a r X i v :a s t r o -p h /0207598v 1 27 J u l 2002
Mon.Not.R.Astron.Soc.000,1–12(2002)Printed 1February 2008
(MN L A T E X style ?le v2.2)
X-ray and γ-ray spectra and variability of the black-hole
candidate GX 339–4
Grzegorz Wardzi′n ski,1?Andrzej A.Zdziarski,1Marek Gierli′n ski,2,3J.Eric Grove,4
Keith Jahoda,5and W.Neil Johnson 4
1
N.Copernicus Astronomical Center,Bartycka 18,00-716Warszawa,Poland
2University
of Durham,Department of Physics,South Road,Durham DH13LE,UK
3Astronomical Observatory,Jagiellonian University,Orla 171,30-244Krak′o w,Poland
4E.O.Hulburt Center for Space Research,Code 7650,Naval Research Laboratory,Washington,DC 20375,USA 5Laboratory for High Energy Astrophysics,NASA Goddard Space Flight Center,Greenbelt,MD 20771,USA
1February 2008
ABSTRACT
We analyse ?ve observations of the X-ray binary GX 339–4by the soft γ-ray OSSE detector on board CGRO simultaneous with either Ginga or RXTE observations.The source was bright during four of them,with the luminosity of L ～1037erg s ?1and the spectrum typical for hard states of accreting black holes,and it was in an o?state during the ?fth one,with L ～1035erg s ?1.Our broad-band spectral ?ts show the mean electron energy of electrons in the Comptonizing plasma decreasing with increasing luminosity within the hard (bright)state.For the observation with the best statistics at soft γ-rays,～1/4of energy in the Comptonizing plasma is probably carried by non-thermal electrons.Then,considering the e?ciency of Comptonized hybrid synchrotron emission allows us to obtain an upper limit on the strength of the magnetic ?eld in the X-ray source.Furthermore,this synchrotron emission is capable of producing the optical spectrum observed in an optically-high state of GX 339–4.In the o?state,the hard X-ray spectrum is consistent with being dominated by bremsstrahlung.The unusually strong Fe K αline observed by the RXTE /PCA during that state is found not to be intrinsic to the source but to originate mostly in the Galactic di?use emission.
Key words:accretion,accretion discs –binaries:general –stars:individual:GX 339–4–gamma-rays:observations –gamma-rays:theory –X-rays:stars.
1INTRODUCTION
The Galactic X-ray source GX 339–4was discovered by the OSO-7satellite (Markert et al.1973).It exhibits state tran-sitions typical for accreting black holes in binaries;it has been observed in the quiescent,o?,hard (low),soft (high)and very high X-ray states.Its X-ray spectral analyses have been done,e.g.,by Ueda,Ebisawa &Done (1994,hereafter U94),Zdziarski et al.(1998,hereafter Z98),Wilms et al.(1999)and Kong et al.(2000).In the soft γ-ray domain,OSSE observations have been studied by Grabelsky (1995),Z98,and Smith et al.(1999),and SIGMA results have been presented by Bouchet et al.(1993)and Trudolyubov et al.(1998).X-ray variability studies have been done,e.g.,by Maejima et al.(1994),Smith &Liang (1999),Nowak,Wilms
?
E-mail:gwar@https://www.doczj.com/doc/674722750.html,.pl
&Dove (1999)and Revnivtsev,Gilfanov &Churazov (2001,hereafter R01).
The source has been also observed in the radio (Fender et al.1999and references therein)and an extended emission from a jet-like elongated structure was reported (Fender et al.1997).Optical observations (e.g.,Grindlay 1979;Motch,Ilovaisky &Chevalier 1982;Motch et al.1983,hereafter M83;Soria et al.1999)have not been able to identify the donor star (see also a discussion in Z98).In fact,the ob-served optical radiation appears to be mostly produced in an accretion ?ow and/or an out?ow.This is supported by the decline of the optical ?ux during a transition from a hard to a soft state (M83;Makishima et al.1986).Interestingly,this type of transition is also accompanied by a decline of the radio ?ux (Corbel et al.2000).
The presence of an accreting black hole in the system is also suggested by its Fourier power spectra having the same characteristics at high frequencies as other black-hole candi-
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dates,but not neutron-star systems(Sunyaev&Revnivtsev 2000).Also,its broad-band energy spectra are remarkably similar to those of a well established black hole binary,Cyg X-1(e.g.,Gierli′n ski et al.1997,1999).However,no reliable constraints on the mass of the compact object exist(see a discussion and references in Z98).
X-ray andγ-spectra of black holes in their hard states are successfully described by models with thermal Comp-tonization of soft photons in optically thin plasmas of a temperature,T～109K,and re?ection of the Comptoniza-tion spectrum from an optically thick,cold(T～106K) medium,presumably an accretion disc(Sunyaev&Tr¨u mper 1979,Zdziarski et al.1995,Gierli′n ski et al.1997).The disc is also likely to serve as the source of soft photons undergoing Comptonization.This view is supported by the correlation between the spectral index of the Comptonization spectrum and the amount of re?ection observed in GX339–4(U94, R01)and in other accreting black holes(Zdziarski,Lubi′n ski &Smith1999;Gilfanov,Churazov&Revnivtsev2000).
The role of magnetic?elds remains an open question. They are probably involved in transfer and generation of energy either via viscosity mechanisms or reconnection pro-cesses.As a consequence,synchrotron radiation should be present and it may serve as a source of soft photons under-going further Comptonization.Though for thermal plasmas this process appears to be typically negligible(Wardzi′n ski &Zdziarski2000,hereafter WZ00),the presence of a weak non-thermal tail strongly ampli?es synchrotron emission (Wardzi′n ski&Zdziarski2001,hereafter WZ01).Then,the synchrotron process can become a very e?ective source of soft photons,comparable to or stronger than the cold disc emission.
Consequently,detection of a non-thermal electron tail via a high-energy tail in a Comptonization spectrum can put constraints on the strength of the magnetic?eld.In particu-lar,observations of Cygnus X-1in its hard state suggest the presence of such a tail(McConnell et al.2000,2002).For this case,WZ01obtained an upper limit on the magnetic ?eld strength in the accretion?ow and found constraints on the geometry.
Here,we study those(and some other)issues in the context of GX339–4.We analyze?ve Ginga and RXTE ob-servations of GX339–4which were simultaneous(or nearly simultaneous)withγ-ray observations by the OSSE detec-tor onboard CGRO.This provides us with data in the useful range from a few keV to a few hundred keV.The data re-duction procedures and models we use are described in Sec-tions2and3,respectively.We present the results of spectral analyses in Sections4and5.Consequences of the possible presence of a non-thermal electrons for accretion?ow mod-els are discussed in Section6.We investigate the connection between the X-ray and optical data in the framework of synchrotron self-Compton models in Section7,while X-ray variability is examined in Section8.Our results are summa-rized in Section9.
2SELECTION AND REDUCTION OF
OBSER V ATIONAL DATA
The data used in this work are listed in Table1.The?rst two data sets are identical with those of Z98.They consist of two Ginga data sets from1991September11and12,with the usable energy range of1.2–30keV,and simultaneous OSSE data in the range from50keV up to several hundred keV. A1per cent systematic error is added in quadrature to the statistical error in each Ginga channel(as in U94).All the OSSE data used here include energy-dependent systematic errors estimated from the uncertainties in the low-energy calibration and response of the detectors using both in-orbit and prelaunch calibration data.They decrease from～3per cent at50keV to～0.3per cent at>～150keV.
The third data set consists of a relatively short RXTE observation on1996July26,which was performed shortly after a two-week long OSSE observation of1996July9–23. For these RXTE data(and other ones used here),we used data from the units0and1of the PCA detector,and used only layer1,which provides the highest signal-to-noise ratio. This choice is favoured by Wilson&Done(2001)based on their study of Crab spectra from the PCA.Also following them,we added a systematic error of0.5per cent to the PCA data.The RXTE data were reduced with the lhea-soft package v. 5.0.4,response matrix v.7.10.Standard data selectrion criteria were applied,namely the Earth ele-vation angle>10?,pointing o?set<0.02?,the time since the peak of the last SAA passage greater than30min and the electron contamination<0.1.We used the
Sky
Spectra and variability of GX339–43 Table 1.A summary of the observational data.The background-subtracted count rates for the LAC,PCA,HEXTE and OSSE instruments are for the1.2–29,3–30,30–100and50–1000keV energy ranges,respectively.
a For HEXTE,the detector live time(i.e.dead-time corrected)is given.
taken into account using the inclination-dependent Green’s functions of Magdziarz&Zdziarski(1995).
In the case of a purely thermal plasma,the Comp-tonization spectrum is characterized by the Thomson op-tical depth,τ,the electron temperature(which we express in energy units,kT,where k is Boltzmann constant),and the temperature of the blackbody seed photons,kT seed.We also consider a hybrid electron distribution,which consists of a Maxwellian up to a electron Lorentz factor,γnth,and a power-law of an energy index,p,above it.Given these pa-rameters,we calculate the ratio,δ,of the energy in the non-thermal electrons to that in the thermal ones.In order to quantify the hardness of a given Comptonization spectrum, we also calculate the4–20keV power-law photon index,Γ, which we obtain by?tting data simulated with the model of (only)Comptonization.
The re?ection is characterized by the solid angle sub-tended by the re?ecting medium,?,its ionization parame-ter,ξ,and the Fe abundance relative to the solar one(Anders &Ebihara1982),A Fe.Here,ξ≡L ion/nR2,L ion is de?ned as the5eV–20keV luminosity in a power law spectrum and n is the density of the re?ector located at distance R from the illuminating source.We use here the ionization model by Done et al.(1992),which is not applicable to very highly ionized Fe(Ballantyne,Ross&Fabian2001),but su?ciently accurate at low/moderate ionization,such as that found in our data.The re?ector temperature is kept at106K,which is about the highest temperature consistent with the model of ionization equilibrium of Done et al.(1992).Compton re?ection is accompanied by a?uorescent Fe Kαline at a rest-frame energy,E Fe,and an equivalent width,W Fe.Both the line and re?ection are relativistically broadened in an ac-cretion disc in the Schwarzschild metric with the emissivity equal to that of a thin disc,extending from an outer radius, r out(assumed to equal103),to an inner one,r in≥6,where r is in the units of GM/c2(Fabian et al.1989).We note here that the values of kT,γnth,and p can be constrained mostly by the OSSE data whereasτ(for given kT)and the re?ection/line parameters are determined mostly by either Ginga or RXTE data.
We assume the column density to the source of N H= 6×1021cm?1.This value was derived from E(B?V)mea-surements and is consistent with results of other methods, see Z98and references therein.We assume the distance to the source of d=4kpc(which agrees with both kinematic and extinction measurements,see Z98).In calculations of re?ection and relativistic broadening,we assume an incli-nation of i=45?,and we also assume M=10M⊙,but we stress that currently there are no constraints on these quantities.
4HARD STATE OBSER V ATIONS
The source?ux(extrapolated to the range of1–1000keV) in the data sets from1to4is F～10?9erg cm?2s?1,which corresponds to the luminosity of L～(1–3)×1037erg s?1 and～1per cent of the Eddington luminosity(at d=4kpc and M=10M⊙assumed here).
