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and CO2 (at 40±60 8C) go to completion in less than 24 h. Alcohols can be used as chaintransfer agents, reducing molecular mass without reduction in polymerization rate.

Measuring phase behaviour

The phase behaviour of the model polymers in CO2 was measured using a high-pressure,variable-volume view cell (D.B. Robinson & Assoc.). This cell is a quartz tube containing a¯oating piston; the entire tube assembly is encased in a windowed, stainless-steel vesselcapable of supporting pressures up to 500 bar. A known amount of solute is added to theview-cell chamber above the piston; the chamber is then sealed and charged with liquidCO2. The pressure on the sample is altered at constant composition via injection of siliconeoil, which moves the ¯oating piston higher in the quartz tube. Initially, the pressure israised to the point where a clear, single-phase solution is obtained. The phase boundary(cloud point, or miscibility pressure) is found subsequently by slowly lowering thepressure until the solution becomes cloudy21,22.

Emulsion experiments

The ability of copolymers to form emulsions in CO2/water mixtures was observed using ahigh-pressure, windowed reactor previously employed for conducting dispersion poly-merizations in CO2 (ref. 23). Water (28% by volume) and surfactant were charged to thereactor, which was then sealed and charged with CO2 to the desired pressure. Stirring wasaccomplished using a high intensity, 3-blade mixer (600 r.p.m.).

Received 10 November 1999; accepted 6 March 2000.

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carbon dioxide at 50 8C. J. Supercrit. Fluids 3, 51±65 (1990),

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6. DeSimone, J. M., Guan, Z. & Elsbernd, C. S. Synthesis of ¯uoropolymers in supercritical carbon

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supercritical carbon dioxide. Macromolecules 28, 8159±8166 (1995).

8. Ghenciu, E. G., Russell, A. J., Beckman, E. J., Steele, L. & Becker, N. T. Solubilization of subtilisin in

CO2 using ¯uoroether-functional amphiphiles. Biotech. Bioeng. 58, 572±580 (1998).

9. Johnston, K. P. et al.Water in carbon dioxide microemulsions: An environment for hydrophiles

including proteins. Science 271, 624±626 (1996).

10. Yazdi, A. V. & Beckman, E. J. Design of highly CO2-soluble chelating agents. 2. Effect of chelate

structure and process parameters on extraction ef®ciency. Ind. Eng. Chem. Res. 36, 2368±2374 (1997).

11. Jessop, P. G., Ikariya, T. & Noyori, R. Homogeneous catalysis in supercritical ¯uids. Chem. Rev. 99,

475±494 (1999).

12. O'Neill, M. L. et al. Solubility of homopolymers and copolymers in carbon dioxide. Ind. Eng. Chem.

Res. 37, 3067±3079 (1998).

13. Rind¯eisch, F., DiNoia, T. P. & McHugh, M. A. Solubility of polymers in supercritical CO2. J. Phys.

Chem. 100, 15581±15587 (1996).

14. Meredith, J. C., Johnston, K. P., Seminario, J. M., Kazarian, S. G. & Eckert, C. A. Quantitative

equilibrium constants between CO2 and Lewis bases from FTIR spectroscopy. J. Phys. Chem. 100,

10837±10848 (1996).

15. Kazarian, S. G., Vincent, M. F., Bright, F. V., Liotta, C. L. & Eckert, C. A. Speci®c intermolecular

interaction of carbon dioxide with polymers. J. Am. Chem. Soc. 118, 1729±1736 (1996).

16. Brandrup, J., Immergut, E. H. & Grulke, E. A.(eds) Polymer Handbook 4th edn Ch. VII, 47±68 (Wiley,

New York,1999).

17. Fink, R., Hancu, D., Valentine, R. & Beckman, E. J. Toward the development of `̀ CO2-philic''

hydrocarbons. 1. Use of side-chain functionalization to lower the miscibility pressure of poly-

dimethylsiloxanes in CO2. J. Phys. Chem. B 103, 6441±6444 (1999).

