silicon is one of the most abundant elements in cosmic dust , comprising around 11% by mass ( 9% elemental abundance ) [ asplund et al . ,
the amount of cosmic dust entering the earth 's atmosphere each day is still quite uncertain [ plane , 2012 ] , with recent estimates in the range of 14 to 150  t  d [ carrillosnchez et al . , 2015
; huang et al . , 2015 ] . the fraction of silicon which ablates from this dust in the upper atmosphere is also highly dependent on the dust size and entry velocity distributions [ carrillosnchez et al . ,
although neutral silicon compounds of extraterrestrial origin have not yet been detected in the mesosphere / lower thermosphere ( mlt ) region between 70 and 120  km , si ions have been measured by rocketborne mass spectrometry over several decades ( see reviews by kopp et al .   and grebowsky and aikin ) .
figure  1a shows vertical profiles of si , fe , and mg averaged from five rocket flights conducted by kopp and coworkers .
two of these rockets were launched from wallops islands ( 37.8n , usa ) at 11:58 lt on 12 august 1976 ( payload 18.1006 [ herrmann et al . , 1978 ] ) and at 14:03 lt on 1 january 1977 ( payload 18.1008 [ meister et al . , 1978 ] ) .
the rest were launched from kiruna ( 67.8n , sweden ) at 01:38 lt on 13 august 1978 ( payload s26/2 [ kopp et al . , 1985 ] ) , at 01:44 lt on 30 november 1980 ( payload 33.009 [ kopp , 1997 ] ) , and at 01:32 lt on 3 august 1982 ( payload s37/p [ kopp et al . , 1984 ] ) .
care needs to be taken when assigning masstocharge ratio ( m / z ) 28 to si , as n2 
  produced by energetic particle precipitation in the lower thermosphere , or h2cn from the mesosphere , have the same masstocharge ratio .
here we have confirmed that the si / si isotopic ratio for each of the profiles that were selected for figure  1 was in agreement with the natural abundance ratio of 0.051 over the altitude range 90110  km [ zbinden et al . , 1975 ] .
rocketborne mass spectrometric observations of si , fe , and mg ( see text for flight details ) : ( a ) averaged vertical profiles of five rocket flights ; ( b and c ) averaged si / fe and mg / fe ratios versus altitude ( squares ) , along with the maximum and minimum ratio values ( dashed lines ) .
the thick solid lines show the corresponding waccm modeled ratios , with minimum and maximum values indicated by thin solid lines .
inspection of figure  1 shows that above 100  km the concentrations of si , fe , and mg are similar , as expected because they have similar cosmic abundances [ asplund et al . , 2009 ] and should ablate with similar efficiencies [ carrillosnchez et al . ,
2015 ] . however , whereas the fe and mg profiles maintain a fairly constant ratio over the entire height range , the relative si concentration decreases by about 2 orders of magnitude below 97  km .
this implies that si is neutralized more easily than other meteoric metal ions in the upper mesosphere , which is an important test of an atmospheric model .
the resulting neutral silicon oxides probably then polymerize with fe and mg oxides / hydroxides to form meteoric smoke particles ( msps ) , a process which has been shown to occur rapidly in the laboratory [ saunders and plane , 2011 ] .
there is tentative spectroscopic evidence , obtained from the solar occultation for ice experiment ( sofie ) instrument on board the aeronomy of ice in the mesosphere ( aim ) satellite , that msps below 85  km are composed of femgsilicates [ hervig et al . ,
lastly , rocketborne measurements of negative ions below 90  km have identified an ion of mass 76 which could be either co4 
  or sio3 
 , though there are strong arguments for the latter [ viggiano et al . , 1982 ] .
the purpose of this paper is to develop a comprehensive model of the ion and neutral chemistry of silicon .
following a series of laboratory kinetic studies on the reactions of si , sio , and si [ eyet et al .
