A predictive model (ETLM) for arsenate adsorption and

A predictive model (ETLM)for arsenate adsorption and surface speciation on oxides consistent with spectroscopic

and theoretical molecular evidence

Keisuke Fukushi 1,Dimitri A.Sverjensky

*

Department of Earth and Planetary Sciences,Johns Hopkins University,Baltimore,MD 21218,USA Received 7September 2006;accepted in revised form 9May 2007;available online 7June 2007

Abstract

The nature of adsorbed arsenate species for a wide range of minerals and environmental conditions is fundamental to pre-diction of the migration and long-term fate of arsenate in natural environments.Spectroscopic experiments and theoretical calculations have demonstrated the potential importance of a variety of arsenate surface species on several iron and aluminum oxides.However,integration of the results of these studies with surface complexation models and extrapolation over wide ranges of conditions and for many oxides remains a challenge.In the present study,in situ X-ray and infrared spectroscopic and theoretical molecular evidence of arsenate (and the analogous phosphate)surface speciation are integrated with an extended triple layer model (ETLM)of surface complexation,which takes into account the electrostatic work associated with the ions and the water dipoles involved in inner-sphere surface complexation by the ligand exchange mechanism.Three reactions forming inner-sphere arsenate surface species

2>SOH tH 3AsO 40?e>SO T2AsO 2àtH tt2H 2O 2>SOH tH 3AsO 40?e>SO T2AsOOH t2H 2O and

>SOH tH 3AsO 40?>SOAsO 22àt2H ttH 2O

were found to be consistent with adsorption envelope,adsorption isotherm,proton surface titration and proton coadsorption of arsenate on hydrous ferric oxide (HFO),ferrihydrite,four goethites,amorphous aluminum oxide,a -Al 2O 3,b -Al(OH)3,and a -Al(OH)3up to surface coverages of about 2.5l mol m à2.At higher surface coverages,adsorption is not the predominant mode of arsenate sorption.The four goethites showed a spectrum of model arsenate surface speciation behavior from predom-inantly binuclear to mononuclear.Goethite in the middle of this spectrum of behavior (selected as a model goethite)showed predicted changes in arsenate surface speciation with changes in pH,ionic strength and surface coverage very closely consis-tent with qualitative trends inferred in published in situ X-ray and infrared spectroscopic studies of arsenate and phosphate on several additional goethites.The model speciation results for arsenate on HFO,a -and b -Al(OH)3were also consistent with X-ray and molecular evidence.

The equilibrium constants for arsenate adsorption expressed in terms of site-occupancy standard states show systematic di?erences for di?erent solids,including the model goethite.The di?erences can be explained with the aid of Born solvation theory,which enables the development of a set of predictive equations for arsenate adsorption equilibrium constants on all oxides.The predictive equations indicate that the Born solvation e?ect for mononuclear species is much stronger than for binuclear species.This favors the development of the mononuclear species on iron oxides such as HFO with high values of the dielectric constant relative to aluminum oxides such as gibbsite with much lower dielectric constants.However,on

0016-7037/$-see front matter ó2007Elsevier Ltd.All rights reserved.doi:10.1016/j.gca.2007.05.018

*

Corresponding author.Fax:+14105167933.

E-mail addresses:fukushi@kenroku.kanazawa-u.ac.jp (K.Fukushi),sver@https://www.doczj.com/doc/2812617617.html, (D.A.Sverjensky).1

Present address:Institute of Nature and Environmental Technology,Kanazawa University,Kakuma-machi,Kanazawa,Ishikawa 920-1192,Japan.

https://www.doczj.com/doc/2812617617.html,/locate/gca

Geochimica et Cosmochimica Acta 71(2007)

3717–3745

hematite and corundum,with similar dielectric constants,the predicted surface speciations of arsenate are similar:at lower pH values and/or higher surface coverages,binuclear species are predicted to predominate,at higher pH values and/or lower sur-face coverages,mononuclear species predominate.

ó2007Elsevier Ltd.All rights reserved.

1.INTRODUCTION

Arsenic has received a great deal of public attention be-cause of its links to certain types of cancers and its high lev-els in some drinking water supplies(Nordstrom,2002; Hopenhayn,2006).Arsenate is the predominant species of arsenic in oxidized aquatic systems(Myneni et al.,1998). The concentration of arsenate in natural waters is strongly in?uenced by adsorption on oxide surfaces(Fuller and Davis,1989;Pichler et al.,1999;Fukushi et al.,2003).To predict the migration and long-term fate of arsenate in nat-ural environments,the behavior and the nature of adsorbed arsenate species must be known for a wide variety of min-erals and over the full range of environmental conditions.

The surface speciation of arsenate on oxide powders and on single crystal surfaces has been studied through X-ray spectroscopic and infrared investigations as well as theoret-ical molecular calculations.On powders,a variety of sur-face species have been inferred from extended X-ray absorption?ne structure(EXAFS)studies.The majority of these studies have been concerned with iron oxides and a very limited range of ionic strengths.For arsenate on fer-rihydrite and FeOOH polymorphs(goethite,akaganeite and lepidocrocite)at pH8and I=0.1,it was inferred that arsenate adsorbed mainly as an inner-sphere bidentate-binuclear complex(Waychunas et al.,1993).Monoden-tate-mononuclear complexes were also inferred.The monodentate/bidentate ratio decreased with increasing arsenate surface coverage.In contrast,Manceau(1995) reinterpreted the EXAFS spectra as indicating bidentate-mononuclear species.The possible existence of such a spe-cies,in addition to the ones described by Waychunas et al.(1993)was described in Waychunas et al.(2005).

All three of the above species were subsequently inferred for arsenate adsorption on goethite from EXAFS results obtained at pH6–9and I=0.1(Fendorf et al.,1997).The monodentate-mononuclear species was inferred to domi-nate at higher pH values and lower surface coverages, whereas the bidentate-binuclear species dominated at lower pH and higher surface coverages.The bidentate-mononu-clear species was detected in only minor amounts at high surface coverage.For arsenate on goethite and lepidocro-cite at pH6,a bidentate-binuclear species was inferred (Farquhar et al.,2002).The same species was inferred for arsenate on goethite,lepidocrocite,hematite and ferrihy-drite at pH4and7and I=0.1through EXAFS combined with molecular calculations(Sherman and Randall,2003). For arsenate on hematite,as a function of pH4.5–8and surface coverage,Arai et al.(2004)interpreted EXAFS data to infer a predominant bidentate-binuclear and a minor amount of a bidentate-mononuclear species.In the only powder studies of aluminum oxides,EXAFS and XANES of arsenate adsorption on b-Al(OH)3at pH4,8,and10and I=0.1and0.8by Arai et al.(2001)showed that arse-nate adsorbs to b-Al(OH)3as a bidentate-binuclear inner-sphere species(their XANES data did not indicate any out-er-sphere species regardless of pH and ionic strength),and an EXAFS study of arsenate on a-Al(OH)3at pH5.5(in dilute Na-arsenate solutions)also showed that arsenate forms an inner-sphere bidentate-binuclear species(Ladeira et al.,2001).