18. Hoe¯ing, T. A., Enick, R. M. & Beckman, E. J. Microemulsions in near critical and supercritical CO2.

J. Phys. Chem. 95, 7127±7129 (1991).

19. Li, J. & Beckman, E. J. Af®nity extraction into CO2. 2. Extraction of heavy metals into CO2 low-pH

aqueous solutions. Ind. Eng. Chem. Res. 37, 4768±4773 (1998).

20. Triolo, F. et al. Critical micelle density for the self-assembly of block copolymer surfactants in

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Acknowledgements

We thank the US DOE, National Petroleum Technology Of®ce, for their support of ourCO2 enhanced oil recovery research, and the US DOE, National Energy TechnologyLaboratory, for their support of our CO2 well fracturing research.

Correspondence and requests for materials should be addressed to E.J.B.(e-mail: beckman@engrng.pitt.edu).

.................................................................Resolving the `opal paradox'in the Southern OceanPhilippe Pondaven*, Olivier Ragueneau*, Paul TreÂguer*,Anne Hauvespre*, Laurent Dezileau² & Jean Louis Reyss²

* Universite de Bretagne Occidentale UMR CNRS 6539,

Institut Universitaire EuropeÂen de la Mer, Place Copernic, TechnopoÃle Brest-Iroise,

29280 PlouzaneÂ, France² Laboratoire des Sciences du Climat et de l'Environnement,Laboratoire mixte CNRS/CEA, 91191 Gif sur Yvette, France..............................................................................................................................................

In the Southern Ocean, high accumulation rates of opalÐwhichforms by precipitation from silica-bearing solutionsÐhave beenfound in the sediment in spite of low production rates of biogenicsilica and carbon in the overlying surface waters. This so-called`opal paradox' is generally attributed to a higher ef®ciency of opalpreservation in the Southern Ocean than elsewhere1,2. Here wereport biogenic silica production rates, opal rain rates in the watercolumn and opal sediment burial rates for the Indian Ocean sectorof the Southern Ocean, which show that the assumed opal paradoxis a result of underestimated opal production rates and over-estimated opal accumulation rates. Our data thus demonstratethat the overall preservation ef®ciency of biogenic opal in thisregion is substantially lower than previously thought2, and that itlies within a factor of two of the global mean3. The comparison ofour revised opal preservation ef®ciencies for the Southern Oceanwith existing values from the equatorial Paci®c Ocean and theNorth Atlantic Ocean shows that spatial differences in preserva-tion ef®ciencies are not the primary reason for the differences insedimentary opal accumulation. The reconciliation of surfaceproduction rates and sedimentary accumulation rates mayenable the use of biogenic opal in the reconstruction of palaeo-productivity when the factors that affect the Si/C ratio are betterunderstood.

Comparison of hydrographic data from two ANTARES cruises(Southern Ocean±Joint Global Ocean Flux Study) performed in theIndian sector of the Southern Ocean along a 628 E transect, duringearly summer 1994 and late winter 1995, reveals marked seasonalnutrient depletion in some surface waters (Fig. 1): this depletion istypical of the Polar Front zone (PFZ), the permanently open oceanzone (POOZ), and the seasonal ice zone (SIZ). In addition,unaltered remnant winter water is observed at the depth of thetemperature minimum (Fig. 1). The salinity in the remnant winterwater layer is within 0.02±0.2% of that observed at the sea surfaceduring winter. The same observation is valid for silicic acid andnitrate, with a concentration in remnant winter water being within0.7±7% of that at the sea surface (Fig. 1). Thus we calculate thevertically integrated nutrient depletion during summer by referenceto the remnant winter water concentrations4±6, with an uncertainty#7%; we assume that the nutrient depletion by phytoplankton(referred to as DSi for silicic acid and DNO-

3 for nitrate) occurs overa period of 90 days in this area, that is, from early November to earlyFebruary5. We then derive an estimate of daily and annual produc-tion rates of Si, N and C from integrated nutrient depletion (seeMethods).