4.1The Ginga-OSSE data
Results of thermal-Comptonization?ts to the
Ginga-OSSE data sets1and2are given in rows1and2of Table2,respec-tively.The former has much better statistics and we discuss it in more detail,but results for the set2are very similar. As it was shown by Z98(see their section5.1),spectral?ts to the Ginga-OSSE data do not constrain the geometry of the Comptonizing plasma and the seed-photon source.Thus, we assume here a simple geometry of a spherical source with seed photons emitted uniformly.We also account for the soft excess present in the data by a blackbody component at the same temperature as that of the seed photons.
We obtain a very good?t to the data set1,with
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Figure 1.(a)Broad-band spectra of GX 339–4.The data sets 1,3and 4(with decreasing ?ux)are shown in the green,red and blue error bars,respectively.The black solid curves give the best thermal ?ts to the data,and the dashed curve gives the best non-thermal ?t to the set 4.(b)The spectral components of the model of the set 1shown separately.Thermal Comptonization,the soft excess,Compton re?ection and the Fe K line are shown by the long-dashed blue,dot-dashed red,short-dashed green and dotted magenta curves,respectively.The solid black line gives the total spectrum.Absorption by the interstellar medium is seen below a few keV.
χ2/ν=46/81.The value of χ2/νmuch smaller than unity results from relatively large systematic errors added to the Ginga data,see Section 2.The ?t components,as well as comparison of this spectrum with spectra from data set 3and 4(analyzed in Section 4.2below)are shown in Fig.1.Fig.2shows the quality of our ?ts to the data sets 1–4.The parameters of the ?t to data set 1are very similar to those obtained by Z98and indicative of a typical hard-state spectrum of black-hole binaries.The main di?erence with respect to the results of Z98in their table 2is the plasma temperature,which we ?t here at kT =46+6?4keV,
whereas Z98obtained kT =57+7
?5keV.This di?erence is due to the model of Comptonization used here being more accurate than that used by Z98.
The ?tted relative normalization of OSSE to Ginga is
close to unity,0.91+0.07?0.07and 0.90+0.1
?0.1for the sets 1and 2,respectively.Hereafter,we give the luminosity normalized to the OSSE data.Such a choice is appropriate for investigating a connection between the luminosity and kT (see Section 4.3)since both are determined mostly by the OSSE data.
In non-homogenous geometries (such as a corona above a disc),an anisotropy break appears at the peak energy of the second-order scattering for a high enough kT ,with de?-ciency of photons below the break with respect to the extrap-
olation of the main power law (e.g.,Poutanen &Svensson
1996).In general,the form or the absence of this break may be then used to constrain the geometry.However,the energy range where it may appear in the case of GX 339–4is similar to that of the soft excess.Consequently,?ts assuming di?er-ent geometries and including the soft excess give very similar statistics [see also discussions in Z98and Nowak,Wilms &Dove (2002)].The presence of the soft excess itself is very signi?cant statistically,e.g.,?χ2=+29for a ?t to the set 1in spherical geometry and without the soft excess.
We also note that our adopted simple model of the soft excess as a blackbody is probably not realistic.In particu-lar,the ?tted kT seed ～0.3keV is about twice higher than that of Cyg X-1in the hard state (Ebisawa et al.1996).In Cyg X-1,the soft excess is consistent with the presence of both blackbody and its Comptonization in a plasma cloud separate from the main Comptoning source (Di Salvo et al.2001;Frontera et al.2001a).This results in the onset of the excess at ～3keV (similar to GX 339–4),but with the excess ～1–3keV emission being mostly due to Comptonization,not blackbody.Consequently,we also have ?tted the soft excess by a second thermal Comptonization component (in addition to the main Comptonization component responsi-ble for the emission at >～3keV).We ?nd the excess can be ?tted by emission of either an optically-thick plasma with τ=6.1and kT =1.4keV (using comptt ,Titarchuk 1994),or optically-thin one with τ=0.43,kT =20keV (using compps ).Both models yield χ2/ν=45/79,and are anal-ogous to the models of the soft excess in Cyg X-1by Di Salvo et al.(2001)and Frontera et al.(2001a),respectively.We conclude that the data do not allow us to distinguish between di?erent soft excess models.
As far as the high-energy end of the measured spectrum is concerned,an important issue is the possible presence of a high-energy tail in the electron distribution.We have found that none of the OSSE data considered in this work have enough statistics at high energies to constrain the electron power law index,p .We have thus chosen p =4,which is close to the values measured in Cyg X-1,see Gierli′n ski et al.(1999),and McConnell et al.(2000,2002),and it was used in the theoretical study of WZ01.
We ?nd that the Ginga -OSSE data are consistent with the presence of a high-energy electron tail,but they do not constrain its amplitude.E.g.,the non-thermal fraction,δ,for
the data set 1is 0.03+0.31
?0.03.The presence of a tail is indicated by the result of Z98,who obtained ?χ2=?4when allowing for the presence of non-thermal electrons in their ?t to the OSSE data from 1991September 5–12.However,an alter-native explanation of the departure of the spectrum for the thermal one can be a distribution of the plasma parameters,in particular kT ,either in time or in space.4.2
The RXTE -OSSE data
Since the usable PCA data extend down only to 3keV (com-pared to 1.2keV for the Ginga data),the soft excess cannot be constrained by them at all.Thus,we neglect its pres-ence for all RXTE -OSSE data.Then,the thermal model applied to the data set 4(?t 4a in Table 2)yields an ac-ceptable χ2/ν=143/148.The normalization of the models to the HEXTE A and B clusters relative to the PCA data
is 0.88+0.03
?0.03and 0.85+0.03?0.03,respectively.On the other hand,
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Spectra and variability of GX 339–45
Table 2.Main parameters of the ?ts in Section
3.The numbers correspond to the data sets in Table 1and a and b denote the thermal and hybrid ?ts,respectively,to the set
4.kT ,L (1–1000keV),ξ,E Fe ,and W Fe are is units of keV,1037erg s ?1,erg s ?1cm,keV and eV,respectively.
Figure 2.(a)The contribution to the total χ2from data bins multiplied by the sign of (data-model)and (b)data-to-model ratios for ?ts presented in Table 2.Red lines represent Ginga or PCA data,while green,magenta and blue lines correspond to the HEXTE A,HEXTE B and OSSE data,respectively.
the relative normalization of models to the OSSE and PCA
data was almost unity,0.98+0.03
?0.03,in spite of the observing time being larger for the OSSE.The results of our ?ts in the X-ray regime are similar to those of Wilms et al.(1999),who analyzed an RXTE observation that took place three days after ours.
Our data set 4has the best quality of all those con-sidered here,and allows us to study the presence of a non-thermal electron tail in the source.We have found it im-proves the ?t (4b in Table 2)very signi?cantly,to χ2/ν=133/147,with the probability of the ?t improvement be-ing by chance of only 10?3(using the F-test,Bevington &
Robinson 1992).The parameters of the hybrid electron dis-tribution are γnth =1.59+0.24
?0.14and kT =46+11?9keV,which
corresponds to δ=0.34+0.22
?0.17(δincreases with decreasing either kT or γnth ).The normalizations of the models to the HEXTE A and B clusters and to the OSSE detector,relative
to the PCA data,were 0.86+0.03
?0.03,0.84+0.03?0.03and 0.92+0.04?0.04,re-spectively.
We caution,however,that the OSSE observation was much longer than the RXTE one,and thus it is possible that the modi?cation of the shape of the OSSE spectrum was due
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not to non-thermal electrons,but resulted from variations of the plasma parameters in time or in space.We have checked these possibilities.First,we allowed for di?erent values of τin thermal?ts to the RXTE and OSSE data.This,how-ever,did not change the?t quality,χ2/ν=142/147,and the di?erence between the two values ofτwas only0.1.We then?t two compps models allowing for di?erent values of τand kT and keeping all other model parameters the same. This signi?cantly improves the?t compared to the previous thermal model,resulting inχ2/ν=135/145,only slightly worse than the hybrid?t.The?tted plasma parameters are kT=61keV,τ=2.1,and kT=83keV,τ=1.1for the two components.Indeed,plasmas in an accretion?ow are expected,on average,to increase its temperature with de-creasing optical depth as a result of less e?ective Compton cooling,in agreement with our?t results.Thus,the data set4is as consistent with emission from regions of di?er-ent kT,τas with the presence of a non-thermal tail in a uniform electron population.The latter interpretation may be favoured by the similarity of our result to those of Mc-Connell et al.(2000,2002)for Cyg X-1.
On the other hand,either thermal or hybrid model applied to the data set3yields unacceptable?ts, e.g.,χ2/ν=202/131in the thermal case.However,both the OSSE lightcurve and that from the All-Sky Moni-tor on board RXTE(available on the public database at https://www.doczj.com/doc/674722750.html,/ASM
Spectra and variability of GX 339–4
7
Figure 3.Relation between the luminosity and (a)the Thomson optical depth,and (b)the average
electron https://www.doczj.com/doc/674722750.html,bels corre-spond to the ?t numbers from Table 2,and the dotted line denotes the purely thermal model to the data set 4,which is statistically less likely than the hybrid model.Solid and dashed curves show the ?tted dependences on L in the cases of advection and cooling dominated ?ows,respectively (see Section 4.3).
seed photons (e.g.,Beloborodov 1999b),which can be due to a constant geometry of the ?ow.We also note that the values of L in our data are close to the maximum in a hot accretion ?ow with advection and Comptonization cooling,L ≈1037y 3/5(αv /0.1)7/5(M/10M ⊙)(Zdziarski 1998),where αv is the viscosity parameter.
5THE OFF-STATE SPECTRUM
During the ?fth observation (Table 1),GX 339–4was by 2orders of magnitude fainter than during the hard-state observations.At this ?ux level,GX 339–4has been classi?ed as being in the o?state,see,e.g.,Kong et al.(2000).We note here that the object also enters even more quiescent states,e.g.,during an observation of Asai et al.(1998),when an upper limit on the source ?ux was about two orders of magnitude below the ?ux of our data.
We ?rst ?t the data with the same thermal model as for the sets 3–4,in which we assume the relative normaliza-tion of the OSSE data to the PCA ones of unity.This pro-vides a statistically acceptable model,with χ2/ν=46/64,unconstrained re?ection,and a broad range of the allowed electron temperature,kT =170+230?150keV.However,the spec-trum shows a distinct hardening at ～7keV,which in turn requires either a very high temperature of the seed pho-tons,kT seed ～1keV,or very strong Compton re?ection,?/2π?1.The former is rather unlikely at the observed low luminosity level,L =8×1034erg s ?1,and the latter has never been observed in any other black-hole binary.We have performed extensive tests checking also the possibility that the hardening is due to the PCA background subtrac-Figure 4.The upper panel shows the o?-state spectrum (er-ror bars)from the ?fth observation,modelled by thermal bremsstrahlung (dashed curve),power-law Comptonization at low energies (dotted curve),and an Fe K line (dot-dashed curve).The solid curve gives the sum.Lower panels give the contribution from data bins to the total χ2and the data to model ratio.
tion uncertainties.We have concluded it to be unlikely and
hereafter consider the hardening to be intrinsic to the source,but still cannot rule out completely a signi?cant e?ect of the background subtraction.