On single crystal surfaces of corundum and hematite, several arsenate surface species have been reported recently. For the(0001)and(10–12)planes of hematite,prepared at pH5with10à4M sodium arsenate solutions,then studied with GIXAFS and surface di?raction in a humid atmo-sphere,71–78%of the adsorbed arsenate was determined to be a bidentate-mononuclear species,with the remainder present as a bidentate-binuclear species(Waychunas et al., 2005).However,in bulk water at pH5,resonant anomalous X-ray re?ectivity and standing-wave studies of the(01–12) planes of corundum and hematite,have established a biden-tate-binuclear species,and the?rst reported occurrence of an outer-sphere or H-bonded arsenate species(Catalano et al.,2006a,b;2007).In the present study,we wish to emphasize that distinguishing between an outer-sphere and H-bonded species is not possible in surface complexa-tion models of reaction stoichiometry,although consider-ations of Born solvation theory may facilitate the distinction.

Overall,the X-ray studies on powders and single crystals provide strong indications of a variety of surface arsenate species,presumably present under di?erent conditions of pH,ionic strength and surface coverage,as well as being present on di?erent solids and crystallographically di?erent surfaces.Even on a single crystal surface,a great variety of possible surface species coordination geometries can be proposed,e.g.monodentate,bidentate and tridentate possi-bilities(Waychunas et al.,2005).However,the most fre-quently reported inner-sphere arsenate species coordination geometries in X-ray studies remain the biden-tate-binuclear,bidendate-mononuclear,and the monoden-tate-mononuclear types of species.In this regard,it should also be emphasized that none of the protonation states of these coordination geometries are established by X-ray studies.A variety of possible protonation states adds even further potential complexity to the speciation of ad-sorbed arsenate.It is here that other spectroscopic tech-niques(e.g.infrared and Raman)and molecular calculations,as well as the reaction stoichiometries in sur-face complexation models can possibly help.

In situ ATR-FTIR studies of arsenate on ferrihydrite and amorphous hydrous ferric hydroxide have inferred that adsorption of arsenate occurred as inner-sphere species (Roddick-Lanzilotta et al.,2002;Voegelin and Hug, 2003).An ex situ FTIR study(Sun and Doner,1996)has

3718K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

inferred binuclear-bridging complexes of arsenate on goe-thite.However,the latter noted that their results could be a?ected by not having bulk water present in their spectro-scopic experiment.In addition,IR studies of arsenate adsorption may only show small or no shifts with changes of pH(Goldberg and Johnston,2001).As a consequence, the assignment of arsenate surface species from infrared and Raman spectra is su?ciently di?cult(Myneni et al., 1998)that a de?nitive in situ study has yet to be done.Con-sequently,in the present study we have made use of in situ infrared results for an analogous anion phosphate.

Phosphate and arsenate have very similar aqueous pro-tonation characteristics and are widely considered to have very similar adsorption characteristics(Waychunas et al., 1993;Hiemstra and van Riemsdijk,1999;Goldberg and Johnston,2001;Arai et al.,2004).Furthermore,infrared studies of phosphate adsorption indicate enough shifts of the spectra with experimental conditions to assign the phos-phate surface species(Tejedor-Tejedor and Anderson,1990; Persson et al.,1996;Arai and Sparks,2001;Loring et al., 2006;Nelson et al.,2006).The phosphate surface species in-ferred by Tejedor-Tejedor and Anderson(1990)have al-ready been used to develop a CD surface complexation model for arsenate on goethite(Hiemstra and van Rie-msdijk,1999).In the present study,we take a similar ap-proach using the studies by Tejedor-Tejedor and Anderson(1990),Arai and Sparks(2001),and Elzinga and Sparks(2007)which are the de?nitive published studies of phosphate adsorption referring to in situ conditions.It should be emphasized here that,in detail,there are di?er-ences between some of the surface species inferred in the above studies.In the present study,we investigated a sur-face complexation application of the species suggested by these authors to see if a consistent set of species would ap-ply to a wide range of oxides.

According to Tejedor-Tejedor and Anderson(1990), phosphate on goethite adopts three surface species:proton-ated bidentate-binuclear,deprotonated bidentate-binuclear and deprotonated monodentate species.The relative abun-dances of these species were shown to be strong functions of pH and surface coverage at an ionic strength of0.01.The protonated bidentate-binuclear species predominated at pH values of about3.6to5.5–6.0(at surface coverages of 190and150l mol/g).The deprotonated bidentate-binu-clear species became predominant between pH values of about6–8.3.The mondentate species was detectable at pH values as low as6at surface coverages of190l mol/g and increased in relative abundance as the surface coverage decreased towards50l mol/g.Consistent results have been obtained for phosphate on ferrihydrite(Arai and Sparks, 2001).The latter assigned protonated bidentate-binuclear species at pH values of4to6and surface coverages of 0.38–2.69l mol/m2and a deprotonated bidentate-binuclear species at pH>7.5,as well as a possible non-protonated Na-phosphate surface species at high pH values.More re-cently,in an investigation of phosphate adsorption on hematite,Elzinga and Sparks(2007)suggested a bridging binuclear protonated species,a protonated mononuclear species and a deprotonated mononuclear species.It was also suggested that the‘‘bridging’’species may instead be mononuclear with a strong H-bond to an adjacent Fe-octa-hedra.Broadly speaking,the in situ infrared studies for phosphate adsorption on iron oxides are consistent with the results of the X-ray studies for arsenate discussed above (although the X-ray studies cannot provide information on protonation states).However,the above infrared studies of phosphate provide invaluable additional information on the possible states of protonation of the surface phosphate species,which we use as a?rst step in developing a surface complexation model for arsenate adsorption below.

