a r X i v :0712.0112v 1 [a s t r o -p h ] 1 D e c 2007Atomic Diagnostics of X-ray Irradiated Protoplanetary Disks
R.Meijerink and A.E.Glassgold
Astronomy Department,University of California,Berkeley,CA 94720
rowin@https://www.doczj.com/doc/a79370448.html,,glassgol@https://www.doczj.com/doc/a79370448.html, and J.R.Najita National Optical Astronomy Observatory,Tucson,AZ 85719najita@https://www.doczj.com/doc/a79370448.html, ABSTRACT We study atomic line diagnostics of the inner regions of protoplanetary disks with our model of X-ray irradiated disk atmospheres which was previously used to predict observable levels of the Ne II and Ne III ?ne-structure transitions at 12.81and 15.55μm.We extend the X-ray ionization theory to sulfur and calculate the fraction of sulfur in S,S +,S 2+and sulfur molecules.For the D’Alessio generic T Tauri star disk,we ?nd that the S I ?ne-structure line at 25.55μm is below the detection level of the Spitzer Infrared Spectrometer (IRS),in large part due to X-ray ionization of atomic S at the top of the atmosphere and to its incorporation into molecules close to the mid-plane.We predict that observable ?uxes of the S II 6718/6732?A forbidden transitions are produced in the upper atmosphere at somewhat shallower depths and smaller radii than the neon ?ne-structure lines.
This and other forbidden line transitions,such as the O I 6300/6363?A and the C I 9826/9852?A lines,serve as complementary diagnostics of X-ray irradiated disk atmospheres.We have also analyzed the potential role of the low-excitation ?ne-structure lines of C I,C II,and O I,which should be observable by SOFIA and Herschel .
Subject headings:accretion,accretion disks –infrared:stars –planetary systems:protoplanetary disks –stars:formation –stars:pre-man-sequence –X-rays:stars
1.Introduction
There is growing evidence for the existence of warm atmospheres in the inner disks of low and intermediate mass young stellar objects(YSOs).They?rst became apparent from observations of the CO overtone bandhead emission near2.3μm in Herbig Ae stars and T Tauri stars(e.g.,Carr1989;Najita et al.2000).More recently,the emission from the fundamental CO ro-vibrational band near4.6μm has been observed in many T Tauri stars (Najita et al.2003),as has the UV?uorescence of molecular hydrogen(e.g.,Herczeg et al. 2002).These observations indicate that temperatures in the range1000-2000K occur over a considerable vertical column density of hydrogen～1021cm?2in the inner disk region. This and other spectroscopic evidence for warm gaseous disk atmospheres were reviewed by Najita et al.(2007),where extensive references are given to earlier work.
Calvet et al.(1991)pioneered the now widely accepted view that disk atmospheres are heated by stellar radiation.In previous publications(Glassgold,Najita&Igea2004, henceforth GNI04)we argued that stellar X-rays play an important role in heating the upper gas layers of circumstellar disks on the following basis.First,signi?cant X-ray emission appears to be a universal aspect of low-mass YSOs;second,X-rays couple strongly to the gas; and third,hard X-rays with energies 1keV can penetrate deeply into disk atmospheres.
One special aspect of X-ray irradiation is that temperatures as large as4000-5000K are achieved high in the atmosphere.We recently pointed out that this hot layer gives rise to signi?cant?ux levels of the?ne-structure lines of neon at12.81μm and15.55μm(Glassgold et al.2007,henceforth GNI07).
The Ne II12.81μm line has now been detected in many YSOs by the Spitzer Infrared Spectrometer(IRS)in nearby star-forming regions(Pascucci et al.2007;Lahuis et al.2007; Espaillat et al.2007)and by MICHELLE at Gemini North(Herczeg et al.2007).The mea-sured?uxes are in good agreement with the predictions in GNI07.These observations support the hypothesis that disk atmospheres are heated and ionized by photons energetic enough to ionize Ne(which has?rst and second ionization potentials of21.56and41.0eV), most likely X-rays.A key motivation in the work of GNI07was the search for clear diagnos-tics of the e?ects of X-ray irradiation.The Ne lines seemed particularly appropriate because hard X-rays generate high ionization states of neon via the Auger e?ect and because neon chemistry is especially simple.Gorti&Hollenbach(2006,private communication)have suggested that EUV radiation may contribute to the neon?uxes,although the emission characteristics of YSOs in this wavelength band are poorly known compared to X-rays.
In this paper we extend the considerations of GNI07and seek other?ne-structure and forbidden transitions that have a potential to complement the neon lines.We have been
guided in part by the intrinsic strength of a line,which we can take as the thermalized emissivity in a transition from an upper to a lower level u→l,
j(u,l)=P(u)xn H A(u,l)E(u,l).(1) Here xn H is the density of the emitting species,P(u)is the population of the upper level,and A(u,l)and E(u,l)are the Einstein A-value and energy of the transition.The last two factors in equation(1)emphasize high frequency transitions,but the other factors are crucial since they require a theory for the ionization of the carrier species(the x factor)and the excitation of the level(the factor P(u)),since they are sensitive to the physical conditions.We have chosen to focus here on the lines of oxygen,sulfur and,to a lesser extent,carbon.Some spectral lines of particular interest are the25.25μm?ne-structure transition of S I,which has been searched for,mostly without success,by Spitzer;the?ne-structure lines of O I, which should be detectable with SOFIA and the PACS imaging spectrometer on Herschel; and various optical-infrared forbidden transitions accessible from the ground.
The atomic carriers of these lines appear in the many disk chemical models developed over the last10-15years(reviewed by Bergin et al.2007).They are closely related to the photon-dominated models(PDR)developed for the interstellar medium.In this case stellar and interstellar radiation generate warm atomic regions in the upper and lower layers of the disks until the UV radiation is absorbed and molecule formation becomes e?cient.Jonkheid and Kamp and their collaborators(Jonkheid et al.2004,2006,2007;Kamp et al.2003)have gone further and calculated the emissivity and lineshape of the?ne-structure lines of C I, C II,and O I.
The63μm?ne-structure line of O I was detected in YSOs with the KAO(e.g.,Cohen et al.1988;Ceccarelli et al.1997)and with ISO(e.g.,Nisini et al.1999;Spinoglio et al.2000; Creech-Eakman et al.2002;Liseau et al.2006),but the interpretation of the results is hampered by the low spatial and spectral resolution of the observations so that it is unclear what fraction of the emission arises from the disk.Disks have also been considered as a possible source of forbidden line emission by Hartigan et al.(1995),Kwan(1997)and St¨o rzer&Hollenbach(2000).The forbidden lines have been well studied in YSOs(see,e.g., the review by Ray et al.2007),and some of the observed“low-velocity-components”of the emission may originate from the disks in these systems(e.g.,Kwan&Tademaru1988,1995). We will return to the discussion of the observations of the?ne-structure and forbidden lines in Section5.
The calculations reported in this paper are exploratory in nature,as were those in GNI07.They examine the ability of X-rays,a well characterized property of TTS,to produce atomic line emission from T Tauri disks.The model employs the continuous disk density distribution developed by D’Alessio et al.(1999)for a generic T Tauri star,and they feature
stellar X-ray heating and ionization in the context of a simpli?ed thermal-chemical model, which will be discussed in more detail in Section2.We do not attempt to?t the observations for any speci?c system,but instead try to derive conclusions that might be applicable to any protoplanetary disk.
The plan of the rest of this paper is as follows.In the next section,we review and update the thermal-chemical model of GNI04.In Section3,we summarize the essentials of the basic ionization theory and extend it to include the X-ray ionization of sulfur.In Section 4,we outline the excitation and?ux calculations for the lines of interest,and then discuss the relevant observations in Section5.The last section summarizes the main results of this paper.
2.Review Of The Model
We use the thermal-chemical model of GNI04with minor corrections and updates.The important processes in determining the thermal balance are X-ray heating,gas-grain heating and cooling,mechanical heating(e.g.,from disk accretion or the wind-disk interaction), and line cooling(Lyα,recombination lines,O I?ne-structure and forbidden lines,and CO rotational and ro-vibrational lines).The chemical network contains about125reactions and 25species.Errors in the speci?cation of these processes have been corrected,and the entire reaction base has been re-evaluated and updated.None of the changes a?ects the conclusions of GNI04and GNI07in any major way.GNI04provide a detailed description of the physical processes,and the chemical reaction base is available from the authors on request or can be downloaded at https://www.doczj.com/doc/a79370448.html,/～rowin/MGN
e?ects on the diagnostic line?uxes must await the development of a more complete model that treats both the gas and the dust self-consistently.