On the other hand,it is possible that spectrum be-low several keV is the standard Comptonization power law,and the hardening at higher energies is due to thermal bremsstrahlung.That process is indeed expected to domi-nate the high-energy spectrum at very sub-Eddington accre-tion rates,see,e.g.,Narayan &Yi (1995),Esin,McClintock &Narayan (1997),Zdziarski (1998).We model the spectrum by the sum of a power law (corresponding to Comptoniza-tion at low energies),thermal bremsstrahlung and a Gaus-sian Fe K αline.This yields a good ?t,with χ2/ν=46/66.
The slope of the low-energy power law is Γ=3.1+1.5
?0.7whereas the bremsstrahlung temperature is unconstrained.We have assumed it to equal 200keV (e.g.,Esin et al.1997),which corresponds to L ～1035erg s ?1,and,e.g.,τ≈0.35and the source radius of R ≈109,with the bremsstrahlung lu-minosity scaling approximately as T 1/2τ2R .The data and the model spectrum are shown in Fig.4.
An important issue here is the origin of the strong Fe K αline seen in the data.In the model with bremsstrahlung,
the line is narrow at E Fe =6.8+0.3
?0.4keV with the photon ?ux of 3.2×10?5cm ?2s ?1,corresponding to W Fe =530+320?260eV.If the line were intrinsic,its energy indicating origin in a strongly ionized medium and the large equivalent width would be di?cult to explain given the very low luminosity
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of the source,when the accretion disc is expected to be cold and far away from the black hole.For example,the Fe K emission is weak in a faint hard state of the black-hole binary XTE J1118+480,at an Edddington ratio somewhat higher than that of the present observation(Frontera et al.2001b).
Thus,we have investigated whether the line may be not intrinsic to GX339–4.In fact,the source lies close to the direction of the Galactic centre,where the Galactic di?use emission is strong.Based on the observations of Yamauchi &Koyama(1993),we have estimated the intensity of the Fe 6.7keV line in the Galactic di?use emission at the direction of GX339–4is≈3×10?5cm?2s?1deg?2.Given the?eld of view of the PCA of～1deg2,the Fe K line seen in our data should be attributed mostly to the Galactic background.
Similarly strong lines were reported and attributed to GX339–4in a number of o?-state PCA observations(includ-ing ours)by Feng et al.(2001),but we believe their origin is also di?use.Furthermore,Nowak et al.(2002)found that the ratio of the line equivalent width to the relative re?ection strength in GX339–4was increasing with the decreasing luminosity,which they claimed to represent an argument against simple reprocessing models of those features.
However,we have checked that the e?ect seen by Nowak et al.(2002)can be explained by the relative contribution of the di?use6.7keV line increasing with the decreasing lumi-nosity.For the two weakest of their observations,where the 3?9keV source?ux was by factors of～13and～40higher than in our observation,the total line equivalent width was W Fe=150eV and W Fe=160eV,respectively.The Galactic di?use emission would then contribute to the observed W Fe at the level of≈40eV and≈13eV,respectively.Then, the agreement between the intrinsic Fe Kαline equivalent width and the strength of re?ection in their data would be signi?cantly improved.
6THE ORIGIN OF SEED PHOTONS AND CONSTRAINTS ON MAGNETIC FIELD Here,we explore some consequences of the possible pres-ence of a non-thermal electron tail,found statistically nec-essary in our uniform-plasma model for the fourth observa-tion.A weak non-thermal tail beyond a Maxwellian distri-bution leads to a moderate hardening of the X-ray power law in the Comptonization spectrum(as repeated scatter-ing o?thermal electrons still dominates at those energies) as well as it yields a weak high-energy photon tail at ener-gies?kT(from scattering o?non-thermal electrons),see, e.g.,WZ01.On the other hand,it can amplify the cyclo-synchrotron emission by a very large factor,due to the fact that the unabsorbed synchrotron radiation is emitted just by the high-energy tail of the electron distribution,which itself is strongly ampli?ed by the tail with respect to the Maxwellian(WZ01).This ampli?ed synchrotron emission within the Comptonizing plasma provides then a copious source of seed photons.For given magnetic?eld strength, B,and the plasma parameters,kT andτ,we can calculate the expected self-Compton luminosity,which can exceed the observed L in general.
This provides a way to constrain B,with the maximum one corresponding to all the seed photons being synchrotron (see section5.3of WZ01).Since we know that a cold medium is also present in the plasma vicinity,which medium is also a copious source of soft blackbody photons,the actual value of B has to be even lower.
First,we consider a hot accretion?ow with nearly-virial ions(e.g.,Abramowicz et al.1995;Narayan&Yi1995).Fol-lowing WZ00,we estimate the equipartition?eld strength within a radius of20GM/c2(where most of the gravitational energy is dissipated)as B?1.4×107G.Then,following the calculations in WZ01and using the hybrid electron distribu-tion?tted to the data set4(δ?0.3,Section4.2),we obtain the synchrotron–self-Compton luminosity of4.3×1038erg s?1,which exceeds the observed one by a factor of～40.The condition that the predicted luminosity does not exceed the observed L leads to B<～2.2×106G.Although this is a factor of several below the equipartition,various processes dissipating magnetic?eld can lead to this condition to be satis?ed in an actual accretion?ow.On the other hand,the self-Compton luminosity from the purely thermal electron distribution?tted to the data set4(Section4.2)would be only1.6×1035erg s?1,i.e.,negligibly small compared to the observed L.Thus,the non-thermal tail ampli?es thus the synchrotron emission by a rather large factor of～3×103. Consequently,most of the seed photons for Comptonization have to be emitted by a cold medium if the tail is very weak or absent.
We have also considered the con?guration of small,ac-tive regions above a cold disc,in which regions dissipation of magnetic?eld occurs(see WZ00for details of the assumed model).Assuming that magnetic?eld dissipates at10per cent of the Alfv′e n speed in10active regions of the size106 cm,the magnetic?eld required to dissipate enough energy to reproduce the observed L would be B?108G.Then, however,the synchrotron–self-Compton luminosity from the hybrid plasma would be～20times the observed L.It would be≤L for B<～2.1×107G,which?eld,however,would not be able to dissipate enough energy to power the observed L. We thus conclude that the non-thermal electron tail?tted to the data rules out the active regions model for the hard state of GX339–4.The same conclusion was obtained by WZ01for the hard state of Cyg X-1.Also,Z98found the model of active regions for the hard state of GX339–4to be ruled out based on independent spectral considerations.
7THE ORIGIN OF THE OPTICAL EMISSION IN THE HARD STATE
GX339–4in an X-ray hard state was observed by the Ariel 6satellite(Ricketts1983),which observation was in part simultaneous with optical observations,which found the source in a very bright state(Motch,Ilovaisky&Chevalier 1981,1982).The simultaneous data from1981May28are analyzed by M83.The1–50keV X-ray spectrum of Ricketts (1983)is,in fact,very similar to our Ginga-OSSE spectra. Given our considerations of the origin of the seed photons for Comptonization in the X-ray regime,it is of great in-terest to check whether the optical emission can be due to the cyclo-synchrotron process in the X-ray emitting plasma. Such origin of the optical emission was suggested by Fabian et al.(1982),but those authors have not performed any cal-culations of the actual e?ciency of that process.
Here,we assume that the plasma temperature and op-
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Spectra and variability of GX 339–4
9
Figure 5.The dereddened IR/optical spectrum (circles)of GX 339–4from 1981May 24–28(circles)and the 1–50keV power-law ?t (thick line)to the 1981May 30–31observation.The thin solid curve shows the thermal Comptonization and re?ection compo-nents of the model to our data set 1(from Ginga and OSSE),and the dashed curve shows the Comptonization component alone,in-cluding its extrapolation to low energies.The thin dotted curve shows a self-absorbed thermal synchrotron spectrum.
tical depth during the 1981observation were the same as those obtained from our X-ray data and consider in de-tail the requirements on other parameters
implied by the cyclo-synchrotron origin of the optical emission.Fig.5shows the unabsorbed spectrum of GX 339–4from the IR to soft γ-rays.The IR/optical data are from Motch et al.(1981),dereddened assuming E (B ?V )=1.2,and the X-ray spec-trum is from Ricketts (1983).
Fig.5also shows the Ginga -OSSE spectrum.We see that the spectra from Ginga -OSSE and Ariel 6are indeed quite similar.Furthermore,the extrapolation to the optical range of the thermal-Compton spectrum ?tted to the Ginga -OSSE spectrum lies just a factor of several below the peak of the optical emission.Thus,the optical emission can indeed provide enough seed photons for Comptonization in the X-ray emitting plasma.
We then assume that the uppermost point in the optical spectrum,EF E ?9×10?10erg cm ?2s ?1at E ?2.7eV,corresponds to cyclo-synchrotron emission at the turnover frequency (i.e.,where the plasma becomes optically thin to synchrotron self-absorption).The corresponding spectrum is shown by the dotted curve in Fig.5.In the purely thermal case and with the plasma parameters as in Table 2,?t 1,the required magnetic ?eld strength and the size of the plasma (assuming spherical geometry,and calculated as in WZ00)are B ～107G and R ～109cm,respectively.(These values are each an order of magnitute higher than those given by Fabian et al.1982.)The required source size is rather large,～103GM/c 2.It can be reduced if either the magnetic ?eld were larger (corresponding to the synchrotron turnover peak at both higher photon energy and ?ux,which is allowed by the data),kT were higher (as its value during the 1981ob-servation is unknown),or the electron distribution contained a non-thermal tail.The last possibility is,in fact,suggested by our data (Section 4.2),and we consider it in detail.We assume the electron power law index of p =4,as before,and calculate the required values of B and R as a function of the fraction of energy in the non-thermal electrons,δ.Results are shown in Fig.6.We see that R is reduced by a factor of
Figure 6.The source size and its magnetic ?eld strength re-quired to explain the optical spectrum of 1981May as due to cyclo-synchrotron emission parametrized by the relative fraction of energy in non-thermal electrons,δ.
several already for δ～5×10?4,and for δ～0.1,both R and
B are reduced by an order of magnitude.The ?eld expected in a hot accretion disc ?ow in equipartition with nearly-virial ions would be B ～106G and ～105G at at R ～108and 109cm,respectively.Thus,R ～102GM/c 2～108cm,the equipartition B ～106G,and δ～0.1represent our pre-ferred set of the plasma parameters of the ?ow explaining the optical emission.
Interestingly,M83found an anticorrelation between the optical emission and the 1–13keV X-rays.An anticorrelation can appear,e.g.,if the cyclo-sychrotron emission is variable (due to variability of some plasma parameters)but the total luminosity is approximately constant.The spectral variabil-ity would then show a pivot between the optical and X-ray ranges,which naturally leads to an anticorrelation between the respective emission.Furthermore,M83found that the optical emission leads the X-rays by 2.8±1.6s.At kT =46keV (Table 2),it takes ～30scatterings to upscatter a 2.7eV photon to 10keV.At τ～3,the source size required for the time lag to be due to the delay during Compton upscattering is then ～109cm,still a plausible value.M83also found a QPO at ～20s in their data,which,interest-ingly,corresponds to the Keplerian frequency at a radius of 2×109cm (at M =10M ⊙).A somewhat lower QPO pe-riod,～3s,was found in the data set 4(R01).The time scale of ?ares of 20ms found by M83can then correspond to the light travel time across the source.A remaining un-resolved issue would be then the lack of an anticorrelation found by M83between the optical photons and those in the 13–20keV range.Possibly,that energy range is dominated by Compton re?ection showing a di?erent timing behaviour than the primary continuum.
