The terminal bulk Lorentz factor of relativistic electron-positron jets

Chemical Engineering Science62(2007)1948–1957/locate/cesStructure and rate of growth of whey protein deposit from in situ electrical conductivity during fouling in a plate heat exchanger Romuald Guérin,Gilles Ronse,Laurent Bouvier,Pascal Debreyne,Guillaume Delaplace∗UR638,Génie des Procédés et Technologie Alimentaires,INRA,F-59651,Villenueve d’Ascq,FranceReceived7August2006;received in revised form13December2006;accepted15December2006Available online30December2006This paper is dedicated to the memory of Dr Jean-Claude LeulietAbstractThe influences of calcium concentrations(70.88mg/l),Reynolds number(2000–5000)and temperature(60.96◦C)upon the deposit structure and the rate of growth deposition have been investigated in a plate heat exchanger.This was done from in situ measurements of the deposit electrical conductivity via implementation of stainless steel electrodes in channels combined with assessments of deposit thickness.Calcium ions affect structures of deposits and increase the rate of deposit growth upon heated surfaces.This was attributed to the formation of weaker size aggregates at higher calcium concentrations and a higher number of calcium bindings,which reinforce adhesion forces between protein aggregates.Structures and appearances of deposits also were affected byflow rates whatever the calcium concentrations.Deposit growth rate was enhanced by increasingflow rate below a critical Reynolds number comprised between3200and5000.On the contrary,above the critical Reynolds number,a limitation of the deposit and/or an escape of the deposit from the fouled layer into the corefluid occurred,caused by the predominance of particle breakage on the deposit formation.Fouling tended to be reduced at higherflow rate.It was noteworthy that rates of growth decrease during fouling experiments which may be explained by an increase in local shear stresses leading to particle breakage.᭧2007Elsevier Ltd.All rights reserved.Keywords:Fouling;Whey protein;Calcium ions;Reynolds number;Shear stress;Deposit structure;Plate heat exchanger;Electrical conductivity1.IntroductionPlate heat exchangers(PHEs)are widely used in food indus-tries.Several advantages in using PHEs have been discussed elsewhere(Corrieu,1980;Bond,1981).The main problems en-countered by users of heat exchangers are linked to fouling,cor-rosion or mechanical resistance.Bott(1992)shows that fouling of heat exchangers,classically observed with dairy products, is in the front row of the industrial preoccupations.Fouling of heated surfaces directly contributes toward increased costs in production and energy losses,cleaning,and hinders a constant product quality and overall process efficiency(Yoon and Lund, 1989;Delplace et al.,1994;Jeurnink and de Kruif,1995;Visser and Jeurnink,1997).∗Corresponding author.E-mail address:delapla@lille.inra.fr(G.Delaplace).0009-2509/$-see front matter᭧2007Elsevier Ltd.All rights reserved. doi:10.1016/j.ces.2006.12.038In dairy industries,deposits consist of a layer of protein aggregates and minerals(Tissier and Lalande,1986).Among all milk proteins, -lactoglobulin has been identified as one of the major contributors to fouling as it undergoes thermal denaturation(Lalande et al.,1985;Lalande and Rene,1988; Gotham et al.,1989).Consequently,whey protein concentrate (WPC)solutions often have applied as a modelfluid to mimic fouling reactions during pasteurisation of milk both in the bulk and in the deposit at heat surfaces.There has been a considerable amount of work showing that fouling affects hydrodynamic and thermodynamic perfor-mances of heat exchangers.These studies,carried out with different dairy product compositions and process conditions, put forward the main parameters which interfere upon the foul-ing deposit mass(De Jong et al.,1992;Belmar-Beiny et al., 1993;Delplace et al.,1994;Delplace and Leuliet,1995;Fryer et al.,1996;Changani et al.,1997;Visser and Jeurnink,1997;R.Guérin et al./Chemical Engineering Science62(2007)1948–19571949Christian et al.,2002;Prakash et al.,2006).The main param-eters were for instance wall temperatures andflow rate as pro-cess parameters and ionic force,type of ions,pH and protein concentration as chemical composition parameters.All these works represent an important step forward in the generation of predictive models both on -lactoglobulin denatu-ration or global thermal performance degradation for the whole heat exchangers(Fryer and Slater,1985;De Jong et al.,1992; Delplace et al.,1994;Fryer et al.,1996;Visser and Jeurnink, 1997).Unfortunately,these models are not powerful enough to explain the distinct cleaning behaviours experimentally ob-served.For instance,Christian et al.(2002)showed that overall cleaning times and cleaning rates,under standard conditions, were dependant on the deposit composition.There is a lack of knowledge concerning the influence of deposit structure and kinetic of deposit mass upon the cleaning efficiency to get rid off the total mass deposit.To overcome these difficulties,stud-ies that report the effect of process parameters and composi-tion upon the structure of the fouled layer are required.The aim of this work was partly to contribute to thisfield.In par-ticular,various controlled conditions offlow rate and calcium concentration of a WPC solution in a PHE were carried out to determine the influence of these parameters upon the structure and the kinetic of fouled layers.The structure and the growth of the fouled layer were estimated in-line from in situ measurements of the electrical conductivity of the fouled deposit.This was done by the im-plementation of two opposite stainless steel electrodes in PHE channels.In the last section,the electrode system was imple-mented in various channels to determine the influence of the temperature upon the deposit.2.Materials and methods2.1.ModelfluidThe modelfluid used in this study was reconstituted from WPC75supplied by Armor Proteines(France).The compo-sition of the powder as given by the manufacturer is shown in Table1.Proteins are the main components of the WPC pow-der(76%w/w)in which -lactoglobulin and -lactalbumin represent63%(w/w)and11%(w/w),respectively.Minerals represented less than4%(w/w)of the total dry weight of the powder.To produce solutions with higher mineral concentra-tion,the powder was dispersed in controlled quality water. Water consisted of a mixture of tap water of Lille(France)and soft water using a water softener(HI-FLO1,Culligan, Purolite C100E resin,France).The calcium and sodium con-tents of tap water,determined by atomic absorption spectropho-tometry(Philips,Pye Unicam),varied in the range170–200 and44–64mg/l,respectively.The range of calcium and sodium contents of the soft water were1.0–3.0and304–341mg/l, respectively.The desired content of calcium of the fouling fluid was obtained by mixing raw water,soft water and afixed amount of powder(1%w/w).Water electrical conductivity var-ied from0.113to0.116S/m at20◦C for calcium concentration varying from35to55mg/l.The product electrical conductivity Table1Composition of WPC powder(Armor Protéines,France)and1.0%WPC solutionComponent WPC75powder(%w/w)1.0%WPC75solution(%w/w) Water 5.599.05Lactose100.1Lipids 3.70.037Protein760.76Casein––-lactoglobulin480.48-lactalbumin8.40.084Other19.80.198Minerals40.04Calcium0.450.007–0.00875 Sodium0.700.0277–0.0472 Potassium0.33N.D.Chloride0.40N.D. Phosphorus0.30N.D. Magnesium0.045N.D.Iron0.008N.D.Other 1.77N.D.Other0.8N.D.:Not determined.Fig.1.Schematic of the experimental setup.varied from0.142to0.146S/m at20◦C for a range of calcium of70–90mg/l.The addition of protein powder to the mixing of water modified the electrical conductivity value of20%. The pH of the modelfluid remained between7.3and7.7.2.2.Fouling experimentThe experimental set-up of pilot plant scale is shown in Fig.1.Although there are two heat exchangers(model V7 plates,Alfa-Laval Vicarb,France)in the setup,the fouling1950R.Guérin et al./Chemical Engineering Science 62(2007)1948–1957ELECTRICAL CONDUCTIVITY SENSOR TEMPERATURE PROBE Pi PLATE NUMBERCi RODUCT CHANNEL NUMBERHOT WATER HOT WATER Fig.2.Heating plate heat exchanger flow arrangement and implementation of stainless steel electrodes inside channels.observations were focused on the second.The first one was used only to pre-heat the model fluid up to 60◦C where fouling was negligible.Water was used as the heating medium.The model fluid was heated from 60to 96◦C in a countercurrent mode.The choice of temperatures was made taking into account the value of the denaturation temperature of the -lactoglobulin protein.Temperature value for the denaturation of -lactoglobulin is 74.76◦C (Matsudomi et al.,1991;Xiong,1992;Gotham et al.,1989;Liu et al.,1994).PHE setup consisted of 13plates form-ing six passes of one channel for the two sides (Fig.2).The equivalent space between two consecutive plates was 3.93mm.In order to keep the feed composition constant,the fluid was not re-circulated once it was heated through PHEs.During ex-periments,the inlet temperature of hot water was adjusted to ensure a constant outlet model fluid temperature close to 96◦C and a constant profile of product temperature along the PHE as a function of time (i.e.,constant heat flux).The fluid foul-ing layer interface temperature in each channel was assumed constant during fouling runs.In the beginning,the PHE was brought to thermal equilibrium and desired process temperature using reverse osmosis (RO)water.The feed was switched from RO water to model fluid and the experimental run was contin-ued for 330min.After the fouling experiment,model fluid was replaced by cold RO water to bring the temperature of PHE and deposits to ambient temperature.Experiments were performed for various calcium concentrations and Reynolds numbers as shown in Table 2.Reynolds numbers were computed based on physical properties of water,assuming that the presence of 1%WPC in water does not modify them significantly.Average Reynolds number for the clean heat exchanger was determined from the distribution of Re along the PHE (Re =2 Q/ w ).Inlet and outlet model fluids and hot water temperatures were measured with platinum resistance probes (type pt100)with a precision of 0.1◦C.Bulk and wall temperatures in chan-nels were measured from J-type thermocouples with a preci-sion of 0.5◦C.Flow rates were measured using electromag-netic flowmeters (Krohne IFM,Germany).All parameters were collected via a data acquisition system (Agilent Technologies 34970A,USA)with an acquisition period of 30s.2.3.Measurements of fouled layer thicknessDeposit thickness on the different plates was obtained by two ways:•Using a pneumatic lifting device of a uniaxial compres-sion machine (DY30Model,Adamel Lhomargy,TMI,USA)which allows to determine the distance between the support of the device and the upper of the fouled or cleaned plate as shown in Fig.3.The precision of the measurement was 0.01mm.The assessments were performed at nine positions on the plate surface.The average value of the deposit thick-ness was computed from the nine positions.•By weighing plates before and after fouling runs using a Mettler apparatus (PM3000,Switzerland)with a preci-sion of 0.1g.From a wet deposit density value equal to 1000kg /m 3(Lalande et al.,1985),the average deposit thick-ness upon each plate was obtained.Of course,this method assumes that the deposit occurs uniformly upon the plate surface.2.4.Electrical conductivity of the depositTwo AISI 304L stainless steel electrodes 0.015×0.01m were implemented in channels C3,C5and C6(Fig.2).Elec-trodes were connected to a commercial conditioning system (STRATOS 2402Cond,Knick,Germany).Electrodes were electrically insulated from metal plates using an insulating stick (Araldite A V138M-HV998,USA).The cell constant of the de-vice was determined with salt solutions whose electrical con-ductivity value was known with precision.The stainless steel electrodes provide an indication of the equivalent electrical resistance R eq through the channel (Fig.4).For fixed operating conditions,the Kirchhoff’s rule allows decoupling the equivalent electrical resistance in terms of fouling fluid electrical resistance (R p )and deposit electrical resistance (R d )as follows:R eq =R p +2R d .(1)R.Guérin et al./Chemical Engineering Science 62(2007)1948–19571951T a b l e 2S u m m a r y o f m e a s u r e d a n d c a l c u l a t e d p a r a m e t e r s d u r i n g h e a t t r a n s f e r t o s t u d y f o u l i n g b e h a v i o u r o f 1%W P C s o l u t i o nR u n M e a n R e (–)C a 2+(m g /l )N a +(m g /l )i ,p (◦C ) o ,p (◦C ) i ,h w (◦C ) o ,h w (◦C )M a s s o f d e p o s i tt =0t ft =0t f t =0t f t =0t fi n c h a n n e l 5(g )A 200072.9344.062.360.096.897.2102.5104.572.873.471.9B 200378.9303.260.059.796.596.6102.6107.771.976.0118.6C 204082.2280.061.561.397.196.3102.7107.973.479.1147.1D 204085.6277.460.461.595.896.9102.0109.271.980.4180.6E 339470.0323.663.863.995.595.7102.0107.475.080.8100.3F 322076.3472.061.361.395.795.5101.7115.973.489.1170.0G 321478.0364.962.662.295.095.0100.0112.374.083.9201.2H 323286.5331.262.763.694.694.6101.4121.773.293.2240.6I 493874.6329.060.861.495.495.2103.4110.974.383.490.2J 492077.4303.061.360.896.296.0103.1113.574.084.994.2K 494277.8340.063.263.995.495.1103.0111.875.286.8116.6L 492687.4306.061.261.495.995.7103.5121.374.393.3190.5R u n¯e d (M D -5)(m m )¯e d (U C M )(m m )w *(◦C ) b (◦C ) e q *(S /m ) p a t b (S /m ) p a t 100◦C (S /m ) d *a t w (S /m )d *a t 100◦C (S /m )k ×104(S /m m i n )A 0.480.4097.991.10.3030.3600.3880.2080.2101.90B 0.800.61101.990.60.3030.3730.4030.2630.2612.33C 0.980.92102.491.60.3070.3710.3980.2850.2832.82D 1.201.16105.490.10.2970.3720.4040.2750.2703.57E 0.670.69103.689.70.2480.3610.3940.1700.1673.96F 1.201.28112.289.70.2840.4720.5040.2510.2408.19G 1.341.42108.889.30.2320.3750.4090.2240.2166.50H 1.601.55118.789.80.3320.4770.5090.3370.3206.88I 0.600.59105.289.80.2460.3910.4230.1470.1425.67J 0.630.63108.590.10.2250.3600.3920.1410.1335.60K 0.780.75106.889.50.2130.3690.4020.1510.1454.75L 1.271.37121.189.80.2730.3790.4110.2280.2096.70p , d a n d e q :f o u l i n g p r o d u c t ,d e p o s i t a n d e q u i v a l e n t e l e c t r i c a l c o n d u c t i v i t y ,r e s p e c t i v e l y ; i ,p a n d o ,p :i n l e t a n d o u t l e t t e m p e r a t u r e o f t h e p r o d u c t ; i ,h w a n d o ,h w :i n l e t a n d o u t l e t t e m p e r a t u r e o f t h e h o t w a t e r ; w a n d b :w a l l a n d b u l k t e m p e r a t u r e i n c h a n n e l 5;¯ed (U C M ):a ve r a g e d e p o s i t t h i c k n e s sf r o m t h e u n i a x i a l c o m p r e s s i o n m a c h i n e ;e d (M D -5):d e p o s i t t h i c k n e s s f r o m m a s s d e p o s i t i n c h a n n e l 5;k :r a t e o f c h a ng e o f th e e q ui v a l e n t e l e c t r i c a l c o n d u c t i v i t y .∗A t330m i n .1952R.Guérin et al./Chemical Engineering Science 62(2007)1948–1957Based on the general relationship linking the electrical resis-tance to the electrical conductivity for a pair of electrodes [ =e E /(AR)with e E the length between the electrodes,A the cross-section and R the electrical resistance]and assuming that (i)the cross-section A is a constant value and (ii)the space of the fluid flow (e fl)is defined as the difference between thespace0.000 N0.005 N e 10.000 N0.005 N e 2Fouling layerStainless steel plateacbdFig.3.The thickness measurement technique using a pneumatic lifting device of a uniaxial compression machine (DY30Model,Adamel Lhomargy,TMI,USA).P 8P 9Isolating materia l Stainless steel electrodes Fluid flow Fouling layer R eqR dR dRp ABFlow directioneEFig.4.Schematic of the fouling layer and equivalent electric resistance diagram.separating the two electrodes (e E )minus the total deposit thick-ness (2e d )(Eq.(2)),the deposit electrical conductivity (DEC, d )can be expressed as a function of model fluid ( p )and equivalent ( eq )electrical conductivities as shown in Eq.(3).e fl=e E −2e d ,(2)d (t =t f )=e E2e d (t =t f ) 1eq (t =tf )−1p+1p−1.