The D’Alessio model does not include X-rays.In our previous studies based on this density distribution,we adopted a“reference”X-ray luminosity of L X=2×1030erg s?1 and a thermal spectrum with kT X=1keV.It is well known that both the X-ray luminosity and spectrum of young stellar objects can change with time,and that they vary widely from source to source.The ionization rate is not very sensitive to the temperature of the spectrum, as shown in Fig.5of Igea&Glassgold(1999).In the Chandra Orion Ultradeep Project (COUP)study of the Orion Nebula Cluster(Getman et al.2005),the X-ray luminosity function for the entire cluster spans5decades from log L X=27?32.Two of these decades of variation may be associated roughly with the dependence of L X on stellar mass and one on a dependence on stellar age(Feigelson et al.2005),leaving two or more unexplained decades. Thus the X-ray luminosity of a pre-main-sequence object with speci?c mass and age may vary over two orders of magnitude.This is consistent with the?ndings of Wolk et al.(2005) for a subset of28solar-mass stars in the Orion Nebula Cluster with masses in the range M?=0.9?1.2M⊙,which have a median X-ray luminosity of log L X=30.25erg s?1.The spread of two orders of magnitudes can only be partly explained by variability,including ?ares.Similar results have been found in the XMM-Newton study of the Taurus-Aurigae cluster(G¨u del et al.2007;Telleschi et al.2007),where the X-ray luminosity ranges over three decades(log L X=28?31).
Our previous choice L X=2×1030erg s?1was consistent with the observations of young T Tauri stars with masses M?～1M⊙and with the X-ray luminosity of well studied sources such as TW Hya(Kastner et al.2002;Stelzer&Schmitt2004).The median X-ray luminosity measured by XEST for classical T Tauri stars(with disks)in the Taurus-Aurigae cluster is L X=5×1029erg s?1,four times smaller than our reference value.In recognition of this di?erence as well as in the observed1-2dex spread in measured luminosity,we will consider a range of X-ray luminosities between L X=2×1029?2×1031erg s?1.X-ray luminosities in this range are likely to yield?uxes for the lines of interest that can be detected with current facilities.
In order to improve the numerical accuracy of the?ux calculations in Section4,the calculations reported here cover an extended range of radii from0.25-100AU,in contrast to GNI07who considered the range1-40AU.In making this extension,we do not consider any structural and physical modi?cations that might occur at very small and very large radii.For example,spectral energy distributions measured with the Spitzer IRS indicate the occurrence of inner holes and rims at distances of the order of several AU(Dullemond et al. 2007).Since we use the D’Alessio model calculations,which varies continuously from0.028
to>500AU,the present calculations do not take into account structures such as holes,gaps, and rims.
The elemental abundances used here and in the?ux calculations to follow are:x He=0.1, x C=2.8×10?4,x O=6.0×10?4,x S=7.0×10?6,x Ne=1.0×10?4,and x Na=1.0×10?6. The abundance of sulfur that we have adopted is in the range suggested by the recent modeling of sulfur molecules observed in the Horsehead Nebula(Goicoechea et al.2006). It is much closer to the solar photospheric/meteoritic value(Asplund et al.2005)than the heavily depleted values used in modeling dark clouds(e.g.,Millar&Herbst1990).UV absorption line studies of the di?use interstellar medium provide no evidence for depletion of sulfur,as they do for more refractory elements(Savage&Sembach1996).Fig.1shows the thermal structure of the reference disk model.The stellar and disk parameters that de?ne the D’Alessio1999model are given in the caption.For high altitudes(N H<1021cm?2) and moderate radii(R<25AU),temperatures as high as4000-5000K are reached.Going deeper into the atmosphere,T undergoes a sharp drop toward mid-plane temperatures in the range from30to200K,depending on radius.Near the mid-plane,where the density is high(n=108?1010cm?3),the gas and the dust are thermally coupled.For these radii (<25AU),the temperature starts high at the top of the atmosphere and then increases further with increasing vertical column density or decreasing altitude(see also Figure2of GNI04).This is a consequence of the balance between X-ray heating and Ly-αcooling that controls the temperature at the very top of the atmosphere.The heating and the cooling are both proportional to the?rst power of the volume density.The small increase in temperature arises from its logarithmic dependence on optical depth,which of course increases with increasing vertical column density.Beyond25AU,the O I?ne-structure lines are the dominant coolants at the disk surface.
3.Ionization theory
The GNI07thermal-chemical program includes the elements H,He,C and O,plus a generic heavy atom represented by Na.X-ray ionization of H,He,H2and C are included explicitly,and that of O implicitly.Generally speaking,X-ray ionization of a cosmic gas occurs by the absorption by the K and L shell electrons of heavy atoms and ions.The resultant photo and Auger electrons then generate many more secondary electrons by the collisional ionization of H and He.The ionization state of a heavy atom A or ion in a mainly atomic gas is determined by several processes:direct X-ray ionization(rateζdir);secondary electron ionization(rateζsec);electronic recombination;and charge transfer to H and He. The latter process may be fast(rate coe?cient～10?9cm3s?1)or slow.In the case of neon
(GNI07),charge transfer is relatively slow and fosters high abundances of neon ions.The ionization rates for atom A,ζdir(A)andζsec(A),are always per atom,whereas the total ionization rateζis per H nucleus.
On the basis of its elemental X-ray absorption cross section,we estimate that the oxygen ionization rates areζdir(O)=17ζandζsec(O)=2.4ζ,whereζis the X-ray ionization rate of the cosmic mix of disk gas.However,near-resonant charge exchange of H+and O is fast and dominates the ionization of oxygen.Thus direct X-ray ionization of oxygen can be ignored, as in GNI04.In the case of carbon,we estimatedζdir(C)=6ζandζsec(C)=4ζ,but now charge exchange of H+and He+with C is very slow,and therefore X-ray ionization of carbon is important and is included explicitly in the thermal-chemical program.
Figure2shows the electron fraction calculated for our model;it exceeds0.01at the top of the atmosphere down to a depth of N H～1019cm?2.The electron fraction decreases more smoothly with vertical column than the temperature.Near the mid-plane,its value is larger than that given by GNI07because ionization due to the radioactive decay of26Al have been included at a rateζ26=4×10?19s?1(Stepinski1992;Glassgold1995;Finocchi&Gail1997). This assumes that the entire disk is optically thick with respect to the1.809MeV decay γ-rays,and that the26Al/27Al ratio has the canonical value found in meteoritic calcium-aluminum inclusions(5×10?5).It also ignores the e?ects of the1Myr mean life of26Al and the possibility that the initial distribution of26Al is spatially inhomogeneous.In light of these simplifying assumptions,it is likely that the rate is even smaller than the one we have adopted,but the exact value is not crucial for the main subject of this work1. We use a separate program to obtain the abundances of neon and sulfur species.The ionization calculation of neon is essentially the same as GNI07.Figure3shows the fractional abundances of Ne+and Ne2+relative to the total abundance of neon.Abundances of the order～0.1or more are found at high altitudes(N H<1021cm?2).It is remarkable that X-ray ionization produces signi?cant abundances of Ne+and Ne2+out to radii as large as 30AU.
The closed shell character of neon means that the complexities of molecule formation and destruction do not enter,and only three species,Ne,Ne+and Ne2+have to be considered in estimating their line?uxes.This is not the case for the calculation of the S I and S II ?ne-structure and forbidden lines.In order to calculate the abundances of S and S+,we have to consider the transition into sulfur molecules,such as SO,SO2and CS,which occurs at large vertical column densities.Figure4gives a schematic overview of sulfur ionization
including a simpli?ed warm chemistry,following Leen&Gra?(1988).
Sulfur ions in the disk are mainly produced by X-ray ionization.Sulfur has L and K edges near0.2and2.5keV and,since we consider X-ray spectra that are not particularly hard (T X 1keV),photons with energies between the L and K edges are the ones most strongly absorbed by sulfur.Because charge exchange with H is fast for highly-ionized sulfur ions, X-ray ionization of sulfur accompanied by the Auger process leads primarily to S2+and S3+. Calculations by Butler&Dalgarno(1980)and Christensen&Watson(1981)suggest that S3+charge exchange with atomic hydrogen is also fast,while that of S2+is slow.Therefore, we only include ions up to S2+,as we did in the case of neon(GNI07).However,in addition to electronic recombination and charge exchange of sulfur ions with atomic hydrogen,we also include the S+H+charge-exchange reaction,which can ionize S at a signi?cant rate below 10000K according to the theoretical calculations of Zhao et al.(2005).Furthermore,the reaction S2++H2,which has been measured to be fast(Chen et al.2003),can signi?cantly reduce the abundance of S2+.
