined t higher tempertures. L 1. I.. , i,...%.92 I z 1. z.84 Cn O &O VLOCITY, mms' FIG. 3. M6ssbuer spectr of smple Fe(D =.2) t 39 K. () in H2; (b) in He. b
3 88 Chemistry: Boudrt et l. Proc. Ntl. Acd. Sci. USA 74 (1977) 4y 3 A [.h B IA. 1o 6A B ~~~~~~~AA S o^ ozo A o A /? / & HrT, Am'. K' H/T, Am1K' FIG. 4. Mgnetiztion (M) versus field/temperture (H/T) in H2. (A) Fe(D =.5).,71 K;, 74 K; O.,65 K; &, 49 K; v, 386 K; 299 Before proceeding, it should be mentioned tht no hysteresis effects were found t those tempertures for which Mversus HIT superposition ws observed. However, devitions from MversusH/T superposition were ccompnied by hysteresis effects when the temperture ws sufficiently lowered, nd the dt reported in these cses were collected by strting t the highest field strength nd progressively recording dt t lower field strengths. Upon completion of the mgnetic susceptibility dt t 77 K, the smple ws heted to 74 K in flowing H2; He ws then flowed over the smple for 1 hr t 74 K, nd dt were collected in sttic He, first t 73 K nd subsequently t 33 nd 77 K. A comprison of these MversusH/T dt in H2 nd He is shown in Fig. 5A nd B. The sme experimentl protocol ws followed to gther similr dt for smple Fe(D =.1) t 71, 536, 31, nd 77 K in sttic H2 (Fig. 4B) nd in both H2 nd He t 31 nd 77 K (Fig. 6A nd B). DISCUSSION Superprmgnetic behvior of smll iron prticles A smll prticle of iron below its Curie pointi.e., single mgnetic dominpossesses single mgnetic moment nd behves like free superprmgnet t sufficiently high tempertures. As temperture is decresed, nisotropies in the mgnetic energy with respect to the mgnetiztion direction of the prticles become more nd more importnt, compred to the therml energy kt (6). Indeed, if represents n nisotropy energy brrier, the relxtion time r for the prticle mgnetiztion depends exponentilly on temperture: T = ro exp(/kt) [1] in which To is constnt. As the temperture is decresed sufficiently so tht r pproches the chrcteristic time for the experiment, the prticle mgnetiztion does not rech therml equilibrium with the pplied field during the time of the experiment. This results in devition from superprmgnetic behvior in the lowmgnetiztion direction for rndomly oriented prticles since mgnetic nisotropy tends to prevent the prticle mgnetic moment from ligning with the pplied field. A useful feture of combining Mossbuer spectroscopy nd mgnetic susceptibility for studying superprmgnetic behvior is tht the criticl time scle is pproximtely 18 sec for Mbssbuer spectroscopy but of the order of 12 sec for mgnetic susceptibility (9). In prticulr, the temperture (TB) 1 2 H/T, Am'K' H/T, Am'K' FIG. 5. Mgnetiztion (M) versus field/temperture (H/T) for Fe(D =.5) bove nd below superprmgnetic trnsition temperture (TB). (A) Above TB., in H2 t 299 K;, in He t 33 K. (B) Below TB., in H2 t 77 K;, in He t 77 K.
4 Chemistry: Boudrt et l. Proc. Ntl. Acd. Sci. USA 74 (1977) A ie 2o H/T, Am1K' H/T, Am' K' FIG. 6. Mgnetiztion (M) versus field/temperture (H/T) for Fe(D =.1) ner nd below superprmgnetic trnsition temperture, (TB). (A) Ner TB, in H2 t 31 K; o, in He t 31 K. (B) Below TB., in H2 t 77 K; 3, in He t 77 K. t which hlf of the metllic iron prticles re superprmgnetic must be very different for both types of experiments. With reference to the Mossbuer dt of Tble 1, TB cn be estimted to be pproximtely 8 K for smple Fe(D =.5). Following the ides of Kundig et l. (1, 11) nd McNbb (12), the mgnetiztion relxtion time t TB for prticles with size equl to the volume verge dimension of the prticle size distribution is pproximtely equl to the nucler Lrmor precession time, TL. Tht is, TI= KTOexp ['TB [2] in which K is n nisotropy energy brrier constnt for mgnetic relxtion, nd (V) is the verge prticle volume. An nisotropy energy brrier constnt of pproximtely 1 J.cm3 cn be thereby clculted for the smll iron prticles. In single crystls of iron, the nisotropy of the mgnetic energy with respect to different crystllogrphic directions (mgnetocrystlline nisotropy) cn be mesured, nd n order of