(3)At the beginning of the fouling experiment (i.e.,clean PHE),the value of the equivalent electrical conductivity,measured by the device,corresponded to the electrical conductivity of the model fluid ( p )at the product temperature.The electrical con-ductivity of the model fluid was invariant during fouling runs since the inlet temperature of hot water was adjusted to ensure a constant product temperature inside channels as a function of time.At the end of fouling runs (i.e.,fouled plates,t =t f )the deposit thickness was measured and the measurement of the equivalent electrical conductivity allowed to obtain the electri-cal conductivity of the deposit.In order to compare electrical conductivity values of each run,all conductivities were deter-mined at 100◦C as follows (Ayadi,2005): d(100◦C )= d( w )+0.0009×(100− w ), p(100◦C )= p( b )+0.0032×(100− b ),(4)where d(100◦C )represents the DEC value at 100◦C, d( w )is the DEC determined from Eq.(3)at the end wall tempera-ture w , p(100◦C )is the electrical conductivity of the fouling product at 100◦C, p( b )represents the value of the electrical conductivity of the product at the bulk temperature b .Considering a deposit temperature nearly constant and an invariant viscosity value for the product,the only parametersR.Guérin et al./Chemical Engineering Science 62(2007)1948–195719530.20.220.240.260.280.30.320.340.360.380.4Time, (min )E q u i v a l e n t e l e c t r i c a l c o n d u c t i v i t y , (S m -1)Fig.5.Equivalent electrical conductivity during fouling run using 1.0%WPC solution with calcium concentration 78.0mg /l at Re =3200.which affect DEC values are mobility and concentration of ions (Benoıˆt and Deransart,1976).However,considering a poor mobility and diffusion of ions from the bulk fluid through the fouled layers due to protein networks,the DEC values are affected in the majority by the concentration of ions embedded inside the protein structure.Thus,these values constitute a good indicator of the deposit structure.3.Results and discussion3.1.Effect of calcium content on foulingTypical equivalent electrical conductivity change as a func-tion of time,measured in-line from the electrodes in the fifth channel,is illustrated in Fig.5.After the switch from RO water to fouling fluid,the equivalent electrical conductivity reaches a maximum value at t =15min.This value corresponds to the electrical conductivity of the product at the bulk temperature.Data reported in Table 2show that product electrical conduc-tivity values at 100◦C are little affected by the modification of the ionic concentration (i.e.,calcium and sodium in the tested range of concentration)of the solution.At the beginning of fouling stages,very slow decreases in equivalent electrical conductivity are recorded with an initial rate k ∗(Fig.5).This region may be attributed to a homogeneous thin layer of irreversibly adsorbed individual protein molecules on clean metal surfaces (Arnebrant et al.,1985;Visser and Jeurnink,1997).Tissier and Lalande (1986)showed that this sublayer had a thickness of 0.02 m after only few minutes of contact;0.4and 1 m after 10and 30min of fouling run.This weak thickness may explain the slight decrease of the slope between t =15and 30min.The slightly decreasing slope (k ∗)indicates that the fouling mechanism starts immediately when fouling product is present in the heating zone,for a temperature higher than unfolding temperature of -lactoglobulin.After this period,the equivalent electrical conductivity decreases24681060657075808590Calcium content, (mg/l)k x 104, (S .m -1.m i n -1)parison of rates of deposit growth (k )as a function of calcium concentration in WPC solution for Re =2000,3200and 5000.(The trend lines represent the curve fit of data .)linearly with time.The rate of electrical conductivity changes k is relatively high (Fig.5).The second decrease in eq may be attributed to the growth and structure changes of fouled layers.Indeed,whatever the Reynolds number,it is observed that the rate of electrical conductivity changes k rises with in-creasing calcium concentrations (Fig.6).This observation is in agreement with Li et al.(1994)observing that calcium induces conformational changes of the -lactoglobulin,facilitating the protein denaturation,but also increases the kinetic of the aggregate formation.A small change in the calcium concen-tration has an important impact upon the kinetic parameter k ,i.e.,the formation of the fouled layer.Fig.7a illustrates the electrical conductivity values of the fouled layer (DEC)obtained at a wall temperature of 100◦C in the fifth channel for varying calcium concentrations at three Reynolds numbers.Whatever the Reynolds number,the DEC increases with the calcium concentration.Considering a low mobility of ions inside the deposit due to protein networks and a constant temperature in C5,this indicates that the DEC1954R.Guérin et al./Chemical Engineering Science 62(2007)1948–19570.10.20.30.4Calcium concentration,(mg.l -1)E l e c t r i c a l c o n d u c t i v i t y o f t h e d e p o s i t , (S .m -1)00.20.40.60.811.21.41.61.8Calcium concentration, (mg.l -1)F o u l e d l a y e r t h i c k n e s s e d , (m m )05001000150020002500300035004000Calcium content, (mg/l)A m o u n t o f d e p o s i t i n c h a n n e l 5, (g /m 2)parison of (a)deposit electrical conductivity at 100◦C,(b)fouled layer deposit and (c)amount of deposit in channel 5after 5.5h of heat transfer in PHE as a function of calcium concentration in WPC solution for Re =2000,3200and 5000.(The trend lines represent the curve fit of data.)is affected by the deposit thickness and its structure which depends on the calcium concentration (Fig.7b).A small change in the calcium concentration has an important impact upon the fouling behaviour.Figs.6and 7indicate that calcium ions (i)are essential in the growth of fouled layers as suggested by Xiong (1992)since amounts of deposit increase with calcium concentration (Fig.7c),(ii)modify the rate of protein aggregation and (iii)lead to a greater cohesion between protein aggregates modify-ing the deposit structure.Indeed,visual analysis of the deposit after fouling runs at Re 3200using 1.0%WPC solutions revealed that fouled layers formed with low calcium content(78mg/l)have a spongy and soft texture whereas deposits formed at higher calcium content (86.5mg/l)are denser and elastic.This observation is in agreement with Pappas and Rothwell (1991)who showed that -lactoglobulin completely aggregated to form compact structures when heated with cal-cium.Simmons et al.(2007)also showed that increasing the levels of calcium had a dramatic effect on the size of the aggre-gates produced,which decreased with increasing mineral con-centration.An explanation for the difference in structure and kinetic is that calcium ions,essentially present in the deposit solid (Tissier and Lalande,1986),lead to lower size aggregates in the range of calcium concentration (70–88mg/l)and favour the growth of fouled layers by formation of bridges between adsorbed proteins and the protein aggregates formed in the bulk (Fig.8).Bridges may be formed via carboxyl groups of amino acids of -lactoglobulin as suggested by Xiong (1992).In-creasing the level of calcium would lead in a higher number of bridges resulting in a bigger stabilisation of protein aggregates as interpreted by Daufin et al.(1987)and Xiong (1992),forming a narrow network which embed other ions present in the solution (i.e.,sodium,magnesium,phosphate,calcium,…),and reinforce the adhesion forces between proteins.3.2.Effect of hydrodynamics conditions on foulingFig.5shows that rates of equivalent electrical conductivity changes are not constant as function of time since the slope of equivalent electrical conductivity decreased after t =180min.This slope modification in eq may be due to a decrease of the aggregate deposit and/or an escape of the deposit from the fouled layer into the core fluid caused by particle breakage.This can be a consequence of an additional local shear stress as deposit thickness evolved (Fig.9).Indeed,shear stress in a channel is a function of channel section which is reduced with the growing fouled layer [ = .¯u. /(2(e E −2e d ))].This confirms the assumption of Kern and Seaton (1959)who were the first to underline that the formation of a fouled layer is a consequence of the rate of aggregate entry and the rate at which they escape.Fig.10illustrates the evolution of the kinetic parameter k during fouling with a 1.0%WPC solution at calcium concen-tration of 78mg /l as a function of Reynolds number.The in-crease of k between Re 2000and 3200can be explained by a weaker size of aggregates at higher shear rate for a fixed tem-perature (Simmons et al.,2007)favouring the growth of the deposit and resulting in a different deposit structures (Fig.8).Deposit masses in channel 5confirm this trend namely for a fixed calcium concentration,the amount of deposit in C5in-creases between Re 2000and 3200(Fig.7c).Nevertheless,the k parameter decreases between Re 3200and 5000at a fixed calcium concentration.Thus,the decrease of the rate of deposit is due to the increase of Reynolds number which may limit the deposit,compact the structure upon the heated surface and increase the rate of particle breakage.Visual analysis of the appearance of the deposit as a function of Reynolds number confirm the trends.Deposit formed after fouling with a calcium concentration close to 78mg /l at Re 2000has a granular aspectR.Guérin et al./Chemical Engineering Science 62(2007)1948–19571955Adsorbed protein AggregatesStainless steel electrodes Stainless steel plate With lower calcium concentraionEmbedded ionsCalcium bindingsWith higher calcium concentraionFig.8.Schematic illustration of the proposed formation of the deposit with lower and higher calcium concentrations of the WPC solution.0.20.40.60.811.21.47076.37886.5Calcium concentration, (mg/l)L o c a l s h e a r s t r e s s , (P a )20406080100120140160180200Shear stress for fouled channel (C5)Shear stress for cleaned channel (C5)Increase of shear stressI n c r e a s e o f s h e a r s t r e s s , (%)Fig.9.Increase in shear stresses due to fouled layer growth as a function of calcium concentrations in 1.0%WPC solutions at Re =3200.probably due to higher size aggregates whereas deposit formed at Re 3200appears more denser (i.e.,lower aggregates size).Finally,the deposit obtained after fouling at Re 5000appears more smooth and compact which may be the consequence of the increase of the local shear stress (Fig.9).Another way to underline the influence of shear stress upon the structure of the deposit is the measurement of the electri-cal conductivity of deposits according to Reynolds numbers for a fixed calcium content and temperature (Fig.7a–c).Fig.7a shows that DEC values are similar at Re 2000and 3200while amounts of deposit in C5,and so the thickness of the deposit (Figs.7b and c),are completely different with a scatter close to 35%.In the same order,amounts of deposit in C5are similar for Re 2000and 5000while the correspondingvalues of DEC1234567200032005000Reynolds number, (-)k x 104, (S m -1 m i n -1)Fig.10.Rates of deposit growth (k )as a function of Reynolds number during fouling runs with a 1.0%WPC solution with calcium concentration comprised between 76.0and 78.0mg /l.differ each other.Moreover,for a fixed calcium concentration,DEC values increase with a variation of Reynolds number from 2000to 3200while a decrease in DEC values can be observed above a critical Reynolds number,which could be comprised between 3200and 5000.Since calcium concentration and tem-perature are invariant and considering a poor mobility of ions due to protein networks,differences in the structure and/or the composition of the deposit can be explained by DEC variations.This indicates that shear stress has a dramatic effect upon the structure and the appearance of the deposit whatever the cal-cium concentrations.The differences in the structure of these。

THE CRYSTAL STRUCTURE OF THE b0PHASE INAl±Mg±Si ALLOYSS.J.ANDERSEN1,2,H.W.ZANDBERGEN2,J.JANSEN2,3,C.TRáHOLT2,U.TUNDAL4and O.REISO41SINTEF Materials Technology,Applied Physics,7034Trondheim,Norway,2National Centre for HREM,Laboratory of Materials Science,Delft University of Technology,Rotterdamseweg137,2628 AL Delft,The Netherlands,3Laboratory for Crystallography,University of Amsterdam,Nieuwe Achtergracht166,1018WV Amsterdam,The Netherlands and4HYDRO Aluminium,Metallurgical Rand D Centre,Sunndalsùra,Norway(Received17November1997)AbstractÐThe crystal structure of b0,one of the strengthening phases in the commercially important Al±Mg±Si alloys,is determined by use of high resolution electron microscopy(HREM)and electron di raction(ED).A trial structure was established from exit wave phase reconstructed HREM images.A least-square re®nement of the model coordinates was done using data from digitally recorded ED patterns.A recently developed computer program(MSLS)was applied,taking into account dynamic scattering.The atomic unit cell contains two units of Mg5Si6.It is C-centred monoclinic,space group C2/m, a=1.51620.002nm,b=0.405nm,c=0.67420.002nm,b=105.320.58.The atomic packing may be regarded as a hard ball packing using clusters,the clusters being(1)centred tetragons of Mg atoms and(2) so-called twin icosacaps where Mg atoms are centred above and below pentagonal rings of four Si atoms an one Mg atom.A growth related stacking fault in the structure is explained by a de®ciency of Mg atoms.A model for the b0/Al interface is given.#1998Acta Metallurgica Inc.1.INTRODUCTION1.1.GeneralThe discovery of the precipitation hardening mech-anism in the beginning of this century in an Al±Cu alloy has had great implications for all technologies requiring light alloys with some strength,and es-pecially for the aerospace and construction technol-ogies.The increase in hardness that the commercial Al alloys achieve upon hardening is usually a factor of2or more.In the Al±Mg±Si(6xxx)alloys such a tremendous increase in strength is caused by pre-cipitates formed from solution,of merely1wt%of Mg and Si that is added to the aluminium.The maximum hardness is achieved when the alloy con-tains a combination of very®ne fully coherent so-called Guinier Preston(GP-I)zones with diameters about2.5nm,and the semicoherent,larger needles, b0(GP-II zones)with a typical size4Â4Â50nm3. The density of these phases is very high.For the b0 needles,a number density in the matrix of about 104/m m3is normal.This is equal to a volume of nearly1%in the material.The6xxx series alloys are not among the strongest aluminium alloys,but they represent a high share of the aluminium pro-ducts in the world(H20%).In1989,about90%of the tonnage extruded in western Europe,was Al±Mg±Si alloys[1].1.2.The precipitation/transformation sequenceThe phases occurring in the Al±Mg±Si alloys have been studied for more than50years due to the commercial importance of these materials.In1948 Geisler and Hill[2]and Gunier and Lambot[3] reported that X-ray Laue pattern zones indicated the formation of small(H2Â2Â10nm3)needles or Guinier Preston(GP)zones,when the temperature was raised to2008C.Further heating caused the zones to thicken into rods,called b',and®nally a large plate-shaped equilibrium phase,b,was seen to form.The latter was known to be of the f.c.c.CaF2 type with a composition Mg2Si.The alloys that were studied were close to the Al±Mg2Si section of the Al±Mg±Si phase diagram;therefore it was assumed that the composition of all the Mg±Si con-taining phases was ter experiments have shown that the precipitation and transformation is quite complicated and that except for the equili-brium phase,b,the phases involved do not have the stoichiometric ratio Mg2Si.In Table1the transformation sequence at low ageing temperatures for alloys near the quasi-binary section Al±Mg2Si of the phase diagram is summar-ised.The range of existence and sizes of the b'rods and b plates depend not only on the heat-treatment, but on several other factors as well,such as cooling rate from homogenisation or extrusion and the number of Al±Fe(+Mn)±Si containing phases (dispersoids)in the material.This will not be dis-cussed in this paper.In the following a discussion of the precipitation/ transformation sequence shown in Table1is given.Acta mater.Vol.46,No.9,pp.3283±3298,1998#1998Acta Metallurgica