As for carbon and oxygen,we can estimate the direct X-ray ionization rate of sulfur from its X-ray absorption cross section.Its energy dependence is very similar to that of the mean X-ray absorption cross section averaged over interstellar or solar abundances.Thus the direct ionization rate of sulfur,resulting from the(L to K)0.2-2.4keV band is basically given by the ratio of the two absorption cross sections at these energies.For example,at1keV,the ratio is≈500.This then is the approximate ratio of the primary or direct X-ray ionization of sulfur(per sulfur nucleus)to that of the mean interstellar atom(per hydrogen nucleus,since abundances are conventionally normed to hydrogen).However,most of the ionization of the gas as a whole comes from secondary-electron ionization of hydrogen(atomic and molecular) and helium.Since there are roughly25such electrons produced per primary ionization,the ratio of the direct sulfur ionization rate per sulfur nucleus to the total X-ray ionization per H nucleus is500/25=20:
ζ(S)dir?20ζ.(2) The secondary electrons generated by X-ray ionization of all of the cosmic elements collisionally excite and ionize S at a rate that is roughly given by the ratio of the electronic ionization cross section of sulfur to that of hydrogen(Maloney et al.1996).This leads to the approximate value,
ζ(S)sec?5ζ.(3) The direct ionization rate is mainly responsible for producing higher S ions,which we lump together into S2+because of fast charge transfer.The secondary ionization rate primarily produces an additional electron,e.g.,it generates S+from S.Some of the sulfur ion rate coe?cients are listed in Table1.Those for radiative recombination are well calculated.As
in the case of neon,however,the rate coe?cients for electron transfer from atomic hydrogen are not well established.They represent an important uncertainty in the results of this paper.
To address the question of whether S remains the dominant species near the mid-plane, we include the formation and destruction of the sulfur molecules,SO,SO2,CS and OCS,by using the warm neutral sulfur chemistry of(Leen&Gra?1988).We also include X-ray ion-ization and destruction of these molecules,assuming that X-ray cross sections for molecules are additive over the constituent atoms,and using the atomic rates discussed above.We also make the simplifying assumptions that a direct absorption of an X-ray by a sulfur molecule always leads to dissociation,and that secondary electronic ionization always produces a molecular ion.The sulfur molecular ions are rapidly destroyed by dissociative recombina-tion.The branching ratios are summarized by Florescu-Mitchell&Mitchell(2006).
Figure5shows the fractional abundances of the sulfur species S+,S,SO2and CS as a function of vertical column density above the disk mid-plane at a radial distance of20AU from the star.We?nd that sulfur is completely locked up in molecules for column densities larger than0.5?1.0×1022cm?2.In this region,neutral formation reactions start to dominate over X-ray destruction as the X-rays get shielded and the increased density enhances the reaction rates.The main species at large column densities is SO2,but there may also be a layer of CS at intermediate column densities.
Figure6shows the S and S+fractions relative to the total abundance of sulfur in the disk for radii between0.25and40AU.S+is the dominant species at the highest altitudes for R<25AU,whereas S assumes that role at intermediate altitudes.Beyond R>25AU, X-ray ionization of sulfur is not strong enough to maintain S+as the dominant species.At low altitudes,we?nd a clear cut-o?in the atomic S abundance,with almost all of the sulfur in molecules.
4.Excitation and Flux Calculations
The?ux calculations for the atomic ions considered in this paper are relatively straight-forward because one needs to deal only with a few levels of relatively low excitation,even for the forbidden lines.For neon,we continue to focus on the ground?ne-structure transitions of Ne+and Ne2+.For O,S and C,we treat the5lowest levels in the ground electronic con?guration:a?ne-structure triplet,that produces mid and far IR lines,and two higher-energy singlet levels that give rise to forbidden optical-IR transitions.For C+,we consider only the ground level?ne-structure doublet that generates the famous158μm line.Simpli-
?cations often occur.For example,the?ne-structure transitions of C I and C II have low critical densities and,because of the high disk densities,are near-thermalized.Similarly, the forbidden lines are usually optically thin and the e?ects of line trapping are small.In the following sections,we discuss speci?c issues that arise in the calculation of the emis-sivities of the lines of interest.We use the line frequencies and A-values in the NIST data base(https://www.doczj.com/doc/a79370448.html,/PhysRefData/ASD/index.html).Electronic excitation rates are now reasonably well established,but those for excitation by H,H2,He and H+are often unknown,except perhaps for O I,C I and C II.References for our choice of rate coe?cients are given in Table2.In those cases where trapping plays a role,e.g.,for the O I and S I ?ne-structure lines,our results apply to a face-on disk.
4.1.Neon
We calculate the optically-thin Ne II and Ne III lines?ne-structure lines at12.81and 15.55μm in the manner of GNI07with the following change.While retaining the two-level population formula for the ground-level doublet of Ne II,we solve exactly for the populations of the ground-level triplet of Ne III2.This more complete excitation calculation leads to an increase in the population of the upper J=0level and,to a lesser extent,the J=1level, and increases the line intensities.
Figure7shows the distribution of the Ne II12.81μm emissivity throughout the disk for the reference X-ray luminosity.Most of the emission is produced at high temperature (～4000K)and high electron abundance,corresponding to radial distances R<25AU and vertical column densities N H<1021cm?2.The largest emissivity does not always occur at the highest altitude above the mid-plane.This is due to an increase of the Ne+density and its speci?c emissivity with increasing depth.The upper J=1/2level is sub-thermally populated and its population is proportional to the electron density,which also increases going down into the atmosphere.
The above calculations assume that the excitation is solely due to electronic collisions. However,we have been reminded that,as the electron fraction decreases with height,colli-sions with atomic hydrogen begin to play a role(D.J.Hollenbach2006,private communi-
(4)
1+5/3C1?2exp925.3/T+1/3exp(?399/T)/C0?1
cation).Using the results of Bahcall&Wolf(1968),Hollenbach&McKee(1989)estimated the rate coe?cient for the de-excitation of the12.81μm transition in collisions with atomic hydrogen to be1.3×10?9cm3s?1.Although the theory of Bahcall and Wolf may give the right order of magnitude(as it does for the excitation of the O I?ne-structure transitions), it is incorrect in principle since it implies that the excitation cross section is proportional to the scattering cross section.According to Bahcall and Wolf,the rate coe?cient in a collision with a neutral atom varies with temperature as T1/6(c.f.the van der Waals potential)and as a constant in a collision with an ion(c.f.the Langevin potential).However,collisional excitation of a?ne-structure transition requires an exchange of a spin between the incident H atom and the target electrons and thus depends on di?erences between potentials,di?erences which decrease more rapidly than1/r6and1/r4for neutral and ionic collisions,respectively.
The full quantum-mechanical calculations for O I and C I(Launay&Roue?1977a; Abrahamsson et al.2007)and for C II(Launay&Roue?1977b;Barinovs et al.2005)bear out the fact that the Bahcall and Wolf theory predicts the wrong temperature dependence for the collisional excitation rate coe?cients by atomic hydrogen.We have compared the recent calculations of Barinovs et al.(2005)for H+C II with the Bahcall and Wolf the-ory,and?nd that the latter over-estimates the rate coe?cient by factors of7.5to5in the temperature range from500-4000K.If something like this reduction factor also applies to H+Ne II,then the order of magnitude of its rate coe?cient for collisional de-excitation of the Ne II?ne-structure doublet is～2×10?10cm3s?1.We have calculated the12.81μm emissivity(including line trapping)with this value for the H de-excitation rate,and?nd that it increases the?ux by about a factor of two.This increase arises mainly at large radial dis-tances,where the deviations from a thermal population are the greatest.We conclude that our calculations based on electronic excitation alone underestimate the Ne II12.81μm?ux, but possibly not by a large factor.Actual calculations of the atomic hydrogen excitation rate would be most welcome.
4.2.Oxygen
Figure8gives the5levels that we consider in calculating?ne-structure and forbidden line emission from atomic oxygen and sulfur.According to Table2,collisional excitation rates for the?ne-structure levels of O I are available for collision partners e,p,H,H2and He. Atomic hydrogen tends to dominate and,even without line trapping,the critical densities are modest,typically n cr(H)<106cm?3.At radii(>25AU),densities of this order are not reached until vertical column densities N H≈1020?1021cm?2.The full emissivity calculation is particularly relevant at large radii.
Figure9shows the spatial distribution of the emissivity of the O I63μm?ne-structure line.The results for the O I146μm line(not shown)are similar.The spatial pro?le is particularly complicated at small radii(<10AU).The emissivity has two peaks going down into the disk(increasing vertical column at?xed radius)that result from a combination of e?ects:density and temperature variations,abundance changes and line-trapping.The declining temperature,the conversion of atomic oxygen into molecules(CO,H2O and O2), and trapping at large columns all tend to decrease the emissivity.These e?ects are illustrated by Figure10,which shows the speci?c emissivity(per O atom).For small column densities, it is constant when the population is thermalized(at radii R<10AU,where the critical densities are reached),or it increases toward a maximum when the critical densities are only attained at larger vertical column densities.Then it decreases again with vertical column density,except at the smallest radii(<1AU),where the rise in temperature due to viscous heating close to the mid-plane has the opposite e?ect.The occurrence of the two peaks in emissivity at intermediate columns is the result of the rapid increase of volumetric density with increasing depth.Signi?cant emission occurs beyond columns of N H=1022cm?2as a consequence of the fact that the excitation energy is relatively low(≈230K)and contributes ～10%of the total line?ux.