, 2010 ; gmez martin et al . , 2009a ; gmez martin et al . , 2009b ; gmez martn and plane , 2011 ] , it is now feasible to make a significant advance on the original silicon model of fritzenwallner and kopp .
here we first demonstrate using highlevel theory that silicic acid ( si(oh)4 ) is a likely sink for silicon in the mlt .
the rate coefficients for a small number of reactions , not hitherto measured , are then calculated using theoretical techniques , before the silicon chemistry scheme is placed into the whole atmosphere community climate model ( waccm ) [ marsh et al . , 2007 ] with a meteoric input function of si .
we have used this model previously to study iron and magnesium chemistry in the mlt [ feng et al . , 2013 ; langowski et al . , 2015 ] .
the modeled si , fe , and mg ratios are shown to compare well against rocket measurements , before the model is used to predict the speciation of neutral silicon in the mlt .
figure  2 is a schematic diagram of the ionmolecule and neutral chemistry of silicon in the mlt .
the rate coefficients of the reactions shown with black arrows have been measured in the laboratory ( see footnotes to table  1 ) ; rate coefficients for the dissociative recombination reactions of siliconcontaining ions with electrons ( dashed grey arrows ) have been set to a typical value for this class of reactions [ florescumitchell and mitchell , 2006 ] ; and the rate coefficients for the reactions shown with red arrows have been calculated , as described below .
schematic diagram of the important reaction pathways for silicon produced by meteoric ablation in the mlt .
solid black arrows depict chemical reactions which have been studied in the laboratory ; dashed line arrows indicate dissociative electron recombination reactions ( see text ) ; solid red arrows depict reactions where the rate coefficients are calculated theoretically in this study .
the main neutral sink is si(oh)4 , which is an important constituent of meteoric smoke ( blue arrow ) .
neutral and ionic gas phase reactions in the silicon model units : unimolecular , s ; bimolecular , cm  molecule  s ; termolecular , cm  molecule  s. the chemical ablation model ( cabmod ) [ vondrak et al . ,
2008 ] predicts that silicon mostly ablates from meteoroids in the form of sio and sio2 , based on the thermodynamic model magma [ schaefer and fegley , 2005 ] .
these oxides will most likely then be dissociated to atomic si through hyperthermal collisions with air molecules , since they have initial velocities in excess of 11  km  s. however , si will immediately be oxidized to sio by reaction with o2 or o3 [ gmez martin et al . , 2009a ] .
in turn , sio is oxidized more slowly to sio2 by reaction with o3 or oh [ gmez martin et al . , 2009b ] .
+  o    sio  +  o2 is exothermic by 63  kj  mol , quantum calculations indicate the existence of a high barrier ( 104.7  kj  mol ) which will make this reaction very slow at mesospheric temperatures [ gmez martin et al .
+  h    sio  +  oh is endothermic by only 6  kj  mol , and detailed balance with the measured rate coefficient for sio  +  oh has been used to estimate its rate coefficient [ plane , 2013 ] , which is listed in table  1 .
here we use quantum theory calculations to explore the hydrolysis of sio2 , in order to determine whether the sequential addition of two h2o molecules can form the stable molecule si(oh)4 under the conditions of the mlt : 
 ( 1)sio2+h2o+mosioh2ho0k=277kjmol1 
 ( 2)osioh2+h2o+msioh4ho0k=290kjmol1where m is a third body ( n2 or o2 ) .
electronic structure calculations using the gaussian 09 suite of programs [ frisch et al . ,
2009 ] were used to map the stationary points on the electronic potential energy surfaces ( pess ) of these reactions .
molecular geometries were first optimized using hybrid density functional theory , which includes some exact hartreefock exchange .
the b3lyp method was used together with the 6311+g(2d , p ) triple zeta basis set .
this large , flexible basis set has both polarization and diffuse functions added to the atoms .
after the optimized geometries were checked for wave function stability , the resulting rotational constants and vibrational frequencies were used in the master equation calculations described below .
more accurate energies ( 15  kj  mol [ foresman and frisch , 1996 ] ) were then determined using the complete basis set ( cbsq ) method of petersson and coworkers [ montgomery et al . , 2000 ] .
all reaction enthalpy changes reported in this paper were calculated at this level of theory .
this shows that after initially forming a sio2h2o complex , rearrangement over a barrier submerged below the energy of the entrance channel leads to the product where three o atoms are now bound to the si .
the pes for reaction ( 2 ) is similar , as shown in figure  3b : a shallow osi(oh)2h2o complex rearranges over a submerged barrier to form si(oh)4 .
the rate coefficients for these reactions were then estimated using riceramspergerkasselmarkus ( rrkm ) theory , employing a solution of the master equation ( me ) based on the inverse laplace transform method [ robertson et al .
the calculations were carried out with the open source program mesmer ( master equation solver for multiwell energy reactions ) [ robertson et al .