The surface structure and protonation state of adsorbed arsenate have been addressed through theoretical density functional theory(DFT)and molecular orbital density functional theory(MO/DFT)calculations(Ladeira et al., 2001;Sherman and Randall,2003;Kubicki,2005).DFT calculations for arsenate with aluminum oxide clusters indi-cated that a bidentate-binuclear species was more stable than bidentate-mononuclear,monodentate-mononuclear or monodentate-binuclear species(Ladeira et al.,2001). From predicted geometries of arsenate adsorbed on iron hydroxide clusters using DFT comparing EXAFS data,it was suggested that arsenate was adsorbed as a doubly pro-tonated species(Sherman and Randall,2003).Predicted energetics indicated that a bidentate-binuclear species was more stable than a bidentate-mononuclear and monoden-tate species.In contrast to these DFT calculations,MO/ DFT calculations by using a di?erent type of iron hydrox-ide clusters(containing solvated waters)showed that deprotonated arsenate surface species resulted in good agreement with spectroscopic data(Kubicki,2005).The bidentate-binuclear con?guration is most consistent with spectroscopic data,but the model Gibbs free energies of adsorption of clusters suggested that the monodentate con?guration is energetically more stable as a cluster.The MO/DFT calculations also indicated a strong preference for arsenate to bind to iron clusters relative to aluminum hydroxide clusters.Detailed molecular simulations of phos-phate on iron oxide clusters(Kwon and Kubicki,2004) emphasize mononuclear species with di?ering protonation states that agree very well with an ex situ infrared study of phosphate on goethite(Persson et al.,1996).

Numerous studies have focused on surface complexation modeling of arsenate on oxides(Goldberg,1986;Dzombak and Morel,1990;Manning and Goldberg,1996;Grossl et al.,1997;Manning and Goldberg,1997;Hiemstra and van Riemsdijk,1999;Gao and Mucci,2001;Goldberg and Johnston,2001;Halter and Pfeifer,2001;Dixit and Hering,2003;Arai et al.,2004;Hering and Dixit,2005). Surface complexation modeling has the capability to predict the behavior and the nature of adsorbed arsenate species as functions of environmental parameters.How-ever,the complexation reactions have not always been con-sistent with in situ spectroscopic results.Instead,with the exception of the study by Hiemstra and van Riemsdijk (1999),regression of macroscopic adsorption data has often been carried out merely to?t the data with the minimum number of surface species(Hering and Dixit,2005).It is now widely recognized that the evidence of oxyanion speciation from spectroscopic studies should be integrated with models describing macroscopic adsorption and

As(V)surface speciation on oxides3719

electrokinetic data(Suarez et al.,1997;Hiemstra and van Riemsdijk,1999;Blesa et al.,2000;Goldberg and Johnston, 2001).

In the present study,we use the results of the in situ X-ray and infrared studies of arsenate and phosphate discussed above to guide the choice of surface species in the extended triple-layer model(ETLM)recently developed to account for the electrostatic e?ects of water-dipole desorption during inner-sphere surface complexation(Sver-jensky and Fuksuhi,2006a,b).We investigate the applica-bility of three spectroscopically identi?ed species by?tting adsorption,proton surface titration in the presence of arse-nate,and proton coadsorption with arsenate on a wide range of oxides including goethite,hydrous ferric oxide (HFO),ferrihydrite,hematite,amorphous aluminum oxide, b-Al(OH)3,a-Al(OH)3and a-Al2O3(Manning and Gold-berg,1996;Jain et al.,1999;Jain and Loeppert,2000;Arai et al.,2001,2004;Gao and Mucci,2001;Goldberg and Johnston,2001;Halter and Pfeifer,2001;Dixit and Hering, 2003).These data were selected to cover wide ranges of pH, ionic strength and surface coverage,and a wider range of oxide types than have been investigated spectroscopically. Other arsenate data examined in the present study(Rietra et al.,1999;Arai et al.,2004;Dutta et al.,2004;Pena et al.,2005,2006;Zhang and Stanforth,2005)did not in-volve a wide enough range of conditions to permit retrieval of equilibrium constants for three surface species.Electro-kinetic data involving arsenate adsorption were also exam-ined in the present study(e.g.Anderson and Malotky,1979; Arai et al.,2001;Goldberg and Johnston,2001;Pena et al., 2006).However,these data refer to a much more limited range of conditions.

The main purpose of the present study is to determine the e?ects of pH,ionic strength,surface coverage and type of solid on the surface speciation of arsenate identi?ed spec-troscopically.The results are then compared with indepen-dent trends established in X-ray and infrared spectroscopic studies for arsenate and phosphate.A second goal of the present study is to provide a predictive basis for arsenate surface speciation on all oxides.By adopting an internally consistent set of standard states,systematic di?erences in the equilibrium constants for the surface arsenate species from one oxide to another can be established and explained with the aid of Born solvation theory.This makes it possi-ble to predict arsenate adsorption and surface speciation on all oxides in1:1electrolyte systems.

2.ETLM TREATMENT OF ARSENATE

ADSORPTION

2.1.Aqueous speciation,surface protonation and electrolyte adsorption

Aqueous speciation calculations were carried out taking into account aqueous ionic activity coe?cients appropriate to single electrolytes up to high ionic strengths calculated with the extended Debye-Huckel equation(Helgeson et al.,1981;Criscenti and Sverjensky,1999).Electrolyte ion pairs used were consistent with previous studies (Criscenti and Sverjensky,1999,2002).Aqueous arsenate protonation equilibria were taken from a recent study (Nordstrom and Archer,2003):

HttH2AsO

4

à?H

3

AsO

4

0;log K?2:30e1T

HttHAsO

4

2à?H

2

AsO

4

à;log K?6:99e2T

HttAsO

4

3à?HAsO

4

2à;log K?11:8e3TAqueous arsenate complexation with the electrolyte cations used in experimental studies can be expected to occur, based on the analogous phosphate systems.However,the lack of experimental characterization of arsenate-electro-lyte cation complexing prevented including this in the present study.Preliminary calculations carried out using Na-complexes of phosphate as a guide to the strength of Na–arsenate complexes indicated that the results of the present study were not signi?cantly a?ected at ionic strengths of0.1and below.