mgnitude vlue of the energy brrier constnt is 12 to 11 JIcm (13). Clerly, this vlue is too smll to explin the present results. If the smple of iron is under stress, n dditionl mgnetic nisotropy my be induced due to mgnetostriction effects. A vlue for this type of nisotropy effect is hrder to estimte, but it hs been found tht this energy brrier constnt is roughly equl to 11 Jcm3 (14) for iron films on MgO supports. Demgnetiztion effects crete mgnetic nisotropy in certin directions in ccordnce with the shpe of the prticle, nd this type of effect is clled "shpe nisotropy." For iron, the energy brrier constnt for shpe nisotropy cn be estimted to be bout 1 Jcm3 for prticle with n spect rtio of.5 (15). For smll prticles, the effect of the surfce must be tken into ccount, nd this could be the origin of yet nother type of mgnetic nisotropy. A phenomenologicl theory of surfce nisotropy hs been proposed by NMel (16), nd vlue for this nisotropy energy brrier cn be estimted to be 17 Jcm2 (17). The conversion of this vlue to volumenormlized energy involves the surfcetovolume rtio of the prticle (since the nisotropy energy brrier is now proportionl to the prticle surfce re insted of the prticle volume), nd for 2.5nm prticle the energy brrier constnt corresponds to c 1 Jcm3. From the Mossbuer spectroscopy vlue of TB = 8 K for smple Fe(D =.5), nd from the time scles of 18 nd 12 sec for the Mossbuer event nd mgnetic susceptibility experiment, respectively, q. 1 gives TB = 9 K for the ltter. This is in excellent greement with the observtion recorded bove, ccording to which the MversusH/T curve t 193 K cn still be superposed with the other curves t higher temperture but not with tht obtined t 77 K. Hence, from direct mgnetic susceptibility dt, TB must be between 77 nd 193 K. Let us note tht, for smple Fe(D =.1), devitions from complete superprmgnetic behvior re observed t 31 K. But these devitions re smll, so tht TB for this smple must be slightly higher, sy round 35 K. In summry, superprmgnetic behvior of the iron prticles studied in this work is clerly indicted in selfconsistent mnner by the mgnetic informtion obtined by techniques with criticl times differing by 11. Let us now exmine chnges in superprmgnetism brought bout by chemisorption. ffect of hydrogen chemisorption on mgnetic nisotropy Upon switching from H2 to He there ws 12% increse in the re of the mgneticlly split spectrl component of metllic iron for Fe(D =.5), 6% increse in the re of the outer peks of the sme component for Fe(D =.2), nd no observble chnge for Fe(D =.1). Also, upon switching from H2 to He, there ws no chnge in the mgnetiztion curves for Fe(D =.5) bove TB (Fig. 5A) nd for Fe(D =.1) bove nd below TB (Fig. 6A nd B). But there ws chnge in the direction of lower mgnetiztion for Fe(D =.5) below TB (Fig. SB). All these dt indicte tht chemisorbed H2 decreses the mgnetic nisotropy brrier of smll (D =.5, D =.2) iron prticles but hs no observble effect on the superprmgnetic behvior of lrger ones. One possible explntion is tht chemisorbed H2 might weken the exchnge interction between metl toms t the surfce nd below the surfce, thereby forming mgneticlly smller prticle. This explntion hs been proposed to explin chnges in mgnetic properties of nickle fter chemisorption of oxygen (18). But for the system H2iron, this explntion is in conflict with the fct tht, for the smllest prticles (D =.5), neither the internl mgnetic field nor the isomer shift were ffected by