Inc.Published by Elsevier Science Ltd.All rights reservedPrinted in Great Britain1359-6454/98$19.00+0.00 PII:S1359-6454(97)00493-X32831.2.1.Atomic clusters.After rapid cooling from homogenisation or extrusion the material is super-saturated with Mg and Si.Due to the higher solubi-lity of Mg in Al,when stored at room temperature or heated,Si ®rst goes out of solution and forms small clusters,but there are also some indications of clustering of Mg [5].The nucleation of Si-clusters will occur at quenched-in vacancies at temperatures as low as À508,below which the vacancy movement becomes very low [6].Storing or heating above À508will cause Mg to di use to the clusters,and Mg±Si phases will pre-cipitate.The di usion of Mg to the Si clusters has been veri®ed through APFIM [5,7]where the ratio of Mg/Si in the average cluster was found to increase with time when heated at 708.Since the number of Si clusters formed will be important for the precipitation of the strengthening GP zones,the storing time at a low temperature before arti®cial ageing is important concerning the material proper-ties.1.2.2.GP zones and the b 0phase .The ®rst phase to precipitate on the small clusters is the GP zones.Based on a TEM study of Al±Mg 2Si [8]Thomas proposed a model for these particles;Mg and Si replace Al in such a ratio that the occupied volume is about the same.He proposed a simple substi-tution along 110-directions with strings of atoms in the sequence Mg±Si±Mg±Mg±Si±Mg.Here two di-ameters of Mg (2Â0.32nm)and one of Si (0.235nm)amounts to 0.874nm,as compared with three diameters of Al (0.859nm).In more recent research the evolution of GP zones in several Al±Mg 2Si alloys was studied by calorimetry [6],in 6061by calorimetry and TEM [5],and by atom-probe ®eld-ion microscopy (APFIM)and TEM/HREM [5,7].These works support the view that there are at least two phases in the size range of the GP-zones,called GP-I and GP-II.For the GP-I type the size is in the range 1±3nm.The crystal structure is unknown.The zones are fully coherent and probably have a spherical shape.Dutta and Allen [9]observed by TEM small spot-like features of ``unresolved''shape of about 2.5nm that should be the GP-I zones.Particles investigated by APFIM [5]with comparable dimensions to these zones seem to have Mg/Si ratios usually less than 1.This composition is therefore di erent from that of the model proposed by Thomas [8].The GP-II zone is the same phase as the currently investigated b 0phase.This phase has the shape of ®ne needles,typically about 4Â4Â50nm 3when the material is in the aged-hardened condition [7,10].In this condition the number density of the nee-dles is high;typically 104/m m 3[10].The b 0phase is fully coherent only along the b -axis.Edwards et al.[7]managed to determine the unit cell of the b 0phase by electron di raction.It was found to be a monoclinic C-centred structure with a =0.153420.012nm,b =0.405nm,c =0.68320.015nm,b =10621.58.The b -axis is along the needle-axis.It is the full coherency of GP-I zones,the semi-coherency of the GP-II zones together with their high number densities that introduce in the alu-minium matrix strain and resistance against move-ment of dislocations,that gives the material its mechanical strength.1.2.3.The b 'phase .The next phase in the trans-formation sequence after the GP-I zones and the b 0phase is the b 'phase.This has a lower Mg/Si ratio than the equilibrium b phase.Lynch et al.found by X-ray microanalysis evidence for a ratio of Mg/Si in the b 'rods in an overaged material to be about 1.73[11],while Matsuma et al.[12]later determined the ratio to be about 1.68.For materials with excess silicon relative to Al±Mg 2Si there may be very small precipitates also of the b 'and a so-called B 'phase that is richer in silicon,or even Si particles [4].Because of this such particles with sizes comparable to b 0[7,4]may be mistaken for the b 0phase.The b 'and the B 'phase are reported as having the hexa-gonal unit cells a =0.705nm,c =0.405nm and a =0.104nm,c =0.405nm,respectively.In Refs [7,4]the relative number of b 0as compared with the smallest b '(and B ')particles was not deter-mined.It was recently suggested that b 'is a h.c.p.structure with a =0.405nm,c =0.67nm [12,13].1.2.4.The b phase.The b phase is the equilibrium phase in this system.It is the only phase up to now with a known structure.It is a CaF 2type f.c.c.structure with a =0.639nm having formula Mg 2Si.The structure may be described as strings of three atoms,Mg±Si±Mg,on the corners and faces of a cube,directed along the diagonals.Table 1.The evolution of Mg±Si phases near the quasi-binary section Al±Mg 2Si (top to bottom)Transformation/precipitation sequence Crystal type Size (nm)Composition Clusters of Si and fewer of Mg unknown unknown Si (Mg)Clusters containing Si and Mg unknown unknown Mg/Si <1Coherent spherical GP-I zonesunknown H 1±3Mg/Si H 1Semi-coherent GP-II zones (b 0needles)monoclinic H 4Â4Â50Mg/Si r 1b 'rods (and B 'rods)hexagonal H 20Â20Â500Mg/Si H 1.7b -Mg 2Si platescubicmicronsMg/Si =2The B 'phase is observed with alloys having excess Si relative to Al±Mg 2Si.It contains more Si than b '[4].ANDERSEN et al.:Al±Mg±Si ALLOY32841.3.SummationSumming up the information above,it appears that the phases that evolve from the very®ne Si-clusters into coarser particles take up progressively more magnesium during the coarsening and trans-formation processes,until an equilibrium compo-sition Mg2Si for the b phase®nally is reached.In this paper we report the structure determi-nation of the b0phase,which must be one of the important hardening phases in the commercial6xxx alloys.The technique used in the structure determi-nation is the through focus exit wave reconstruction technique in high resolution electron microscopy,in combination with quantitative electron di raction.2.EXPERIMENTAL2.1.Material and sample preparationThe as-received material was in the shape of extruded sections.It was supplied by HYDRO Aluminium AS(Sunndalsùra).The composition of the material was Al±0.2Fe±0.5Mg±0.53Si±0.01Mn (wt%).The material is from the same batch and extruded sections as investigated in Refs[10,14], there labelled as A and C,respectively.Specimen preparation and location in the extruded section of the samples for TEM are described in Refs[10,14]. Prior to the arti®cial ageing(5h at1858)the ma-terial had undergone a rather standard processing for an extrusion product.After the jet-polishing, specimens were stored in methanol.Most of the TEM experiments were performed within a day after specimen preparation.2.2.TEM equipment and experimental dataAll TEM work was performed using a PHILIPS CM30-ST/FEG electron microscope operated at 300kV.The microscope is equipped with a Photometrix1024Â1024slow scan CCD camera (12bits dynamical range),enabling a linear record-ing of HREM and ED puter control of the CCD camera and the microscope is handled with a Tietz software package.In this way series of 15±20HREM images with focus increments of typi-cally 5.2nm were recorded for each exit wave reconstruction.For the high resolution work suitable aluminium grains were selected and tilted into a h100i zone axis.HREM images were recorded at room tem-perature on as thin areas as possible,typically4±10nm.Needles were selected that could be viewed along their[010]zone axis.In this situation,the needles usually extend through the whole thickness of the specimen,such that no image blurring occurs due to overlap with the matrix.For a single image, the exposure time was usually about1s.For the di raction experiments a small spot-size (5±10nm)was used with exposure times of1±5s. Two zone-axes of the needles were chosen;[010]and[001].For the latter,the aluminium grain was tilted to a h310i zone axis,where statistically one out of six needles is in the correct orientation. Many of the needles contain stacking-faults or sec-ond phases.For a reliable structure determination it is important that the area where a di raction pat-tern is taken is free of defects.Given the resolution of the microscope it should be relatively easy to select single crystalline b0particles.However,to prevent the rapid contamination of the illuminated area that is typical for this kind of specimen at room temperature,the specimen was cooled to about100K.The sample cooling holder has a much poorer mechanical stability resulting in such a loss of resolution that selection of single crystal b0particles was di cult.Because of this ED pat-terns were taken from each particle encountered. Therefore quite many di raction patterns had to be discarded because of streaking and twinning prob-ably caused by the stacking-faults or sometimes extra spots caused by a intergrown phase that was determined to be b'.Five[010]di raction patterns were selected.For the[001]zone axis there is a greater chance of``cross-talk''due to more overlap of the matrix with the crystal,and suitable di rac-tion patterns for the re®nement were more di cult to®nd.Here®ve of the16recorded patterns were from the correct projection or particle.Only two of these patterns could later be re®ned.In addition to the problem with overlap spots from the b'phase, the reason was also the strong interference with the aluminium matrix in this projection that made sub-traction of the background di cult.The thickness of the investigated areas were somewhat larger for the di raction experiments than for the HREM ex-periments.The subsequent re®nements showed that the thickness usually exceeded10nm.In Fig.6, parts of two of the digitally recorded di raction images are shown.This®gure also shows some streaking caused by oversaturation of the CCD camera,which was not equipped with over¯ow pro-tection.The streaks and the aluminium di raction re¯ections were excluded from the images prior to data reduction.The exit wave reconstruction of the HREM focus series were done with a software package based on algorithms developed by Van Dyck and Coene[15±17].Given the coherency of the presently available ®eld emission guns the structural information in ordinary HREM images goes well beyond the point-to-point resolution in the electron microscope. The reconstruction method takes advantage of the knowledge about the transfer function,e.g.how the microscope optics distorts the electron wave after leaving the crystal(the exit wave)on its way to the image plane.This distortion is also a function of defocus.A series of HREM images are recorded at intervals of known defocus.The amplitude and phase information that is mixed up in the HREM images is retrieved through digital processing,andANDERSEN et al.:Al±Mg±Si ALLOY3285corrections for focus and spherical aberration are done.Furthermore,since typically15±20images are used in the reconstruction a considerable reduction in noise is attained.The exit wave is thus independent of various aberrations of the electron microscope, but it is still dependent on the specimen thickness. Only for very small specimen thicknesses is the exit wave very similar to the projected potential,viz.the projected atomic structure.For thicker sections,e.g. more than about10nm for the presently presented exit wave image,the local contrast in the exit wave can be quite di erent from the local scattering poten-tial.Thus,for such thicknesses a higher brightness at a certain point in the phase image of the exit wave as compared to other points,does not have to imply the presence of a locally more strongly scattering atom at this point.The good news is that the positions of the bright dots should correlate well with the location of the atoms.In the presently used electron microscope the res-olution is enhanced from0.20nm to about0.14nm. The HREM images presented in this work are recombined exit wave phase images.See Coene et al.[17],Zandbergen et al.[18]and Op de Beeck et al.[19]for examples and discussion of the method. The re®nement of the structure was done using the computer programme package MSLS[20].The CCD images with the di raction patterns were cor-rected for the¯at®eld(variation in the pixel sensi-tivity)and over¯ow during read-out of the CCD camera.Spurious X-ray signals and the Al di rac-tion spots were omitted.Automatic indexing and data reduction on the patterns were done.The obtained two-dimensional indices of the images were next transformed into the correct hkl indices so that the di raction data sets could be combined. MSLS was used for re®nement of the trial structure coordinates as obtained from the reconstructed exit wave.This program re®nes coordinates based on the least-squares procedure using the multi-slice al-gorithm to account for the dynamic di raction.The parameters re®ned were the thickness,the scaling factor,the centre of the Laue circle for each of the data sets,and the atomic coordinates and tempera-ture factors.The R-value used as measure of the correctness of the structure is de®ned as R=a(I calcÀI obs)2/a(I obs)2.Only the signi®cant re¯ections(I obs>2s(I obs))were used.R-values between2and6%are being quoted for the most reliably determined structures.3.RESULTS/DISCUSSION3.1.Conventional HREM/TEMConventional TEM shows the interior of the Al grains to mainly contain particles having a®ne nee-dle shape.The needles lay along h100i Al directions. Figure1gives an example.It is a bright®eld image in an Al h100i zone axis where the needles clearly point in two normal directions.The dark spots are needles pointing in the viewing direction.The exper-imental di raction patterns as well as HREM images show that the needle shaped particles mostly are of one kind,the monoclinic phase that is usually referred to as the b0phase.Figure2shows a HREM image with one such needle.Such images show the precipitates to be coherent along the nee-dle direction(their b-axis)with a h100i Al direction. This con®rms that their cell parameter is the same as aluminium,b=0.405nm.Many of the b0precipitates were found to con-tain stacking faults.In some precipitates an inter-growth of b0with another phase was observed.It is most probably the b'phase which has the hexago-nal axis along the needle direction.Sometimes this phase was found to exist alone.The cell parameter a=0.705nm has been con®rmed from exit wave simulated images.These images will be published later.In the same material coarser rods of the b' phase have earlier been investigated;It was reported that they nucleate on®ne Al±Fe±Si particles[14].It may be expected that much of the b'particles nucle-ate on b0since with longer arti®cial ageing times the micro-structure will contain an increasing amount of rods of b'.By selected area electron dif-fraction the coarse b'phase in this material was determined to have a hexagonal structure with a H0.71nm,c H0.41nm.The a-axis therefore®ts well with the phase intergrown with b0.The struc-ture of the small and large b'is therefore probably the same.We did not observe any B'phase in the material.3.2.Elemental analysis of the b0phaseWe performed several X-ray analyses of the small precipitates with the spot along the needle axis. Due to the very thin specimen areas(10±40nm)the spectra obtained should in principle not be signi®-cantly in¯uenced by absorption in the specimen, which is the most important reason for deviations from the actual concentration.In spite of the small size of the spot(1±2nm),there was always an Al peak present in the spectrum,of varying height. This is partly caused by stray electrons travelling down the column of the electron microscope which are not focused with the rest of the electrons in the beam probe and therefore many hit aluminium. Secondly,because during analysis the beam is par-allel to the needle axis,i.e.to the[010]zone axis of b0,this implies an e ective beam broadening by the elastic scattering of some electrons into aluminium. For some of the recordings there is also an e ect of specimen drift during recording.Another e ect is the contamination layer and the(aluminium)oxide layer on the surface of the particle which primarily contains Al.The EDS experiments could therefore not rule out that some Al is contained in the precipitate.As a standard for determining the K-ratios a mineral forsterite was used whose mainANDERSEN et al.:Al±Mg±Si ALLOY 