On the other hand,Fabian et al.(1982)proposed that the anticorrelation is due to the X-rays below 13keV being due to emission of colder clouds surrounding the hot plasma (emitting both the optical emission and X-rays above 13keV).However,present ?ts to X-ray spectra of GX 339–4
c
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10G.Wardzi′n ski et al.
as well as other black-hole binaries in the hard state tend to rule out this possibility,indicating that the entire X-ray emission is dominated by a single power law(e.g.,U94;Z98, Gierli′n ski et al.1997).
We note that similar optical/X-ray behaviour has been observed from the black-hole binary XTE J1118+480(Kan-bach et al.2001).Optical emission from that object is very strong,comparable to X-rays,similar to the case of GX339–4.Also,a similar anti-correlation between optical and X-ray ?ux was observed,with the optical minimum leading the X-rays maximum by～2s.Furthermore,the optical emis-sion has a narrower auto-correlation function than that of X-rays,which implies that the primary variability is in the optical band.It is then possible that the optical emission is cyclo-synchrotron,which is then Comptonized up to the X-ray range.The anticorrelation can be explained as in GX 339–4,by spectral pivoting between the optical and X-ray
bands.
The site of the hot plasma could be in principle an out-?ow,possibly a jet,which presence is indicated by radio ob-servations in the hard state(e.g.,Fender et al.1997,1999; Corbel et al.2000).In fact,double-peaked emission lines have been found in the soft state of GX339–4by Soria et al.(1999),whereas they observed broad,single-peaked pro-?les in the hard state.They attributed the di?erence in the line pro?les to the origin of the line in the out?ow in the hard state and in the disc in the soft state.Also Wu et al.(2001) reached a similar conclusion.On the other hand,there is no natural interpretation to the frequency of the optical QPO in the out?ow model.A way to test the origin of the optical radiation would be to measure its polarization,which would be non-zero in an out?ow with a directed magnetic?eld.
While the optical spectrum may in principle be either quasi-thermal and produced in an accretion?ow or purely non-thermal and produced in a jet,our?ts to theγ-ray high-energy cuto?con?rm that the distribution of electrons producing the main X/γ-ray continuum in the hard state has a predominantly thermal character(even if it does orig-inate in an out?ow,as,e.g.,in the coronal out?ow model of Beloborodov1999a).This represents a strong argument against the model of the X/γ-ray continuum of black-hole binaries as being predominantly non-thermal(Marko?,Fal-cke&Fender2001).In that model,the predicted position of the cuto?in the photon spectrum is very sensitive to the magnetic?eld strength and details of acceleration and cooling.Marko?et al.(2001)deal with this problem by?ne-tuning the high-energy cuto?in the distribution of the non-thermal electrons.However,virtually all black-hole binaries in the hard state have remarkably uniform high-energy cut-o?s(e.g.,Grove et al.1998;Z98;Gierli′n ski et al.1997), which thus represents a severe problem for the non-thermal model.On the other hand,this uniformity is accounted for in the thermal(or quasi-thermal)model,in which the Comp-ton cooling(e.g.,Zdziarski1998)and/or e±pair production (e.g.,Malzac,Beloborodov&Poutanen2001)naturally con-strain the electron temperature to～50–100keV.
8X-RAY V ARIABILITY
The fractional variability of GX339–4in X-rays was in-vestigated by,e.g.,Maejima et al.(1984),Nowak et
al.Figure7.The fractional rms X-ray variability of GX339–4in the PCA data of the set4for four ranges of frequency. (1999),Lin et al.(2000)and R01and was found to be,in general,energy-dependent.Here,we investigate the energy-dependence of the X-ray variability in the RXTE data of the set4,which has the best statistics of the data sets studied by us.We use all layers in all available PCA detectors(PCUs 0–4)in order to obtain the best possible photon statistics.
We construct light curves in a number of energy bands with di?erent bin size,?T.For each lightcurve,we inte-grate the power density spectrum in the frequency range from0.001Hz up to the upper frequency of1/(2?T),from which we obtain the(Poisson-corrected)rms variability di-vided by the mean count rate.The latter has been corrected for the instrumental background,which is strong,especially at E>～20keV.The results are presented in Fig.7.
A common feature of all the shown dependencies is a decrease of the rms/mean starting at E～7keV.This agrees with a general trend of the fractional rms decreasing with increasing X-ray energy in other black-hole binaries in the hard state(Revnivtsev et al.2000).In our case,the ratio of the rms at E?7keV to that at E?7keV increases with the increasing upper frequency.
R01have studied a number of PCA data for GX339–4 including our set4and found that the re?ection component is much more variable at<～0.1Hz than at～10Hz.This e?ect will result in a reduction of the rms at E>～10keV. However,we have checked that the dependencies of rms on E in Fig.7cannot be explained just by a superposition of di?erent values of the rms for the power law and for re-?ection.Also,the ratio of the rms/mean at high energies to that at low energies would decrease with the increasing upper frequency whereas we observe the opposite behaviour.
It is thus more likely that we observe a change of the variability pattern in the Comptonization continuum itself. We propose that it could take place in a similar scenario to that considered in Section7when analyzing the optical and X-ray https://www.doczj.com/doc/674722750.html,ly,if the total Comptonization luminosity remains constant but the?ux in seed photons varied,this would result in a pivoting of the spectrum.The pivot energy would in general depend on the spectral index
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Spectra and variability of GX339–411
and the temperatures of the electrons and the seed photons. Because a part of the spectrum closer to the pivot energy would be less variable than that further away,this scenario can qualitatively reproduce the observed rms/mean for the pivot at E>～20keV.The dependence on the upper frequency can be explained if the pivoting occured mostly on long time scales.We note that a similar pivoting is indeed observed in Cyg X-1on very long time scales(Zdziarski et al.2002).
We note that the pivoting energy required by the above interpretation is di?erent from that needed for ex-plaining the optical/X-ray anticorrelation by varying cyclo-synchrotron seed photons in Section7.For that,the pivot energy has to be obviously between the optical and X-ray ranges.Thus,the two interpretations are mutually exclusive. We have also calculated that the pivot at E>～20keV im-plies kT seed>～0.1keV,which rules out the cyclo-synchrotron origin of the seed photons in our data set4.We point out, however,that the two variability patterns were observed in two di?erent observations of GX339–4(separated by15 years),during which the state of the source could be di?er-ent.Also,the cause of the dependence of the rms on E shown in Fig.7could be di?erent than due to pivoting.It can pos-sibly be explained,e.g.,by models of magnetic avalanches (e.g.,Poutanen&Fabian1999),which predict complicated patterns of variability of?ares on di?erent time scales.
9CONCLUSIONS
We have analyzed four broad band X/γ-ray spectra of GX 339–4in the hard state and found that they are well?tted by Comptonization being predominantly thermal,Compton re?ection and?uorescent Fe K emission with the strength compatible with that of the re?ection.This provides a fur-ther con?rmation of the dominance of those physical pro-cesses in this object,and black-hole binaries in the hard state in general.It also argues against the non-thermal model for the origin of the X/γ-ray continuum of black-hole binaries by Marko?et al.(2001).We also study time variability in our best X-ray data set,and?nd a decline of the fractional rms with increasing photon energy,again consistent with previous?ndings for this source.
Our?fth observation was in an o?state,with the X-ray?ux two orders of magntitude below that in the hard state.Our major?nding here is that the very strong Fe K line present in our data(as well as in other reported proportional-counter o?-state observations of this source)is not intrinsic to GX339–4,but is due to the strong di?use 6.7keV emission in the Galactic Center region.
We also obtain a number of other results,which,how-ever,are less unambiguous and require future further stud-ies.This is due to either the limitations of the available data or insu?cient theoretical understanding at the present time.
In the o?state,we?nd a spectral hardening at～7 keV,which we?nd to be incompatible with thermal Comp-tonization but,rather,compatible with the presence of a bremsstrahlung spectral component.Such a component is in agreement with theoretical predictions,but its unambiguous detection is hampered by the low signal-to-noise ratio and lack of su?cient coverage at high energies.
In the hard state,we?nd a statistically signi?cant de-parture from the pure thermal Comptonization spectrum at high energies in our best spectrum.We interpret it as due to the presence of a weak high-energy tail in the electron distribution.However,we cannot rule out an alternative ex-planation of the e?ect of the plasma parameters varying in space and/or time.
The possible presence of a high-energy electron tail has implications for the strength of the magnetic?eld in the source,from the consideration of Compton scattering of the cyclo-synchrotron emission.The magnetic?eld strength is constrained to values somewhat below equipartition(with hot ions)in the case of a hot accretion disc.
Interestingly,the four hard-state spectra have very sim-ilar intrinsic X-ray slope,Γ?1.75.On the other hand,the high-energy cuto?energy decreases with increasing luminos-ity,and,correspondingly,the?tted Thomson optical depth of the plasma increases with luminosity.The signi?cance of the correlations is strongly increased if we allow for the presence of a high-energy electron tail in our model.Such a correlation is in agreement with theoretical predictions for hot accretion?ows.Still,it is based only on the four avail-able spectra,and studies of more broad-band spectra with similar X-ray slope,Γ,are highly desirable.
We also study the origin of the strong optical emission found in the past to be associated with the X-ray bright hard state.We?nd the reported optical emission can be due to the cyclo-sychrotron process,and the emission also provides seed photons for Comptonization.The presence of a high-energy electron tail alleviates constraints on the emission region,allowing it to be smaller and with a weaker?eld. The reported optical/X-ray anticorrelation can be due to the synchrotron emission being variable at an approximately constant total luminosity,which leads to a spectral pivot between the optical and X-ray bands.
On the other hand,we?nd the dependence of the rms variability on energy can be also explained by variable seed photons,but the pivot point is then at>～20keV,i.e.,in con-?ict with the previous model.Thus,a comprehensive model of both of these variability patterns requires more compli-cations,probably more source components. ACKNOWLEDGMENTS
This research has been supported in part by the Foun-dation for Polish Science and KBN grants5P03D00121, 5P03D00821and2P03D00514.We are very grateful to Mike Revnivtsev for his help with the variability analysis and the suggestion to consider the di?use Fe K emission.We also thank Bo˙z ena Czerny,Chris Done,Piotr Lubi′n ski,Joanna Miko l ajewska,Marek Sikora and Piotr˙Zycki for valuable and inspiring discussions.