, 2012 ] , which determines the temperature and pressuredependent rate coefficient from the full microcanonical description of the system time evolution by performing an eigenvector / eigenvalue analysis similar to that described by bartis and widom .
the internal energies of the intermediates on the pes were divided into a contiguous set of grains ( width 50  cm ) containing a bundle of rovibrational states .
each grain was then assigned a set of microcanonical rate coefficients linking it to other intermediates , calculated by rrkm theory .
for dissociation to reactants , microcanonical rate coefficients were determined using inverse laplace transformation to link them directly to the capture rate coefficient , which was set to 3    10 ( t/200  k )  cm  molecule  s , where the small positive temperature dependence is characteristic of a longrange potential governed by dispersion forces [ georgievskii and klippenstein , 2005 ] .
( a ) potential energy surface for the recombination of sio2 and h2o to form osi(oh)2 ; ( b ) potential energy surface for the recombination of osi(oh)2 and h2o to form si(oh)4 .
color scheme : si ( grey ) , o ( red ) , and h ( white ) .
the probability of collisional transfer between grains was estimated using the exponential down model , where the average energy for downward transitions was set to  <  e  >  down  =  300  cm [ gilbert and smith , 1990 ] .
because reactions ( 1 ) and ( 2 ) are fast and hence well into the falloff region between third and secondorder kinetics even at the low pressures of the mlt , the mesmer calculations of k 
 rec over a range of t and p were fitted to the standard lindemann expression containing the low and highpressure limiting rate coefficients , k 
 rec,0 and k 
 rec, , modified by a broadening factor f 
 c [ sander et al . ,
molecular properties of the stationary points on the potential energy surfaces in figure  3 , calculated at the b3lyp/6311+g(2d , p ) level of theory importantly , both osi(oh)2 and si(oh)4 are stable with respect to reaction with o , h , and oh : 
 ( 3)osioh2+ohosio2+ohho0k=82kjmol1 
 ( 4)osioh2+hhosio+h2oh00k=36kjmol1 
 ( 5)osioh2+ohhosio2+h2oho0k=20kjmol1 
 ( 6)sioh4+oosioh3+ohho0k=89kjmol1 
 ( 7)sioh4+hsioh3+h2oho0k=88kjmol1 
 ( 8)sioh4+ohosioh3+h2oho0k=20kjmol1 
  thus , si(oh)4 should be the main sink for meteorablated silicon , as we demonstrate in section 3 .
si(oh)4 should eventually polymerize with metallic species ( e.g. , feoh , mg(oh)2 ) to form msps .
although not the subject of this paper , we have shown that these polymerization reactions are exothermic .
for example , the condensation reaction 
 ( 9)feoh+sioh4feosioh3+h2oho0k=21kjmol1 
  metal atoms such as fe and mg become ionized in the lower thermosphere mostly through charge transfer with ambient no and o2 
  ions [ plane et al . , 2015 ] .
however , the concentration of si must be negligible due to the fast reaction si  +  o2    sio  +  o ( ( r1 ) in table  1 ) .
the calculated adiabatic ionization energies of sio and sio2 are 11.5 and 12.5  ev , respectively .
when compared with the calculated ionization energies of no and o2 , which are respectively 9.3 and 12.2  ev , it is clear that the only exothermic charge transfer reaction is 
 ( 10)sio+o2+sio++o2ho0k=67kjmol1 
  as shown in figure  2 , this appears to be the only route for ionizing neutral si compounds .
the resulting sio must then be reduced to the observed si ( figure  1 ) by reaction with atomic o : 
 ( 11)sio++osi++o2ho0k=27kjmol1 
  here we have assigned the rate coefficients for reactions ( 10 ) and ( 11 ) to their calculated langevin capture rates ( ( r8 ) and ( r9 ) in table  1 ) .
it should be noted that langevin theory provides an upper limit to the rate coefficient for an ionmolecule reaction [ smith , 1980 ] .
however , as is shown in the modeling section below , the unexpectedly high measured densities of si relative to other metallic ions are already challenging to explain with both reactions ( 10 ) and ( 11 ) set to their langevin capture rates , which implies that their rate coefficients must be very close to these capture rates .
2008 ] predicts that silicon mostly ablates from meteoroids in the form of sio and sio2 , based on the thermodynamic model magma [ schaefer and fegley , 2005 ] .
these oxides will most likely then be dissociated to atomic si through hyperthermal collisions with air molecules , since they have initial velocities in excess of 11  km  s. however , si will immediately be oxidized to sio by reaction with o2 or o3 [ gmez martin et al . , 2009a ] . in turn
, sio is oxidized more slowly to sio2 by reaction with o3 or oh [ gmez martin et al . , 2009b ] .