5 81 Chemistry: Boudrt et l. H2 chemisorption (Tble 1), nd no effect of H2 chemisorption on mgnetiztion ws detected bove TB (Fig. SA). Possible rtefcts due to ccidentl oxygen chemisorption or interction with the MgO support cn lso be discounted by these observtions s well s by the constncy in totl metllic spectrl re (Tble 1) when H2 ws replced by He. The chnge of mgnetic nisotropy by chemisorption hs been reported in the cse of H2 on nickel (19) nd, more recently, in the cse of dsorbed orgnic molecules on smll finite prticles (2, 21). The lst question concerning the H2iron system is: If H2 chemisorption does decrese the mgnetic nisotropy brrier of prticles of iron with D =.2 or.5, how does it do it? The best explntion seems to be tht bsed on Neel's concept of surfce mgnetic nisotropy. The vlue of the nisotropy brrier constnt for Fe(D =.5) is comptible with either Neel's estimtes of surfce mgnetic nisotropy or shpe nisotropy. It is perhps impossible to distinguish between these effects for prticles with dimeters s smll s 1.5 nm. Indeed, if chemisorption induces chnges in surfce structure, it must lso chnge the shpe of these very smll prticles. Such chnges re not expected for lrger prticles, t lest t moderte tempertures nd during reltively short periods of observtion. This is indeed wht ws observed in the present work. Conclusion A combintion of observtions by Mossbuer spectroscopy nd conventionl mgnetic studies hs led to the conclusion tht chemisorbed hydrogen decreses the mgnetic nisotropy brrier of very smll metllic iron prticles (c 1.5 nm) but does not do so in ny observble mnner for lrger prticles (c 8 nm). This effect is ttributed to chnges in surfce structure nd/or shpe of the smller prticles. Stimulting discussions with Drs. J. H. Anderson nd J. H. Sinfelt re hertily cknowledged; we wish to thnk B. Turnhm for vlued help. Support of this work by Ntionl Science Foundtion Grnt GK Proc. Ntl. Acd. Sci. USA 74 (1977) 17451X is grtefully cknowledged. J.A.D ws Ntionl Science Foundtion Fellow during the course of this work. Thnks re lso due to xxon Reserch nd ngineering Co. for.generous finncil help. 1. Boudrt, M., Delbouille, A., Dumesic, J. A., Khmmoum, S. & Topsoe, H. (1975) J. Ctl. 37, Dumesic, J. A., Topsoe, H., Khmmoum, S. & Boudrt, M. (1975) J. Ctl. 37, Dumesic, J. A., Tops6e, H. & Boudrt, M. (1975) J. Ctl. 37, Topsoe, H., Dumesic, J. A. & Boudrt, M. (1973) J. Ctl. 28, Turnhm, B. (1974) Ph.D. Disserttion, Stnford University. 6. Dumesic, J. A. & Topsoe, H. (1976) Adv. Ctl Housley, R., rickson, N.. & Dsh, J. D. (1964) Nucl. Instrum. Methods 27, Selwood, P. W. (1962) Adsorption nd Collective Prmgnetism (Acdemic Press, New York), Chp. 3, pp Ben, C. P. & Livingston, J. D. (1959) J. Appl. Phys. 3,12 S129 S. 1. Kundig, W., Bommel, H., Constbris, G. & Lindquist, R. H. (1966) Phys. Rev. 142, Kfundig, W., Ando, K. J., Lindquist, R. H. & Constbris, G. (1966) Czech. J. Phys. 17, McNbb, T. K. (1968) Ph.D. Disserttion, University of Western Austrli. 13. Morrish, A. H. (1965) The Physicl Principles of Mgnetism, (John Wiley nd Sons, New York), p Kirenski, L. V., Pynko, G. P. & Pynko, V. G. (1975) J. Appl. Phys. 39, Morrish, A. H. (1968) J. Appl. Phys. 39, NMel, L. (1954) J. Phys. Rdium 15, Jcobs, I. S. & Ben, C. P. (1963) in Mgnetism, eds. Rdo, G. T. & Suhl, H. (Acdemic Press, New York), Vol. III. 18. Geus, J. W. & Nobel, A. P. P. (1966) J. Ctl. 6, Dietz, R.. & Selwood, P. W. (1961) J. Chem. Phys. 35, Berkowitz, A.., Lhut, J. A., Jcobs, I. S., Levinson, L. M. & Forester, D. W. (1975) Phys. Rev. Lett. 34, Morup, S., Tops6e, H. & Lipk, J. (1976) Intl. Conf. Mossbuer Spect. (Corfu, Greece).
Acceptance Sampling by Attributes
Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire
More informationTests for the Ratio of Two Poisson Rates
Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson
More informationMeasuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n1)/ E/[ n(n1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
More informationSimulation of Eclipsing Binary Star Systems. Abstract
Simultion of Eclipsing Binry Str Systems Boris Yim 1, Kenny Chn 1, Rphel Hui 1 Wh Yn College Kowloon Diocesn Boys School Abstrct This report briefly introduces the informtion on eclipsing binry str systems.
More informationMinimum Energy State of Plasmas with an Internal Transport Barrier
Minimum Energy Stte of Plsms with n Internl Trnsport Brrier T. Tmno ), I. Ktnum ), Y. Skmoto ) ) Formerly, Plsm Reserch Center, University of Tsukub, Tsukub, Ibrki, Jpn ) Plsm Reserch Center, University
More informationCalculus  Activity 1 Rate of change of a function at a point.