The sample characteristics and surface protonation and electrolyte adsorption equilibrium constants used in the present study are summarized in Table1.Although HFO and ferrihydrite might be thought to have extremely similar surface chemical properties,we distinguished between them in our previous study of As(III)adsorption(Sverjensky and Fukushi,2006b).By using di?erences in the pH ZPC(i.e.7.9 vs.8.5,respectively,Table1),we inferred di?erent e?ective dielectric constants for these solids,which facilitated the use of Born solvation theory to explain the di?erent magnitudes of the log K values for As(III)adsorption.It will be shown below that the same approach works for di?erences in arse-nate adsorption,at least for these speci?c HFO and ferrihy-drite samples.Surface protonation constants referring to the site-occupancy standard states(denoted by the super-

script‘‘h’’),i.e.log K h

1

and log K h

2

,were calculated from val-

ues of pH ZPC and D p K h

n

(Sverjensky,2005)using

log K h

1

?pH ZPCà

D p K h

n

2

e4Tand

log K h

2

?pH ZPCt

D p K h

n

2

e5T

Values of pH ZPC were taken from measured low ionic strength isoelectric points or point-of-zero-salt e?ects cor-rected for electrolyte adsorption(Sverjensky,2005).For goethite and HFO examined by Dixit and Hering(2003), neither isoelectric points nor surface titration data were re-ported.The value of pH ZPC for the goethite was predicted for the present study using Born solvation and crystal chemical theory(Sverjensky,2005).For HFO,the pH ZPC was assumed to be the same as in Davis and Leckie (1978),consistent with our previous analysis for arsenite adsorption on the same sample of HFO(Sverjensky and

Fukushi,2006).Values of D p K h

n

were predicted theoreti-cally(Sverjensky,2005).

For convenience,protonation constants referring to the hypothetical 1.0molar standard state(denoted by the superscript‘‘0’’)are also given in Table1.The relationship between the two standard states is given by(Sverjensky, 2003)

3720K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

log K0

1?log K h

1

àlog

N S A S

N A

e6T

log K0

2?log K h

2

tlog

N S A S

N A

e7T

where,N S represents the surface site density on the s th solid sorbent(sites mà2);Nàrepresents the standard state sorbate species site density(sites mà2);A S represents the BET sur-face area of the s th solid sorbent(m2gà1);Aàrepresents a standard state BET surface area(m2gà1).

In the present study,values of Nà=10·1018sites mà2 and Aà=10m2gà1are selected for all solids.

Electrolyte adsorption equilibrium constants referring to

site-occupancy standard states,log K h

Mtand log K h

Là

,and

capacitances,C1,were obtained from regression of proton surface charge data when such data were available.Other-wise,these parameters were obtained from theoretical pre-dictions(Sverjensky,2005).For convenience,Table1also contains values of the electrolyte adsorption equilibrium constants relative to the>SOH species(denoted by the superscript‘‘*’’)and with respect to the hypothetical1.0

molar standard state,i.e.log?K0

Mtand log?K0

Là

.The rela-

tionships of log?K0

Mtand log?K0

Là

to log K h

Mt

and log K h

Là

are given by(Sverjensky,2003,2005)

log?K0

Mt?log K h

Mt

àpH ZPCà

D p K h

nàlog

N S A S

N A

e8T

log?K0

Là?log K h

Là

tpH ZPCà

D p K h

n

2

àlog

N S A S

N A

e9T

Surface areas(A S)were taken from experimental measure-ments(BET)for goethite,a-Al(OH)3,b-Al(OH)3and a-Al2O3.However,for samples of HFO,ferrihydrite and am?AlO,it was assumed that the surface areas are 600m2.gà1consistent with recommendations made previ-ously(Davis and Leckie,1978;Dzombak and Morel, 1990)and our previous analyses of arsenite and sulfate adsorption on these oxides.

Site densities(N S)together with arsenate adsorption equilibrium constants were derived from regression of adsorption data where these data referred to a wide enough range of surface coverages.This procedure was adopted because oxyanions probably form inner-sphere complexes on only a subset of the total sites available,most likely the singly coordinated oxygens at the surface(Catalano et al.,2006a,b,c,d;2007;Hiemstra and van Riemsdijk, 1999).Theoretical estimation of these site densities is impossible for powdered samples when the proportions of the crystal faces are unknown,as is the case for all the experimental studies analyzed below.Furthermore,for goethites,surface chemical characteristics vary widely,even for those synthesized in the absence of CO2(Sverjensky, 2005).Together with site densities for goethites already published(Sverjensky and Fukushi,2006a,b),the goethite site densities obtained by regression in the present study, with one exception,support an empirical correlation between site density and surface area of goethite(Fukushi and Sverjensky,2007).This correlation should enable estimation of site densities for those goethites for which oxyanion adsorption data over a wide range of surface coverage are not available.In the cases of arsenate adsorp-tion on HFO,ferrihydrite,goethite from Dixit and Hering (2003),and b-Al(OH)3and am?AlO,the site densities were taken from our previous regression of arsenite adsorption data(Sverjensky and Fukushi,2006b).We used a single site density for each sample applied to all the surface equilibria as described previously(Sverjensky and Fukushi,2006b). All the calculations were carried out with the aid of the computer code GEOSURF(Sahai and Sverjensky,1998).

2.2.Arsenate adsorption reaction stoichiometries

We constructed our ETLM for arsenate adsorption on oxides by choosing surface species based on the in situ X-ray and infrared spectroscopic studies of phosphate and arsenate and the molecular calculations for arsenate interaction with metal oxide clusters.We used three reaction stoichiometries expressed as the formation of inner-sphere surface species as illustrated in Fig.1. Additional species could be incorporated into the model, but even the data analyzed in the present study,which refers to a wide range of experimental conditions,did not permit retrieval of equilibrium constants for more than three surface species.We tested numerous reaction stoichiometries,but found that the best three reaction stoichiometries involved surface species identical to the ones proposed in the in situ ATR-FTIR study of phosphate adsorption on goethite(Tejedor-Tejedor and Anderson, 1990)discussed above.For the most part,these species are also consistent with the X-ray studies cited above.

The three reactions produce a deprotonated bidentate-binuclear species according to

2>SOHtH3AsO

4

0?e>SOT

2

AsO

2

àtHtt2H

2

O

e10T

?K h

e>SOT2AsO

2

à?

ae>SOT

2

AsO

2

àa Hta2H2O

a2

>SOH

a H

3AsO40

10FeD W r;10T

2:303RTe11T

a protonated bidentate-binuclear species according to

2>SOHtH3AsO

4

0?e>SOT

2

AsOOHt2H2Oe12T

?K h

e>SOT2AsOOH

?

ae>SOT

2

AsOOH

a2

H2O

a

>SOH

a H

3AsO40

10FeD W r;12T

2:303RTe13Tand a deprotonated monodentate species according to

>SOHtH3AsO

4

0?>SOAsO

3

2àt2HttH

2

Oe14T

?K h

>SOAsO

3

2à?

a>SOAsO

3

2àa2Hta H2O

a>SOH a H

3AsO40

10FeD W r;14T

2:303RTe15T

Here,the superscript‘‘h’’again represents site-occupancy standard states(Sverjensky,2003,2005).The exponential terms contain the electrostatic factor,D W r,which is a reac-tion property arising from the work done in an electric?eld when species in the reaction move on or o?the charged sur-face.It is evaluated taking into account the adsorbing ions and the water dipoles released in Eqs.(10),(12)and(14). Electrostatic work is done in both instances and is re?ected in the formulation of D W r(Sverjensky and Fukushi, 2006a,b).