3286components are MgO and SiO 2with a composition so that the Mg/Si atomic ratio is 2.Not taking into account the possible systematic deviations,the EDS experiments indicated that the atomic ratio for Mg/Si was close to or even below 1.The accuracy of these measurements were on the order of 10%.However,they ruled out the earlier accepted ratio of 2for the b 0phase.EDS measurements were also performed on larger particles of the b 'and b -Mg 2Si phases which had been extracted from the alu-minium matrix.These phases gave compositions near the expected,as listed in Table 1.The accuracy here was much better for thin sections since the alu-minium matrix could be avoided entirely.3.3.Exit wave reconstruction3.3.1.The unit cell.Coherency of the b 0phase with the matrix .In Fig.3a reconstructed exit wave (phase)of a b 0particle in the [010]orientation embedded in aluminium is shown.The b 0[010]direction is parallel to a h 100i type aluminium zone axis and is along the needle.Atomic columns in the viewing direction in the image appear as bright dots.The columns in the Al matrix are clearly resolved;in this projection the separation between nearest neighbor columns are 0.2025nm,or half the Al unit cell length.Due to the face centering of alu-minium the nearest neighbor atom columns are also shifted 0.2025nm in the viewing direction relative to each other.In the ®gure circles are drawn that indicate the two di erent height positions of the atoms in the viewing direction.The lattice image of the Al matrix changes over the image due to local variations in tilt.The b 0unit cell is outlined in the particle.Due to the C-centering,the a -axis is twice the apparent periodicity.By calibrating the magni®cation of the image using the aluminium lattice,the unit cell was established to be a =1.51620.002nm,c =0.67420.002nm and b H 105±1068.HREM of other nee-dles lying in the normal direction (Fig.2)have shown that there is a full coherence between the crystal along the b -axis with the same periodicity as the aluminium matrix;therefore b =0.405nm.In the re®nement of di raction images for this zone axis,the monoclinic angle is calculated.It was found to have a mean value b =105.320.58when averaged over 7di raction patterns.The b 0unit cell is closely related to the alu-minium lattice.From di raction patterns (Fig.5)asFig.1.A typical low magni®cation micrograph of b 0needles in a h 001i Al zone axis.Needles are directed along the three h 100i Al directions and appear therefore point-like (dark spots)in the viewing direction.The needles have a mean diameter of about 4nm,and an average length about 50nm.Alarger b 'rod (white appearance)is directed in the viewing direction in the centre of the image.ANDERSEN et al.:Al±Mg±Si ALLOY 3287well as from the exit wave (Fig.3)the following relationship between the phases can be found; 001 Al k 010 b 0,"310 Al k 001 b 0,230 Al k 100 b 0This relationship is the same as found earlier byEdwards et al.[7].A corresponding super cell in aluminium can be de®ned by real vectors ~ab 0 2~a Al 3~b Al ,~b b 0~c Al ,~c b 0 À32~a Al 12~b Alwith respective lengths 1.46,0.405and 0.64nm witha monoclinic angle of 105.38.Half of this super cellis outlined in Fig.3on the left side of the b 0par-ticle.The super cell is also C-centred monoclinicsince two neighbor corners of the half cell along ~ab 0fall on Al atoms in di erent layers.The unit cell for b 0is slightly larger than this Al super cell;3.8%along ~ab 0and 5.3%along ~c b 0.The half super cell (asymmetric unit)contains 11Al atoms.The coherency between b 0and aluminium aids in quantifying the shift of the stacking fault (sf)in the particle that is indicated in Fig.3;By using the Al matrix as reference it can be veri®ed that Al atoms at the left interface,at the upper part (e.g.near the white corners of the unit cell of b 0)are at a di er-ent height relative to similar atoms of b 0on the lower part (here with a black ®ll){.This is illus-trated by the two outlined (half)super cells in the Al matrix that are related to the unit cell of b 0in the upper and lower part of the particle.These super cells are shifted a vector a Al [101]/2relative to each other,which indicates that the shift across the stacking fault in the particle is nearly the same.This shift vector is a Burgers vector of the most common dislocation in aluminium.A model of the fault is given in Section5.Fig.2.Ordinary HREM image of b 0-needle in an h 001i zone axis in Al.The c -axis of the needle is in the plane,and the coherency with h 100i Al in the needle direction is evident.As expected,there is no exact zone axis of b 0along the viewing direction h 001i Al zone axis.The left part of the picture was fourier ®ltered;A high pass ®lter was applied to the upper part and a low pass ®lter to the lower partto extract the periodic information from Al (upper)and the b 0-phase (lower)only.{Alternatively,assume the corners of the outlined unit cells of b 0on each side of the stacking fault to be at thesame heights along ~cb 0.The atoms to the left of Ðand in the matrix outside Ðthese corners must then necessarily have similar heights,since the atomic con®guration and distances to the left of these corners are similar,whether above or below the stacking fault.This assumption must be wrong;When keeping track of the atomic columns in the matrix it leads to the conclusion of an Al atom being at two heights at the same time.Therefore,the corners ofthe unit cells along ~cb 0have di erent heights across the stacking fault.ANDERSEN et al.:Al±Mg±Si ALLOY3288In Fig.4the coherency between the two phases can be studied in more detail.This image is a Fast Fourier Transformation (FFT)of part of Fig.3.Only the lower part of the b 0precipitate is included to reduce streaking caused by the stacking fault.After applying a Fourier ®lter (selecting the con-tents inside the circles superposed on the FFT of Fig.4)the Al re¯ections plus the 610,610,403and 403re¯ections of b 0contribute to the image in Fig.5.The white arrows indicate interface dislo-cations between the particle and matrix.For example,the b 0(601)lattice planes with a spacing d 601=0.211nm are parallel with the Al (200)planes with a spacing of 0.203nm.Therefore,one interface dislocation is expected for each 25Al d 200spacings (normal to the [100]axis in the ®gure).Similarly,for the 403planes,for each 20Al d 020spacing one expects an interface dislocation.The spacings between dislocations observed in Fig.5are di erent from the theoretical ones.The reason for this devi-ation is probably variation in local strain in the particle caused by the stacking fault.Although the exact dislocation is not clear in the image,a matrix dislocation found (marked ``d '')also complicates the situation concerning the mis®t dislocations.This dislocation is found to have a Burgers vector b =0.5a Al [101],as was found when a Burgers vec-tor loop was performed around the particle.This is indicated by the open arrow (d).In Fig.6,two ex-perimental di raction images from the [010]and [001]zone axes are shown.The b 0610and 403re¯ections that coincide with the 200and 020Al matrix re¯ections can also be seen in Fig.6(a).In Fig.6(b)the perfect coherency relation of the (010)lattice planes of the b 0phases with (200)lattice planes can be seen from the overlap of the respect-ive di raction spots.3.3.2.Extraction of the atomic coordinates for b 0from the exit wave images .Figure 7(a)is an increased magni®cation of part of Fig.3.Here the atomic columns are represented as white dots.From this image the atomic positions were esti-mated using the following assumptions:(1)The number of atoms in the unit cell is 22,just as the number of atoms in the similar super cell in aluminium.The number ®ts the apparentnumberFig.3.Phase of an reconstructed exit wave of a typical b 0needle in Al is shown.The needle is viewed head-on along its [010]axis,and along an Al h 001i zone axis.Atomic columns appear white.The b 0unit cell and half the corresponding super cell in Al are outlined.Similarly ®lled circles in the matrix or in the precipitate are atoms (Al or Mg)at the same height.A stacking fault (sf)is indicated.The shiftacross the stacking fault can be determined to be a Al [101]/2.ANDERSEN et al.:Al±Mg±Si ALLOY 3289。

Annu.Rev.Mater.Res.2001.31:1–23Copyright c2001by Annual Reviews.All rights reserved S YNTHESIS AND D ESIGN OF S UPERHARDM ATERIALSJ Haines,JM L´e ger,and G BocquillonLaboratoire de Physico-Chimie des Mat´e riaux,Centre National de la Recherche Scientifique,1place Aristide Briand,92190Meudon,France;e-mail:haines@cnrs-bellevue.fr;leger@cnrs-bellevue.frKey Words diamond,cubic boron nitride,carbon nitride,high pressure,stishovite s Abstract The synthesis of the two currently used superhard materials,diamond and cubic boron nitride,is briefly described with indications of the factors influencing the quality of the crystals obtained.The physics of hardness is discussed and the importance of covalent bonding and fixed atomic positions in the crystal structure,which determine high hardness values,is outlined.The materials investigated to date are described and new potentially superhard materials are presented.No material that is thermodynamically stable under ambient conditions and composed of light (small)atoms will have a hardness greater than that of diamond.Materials with hardness values similar to that of cubic boron nitride (cBN)can be obtained.However,increasing the capabilities of the high-pressure devices could lead to the production of better quality cBN compacts without binders.INTRODUCTIONDiamond has always fascinated humans.It is the hardest substance known,based on its ability to scratch any other material.Its optical properties,with the highest refraction index known,have made it the most prized stone in jewelry.Furthermore,diamond exhibits high thermal conductivity,which is nearly five times that of the best metallic thermal conductors (copper or silver)at room temperature and,at the same time,is an excellent electrical insulator,even at high temperature.In industry,the hardness of diamond makes it an irreplaceable material for grinding tools,and diamond is used on a large scale for drilling rocks for oil wells,cutting concrete,polishing stones,machining,and honing.The diamonds used for industry are now mostly man-made because their cutting edges are much sharper than those of natural diamonds,which have been eroded by geological time.The synthesis of diamond has been a goal of science from Moissant at the end of the nineteenth century to the successful synthesis under high pressures in 1955(1).However,diamond has a major drawback in that it reacts with iron and cannot be used for machining steel.This has prompted the synthesis of a second superhard0084-6600/01/0801-0001$14.001A n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r gb y C h i n e s e Ac ade m y of S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .2HAINESL ´EGERBOCQUILLONmaterial,cubic boron nitride (cBN),whose structure is derived from that of dia-mond with half the carbon atoms being replaced by boron and the other half by nitrogen atoms.The resulting compound is half as hard as diamond,but it does not react with iron and can be used for machining steel.Cubic boron nitride does not exist in nature and is prepared under high-pressure high-temperature conditions,as is synthetic diamond.However,its synthesis is more difficult,and it has not been possible to prepare large crystals.Industry is thus looking for new superhard ma-terials that will need to be much harder than present ceramics (Si 3N 4,Al 2O 3,TiC).Hardness is a quality less well defined than many other physical properties.Hardness was first defined as the ability of one material to scratch another;this corresponds to the Mohs scale.This scale is highly nonlinear (talc =1,diamond =10);however,this definition of hardness is not reliable because materials of similar hardness can scratch each other and the resulting value depends on the specific details of the contact between the two materials.It is well known (2)that at room temperature copper can scratch magnesium oxide and at high temperatures cBN can scratch diamond (principle of soft indenter).Another,more accurate,way of defining and measuring hardness is by the indentation of the material by a hard indenter.According to the nature and shape of the indenter,different scales are used:Brinell,Rockwell,Vickers,and Knoop.The last two are the most frequently used.The indenter is made of a pyramidal-shaped diamond with a square base (Vickers),or elongated lozenge (Knoop).The hardness is deduced from the size of the indentation produced using a defined load;the unit is the same as that for pressure,the gigapascal (GPa).Superhard materials are defined as having a hardness of above 40GPa.The hardness of diamond is 90GPa;the second hardest material is cBN,with a hardness of 50GPa.The design of new materials with a hardness comparable to diamond is a great challenge to scientists.We first describe the current status of the two known super-hard materials,diamond and cBN.We then describe the search for new bulk super-hard materials,discuss the possibility of making materials harder than diamond,and comment on the new potentially superhard materials and their preparation.DIAMOND AND CUBIC BORON NITRIDE DiamondThe synthesis of diamond is performed under high pressure (5.5–6GPa)and high temperature (1500–1900K).Carbon,usually in the form of graphite,and a transi-tion metal,e.g.iron,cobalt,nickel,or alloys of these metals [called solvent-catalyst (SC)],are treated under high-pressure high-temperature conditions;upon heating,graphite dissolves in the metal and if the pressure and temperature conditions are in the thermodynamic stability field of diamond,carbon can crystallize as dia-mond because the solubility of diamond in the molten metal is less than that of graphite.Some details about the synthesis and qualities of diamond obtained by this spontaneous nucleation method are given below,but we do not describe the growthA n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r gb y C h i n e s e Ac ade m y of S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .SUPERHARD MATERIALS 3of single-crystal diamond under high pressure,which is necessary in order to ob-tain large single crystals with dimensions greater than 1mm.Crystals of this size are expensive and represent only a very minor proportion of the diamonds used for machining;they are principally used for their thermal properties.It is well known that making diamonds is relatively straightforward,but control-ling the quality of the diamonds produced is much more difficult.Improvements in the method of synthesis since 1955have greatly extended the size range and the mechanical properties and purity of the synthetic diamond crystals.Depending on the exact pressure (P )and temperature (T )of synthesis,the form and the nature of the carbon,the metal solvent used,the time (t )of synthesis,and the pathways in P-T-t space,diamond crystals (3,4)varying greatly in shape (5),size,and fri-ability are produced.These three characteristics are used to classify diamonds;the required properties differ depending on the industrial application.Friability is related to impact strength.It is the most important mechanical property for the practical use of superhard materials,and low friability is required in order for tools to have a long lifetime.In commercial literature,the various types of diamonds are classed as a function of their uses,which depend mainly on their friabilities,but the numerical values are not given,so it is difficult to compare the qualities of diamonds from various sources.The friability,which is defined by the percentage of diamonds destroyed in a specific grinding process,is obtained by subjecting a defined quantity of diamonds to repeated impacts by grinding in a ball-mill or by the action of a load falling on them.The friability values depend strongly on the experimental conditions used,and only values for crystals measured under the same conditions can be compared.The effect of various synthesis parameters on their quality can be evaluated by considering the total mass of diamond obtained in one experiment,the distribution size of these diamonds,and the friability of the diamonds of a defined size.A first parameter is the source of the carbon.Most carbon-based substance can be used to make diamonds (6),but the nature of the carbon source has an effect on the quantity and the quality of synthetic diamonds.The best carbon source for diamond synthesis is graphite,and its characteristics are important.The effect of the density,gas permeability,and purity of graphite on the diamond yield have been investigated using cobalt as the SC (7).Variations of the density and gas permeability have no effect on the diamond yield,but carbon purity is important.The main impurity in synthetic graphite is CaO.If good quality diamonds are required,the calcium content should be kept below 1000ppm in order to avoid excessive nucleation on the calcium oxide particles.A second factor that alters the quality of diamonds is the nature of the SC.The friability and the size distribution are better with CoFe (alloy of cobalt with a small quantity of iron)than with invar,an iron-nickel alloy (Table 1:Ia,Ib;Figure 1a ).Another parameter is how the mixture of carbon and SC is prepared.When fine or coarse powders of intimately mixed graphite and SC are used,a high yield of diamonds with high friabilities is obtained (8).These diamonds are very small,A n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .4HAINESL ´EGERBOCQUILLONTABLE 1Friabilities of some diamonds as a function of the details of the synthesis process fora selected size of 200–250µmSDA a MBS a 100+70Ia Ib IIa IIb IIc IIIa IIIb Synthesis CoFeInvar 1C-2SC 1C-1SC 2C-2SC Cycle A Cycle B detail stacking stacking stacking Friability 74121395053637250(%)aThe SDA 100+is among De Beers best diamond with a very high strength that is recommended for sawing the hardest stones and cast refractories.MBS 70is in the middle of General Electric’s range of diamonds for sawing and drilling.Other diamonds were obtained in the laboratory using a belt–type apparatus with a working chamber of 40mm diameter.