Nme: Clss: p 77 Mths Helper Plus Resource Set. Copright 00 Bruce A. Vughn, Techers Choice Softwre Clculus  Activit Rte of chnge of function t point. ) Strt Mths Helper Plus, then lod the file: Clculus
More informationTHERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION
XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es
More informationConducting Ellipsoid and Circular Disk
1 Problem Conducting Ellipsoid nd Circulr Disk Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 (September 1, 00) Show tht the surfce chrge density σ on conducting ellipsoid,
More informationOn the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou
On the Uncertinty of Sensors Bsed on Mgnetic Effects E. ristoforou, E. Kyfs, A. Kten, DM Kepptsoglou Ntionl Technicl University of Athens, Zogrfou Cmpus, Athens 1578, Greece Tel: +3177178, Fx: +3177119,
More informationPurpose of the experiment
Newton s Lws II PES 6 Advnced Physics Lb I Purpose of the experiment Exmine two cses using Newton s Lws. Sttic ( = 0) Dynmic ( 0) fyi fyi Did you know tht the longest recorded flight of chicken is thirteen
More informationNUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.
NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with
More informationMATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs
MATHS NOTES The Institute of Eduction 06 SUBJECT: Mths LEVEL: Higher TEACHER: Aidn Rontree Topics Covered: Powers nd Logs About Aidn: Aidn is our senior Mths techer t the Institute, where he hs been teching
More informationChapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses
Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of
More information4. CHEMICAL KINETICS
4. CHEMICAL KINETICS Synopsis: The study of rtes of chemicl rections mechnisms nd fctors ffecting rtes of rections is clled chemicl kinetics. Spontneous chemicl rection mens, the rection which occurs on
More informationThe International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O
IAPWS R7 The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem
More informationExperiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION
Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Purpose: Prt I: The cid ioniztion constnt of wek cid is to be determined, nd the cid is identified ccordingly.
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationVibrational Relaxation of HF (v=3) + CO
Journl of the Koren Chemicl Society 26, Vol. 6, No. 6 Printed in the Republic of Kore http://dx.doi.org/.52/jkcs.26.6.6.462 Notes Vibrtionl Relxtion of HF (v3) + CO Chng Soon Lee Deprtment of Chemistry,
More informationPartial Derivatives. Limits. For a single variable function f (x), the limit lim
Limits Prtil Derivtives For single vrible function f (x), the limit lim x f (x) exists only if the righthnd side limit equls to the lefthnd side limit, i.e., lim f (x) = lim f (x). x x + For two vribles
More informationSection 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40
Mth B Prof. Audrey Terrs HW # Solutions by Alex Eustis Due Tuesdy, Oct. 9 Section 5. #7,, 6,, 5; Section 5. #8, 9, 5,, 7, 3; Section 5.3 #4, 6, 9, 3, 6, 8, 3; Section 5.4 #7, 8,, 3, 5, 9, 4 5..7 Since
More informationJackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell
Jckson 2.26 Homework Problem Solution Dr. Christopher S. Bird University of Msschusetts Lowell PROBLEM: The twodimensionl region, ρ, φ β, is bounded by conducting surfces t φ =, ρ =, nd φ = β held t zero
More information20 MATHEMATICS POLYNOMIALS
0 MATHEMATICS POLYNOMIALS.1 Introduction In Clss IX, you hve studied polynomils in one vrible nd their degrees. Recll tht if p(x) is polynomil in x, the highest power of x in p(x) is clled the degree of
More informationStrategy: Use the Gibbs phase rule (Equation 5.3). How many components are present?
University Chemistry Quiz 4 2014/12/11 1. (5%) Wht is the dimensionlity of the threephse coexistence region in mixture of Al, Ni, nd Cu? Wht type of geometricl region dose this define? Strtegy: Use the
More informationDIRECT CURRENT CIRCUITS
DRECT CURRENT CUTS ELECTRC POWER Consider the circuit shown in the Figure where bttery is connected to resistor R. A positive chrge dq will gin potentil energy s it moves from point to point b through
More information#6A&B Magnetic Field Mapping
#6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by
More informationDistance And Velocity
Unit #8  The Integrl Some problems nd solutions selected or dpted from HughesHllett Clculus. Distnce And Velocity. The grph below shows the velocity, v, of n object (in meters/sec). Estimte the totl
More informationLecture 1. Functional series. Pointwise and uniform convergence.
1 Introduction. Lecture 1. Functionl series. Pointwise nd uniform convergence. In this course we study mongst other things Fourier series. The Fourier series for periodic function f(x) with period 2π is
More informationLecture 14: Quadrature
Lecture 14: Qudrture This lecture is concerned with the evlution of integrls fx)dx 1) over finite intervl [, b] The integrnd fx) is ssumed to be relvlues nd smooth The pproximtion of n integrl by numericl
More informationMACsolutions of the nonexistent solutions of mathematical physics
Proceedings of the 4th WSEAS Interntionl Conference on Finite Differences  Finite Elements  Finite Volumes  Boundry Elements MACsolutions of the nonexistent solutions of mthemticl physics IGO NEYGEBAUE
More informationEnergy Bands Energy Bands and Band Gap. Phys463.nb Phenomenon
Phys463.nb 49 7 Energy Bnds Ref: textbook, Chpter 7 Q: Why re there insultors nd conductors? Q: Wht will hppen when n electron moves in crystl? In the previous chpter, we discussed free electron gses,
More informationSTEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA. 0 if t < 0, 1 if t > 0.
STEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA STEPHEN SCHECTER. The unit step function nd piecewise continuous functions The Heviside unit step function u(t) is given by if t
More informationFreely propagating jet
Freely propgting jet Introduction Gseous rectnts re frequently introduced into combustion chmbers s jets. Chemicl, therml nd flow processes tht re tking plce in the jets re so complex tht nlyticl description
More informationQuantum Physics II (8.05) Fall 2013 Assignment 2
Quntum Physics II (8.05) Fll 2013 Assignment 2 Msschusetts Institute of Technology Physics Deprtment Due Fridy September 20, 2013 September 13, 2013 3:00 pm Suggested Reding Continued from lst week: 1.
More informationPhysics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:
Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You
More informationContinuous Random Variables
STAT/MATH 395 A  PROBABILITY II UW Winter Qurter 217 Néhémy Lim Continuous Rndom Vribles Nottion. The indictor function of set S is relvlued function defined by : { 1 if x S 1 S (x) if x S Suppose tht
More informationA SignalLevel Fusion Model for ImageBased Change Detection in DARPA's Dynamic Database System
SPIE Aerosense 001 Conference on Signl Processing, Sensor Fusion, nd Trget Recognition X, April 160, Orlndo FL. (Minor errors in published version corrected.) A SignlLevel Fusion Model for ImgeBsed
More informationInterpreting Integrals and the Fundamental Theorem
Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of
More informationChapter 4 Contravariance, Covariance, and Spacetime Diagrams
Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz
More information(See Notes on Spontaneous Emission)
ECE 240 for Cvity from ECE 240 (See Notes on ) Quntum Rdition in ECE 240 Lsers  Fll 2017 Lecture 11 1 Free Spce ECE 240 for Cvity from Quntum Rdition in The electromgnetic mode density in free spce is
More informationMath 113 Exam 2 Practice
Mth 3 Exm Prctice Februry 8, 03 Exm will cover 7.4, 7.5, 7.7, 7.8, 8.3 nd 8.5. Plese note tht integrtion skills lerned in erlier sections will still be needed for the mteril in 7.5, 7.8 nd chpter 8. This
More informationA027 Uncertainties in Local Anisotropy Estimation from Multioffset VSP Data
A07 Uncertinties in Locl Anisotropy Estimtion from Multioffset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.
More information7.6 The Use of Definite Integrals in Physics and Engineering
Arknss Tech University MATH 94: Clculus II Dr. Mrcel B. Finn 7.6 The Use of Definite Integrls in Physics nd Engineering It hs been shown how clculus cn be pplied to find solutions to geometric problems
More informationpivot F 2 F 3 F 1 AP Physics 1 Practice Exam #3 (2/11/16)
AP Physics 1 Prctice Exm #3 (/11/16) Directions: Ech questions or incomplete sttements below is followed by four suggested nswers or completions. Select one tht is best in ech cse nd n enter pproprite
More information8 Laplace s Method and Local Limit Theorems
8 Lplce s Method nd Locl Limit Theorems 8. Fourier Anlysis in Higher DImensions Most of the theorems of Fourier nlysis tht we hve proved hve nturl generliztions to higher dimensions, nd these cn be proved
More informationLecture 5. Selected aspects of thermodynamics for adsorption, diffusion and desorption
Physics 986b Lecture 5 Selected spects of thermodynmics for dsorption, diffusion nd desorption Physisorption Chemisorption Surfce Bonding Mechnisms of dsorption/diffusion/desorption References: 1) Zngwill,
More informationl 2 p2 n 4n 2, the total surface area of the
Week 6 Lectures Sections 7.5, 7.6 Section 7.5: Surfce re of Revolution Surfce re of Cone: Let C be circle of rdius r. Let P n be n nsided regulr polygon of perimeter p n with vertices on C. Form cone
More informationThermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report
Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block
More informationarxiv: v3 [condmat.mtrlsci] 15 Jul 2016
On the mgnetiztion process in ferromgnetic mterils Ruben Khchturyn nd Vhrm ekhitrin Institute for Physicl Reserch, NA of Armeni, Ashtrk, Armeni (Dted: July 18, 2016) rxiv:1506.01805v [condmt.mtrlsci]
More informationExperiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION
Experiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Purpose: Prt I: The cid ioniztion constnt of wek cid is to be determined, nd the cid is identified ccordingly. Prt II: The
More information1 Error Analysis of Simple Rules for Numerical Integration
cs41: introduction to numericl nlysis 11/16/10 Lecture 19: Numericl Integrtion II Instructor: Professor Amos Ron Scries: Mrk Cowlishw, Nthnel Fillmore 1 Error Anlysis of Simple Rules for Numericl Integrtion
More information1 APPLICATIONS OF SCHRÖDINGER S EQUATION AND BAND THEORY
1 APPLICATIONS OF SCHRÖDINGER S EQUATION AND BAND THEORY 1.1 INTRODUCTION We hve lredy noted tht Schrödinger ws influenced by the mtter wve postulte of de Broglie. In order to describe the behviour of
More informationSeries: Elementary, then Taylor & MacLaurin
Lecture 3 Series: Elementry, then Tylor & McLurin This lecture on series strts in strnge plce, by revising rithmetic nd geometric series, nd then proceeding to consider other elementry series. The relevnce
More information13.3 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS
33 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS As simple ppliction of the results we hve obtined on lgebric extensions, nd in prticulr on the multiplictivity of extension degrees, we cn nswer (in
More informationA. Limits  L Hopital s Rule ( ) How to find it: Try and find limits by traditional methods (plugging in). If you get 0 0 or!!, apply C.! 1 6 C.