3722K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

We place the charge of the adsorbing protons on the 0-plane and the charge of the oxyanion on the b -plane.This is a departure from the practice of placing the oxyanion charge on the 0-plane for inner-sphere complexes in the TLM (Hayes et al.,1988).In our calculations,with the dipole modi?cation and the arsenate or protonated arse-nate charge on the b -plane,the ETLM is able to describe a wide variety of arsenate adsorption data.As noted below,the same location for the charge has recently been used for arsenate adsorption on hematite (Arai et al.,2004).For the sake of completeness,we have also included in the present paper some model calculations in which the arsenate or protonated arsenate are placed on the 0-plane (as originally advocated by Hayes et al.)in conjunction with our dipole correction.This approach results in very poor ?ts to adsorption and surface proton titration data (see below).In the ETLM,the water dipole(s)leaving the charged surface experience a change in potential equal to àn (W 0àW b )where n is the number of desorbed waters per reaction.For the reactions in Eqs.(11),(13)and (15),this results in

D W r ;10?2W 0à3W b à2eW 0àW b T?àW b e16TD W r ;12?2W 0à2W b à2eW 0àW b T?0e17TD W r ;14?W 0à3W b àeW 0àW b T?à2W b

e18T

Interestingly,Eq.(16)is the same overall result for D W r as found in a recent study using the CD-TLM approach for arsenate on hematite (Arai et al.,2004).In the latter study,

it was found by regression of adsorption data that D W 10=àW b ?tted the data better than alternate fractional distributions of charge.In this study we explain D W r ,10=àW b in terms of the dipole correction to the TLM without the need for a CD approach.

We wish to emphasize here that alternate states of arse-nate reaction stoichiometry could not ?t the bulk arsenate adsorption data.In particular,the mononuclear mono-or diprotonated arsenate surface species did not yield as good a ?t to the experimental adsorption and surface titration data.Having said this,it is still true that surface species in addition to those given in Fig.1may be present in the real systems,but di?cult to detect using surface complexa-tion models.This possibility arises when two di?erent sur-face species have extremely similar,if not identical,reaction stoichiometries.For example,a bidentate-mono-nuclear arsenate species (suggested by some X-ray studies,see above)is clearly not included in Fig.1.However,such a species could have a reaction stoichiometry such as >S eOH T2tH 3AsO 40?>SO 2AsO 2àtH tt2H 2O

e19T

which is so similar to that in Eq.(10)that it would be dif-?cult to detect the di?erence in a surface complexation model without examining data referring to a very wide range of surface coverages.Another possible reaction stoi-chiometry for a bidentate-mononuclear species would be >SOH tH 3AsO 40?>SO 2AsO 22àt2H ttH 2O

e20T

ETLM treatment for arsenate adsorption on oxides

Deprotonated bidentate-binuclear arsenate

O S O s A H H O

H O S H O s A 2220

432)(2++>=+>+?RT

F H

O s A SOH O

H O S O s A H O S O s A r a a a a a K 2.303)

(22)

()

(10

04

322

2

2

2

ΔΨ>>>+??

=

O

H AsOOH SO H O S H O s A 220432)(2+>=+>RT F H O s A SOH O H AsOOH SO AsOOH

SO r a a a a K 2.303)

(2

2)()(1004

3222ΔΨ>>>=O

H H SOAsO H O S H O s A 2230

432++=>+>+?RT

F H

O s A SOH O H H SOAsO SOAsO r a a a a a K 2.303)(2

10

4

322323

ΔΨ>>>+??=

β

ββΨ?=Ψ?Ψ?Ψ?Ψ=ΔΨM L T E 232()00r M L T E 222()0

00=Ψ?Ψ?Ψ?Ψ=ΔΨββr β

ββΨ?=ΨΨ??Ψ?Ψ=ΔΨ2)(3M L T E 00r Protonated bidentate-binuclear arsenate

Monodentate arsenate

As(V)surface speciation on oxides 3723

which has the same reaction stoichiometry as that in Eq.

(14).However,the reaction in Eq.(20)involves a coordina-tion increase for the surface metal,which may be detectable through the comparison of theoretical molecular calcula-tions with infrared data(e.g.Yoon et al.,2004).

Another interesting possibility involves outer-sphere or H-bonded surface species.All the above arsenate surface reactions involve inner-sphere species.Until recently,no outer-sphere-type surface species for arsenate had been di-rectly detected in experimental spectroscopic studies.The recent reports of such a species(Catalano et al.,2006a,b) are of great interest because they bring arsenate surface spe-ciation in line with almost all other oxyanions for which both inner-and outer-sphere(or H-bonded)species have been reported.In our study,we have examined many pos-sible speciation schemes involving di?erent inner-and out-er-sphere(or H-bonded)species for consistency with the bulk adsorption data,and have only come up with one pos-sible reaction stoichiometry for an outer-sphere(or H-bonded species)given by

2>SOHtH3AsO

40?e>SOHT

2

–AsO2eOHT

2

àtHt

e21T

?K h

e>SOHT2AsO2eOHT2à?

ae>SOHT

2

–AsO2eOHT2à

a Ht

a2

>SOH

a H

3AsO40

10FeD W r;21T

2:303RTe22T

D W r;21?àW be23TIt can be seen that Eq.(21)di?ers from Eq.(10)only by the release of two waters in the latter reaction.For example, subtracting Eq.(21)from(10)gives

e>SOHT

2–AsO2eOHT

2

à?e>SOT

2

AsO

2

àt2H

2

Oe24T

K h?

ae>SOT

2

AsO

2

à

ae>SOHT

2

–AsO2eOHT2à

a2

H2O

e25T

Based on Eqs.(24)and(25),it can be expected that the rela-tive activities of the two arsenate surface species will be a function of the activity of water only.The ratio should be independent of pH and surface loading.It is interesting to note that preliminary experimental studies indicate that the ratio of the inner-and outer-sphere arsenate surface species is experimentally insensitive to the arsenate concentration in solution(Catalano et al.,2006b),which is consistent with Eqs.(24)and(25).Large variations in ionic strength might a?ect the activity of water,and hence the relative activities of the arsenate species,but would still be di?cult to detect by surface complexation modeling.Overall,we wish to emphasize that it is the relative importance of the three reac-tion stoichiometries in Fig.1that we can establish in our analysis of bulk experimental data.Additional surface spe-cies such as those described above may also be present in experimental systems,but would require additional experi-mental results to establish their relative importance.