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This paper has been typeset from a T E X/L A T E X?le prepared by the author.
c 2002RAS,MNRAS000,1–12
第18章X射线光电子能谱分析 18.1 引言 固体表面分析业已发展为一种常用的仪器分析方法，特别是对于固体材料的分析和元素化学价态分析。目前常用的表面成分分析方法有：X射线光电子能谱（XPS）, 俄歇电子能谱(AES)，静态二次离子质谱(SIMS)和离子散射谱(ISS)。AES 分析主要应用于物理方面的固体材料科学的研究，而XPS的应用面则广泛得多，更适合于化学领域的研究。SIMS和ISS由于定量效果较差，在常规表面分析中的应用相对较少。但近年随着飞行时间质谱（TOF-SIMS）的发展，使得质谱在表面分析上的应用也逐渐增加。本章主要介绍X射线光电子能谱的实验方法。 X射线光电子能谱（XPS）也被称作化学分析用电子能谱（ESCA）。该方法是在六十年代由瑞典科学家Kai Siegbahn教授发展起来的。由于在光电子能谱的理论和技术上的重大贡献，1981年，Kai Siegbahn获得了诺贝尔物理奖。三十多年的来，X射线光电子能谱无论在理论上和实验技术上都已获得了长足的发展。XPS已从刚开始主要用来对化学元素的定性分析，业已发展为表面元素定性、半定量分析及元素化学价态分析的重要手段。XPS的研究领域也不再局限于传统的化学分析，而扩展到现代迅猛发展的材料学科。目前该分析方法在日常表面分析工作中的份额约50%，是一种最主要的表面分析工具。 在XPS谱仪技术发展方面也取得了巨大的进展。在X射线源上，已从原来的激发能固定的射线源发展到利用同步辐射获得X射线能量单色化并连续可调的激发源；传统的固定式X射线源也发展到电子束扫描金属靶所产生的可扫描式X射线源；X射线的束斑直径也实现了微型化，最小的束斑直径已能达到6μm大小, 使得XPS在微区分析上的应用得到了大幅度的加强。图像XPS技术的发展，大大促进了XPS在新材料研究上的应用。在谱仪的能量分析检测器方面，也从传统的单通道电子倍增器检测器发展到位置灵敏检测器和多通道检测器，使得检测灵敏度获得了大幅度的提高。计算机系统的广泛采用，使得采样速度和谱图的解析能力也有了很大的提高。 由于XPS具有很高的表面灵敏度，适合于有关涉及到表面元素定性和定量分析方面的应用，同样也可以应用于元素化学价态的研究。此外，配合离子束剥离技术和变角XPS技术，还可以进行薄膜材料的深度分析和界面分析。因此，XPS 方法可广泛应用于化学化工，材料，机械，电子材料等领域。 18.2 方法原理 X射线光电子能谱基于光电离作用，当一束光子辐照到样品表面时，光子可以被样品中某一元素的原子轨道上的电子所吸收，使得该电子脱离原子核的束缚，以一定的动能从原子内部发射出来，变成自由的光电子，而原子本身则变成一个激发态的离子。在光电离过程中，固体物质的结合能可以用下面的方程表示： E k = hν- E b - φs （18.1）
X射线光电子能谱分析 1 引言 固体表面分析业已发展为一种常用的仪器分析方法，特别是对于固体材料的分析和元素化学价态分析。目前常用的表面成分分析方法有：X射线光电子能谱（XPS）, 俄歇电子能谱(AES)，静态二次离子质谱(SIMS)和离子散射谱(ISS)。AES分析主要应用于物理方面的固体材料科学的研究，而XPS的应用面则广泛得多，更适合于化学领域的研究。SIMS和ISS由于定量效果较差，在常规表面分析中的应用相对较少。但近年随着飞行时间质谱（TOF-SIMS）的发展，使得质谱在表面分析上的应用也逐渐增加。本章主要介绍X射线光电子能谱的实验方法。 X射线光电子能谱（XPS）也被称作化学分析用电子能谱（ESCA）。该方法是在六十年代由瑞典科学家Kai Siegbahn教授发展起来的。由于在光电子能谱的理论和技术上的重大贡献，1981年，Kai Siegbahn获得了诺贝尔物理奖。三十多年的来，X射线光电子能谱无论在理论上和实验技术上都已获得了长足的发展。XPS已从刚开始主要用来对化学元素的定性分析，业已发展为表面元素定性、半定量分析及元素化学价态分析的重要手段。XPS的研究领域也不再局限于传统的化学分析，而扩展到现代迅猛发展的材料学科。目前该分析方法在日常表面分析工作中的份额约50%，是一种最主要的表面分析工具。 在XPS谱仪技术发展方面也取得了巨大的进展。在X射线源上，已从原来的激发能固定的射线源发展到利用同步辐射获得X射线能量单色化并连续可调的激发源；传统的固定式X射线源也发展到电子束扫描金属靶所产生的可扫描式X射线源；X射线的束斑直径也实现了微型化，最小的束斑直径已能达到6 m 大小, 使得XPS在微区分析上的应用得到了大幅度的加强。图像XPS技术的发展，大大促进了XPS在新材料研究上的应用。在谱仪的能量分析检测器方面，也从传统的单通道电子倍增器检测器发展到位置灵敏检测器和多通道检测器，使得检测灵敏度获得了大幅度的提高。计算机系统的广泛采用，使得采样速度和谱图的解析能力也有了很大的提高。 由于XPS具有很高的表面灵敏度，适合于有关涉及到表面元素定性和定量分析方面的应用，同样也可以应用于元素化学价态的研究。此外，配合离子束剥离技术和变角XPS技术，还可以进行薄膜材料的深度分析和界面分析。因此，XPS方法可广泛应用于化学化工，材料，机械，电子材料等领域。 2 方法原理 X射线光电子能谱基于光电离作用，当一束光子辐照到样品表面时，光子可以被样品中某一元素的原子轨道上的电子所吸收，使得该电子脱离原子核的束缚，以一定的动能从原子内部发射出来，变成自由的光电子，而原子本身则变成
第十四章 X-射线光电子能谱法 14．1 引言 X-射线光电子谱仪（X-ray Photoelectron Spectroscopy，简称为XPS），经常又被称为化学分析用电子谱（Electron Spectroscopy for Chemical Analysis，简称为ESCA），是一种最主要的表面分析工具。自19世纪60年代第一台商品化的仪器开始，已经成为许多材料实验室的必不可少的成熟的表征工具。XPS发展到今天，除了常规XPS外，还出现了包含有Mono XPS (Monochromated XPS, 单色化XPS，X射线源已从原来的激发能固定的射线源发展到利用同步辐射获得X射线能量单色化并连续可调的激发源), SAXPS ( Small Area XPS or Selected Area XPS, 小面积或选区XPS，X射线的束斑直径微型化到6μm) 和iXPS（imaging XPS, 成像XPS）的现代XPS。目前，世界首台能量分辨率优于1毫电子伏特的超高分辨光电子能谱仪（通常能量分辨率低于1毫电子伏特）在中日科学家的共同努力下已经研制成功，可以观察到化合物的超导电子态。现代XPS拓展了XPS的内容和应用。 XPS是当代谱学领域中最活跃的分支之一，它除了可以根据测得的电子结合能确定样品的化学成份外，XPS最重要的应用在于确定元素的化合状态。XPS可以分析导体、半导体甚至绝缘体表面的价态，这也是XPS的一大特色，是区别于其它表面分析方法的主要特点。此外，配合离子束剥离技术和变角XPS技术，还可以进行薄膜材料的深度分析和界面分析。XPS表面分析的优点和特点可以总结如下： ⑴固体样品用量小，不需要进行样品前处理，从而避免引入或丢失元素所造成的错误分析 ⑵表面灵敏度高，一般信息采样深度小于10nm ⑶分析速度快，可多元素同时测定 ⑷可以给出原子序数3-92的元素信息，以获得元素成分分析 ⑸可以给出元素化学态信息，进而可以分析出元素的化学态或官能团 ⑹样品不受导体、半导体、绝缘体的限制等 ⑺是非破坏性分析方法。结合离子溅射，可作深度剖析 目前，XPS主要用于金属、无机材料、催化剂、聚合物、涂层材料、纳米材料、矿石等各种材料的研究，以及腐蚀、摩擦、润滑、粘接、催化、包覆、氧化等过程的研究，也可以用于机械零件及电子元器件的失效分析，材料表面污染物分析等。 14.2 基本原理 XPS方法的理论基础是爱因斯坦光电定律。用一束具有一定能量的X射线照射固体样品，入射光子与样品相互作用，光子被吸收而将其能量转移给原子的某一壳层上被束缚的电子，此时电子把所得能量的一部分用来克服结合能和功函数，余下的能量作为它的动能而发射出来，成为光电子，这个过程就是光电效应。 该过程可用下式表示: hγ=E k+E b+E r（14.1） 式中: hγ：X光子的能量（h为普朗克常数，γ为光的频率）；
第十四章 X射线衍射分析法 14.1概述 X射线衍射法是一种研究晶体结构的分析方法，而不是直接研究试样内含有元素的种类及含量的方法。当X射线照射晶态结构时，将受到晶体点阵排列的不同原子或分子所衍射。X射线照射两个晶面距为d的晶面时，受到晶面的反射，两束反射X光程差2dsinθ是入射波长的整数倍时，即 2dsinθ=nλ （n为整数） 两束光的相位一致，发生相长干涉，这种干涉现象称为衍射，晶体对X 射线的这种折射规则称为布拉格规则。θ称为衍射角（入射或衍射X射线与晶面间夹角）。n相当于相干波之间的位相差，n＝1，2…时各称0级、1级、2级……衍射线。反射级次不清楚时，均以n＝1求d。晶面间距一般为物质的特有参数，对一个物质若能测定数个d及与其相对应的衍射线的相对强度，则能对物质进行鉴定。 X射线衍射分析方法在材料分析与研究工作中具有广泛的用途。在此主要介绍其在物相分析等方面的应用。 14.1.1 物相定性分析 1．基本原理 组成物质的各种相都具有各自特定的晶体结构(点阵类型、晶胞形状与大小及各自的结构基元等)，因而具有各自的X射线衍射花样特征(衍射线位置与强度)。对于多相物质，其衍射花样则由其各组成相的衍射花样简单叠加而成。由此可知，物质的X射线衍射花样特征就是分析物质相组成的“指纹脚印”。制备各种标准单相物质的衍射花样并使之规范化（1969年成立了国际性组织“粉末衍射标准联合会(JCPDS)”，由它负责编辑出版“粉末衍射卡片”，称PDF卡片），将待分析物质(样品)的衍射花样与之对照，从而确定物质的组成相，这就是物相定性分析的基本原理与方法。 2．物相定性分析的基本步骤 (1) 制备待分析物质样品，用衍射仪获得样品衍射花样。 (2) 确定各衍射线条d值及相对强度I/I1值(Il为最强线强度)。 (3) 检索PDF卡片。 PDF卡片检索有三种方式： 1）检索纸纸卡片 物相均为未知时，使用数值索引。将各线条d值按强度递减顺序排列；按三强线条d1、d2、d3的d—I/I1数据查数值索引；查到吻合的条目后，核对八强线的d—I/I1值；当八强线基本符合时，则按卡片编号取出PDF卡片。若按d1、d2、d3顺序查找不到相应条目，则可将d1、d2、d3按不同顺序排列查找。查找索引时，d值可有一定误差范围：一般允许
X射线荧光光谱分析 X射线是一种电磁辐射，其波长介于紫外线和γ射线之间。它的波长没有一个严格的界限，一般来说是指波长为0.001-50nm的电磁辐射。对分析化学家来说，最感兴趣的波段是0.01-24nm，0.01nm左右是超铀元素的K系谱线，24nm则是最轻元素Li的K系谱线。1923年赫维西(Hevesy, G. Von)提出了应用X射线荧光光谱进行定量分析，但由于受到当时探测技术水平的限制，该法并未得到实际应用，直到20世纪40年代后期，随着X射线管、分光技术和半导体探测器技术的改进，X荧光分析才开始进入蓬勃发展的时期，成为一种极为重要的分析手段。 1.1 X射线荧光光谱分析的基本原理 当能量高于原子内层电子结合能的高能X射线与原子发生碰撞时，驱逐一个内层电子而出现一个空穴，使整个原子体系处于不稳定的激发态，激发态原子寿命约为10-12-10-14s，然后自发地由能量高的状态跃迁到能量低的状态。这个过程称为驰豫过程。驰豫过程既可以是非辐射跃迁，也可以是辐射跃迁。当较外层的电子跃迁到空穴时，所释放的能量随即在原子内部被吸收而逐出较外层的另一个次级光电子，此称为俄歇效应，亦称次级光电效应或无辐射效应，所逐出的次级光电子称为俄歇电子。它的能量是特征的，与入射辐射的能量无关。当较外层的电子跃入内层空穴所释放的能量不在原子内被吸收，而是以辐射形式放出，便产生X射线荧光，其能量等于两能级之间的能量差。因此，X射线荧光的能量或波长是特征性的，与元素有一一对应的关系。图1-1给出了X射线荧光和俄歇电子产生过程示意图。