+  o    sio  +  o2 is exothermic by 63  kj  mol , quantum calculations indicate the existence of a high barrier ( 104.7  kj  mol ) which will make this reaction very slow at mesospheric temperatures [ gmez martin et al . , 2009b ] .
+  h    sio  +  oh is endothermic by only 6  kj  mol , and detailed balance with the measured rate coefficient for sio  +  oh has been used to estimate its rate coefficient [ plane , 2013 ] , which is listed in table  1 .
here we use quantum theory calculations to explore the hydrolysis of sio2 , in order to determine whether the sequential addition of two h2o molecules can form the stable molecule si(oh)4 under the conditions of the mlt : 
 ( 1)sio2+h2o+mosioh2ho0k=277kjmol1 
 ( 2)osioh2+h2o+msioh4ho0k=290kjmol1where m is a third body ( n2 or o2 ) . electronic structure calculations using the gaussian 09 suite of programs [ frisch et al . ,
2009 ] were used to map the stationary points on the electronic potential energy surfaces ( pess ) of these reactions .
molecular geometries were first optimized using hybrid density functional theory , which includes some exact hartreefock exchange .
the b3lyp method was used together with the 6311+g(2d , p ) triple zeta basis set .
this large , flexible basis set has both polarization and diffuse functions added to the atoms .
after the optimized geometries were checked for wave function stability , the resulting rotational constants and vibrational frequencies were used in the master equation calculations described below .
more accurate energies ( 15  kj  mol [ foresman and frisch , 1996 ] ) were then determined using the complete basis set ( cbsq ) method of petersson and coworkers [ montgomery et al . , 2000 ] .
all reaction enthalpy changes reported in this paper were calculated at this level of theory .
this shows that after initially forming a sio2h2o complex , rearrangement over a barrier submerged below the energy of the entrance channel leads to the product where three o atoms are now bound to the si .
the pes for reaction ( 2 ) is similar , as shown in figure  3b : a shallow osi(oh)2h2o complex rearranges over a submerged barrier to form si(oh)4 .
the rate coefficients for these reactions were then estimated using riceramspergerkasselmarkus ( rrkm ) theory , employing a solution of the master equation ( me ) based on the inverse laplace transform method [ robertson et al . , 2007 ] .
the calculations were carried out with the open source program mesmer ( master equation solver for multiwell energy reactions ) [ robertson et al . , 2012 ] , which determines the temperature and pressuredependent rate coefficient from the full microcanonical description of the system time evolution by performing an eigenvector / eigenvalue analysis similar to that described by bartis and widom .
the internal energies of the intermediates on the pes were divided into a contiguous set of grains ( width 50  cm ) containing a bundle of rovibrational states .
each grain was then assigned a set of microcanonical rate coefficients linking it to other intermediates , calculated by rrkm theory .
for dissociation to reactants , microcanonical rate coefficients were determined using inverse laplace transformation to link them directly to the capture rate coefficient , which was set to 3    10 ( t/200  k )  cm  molecule  s , where the small positive temperature dependence is characteristic of a longrange potential governed by dispersion forces [ georgievskii and klippenstein , 2005 ] .
( a ) potential energy surface for the recombination of sio2 and h2o to form osi(oh)2 ; ( b ) potential energy surface for the recombination of osi(oh)2 and h2o to form si(oh)4 .
color scheme : si ( grey ) , o ( red ) , and h ( white ) .
the probability of collisional transfer between grains was estimated using the exponential down model , where the average energy for downward transitions was set to  <  e  >  down  =  300  cm [ gilbert and smith , 1990 ] . because reactions ( 1 ) and ( 2 ) are fast and hence well into the falloff region between third and secondorder kinetics even at the low pressures of the mlt , the mesmer calculations of k 
 rec over a range of t and p were fitted to the standard lindemann expression containing the low and highpressure limiting rate coefficients , k 
 rec,0 and k 
 rec, , modified by a broadening factor f 
 c [ sander et al . ,
molecular properties of the stationary points on the potential energy surfaces in figure  3 , calculated at the b3lyp/6311+g(2d , p ) level of theory importantly , both osi(oh)2 and si(oh)4 are stable with respect to reaction with o , h , and oh : 
 ( 3)osioh2+ohosio2+ohho0k=82kjmol1 
 ( 4)osioh2+hhosio+h2oh00k=36kjmol1 
 ( 5)osioh2+ohhosio2+h2oho0k=20kjmol1 
 ( 6)sioh4+oosioh3+ohho0k=89kjmol1 
 ( 7)sioh4+hsioh3+h2oho0k=88kjmol1 
 ( 8)sioh4+ohosioh3+h2oho0k=20kjmol1 
  thus , si(oh)4 should be the main sink for meteorablated silicon , as we demonstrate in section 3 .