(C,graphite;SC,solvent-catalyst.)with metal inclusions,and they are linked together with numerous cavities filled with SC.A favorable geometry in order to obtain well-formed diamonds is to stack disks of graphite and SC.The effect of local concentration has been exam-ined by changing the stacking of these disks (Table 1:IIa,IIb,IIc;Figure 1b ).The method of stacking modifies the local oversaturation of dissolved carbon and thus the local spontaneous diamond germination.For the synthesis of dia-mond,the heating current goes directly through the graphite-SC mixture.Because the electrical resistivity of the graphite is much greater than that of the SC,the temperature of the graphite is raised by the Joule effect,whereas that of the SC increases mainly because of thermal conduction.Upon increasing the thickness of the SC disk,the local thermal gradient increases and the dissolved atoms of carbon cannot move as easily;the local carbon oversaturation then enhances the spontaneous diamond germination.This enables one to work at lower tempera-tures and pressures,which results in slower growth and therefore better quality diamonds.Another important factor for the yield and the quality of the diamonds is the pathway followed in P-T-t space.The results of two cycles with the same final pressure and temperature are shown.In cycle A (Figure 1d ),the graphite-SC mixture reaches the eutectic melting temperature while it is still far from the equilibrium line between diamond and graphite;as a result spontaneous nucleation is very high and the seeds grow very quickly.These two effects explain the high yield and the poor quality and small size and high friability of the diamonds compared with those obtained in cycle B (Figure 1d ;see Table 1IIIa and IIIb and Figure 1c ).Large crystals (over 400µm)of good quality are obtained when the degree of spontaneous nucleation is limited.The pathway in P-T-t space must then remain near the graphite-diamond phase boundary (Figure 1d ),and the time of the treatment must be extended in the final P-T-t conditions.Usually,friability increases with the size of the diamonds.Nucleation takes place at the beginning of the synthesis when the carbon oversaturation is important,and the carbon in solution is then absorbed by the existing nuclei,which grow larger.A n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .SUPERHARD MATERIALS5Figure 1Size distribution of diamonds in one laboratory run for different synthesis pro-cesses;effects of (panel a )the nature of the metal,(panel b )the stacking of graphite and metal disks,(panel c )the P-T pathway.(Panel d )P-T pathways for synthesis.1:graphite-diamond boundary and 2:melting temperature of the carbon-eutectic.The diamond synthesis occurs between the boundaries 1and 2.The growth time is about the same for all the crystals,thus those that can grow more quickly owing to a greater local thermal gradient become the largest.Owing to their rapid growth rate,they trap more impurities and have more defects,and therefore their friability is higher.Similarly,friability increases with the diamond yield.The diamonds produced by the spontaneous nucleation method range in size up to 800–1000µm.The best conditions for diamond synthesis correspond to a compromise between the quantity and the quality of the diamonds.A n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .6HAINESL ´EGERBOCQUILLONCubic Boron NitrideCubic boron nitride (cBN)is the second hardest material.The synthesis of cBN isperformed in the same pressure range as that for diamond,but at higher tempera-tures,i.e.above 1950K.The general process is the same;dissolution of hexagonal boron nitride (hBN)in a solvent-catalyst (SC),followed by spontaneous nucle-ation of cBN.However,the synthesis is much more complicated.The usual SCs are alkali or alkaline-earth metals and their nitrides (9):Mg,Ca,Li 3N,Mg 3N 2,and Ca 3N 2.All these SCs are hygroscopic,and water or oxygen are poisons for the synthesis.Thus great care must be taken,which requires dehydration of the materials and preparation in glove boxes,to avoid the presence of water in the high-pressure cell.Furthermore,the above compounds react first with hBN to form inter-mediate compounds,Li 3BN 2,Mg 3B 2N 4,or Ca 3B 2N 4,which become the true SC.These compounds and the hBN source are electrical insulators,thus an internal furnace must be used,which makes fabrication of the high pressure cell more complicated and reduces the available volume for the samples.In addition,the chemical reaction involved is complicated by this intermediate step,and in gen-eral the yield of cBN is lower than for diamond.Work is in progress to determine in situ which intermediate compounds are involved in the synthesis process.The crystals of cBN obtained from these processes are of lower quality (Figure 2)and size than for diamond.Depending on the exact conditions,orange-yellow or dark crystals are obtained;the color difference comes from a defect or an excess of boron (less than 1%);the dark crystals,which have an excess of born,are harder.As in the synthesis of diamond,the initial forms of the SC source,hBN,play important roles,but the number of parameters is larger.For the source of BN,it is better to use pressed pellets of hBN powder rather than sintered hBN products,as the latter contain additives (oxides);a very fine powder yields a better reactivity.Doping of Li,Ca,or Mg nitrides with Al,B,Ti,or Si induces a change in the morphology and color of cBN crystals,which are dark instead of orange,are larger (500µm),have better shapes and,in addition,gives a higher yield (10).Use of supercritical fluids enables cBN to be synthesized at lower pressures and temperatures (2GPa,800K),but the resulting crystal size is small (11).Diamond and cBN crystals are produced on a large scale,and the main problem is how to use them for making viable tools for industry.Different compacts of these materials are made (12)for various pacts of diamonds are made using cobalt as the SC.The mixture is treated under high-pressure high-temperature conditions,at which superficial graphitization of the diamonds takes place,and then under the P-T-t diamond synthesis conditions so as to transform the graphite into diamond and induce intergranular growth of diamonds.The diamond compacts produced in this way still contain some cobalt as a binder,but their hardness is close to that of single-crystal pacts of cBN cannot be made in the same way because the SCs are compounds that decompose in air.Sintering without binders (13)is possible at higher pressures of about 7.5–8GPa and temperatures higher than 2200K,but these conditions are currently outside the range of thoseA n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y.SUPERHARD MATERIALS7Figure 2SEM photographs of diamond (top )and cBN (bottom )crystals of different qualities depending on the synthesis conditions (the long vertical bar corresponds to a distance of 100µm).Top left :good quality mid-sized diamonds of cubo-octahedral shape with well-defined faces and sharp edges;top right :lower quality diamonds;bottom left :orange cBN crystals;bottom right :very large black cBN crystals of better shapes.A n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .8HAINESL ´EGERBOCQUILLONused in industrial pacts of cBN with TiC or TaN binders are ofmarkedly lower hardness because there is no direct bonding between the superhard crystals,in contrast to diamond compacts.In addition,they are expensive,and this has motivated the search for other superhard materials.SEARCH FOR NEW SUPERHARD MATERIALSOne approach for increasing hardness of known materials is to manipulate the nanostructure.For instance,the effect of particle size on the hardness of materials has been investigated.It is well known that high-purity metals have very low shear strengths;this arises from the low energy required for nucleation and motion of dislocations in metals.The introduction of barriers by the addition of impurities or grain size effects may thus enhance the hardness of the starting phase.In this case,intragranular and intergranular mechanisms are activated and compete with each other.As each mechanism has a different dependency on grain size,there can be a maximum in hardness as the function of the grain size.This effect of increasing the hardness with respect to the single-crystal value does not exist in the case of ceramic materials.In alumina,which has been thoroughly studied,the hardness (14)of fine-grained compacts is at most the hardness of the single crystal.When considering superhard materials,any hardness enhancement would have to come from the intergranular material,which would be by definition of lower hard-ness.In the case of thin films,it has been reported that it is possible to increase the hardness by repeating a layered structure of two materials with nanometer scale dimensions,which are deposited onto a surface (15).This effect arises from the repulsive barrier to the movement of dislocations across the interface between the two materials and is only valid in one direction for nanometer scale defor-mations.This could be suitable for coatings,but having bulk superhard materials would further enhance the unidirectional hardness of such coatings.In addition,hardness in these cases is determined from tests at a nanometer scale with very small loads,and results vary critically (up to a factor of three)with the nature of the substrate and the theoretical models necessary to estimate quantitatively the substrate’s influence (16).We now discuss the search for bulk superhard materials.Physics of HardnessThere is a direct relation between bulk modulus and hardness for nonmetallic ma-terials (Figure 3)(17–24),and here we discuss the fundamental physical properties upon which hardness depends.Hardness is deduced from the size of the inden-tation after an indenter has deformed a material.This process infers that many phenomena are involved.Hardness is related to the elastic and plastic properties of a material.The size of the permanent deformation produced depends on the resistance to the volume compression produced by the pressure created by the indenter,the resistance to shear deformation,and the resistance to the creation and motion of dislocations.These various types of resistance to deformation indicateA n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .SUPERHARD MATERIALS 9Figure 3Hardness as a function of the bulk modulus for selected materials (r-,rutile-type;c,cubic;m,monoclinic).WC and RuO 2do not fill all the requirements to be superhard (see text).which properties a material must have to exhibit the smallest indentation possible and consequently the highest hardness.There are three conditions that must be met in order for a material to be hard:The material must support the volume decrease created by the applied pressure,therefore it must have a high bulk modulus;the material must not deform in a direction different from the applied load,it must have a high shear modulus;the material must not deform plastically,the creation and motion of the dislocations must be as small as possible.These conditions give indications of which materials may be superhard.We first consider the two elastic properties,bulk modulus (B)and shear modulus (G),which are related by Poisson’s ratio (ν).We consider only isotropic materials;a superhard material should preferably be isotropic,otherwise it would deform preferentially in a given direction (the crystal structure of diamond is isotropic,but the mechanical properties of a single crystal are not fully isotropic because cleavage may occur).In the case of isotropic materials,G =(3/2)B (1−2ν)/(1+ν);In order for G to be high,νmust be small,and the above expression reduces thenA n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .10HAINESL ´EGERBOCQUILLONto G =(3/2)B (1−3ν).The value of νis small for covalent materials (typicallyν=0.1),and there is little difference between G and B:G =1.1B.A typical value of νfor ionic materials is 0.25and G =0.6B;for metallic materials νis typically 0.33and G =0.4B;in the extreme case where νis 0.5,G is zero.The bulk and shear moduli can be obtained from elastic constants:B =(c 11+2c 12)/3,G =(c 11−c 12+3c 44)/5.Assuming isotropy c 11−c 12=2c 44,it follows that G =c 44;Actually G is always close to c 44.In order to have high values of B and G,then c 11and c 44must be high with c 12low.This is the opposite of the central forces model in which c 12=c 44(Cauchy relation).The two conditions,that νbe small and that central forces be absent,indicate that bonding must be highly directional and that covalent bonding is the most suitable.This requirement for high bulk moduli and covalent or ionic bonding has been previously established (17–19,21–24)and theoretical calculations (19,25,26)over the last two decades have aimed at finding materials with high values of B (Figure 3).The bulk modulus was used primarily for the reason that it is cheaper to calculate considering the efficient use of computer time,and an effort was made to identify hypothetical materials with bulk moduli exceeding 250–300GPa.At the present time with the power of modern computers,elastic constants can be obtained theoretically and the shear modulus calculated (27).The requirement for having directional bonds arises from the relationship be-tween the shear modulus G and bond bending (28).Materials that exhibit lim-ited bond bending are those with directional bonds in a high symmetry,three-dimensional lattice,with fixed atomic positions.Covalent materials are much better candidates for high hardness than ionic compounds because electrostatic interac-tions are omnidirectional and yield low bond-bending force constants,which result in low shear moduli.The ratio of bond-bending to bond-stretching force constants decreases linearly from about 0.3for a covalent material to essentially zero for a purely ionic compound (29,30).The result of this is that the bulk modulus has very little dependence on ionicity,whereas the shear modulus will exhibit a relative de-crease by a factor of more than three owing entirely to