K层电子被逐出后,其空穴可以被外层中任一电子所填充，从而可产生一系列的谱线，称为K系谱线：由L层跃迁到K层辐射的X射线叫Kα射线,由M层跃迁到K层辐射的X射线叫Kβ射线……。同样,L层电子被逐出可以产生L系辐射(见图1-2)。
地理时间计算部分专题练习 1、9月10日在全球所占的围共跨经度90°，则时间为：( ) A. 10日2时 B. 11日2时 C. 10日12时 D. 11日12时 3、时间为2008年3月1日的2点，此时与处于同一日期的地区围约占全球的：( ) A. 一半 B. 三分之一 C. 四分之一 D. 五分之一 4、图中两条虚线，一条是晨昏线，另一条两侧大部分地区日期不同，此时地球公转速度较慢。若图中的时间为7日和8日，甲地为（ ） Ａ．７日４时 Ｂ．８日８时 Ｃ．７月８时 Ｄ．８月４时 2004年3月22日到4月3日期间，可以看到多年一遇的“五星连珠”天象奇观。其中水星是最难一见的行星，观察者每天只有在日落之后的1 小时才能看到它。图中阴影部分表示黑夜，中心点为极地。回答5—7题 5．图4中①②③④四地，可能看到“五星连珠”现象的是( ) A ．① B ．② C ．③ D ．④ 6．在新疆的吐鲁番（约890 E ）观看五星连珠现象，应该选择的时间段（时间）是( ) A ．18时10分至19时 B ．16时10分至17时 C ．20时10分至21时 Ｄ．21时10分至22时 7．五星连珠中，除了水星外，另外四颗星是( ) A ．金星、木星、土星、天狼星 B ．金星、火星、木星、海王星 C ．火星、木星、土星、天王星 D ．金星、火星、土星、木星 （2002年）下表所列的是12月22日甲、乙、丙、丁四地的白昼时间，根据表中数据回答下8-10题。 甲地 乙地 丙地 丁地 白昼长 5∶30 9∶09 11∶25 13∶56 8、四地中属于南半球的是（ ） A.甲地 B.乙地 C.丙地 D.丁地 9、四地所处纬度从高到低顺序排列的是（ ） A.甲乙丙丁 B.甲乙丁丙 C.丙丁乙甲 D.丁丙乙甲 10、造成四起白昼时间差异的主要因素是（ ） ①地球的公转 ②地球自转 ③黄赤交角的存在 ④地方时的不同 A.①② B.②③ C.③④ D.①③ 2002年1月1日，作为欧洲联盟统一货币的欧元正式流通，这将对世界金融的整体格局产生重要影响。回 答4-5题： 11、假定世界各金融市场均在当地时间上午9时开市，下午5时闭市。如果某投资者上午9时在法兰克福（东经8.50 ）市场买进欧元，12小时后欧元上涨，投资者想尽快卖出欧元，选择的金融市场应位于：（ ） A.东京（东经139.50 ） B.（东经1140 ） C.伦敦 D.纽约（西经740 ） ① ④ ② ③
第一讲 X 射线荧光及其分析原理 1、X 射线 X 射线是一种电磁波，根据波粒二相性原理，X 射线也是一种粒子，其每个粒子根据下列公式可以找到其能量和波长的一一对应关系。 E ＝hv=h c/λ 式中h 为普朗克常数，v 为频率，c 为光速，λ为波长。 可见其能量在0.1 ~100（kev ）之间。 γ X 紫 可 红 微 短 长 射 射 外 见 线 线 线 光 外 波 波 波 波长 X 射线的产生有几种 1、高速电子轰击物质，产生韧致辐射和标识辐射。其产生的韧致辐射的X 射线的能量取决于 电子的能量，是一个连续的分布。而标识辐射是一种能量只与其靶材有关的X 射线。 E kev A o ().() = 123964 λ
常见的X射线光管就是采用的这种原理。其X射线能量分布如下： 能量 2、同位素X射线源。 同位素在衰变过程中，其原子核释放的能量，被原子的内层电子吸收，吸收后跳出内层轨道，形成内层轨道空位。但由于内层轨道的能级很低,外层电子前来补充，由于外层电子的能量较高，跳到内层后，会释放出光能来，这种能就是X射线。这就是我们常见的同位素X射线源。由于电子的能级是量化的，故释放的射线的能量也是量化的,而不是连续的。
能量 3、同步辐射源。 电子在同步加速器中运动，作园周运动，有一个恒定的加速度，电子在加速运动时，会释放出X射线，所以用这种方法得到的X射线叫同步辐射X射线。 2、X射线荧光 实际上，有很多办法能产生X射线，例如用质子、α射线、λ射线等打在物质上，都可以产生X射线，而人们通常把X射线照射在物质上而产生的次级X射线叫X射线荧光（X—Ray Fluorescence），而把用来照射的X射线叫原级X射线。所以X射线荧光仍是X射线。 3、特征X射线 有人会问，为什么可以用X射线来分析物质的成分呢？这些都归功于特征X射线。 早在用电子轰击阳极靶而产生X射线时，人们就发现，有几个强度很高的X射线，其能量并没有随加速电子用的高压变化，而且不同元素的靶材，其特殊的X射线的能量也不一样，人们把它称为特征X射线，它是每种元素所特有的。莫塞莱（Moseley）发现了X射线能量与原子序数的关系。 E∝（z-σ） E是特征X射线能量，Z是原子序数，σ是修正因子。 这就是著名的莫塞莱定律，它开辟了X射线分析在元素分析中的应用。 为什么会有特征X射线的出现呢？这可以从玻尔的原子结构理论找到答案。原子中的电子都在一个个电子轨道上运行，而每个轨道的能量都是一定的，叫能级。内层轨道能级较低，外层轨道能级较高，当内层的电子受到激发（激发源可以是电子、质子、α粒子、λ射线、X射线等），有足够的能量跳出内层轨道，那么，较外层的电子跃迁到内层的轨道进行补充，由于是从高能级上跳往低能级上，所以会释放出能量，其能量以光的形式放出，这就是特征X射线。 M层 Lα较高能级
X射线荧光分析的基本原理 欧阳光明（2021.03.07） 1. 绪论 物质是由各种元素按照不同的构成方式构成的。各种元素的原子是由原子核和一定数目的核外电子构成。不同元素的原子，原子核中质子和中子的数量不同，核外电子数也不同，具有不同的原子结构。核外电子的能量也各不相同，这些能量不同的原子按能量大小分层排列，离原子核最近的电子层称为K电子层，其外依次为L,M,N,O…层。K层上的电子能量最低，由里向外，电子的能量逐渐升高。原子在未接受足够的能量时，处于基态，即稳定状态，此时，K层最多容纳2个电子，L层最多容纳8个电子，M层最多容纳18个电子……。当使用高能射线（如X射线）照射物质时，物质中的原子的内层电子被高能射线逐出原子之外，在内层电子层上即出现一个“空穴”。具有较高能量的外层电子立即补充这一“空穴”而发生跃迁。发生跃迁的电子将多余的能量（两个电子层能量之差）释放出来。释放出来的能量以电磁波的形式向四周发射，其波长恰好在X射线的波长范围内（0.001～10nm）。为了与照射物质的X射线（初级X射线）相区别，将被照射物质发出的X射线（二次X射线）称为荧光X射线（荧光即光致发光之意）。对于K 层电子而言，L层电子向K层电子跃迁时放射出的荧光X射线称为Kα谱线，M层电子向K层电子跃迁时放射出的荧光X射线称为Kβ谱线，其他层的电子发生跃迁时的情况依此类推（如图 1.1所示）。利用被测物质发出的荧光X射线进行物质化学成分的定性分析或定量分析，称为X射线荧光光谱分析。 图1.1原子结构示意图 在形成的线系中，各谱线的相对强度是不同的，这是由于跃迁几率不同。对K层电子而言,特定元素的荧光X射线Kα>Kβ,对于同一种元素而言，强谱线只有1-2条,特征谱线比较简单，易于分析，光谱干扰小。 2. X射线与固体之间的相互作用
一、X光电子能谱分析的基本原理 X光电子能谱分析的基本原理：一定能量的X光照射到样品表面，和待测物质 发生作用，可以使待测物质原子中的电子脱离原子成为自由电子。该过程可用 下式表示： hn=Ek+Eb+Er （1） 其中:hn：X光子的能量；Ek：光电子的能量；Eb：电子的结合能；Er：原子的 反冲能量。其中Er很小，可以忽略。 对于固体样品，计算结合能的参考点不是选真空中的静止电子，而是选用费米 能级，由内层电子跃迁到费米能级消耗的能量为结合能Eb，由费米能级进入真 空成为自由电子所需的能量为功函数Φ，剩余的能量成为自由电子的动能Ek，式(1)又可表示为： hn=Ek+Eb+Φ（2） Eb=hn-Ek-Φ（3）仪器材料的功函数Φ是一个定值，约为 4 eV，入射X光子能量已知，这样， 如果测出电子的动能Ek，便可得到固体样品电子的结合能。各种原子，分子的 轨道电子结合能是一定的。因此，通过对样品产生的光子能量的测定，就可以 了解样品中元素的组成。元素所处的化学环境不同，其结合能会有微小的差别，这种由化学环境不同引起的结合能的微小差别叫化学位移，由化学位移的大小 可以确定元素所处的状态。例如某元素失去电子成为离子后，其结合能会增加，如果得到电子成为负离子，则结合能会降低。因此，利用化学位移值可以分析 元素的化合价和存在形式。 二、电子能谱法的特点 (1)可以分析除H和He以外的所有元素；可以直接测定来自样品单个能级光电 发射电子的能量分布，且直接得到电子能级结构的信息。(2)从能量范围看，如果把红外光谱提供的信息称之为“分子指纹”，那么电子能谱提供的信息可称 作“原子指纹”。它提供有关化学键方面的信息，即直接测量价层电子及内层 电子轨道能级。而相邻元素的同种能级的谱线相隔较远，相互干扰少，元素定 性的标识性强。 (3)是一种无损分析。 (4)是一种高灵敏超微量表面分析技术，分析所需试样约10-8g即可，绝对灵敏
【干货】玩转XPS丨案例解析X射线光电子能谱（XPS）八大应用！ 表面分析技术 (Surface Analysis)是对材料外层(the Outer-Most Layers of Materials (<100nm))的研究的技术。 X射线光电子能谱简单介绍 XPS是由瑞典Uppsala大学的K. Siegbahn及其同事历经近20年的潜心研究于60年代中期研制开发出的一种新型表面分析仪器和方法。鉴于K. Siegbahn教授对发展XPS领域做出的重大贡献，他被授予1981年诺贝尔物理学奖。 X射线激发光电子的原理 XPS现象基于爱因斯坦于1905年揭示的光电效应，爱因斯坦由于这方面的工作被授予1921年诺贝尔物理学奖； X射线是由德国物理学家伦琴（Wilhelm Conrad R?ntgen，l845-1923）于1895年发现的，他由此获得了1901年首届诺贝尔物理学奖。
X射线光电子能谱（XPS ，全称为X-ray Photoelectron Spectroscopy）是一种基于光电效应的电子能谱，它是利用X射线光子激发出物质表面原子的内层电子，通过对这些电子进行能量分析而获得的一种能谱。 这种能谱最初是被用来进行化学分析，因此它还有一个名称，即化学分析电子能谱（ESCA，全称为Electron Spectroscopy for Chemical Analysis）。XPS谱图分析中原子能级表示方法 XPS谱图分析中原子能级的表示用两个数字和一个小字母表示。例如:3d5/2（1）第一个数字3代表主量子数(n)； （2）小写字母代表角量子数; （3）右下角的分数代表内量子数j
小学三年级数学《简单的时间计算》教案范文三篇时间计算是继二十四时计时法的学习之后安排的一个内容。下面就是小编给大家带来的小学三年级数学《简单的时间计算》教案范文，欢迎大家阅读! 教学目标： 1、利用已学的24时记时法和生活中对经过时间的感受，探索简单的时间计算方法。 2、在运用不同方法计算时间的过程中，体会简单的时间计算在生活中的应用，建立时间观念，养成珍惜时间的好习惯。 3、进一步培养课外阅读的兴趣和多渠收集信息的能力。 教学重点： 计算经过时间的思路与方法。 教学难点： 计算从几时几十分到几时几十分经过了多少分钟的问题。 教学过程： 一、创设情景，激趣导入 1、谈话：小朋友你们喜欢过星期天吗?老师相信我们的星期天都过得很快乐!明明也有一个愉快的星期天，让我们一起来看看明明的一天，好吗? 2、小黑板出示明明星期天的时间安排。 7：10-7：30 起床、刷牙、洗脸; 7：40-8：20 早锻炼; 8：30-9：00 吃早饭; 9：00-11：00 看书、做作业 …… 3、看了刚才明明星期天的时间安排，你知道了什么?你是怎么知道的?你还想知道什么?