si(oh)4 should eventually polymerize with metallic species ( e.g. , feoh , mg(oh)2 ) to form msps .
although not the subject of this paper , we have shown that these polymerization reactions are exothermic .
metal atoms such as fe and mg become ionized in the lower thermosphere mostly through charge transfer with ambient no and o2 
  ions [ plane et al . , 2015 ]
. however , the concentration of si must be negligible due to the fast reaction si  +  o2    sio  +  o ( ( r1 ) in table  1 ) .
the calculated adiabatic ionization energies of sio and sio2 are 11.5 and 12.5  ev , respectively .
when compared with the calculated ionization energies of no and o2 , which are respectively 9.3 and 12.2  ev , it is clear that the only exothermic charge transfer reaction is 
 ( 10)sio+o2+sio++o2ho0k=67kjmol1 
  as shown in figure  2 , this appears to be the only route for ionizing neutral si compounds .
the resulting sio must then be reduced to the observed si ( figure  1 ) by reaction with atomic o : 
 ( 11)sio++osi++o2ho0k=27kjmol1 
  here we have assigned the rate coefficients for reactions ( 10 ) and ( 11 ) to their calculated langevin capture rates ( ( r8 ) and ( r9 ) in table  1 ) .
it should be noted that langevin theory provides an upper limit to the rate coefficient for an ionmolecule reaction [ smith , 1980 ] .
however , as is shown in the modeling section below , the unexpectedly high measured densities of si relative to other metallic ions are already challenging to explain with both reactions ( 10 ) and ( 11 ) set to their langevin capture rates , which implies that their rate coefficients must be very close to these capture rates .
the global si atmospheric model ( termed here waccmsi ) is constructed from three components : ( i ) waccm version 4 , a  hightop  coupled chemistryclimate model with an upper boundary at 6.0    10  hpa ( ~140  km ) ; ( ii ) a description of the neutral and ionmolecule chemistry of si ( figure  2 and table  1 ) ; and ( iii ) the meteoroid input function ( mif ) , which specifies the temporal and geographical input of meteoric si atoms into the mlt .
the mif was calculated using the astronomical characteristics of the sporadic meteor complex to estimate the global meteoric mass flux deposited at each altitude within the mlt , at all latitudes for each day of the year [ fentzke and janches , 2008 ] .
cabmod was then used to compute the injection rates of individual metallic elements as a function of altitude [ vondrak et al . ,
further details are given in our previous studies on fe and na [ feng et al .
, 2013 ; marsh et al . , 2013 ] . the si mif is illustrated in figure  4 .
the peak si injection rate of 0.018  atom  cm  s occurs around 97  km , and the annual mean si ablation flux is 2.9    10  atom  cm  s ( 0.60  t  d over the earth ) .
it should be noted that this mif predicts a na flux of the required magnitude for modeling the mesospheric na layer with waccm [ marsh et al . ,
in fact , lidar measurements of the actual na atom flux [ gardner et al .
, 2014 ; huang et al . , 2015 ] indicate that the na flux may be underestimated by an order of magnitude , which would imply that waccm requires additional vertical transport processes besides eddy diffusion in the mlt [ gardner and liu , 2010 ] . from the point of view of the present study , where we are more concerned with the relative abundances of si , fe , and mg , this is less of an issue ,
although it does have implications for the transport of silicon species to high latitudes ( see below ) .