the change in bond character.Thus for a given value of the bulk modulus,an ionic compound will have a lower shear modulus than a covalent material and consequently a lower hardness.There is an added enhancement in the case of first row atoms because s-p hybridization is much more complete than for heavier atoms.The electronic structure also plays an important role in the strength of the bonds.In transition metal carbonitrides,for example,which have the rock-salt structure,the hardness and c 44go through a maximum for a valence electron concentration of about 8.4per unit cell (31).The exact nature of the crystal and electronic structures is thus important for determin-ing the shear modulus,whereas the bulk modulus depends mainly on the molar volume and is less directly related to fine details of the structure.This difference is due to the fact that the bulk modulus is related to the stretching of bonds,which are governed by central forces.Materials with high bulk moduli will thus be based on densely packed three-dimensional networks,and examples can be found among covalent,ionic,and metallic materials.In ionic compounds,the overall structure isA n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .principally defined by the anion sublattice,with the cations occupying interstitial sites,and compounds with high bulk moduli will thus have dense anion packing with short anion-anion distances.The shear modulus,which is related to bond bending,depends on the nature of the bond and decreases dramatically as a func-tion of ionicity.In order for the compound to have a high shear modulus and high hardness (Figure 4),directional (covalent)bonding and a rigid structural topology are necessary in addition to a high bulk modulus.A superhard material will have a high bulk modulus and a three-dimensional isotropic structure with fixed atomic positions and covalent or partially covalent ionic bonds.Hardness also depends strongly on plastic deformation,which is related to the creation and motion of dislocations.This is not controlled by the shear modulus but by the shear strength τ,which varies as much as a factor of 10for different materials with similar shear moduli.It has been theoretically shown that τ/G is of the order of 0.03–0.04for a face-centered cubic metal,0.02for a layer structure such as graphite,0.15for an ionic compound such as sodium chloride,and 0.25for a purely covalent material such as diamond (32).Detailed calculationsmustFigure 4Hardness as a function of the shear modulus for selected materials (r-,rutile-type;c,cubic).A n n u . R e v . M a t e r . R e s . 2001.31:1-23. D o w n l o a d e d f r o m a r j o u r n a l s .a n n u a l r e v i e w s .o r g b y C h i n e s e A c a d e m y o f S c i e n c e s - L i b r a r y o n 05/16/09. F o r p e r s o n a l u s e o n l y .。

a rXiv:as tr o-ph/36332v117J un23A Role of the Boundary Shear Layer in Modeling of Large Scale Jets 1 L .Stawarz and M.Ostrowski Obserwatorium Astronomiczne,Uniwersytet Jagillonski,ul.Orla 171,30-244,Krak´o w,Poland 1Introduction:the aim of the study Large scale extragalactic jets,extending from a few to a few hundreds of kilo-parsecs from active galactic nuclei (AGNs),were frequently studied at radio frequencies.Recently,Hubble and Chandra telescopes gathered new detailedinformation about optical and X-ray emission of some of these objects.For a few hundreds of radio jets we know,only ∼20are observed at optical frequencies.Most of them are short and faint,with only a few exceptions al-lowing for detailed spectroscopic and morphological studies,like e.g.3C 273(Jester et al.,2001).Surprisingly,the large scale jets can be very prominent at X-rays in many different types of radio-loud AGNs.Up to now,more than 30jets were detected by Chandra at 1−10keV energy range,although a nature of this emission is still under debate.The Hubble observations indicate with no doubt a synchrotron nature of the optical emission.The first conclusion from the optical maps is a requirement of electron reacceleration within the whole jet volume,as their radiative lifetimesare usually much shorter than the time required for light to travel between the successive shocks.Sub-equipartition magneticfield and highly relativistic bulk velocities alone cannot remove this problem(Jester et al.,2001).Also,a spectral character of the radio-to-optical continuum,if carefully analyzed,is not consistent with simple versions of the shock-in-a-knot models.The X-ray observations are even more puzzling,because in many cases it is not clear if the detected keV photons–probably non-thermal in nature–result from synchrotron or inverse-Compton emission.In any case,in order to explain the observed high luminosities and spectra of the Chandra jets,one has to invoke more or less extreme conditions,like large beaming factors or presence of very high energy electrons(Harris&Krawczynski,2001).Once again,details of the electron acceleration processes responsible for the observed X-ray emission are not clear.On the other hand,radio and optical observations reveal also a complex jet spatial structure indicating a spine-boundary shear layer morphology.As emphasized below,such boundary shear layers are prevailed sites of particle acceleration,especially in cases of relativisticflows,and therefore should be seriously considered as an option/addition to the shock-in-a-knot models in studying the jet multiwavelength emission.In fact,contribution of the shear layer to the jet radiative output results not only from the involved electron ac-celeration,but also from kinematic effects influencing the composed relativis-tic jet spectrum.Recent optical and X-ray observations give us an important insight into the mentioned processes and effects.2Sheared jets:electron accelerationAs pointed by de Young(1986),interaction between the jet matter and the surrounding medium result in formation of the shear layer at the jet bound-ary.Such boundary regions are likely to be highly turbulent because of their very high Reynold numbers.Therefore,stochastic particle acceleration acting thereby seems to be also inevitable.Numerical simulations confirm presence of the turbulent layer with a velocity shear surrounding fast central spine of the jet(Aloy et al.,1999),although the exact nature of the shear regions is still hardly known.With no doubt,they play an important role in stabilizing theflow with respect to the Kelvin-Helmholtz(KH)instabilities(Birkinshaw, 1991).They are the places where the large-scale KH instabilities form and cascade to shorter wavelengths,which dissipate turbulence energy by reso-nant interactions with thermal and relativistic particles(Eilek,1982).Such stochastic interactions can be additionaly influenced by weak oblique shocks developed within the boundary shear regions,as suggested once again by nu-merical simulations.In addition,a presence of the velocity gradient can also modify the particle energy distribution due to effects of a‘cosmic ray viscosity’,discussed e.g.by Ostrowski(2000).Thus,modeling of the electron accelera-tion processes acting within the boundary shear layers of large scale jets is difficult and requires several assumptions about the boundary layer internal structure.One of these assumptions refers to the magneticfield configuration and intensity.Both observations and theoretical considerations suggest that the magneticfield in the boundary regions is parallel on average to the jet axis due to shearing effects.One should expect that a strong velocity shear may influence not only the magneticfield configuration,but also its intensity by a dynamo process(Urpin,2002).An order-of-magnitude analysis of time scales connected with electron momen-tum and spatial diffusion in a boundary layer medium shows,that for typi-cal parameters of the large scale relativistic jets in powerful radio sources the boundary layer electrons undergo mainly second-order Fermi acceleration,and that the time scale for electron escape from the acceleration region is extremely long as compared to the radiative losses time scale(Stawarz&Ostrowski, 2002a).As a result,electrons form aflat power-law energy distribution with a harder high energy component modelled by us as a pile-up bump at the maxi-mum energy(Ostrowski,2000).Under the condition of continuous and efficient electron acceleration acting within the whole highly turbulent boundary layer volume,involving large amplitude MHD turbulence leading to the scattering mean free path comparable to the electron gyroradius,a balance between ac-celeration and radiative losses allow for electron maximum energy,typically,∼108m e c2.One should note,however,that formation of the terminal Eeqhard component in the electron energy spectrum can be a non-stationary process(Stawarz&Ostrowski,2002b).In principle,its normalization grows with time for the considered continuous particle injection,while its spectral width increases over larger and larger energy range due to momentum dif-fusion.In Stawarz&Ostrowski(2002a)we modeled the pile-up bump as a monoenergetic peak with total energy density limited by the equipartition with the magneticfield.This requires further studies of the electron energy evolution(Stawarz&Ostrowski,2003).However,we would like to stress out, that the pile-up effects forming afinal stationary hard spectral component at the highest electron energies seem to be inevitable in the considered case of the boundary layer acceleration.3Conclusions:boundary shear layer emissionIt is known,that emission from the shear boundary layer can decrease jet-counterjet radio brightness asymmetry,influencing estimations of the jet bulk Lorentz factors(Komissarov,1990).Also,because of the kinematic effects, different radiationfields can dominate the inverse-Compton emission of the boundary layer electrons as compared to the spine electrons,affecting theobserved jet high energy radiation(Celotti et al.,2001).However,an impor-tant effect of the boundary shear layer on the jet radiative output is due to stochastic and continuous electron acceleration acting within the whole boundary layer volume,most likely resulting in effective accumulation of the radiating electrons around the maximum energy E eq.For typical large scale jet parameters,synchrotron radiation of the electrons with E≪E eq can ac-count for almost constant along the jet radio-to-optical continuum,while the electrons with E∼E eq can be responsible–at least for some sources–for the relatively strong X-ray emission detected by Chandra(Stawarz&Ostrowski, 2002a).Combination of the effects connected with spectral pile-ups and rel-ativistic beaming in a medium with velocity shear,as well as an interplay between the stochastic and the shock acceleration,can possibly explain spec-tral variety and complexity of the Chandra jets.In our simple model we in fact consider two distinct relativistic electron pop-ulations,which differ because of the spatial location(knots–jet edges), nature of the acceleration(regular–stochastic)and kinematic effects in-volved(fast central spine–shear boundary layer).However,additional pro-cesses can also lead to several complications of such simple two-population model,like for instance formation of oblique shocks within the boundary re-gion(Bicknell&Melrose,1982)or a turbulent mixing of the spine and the boundary layer medium.Whatever the case is,the efficient particle accelera-tion taking place at the jet boundary can influence the observed jet radiative properties.By its nature,it is also connected with the issue of jet internal structure and jet stability in relates to the MHD instabilities excited at the jet surface.Thus,to understand multiwavelength emission of the jets it is important to study a role of its boundary shear layer,and the acceleration processes acting thereby.ReferencesAloy,M.A.,et al.1999,ApJL,523,L125Bicknell,G.V.,Melrose,D.B.1982,ApJ,262,511Birkinshaw,M.1991,MNRAS,252,505Celotti,A.,Ghisellini,G.,Chiaberge,M.2001,MNRAS,321,L1de Young,D.S.1986,ApJ,307,62Eilek,J.A.1982,ApJ,254,472Harris,D.E.,Krawczynski,H.2001,ApJ,565,244Jester,S.,et al.2001,A&A,373,447Komissarov,S.S.1990,SvAL,16,284Ostrowski,M.2000,MNRAS,312,579Stawarz, L.,Ostrowski,M.2002a,ApJ,578,763Stawarz, L.,Ostrowski,M.2002b,PASA,19,22Stawarz, L.,Ostrowski,M.2003,in preparationUrpin,V.2002,A&A,in press。

Types SCR and SCR-D Indoor current transformersProduct features−600 volt, indoor, 10 kV BIL−25 - 400 Hertz−P rimary amperes: 50 - 5000−M echanical rating: 180 x rated current−T hermal rating: 80 x rated current, one second−C ontinuous current rating factor:2.0 @ 30°C ambient1.5 @ 55°C ambientApplicationThe SCR and SCR-D current transformers are used as the source of current for relaying and metering. The deeper case SCR-D is used when high burden relaying and metering is required.Construction featuresThe ring-type core is insulated and toroidally wound with a fully distributed secondary winding. The protective case, made of an impact-resistant polycarbonate, is ultrasonically sealed. Secondary terminalsSecondary terminals are 8-32 brass terminal screws with hardware. Space is available for a maximum of five terminals to accommodate multi-ratio designs.CurvesSaturation, overcurrent, ratio correction factor, and phase-angle curves are available upon request.Test reportsIEEE test reports are stored electronically and can be e-mailed in various formats at the time of shipment.StandardsThis unit meets all applicable IEEE and NEMA standards and is a UL Recognized Component.DimensionsTypes SCR (approximate weight: 32 lbs)Types SCR-D (approximate weight: 62 lbs)Provided by Northeast Power Systems, Inc. 1V A P 428791-D B J u l y 2013 R e v . BFor more information please contact:ABB Inc.Medium Voltage Distribution Components 3022 NC 43 North Pinetops, NC 27864 USAPhone: +1 252 827 3212Fax: +1 252 827 /mediumvoltageNote:The information contained in this document is for general information purposes only. While ABB strives to keep the information up to date and correct, it makes no representations or warranties of any kind, express or implied, about the completeness, accuracy, reliability, suitability or availability with respect to theinformation, products, services, or related graphics contained in the document for any purpose. Any reliance placed on such information is therefore strictly at your own risk. ABB reserves the right to discontinue any product or service at any time.Copyright 2004 ABB. All rights reserved.Additional styles available upon request. Contact your ABB sales representative orcall +1-252-827-3212 for more information.UL Recognized Component; File No. E96461Selection guidePrimary ampere rating B-0.1B-0.2B-0.5B-0.9B-1.8IEEE relaying accuracy StylenumberType SCR (7.02" window)50 4.8 4.8---C59628A62G1775 2.4 4.8---C109628A62G18100 2.4 4.8---C109628A62G011500.6 1.2 2.4--C209628A62G022000.6 1.2 1.2--C209628A62G032500.60.6 1.2 2.4-C209628A62G043000.60.60.6 1.2 2.4C209628A62G054000.30.60.6 1.2 2.4C509628A62G065000.30.30.30.6 1.2C509628A62G076000.30.30.30.6 1.2C1009628A62G088000.30.30.30.60.6C1009628A62G0910000.30.30.30.30.3C1009628A62G1012000.30.30.30.30.3C2009628A62G1115000.30.30.30.30.3C2009628A62G1220000.30.30.30.30.3C2009628A62G1325000.30.30.30.30.3C2009628A62G1430000.30.30.30.30.3C2009628A62G1540000.30.30.30.30.3C2009628A62G16Multi-ratio, IEEE, 5 Terminal 6000.30.30.30.6 1.2C1009628A64G0112000.30.30.30.30.3C2009628A64G0220000.30.30.30.30.3C2009628A64G0330000.30.30.30.30.3C2009628A64G0440000.30.30.30.30.3C2009628A64G0550000.30.30.30.30.3C2009628A64G06IEEE metering accuracy Selection guidePrimary ampere rating B-0.1B-0.2B-0.5B-0.9B-1.8IEEE relaying accuracy StylenumberType SCR-D (7.02" window)50 1.2 2.4---C109628A63G1775 2.4 2.4 4.8--C209628A63G181000.6 1.2 2.4--C209628A63G011500.6 1.2 1.2 2.4 4.8C509628A63G022000.30.30.6 1.2 2.4C509628A63G032500.30.30.60.6 2.4C509628A63G043000.30.30.30.6 1.2C1009628A63G054000.30.30.30.60.6C1009628A63G065000.30.30.30.30.3C1009628A63G076000.30.30.30.30.3C2009628A63G088000.30.30.30.30.3C2009628A63G0910000.30.30.30.30.3C2009628A63G1012000.30.30.30.30.3C4009628A63G1115000.30.30.30.30.3C4009628A63G1220000.30.30.30.30.3C4009628A63G1325000.30.30.30.30.3C4009628A63G1430000.30.30.30.30.3C4009628A63G1540000.30.30.30.30.3C4009628A63G16Multi-ratio, IEEE, 5 Terminal6000.30.30.30.30.6C2009628A65G0112000.30.30.30.30.3C4009628A65G0220000.30.30.30.30.3C4009628A65G0330000.30.30.30.30.3C4009628A65G0440000.30.30.30.30.3C4009628A65G0550000.30.30.30.30.3C4009628A65G06IEEE metering accuracy Provided by Northeast Power Systems, Inc. STANDARD CURRENTTRANSFORMER MULTI-RATIO TAPSBURDEN STANDARDS136Provided by Northeast Power Systems, Inc. 42879 CurvesR e f e r t o P r i c e L i s t 42-800 f o r m o r e i n f o r m a t i o n J a n u a r y 2001ABB Power Distribution655 Century Point Lake Mary, FL 32476 Tel: + 1-800-929-7947 Fax: + 1-407-732-2132/distributionProvided by Northeast Power Systems, Inc.。