A. Limits  L Hopitl s Rule Wht you re finding: L Hopitl s Rule is used to find limits of the form f ( x) lim where lim f x x! c g x ( ) = or lim f ( x) = limg( x) = ". ( ) x! c limg( x) = 0 x! c x! c
More informationBIFURCATIONS IN ONEDIMENSIONAL DISCRETE SYSTEMS
BIFRCATIONS IN ONEDIMENSIONAL DISCRETE SYSTEMS FRANCESCA AICARDI In this lesson we will study the simplest dynmicl systems. We will see, however, tht even in this cse the scenrio of different possible
More informationFlow in porous media
Red: Ch 2. nd 2.2 PART 4 Flow in porous medi Drcy s lw Imgine point (A) in column of wter (figure below); the point hs following chrcteristics: () elevtion z (2) pressure p (3) velocity v (4) density ρ
More informationNonLinear & Logistic Regression
NonLiner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find
More information5.04 Principles of Inorganic Chemistry II
MIT OpenCourseWre http://ocw.mit.edu 5.04 Principles of Inorgnic Chemistry II Fll 2008 For informtion bout citing these mterils or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.04, Principles of
More informationPhys 7221, Fall 2006: Homework # 6
Phys 7221, Fll 2006: Homework # 6 Gbriel González October 29, 2006 Problem 37 In the lbortory system, the scttering ngle of the incident prticle is ϑ, nd tht of the initilly sttionry trget prticle, which
More informationMath 0230 Calculus 2 Lectures
Mth Clculus Lectures Chpter 7 Applictions of Integrtion Numertion of sections corresponds to the text Jmes Stewrt, Essentil Clculus, Erly Trnscendentls, Second edition. Section 7. Ares Between Curves Two
More informationFBR Neutronics: Breeding potential, Breeding Ratio, Breeding Gain and Doubling time
FBR eutronics: Breeding potentil, Breeding Rtio, Breeding Gin nd Doubling time K.S. Rjn Proessor, School o Chemicl & Biotechnology SASTRA University Joint Inititive o IITs nd IISc Funded by MHRD Pge 1
More information200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes
PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write
More informationCS667 Lecture 6: Monte Carlo Integration 02/10/05
CS667 Lecture 6: Monte Crlo Integrtion 02/10/05 Venkt Krishnrj Lecturer: Steve Mrschner 1 Ide The min ide of Monte Crlo Integrtion is tht we cn estimte the vlue of n integrl by looking t lrge number of
More informationPolynomial Approximations for the Natural Logarithm and Arctangent Functions. Math 230
Polynomil Approimtions for the Nturl Logrithm nd Arctngent Functions Mth 23 You recll from first semester clculus how one cn use the derivtive to find n eqution for the tngent line to function t given
More information) (m + M B. )]c 2 (2.1) (T + T A ) (2.2) 2π 2 dn. = de
References .54 Neutron Interctions nd Applictions (Spring 003) Lecture (/11/03) Neutron Rection Systemtics  Energy Vritions of Cross Sections, Nucler Dt Enrico Fermi, Nucler Physics, Lecture Notes
More informationapproaches as n becomes larger and larger. Since e > 1, the graph of the natural exponential function is as below
. Eponentil nd rithmic functions.1 Eponentil Functions A function of the form f() =, > 0, 1 is clled n eponentil function. Its domin is the set of ll rel f ( 1) numbers. For n eponentil function f we hve.