( a ) the seasonal variation of the silicon meteoric input flux ( 10  atom  cm  s ) as a function of latitude and month ; ( b ) the annual average global si injection profile . waccmsi was run from 2004 to 2013 ( after a 10  year spinup ) , with dynamical fields nudged in the troposphere and stratosphere to the goddard earth observing system 5 ( geos5 ) meteorological data set , as described by feng et al . .
a nudging coefficient value ( 0.01 ) was used when assimilating the geos5 analysis into waccm , so that 1% of the meteorological conditions were combined with waccm fields below 60  km at every model dynamics time step . above 60 
the waccmsi output was sampled every 30  min for the rocket locations at 38n and 68n ( see section 1 ) .
figure  5 illustrates the vertical profiles of the major si species predicted by waccmsi at 38n in august at local noon ( 1113 lt ) .
these profiles have been averaged from 7  years of data ( 20052011 ) . a rocketborne profile of si ( flight 18.1006 [ herrmann et al . , 1978 ] ) for the same month , latitude , and local time is shown for comparison with the modeled si profile .
the layers of meteoric atomic ions tend to be highly perturbed by gravity waves and tides coupling with the lorentz force from the earth 's magnetic field ; these effects can be observed in the ca layer , which ( uniquely ) has been observed with high spatial and temporal resolution by lidar [ gerding et al . , 2000 ] .
since a rocketborne measurement provides a ~20  s snapshot , the agreement is surprisingly good .
the sporadic e layer at 116  km is not predicted by waccm ( since these tend to be subscale , transient phenomena ) , but the underside of the si layer is well captured by the model .
similarly good agreement is observed for flight 18.1008 at 37.8n in january [ meister et al . , 1978 ] , and flight s37/p at 67.8n in august [ kopp et al . , 1984 ] .
modeled vertical profiles of the major neutral and ionic sibearing species at 38n , august and local noon .
profiles of si ( filled circles ) and m / z 45 , tentatively assigned to sioh ( grey squares ) , measured by rocket payload 18.1006 on 12 august 1976 [ herrmann et al . , 1978 ] .
si is predicted to be the major silicon species only above 110  km , in contrast to metals such as na and fe where the ions dominate over the neutral atoms above ~95  km [ feng et al . , 2013 ; marsh et al . ,
there are two reasons for this : first , the relative difficulty of ionizing neutral silicon ( which occurs only through charge transfer of sio with o2 
 , as discussed in section 2.2 ) and second , the reactions of si and sio with o3 ( ( r11 ) and ( r15 ) in table  1 ) , which produce neutral sio and sio2 , respectively .
this explains the rapid decrease in si below 97  km , illustrated in figure  1a .
figure  5 also shows that the only other significant ion is sioh , which forms through fast reactions of si with h2o , sio with h2 and h2o , and sio2 
  with h ( figure  2 and table  1 ) .
observed signals at m / z 45 [ goldberg and aikin , 1972 ; zbinden et al .
, 1975 ] have previously been assigned to sioh [ kopp et al . , 1995 ;
zbinden et al . , 1975 ] . although close to the background noise , the m / z 45 signal from payload 18.1006 shown in figure  5 agrees very well at 105  km ( 45/28  =  0.004 ) with previous observations ( 45/28  =  0.003 [ goldberg and aikin , 1972 ] ) and is within a factor of 10 of the modeled [ sioh ] /[si ] ratio at the si peak
. however , figure  5 also shows an enhancement of the m / z 45 signal below 100  km , which is not consistent with the modeled profile of sioh . in view of the modeling results ,
it is unlikely that sioh , sio2 
 , and sioh2 
  contribute respectively to the m / z 45 , 60 , and 61 signals observed in other studies below 100  km and tentatively attributed to these species [ goldberg , 1975 ; kopp et al . ,
figures  1b and 1c compare the modeled [ si]/[fe ] and [ mg]/[fe ] ratio profiles , respectively , to the rocket averages ( see section 1 for details of the five flights ) . note that because the ratio from each of the five flights used to produce figure  1 ( see section 1 ) is averaged , the average ratios plotted in figures  1b and 1c are different from the ratios of the averaged profiles in figure  1a .
the modeled ion ratio corresponding to each rocket flight is a 7  year average ( 20052011 ) value calculated within 2  h of the local time of the launch , and in the same month and location .
the modeled si is from this study , while the modeled fe and mg are from feng et al .   and langowski et al .
the vertical dashdotdot lines in figures  1b and 1c show the ci chondritic abundance ratio of si and mg to fe [ asplund et al . , 2009 ] . above 105  km
the [ si]/[fe ] ratio becomes superchondritic , which is indeed a common feature of all the rocket ion profiles reported to date ( e.g. , aikin and goldberg , goldberg , zbinden et al . , and all the profiles used in this study from kopp and coworkers ) .
comparison with the ratio calculated from waccm shows that the model may underpredict the [ si]/[fe ] ratio , although the range of observed ratios overlaps the ( much smaller ) range of the modeled ratio .