The relationships of the site-occupancy standard states to the hypothetical1.0M standard state for the arsenic sur-face species are given by

log?K h

e>SOT2AsO

2à?log

?K0

e>SOT2AsO

2

àtlog

eN S A ST2

N A

C S

!

e26T

log?K h

e>SOT2AsOOH

?log?K0

e>SOT2AsOOH

tlog

eN S A ST2

N A

C S

!

e27T

log?K h

>SOAsO

3

2à?log

?K0

>SOAsO

3

2àtlog

N S A S

N A

e28T

where C S denotes solid concentration(g Là1).

The equilibrium constants represented relative to the

species>SOH,expressed by the superscript‘‘*’’in Eqs.

(11),(13)and(15),depend on the pH ZPC and D p K h

n

of solid

samples.It is convenient to correct for di?erences in the

pH ZPC and D p K h

n

with the following equations(Sverjensky,

2005):

log K h

e>SOT2AsO

2

à?log

?K h

e>SOT2AsO

2

àà2pH ZPCtD p K

h

n

e29T

log K h

e>SOT2AsOOH

?log?K h

e>SOT2AsOOH

à2pH ZPCtD p K h

n

e30T

log K h

>SOAsO

3

2à?log

?K h

>SOAsO

3

2ààpH ZPCt

D p K h

ne31T

The resultant values of K h

e>SOT2AsO

2

à,K

h

e>SOT2AsOOH

and

K h

>SOAsO

3

2à

are independent of the site density,surface area

or solid concentration of the speci?c samples,as well as the

pH ZPC and D p K h

n

used in the experiments.Values of the log-

arithms of the above equilibrium constants are summarized

in Table2.

2.3.Uncertainties in experimental data and regression

procedures

The assessment of uncertainties in individual experimental

datasets involving arsenate is often not provided by the exper-

imentalists.However,as a guide,the reproducibility of the

percent As(V)adsorbed on goethite reported by Gao and

Mucci(2001)was about±3%of the total As.It is likely that

at low extents of adsorption the uncertainties would be signif-

icantly greater.Unless otherwise stated,these uncertainties

have been used as a guide in the analysis discussed below,

resulting in an overall uncertainty for the log?K0

j

values of

adsorption of the j th arsenate species of about±0.3.Uncer-

tainties in values of log K h

j

,calculated with Eqs.(29)–(31)will

be signi?cantly larger because of uncertainties in the values of

D p K h

n

and pH ZPC and may be of the order of±0.5.In some

cases,where experimental data for adsorption over a range of

surface coverages as well as a range of pH and ionic strength

values were available,equilibrium constants and site densities

were derived simultaneously.The uncertainties in the resul-

tant equilibrium constants are within those cited above(see

also in the discussion given below).

Regression of a wide variety of experimental data includ-

ing adsorption envelope,isotherm,proton surface titration

and proton coadsorption of arsenate discussed below was

carried out by direct simulation of the experimental data gen-

erating values of the equilibrium constants log?K0

j

(and,in

some instances site densities).In the absence of quantitative

measures of uncertainty in the experimental studies,each

dataset was regressed taking into account the general uncer-

3724K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

tainties indicated above,as well as apparent scatter in the experimental results.An iterative regression approach was used to ensure the consistency of regression results for di?er-ent types of experimental data in a given system.Conversion

of the values of log?K0

j to values of log K h

j

(referring to site-

occupancy standard states)enabled direct comparison of the results of experimental studies of di?erent samples of the same type of solid as well as arsenate adsorption on di?erent solids.These di?erences are analysed below.In this way the experimental results for arsenate adsorption in many di?er-ent laboratories can be integrated into a single predictive description.

3.APPLICATION TO ARSENATE ADSORPTION

3.1.Adsorption of arsenate on goethite from Dixit and Hering(2003),Gao and Mucci(2003),Antelo et al.(2005), Manning and Goldberg(1996)

Arsenate adsorption data are analyzed below for four synthetic goethites(Table1)chosen because they refer to a wide range of arsenate adsorption conditions.Of these, only one(Antelo et al.,2005)excluded CO2during the syn-thesis of the goethite and during the arsenate adsorption study.However,the Dixit and Hering(2003)study tried several experiments with and without CO2present and found no signi?cant di?erence in arsenate adsorption.Sim-ilarly,Arai et al.(2004)demonstrated that only partial pres-sures of carbon dioxide higher than atmospheric a?ected arsenate adsorption signi?cantly.Data for a?fth goethite (Rietra et al.,1999),referring to a narrow range of condi-tions of arsenate and proton coadsorption are considered below as a test of the predictive correlations to be discussed below.

The adsorption data depicted in Fig.2a and b refer to arsenate adsorption envelopes over a range of surface cov-erages and an adsorption isotherm on goethite at a single ionic strength(Dixit and Hering,2003).The solid curves in Fig.2a and b represent regression calculations using the three reactions given in Fig.1.It should be emphasized that the site density used in the present calculations was not a regression parameter.Only the three equilibrium con-stants were regression parameters.The site density was ta-ken from independent ETLM analysis of arsenite adsorption on the same goethite(Sverjensky and Fukushi, 2006a,b).It can be seen in Fig.2a that the solid curves pro-vide a close description of the arsenate adsorption data over a wide range of pH and surface coverage(error bars are not reported in the study by Dixit and Hering,2003).

The solid points in Fig.2b represent the two highest sur-face coverages at pH4in Fig.2a(50and100l M of arse-nate).The two lowest coverage data are not included in Fig.2b because of high uncertainties of the aqueous arse-nate concentrations near100%adsorption.It can be seen in Fig.2b that although the model calculation provides a close description of much of the isotherm data,it systemat-ically underestimates the amount of adsorbed arsenate at surface coverages above approximately10à5.6mol.mà2 (2.5l mol mà2).Under these conditions,arsenate appar-ently accumulates at the surface through processes other than adsorption alone,for example surface precipitation, surface polymerization or di?usion into the structure(Ra-ven et al.,1998;Jain et al.,1999;Stanforth,1999;Zhang and Stanforth,2005;Jia et al.,2006).