Figure 2a illustrates the latitudinal variations of the summer/winter contrast in concentrations of dissolved silicic acid andnitrate in the Indian sector of the Southern Ocean. The nutrientdepletion of surface waters reaches a latitudinal average of 13.31 64.94 mmol Si m-3 and 3.01 6 1.16 mmol NO-

3 m-3 (6s.d.), illus-trating the excess of silicic acid utilization compared to nitrateutilization in this region. Note that our estimate of nutrientdepletion may be on the low side as further depletion may haveoccurred later in the season, after the ANTARES 2 cruise. The

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excess of silicic acid utilization compared to nitrate utilization hasbeen also documented for the Atlantic7 and Paci®c8 sectors of thePOOZ. The higher silicic acid depletion compared to nitratedepletion south of the PFZ may originate from the increase of theregenerated nitrogen production during summer5,9, and fromdifferential effects of light10 and nutrient limitation, especially Fe(ref. 11), on the Si/N uptake ratios.

Figure 2b indicates the vertically integrated nutrient depletion atthe early summer ANTARES 2 stations. A signi®cant latitudinalvariation in the magnitude of the silicic acid depletion is seen. Thedepletion of silicic acid is highest in the POOZ, south of the PFZ,with an average of 2.31 6 0.49 mol Si m-2 (6s.d.) between 518 S and588 S (Fig. 2b and Table 1). The latitudinal variations of the nitratedepletion are lower than for silicic acid, ranging from a minimum of

0.14 6 0.07 mol NO-3 m-2 within the SIZ to a maximum of 0.53 6

0.10 mol NO-3 m-2 within the POOZ and the PFZ (Fig. 2b and Table

1). Table 1 gives an estimate of the average daily production rate ofbiogenic silica for the 90 days of the spring±summer period (seeMethods). The production reaches a maximum of 30.3 66.0 mmol Si m-2 d-1 within the POOZ, and values which are 33%lower in the PFZ and 56% lower in the SIZ (Table 2). Conversely, thenitrogen production of 13.5 6 5.5 mmol N m-2 d-1 for the POOZ is16% lower than in the PFZ, and 37% higher than in the SIZ (Table2).

For both the PFZ and the SIZ, our estimates of the daily spring±summer Si and N production rates for 1994 are consistent with insitu measurements obtained for the Indian sector9 or in the Atlanticand Paci®c sectors2,12. For the POOZ however, the estimated daily

Table 1 Estimated production rates for the Indian sector of the Southern Ocean during spring±summer 1994

Provinces* Nutrient depletion² Correction³ f-ratio§ Estimated production rateskover 90 days

DSi DNO-3 CSi CN PSi PN PC

(mil m-2) (mol m-2) (mmol m-2 d-1)...................................................................................................................................................................................................................................................................................................................................................................

PFZ 1.44 6 0.37 0.53 6 0.10 0.38 6 0.03 0.21 6 0.05 0.51 6 0.14 20.2 6 4.4 16.1 6 8.8 90.7 6 49.6POOZ 2.31 6 0.49 0.53 6 0.10 0.42 6 0.05 0.21 6 0.05 0.61 6 0.17 30.3 6 6.0 13.5 6 6.7 76.1 6 37.8SIZ 0.69 6 0.26 0.14 6 0.07 0.51 6 0.10 0.23 6 0.06 0.51 6 0.18 13.3 6 4.0 8.1 6 5.6 45.7 6 31.6...................................................................................................................................................................................................................................................................................................................................................................

* Provinces: Polar Front zone (PFZ; ,518 S), permanently open ocean zone (POOZ; .518 S and ,588 S), and seasonal ice zone (SIZ; $588 S).² Average vertically integrated nutrient depletion (6s.d.) at the Antares 2 stations.³ Average correction (Ci 6 s.d.) from diffusion (Di), plus advection (Ai), and plus regeneration (Ri ) of nutrients within the surface mixed layer. The province average for DSi and DNO3

are 0.04 60.01 mol -2 and 0.01 6 0.01 mol NO-

3 m-2 for the PFZ, 0.08 6 0.03 mol Si m-2 and 0.01 6 0.01 mol NO-3 m-2 for the POOZ, and 0.17 6 0.08 mol Si m-2 and 0.02 6 0.02 mol NO-