二、自主探究，寻找方法 1、谈话：小明在星期天做了不少的事，那你知道小明做每件事情用了多少时间吗?每 个小组从中选出2件事情计算一下各用了多少时间。 (1)分组学习。 (2) 集体交流。 2、根据学生的提问顺序学习时间的计算。从整时到整时经过时间的计算。 (1)学生尝试练习9：00-11：00明明看书、做作业所用的时间。 (2)交流计算方法：11时-9时=2小时。 3、经过时间是几十分钟的时间计算。 (1)明明从7：40到8：20进行早锻炼用了多少时间呢? 出示线段图。 师：7：00-8：00、8：00-9：00中间各分6格，每格表示10分钟，两个线段下边 的箭头分别指早锻炼开始的时间和结束的时间，线段图涂色部分表示早锻炼的时间。谈话：从图上看一看，从7时40分到8时经过了多少分钟?(20分)从8时到8时20分又经过 了多少时间?所以一共经过了多少分钟。(20+20=40分)小朋友们，如果你每天都坚持锻炼 几十分钟，那你的身体一定会棒棒的。 (2)你还能用别的方法计算出明明早锻炼的时间吗?(7：40-8：40用了一个小时，去掉 多算的20分，就是40分。或者7：20-8：20用了1个小时，去掉多算的20分，就是 40分。) (3)练习：找出明明的一天中做哪些事情也用了几十分钟? 你能用自己喜欢的方法计算出明明做这几件事情用了几十分钟吗?你是怎么算的? 三、综合练习，巩固深化 1、想想做做1：图书室的借书时间。你知道图书室每天的借书时间有多长吗? 学生计算。 (1)学生尝试练习，交流计算方法。 (2)教师板书。 2、想想做做2。 (1)学生独立完成。 (2)全班交流。
X射线衍射分析 摘要： X射线衍射分析是一种重要的晶体结构和物相分析技术，广泛应用于冶金、石油、化工、科研、航空航天、教学、材料生产等领域。本文简要介绍X射线衍射原理，X射线衍射仪器的结构、原理，及其在地质学、医学等自然科学领域中的应用。 前言： 1895年伦琴发现X射线，又称伦琴射线。德国科学家劳厄于1912年发现
了X射线衍射现象，并推导出劳厄晶体衍射公式。随后，英国布拉格父子又将此衍射关系用简单的布拉格方程表示出来。到上世纪四、五十年代，X射线衍射的原理、方法及在其他各方面的应用逐渐建立。在各种测量方法中，X射线衍射方法具有不损伤样品、无污染、快捷、测量精度高、能得到有关晶体完整性的大量信息等优点。X射线衍射技术可以探究晶体存在的普遍性和特殊性能，使得其在冶金、石油、岩石矿物、科研、航空航天、材料生产等领域的被广泛应用。 关键词：方法，衍射，原理，应用 X射线衍射仪的原理 1.X射线衍射原理 当X射线沿某方向入射某一晶体的时候，晶体中每个原子的核外电子产生的相干波彼此发生干涉。当每两个相邻波源在某一方向的光程差等于波长λ的整数倍时，它们的波峰与波峰将互相叠加而得到最大限度的加强，这种波的加强叫做衍射，相应的方向叫做衍射方向，在衍射方向前进的波叫做衍射波。光程差为0的衍射叫零级衍射，光程差为λ的衍射叫一级衍射，光程差为nλ的衍射叫n级衍射。n不同，衍射方向的也不同。 由于常用的X射线波长约在2.5A～0.5A之间，与晶体中的原子间距(1A)数量级相同，因此可以用晶体作为X射线的衍射光栅，这就使得用X射线衍射进行晶体结构分析成为可能。 在晶体的点阵结构中，具有周期性排列的原子或电子散射的次生X射线间相互干涉的结果，决定了X射线在晶体中衍射的方向，所以通过对衍射方向的测定，可以得到晶体的点阵结构、晶胞大小和形状等信息。 晶体结构=点阵+结构基元，点阵又包括直线点阵，平面点阵和空间点阵。在x 射线作用下晶体的散射线来自若干层原子面，除同一层原子面的散射线互相干涉外，各原子面的散射线之间还要互相干涉。 光栅衍射 当光程差(BD+BF)=2dsinθ等于波长的整数倍nλ时，相邻原子面散射波干涉加强，即干涉加强条件为： 2dsinθ=nλ 一、X射线衍射法
三．X 射线衍射的基本原理 3.1 Bragg 公式 晶体的空间点阵可划分为一族平行而等间距的平面点阵，两相邻点阵平面的间距为d hkl 。晶体的外形中每个晶面都和一族平面点阵平行。 当X 射线照射到晶体上时，每个平面点阵都对X 射线射产生散射。取晶体中任一相邻晶面P 1和P 2，如图3.1所示。两晶面的间距为d ，当入射X 射线照射到此晶面上时，入射角为θ，散射X 射线的散射角也同样是θ。这两个晶面产生的光程差是： θsin 2d OB AO =+=? 3.1 当光程差为波长λ 的整数倍时，散射的X 射线将相互加强，即衍射： λθn d hkl =sin 2 3.2 上式就是著名的Bragg 公式。也就是说，X 射线照射到晶体上，当满足Bragg 公式就产生衍射。式中：n 为任意正整数，称为衍射级数。入射X 射线的延长线与衍射X 射线的夹角为2θ（衍射角）。为此，在X 射线衍射的谱图上，横坐标都用2θ 表示。 图3.1 晶体对X 射线的衍射 由Bragg 公式表明：d hkl 与θ 成反比关系，晶面间距越大，衍射角越小。晶面间距的变化直接反映了晶胞的尺寸和形状。每一种结晶物质，都有其特定的结构参数，包括点阵类型、晶胞大小等。晶体的衍射峰的数目、位置和强度，如同人的指纹一样，是每种物质的特征。尽管物质的种类有成千上万，但几乎没有两种衍射谱图完全相同的物质，由此可以对物质进行物相的定性分析。
3.2 物相分析 物相的定义是物质存在的状态，如同素异构体SiO2、TiO2分别有22种和5种晶体结构。除了单质元素构成的物质如铜、银等以外，X射线衍射分析的是物相（或化合物），而不是元素成分。 对于未知试样，为了了解和确定哪些物相时，需要定性的物相分析。 正如前述，晶体粉末衍射谱图，如人的指纹一样，有它本身晶体结构特征所决定。因而，国际上有一个组织——粉末衍射标准联合会（JCPDS）后改名为JCPDS－衍射数据国际中心专门负责收集、校订、编辑和发行粉末衍射卡片（PDF）的工作。自1941年以来，共发行衍射卡片近20万个。为了使大量的卡片方便进行人工物相鉴定，还出版了对这些卡片进行检索的索引。PDF卡片的标准形式如图3.2所示，对应此图编号的内容说明如表3.1所示。 图 图3.2 PDF卡片的标准形式 每一张卡片上不一定包括表3.1所述的所有内容，但有效数据都将一一列出。 物相分析的方法就是将未知试样与标准卡片上数据进行对比，由此来确定物相。先测试未知试样，然后按图3.3所示的步骤从PDF索引中查找。找出该物相的卡片号后，按卡片号查该物相的卡片，仔细核对后再判定该物相。
第二十三章 X射线光电子能谱 1954年以瑞典Siegbahn教授为首的研究小组观测光峰现象，不久又发现了原子内层电子能级的化学位移效应，于是提出了ESCA(化学分析电子光谱学)这一概念。由于这种方法使用了铝、镁靶材发射的软X射线，故也称为X-光电子能谱(X-ray Photoelectron Spectroscopy)。X光电子能谱分析技术已成为表面分析中的常规分析技术，目前在催化化学、新材料研制、微电子、陶瓷材料等方面得到了广泛的应用。 23.1 基本原理 固体表面分析，特别是对固体材料的分析和元素化学价态分析，已发展为一种常用的仪器分析方法。目前常用的表面成分分析方法有：X射线光电子能谱（XPS）, 俄歇电子能谱(AES)，静态二次离子质谱(SIMS)和离子散射谱(ISS)。AES分析主要应用于物理方面的固体材料（导电材料）的研究，而XPS的应用面则广泛得多，更适合于化学领域的研究。SIMS 和ISS由于定量效果较差，在常规表面分析中的应用相对较少。但近年随着飞行时间二次离子质谱（TOF-SIMS）的发展，使得质谱在表面分析上的应用也逐渐增加。 X射线光电子能谱最初是由瑞典科学家K.Siegbahn等经过约20年的努力而建立起来的，因在化学领域的广泛应用，被称为化学分析用电子能谱（ESCA）。由于最初的光源采用了铝、镁等的特性软X射线，该技术又称为X射线光电子能谱（XPS）。1962年，英国科学家D.W.Turner等建造出以真空紫外光作为光源的光电子能谱仪，在分析分子内价电子的状态方面获得了巨大成功，同时又用于固体价带的研究，与X射线光电子能谱相对照，该方法称为紫外光电子能谱（UPS） XPS的原理是基于光的电离作用。当一束光子辐射到样品表面时，样品中某一元素的原子轨道上的电子吸收了光子的能量，使得该电子脱离原子的束缚，以一定的动能从原子内部发射出来，成为自由电子，而原子本身则变成处于激发态的离子，如图23-1所示。在光电离过程中，固体物质的结合能可用下面的方程式表示： E b=hγ- E k -φs（23-1） 式中: E k为射出的光子的动能；hγ为X射线源的能量；E b为特定原子轨道上电子的电离能或结合能（电子的结合能是指原子中某个轨道上的电子跃迁到表面Fermi能级（费米能级）所需要的能量）；φs为谱仪的功函数。 由于φs是由谱仪的材料和状态决定，对同一台谱仪来说是一个常数，与样品无关，其平均值为3 eV ~4eV。因此，（1）式可简化为： E b =hγ- E k’ （23-2） 由于E k’可以用能谱仪的能量分析器检出，根据式（23-2）就可以知道E b。在XPS分析中，由于X射线源的能量较高，不仅能激发出原子轨道中的价电子，还可以激发出内层轨道电子，所射出光子的能量仅与入射光子的能量及原子轨道有关。因此，对于特定的单色激发光源及特定的原子轨道，其光电子的能量是特征性的。当固定激发光源能量时，其光子的能量仅与元素的种类和所电离激发的原子轨道有关，对于同一种元素的原子，不同轨道上的电子的结合能不同。所以可用光电子的结合能来确定元素种类。图23-1表示固体材料表面受X射线激发后的光电离过程[1]。