Single-atom catalysis of CO oxidation using Pt1/FeO xBotao Qiao,1 Aiqin Wang,1 Xiaofeng Yang,2 Lawrence F. Allard,3 Zheng Jiang,4 Yitao Cui,5 Jingyue Liu,6, 1* Jun Li2* and Tao Zhang1*1State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China. 2Department of Chemistry, Tsinghua University, Beijing 100084, China. 3Materials Science and Technology Division, Oak R idge National Laboratory, Oak R idge, TN 37831, USA. 4Shanghai Synchrotron R adiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201204, China. 5State Key Laboratory of Molecular R eaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China. 6Center for Nanoscience, Department of Physics & Astronomy, and Department of Chemistry & Biochemistry, University of Missouri-St. Louis, Missouri 63121, USA.* To whom correspondence should be addressed. E-mail: taozhang@ (T. Zhang); liuj@ (J. Liu); junli@(J. Li)Table of ContentsSupplementary Fig. S1............................................................................................3 and 4 Supplementary Fig. S2 (5)Supplementary Fig. S3 (6)Supplementary Fig. S4 (7)Supplementary Fig. S5 (8)Supplementary Fig. S6 (9)Supplementary Fig. S7 (10)Effect of impurity on the catalyst (11)Supplementary Fig. S8 (12)Supplementary Fig. S9 (13)Supplementary Fig. S10 (14)Catalytic stability of Pt1/FeO x (15)Supplementary Fig. S11 (15)Supplementary Fig. S12 (16)Supplementary Fig. S13 (17)Computational Details (18)Supplementary Figure S14 (20)Supplementary Fig. S15 (21)Supplementary Fig. S16 (22)Understanding the Remarkable Catalytic Activity of Pt1/FeO x (23)Supplementary Fig. S17 (24)Supplementary Table S1 (25)Supplementary Table S2 (26)Supplementary Table S3 (27)Supplementary Table S4 (28)Supplementary Table S5 (29)References (30)baSupplementary Fig. S1 Representative aberration-corrected HAADF-STEM images of sample A with high magnification (a, b) and with relatively low magnification (c). Only Pt single atoms were observed.cSupplementary Fig. S2 Aberration-corrected HAADF-STEM images of sample B with a relatively low magnification.It showed the presence of sub-nanometer Pt clusters and absence of larger Pt clusters or particles.Supplementary Fig. S3 The observed frequencies of single P t atoms and P t clusters in sample B. By assuming that a cluster of 0.2~0.5 nm contains about10 atoms, a 0.5~1 nm cluster contains about 20 atoms, and a 1-2 nm cluster contains about 60 atoms (a rough estimation based on HAADF images), one can estimate that the single Pt atoms in sample B represent only about 1.8 atom% of the total amount of Pt.Supplementary Fig. S4 XRD patterns of samples A and B after reduction at 200 o C for 30 min with 10% H2/He.Supplementary Fig. S5 k1-weighted raw EXAFS spectra at the P t L3-edge for sample A, sample B, P t foil, and P tO2. Both sample A and sample B are characterized by the absence of oscillations at high k region of k > 8 Å-1, indicating the dominance of low-Z backscatters which should be oxygen in our system.Supplementary Fig. S6 FT-IR spectra of CO adsorption on sample B. (a) Introduction of 8.1 torr CO followed by evacuation for 30 min, and then introduction of O2 up to 10.0 torr. A new peak evolved at 2070 cm-1 after introduction of O2, indicating the Pt0 clusters were oxidized. (b) Introduction of 5.1 torr CO followed by introduction of H2 up to 16.2 torr. The peak position and intensity were not changed with introduction of H2.Supplementary Fig. S7 FT-IR spectra of CO adsorption on sample A. The two figures indicate that the introduction of O2 (a, pre-adsorption of 8.0 torr CO followed by evacuation for 30 min, and then introduction of O2 to the corresponding pressure) or H2 (b, pre-adsorption of 11.5 torr CO followed by evacuation for 30 min, and then introduction of H2 to the corresponding pressure) did not result in any changes in the vibration frequency of CO.Effect of impurity on the catalystThe stability and catalytic activity of single Pt atoms on the F eO x support are exceptional. To exclude the possible effect of the impurities on the support surface, we made further compositional analyses of the FeO x support. The result shows that the main impurity is sodium (0.49 wt%) originating from the sodium carbonate that we used as a precipitation agent. Other impurities, including Si, Mn, and Ca, are less than 0.2 wt% in total; these impurities were probably introduced by the iron nitrate reagent. The blank test shows that the impurities have little influence on the catalytic performance of the single Pt atom catalyst.Very recently, it has been reported that Na+ may play a crucial role in stabilizing the OH- associated with Pt single atoms, and then largely boosts the catalytic activity for water-gas shift reaction1. To investigate if the Na+ in our Pt1/FeO x catalyst has a similar promotional effect on the catalytic activity, we conducted a control experiment by replacing sodium carbonate with ammonium carbonate as the precipitating agent. The resulting catalyst was evaluated for the PROX reaction. As shown in Supplementary Fig. S9, the catalytic performance of the Na-free sample is comparable to that of sample A. Therefore, we can unambiguously conclude that the presence of Na+ in our catalyst A does not affect the exceptional activity of the Pt1/FeO x catalyst.Supplementary Fig. S8 O 1s XPS spectrum of sample A. The shoulder centered at 532.0 eV is mainly due to the hydroxyl groups on the FeO x support.Supplementary Fig. S9The catalytic performance of the Na-free sample for PROX reaction. Reaction conditions: flow rate: 25 mL/min; catalyst: 83 mg; reaction temperature: 80 o C.Supplementary Fig. S10 CO conversion (solid symbols) and CO 2 selectivity (open symbols) with the time-on-stream for P ROX reaction at 80 o C. The feed gas composition was 40 vol% H 2, 1 vol% CO, 1 vol% O 2 and balance He. Space velocities were (a), 2.1×106 ml ·g Pt -1·h -1 for sample A, 7.5×105 ml ·g Pt -1·h -1 for sample B, and 4.3×105 ml ·g Au -1·h -1 for Au/Fe 2O 3 and (b), 1.1 × 107 ml ·g Pt -1·h -1 for sample A .baCatalytic stability of Pt1/FeO xTo further investigate the stability of sample A against reduction or oxidation treatments, we first tested the catalytic performance of freshly reduced sample A under an increased space velocity to control the CO conversion at about 30% (Supplementary Fig. S11). Then, after the reaction, the sample was treated with 5 vol% O2/He at 200 o C for 30 min followed by re-evaluation under PROX conditions. The result showed that the CO conversion decreased by 5% after such an oxidation treatment. The activity decay was most probably caused by the partial oxidation of low-valence Fe during the oxidation treatment3,4. However, upon re-reduction at 200 o C with H2 for 30 min, the CO conversion was restored again to the same level as that of the fresh catalyst. Such oxidation-reduction treatments were conducted several times and no irreversible deactivation was observed. This result suggests that the Pt atoms in sample A did not agglomerate under mild oxidation-reduction conditions.Supplementary Fig. S11 The catalytic performance of sample A after sequential reduction and oxidation treatments at 200 o C for two cycles.Supplementary Fig. S12 Representative HAADF images of sample A after a steady reaction period of 1000 min under typical PROX conditions. The STEM images show that even after 1000 min run the Pt 1/FeO x catalyst still primarily consists of isolated individual Pt atoms dispersed onto the FeO x nanocrystallites.Supplementary Fig. S13In-situ DIRFT spectra of CO adsorbed on sample A with the time-on-stream for P ROX reaction at 80 o C. The feed gas composition was 40 vol% H2, 1 vol% CO, 1 vol% O2 and balance He. Space velocity was 1×108 ml·g Pt-1·h-1. All the spectra were obtained by purging with He for 5 min to remove the gas peak of CO.DOI: 10.1038/NCHEM.1095Computational DetailsThe (0001) surfaces of α-Fe2O3 were represented by a periodic slab model, constructed using bulk cell dimensions: a = b = 5.04 Å and c = 13.72 Å. Sinceα-Fe2O3 is antiferromagnetic and has atomic moment on iron atoms, we used theprimitive rhombohedral unit cell of Fe2O3 with the magnetic configuration (+ – – +)to build the surface slab, which was previously proved to be energetically the mostfavored magnetic configuration for α-Fe2O35. The repeated slabs were separated fromtheir neighboring images by a 12 Å-width vacuum in the direction perpendicular tothe surface. Considering the usually very large relaxations of the Fe2O3 surfaces6,7, wechose slabs containing 12 layers of Fe atoms, and 5, 6, and 7 atomic layers of O3 tomodel the double-Fe-terminated, single-Fe-terminated, and the O3-terminated surfaces,respectively. The 10 top-layer slabs of the surface were allowed to relax while theother layers beneath the surface were frozen during the geometry optimizations.The theoretical calculations were performed at the level of relativistic density functional theory (DF T) using the Vienna ab-initio simulation package (VASP)8-11.The core and valence electrons were represented by the projector augmented wave(PAW) method and plane-wave basis functions with a kinetic energy cut-off of 400eV12,13. Inasmuch as Pt has significant relativistic effects, the mass-velocity andDarwin relativistic effects were included through the PAW potentials. Thegeneralized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE)exchange-correlation functional was used in the calculations14. A Monkhorst-Packgrid of size of 3×3×1 was used to sample the surface Brillouin zone15. Ground-stateatomic geometries were obtained by minimizing the forces on the atoms to below 0.02 eV/Å. Because of the strong d-electron correlation effects for F e, the calculations were carried out with the DF T+U method, using the formalism suggested by Liechtenstein and Dudarev et al.16. The parameters were set at U = 4 eV and J = 1 eV according to previous reports17. We have also investigated how the values of U affect the thermodynamics of CO adsorption and its vibrational frequencies. The results of such calculations are listed in Supplementary Table S5. It can be seen that the different U terms have only little influence on the adsorption energy of CO. Especially, the vibrational frequencies of the CO stretching mode at different U terms are almost constant, indicating that the U and J terms are reliable for our systems.The transition states were obtained by relaxing the force below 0.05 eV/Å by using the CI-NEB method18Supplementary Figure S14 Differently located sites for P t atom over three Fe 2O 3(001) surfaces with different termination (I, Single-Fe-terminated; II, Double-Fe-terminated; III, O 3-terminated), and the relaxation of surfaces in the z-direction relative to an unrelaxed surface.Supplementary Fig. S15 Top and side view of the Fe2O3 (0001) O3-termination hematite surface. Only the threefold hollow (TH) sites are marked.Supplementary Fig. S15 Top and side view of the Fe2O3 (0001) O3-termination hematite surface. Only the threefold hollow (TH) sites are marked.Supplementary Fig. S16 H2-TPR profiles of Fe2O3 (a), Sample A (b) and Sample B (c).DOI: 10.1038/NCHEM.1095Understanding the Remarkable Catalytic Activity of Pt1/FeO xIn order to understand the remarkable catalytic role of single-Pt-atoms, we compared the properties of Ptδ+ in the single-Pt-atoms anchored on the FeO x supportand Pt(0) in the metallic Pt x clusters. Calculations were carried out to reveal theorbital interactions between CO and Pt-(O-)3 cluster and the orbital interactionsbetween CO and Pt10 cluster. Here in the Pt-(O-)3 cluster the oxygen atoms weresaturated by H atoms to approximately preserve the correct coordination environment.The Pt10 cluster was selected to approximately represent a small Pt cluster. All thesecluster calculations and orbital interaction analyses were performed with ADFprogram (ADF, ) using PBE exchange-correlation functional andthe TZ2P basis sets. The orbital interactions are depicted in Supplementary Fig. S17.Our model calculations indicate that upon adsorption of CO the 5d-orbitaloccupation of the Ptδ+ single-atom anchored on the three O-atoms from the supportsurface is 7.996e-, which is significantly lower than that of the Pt(0) atoms in thecluster (8.6e- ~ 8.8e-). Therefore the d-orbital vacancy is larger for the single-Pt atomsthan for the metallic Pt(0) in the clusters or bulk Pt. As a result, the back-donationinteraction from Pt to CO is much smaller for Ptδ+ than for Pt(0). Indeed, as shown inFigure S17, the CO 2π∗-orbitals are raised only slightly (to -2.168 ~ -2.195 eV), butthey are pushed to much higher energies (-1.865 ~ -1.806 eV) due to Pt(5d)-CO(2π*)back-donation interaction. Accordingly, the calculated charge-transfer from Pt to COis only 1/3 for Ptδ+ than for Pt(0), indicating that the CO-adsorption is weaker on Ptδ+than on Pt(0). This is not only consistent with the experimental IR frequency shifts,but also explains the high catalytic activity. Because CO cannot adsorb strongly on the Ptδ+ center, this single-Pt-atom is less poisoned by CO and more accessible for O2, which lead to lower activation barrier.Supplementary Fig. S17 Orbital interactions between CO and P t single atoms and Pt cluster. All the molecular levels with major Pt 5d-character are represented by the hatched area. The Pt dπ-type orbitals (d xz,yz) of Pt atoms will interact with the 2π* orbital of CO, while the Pt dσ-type orbital will mix with the 5σ orbital of CO.Supplementary Table S1 EXAFS parameters of three candidate models of samples A (Δk = 2.8 to 10.0 Å-1).Sample Shell N R(Å) ∆σ2x103(Å2)∆E o(eV)R-factorPt-O 1.9 2.02 4.19 9.8 0.037 Sample A(Model I)Pt-Fe 0.9 2.88 1.73 -10.0Pt-O 1.6 2.01 1.00 10.8 0.045 Sample A(Model II)Pt-Fe 1.0 2.53 11.6 2.9Pt-O 1.4 2.01 1.00 10.5 0.087 Sample A(Model III)Pt-Pt 2.0 2.55 10.1 -10.0N, coordination number; R, distance between absorber and backscatter atoms; Δσ2, change in the Debye–Waller factor value relative to the Debye–Waller factor of the reference compound; ΔE0, inner potential correction accounting for the difference in the inner potential between the sample and the reference compound. Error bounds (accuracies) characterizing the structural parameters obtained by EXAFS spectroscopy are estimated to be as follows: N, ±20%; R, ±1%; Δσ2, ±20%; and ∆E o, ±20%. R-factor is always used when you are comparing different models or the quality of the fit is actually in question. Better you fitting the curve, smaller R-factor value you’ll get it. Generally, an acceptable R-factor should be smaller than 5%. According to the R-factor of different models, model I is the most reasonable model. It is specially noted that the fitting result based on model III has a R-factor of 0.087, which is too large to be acceptable. Therefore, it is convinced that there is no Pt-Pt bonding in sample A.Supplementary Table S2 S pecific reaction rates and turnover frequencies (TOFs) of some typical Pt catalysts reported in literatures.Pt loadings (wt%) Reaction Temperature(o C)Specific rate×102(mol CO h-1 g/Pt-1)TOF×102(s-1)NotePt/Al2O30.4 CO oxidation 150 -- 0.36 Ref 19 Pt/SiO2 5 CO oxidation 150 -- 0.072 Ref 19 Pt/CeO x/Al2O30.4 CO oxidation 50 --0.29 Ref 19 Pt/MnO x/SiO2 5 CO oxidation 50 -- 0.19 Ref 19 Pt/CoO x/SiO2 5 CO oxidation 0 --0.33 Ref 19 Pt/SiO2 2 CO oxidation >100 --<7 Ref 20 Pt/TiO2 1.0 CO oxidation 27 < 6.84 < 0.38 Ref 21 Pt/TiO20.5 CO oxidation 27 < 0.86 < 0.92 Ref 21 K-Pt/Al2O3 2 PROX 80 24.4 3.3 Ref 22 M-Pt/Al2O3a 2 CO oxidation,PROX100 -- <4 