3 m-2 for the SIZ. The advectionand the regeneration ¯uxes are assumed to be distributed uniformly throughout the region of study; ASi = 0.28 mol Si m-2 and ANO3

= 0.03 mol N m-2, and RSi = 0.06 6 0.02 mol Si m-2 and RNO3- 0.17 6

0.04 mol N m-2 (see Methods).§ Average f-ratio (6s.d.) using data from Semeneh et al.9

kProvince average daily production rates (6s.d), with PSi = (DSi + CSi)103/90-days and PN = [DNO-3 + CNO3

] 103/f-ratio/90-days. PC is calculated using a C/N elemental molar ratio of 62/11 �ref: 4�.

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Figure 1 Hydrographic properties at three ANTARES stations. Filled circles, the late winter

ANTARES 3 cruise (11±17 October 1994); open circles, the early summer ANTARES 2

cruise (2±7 March 1994). a, Station A17 (628 E±508 30' S) located in the Polar Front

zone (PFZ); b, station A15 (628 E, 538 30' S) located in the permanently open ocean zone

(POOZ); and c, station A12 (628 E, 588 00' S) located at the northern limit of the seasonal

ice zone (SIZ). The unaltered remnant winter water observed at the early summer

ANTARES 2 stations is located at the depth of the temperature minimum, that is, 100±

200 m.

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production of biogenic silica reported in Table 1 is 4±5 times higherthan the highest measurements of 6.76 mmol Si m-2 d-1 recorded inthe Paci®c sector of the POOZ2, and 5±8 times higher than thehighest measurements of 4.40 mmol Si m-2 d-1 recorded during thelate winter and late summer ANTARES 3 and ANTARES 2 cruises13,respectively. Note that the same difference holds for the measuredand estimated nitrogen and carbon production rates. As alreadyargued4, the method used here for estimating the silicon andnitrogen production rates in the surface layer is conservative, as itinherently records short-time events such as blooms which mayhave been missed by discrete sampling in the POOZ. Directmeasurements of biogenic silica export ¯uxes recorded by sedimenttraps deployed in the POOZ at 528 S during austral summer 1994/1995 provide direct evidence for the occurrence of a diatom bloombefore the ANTARES 2 cruise (Fig. 3). Fluxes recorded by traps inlate February 1994 reach a maximum of 12.66 mmol Si m-2 d-1 and

of 1.85 mmol C m-2 d-1 at 1,271 m (Fig. 3), among the highest valuesever recorded for biogenic silica export ¯uxes.

Spring±summer production rates (Table 1) plus the estimateof the autumn±winter production (see Methods) results in anannual biogenic silica production for the POOZ of 3.34 60.54 mol Si m-2 yr-1 (Table 2), being ,3±4 times higher than theupper limit of 1 mol Si m-2 yr-1 proposed by Nelson et al.2. Similarly,the estimated annual carbon production for the POOZ of 8.91 62.79 mol C m-2 yr-1 is ,2±3 times higher than previous estimatesproposed for this area5,14. Note that our estimate of the annualcarbon production for the POOZ is consistent with model-derivedestimates for the same area (7.60 mol C m-2 yr-1, ref. 15), and withrecent results obtained from satellite data16.

Compared with other oceanic basins (Table 2), the estimatedannual biogenic silica production rate for the POOZ is 2±3 timeshigher than in the high-nutrient low chlorophyll (HNLC) equatorial

Table 2 Annual production of biogenic silica, opal rain rate and 230Th-normalized accumulation rates of opal

Flux(mol Si m-2 yr-1)

Indian sector of the Southern Ocean* Equatorial Paci®c Ocean North Atlantic Ocean Global mean

PFZ POOZ SIZ HNLC area² Oligotroph³ Mesotroph§ (ref. 3)...................................................................................................................................................................................................................................................................................................................................................................