The1D2?3P J O I6300/6363?A and the1S0?1D25577?A forbidden transitions are optically thin and sub-thermally excited.In addition to the electronic rate coe?cients (Zatsarinny&Tayal2003),the collisional de-excitation rate of the1D2level by atomic hy-drogen has been calculated by Krems et al.(2006).It varies little between500-6000K,where it has a mean value of8×10?13cm3s?1to within25%.At4000K,the collisional electron de-excitation rate is3×10?9cm3s?1for the1D2level,so electronic collisions dominate over those with atomic hydrogen for x e>2.5×10?4.If we consider only electronic collisions, then an upper limit to the critical density for the6300/6363?A transitions is n e≈106cm?3, while that for the5577?A transition is n e≈108cm?3.In the absence of calculations for the 1S0level,we have adopted the value,10?12cm3s?1,for the H rate coe?cient.Thus the6300 and6363?A lines are populated near-thermally,and we can use the two-level formulae given in equations(3-2)and(3-3)of GNI07that allow for the e?ects of?nite values of the critical density.The emissivity for both lines is then given by equation1.The1S0uppermost level is so far from being thermalized that we can calculate the?ux of the5577?A line by using the extreme low-density collisional-excitation limit,in which every excitation leads to the production of a photon.
Figure11shows that the O I forbidden lines trace the upper atmosphere of the disk, where the atomic oxygen abundance is constant.The O I6300/6363?A lines are generated within25AU,a somewhat smaller range than the neon?ne-structure lines,while the5577?A line(not shown)originates from radii inside15AU.These calculations of forbidden line
?uxes necessarily ignore an e?ect of the UV photodissocation of OH,which leads to signi?cant branching to the exited1D2level of O,producing?uorescent emission of the O I6300/6363?A lines(St¨o rzer&Hollenbach2000).Because signi?cant OH abundances only occur at large depths in our model,this e?ect might become important at large radii due to OH photo-dissociation by the stellar or interstellar/intracluster FUV radiation?eld.
4.3.Sulfur
We focus on the mid-IR?ne-structure lines of S I and the6718/6732?A forbidden tran-sitions of S II;the?ne-structure lines of S III are likely to be too weak to be observable at the present time.In accord with Figure8,the calculation of the S I?ne-structure emis-sion is similar to that just described for O I.The big di?erence is that little if anything is known about the excitation of these lines by collision partners other than electrons.Thus the present?ux estimates are lower limits.The calculations take line trapping into account and solve the three-level?ne-structure population problem exactly,including the the weak J=0?2quadrupolar transition.
Figure12shows the spatial distribution of the S I25.25μm?ne-structure line emissivity for the reference model.The appearance of the56.33μm emissivity(not shown)is similar, but it is concentrated toward smaller radii and higher altitudes.As in the case of O I,the variation of the?ne-structure emission with depth at?xed radius is non-monotonic,and again there are several factors that contribute to this behavior.First,there are the chemical changes already mentioned,where sulfur changes from S+to S at high altitudes and from S to sulfur molecules at low altitudes.Thus the emission peaks at intermediate altitudes,at a vertical column of N H～1021cm?2at R=0.25AU and near N H～1019cm?2at R= 25AU.Second,the increase of volumetric density with depth also promotes?ne-structure emission,whereas the overall temperature decrease has the opposite e?ect.Figure13shows the variation of the speci?c emissivity with vertical column at?xed radius.For radii in the range1-25AU,the emissivity per S atom of the J=1?0level changes from sub-thermal to thermal as the density increases with increasing depth.At somewhat larger column densities, the speci?c emissivity decreases due to decreases in both temperature and electron density.
The transition of atomic sulfur into molecules such as SO and SO2has little e?ect on the absolute level of the S I?ne-structure emission.This is due to the fact that electronic excitation has already become ine?ective for N H<1022cm?2before molecule formation occurs.In order to gauge the importance of H atom collisions,we carried out a calculation where we assumed that the S I?ne-structure de-excitation rates are about the same as for O I,speci?cally k(H)=5.0×10?11T0.4for all transitions.The S I25.25and56.33μm
emission is then increased by factors of10or more over that for electron collisions only.This serves to indicate the importance of extending the calculation of H excitation rates to heavy atoms and ions such as Ne II and S I.
We estimate the emission of the S II forbidden lines in the optically thin approximation. We concentrate on the2D5/2,3/2-4S3/2transitions with wavelengths near6700?https://www.doczj.com/doc/a79370448.html,ing the electron collisions strengths from Tayal(1997),we?nd electron critical densities,n cr～104?105cm?3s?1,and conclude that the lines are almost thermalized.We also considered the possible role of the H++S→S++H charge exchange,which mainly branches to the upper2P J level of S+,and then decays with the emission of photons with wavelengths near4070?A,6700?A,and1μm.We?nd that this process does not increase the6718and 6732?A line emissivities,probably because the rate coe?cient for charge exchange is small (～5×10?12cm3s?1)and because the high density tends to a thermalize the level population. In Figure14,we show the emissivity of S II6718?A line(the6733?A line is very similar).These lines trace the warm upper layers of the disk.Signi?cant emission arises only from regions with temperatures in the range2000-5000K.
4.4.Carbon
The energy levels of the ground con?guration of C I are similar to those of O I and S I shown in Figure8,except that the scale of the energy level separations is reduced and the ordering of the total angular momentum quantum number J in the ground state triplet is inverted.The upper?ne-structure levels have energies E2/k=62.5K and E1/k= 23.62K and give rise to far-infrared lines with wavelengthsλ(1?0)=609.135μm and λ(2?1)=370.144μm.In addition to these lines,we calculate the emissivity of the forbidden lines at9827and9853?A that emanate from the?rst1D2level of C I above ground.For C II,we only consider the?ne-structure doublet,with excitation energy and wavelength,?E(3/2?1/2)/k=91.2K andλ(3/2?1/2)=157.7μm,and ignore the2300?A lines that arise from the next4P level.
The A values of the C I and C II?ne-structure transitions are very small(～10?7s?1 for C I and2.3×10?6s?1for C II),which implies that the critical densities for all of these transitions are low(<104cm?3,based on the collisional rate coe?cients referenced in Table 2).Thus we can estimate the emissivities assuming that the?ne-structure levels are in thermal equilibrium(but we do include line-trapping).The integrated?uxes for a nominal distance of140pc are given in Table3.The?ux of the C II158μm line is very small,but the369μm line of C I appears to be in the observable range,as may even be the case for the 609μm line.
We estimate the the C I9827and9853?A forbidden line emission in the optically thin https://www.doczj.com/doc/a79370448.html,ing Table2,the critical density of the1D2level at4000K is1.96×104cm?3s?1,and the level is close to being thermalized.The density-dependent correction for sub-thermal excitation is made in the same way as for O I,as described in Section4.2.The spatial distribution of the C I9827?A emission is shown in Fig.15.The emission is peaked at small vertical column densities,much like the O I6300?A emission in Fig.11.The integrated line?ux given in Table3is somewhat smaller than the?ux of the O I6300?A line,but still in the potentially observable range.Of course all of these statements about the detectability of neutral carbon lines stand to be corrected(and reduced)when interstellar/intracluster UV radiation is included in the ionization theory.
5.Discussion
In this section we discuss the most important results of this paper in the context of both existing and prospective observations.We treat high and low excitation lines separately,since they trace di?erent parts of the disk.We?rst summarize in Table3the line?uxes for?ve values of the stellar X-ray luminosity that range from L X=2×1029?2×1031erg s?1.To ensure accurate results for values of L X larger than standard,we have calculated the disk properties and emissivities out to100AU.The calculations pertain to the case where X-ray heating of the disk atmosphere dominates mechanical heating(αh=0.01in the notation of GNI04).As discussed in Section2,the underlying density model is the generic T Tauri disk model of D’Alessio et al.(1999);the parameters for the model are given in the caption of Fig.1.The“reference”model that we have used throughout has an X-ray luminosity of L X=2×1030erg s?1;the?uxes for this case are given in the middle column of the Table.
The values shown in the other columns illustrate how sensitive the modeling results are to the choice of X-ray luminosity.Table3encompasses a range of100in X-ray luminosity, which is roughly the spread seen by the COUP and XEST projects for T Tauri stars in the Orion Nebula and Taurus-Aurigae clusters of the same mass and age.Were we to choose the median L X for Taurus-Aurigae(Telleschi et al.2007)for the reference model,the second column of?uxes would be appropriate.According to the discussion in the previous sections, all of the?ux estimates are themselves uncertain to varying degrees due to uncertainties in the rate coe?cients and other limitations of the model.In particular,the?uxes for the neon and sulfur?ne-structure lines are lower limits because of the omission of collisional excitation by H atoms.