Ref 23 Pt3Sn/C ~16.6 PROX 80 -- 15 Ref 24 a M=Li, Na, K, Rb, CsSupplementary Table S3 Differently located sites for P t atom over three Fe2O3(001) surfaces with different termination.Single-Fe-terminated Double-Fe-terminated O3-terminatedSites Energy/eV Sites Energy/eV Sites Energy/eVTH_a -2.25 Top_Fe_a -4.17 TH_a -6.03TH_b -2.60 Top_Fe_b -5.29 TH_b -4.24Top_Fe -2.02 TH_a -4.22 TH_c -6.67Top_O -3.10 Bridge_Fe -5.51 TH_d -6.39Bridge_O -2.80 Top_O -5.34Bridge_O_a -5.32Bridge_O_b -5.89Bridge_O_c -4.24*TH, top, and bridge represent the three-fold hollow, top and bridge sites, respectively (see Figure S11)Supplementary Table S4Bader charge, CO adsorption energies, and vibrational frequencies for CO adsorption at Pt single atoms on Fe2O3-O vac and on free Pt10 cluster.Pt/Fe2O3-O vac Pt10Bader charges (|e|) 0.45 --νC-O (cm-1) 2062 2018E ad-CO (eV) -1.96 -3.05Supplementary Table S5 The effects of U terms on the adsorption properties of CO over Pt1/Fe2O3(001).U / eV (J=1 eV) 2.0 3.0 4.0 5.0 6.0 8.0E ad(CO) / eV -1.90 -1.93 -1.96 -1.99 -2.02 -2.25νCO /cm-12058 2061 2062 2062 2062 2066DOI: 10.1038/NCHEM.1095References1Zhai, Y. et al. Alkali-stabilized Pt-OH x species catalyze low-temperature water-gas shift reactions. Science329, 1633-1636 (2010).2Liu, K. et al. Microkinetic Study of CO Oxidation and PROX on Ir-Fe Catalyst. Ind. Eng.Chem. Res.50, 758-766(2010).3F u, Q. et al. Interface-confined ferrous centers for catalytic oxidation. Science328, 1141-1144 (2010).4Liu, K. et al. Quasi in situ 57Fe Mossbauer spectroscopic study: Quantitative correlation between Fe2+ and H2 concentration for PROX over Ir-Fe/SiO2 catalyst. J. Phys. Chem. C114, 8533-8541 (2010).5Sandratskii, L. M., Uhl, M. & Kübler, J. Band theory for electronic and magnetic properties of α-Fe2O3. J. Phys.: Condens. Matter8, 983-989 (1996).6Wang, X. G. et al. The hematite (α-Fe2O3) (0001) surface: Evidence for domains of distinct chemistry. Phys. Rev. Lett.81, 1038-1041 (1998).7Lübbe, M. & Moritz, W. A LEED analysis of the clean surfaces of α-Fe2O3 (0001) and α-Cr2O3 (0001) bulk single crystals. J. Phys.: Condens. Matter21, 134010 (2009).8Kresse, G. & Hafner, J. Abinitio molecular-dynamics for liquid-metals. Phys. Rev. B 47, 558-561 (1993).9Kresse, G. & Hafner, J. Ab-initio molecular-dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium. Phys. R ev. B.49, 14251-14269(1994).10Kresse, G. & Furthmuller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15-50 (1996).11Kresse, G. & F urthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B54, 11169-11186 (1996).12Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B50, 17953-17979 (1994).13Kresse, G. & Joubert, J. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B59, 1758-1775 (1999).14Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation madeNATURE CHEMISTRY | /naturechemistry 31DOI: 10.1038/NCHEM.109531 simple. Phys. Rev. Lett. 77, 3865-3868 (1996).15 Monkhorst, H. J. & Pack, J. D. Special points for brillouin-zone integrations. Phys. Rev.B . 13, 5188-5192 (1976).16 Dudarev, S. L. et al. Electronic structure and elastic properties of strongly correlatedmetal oxides from first principles: LSDA+U SIC-LSDA and EELS study of UO 2 and NiO. Phys. Status Solidi A 166, 429-443 (1998).17 Rollmann, G., Rohrbach, A., Entel, P. & Hafner, J. F irst-principles calculation of thestructure and magnetic phases of hematite. Phys. Rev. B 69, 165107 (2004).18 Henkelman, G., Uberuaga, B. P. & Jónsson, H. A climbing image nudged elastic bandmethod for finding saddle points and minimum energy paths. J. Chem. Phys 113, 9901-9904 (2000).19 Mergler, Y. J., van Aalst, A., van Delft, J. & Nieuwenhuys, B. E. CO oxidation overpromoted Pt catalysts. Appl. Catal. B 10, 245-261 (1996).20 Gracia, F. J., Bollmann, L., Wolf, E. E., Miller, J. T. & Kropf, A. J. In situ FTIR, EXAFS,and activity studies of the effect of crystallite size on silica-supported Pt oxidation catalysts. J. Catal. 220, 382-391 (2003).21 Bamwenda, G. R., Tsubota, S., Nakamura, T. & Haruta, M. The influence of thepreparation methods on the catalytic activity of platinum and gold supported on TiO 2 for CO oxidation. Catal. Lett. 44, 83-87 (1997).22 Minemura, Y. et al. Preferential CO oxidation promoted by the presence of H 2 overK-Pt/Al 2O 3. Chem. Commun., 1429-1431 (2005).23 Minemura, Y., Kuriyama, M., Ito, S.-i., Tomishige, K. & Kunimori, K. Additive effect ofalkali metal ions on preferential CO oxidation over Pt/Al 2O 3. Catal. Commun. 7, 623-626 (2006).24 Schubert, M. M. et al. Bimetallic PtSn catalyst for selective CO oxidation in H 2-richgases at low temperatures. Phys. Chem. Chem. Phys. 3, 1123-1131 (2001).© 2011 Macmillan Publishers Limited. All rights reserved.。

a r X i v :c o n d -m a t /0506616v 1 [c o n d -m a t .s t a t -m e c h ] 23 J u n 2005Europhysics Letters PREPRINT Electromagnetic instability of the Thomson Problem Jayme De Luca (∗),Savio B.Rodrigues (∗∗)and Yan Levin (∗∗∗)∗Departamento de F´ısica,Universidade Federal de S˜a o Carlos,Rod.Washington Luiz km 235,13565-905,Caixa Postal 676,S˜a o Carlos,SP,Brazil ∗∗Departamento de Matem´a tica,Universidade Federal de S˜a o Carlos,Rod.Washington Luiz km 235,13565-905,Caixa Postal 676,S˜a o Carlos,SP,Brazil ∗∗∗Instituto de F´ısica,Universidade Federal do Rio Grande do Sul Caixa Postal 15051,CEP 91501-970,Porto Alegre,RS,Brazil –Order-disorder transformations;statistical mechanics of model systems.PACS.71.10.-w –Electron gas-theories and models.Abstract.–The classical Thomson problem of n charged particles confined to the surface of a sphere of radius a is analyzed within the Darwin approximation of electrodynamics.For n <n c (a )the ground state corresponds to a hexagonal Wigner crystal with a number of topological defects.However,if n >n c (a )the Wigner lattice is unstable with respect to small perturbations and the ground state becomes spontaneously magnetized for finite n .The Thomson problem,finding the ground state of electrons inside a sphere with a uniform neutralizing background,has a time honored position in the history of modern physics [1–7].The original question was posed by J.J.Thomson [8]after his discovery of the electron in 1897.Thomson conjectured that the knowledge of the positions of the electrons inside the atoms is essential to understanding the regularity of the chemical elements in the periodic table.At the time,however,proton still had to wait 14years to be discovered,so in order to keep his atom neutral,Thomson was forced to introduce a uniform neutralizing background.The model became known as the “plum pudding”atom and the question that needed to be answered was:What are the positions of the electrons inside a uniformly (positively)charged sphere?Surprisingly,after more than a century this problem still has no general solution.If the background charge is made to vanish,the electrostatic energy will be a minimum only if all the electrons are located at the surface.This is a general consequence of the Earn-shaw theorem [9]which precludes existence of a stable equilibrium with purely electrostatic interactions.Curiously,the Coulomb potential is precisely on the border line where this be-havior is possible.If instead of 1/r ,the electrons would interact by a 1/r 1+ǫpotential with ǫ>0,the bulk occupation of the sphere would be energetically favorable for a sufficiently large number of electrons [10].Unfortunately,even the restricted surface Thomson problemsremains unsolved for an arbitrary number of electrons [11,12].2EUROPHYSICS LETTERS In this letter we will show that if the relativistic corrections to the Coulomb law are properly taken into account,even our intuitive picture of the ground state as consisting of stationary particles located atfixed positions on the surface of a sphere must be abandoned. Instead,wefind that for sufficiently large electron density,the energy is minimized by the particles undergoing a coherent motion and the sphere becomes spontaneously magnetized!The starting point for our analysis is the well known Darwin Lagrangian[13–23],which takes into account the relativistic corrections to the Coulomb law resulting from the particle motion,L=−mc2 ic2−1r ij+1r ij[v i·v j+(v i·ˆr ij)(v j·ˆr ij)].(1)Eq.(1)is correct to order v2/c2.The velocity-dependent correction to the Coulomb energy arises from the electromagnetic coupling between the moving particles.Since the Lagrangian (1)does not contain explicit time dependence,the energy of the systemE= i v i·∂Lc2+1r ij+1r ij[v i·v j+(v i·ˆr ij)(v j·ˆr ij)].(3) The ground state for n electrons on the surface of a sphere of radius a is then determined by the minimization of Eq.(3).We note that if the terms of order1/c2are neglected,we recover the classical formulation of the Thomson problem in which the electromagnetic coupling between the electrons is purely of the Coulomb form.In this case,the velocity dependent contribution to the Hamiltonian is positive or zero,and the ground state corresponds to stationary particles residing atfixed positions on the surface of the sphere.For large n,this structure resembles a hexagonal Wigner crystal containing some topological defects.In general,however,the1/c2terms can not be omitted and a full minimization of Eq.(3)must be performed.To proceed,it is convenient to rewrite the energy in adimensional form.Defining the reduced displacement and velocity as r∗=r/a and v∗=v/c,the reduced energy becomesE∗≡E r e 2a∗ i=j14a∗ i=j1Jayme De Luca,Savio B.Rodrigues and Yan Levin:The Thompson Problem3 electrons.This however,is not of great importance since the metastable states have energies very close to that of the exact ground state[10,25].Performing the minimization of E∗wefind that for reduced surface charge densityσ∗=n/a∗2such thatσ∗<σ∗c(subcritical region),the electrons form a stationary Wigner crystal with some topological defects.Above the critical charge densityσ∗>σ∗c(supercritical region),the Wigner crystal,however,becomes unstable and a new ground state with moving electrons is formed.In Fig.1we show the characteristic distribution of particles in this new ground state.The arrows indicate the relative magnitude and direction of the particle velocities.Thefigure shows bands of correlated antiferromagnetic8 v∗4i+1r∗ij,(5)where I is a2n×2n identity matrix and D is a position dependent matrix constructed from the last term of Eq.(4).The quadratic term in velocity is non-negative if all the eigenvalues of the matrix1A=I+4EUROPHYSICS LETTERS negative,the Wigner lattice will lose stability,and a new ground state,with energy below that of the Wigner crystal will be established.The phase transition occurs when λA min =0,where λA min is the minimum eigenvalue of the matrix A .It is important to note that the energetic bifurcation of Eq.(5)is simultaneous with the dynamical instability of the Wigner lattice.If the Euler-Lagrange equations of motion are linearized around the stationary positions of the Wigner lattice,one can show that the Lya-punov instability occurs precisely when A loses convexity.Unfortunately,in the supercritical region,the equations of motion are differential-algebraic and due to the singularity of A are very difficult to integrate numerically [26].To determine the critical charge concentration at which the Wigner crystal loses stability,we adopt the following procedure.For a given number of electrons n ,the Coulomb energy is minimized to determine the positions of all the particles.For purely Coulombic interactions,the ground state location of the electrons is independent of the size of the sphere,since a scales out of the expression for the electrostatic energy.Once the ground state coordinates are known,the eigenvalues λD of the matrix D can be calculated numerically.The criticality condition λA min =0is then equivalent to the requirements that λD min =−a ∗.In Fig.2we show the result of this procedure.0 51015100 200 300 400 500 600 700 800 9001000Jayme De Luca,Savio B.Rodrigues and Yan Levin :The Thompson Problem 5Clearly,µ∗is just proportional to the total magnetic moment of the sphere.In the subcritical region,the electron velocities arezero and µ∗=0.The value of the magnetic moment in the supercritical region is plotted in Fig.3.We find that if the magnetic moment is scaled with n −2/5and is plotted as a function of the reduced surface charge concentration σ∗−σ∗c ,all the points for different values of a and n fall on the same universal curve,g (x )=0.545x 1/2.(9)Thus,although locally the orientation of the velocity vectors is antiferromagnetic,globally the symmetry is broken and the sphere acquires a net magnetic moment.The magnetic moment is sub-extensive and vanishes with a square root singularity as σ→σ+c .0 0.020.040.060.080.10 0.005 0.01 0.015 0.02d ,(11)6EUROPHYSICS LETTERS where M is the Madelung constant and d is the characteristic size of the Wigner-Seitz cell,πd2n=4πbining Eqs.(10)and(11)we arrive at a very simple expression for the Coulomb energy of n electrons on the surface of the sphereE C=n2q22a.(12)Eq.(12)with M=1.1046gives a very accuratefit to the ground state energy of the surface Thomson problem with purely Coulomb interactions[10,27].Note that for a planar OCP[29] M=1.1061,so that the topological defects affect very little the value of the Madelung constant.It is also important to notice that although E C is not extensive,∆E C≡12a(13)is.Therefore,if∆E C/n is plotted as a function of n/a2for different combinations of n and a,all points should fall onto one universal curve,f(x)=−Mx.(14)We can now check if this universality also holds for the Thomson problem with the Darwin coupling between the particles.That is if∆E∗≡E∗−1−n2Jayme De Luca,Savio B.Rodrigues and Yan Levin :The Thompson Problem 7-2.5-2-1.5-1-0.50 2 4 6 8 10 12 148EUROPHYSICS LETTERS[28]Y.Levin,Rep.Prog.Phys.65,1577(2002).[29]R.C.Gann,S.Chakravarty,and G.V.Chester,Phys.Rev.B20,326(1979).[30] A.Alastuey and W.Appel,Physica A276,508(2000).[31]W.Appel and A.Alastuey,Phys.Rev.E59,4542(1999).。

第48卷第9期 2020年9月硅 酸 盐 学 报Vol. 48，No. 9 September ，2020JOURNAL OF THE CHINESE CERAMIC SOCIETY DOI ：10.14062/j.issn.0454-5648.20190806Ce 3+掺杂对0.65CaTiO 3–0.35LaAlO 3陶瓷微波介电性能的影响罗捷宇，李月明，李志科，王竹梅，洪 燕，沈宗洋(景德镇陶瓷大学材料科学与工程学院；中国轻工业功能陶瓷材料重点实验室；江西省能量存储与转换陶瓷材料工程实验室，江西 景德镇 333403)摘 要：以EDTA 为络合剂，采用聚合物前驱体法合成了0.65CaTiO 3–0.35(La 1–x Ce x )AlO 3(CTLCA–x )微波介质陶瓷。

研究了Ce 3+取代La 3+对陶瓷微波介电性能、显微结构以及晶体结构的影响。

结果表明：采用聚合物前驱体法合成的CTLCA–x 陶瓷，相比于传统固相法，烧结温度降低了125 ℃左右，在所研究的组成范围内均能形成正交相固溶体，随着Ce 3+掺杂量x 的逐渐增加，单位晶胞体积减小，陶瓷的品质因数Q×f 和介电常数εr 均增加，但频率温度系数τf 下降。

当x =0.2时，CTLCA –0.2陶瓷在1 325 ℃保温3 h 烧结后具有最佳的微波介电性能：εr =42.7，Q×f=39 159 GHz ，τf = –7×10–6/℃。

关键词：微波介质陶瓷；聚合物前驱体法；高品质因数；铈离子取代中图分类号：TU528 文献标志码：A 文章编号：0454–5648(2020)09–1383–07 网络出版时间：2020–07–13Effect of Ce 3+Doping on 0.65CaTiO 3–0.35LaAlO 3 Microwave Dielectric CeramicsLUO Jieyu , LI Yueming , LI Zhike , WANG Zhumei , HONG Yan , SHEN Zongyang(School of Materials Science and Engineering, Jingdezhen Ceramic Institute; China National Light Industry Key Laboratory of Functional Ceramic Materials; Energy Storage and Conversion Ceramic Materials Engineering Laboratory of Jiangxi Province;Jingdezhen 333403, Jiangxi, China)Abstract: 0.65CaTiO 3–0.35(La 1–x Ce x )AlO 3 (CTLCA–x ) microwave dielectric ceramic was successfully synthesized by the polymeric precursor method using EDTA as a chelating agent. The effects of Ce 3+ ion doping on the microwave dielectric properties, microscopic structure and crystal structure were studied. The result indicated that the sintering temperature of CTLCA–x ceramic prepared by polymer precursor method was decreased by about 125 ℃compared with conventional mixed solid method, a single orthorhombic phase for all the compositions can form and the unit cell volume increases linearly with the doping content x . Ce 3+ ion dopant can increased the quality factor and dielectric constant, but the temperature coefficient of resonant frequency decreased. When x = 0.2, the optimal microwave dielectric properties of εr =42.7, Q×f =39 159 GHz, and τf = –7×10–6/℃ for the CTLCA–0.2 ceramics could be obtained, which sintered at 1 325 ℃ for 3 h.Keywords: microwave dielectric ceramic; polymeric precursor method; high quality factor; cerium ion-doped移动通讯技术在近10年来取得了重大突破，通讯器件越发微型化和高性能化。