More informationFactors affecting the phonation threshold pressure and frequency
3SC Fctors ffecting the phontion threshold pressure nd frequency Zhoyn Zhng School of Medicine, University of Cliforni Los Angeles, CA, USA My, 9 57 th ASA Meeting, Portlnd, Oregon Acknowledgment: Reserch
More informationElectric Potential. Concepts and Principles. An Alternative Approach. A Gravitational Analogy
. Electric Potentil Concepts nd Principles An Alterntive Approch The electric field surrounding electric chrges nd the mgnetic field surrounding moving electric chrges cn both be conceptulized s informtion
More informationIntroduction to Mechanics Practice using the Kinematics Equations
Introduction to Mechnics Prctice using the Kinemtics Equtions Ln Sheridn De Anz College Jn 24, 2018 Lst time finished deriing the kinemtics equtions some problem soling prctice Oeriew using kinemtics equtions
More informationMath 360: A primitive integral and elementary functions
Mth 360: A primitive integrl nd elementry functions D. DeTurck University of Pennsylvni October 16, 2017 D. DeTurck Mth 360 001 2017C: Integrl/functions 1 / 32 Setup for the integrl prtitions Definition:
More informationBasic model for traffic interweave
Journl of Physics: Conference Series PAPER OPEN ACCESS Bsic model for trffic interweve To cite this rticle: Dingwei Hung 25 J. Phys.: Conf. Ser. 633 227 Relted content  Bsic sciences gonize in Turkey!
More informationContinuous probability distributions
Chpter 1 Continuous probbility distributions 1.1 Introduction We cll x continuous rndom vrible in x b if x cn tke on ny vlue in this intervl. An exmple of rndom vrible is the height of dult humn mle, selected
More informationdifferent methods (left endpoint, right endpoint, midpoint, trapezoid, Simpson s).
Mth 1A with Professor Stnkov Worksheet, Discussion #41; Wednesdy, 12/6/217 GSI nme: Roy Zho Problems 1. Write the integrl 3 dx s limit of Riemnn sums. Write it using 2 intervls using the 1 x different
More informationRates of chemical reactions
Rtes of chemicl rections Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) 2 5 2 2 n(1 α) 2αn
More informationinteratomic distance
Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule
More informationHT Module 2 Paper solution. Module 2. Q6.Discuss Electrical analogy of combined heat conduction and convection in a composite wall.
HT Module 2 Pper solution Qulity Solutions wwwqulitytutorilin Module 2 Q6Discuss Electricl nlogy of combined het conduction nd convection in composite wll M16Q1(c)5m Ans: It is frequently convient to
More informationSection 14.3 Arc Length and Curvature
Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in
More information10/25/2005 Section 5_2 Conductors empty.doc 1/ Conductors. We have been studying the electrostatics of freespace (i.e., a vacuum).
10/25/2005 Section 5_2 Conductors empty.doc 1/3 52 Conductors Reding Assignment: pp. 122132 We hve been studying the electrosttics of freespce (i.e., vcuum). But, the universe is full of stuff! Q: Does
More informationUniversity of Washington Department of Chemistry Chemistry 453 Winter Quarter 2010 Homework Assignment 4; Due at 5p.m. on 2/01/10
University of Wshington Deprtment of Chemistry Chemistry 45 Winter Qurter Homework Assignment 4; Due t 5p.m. on // We lerned tht the Hmiltonin for the quntized hrmonic oscilltor is ˆ d κ H. You cn obtin
More informationC Nuclear Magnetic Resonance
Inherent Difficulties Low bundnce of 13 C (1.1% vs, 99.9% for 1 H) Lower gyromgnetic rtio (1/4 tht of 1 H)  13 C: 67.28 vs. 1 H 267.531/2 1,000,000 nuclei t 60 MHz E ΔE +1/2 1,000,009 nuclei t 60 MHz
More informationDynamics: Newton s Laws of Motion
Lecture 7 Chpter 4 Physics I 09.25.2013 Dynmics: Newton s Lws of Motion Solving Problems using Newton s lws Course website: http://fculty.uml.edu/andriy_dnylov/teching/physicsi Lecture Cpture: http://echo360.uml.edu/dnylov2013/physics1fll.html
More informationa * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2
18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the dspcing etween plnes ppers in expressions
More informationFundamentals of Analytical Chemistry
Homework Fundmentls of nlyticl hemistry hpter 9 0, 1, 5, 7, 9 cids, Bses, nd hpter 9(b) Definitions cid Releses H ions in wter (rrhenius) Proton donor (Bronsted( Lowry) Electronpir cceptor (Lewis) hrcteristic
More informationA New Statistic Feature of the ShortTime Amplitude Spectrum Values for Human s Unvoiced Pronunciation
Xiodong Zhung A ew Sttistic Feture of the ShortTime Amplitude Spectrum Vlues for Humn s Unvoiced Pronuncition IAODOG ZHUAG 1 1. Qingdo University, Electronics & Informtion College, Qingdo, 6671 CHIA Abstrct:
More informationCOMPTON SCATTER AND XRAY CROSSTALK AND THE USE OF VERY THIN INTERCRYSTAL SEPTA IN HIGH RESOLUTION PET DETECTORS
COMPTON SCATTER AND XRAY CROSSTALK AND THE USE OF VERY THIN INTERCRYSTAL SEPTA IN HIGH RESOLUTION PET DETECTORS C.S. Levin, M.P. Torni, S.R. Cherry, L.R. McDonld, E.J. Hoffmn Div. of Nucler Medicine
More information1 Online Learning and Regret Minimization
2.997 DecisionMking in LrgeScle Systems My 10 MIT, Spring 2004 Hndout #29 Lecture Note 24 1 Online Lerning nd Regret Minimiztion In this lecture, we consider the problem of sequentil decision mking in
More informationSynoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences?