Production 2.43 6 0.39 3.34 6 0.54 1.62 6 0.58 1.42 0.24 0.30 6 0.07 0.69 6 0.12Rain ± 0.51 0.05 0.14 0.02 0.062 6 0.025 0.08 6 0.05Accumulation 0.075 6 0.042 0.210 6 0.040 ± 0.016 0.001 0.008 0.017 6 0.003WCPE (%)k ± 15.3 6 2.5 3.1 6 1.1 9.9 8.3 20.7 6 13.2 11.6 6 9.2OPE (%)¶ 3.1 6 2.2 6.3 6 2.2 ± 1.1 0.4 2.7 6 0.6 2.5 6 0.9...................................................................................................................................................................................................................................................................................................................................................................

* This study. Average annual production rates (P*Si 6 s.d.) estimated at the ANTARES 2 transect (1994); P*

Si = DSi + CSi + WSi, with DSi and CSi as reported in Table 1, and with the winter±autumn production(WSi) varying from 0.61 mol Si m-2 within the PFZ and the POOZ to 0.42 6 0.22 mol Si m-2 within the SIZ (see Methods). Annual rain rates measured by means of sediment traps (depth $ 3,000 m) betweenFebruary 1994 and February 1995; POOZ: 528 S±618 E; SIZ: 638 S±708 E (ANTARES programme). 230Th-normalized accumulation rates (6s.d.) in the same region; PFZ: cores KTP11 (498 S±588 E) andKTB13 (508 S±588 E); POOZ: cores KTB06 (528 S±618 E), MD84-551 (558 S±738 E) and MD84-552 (558 S±718 E).² Equatorial Paci®c; references: production (ref. 17); rain rate (ref. 20); accumulation (ref. 26).³ Western Sargasso Sea; references: production (ref. 18); rain rate (ref. 21); accumulation (ref. 27).§ Northeast Atlantic; references: production (ref. 15 and O.R., unpublished data); rain rate and accumulation (O.R., unpublished data).kWCPE: water column preservation ef®ciency (rain/production).¶ OPE: overall preservation ef®ciency (accumulation/production). Note that the historical estimates for production and accumulation rates in the PFZ and POOZ were 1.0 mol Si m-2 yr-1 (ref. 2) and 0.40±0.42 mol Si m-2 yr-1 (without correction from focusing; ref. 25), respectively; that is, an OPE of ,40% for this area.

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the Indian sector of the Southern Ocean during summer 1994. a, Concentrations of

dissolved silicic acid (circles) and nitrate (squares) in the summer surface water (open

symbols) and remnant winter water (®lled symbols) of the Indian sector of the Southern

Ocean at the early summer ANTARES 2 stations. b, Estimated vertically integrated nutrient

depletion of silicic acid (circles) and nitrate (squares) at the early summer ANTARES 2

stations (67%). The dashed line indicates the depth of the mixed layer. The position of the

Polar Front (PF) during early summer 1994 is indicated with the dotted line; the

northernmost limit of the winter ice cover is also indicated (WIC). These limits de®ned the

three provinces, namely the Polar Front zone (PFZ), the permanently open ocean zone

(POOZ) and the seasonal ice zone (SIZ). A17, A15 and A12 are the position of the stations

reported in Fig. 1.

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Paci®c17, and more than one order of magnitude higher than in theAtlantic Ocean (refs 15 and 18, and O.R., unpublished data).Similarly, water-column annual export ¯uxes in the POOZ of0.51 mol Si m-2 yr-1 (Table 2) are the highest reported19. They are3±4 times higher than in the equatorial Paci®c20 and 4±25 timeshigher than in the North Atlantic (ref. 21 and O.R., unpublisheddata). Combining production and sediment-trap data results in anestimate of water-column preservation ef®ciency of 15.3 6 2.3% forthe POOZ (Table 2). This value is 23±53% higher than the value forthe oligotrophic Atlantic or the HNLC equatorial Paci®c, butsimilar to the value for the mesotrophic northeast Atlantic(Table 2). We note that the areas with the highest opal water-column preservation ef®ciency are sites with a high seasonality22,and exhibit the highest export/production ratio for carbon22.