The sensitivity of the integrated line?uxes to the X-ray luminosity can vary from one line to another,since they may originate in di?erent parts of the disk with di?erent physical
properties.We illustrate this in Fig.16,which shows how some of the line?uxes vary with L X,normalized to the standard model.The C I369μm line luminosity depends very weakly on L X,since most of the emission is produced at intermediate column densities (N H～1022cm?2)where the X-ray?ux is strongly attenuated.The O I63μm luminosity shows a somewhat steeper dependence,because it is produced both at high altitudes,where the X-ray?ux is large,and close to the midplane,where the X-ray?ux is small(and the gas and dust temperatures are almost the same).The optically thin O I5577?A emission displays the strongest dependence on L X because,with its relatively high excitation temperature,it is only produced in the warmest part of the disk fully exposed to stellar X-rays.The other forbidden lines and the S I?ne-structure lines(not shown),behave very much like the Ne II ?ne-structure line.The almost linear relation between Ne II line?ux and L X arises from the dependence of the emissivity on n2e(c.f.Eq.4-1of GNI07).In its present form,Fig,16 is not meant to suggest a general empirical correlation of line?uxes with X-ray luminosity, simply because the stellar and disk properties of the reference model have been held?xed in the calculations for this?gure.
5.1.High excitation lines
5.1.1.Neon Fine-Structure Lines
The neon?ne-structure line?uxes(Table3)are close to but more accurate than GNI07. The Ne III?ux is40%larger since the calculations extend to smaller radii(R=0.25AU).The Ne II12.81μm line emission arises from the top of the atmosphere,where the temperature and electron density are high.We?nd signi?cant contributions to the integrated emission out to R=25AU.The emissivity per unit radius is determined by the column density in the upper level(c.f.Eq.3-7of GNI07).This quantity is plotted in the upper panel of Fig.17 against the radius R.In contrast to Fig.4of GNI07,there is no dip near5AU,thanks to more accurate and closer spaced calculations.When we assume Keplerian rotation to convert from column density to a velocity distribution function P(v)(c.f.Eq.3-8of GNI07), the peak in P(v)occurs at v=0.25v(1AU),which corresponds to a peak in the emissivity per unit area at16AU.The bottom panel of Fig.17shows that P(v)has a long tail extending to high velocity.The ratio of the Ne III15.55μm to the Ne II12.81μm?ux is of order0.1. GNI07considered the detection of the Ne III line to be a near de?nitive diagnostic of X-ray ionization of neon.However,using a disk model dominated by stellar EUV radiation, Hollenbach&Gorti(2007,private communication),?nd a range of possible NeIII/NeII ratios (0.1-6)depending on the the nature of the EUV spectrum.Thus it is not immediately clear whether the Ne III/Ne II?ne-structure line ratio can serve as a discriminant between EUV
and X-ray irradiation.
The Ne II12.81μm line has now been detected in T Tauri disks in about20cases from the ground and from space(by the IRS on Spitzer:Pascucci et al.2007;Lahuis et al.2007; Espaillat et al.2007;and MICHELLE on Gemini North:Herczeg et al.2007).The detected ?ux levels are of order10?14erg cm?2s?1;they are within a factor of few agreement with our model calculations.The weaker15.55μm of Ne III line has been tentatively detected in only one case(Sz102,Lahuis et al.2007).Based on the3σdetection of the Ne III line, the Ne III/Ne II ratio is≈0.06,which might be compared with a ratio～0.1derived from Table3.Perhaps what is most interesting about this T Tauri star is that it has the second brightest Ne II line detected in the Lahuis et al.survey.Its?ux is an order of magnitude larger than the value for our reference model,after correction for the distance of200pc. Detailed modeling of the disk around this star would be of considerable interest.For the case of nearby TW Hya,Herczeg et al.(2007)measure the luminosity for the Ne II12.81μm line to be4.8×10?6L⊙,which is20%larger than the result for our reference model in Table 3.
From a small number of detections of the Ne II12.81μm line the Spitzer Lagacy pro-gram,“Formation and Evolution of Planetary Systems”(FEPS),Pascucci et al.(2007)have suggested that a linear correlation may exist between the Ne II and X-ray luminosities.To-gether with their detection of the Ne II line in CS Cha and that for TW Hya,based on data obtained by Uchida et al.(2004),Espaillat et al.(2007)argue against such a corre-lation.The range of L X in these papers is small,1.5for Pascucci et al.(2007)and2.25 for Espaillat et al.(2007),the same order of magnitude as the observed variability in the X-ray luminosity.Aside from the intrinsic di?culty of deducing a meaningful correlation on the basis of a small dynamical range in YSO X-ray luminosity,it is important to keep in mind that the line?uxes depend on many other stellar and disk properties,e.g.,the stellar temperature,mass,and age and the disk mass,accretion rate,and the amount of dust grain growth and settling.The theoretical calculations shown in Fig.16may not be relevant in this context because they assume that the disk structure is?xed while L X is varied.To pursue the question of the existence of a correlation with L X,T Tauri stars with similar properties,both stellar and disk,should be considered.A more practical approach might be to focus in depth on a few speci?c cases with well observed properties and to use observed X-ray spectra.
Using the MICHELLE spectrometer at Gemini North,Herczeg et al.(2007)have ob-tained a spectrally resolved Ne II line pro?le for TW Hya,which has a nearly face-on disk. The line is centered at the stellar radial velocity,consistent with a disk origin,but the line is broad with FWHM of～22km s?1.The rotational broadening in our models(Fig.5of
GNI07and Fig.17of this paper),when corrected for inclination,cannot explain the ob-served line width,even though the present calculations extend to radii as small as0.25AU. Although our calculations agree with the measured Ne II luminosity,the rotational broad-ening in the model is small because it arises from relatively large radii,as shown in Fig.17. As discussed by Herczeg et al.(2007),two interesting explanations of the line width seen TW Hya that deserve consideration are transonic turbulence and photo-evaporative out?ows from the disk(Hollenbach et al.2000;Font et al.2004).These possibilities raise interesting challenges for future research.If the hole is produced by photo-evaporation,then the wind itself will generate line emission.Furthermore,the inner rim of the hole will be irradiated more or less directly by the star,as in the model of Chiang&Murray-Clay(2007),again producing characteristic line emission.
5.1.2.Sulfur Fine-Structure Lines
We consider the S I?ne-structure lines to be“high-excitation”because the associated excitation energies,476K and825K,are larger than the temperatures characteristic of the outer disk,as are the?ne-structure levels of the neon ions.As discussed in Section3, the X-ray ionization theory for neon and sulfur,where charge exchange plays an important role,are also similar.Reference to Table3shows that the integrated S I?ne-structure emission for our reference model is～20smaller than for the Ne II line.Fig.12shows that the strongest emission of the S I25.25μm line comes from a relatively thin layer between N H=1019?1021cm?2for R<10AU.This situation and the attendant weakness of the 25.25μm line occur because sulfur is in the form of S+at higher altitudes and electronic excitation becomes weak at lower altitudes(c.f.Figs.5and6).
The S I25.25μm line was not detected by the Spitzer c2d and FEPS teams.Pascucci et al. (2007)put upper limits on the residual gas in the disks around their survey of older T Tauri stars with ages between5and100Myr using the model calculations of Gorti&Hollenbach (2004).From Table3,which is based on pure electronic excitation,the S I?ne-structure lines from younger T Tauri disks would be similarly di?cult to detect.However,if the atomic H collision rates for S I are similar to those for O I,the predicted?uxes would approach the observable range.It is important to recall several other caveats that pertain to our calcula-tions:the uncertainties in sulfur chemistry,the total abundance of gaseous sulfur in disks, and the poorly known charge-exchange rate coe?cients.
5.1.3.Forbidden Lines
Table3gives the?uxes for our reference model of a sample of forbidden lines,as cal-culated in Section4:O I6300/6363?A,O I5577?A,S II6718/6731?A;C I9827/9853?A.We have identi?ed them as potential diagnostics of the warm and highly-ionized gas produced by X-ray irradiation in the upper atmosphere of the inner disk.These lines are generated within the same radial distance range as the Ne II12.81and15.55μm lines,but at somewhat higher elevations.In principle,they can provide complementary checks on our picture of X-ray irradiation.As discussed in Section4,the accuracy of the calculations varies somewhat from line to line,depending on the reliability of the atomic data and on the completeness of the model itself.For example,we have ignored the role of stellar or interstellar/intracluster FUV radiation,which could enhance the ionization of carbon at high altitudes and thereby reduce the amount of neutral carbon and the strength of the C I forbidden lines.Similarly, the S II6718?A line strength is a?ected by the sulfur atoms being converted into molecules. With this proviso,we can see from Table3that many of the forbidden lines generated in the upper disk atmosphere are observable in nearby star-forming regions such as Taurus-Aurigae in the sense that the predicted?uxes are 10?15erg cm?2s?1,notably O I6300/6363?A, C I9827/9853?A,and perhaps S I6718/6733?A.