Synoptic Meteorology I: Finite Differences 1618 September 2014 Prtil Derivtives (or, Why Do We Cre About Finite Differences?) With the exception of the idel gs lw, the equtions tht govern the evolution
More informationLecture 6. Thermodynamics and Kinetics for Adsorption, Diffusion and Desorption
Physics 986 Lecture 6 Thermodynmics nd Kinetics for Adsorption, Diffusion nd Desorption Physisorption Chemisorption Surfce Bonding Kinetics of Adsorption/Diffusion/Desorption References: ) Zngwill, Chpter
More informationVersion 001 HW#6  Electromagnetism arts (00224) 1
Version 001 HW#6  Electromgnetism rts (00224) 1 This printout should hve 11 questions. Multiplechoice questions my continue on the next column or pge find ll choices efore nswering. rightest Light ul
More informationSolutions to Supplementary Problems
Solutions to Supplementry Problems Chpter 8 Solution 8.1 Step 1: Clculte the line of ction ( x ) of the totl weight ( W ).67 m W = 5 kn W 1 = 16 kn 3.5 m m W 3 = 144 kn Q 4m Figure 8.10 Tking moments bout
More informationMath 113 Exam 1Review
Mth 113 Exm 1Review September 26, 2016 Exm 1 covers 6.17.3 in the textbook. It is dvisble to lso review the mteril from 5.3 nd 5.5 s this will be helpful in solving some of the problems. 6.1 Are Between
More informationDetermination of the activation energy of silicone rubbers using different kinetic analysis methods
Determintion of the ctivtion energy of silicone rubbers using different kinetic nlysis methods OU Huibin SAHLI ohmed BAIEE Thierry nd GELIN JenClude FETOST Institute / Applied echnics Deprtment, 2 rue
More informationRole of Missing Carotenoid in Reducing the Fluorescence of Single Monomeric Photosystem II Core Complexes
Electronic Supplementry Mteril (ESI for Physicl Chemistry Chemicl Physics. This journl is the Owner Societies 017 Supporting Informtion Role of Missing Crotenoid in Reducing the Fluorescence of Single
More information3.1 Review of Sine, Cosine and Tangent for Right Angles
Foundtions of Mth 11 Section 3.1 Review of Sine, osine nd Tngent for Right Tringles 125 3.1 Review of Sine, osine nd Tngent for Right ngles The word trigonometry is derived from the Greek words trigon,
More informationHandout: Natural deduction for first order logic
MATH 457 Introduction to Mthemticl Logic Spring 2016 Dr Json Rute Hndout: Nturl deduction for first order logic We will extend our nturl deduction rules for sententil logic to first order logic These notes
More informationThe Atwood Machine OBJECTIVE INTRODUCTION APPARATUS THEORY
The Atwood Mchine OBJECTIVE To derive the ening of Newton's second lw of otion s it pplies to the Atwood chine. To explin how ss iblnce cn led to the ccelertion of the syste. To deterine the ccelertion
More informationA chemical kinetic model for reactive transformations of aerosol particles
00. Chpter 4 A chemicl kinetic model for rective trnsformtions of erosol prticles Previous models of heterogeneous interctions hve focused on rective trce gs depletion in cloud or erosol prticles nd droplets.,,3
More informationDielectric Anisotropy of Wood. Author(s) NORIMOTO, Misato; YAMADA, Tadashi.
The Dielectric Properties of Wood V TitleProperties of the Chemicl Constitu Dielectric Anisotropy of Wood Author(s) NORMOTO, Misto; YAMADA, Tdshi Cittion Wood reserch : bulletin of the Woo University (1972),
More informationPrecalculus Spring 2017
Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify
More information