These results have implications in the context of the `opalparadox', by which high opal accumulation would occur in sedi-ments despite low production of biogenic silica in overlying surfacewaters2. Nelson et al.2 suggested an overall preservation ef®ciencysubstantially higher than anywhere else as an explanation for thisparadox. However, the calculations we report above can be com-bined with opal accumulation rates to calculate overall preservationef®ciencies. Note that opal accumulation rates may be affected bypost-depositional sediment redistribution by bottom currents. Thisproblem has been alleviated here by normalizing opal ¯ux to excess230Th activity in sediments23,24, a method that corrects for sedimentfocusing or winnowing and provides estimates of preservedaccumulation rate. Thus, an opal accumulation rate of 0.210 60.040 mol Si m-2 yr-1 can be estimated for sediments underlying theIndian sector of the POOZ; this rate is ,2 times lower thanpreviously thought25 (Table 2). Although focusing has beencorrected for, this value is respectively 12, 31 and 185 timeshigher than for the equatorial Paci®c26, the mesotrophic northeastAtlantic (O.R., unpublished data) and the oligotrophic Atlantic27

(Table 2). The overall preservation ef®ciency of 6.3 6 2.2% inferredfor the POOZ is thus 5±10 times lower than the value of 40%previously thought (Table 2). A similar observation is valid for the

PFZ with an overall preservation ef®ciency of 3.1 6 2.2%, that is,7±45 times lower than previously thought (Table 2). This calcula-tion shows that the overall preservation ef®ciency for the Indiansector of the POOZ is only ,2 times higher than the global mean of2.5 6 0.9% (ref. 3); it is also only ,2 times higher than, for example,the value for the northeast Atlantic where little opal accumulates(Table 2). For the PFZ, the overall preservation ef®ciency is similarto the global mean and to the value for the northeast Atlantic.

This calculation shows that opal accumulation is higher in theSouthern Ocean than anywhere else; this is mostly because of ahigher biogenic opal rain rate, in turn due to higher biogenic silicaproduction rates in surface waters. Spatial differences in opalpreservation play a role, but as a modulation factor only and notas a primary factor. This conclusion has implications for the use ofthe opal sedimentary record as a proxy for past export siliceousproductivity. If opal is to be used as a tracer of palaeoproductivity(and of the ef®ciency of the biological pump) in response to pastclimate change, we need to achieve a better understanding of thefactors controlling the degree of coupling between the silicon andcarbon biogeochemical cyclesÐboth in the water column and inthe sediments. M

MethodsBiogenic silica daily production rates

Estimates of biogenic silica daily production rates are derived from integrated silicic aciddepletion (DSi) by taking into account, during the 90 d of the productive period, the inputof silicic acid into the surface layer by (1) vertical diffusion (DSi), (2) lateral advection(ASi), and (3) the regeneration of silicic acid through dissolution of biogenic silica withinthe surface mixed layer (RSi). Thus, the spring±summer production of biogenic silica (PSi)is written:

PSi � DSi � DSi � ASi � RSi �1�

The diffusive ¯ux of silicic acid through the pycnocline during spring±summer, DSi, iscalculated using the diffusion coef®cient Kz = 0.5 cm2 s-1 (ref. 28), and the vertical gradientof silicic acid at the ANTARES 2 stations. From north to south, this gradient rangesbetween 0.09 to 0.66 mmol Si m-4, with maxima occurring within the SIZ. Thus, thecalculated diffusion rates varies from 0.33 within the PFZ to 2.89 mmol Si m-2 d-1 withinthe SIZ, or 0.03±0.26 mol Si m-2 integrated over a period of 90 d. The advective ¯ux, ASi, iscalculated assuming a permanent input of silicic acid at the Antarctic Divergence (AD),and a permanent output of silicic acid through the Antarctic Intermediate Water (AAIW)at the Polar Front (PF), following the calculation proposed by Jacques5. Thus, we assumethat ASi is distributed uniformly over the transect. The concentration of silicic acid in the¯ow entering the surface layer at the AD is ,60 mmol m-3; in the AAIW it has droppeddown to ,15 mmol Si m3. With a surface area of 26 ´ 1012 m2 between AD and PFZ, thenorthward current being 18 ´ 1011 m3 d-1, we infer a mean silicic acid advective ¯ux of3.11 mmol Si m-2 d-1 (that is, 0.28 mol Si m-2 per 90 d). Although a uniform distributionof ASi is assumed, the error introduced may be small compared to the value of DSi (Table 1).