inspection of figure  5 shows that there is a substantial amount of sio above 100  km , in excess over si up to nearly 110  km .
although this is potentially an additional source of si , it should be remembered that the rate coefficients of reactions ( 9 ) and ( 11 ) are already set to their langevin upper limits ( table  1 ) to maximize the production of si from sio via charge transfer with o2 
 , and it is difficult to see another route to ionize sio .
it is important to note that the si mif we have used here is not scaled with respect to the na mif .
in contrast , when modeling the fe and mg layers using waccm , the mifs for fe and mg had to be divided by factors of 4 and 15 , respectively , compared with na [ feng et al . , 2013 ; langowski et al . , 2015
; marsh et al . , 2013 ] . in their modeling study , fritzenwallner and
kopp   also pointed out an apparent lack of differential ablation of si with respect to na .
cabmod treats meteoroids essentially as olivine particles ( femgsio4 ) which melt at 1850  k [ vondrak et al . ,
si is predicted to ablate slightly less efficiently than fe but has a slightly higher elemental abundance [ asplund et al . ,
2009 ] : the result is that for a range of mifs with different mass and velocity distributions the si / fe ablation ratio ranges from 0.79 to 1.1 [ carrillosnchez et al . , 2015 ] .
in contrast , the implication of figure  1b is that the si / fe ablation ratio is at least 4 .
one explanation for this may be that most of the cosmic dust particles entering the earth 's atmosphere is of cometary origin [ nesvorn et al . ,
2010 ] , and there is some evidence that fe is depleted by a factor of ~2 with respect to si in particles returned from the stardust mission [ flynn et al . , 2006 ; gainsforth et al . ,
2015 ] . however , that would not account fully for the seemingly efficient ablation of si with respect to fe .
waccmsi correctly predicts the rapid decrease in the [ si]/[fe ] ratio below 100  km .
note that below 90  km , there is probably a significant contribution to the m / z 28 signal from h2cn [ kopp et al .
, 1995 ] ( the si / si ratio is also incorrect , but this may be due to a contribution from hco at m / z 29 [ zbinden et al .
, 1975 ] ) . in contrast to figure  1b , figure  1c illustrates that waccm captures very well the measured [ mg]/[fe ] ratio from 85 to 110  km , which is close to chondritic .
figure  5 shows that sio is predicted to be a major silicon species , occurring in a layer which peaks at ~97  km with a global average density of ~5000  cm .
sio is therefore the counterpart of the layers of metal atoms such as na and fe , which occur 512  km lower in the atmosphere .
sio2 is a significant but never dominant species because it is formed via the oxidation of sio by o3 and oh which are relatively slow ( ( r3 ) and ( r4 ) in table  1 ) , compared with its reduction by h ( ( r5 ) in table  1 ) or addition of h2o ( r1 ) .
the global average lifetimes of si , sio and sio2 can be estimated by dividing the column abundances of their layers ( figure  5 ) by the meteoric ablation flux of si ( 2.9    10  atom  cm  s  see above ) .
this yields individual lifetimes of 0.5 , 1.9 , and 0.6  days , respectively , or a total lifetime of these chemically labile si species of 3.0  days .
viggiano et al .   measured a negative ion with mass 76 and a density of a few 100  cm below 80  km , which is about 2% of the predicted si(oh)4 concentration below 80  km in figure  5 .
having argued that mass 76 ion was more likely sio3 
  than co4 
 , viggiano et al . then speculated that sio3 
  could be produced by the rapid dissociative attachment of electrons to msps .
have shown that electron attachment to msps produces heavy charged particles ( > 3000  amu ) , dissociative attachment to form sio3 
  could be a minor reaction channel .
figure  6 illustrates the model diurnally averaged column abundances above 80  km of the major silicon species , si , sio , and si(oh)4 , as a function of latitude and month ( for the years 20042013 ) . there are a number of striking features .
first , si and sio exhibit a summertime maximum , particularly at high latitudes , where si increases by a factor of ~10 and sio by a factor of ~4 , compared to midwinter .
second , the maxima in these species are not centered about the solstice but are shifted into late summer ( by 2  months , in the case of sio ) .
third , in contrast to si and sio , si(oh)4 exhibits a wintertime maximum , again more pronounced at high latitudes where si(oh)4 increases by a factor of ~5 .
note that the maximum is in early winter , about 1  month before the solstice .
diurnally averaged column abundances ( 10  cm ) between 80 and 110  km of the major silicon species as a function of latitude and month , predicted by waccmsi : ( a ) si , ( b ) sio , and ( c ) si(oh)4 .