Many of these lines have been measured in T Tauri stars.The most dramatic manifes-tation of the forbidden lines is their tracing of high-velocity out?ows or jets from YSOs(e.g., Ray et al.2007).But these?ows have a low-velocity as well as a high-velocity component (Kwan&Tademaru1988,1995;Hirth et al.1997).Kwan(1997)suggested that the low ve-locity component(LVC)originates in the inner regions of T Tauri disks(R<2AU)3.Other possible sources for the origin of the LVC is a MHD disk wind(e.g.,Pudritz et al.2007)or a photoevaporative out?ow(e.g.,Hollenbach et al.2000;Font et al.2004).
Hartigan et al.(1995)have obtained extensive data on forbidden line emission from T Tauri stars.The LVC is ubiquitous,with a typical line luminosity of～10?4L⊙,an order of magnitude larger than the luminosity of our reference model,8.0×10?6L⊙.They also?nd O I5577?A to O I6300?A line ratios in the range～0.2?0.5;our model predicts ～0.1.These numbers may signify the di?culty of applying our X-ray irradiated disk model to observations such as the optical forbidden lines that are sensitive to the other dynamic entities that are operative in accreting young stars,e.g.,the various?ows that arise near the inner edge of the disk.Hartigan et al.de?ne the LVC to include velocities as high as60 km s?1,thereby increasing the possibility of including emission from such?ows.A cleaner
comparison case for our model might be provided by an X-ray bright star with a relatively low accretion rate,where the emission from out?ows would be reduced.
Because TW Hya has a low mass-loss rate and a small accretion rate,it would be a good case for detailed modeling.Herczeg et al.(2007)detected the O I6300/6363?A lines in TW Hya at moderately high spectral resolution.The luminosity of the6300?A line,7.0×10?6L⊙, is close to the result given in Table3,8.0×10?6L⊙,recalling the good agreement for the luminosity of the Ne II12.81μm line.The6300?A line is centered on the stellar velocity, and it has a signi?cantly narrower width than the Ne II line,but one that is still too large to be explained by pure rotational broadening.Again,interesting possible explanations to consider in future modeling are a turbulent atmosphere and photo-evaporation.
5.2.Low excitation lines
We next consider the low-excitation lines that arise from the?ne-structure levels of O I (excitation energies228K and327K),C I(excitation energies23.6K and62.5K)and C II (excitation energy91.2K);they give rise to far-infrared emission at63and145μm(O I), 609and370μm(C I),and158μm(C II).Table3shows that the O I?ne-structure lines are potential diagnostics of both the moderately warm,ionized gas produced by X-rays,and the cooler gas at large perpendicular column densities.As shown in Fig.9,O I63μm line emission extends down toward the mid-plane region,especially at small radial distances, due to the incomplete conversion of atomic oxygen into molecules and the relatively low excitation temperature of the J=1?2transition.
The63μm line has been observed around T Tauri stars with the KAO(e.g.,Cohen et al.1988;Ceccarelli et al.1997)and ISO(e.g,Spinogolio et al.2000;Creech-Eakman et al.2002;Liseau et al.2006).These observations were made with large beams(tens of arc seconds)and with moderate spatial resolution(50-300km s?1).A typical?ux for a T Tauri star in Taurus-Aurigae is quite large,～10?12?10?11erg cm?2s?1,and may include emission from other circumstellar material and not just disks.On the other hand,the?ux calculations in Table3probably underestimate the?ux,even though they integrate out to 100AU,especially for the carbon lines.Jonkheid et al.(2004)have applied a code developed for(UV)photon-dominated regions to the surface layers of a?aring disk,and?nd that the ?uxes of the O I,C I,and C II?ne-structure lines are all of comparable brightness,and not that much weaker than the CO(J=1?0)line.Photo-ionization of neutral carbon by external FUV radiation can enhance the abundance of C+and increase the?ux of the C II 158μm line.Our model would have to be extended to include UV irradiation in order to get a fuller understanding of these low-excitation diagnostic lines.