The regeneration term RSi is estimated from the latitudinal-average biogenic silicaconcentration within the mixed layer during summerÐ70.92 6 26.20 mmol Si m-2 alongthe ANTARES 2 transect13Ðassuming the speci®c dissolution rate of biogenic silica to be0.010 d-1 for this region29. Thus, the dissolution rate within the mixed layer for theIndian sector is estimated to be 0.71 6 0.26 mmol Si m-2 d-1, that is, RSi equals0.06 6 0.02 mol Si m-2 per 90 d. Note that RSi is assumed to be uniform throughout thestudied area. Although this may not be strictly true, the numerical value of RSi is smallcompared to the other terms (Table 1).

Nitrogen daily production rates

Estimates of nitrogen production rates are derived from vertically integrated nitratedepletion by taking into account the same correcting factors as for biogenic silica. Thus,the spring±summer production of particulate organic nitrogen (PN) is written:

PN � �DNO 23 � DNO3

� ANO3� RNO3

�=f -ratio �2�

From north to south, the nitrate gradient ranges from 0.02 to 0.14 mmol NO-3 m-4. Thus,

the diffusive ¯ux of nitrate, DNO3, varies from 0.11 to 0.56 mmol NO-

3 m-2 d-1 (equivalentto 0.01±0.05 mol NO-

3 m-2 per 90 d). In addition, the advective ¯ux, ANO3, is estimated to

be 0.28 mmol NO-3 m-2 d-1 (ref. 5) (equivalent to 0.03 mol N m-2 per 90 d).

For the late summer ANTARES 1 stations, the average nitrite oxidation rate is1.92 6 0.42 mmol N m-2 d-1 (ref. 30); that is, RNO3

equals 0.17 6 0.04 mol N m-2 per 90 d.In addition, in equation (2), the fraction of total nitrogen production sustained by

ammonium or urea is deduced from shipboard determination of the f-ratio at theANTARES 2 stations9 (Table 1).

Estimate of the annual Si and C production

The calculation of the annual Si and C production (P*Si and P*

C) requires the estimation of

0

2

4

6

8

10

12

14

J F M A M J J A S O N D J F

a

0.0

0.5

1.0

1.5

2.0

J F M A M J J A S O N D J F

b

Month

mm

ol C

org

m–2

d–1

mm

ol S

i m–2

d–1

Figure 3 Average daily export ¯uxes of particulate organic Si and C in the Indian sector of

the Southern Ocean. a, Data for biogenic silica, and b, data for organic carbon, measured

by sediment traps at 528 S±628 E in the Indian sector of the Southern Ocean (POOZ)

between January 1994 and January 1995 (ANTARES Southern Ocean-JGOFS

programme; P.T., unpublished data). The sediment traps were positioned at depths of

1,271 m (bold line) and 4,023 m (thin line). The arrows represent the period of the

ANTARES 2 cruise (2±7 March 1994).

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letters to nature

172 NATURE | VOL 405 | 11 MAY 2000 | www.nature.com

the part of the production that takes place during autumn and winter (WSi and WC, whichencompass 275 d). Thus, the annual production of Si and C are written:

PpSi � PSi � W Si �3a�

PpC � PN�C=N� � W C �3b�

In equation (3b), C/N = 62/11 (mol mol-1) is the cellular elemental composition for thisarea4. The autumn±winter productivity is estimated from discrete measurements of Si andC production rates, using the 32Si and 14C isotopic technique, during the late winterANTARES 3 cruise13. In the ice-free area, the productivity was 2.2 mmol Si m-2 d-1, and7.5 mmol Cm-2 d-1. Assuming constancy throughout winter and autumn in the ice-freearea, this leads to a maximum of WSi = 0.61 mol Si m-2 and WC = 2.06 mol C m-2. Note thatthese values are consistent, within 615%, with model-derived estimates of winter andautumn production for the ice-free Indian sector of the Southern Ocean15. South of 588 S,that is, the northernmost limit of the ice extent during winter, WSi and WC were correctedusing estimates of the seasonal ice-cover from the ERS1 satellite. For each month, weassume that the production is negligible when a station is totally covered by sea ice.