The predicted surface speciation as a function of pH and surface coverage at the highest and lowest arsenate concentrations in Fig.2a can be seen in Fig.2c and d. These predictions serve as a test of the model which can be compared with qualitative trends in speciation with pH and surface coverage de?ned spectroscopically which were not used in the regression calculations.In Fig.2c, which refers to a relatively high surface coverage (2.2l mol mà2at60%adsorption),the protonated biden-tate-binuclear species is predicted to predominate at the lowest pH values of3–5,and the deprotonated biden-tate-binuclear species at pH values of5–8.This agrees remarkably well with trends inferred from the in situ FTIR study of phosphate on goethite at similar surface coverages(1.9–2.3l mol mà2,(Tejedor-Tejedor and Anderson,1990):a protonated bidentate-binuclear species at pH3.6to5.5–6.0and a deprotonated bidentate-binu-clear species between pH values of about6–8.3.

It can also be seen in Fig.2c that the relative importance of the mononuclear species increases with pH and it pre-dominates at pH values of9–10.At the lower surface cov-erage of Fig.2d,0.37l mol mà2at100%adsorption,it can be seen that the mononuclear species is predicted to domi-nate from pH values of about4.5–10.Both trends are consis-tent with inferences about the relative importance of the mononuclear species from EXAFS and IR spectroscopy as a function of oxyanion loading and pH(Tejedor-Tejedor and Anderson,1990;Waychunas et al.,1993;Fendorf et al.,1997).It should be noted that the mononuclear species was not detected in other EXAFS studies(Farquhar et al., 2002;Sherman and Randall,2003).However,Farquhar et al.(2002)obtained their spectra for adsorption conditions of pH5.5–6.5and coverage of6l mol mà2,and Sherman and Randall(2003)used adsorption conditions of pH3.9 and1l mol mà2.Under these conditions,the present calcu-lations indicate that the mononuclear species should not be important compared to the bidentate-binuclear species.

Overall,the predictions depicted in Figs.2c and d agree very well with the speciation trends indicated by the inde-pendently established in situ FTIR and X-ray studies of phosphate and arsenate on goethite,which provides strong support for the model reactions proposed in Fig.1.It also indicates that the surface chemistry of the Dixit and Hering (2003)goethite(with respect to arsenate speciation)is con-sistent with the surface chemistry of the goethites synthe-sized by Farquhar et al.(2002),Fendorf et al.(1997), Sherman and Randall(2003),Tejedor-Tejedor and Ander-son(1990)and Waychunas et al.(1993).Similar predicted trends of surface speciation were found using the CD model approach for phosphate surface complexation on goethite (Hiemstra and van Riemsdijk,1999).It will be shown below that experimental results for arsenate on another very sim-ilar goethite from the van Riemsdijk laboratory(in Rietra et al.,1999)are also consistent with the type of speciation discussed above and typi?ed by the model results for the Dixit and Hering(2003)goethite.

3726K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

As(V)surface speciation on oxides3727

The data in Fig.2a also permit a test of an alternate ap-proach to the surface complexation modeling described above.If instead of placing the charge of the arsenate or biarsenate ion on the b-plane,it is placed on the0-plane, in conjunction with the same water dipole correction de-scribed above,the values of D W r in Eqs.(11),(13)and (15)become equal toà3W0à2W b,à2W0à2W b,and à3W0+W b,respectively(Footnote in Table2).The results of applying this approach to the adsorption data are de-picted in Fig.2e.The calculated model curves in Fig.2e do not have the correct shape to?t the data adequately(an-other example of the poor model behavior associated with the0-plane assumption is given below).The predicted sur-face speciation for the highest surface coverage in Fig.2e is shown in Fig.2f.It can be seen that the predominant spe-cies is the mononuclear species,in contrast to the corre-sponding ETLM calculation shown in Fig.2c.

Fig.3a and b show experimental proton surface titration and arsenate adsorption data on goethite at much higher io-nic strengths(Gao and Mucci,2001).The solid curves in Fig.3b represent regression calculations with the ETLM again using the surface species from Fig.1.In these calcula-tions,the site density was retrieved together with the three equilibrium constants for arsenate adsorption.Predicted surface speciation plots are shown in Fig.3c and d for the highest and lowest surface coverages from Fig.3b.It can be seen that the deprotonated bidentate species is dominant except at the highest and lowest pH conditions.As in Fig.2c and d,the protonated bidentate-binuclear species becomes important at low pH conditions whereas the importance of the monodentate species increases with pH and decreases with surface coverage.However,in contrast to the goethite in Fig.2c and d,the mononuclear species in Fig.3c and d is dominant only at pH values above9.A direct comparison between the Dixit and Hering goethite and the Gao and Mucci goethite can be made using Figs.2d and3e,which are constructed for the same ionic strength and surface cov-erage.It can clearly be seen that the predicted surface speci-ations for the two goethites di?er signi?cantly(see below).

Experimental surface titration and arsenate adsorption isotherm data for a third goethite from Antelo et al. (2005)are depicted in Fig.4a–c.Experimental uncertainties are not cited by the authors for these data,nevertheless it can be seen in Fig.4b and c that the solid regression curves generated in the present study provide a representation of the data within about10%.In these calculations,the site density and the equilibrium constants for arsenate adsorp-tion were all obtained.The predicted speciation plots in Fig.4d–f show a marked predominance of the monode-nate-mononuclear species at high pH values.In particular, Fig.4f was constructed to represent the same conditions as in Figs.2d and3e in order to directly compare the three goethites.It can be seen in Fig.4f that the Antelo et al.goe-thite shows an extremely high predominance of the mono-nuclear species.In this regard,it forms an end-member for the goethites analyzed in the present study.It is interest-ing to note recent preliminary ATR-FTIR spectroscopic re-ports of mononuclear phosphate and arsenate on goethite (Loring et al.,2006;Nelson et al.,2006).On hematite, in situ ATR-FTIR results have also been interpreted in terms of possible mononuclear protonated and deproto-nated phosphate complexes,although at least one of these was suggested to have been‘‘bridging’’in the sense of being strongly H-bonded to a second Fe-octahedron(Elzinga and Sparks,2007).

Experimental arsenate adsorption data for a fourth goe-thite(Manning and Goldberg,1996)are depicted in Fig.5a. The solid curves in Fig.5a again represent regression calcu-lations using the reactions in Fig.1.In these calculations,a predicted site density was used based on the linear correla-tion between site density and BET surface area for goethites developed previously(Fukushi and Sverjensky,2007).It can be seen in Fig.5a that the calculated curve for the high-er arsenate concentration results in a signi?cant underesti-mation of the amount adsorbed at pH values less than 4.5,which may indicate the need for an additional surface species of arsenate.In contrast,the calculated curve for the lower arsenate concentration slightly overestimates the amount adsorbed at pH values above9.