the summertime maxima of si and sio are explained by the longer periods of sunlight causing increased ionization of the mlt , particularly at high latitudes . as shown in figure  2 , si and sio
are closely coupled , principally through reactions ( r8 ) , ( r9 ) , ( r10 ) , ( r11 ) , and ( r13 ) in table  1 .
the shift in the peak toward autumn results from the si mif , which peaks in autumn and is a minimum in spring ( figure  4 ) .
the reason that a signature of the mif appears in these species is that they are relatively shortlived before conversion to the permanent sink si(oh)4 .
this contrasts with the metals such as na and fe , where the metal atoms and ions persist much longer above 80  km before being permanently removed to msps ; hence , longrange transport tends to remove the signature of the mif [ feng et al .
, 2013 ; marsh et al . , 2007 ] . because si(oh)4 forms rapidly via hydration of sio2 ( reactions ( 1 ) and ( 2 ) ) , and there is no sink apart from the slow formation of meteoric smoke , its global behavior reflects the meridional circulation in the upper mesosphere : high concentrations of si(oh)4 arise from convergence of the meridional wind over the winter pole , particularly in early winter because of the autumnal maximum of the mif in the relevant hemisphere , and low concentrations due to divergence of the meridional wind away from the summer pole
in this study we present a new model for silicon chemistry in the mlt , based on a number of recent laboratory kinetic studies of si , sio , and si [ eyet et al . , 2010 ;
we have also used theoretical calculations to show that the likely fate of sio2 in the mlt is a twostep hydration to silicic acid .
si(oh)4 appears to be a very stable sink for silicon , whose likely fate is polymerization with metal oxides and hydroxides to form msps .
the new model is therefore a significant advance on the previous work of fritzenwallner and kopp .
inclusion of this new silicon chemistry model in the 3d atmospheric model waccm has revealed a number of interesting contrasts with other wellknown meteoric species such as na and fe .
first , the counterpart of the na and fe layers is a layer of sio , which is predicted to peak around 97  km .
second , the only route to ionize neutral silicon species appears to be charge transfer between sio and o2 
 , whereas metal atoms can also charge transfer with no and undergo relatively fast photoionization [ plane et al . ,
the silicon oxide ions also undergo neutralizing reactions with o3 ( figure  2 and ( r11 ) and ( r15 ) in table  1 ) , which do not occur in the case of other meteoric species ( e.g. , fe and feo ) .
it is therefore particularly striking that si has consistently been observed to be the major meteoric ion around 110  km .
since fe and mg should be the major forms of these two metals at 110  km [ feng et al . , 2013 ; langowski et al . , 2015 ] , this implies that the relative injection rate of si from meteoric ablation , compared to metals such as fe and mg , is significantly larger than expected based on their relative chondritic abundances .
this surprising observation is not yet fully explained . finally , the global abundances of sio and si(oh)4 show clear evidence of the seasonal meteoric input function , which is seen to a much smaller extent in the case of other meteoric reservoir species such as feoh [ feng et al . , 2013 ] , nahco3 [ marsh et al . ,
 abstractsilicon is one of the most abundant elements in cosmic dust , and meteoric ablation injects a significant amount of si into the atmosphere above 80  km . in this study , a new model for silicon chemistry in the mesosphere / lower thermosphere 
 is described , based on recent laboratory kinetic studies of si , sio , sio2 , and si+ . electronic structure calculations and statistical rate theory 
 are used to show that the likely fate of sio2 is a twostep hydration to silicic acid ( si(oh)4 ) , which then polymerizes with metal oxides and hydroxides to form meteoric smoke particles . 
 this chemistry is then incorporated into a whole atmosphere chemistryclimate model . 
 the vertical profiles of si+ and the si+/fe+ ratio are shown to be in good agreement with rocketborne mass spectrometric measurements between 90 and 110  km . 
 si+ has consistently been observed to be the major meteoric ion around 110  km ; this implies that the relative injection rate of si from meteoric ablation , compared to metals such as fe and mg , is significantly larger than expected based on their relative chondritic abundances . 
 finally , the global abundances of sio and si(oh)4 show clear evidence of the seasonal meteoric input function , which is much less pronounced in the case of other meteoric species . 
Introduction
Chemistry of Silicon in the MLT
Neutral Chemistry
Ion Chemistry
Atmospheric Modeling
Discussion
Conclusions