从劳厄发现晶体X射线衍射谈起 摘要：文章从劳厄发现晶体X射线衍射的前因后果谈起。劳厄的这个发现产生了两个新学科，即X射线谱学和X射线晶体学。文中还回顾了布拉格父子对这两个新学科所作的重大贡献，并阐述了X射线晶体学的深远影响。 今年是劳厄（von Lane M）发现晶体X射线衍射九秩之年。 从1895年伦琴（R0ntgen W C）发现X射线到1926年薛定愕（Schrodinger）奠定量子力学基础的30多年是现代物理学诞生和成长的重要时期。在此期间的众多重大发现中，1912年劳厄的发现发挥了极为及时而又十分深远的影响，是很值得我们通过回顾和展望来纪念它的。 我们先来了解一下劳厄发现的前因后果。1912年劳厄发现晶体X射线衍射时是在德国慕尼黑大学理论物理学教授索未菲（Sommerfeld）手下执教。除理论物理教授索未菲外，在这个大学中还有发现X射线的物理学教授伦琴和著名的晶体学家格罗特（Groth）。当时，劳厄对光的干涉作用特别感兴趣，索末菲则在考虑X射线的本质和产生的机制问题，而格罗特是晶体学权威之一，并著书Chemische KristallograPhic （化学晶体学）数卷。身在这样的学府中，劳厄当时通过耳闻目睹也就对 晶体中原子是按三维点阵排布以及X射线可能是波长很短的电磁波这样的想法不会感到陌生或难于接受了。而且看来正当而立之年的他是很想在光的干涉作用上做点文章的。真可谓机遇不负有心人了。这时，索末菲的博士生埃瓦尔德（Ewald P P）来请教劳厄，谈到他正在研究关于光波通过晶体中按三维点阵排布的原子会产生什么效应。这对劳厄有所触发并想到：如果波长短得比晶体中原子间距离更短时又当怎样？而X射线可能正是这样的射线。他意识到，说不定晶体正是能衍射X射线的三维光栅呢。现在劳厄需要考虑的大事是做实验来证实这个想法。当时索末菲正好有个助教弗里德里希（Friedrich W） ，他曾从伦琴教授那里取得博士学位。 他主动要去进行这样的实验。经过几次失败后，他终于取得了晶体的第一个衍射图「（见图1）」。晶体是五水合硫酸铜（CuSO4·5H2O）。 劳厄的发现经过进一步的工作很快取得了一箭双雕的效果：既明确了X射线的本质，测定了波长，开创了X射线谱学，又使测定晶体结构的前景在望，从而将观察晶体外形所得结论经过三维点阵理论发展到230个空间群理论的晶体学，提升为X射线晶体学。这个发现产生的两个新学科，几乎立即给出了一系列在科学中有重大影响的结果。英国的布拉格父子（Bragg W H和Bragg W L）在奠定这两个新学科的基础中起了非常卓越的作用。他们使工作的重心从德国转到英国。将三个劳厄方程（衍射条件）压缩成一个布拉格方程（定律）的小布拉格曾把重心转移的原因归之于老布拉格设计的用起来得心应手的电离分光计”。既然晶体是X射线的衍射光栅，那么，为了测定X射线的波长，光栅的间距当如何得出？1897年巴洛（Barlow W）预测过最简单的晶体结构型式，其中有氯化钠所属的型式。根据当时已知的NaCI的化学式量（58.46）和阿伏伽德罗常数（6.064×1023）以及晶体密度（2.163g/cm2），可以推算出氯化钠晶体（10）原子面的间距d＝2.814×10－8cm。 布拉格父子的工作是有些分工的：老布拉格用他的电离分光计侧重搞谱学，很快发现X射线谱中含有连续谱和波长取决于对阴极材料的特征谱线。此后，测定晶体结构主要依靠特征射线。同时还观察到同一跃迁系特征射线的频率是随对阴极材料在元素周期系中的排序递增的，这种频率的排序给出了原子序数。这是对化学中总结出来的元素周期律作出的呼应。小布拉格的工作是沿着X射线晶体学的方向发展的。他一生中从氯化钠和金刚石一直测到蛋白质的晶体结构。从1913年起，他在两年中一连测定了氯化钠、金刚石、硫化锌、黄铁矿、荧石和方解石等的晶体结构。这一批最早测定的晶体结构虽然极为简单，但很有代表性，而且都足以让化学和矿物学界观感一新。同时为测定参数较多和结构比较复杂的晶体结构也进行了理论和技术方面的准备。X射线晶体学能不断采用新技术和解决周相问题的新方法，使结构测定的对象
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)。
晶体X射线衍射实验报告全解
中南大学 X射线衍射实验报告 材料科学与工程学院材料学专业1305班班级 姓名学号0603130500 同组者无 黄继武实验日期2015 年12 月05 日指导教 师 评分分评阅人评阅日 期 一、实验目的 1)掌握X射线衍射仪的工作原理、操作方法； 2)掌握X射线衍射实验的样品制备方法； 3)学会X射线衍射实验方法、实验参数设置，独立完成一个衍射实验测试； 4)学会MDI Jade 6的基本操作方法； 5)学会物相定性分析的原理和利用Jade进行物相鉴定的方法； 6)学会物相定量分析的原理和利用Jade进行物相定量的方法。 本实验由衍射仪操作、物相定性分析、物相定量分析三个独立的实验组成，实验报告包含以上三个实验内容。 二、实验原理
1 衍射仪的工作原理 特征X射线是一种波长很短(约为20～0.06nm)的电磁波，能穿透一定厚度的物质，并能使荧光物质发光、照相乳胶感光、气体电离。在用电子束轰击金属“靶”产生的X射线中，包含与靶中各种元素对应的具有特定波长的X射线，称为特征（或标识）X射线。考虑到X射线的波长和晶体内部原子间的距离相近，1912年德国物理学家劳厄(M.von Laue)提出一个重要的科学预见：晶体可以作为X射线的空间衍射光，即当一束X射线通过晶体时将发生衍射，衍射波叠加的结果使射线的强度在某些方向上加强，在其他方向上减弱。分析在照相底片上得到的衍射花样，便可确定晶体结构。这一预见随即为实验所验证。1913年英国物理学家布拉格父子(W. H. Bragg, W. L Bragg)在劳厄发现的基础上，不仅成功地测定了NaCl、KCl等的晶体结构，并提出了作为晶体衍射基础的著名公式──布拉格定律： 2dsinθ=nλ 式中λ为X射线的波长，n为任何正整数。当X射线以掠角θ（入射角的余角，又称为布拉格角）入射到某一点阵晶格间距为d的晶面面上时，在符合上式的条件下，将在反射方向上得到因叠加而加强的衍射线。 2 物相定性分析原理 1) 每一物相具有其特有的特征衍射谱，没有任何两种物相的衍射谱是完全相同 的 2) 记录已知物相的衍射谱，并保存为PDF文件 3) 从PDF文件中检索出与样品衍射谱完全相同的物相 4) 多相样品的衍射谱是其中各相的衍射谱的简单叠加，互不干扰，检索程序能 从PDF文件中检索出全部物相 3 物相定量分析原理 X射线定量相分析的理论基础是物质参与衍射的体积活重量与其所产生的衍射强度成正比。 当不存在消光及微吸收时，均匀、无织构、无限厚、晶粒足够小的单相时，多晶物质所产生的均匀衍射环上单位长度的积分强度为： 式中R为衍射仪圆半径，V o为单胞体积，F为结构因子，P为多重性因子，M为温度因子，μ为线吸收系数。 三、仪器与材料 1)仪器：18KW转靶X射线衍射仪 2)数据处理软件：数据采集与处理终端与数据分析软件MDI Jade 6 3)实验材料：CaCO3+CaSO4、Fe2O3+Fe3O4
《X射线荧光光谱分析的基础知识》讲义 廖义兵 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，成为一种极为重要分析手段。 一、X射线荧光光谱分析的基本原理 元素的原子受到高能辐射激发而引起内层电子的跃迁，同时发射出具有一定特殊性波长的X射线，根据莫斯莱定律，荧光X射线的波长λ与元素的原子序数Z有关，其数学关系如下： λ=K(Z? s) ?2 式中K和S是常数。 而根据量子理论，X射线可以看成由一种量子或光子组成的粒子流，每个光具有的能量为： E=hν=h C/λ 式中，E为X射线光子的能量，单位为keV；h为普朗克常数；ν为光波的频率；C为光速。 因此,只要测出荧光X射线的波长或者能量,就可以知道元素的种类，这就是荧光X射线定性分析的基础。此外,荧光X射线的强度与相应元素的含量有一定的关系，据此，可以进行元素定量分析。 图1为以准直器与平面单晶相组合的波长色散型X射线荧光光谱仪光路示意图。 图1 平面晶体分光计光路示意图 A—X射线管；B—试料；C—准直器；D—分光晶体；E—探测器 由X射线管（A）发射出的X射线（称为激发X射线或一次X射线）照射到试料（B），试料（B）中的元素被激发而产生特征辐射（称为荧光X射线或二次X
X射线荧光光谱仪结构和原理 第一章 X荧光光谱仪可分为同步辐射X射线荧光光谱、质子X射线荧光光谱、全反射X射线荧光光谱、波长色散X射线荧光光谱和能量色散X射线荧光光谱等。 波长色散X射线荧光光谱可分为顺序（扫描型）、多元素同时分析型（多道）谱仪和固定道与顺序型相结合的谱仪三大类。顺序型适用于科研及多用途的工作，多道谱仪则适用于相对固定组成和批量试样分析，固定道与顺序式相结合则结合了两者的优点。 X射线荧光光谱在结构上基本由激发样品的光源、色散、探测、谱仪控制和数据处理等几部分组成。 §1.1 激发源 激发样品的光源主要包括具有各种功率的X射线管、放射性核素源、质子和同步辐射光源。波长色散X射线荧光光谱仪所用的激发源是不同功率的X射线管，功率可达4~4.5kW，类型有侧窗、端窗、透射靶和复合靶。能量色散X射线荧光光谱仪用的激发源有小功率的X射线管，功率从4~1600W，靶型有侧窗和端窗。靶材主要有Rh、Cr、W、Au、Mo、Cu、Ag等，并广泛使用二次靶。现场和便携式谱仪则主要用放射性核素源。 激发元素产生特征X射线的机理是必须使原子内层电子轨道产生电子空位。可使内层轨道电子形式空穴的激发方式主要有以下几种：带电粒子激发、电磁辐射激发、内转换现象和核衰变等。商用的X射线荧光光谱仪中，目前最常用的激发源是电磁辐射激发。电磁辐射激发源主要用X射线管产生的原级X射线谱、诱发性核素衰变时产生的γ射线、电子俘获和内转换所产生X射线和同步辐射光源。 §1.1.1 X射线管 1、X射线管的基本结构 目前在波长色散谱仪中，高功率X射线管一般用端窗靶，功率3~4KW，其结构示意图如下：