中国古代时间的计算方法（1） 现时每昼夜为二十四小时，在古时则为十二个时辰。当年西方机械钟表传入中国，人们将中西时点，分别称为“大时”和“小时”。随着钟表的普及，人们将“大时”忘淡，而“小时”沿用至今。 古时的时（大时）不以一二三四来算，而用子丑寅卯作标，又分别用鼠牛虎兔等动物作代，以为易记。具体划分如下：子（鼠）时是十一到一点，以十二点为正点；丑（牛）时是一点到三点，以两点为正点；寅（虎）时是三点到五点，以四点为正点；卯（兔）时是五点到七点，以六点为正点；辰（龙）时是七点到九点，以八点为正点；巳（蛇）时是九点到十一点，以十点为正点；午（马）时是十一点到一点，以十二点为正点；未（羊）时是一点到三点，以两点为正点；申（猴）时是三点到五点，以四点为正点；酉（鸡）时是五点到七点，以六点为正点；戌（狗）时是七点到九点，以八点为正点；亥（猪）时是九点到十一点，以十点为正点。 古人说时间，白天与黑夜各不相同，白天说“钟”，黑夜说“更”或“鼓”。又有“晨钟暮鼓”之说，古时城镇多设钟鼓楼，晨起（辰时，今之七点）撞钟报时，所以白天说“几点钟”；暮起（酉时，今之十九点）鼓报时，故夜晚又说是几鼓天。夜晚说时间又有用“更”的，这是由于巡夜人，边巡行边打击梆子，以点数报时。全夜分五个更，第三更是子时，所以又有“三更半夜”之说。 时以下的计量单位为“刻”，一个时辰分作八刻，每刻等于现时的十五分钟。旧小说有“午时三刻开斩”之说，意即，在午时三刻钟（差十五分钟到正午）时开刀问斩，此时阳气最盛，阴气即时消散，此罪大恶极之犯，应该“连鬼都不得做”，以示严惩。阴阳家说的阳气最盛，与现代天文学的说法不同，并非是正午最盛，而是在午时三刻。古代行斩刑是分时辰开斩的，亦即是斩刑有轻重。一般斩刑是正午
竭诚为您提供优质文档/双击可除 excel表格日期计算 篇一：excel中几个时间计算公式 假设b2为生日 =datedif(b2,today(),"y") datediF函数，除excel2000中在帮助文档有描述外，其他版本的excel在帮助文档中都没有说明，并且在所有版本的函数向导中也都找不到此函数。但该函数在电子表格中确实存在，并且用来计算两个日期之间的天数、月数或年数很方便。微软称，提供此函数是为了与lotus1-2-3兼容。 该函数的用法为 “datediF(start_date,end_date,unit)”，其中start_date 为一个日期，它代表时间段内的第一个日期或起始日期。end_date为一个日期，它代表时间段内的最后一个日期或结束日期。unit为所需信息的返回类型。 “y”为时间段中的整年数，“m”为时间段中的整月数，“d”时间段中的天数。“md”为start_date与end_date日期中天数的差，可忽略日期中的月和年。“ym”为start_date 与end_date日期中月数的差，可忽略日期中的日和年。“yd”
为start_date与end_date日期中天数的差，可忽略日期中的年。比如，b2单元格中存放的是出生日期（输入年月日时，用斜线或短横线隔开），在c2单元格中输入 “=datedif(b2,today(),"y")”（c2单元格的格式为常规），按回车键后，c2单元格中的数值就是计算后的年龄。此函数在计算时，只有在两日期相差满12个月，才算为一年，假如生日是20xx年2月27日，今天是20xx年2月28日，用此函数计算的年龄则为0岁，这样算出的年龄其实是最公平的。 身份证号提取年龄 =datediF(--text((len(a1)=15)*19”即可获得当时的日期时间； 2、使用公式：用=now()而非=date()，=date()只有日期，然后进行菜单“工具->选项”，选择“重新计算”页，选中“人工重算”，勾不勾选“保存前自动重算”看自己的需要和想法了，如果勾选了，那日期时间那总是最后一次保存的日期时间，不勾选的话，如果你的表格中有公式记得准备存前按F9 篇二：excel中如何计算两个日期之间的月数 excel中如何计算两个日期之间的月数
高中地理计算公式 一、时间的计算 1、求时区： 时区数＝已知经度／15°（商四舍五入取整数，即为时区数） 2、求区时： 所求区时＝已知区时±时区差（东加西减） 3、求地方时： 所求地方时＝已知地方时±4分钟／度×经度差（东加西减） 二、太阳高度的计算 1、求正午太阳高度： H＝90°－︱纬度差︱（纬度差指当地纬度与太阳直射纬度之间的差） 2、求子夜太阳高度： H＝︱纬度和︱－90°（纬度和指当地纬度与太阳直射纬度之间的和） 3、求南北两楼的楼间距： L＝h?cotH (h为楼高，H为该地一年中最小的正午太阳高度) 三、昼夜长短的计算 1、求昼长： （1）昼长＝昼弧∕15° （2）昼长＝日落时间－日出时间 （3）昼长＝24－夜长 （4）昼长＝（12－日出地方时）×2 （5）昼长＝（日落地方时－12） 2、求夜长 （1）夜长＝夜弧∕15° （2）夜长＝24－昼长 （3）夜长＝（24－日落地方时）×2 （4）北半球某纬度的夜长＝南半球同纬度的昼长 四、日出、日落时刻的计算 １、求日出时刻： （1）日出时刻＝当地纬线与晨线交点的时刻（2）日出时刻＝12－昼长∕2 2、求日落时刻： （1）日落时刻＝当地纬线与昏线交点的时刻（2）日落时刻＝12＋昼长∕2 五、球面距离的计算 （1）赤道和经线上的距离111Km×度数 （2）纬线上的距离＝111Km×度数?COSθ(θ为当地的纬度) （3）对趾点的计算:经度互补,一东一西；纬度相等,一南一北。 六、比例尺的计算 （1）比例尺＝图上距离∕实地距离 （2）缩放图幅面积＝原图幅面积×比例尺缩放的平方 七、相对高度的计算 （1）陡崖相对高度：（n－1）d≤H＜(n＋1)d (n为等高线条数，d为等高距) （2）H＝T∕6°×1000米 (H为两地相对高度,T为两地温差)
X射线光电子能谱的原理及应用（XPS） （一）X光电子能谱分析的基本原理 X光电子能谱分析的基本原理：一定能量的X光照射到样品表面，和待测物质发生作用，可以使待测物质原子中的电子脱离原子成为自由电子。该过程可用下式表示: hn=Ek+Eb+Er 其中: hn：X光子的能量；Ek：光电子的能量；Eb：电子的结合能；Er：原子的反冲能量。其中Er很小，可以忽略。 对于固体样品，计算结合能的参考点不是选真空中的静止电子，而是选用费米能级，由内层电子跃迁到费米能级消耗的能量为结合能Eb，由费米能级进入真空成为自由电子所需的能量为功函数Φ，剩余的能量成为自由电子的动能Ek， 式(103)又可表示为：hn=Ek+Eb+Φ （10.4）Eb= hn- Ek-Φ （10.5） 仪器材料的功函数Φ是一个定值，约为4eV，入射X光子能量已知，这样，如果测出电子的动能Ek，便可得到固体样品电子的结合能。各种原子，分子的轨道电子结合能是一定的。因此，通过对样品产生的光子能量的测定，就可以了解样品中元素的组成。元素所处的化学环境不同，其结合能会有微小的差别，这种由化学环境不同引起的结合能的微小差别叫化学位移，由化学位移的大小可以确定元素所处的状态。例如某元素失去电子成为离子后，其结合能会增加，如果得到电子成为负离子，则结合能会降低。因此，利用化学位移值可以分析元素的化合价和存在形式。 （二）电子能谱法的特点 ( 1 )可以分析除H 和He 以外的所有元素；可以直接测定来自样品单个能级光电发射电子的能量分布，且直接得到电子能级结构的信息。 ( 2 )从能量范围看，如果把红外光谱提供的信息称之为“分子指纹”，那么电子能谱提供的信息可称作“原子指纹”。它提供有关化学键方面的信息，即直接测量价层电子及内层电子轨道能级。而相邻元素的同种能级的谱线相隔较远，相互干扰少，元素定性的标识性强。 ( 3 )是一种无损分析。 ( 4 )是一种高灵敏超微量表面分析技术。分析所需试样约10 -8 g 即可，绝对灵敏度高达10 -18 g ，样品分析深度约2nm 。 (三) X 射线光电子能谱法的应用 ( 1 )元素定性分析 各种元素都有它的特征的电子结合能，因此在能谱图中就出现特征谱线，可以根据这些谱线在能谱图中的位置来鉴定周期表中除H 和He 以外的所有元素。通过对样品进行全扫描，在一次测定中就可以检出全部或大部分元素。 ( 2 )元素定量分折 X 射线光电子能谱定量分析的依据是光电子谱线的强度(光电子蜂的面积)反映了原于的含量或相对浓度。在实际分析中，采用与标准样品相比较的方法来对元素进行定量分析，其分析精度达1 ％～ 2 ％。 ( 3 )固体表面分析 固体表面是指最外层的1 ～10 个原子层，其厚度大概是(0.1~1) n nm 。人们早已认识到在固体表面存在有一个与团体内部的组成和性质不同的相。表面研究包括分析表面的元素组成和化学组成，原子价态，表面能态分布。测定表面原子的电子云分布和能级结构等。X 射线 光电子能谱是最常用的工具。在表面吸附、催化、金属的氧化和腐蚀、半导体、电极钝化、薄膜材料等方面都有应用。 ( 4 )化合物结构签定 X 射线光电子能谱法对于内壳层电子结合能化学位移的精确测量，能提供化学键和电荷