Combining Tables 1 and 2 shows that the spring±summer production represents from70% (PFZ) to .90% (SIZ) of the annual biogenic silica production.

Received 22 October; accepted 1 March 2000.

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Acknowledgements

We thank J. Morvan, C. Jeandel, M. Fiala and P. Mayzaud for taking care of the mooringsand sediment traps during the ANTARES programme; the of®cers, engineers and crew ofRV Marion Dufresne for their help during the ANTARES cruises; CERSAT (IFREMER/PlouzaneÂ, France) for providing ERS1 satellite estimates of the seasonal ice-cover; R.Lampitt and A. Gooday for taking care of the moorings, sediment traps and multiple coresduring the BENGAL programme in the North East Atlantic; and R. C. Dugdale forcritically reading the manuscript. This work was supported by ReÂgion Bretagne (P.P.), theInstitut National des Sciences de l'Univers (INSU/CNRS), and the French Polar ResearchInstitute (IFRTP/CNRS).

Correspondence and requests for materials should be addressed to P.P.(e-mail: philippe.pondaven@univ-brest.fr).

.................................................................Constraints on the compositionof the Earth's corefrom ab initio calculationsD. AlfeÁ*, M. J. Gillan² & G. D. Price*

* Research School of Geological and Geophysical Sciences, Birkbeck College and

University College London, Gower Street, London WC1E 6BT, UK² Physics and Astronomy Department, University College London, Gower Street,

London WC1E 6BT, UK

..............................................................................................................................................

Knowledge of the composition of the Earth's core1±3 is importantfor understanding its melting point and therefore the tempera-ture at the inner-core boundary and the temperature pro®le of thecore and mantle. In addition, the partitioning of light elementsbetween solid and liquid, as the outer core freezes at the inner-core boundary, is believed to drive compositional convection4,which in turn generates the Earth's magnetic ®eld. It is generallyaccepted that the liquid outer core and the solid inner core consistmainly of iron1. The outer core, however, is also thought tocontain a signi®cant fraction of light elements, because itsdensityÐas deduced from seismological data and other measure-mentsÐis 6±10 per cent less than that estimated for pure liquidiron1±3. Similar evidence indicates a smaller but still appreciablefraction of light elements in the inner core5,6. The leading candi-dates for the light elements present in the core are sulphur, oxygenand silicon3. Here we obtain a constraint on core compositionderived from ab initio calculation of the chemical potentials oflight elements dissolved in solid and liquid iron. We presentresults for the case of sulphur, which provide strong evidenceagainst the proposal that the outer core is close to being a binaryiron±sulphur mixture7.

Our proposed constraint is simply stated. If, as commonlyassumed, the solid and liquid are in thermodynamic equilibriumat the inner-core boundary (ICB), the chemical potentials of a givenelement in both phases must be equal at the boundary. Thiscondition determines the ratio of concentrations of elements inthe solid and the liquid phase, and hence the relation between theouter-core and inner-core densities, which must agree with seismicmeasurements of these densities.

The chemical potential mX of a solute X in a solid or liquidsolution is conventionally expressed as mX � m²

X � kBT ln aX , wherem²

X is a constant and aX is the activity8. To re¯ect the fact that aX

becomes equal to the mole fraction cX in the dilute limit cX ! 0, it iscommon practice to write aX � gXcX , where the activity coef®cient,gX, has the property gX ! 1 as cX ! 0 (ref. 8). Here we rearrange theexpression for mX as mX � mÄX � kBT ln cX , where mÄX is de®ned to beequal to m²

X � kBT ln gX. Equality of the chemical potentials mlX and

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