X 射线衍射分析 1实验目的 1、 了解X 衍射的基本原理以及粉末X 衍射测试的基本目的； 2、 掌握晶体和非晶体、单晶和多晶的区别； 3、 了解使用相关软件处理XRD 测试结果的基本方法。 2实验原理 1、 晶体化学基本概念 晶体的基本特点与概念：①质点（结构单元）沿三维空间周期性排列（晶 体 定义），并有对称性。②空间点阵：实际晶体中的几何点，其所处几何环境和 物质环境均同，这些“点集”称空间点阵。③晶体结构 =空间点阵+结构单元。非 晶部分主要为无定形态区域，其内部原子不形成排列整齐有规律的晶格。 对于大多数晶体化合物来说，其晶体在冷却结晶过程中受环境应力或晶核数目、 成核方式等条件的影响，晶格易发生畸变。分子链段的排列与缠绕受结晶条件的 影响易发生改变。晶体的形成过程可分为以下几步：初级成核、分子链段的 图1 14 种Bravais 点阵 表面延伸、链松弛、链的重吸收结晶、表面成核、分子间成核、晶体生长、晶体 生长完善。Bravais 提出了点阵空间这一概念，将其解释为点阵中选取能反映空 间点阵周期性与对称性的单胞，并要求单胞相等棱与角数最多。满足上述条件棱 间直角最多，同时体积最小。1848年Bravais 证明只有14种点阵。 Bravais lattice Cryslal DerBCfliptlcn CSlnwle) cubic Cubic a - b=? E , a = = 90B BaO/-rentered F*韓?“nl ?喇 (Simple) T etr-Aa^n^ i = b*C i .a=g = 7=SCi , Boa^-tentered ler^go>nal CGlnwle) DfthDmunbic Orlharhanbir 目日即亡时恒创 Orlhorhcmbic Oase-ceMered Offliorhombic Fac$-LBnter$d OnhorhChibie (Simple) Rhombol*edrai Rhombohedr^i (Trigonal) R = b = (;&= p= 7^ 90' 闭卿闾扫D 城帕1 H 曲g 肿对 a = b?iC fc tt=ft=0I]-a 7=12D - ⑻側 1.) MOnlQClHiC Monoclinic a c s a = y= go ■，&4 ger Monodlnlc ： (Slrrwle)AnDithl￡： Anotlhic (Triclinic) a * ： UH p 9D" PDFhAAiNT uaes Ehe 他 dfescnbing lhe pallerrt I Ellice cubic tatnigond orthortiombic rhonibdhedral hdxa.goinal (trigcnal) anortluc (tricl i me) iriufiOchrr ic
第一章 X 射线荧光光谱仪的结构和性能 X 荧光光谱仪可分为同步辐射 X 射线荧光光谱、质子 X 射线荧光光谱、全反射 X 射线荧光光谱、波长色散 X 射线荧光光谱和能量色散 X 射线荧光光谱等。 波长色散 X 射线荧光光谱可分为顺序(扫描型、多元素同时分析型(多道谱仪和固定道与顺序型相结合的谱仪三大类。顺序型适用于科研及多用途的工作, 多道谱仪则适用于相对固定组成和批量试样分析,固定道与顺序式相结合则结合了两者的优点。 X 射线荧光光谱在结构上基本由激发样品的光源、色散、探测、谱仪控制和数据处理等几部分组成。 §1.1 激发源 激发样品的光源主要包括具有各种功率的 X 射线管、放射性核素源、质子和同步辐射光源。波长色散 X 射线荧光光谱仪所用的激发源是不同功率的 X 射线管, 功率可达 4~4.5kW, 类型有侧窗、端窗、透射靶和复合靶。能量色散 X 射线荧光光谱仪用的激发源有小功率的 X 射线管,功率从 4~1600W,靶型有侧窗和端窗。靶材主要有 Rh 、 Cr 、 W 、 Au 、 Mo 、 Cu 、 Ag 等,并广泛使用二次靶。现场和便携式谱仪则主要用放射性核素源。 激发元素产生特征 X 射线的机理是必须使原子内层电子轨道产生电子空位。可使内层轨道电子形式空穴的激发方式主要有以下几种:带电粒子激发、电磁辐射激发、内转换现象和核衰变等。商用的 X 射线荧光光谱仪中,目前最常用的激发源是电磁辐射激发。电磁辐射激发源主要用 X 射线管产生的原级 X 射线谱、诱发性核素衰变时产生的γ射线、电子俘获和内转换所产生 X 射线和同步辐射光源。 §1.1.1 X射线管 1、 X 射线管的基本结构
1914年诺贝尔物理学奖——晶体的X射线衍射 1914年诺贝尔物理学奖授予德国法兰克福大学的劳厄（Max vonLaue，1879—1960），以表彰他发现了晶体的X射线衍射。 劳厄发现X射线衍射是20世纪物理学中的一件有深远意义的大事，因为这一发现不仅说明了X射线是一种比可见光波长短1000倍的电磁波，使人们对X 射线的认识迈出了关键的一步，而且还第一次对晶体的空间点阵假说作出了实验验证，使晶体物理学发生了质的飞跃。这一发现继佩兰（Perrin）的布朗运动实验之后，又一次向科学界提供证据，证明原子的真实性。从此以后，X射线学在理论和实验方法上飞速发展，形成了一门内容极其丰富、应用极其广泛的综合学科。 劳厄当时正在德国慕尼黑大学任教。他是1909年来到慕尼黑大学的，因为那时索末菲正在那里。索末菲的讲课和讨论班吸引了许多年轻的物理学家来到慕尼黑，讨论的主题都与当时物理学在理论和实验方面的新的概念和发现有关。其中有关X射线的本性的各种看法也是主题之一。劳厄在理论物理学方面有很深的造诣，同时也密切关注实际物理现象，特别是在光学和辐射方面。他很早就对狭义相对论发生了兴趣，曾从光学的光行差现象为相对论提供了独特的证明，并写了一本小册子介绍相对论。劳厄自从1909年来到慕尼黑大学后，由于受到伦琴的影响，注意力始终放在X射线的本性上。他完全了解有关这方面的研究现状和面临的困境，他倾向于波动说，知道问题的关键在于实现X射线的干涉或衍射。正好这时索末菲把编纂《数学科学百科全书》中“波动光学”条目的任务交给劳厄。为此劳厄研究了晶格理论。晶体的点阵结构在当时虽然还是一种假设，但是在劳厄看来却是合情合理的。他坚决站在原子论这一边，反对某些哲学家怀疑原子存在的观点。他认为：没有什么无懈可击的认识论论据能够驳斥这一事实，实际经验却不断地提供新鲜证据支持这一事实。由于他对晶体空间点阵有如此深刻的认识，所以当索末菲的博士研究生厄瓦尔德（P.Ewald）和他讨论晶体光学问题时，他敏锐地抓住了晶格间距的数量级，判定晶体可以作为X射线的天然光栅。他的灵感来自他日夜的苦思，同时也是由于他对这两个互不相干的假设都有明确具体的概念。劳厄不止一次地提到：如果不确信原子的存在，他永远也不会想到利用X射线透射的方法来进行实验。据劳厄和厄瓦尔德回忆，具体过程是这样的： 1912年2月的一天，厄瓦尔德来到劳厄的房间，求劳厄帮助解决如何用数学研究光对偏振原子点阵的作用。尽管劳厄帮不了他的忙，仍热心地建议他们第二天在研究所碰头，并去他家里在晚饭前后讨论。他们按约会面，步行穿过鲁德维希（Ludwig）大街后，厄瓦尔德开始向劳厄一般性地介绍他正在从事的课题，出乎他的意料，劳厄对这方面并不了解。他向劳厄解释，他是怎样依照色散的一般理论假设在点阵排列中振子的位置。劳厄反问他为什么要这样假设。厄瓦尔德回答说，人们认为晶体具有这种内部的规律性。看起来劳厄对此感到新奇。这时他们已经进入花园。劳厄问道：振子之间的距离多大？对此，厄瓦尔德回答说，
X 射线衍射实验报告 材料科学与工程 学院 材料科学与工程 专业 班级 姓 名 学号 同组者 实验日期 年 月 日 指导教师 评分 分 评阅人 评阅日期 一 实验设计背景与实验目的 1 实验设计背景 Al-Zn-Mg 合金是中强可焊铝合金，σb 达到500MPa ，延伸率为15%，电导率为30IACS%，具有较好的强度和延伸率，抗腐蚀性能较好。用作航空航天和地面设备的结构材料。是目前材料研究的一个重要课题。 该合金是可热处理强化合金，合金通过固溶-淬火-时效，时效温度不同，析出GP 区、η'相或η相。后两者具有六方结构，基本化学组成为MgZn2。而GP 区为5-10nm 的球状粒子。析出相不同，其合金性能也不相同。 图1 Al-Zn-Mg 合金的不同处理态TEM 观察 a)Al 固溶态(基体) b) 120℃/24h 时效态 c)180℃/24h 时效态 同一合金，固溶态的物相应为单相，而时态效为双相（基体和析出相），因 0.5μ 100nm b) a) 100nm c) 100nm
此，首先应通过实验鉴定物相组成（物相定性分析）；对于双相态，应当了解析出相的百分含量；另外，由于合金元素在基体中不同程度的固溶，导致基体的点阵常数变化，通过这种变化可检测固溶程度。 2 实验目的 了解X射线衍射仪的结构，操作规程，掌握MDI JADE的使用方法； 掌握X射线在新材料开发中的实际应用方法（物相定性分析、物相定量分析和点阵常数精确测定）。 掌握新材料开发的最新进展和新实验方法和技巧。 二实验原理 1、X射线衍射仪 （1）X射线管 X射线管工作时阴极接负高压，阳极接地。灯丝附近装有控制栅，使灯丝发出的热电子在电场的作用下聚焦轰击到靶面上。阳极靶面上受电子束轰击的焦点便成为X射线源，向四周发射X射线。在阳极一端的金属管壁上一般开有四个射线出射窗口。转靶X射线管采用机械泵+分子泵二级真空泵系统保持管内真空度，阳极以极快的速度转动，使电子轰击面不断改变，即不断改变发热点，从而达到提高功率的目的
中南大学 X射线衍射实验报告 材料科学与工程学院材料学专业1305班班级姓名学号06031305 00 同组者无 实验日期201 5 年1 2 月05 日指导教师黄继武 评分分评阅人评阅日期 一、实验目的 1)掌握X射线衍射仪的工作原理、操作方法； 2)掌握X射线衍射实验的样品制备方法； 3)学会X射线衍射实验方法、实验参数设置，独立完成一个衍射实验测试； 4)学会MDI Jade 6的基本操作方法； 5)学会物相定性分析的原理和利用Jade进行物相鉴定的方法； 6)学会物相定量分析的原理和利用Jade进行物相定量的方法。 本实验由衍射仪操作、物相定性分析、物相定量分析三个独立的实验组成，实验报告包含以上三个实验内容。 二、实验原理
式中λ为X射线的波长，n为任何正整数。当X射线以掠角θ（入射角的余角，又称为布拉格角）入射到某一点阵晶格间距为d的晶面面上时，在符合上式的条件下，将在反射方向上得到因叠加而加强的衍射线。 2 物相定性分析原理 1) 每一物相具有其特有的特征衍射谱，没有任何两种物相的衍射谱是完全相同的 2) 记录已知物相的衍射谱，并保存为PDF文件 3) 从PDF文件中检索出与样品衍射谱完全相同的物相 4) 多相样品的衍射谱是其中各相的衍射谱的简单叠加，互不干扰，检索程序能从PDF文件中检索出全部物相 3 物相定量分析原理 X射线定量相分析的理论基础是物质参与衍射的体积活重量与其所产生的衍射强度成正比。 当不存在消光及微吸收时，均匀、无织构、无限厚、晶粒足够小的单相时，多晶物质所产生的均匀衍射环上单位长度的积分强度为： 式中R为衍射仪圆半径，V o为单胞体积，F为结构因子，P为多重性因子，M为温度因子，μ为线吸收系数。 三、仪器与材料 1)仪器：18KW转靶X射线衍射仪