Predicted speciation plots for the goethite studied by Manning and Goldberg(1996)are shown in Fig.5b–d.It can be seen in Fig.5b and c that the surface speciation for this goethite is similar to that shown above for the Dixit and Her-ing goethite.A more accurate comparison can be made with the aid of Fig.5d,where the surface coverage and ionic strength are the same as in Fig.2d.The speciation in Fig.5d is actually intermediate between the speciation for that shown in Fig.2d and the Antelo et al.goethite in Fig.4f.

In summary,our model speciation results for the behav-ior of arsenate adsorption on the four goethites studied here vary quite markedly.We select the goethite from Dixit and Hering(2003)as a model goethite because the calculated trends in speciation with pH and surface coverage for this goethite agree well with the trends inferred from the infra-red and X-ray studies by Farquhar et al.(2002),Fendorf et al.(1997),Sherman and Randall(2003),Tejedor-Tejedor and Anderson(1990),and Waychunas et al.(1993).On our model goethite,binuclear or mononuclear arsenate surface species occur depending on the environmental conditions. In contrast,on the Antelo et al.(2005),Gao and Mucci (2001)and Manning and Goldberg(1996)goethites,the model arsenate surface speciation is dominated either by the binuclear or by the mononuclear surface species,when a consistent set of environmental conditions are compared.

One possible explanation for variation in goethite/arse-nate surface chemistry could result from di?erent adsorp-tion characteristics on di?erent crystal faces that may be developed on the di?erent goethite samples.Unfortunately, the proportions of di?erent crystal faces on the samples dis-cussed above are not known.However,comparisons of the di?erent goethites studied here can be made in terms of the site densities derived for arsenate adsorption.It can be seen in Fig.6that the site densities of the Antelo et al.(2005), Dixit and Hering(2003)and Gao and Mucci(2001)goeth-ites derived by regression,lie close to the correlation with surface area depicted by the solid line.Estimated uncertain-ties in the site densities are about±0.3sites nmà2.Sensitiv-ity analysis of the regression calculations indicated that such an uncertainty corresponds to about±0.2in the equi-librium constants generated simultaneously.All three are

3728K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

As(V)surface speciation on oxides3729

3730K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

therefore in reasonable agreement with the additional data shown on the plot derived from regression of sulfate and oxalate adsorption data.The negative slope of the line in Fig.6is qualitatively consistent with results for carbonate on goethites with di?erent surface areas(Villalobos et al., 2003).

The di?erences of site densities for the goethites may re-sult from fundamental di?erences in sample characteristics for each goethite.For example,if arsenate only adsorbs on singly coordinated oxygen groups,e.g.>O4FeO(H)or >O5FeO(H)groups(Catalano et al.,2006a,b,c,d,2007), the availability of these groups will depend on the propor-tions of di?erent faces making up the surface area of the goethite samples.As already noted,the proportions of dif-ferent crystal faces for the goethite samples in Fig.6are not known,although it has been suggested by Rietra et al. (2001)that their goethite synthesis method produces (101)and(210)faces(Pnma space group).

In an independent study of the surface protonation char-acteristics of goethite,signi?cant di?erences in the propor-tions of crystal faces have been demonstrated for two goethites with di?erent surface areas(Gaboriaud and Ehr-hardt,2003).On a goethite with intermediate surface area (49m2gà1),the(001)face was much more abundant than the(101)face(Pnma space group).On a high surface area goethite(95m2gà1),the reverse distribution was found. The(001)face of goethite has a site density for singly-coor-dinated oxygens of3.3sites nmà2(Koretsky et al.,1998). However,if we assume that the(001)face is faceted with (210)faces(Weidler et al.,1996),which have a site density of7.4sites nmà2,then the overall site density for the faceted (001)surface may approach6–7sites nmà2,depending on the degree of faceting.In contrast,the(101)face has a much lower site density of singly-coordinated oxygens, 3.0sites nmà2.As a consequence,a goethite with a high pro-portion of faceted(001)surfaces relative to(101)surfaces

As(V)surface speciation on oxides3731

should have a relatively high site density of singly-coordi-nated oxygens,i.e.the49m2gà1sample referred to above should have a higher oxyanion-determined site density than the95m2gà1sample.Qualitatively,this is consistent with and could explain the negative slope of the line in Fig.6. Lower surface area goethites studied by Pre′lot et al.(2003) with BET values of18and38m2gà1also had the(001)face predominating over the(101)face,with a terminal(121) face developed.Further work in characterizing all the faces on goethite samples with di?erent surface areas is clearly needed for the actual samples used in adsorption studies.

Another possible explanation for the variation in goethite surface speciation obtained above is contamination by other ferric oxides(e.g.hydrous ferric oxide,HFO).It will be shown below that the model surface speciation for arsenate on HFO and the equilibrium constants of adsorption are sig-ni?cantly di?erent to those of the model goethite of Dixit and Hering discussed above.Our previous ETLM analyses for sulfate and selenate adsorption on goethite also showed sig-ni?cant di?erences in both site density and log K h values for di?erent goethites(Fukushi and Sverjensky,2007).Some of these di?erences were attributed to contamination by atmo-spheric carbonate(which binds more strongly than sulfate, the opposite to arsenate as noted above)and/or contamina-tion by amorphous hydrous ferric oxides during the synthesis of the specimen,which could change the fundamental surface characteristics of the goethites.

3.2.Adsorption of arsenate on HFO from Dixit and Hering (2003)

The adsorption data depicted in Fig.7a and b refer to arsenate adsorption edges and an isotherm on HFO, respectively(Dixit and Hering,2003).The solid curves in Fig.7a and b represent regression calculations using the three reactions in Fig.1and a site density used previously for arsenite on the same HFO sample(Sverjensky and Fukushi,2006b).It can be seen that the calculated curves provide a close description of the arsenate adsorption data over a range of pH and surface coverage except at the con-ditions of the lowest pH and highest surface coverages (Fig.7a and b).At pH4and surface coverages greater than 2.8l mol mà2the calculated curves underestimate the amount of arsenic at the surface.This could indicate the need for an additional surface species.However,the iso-therm result is very similar to the goethite case discussed above,which was attributed to surface precipitation,poly-merization or di?usion in the bulk structure.Jia et al. (2006)have documented surface precipitation of arsenate on ferrihydrite by means of X-ray di?raction and infrared spectroscopy.They showed that surface precipitation of ferric arsenate occurred at pH values of3–5and surface coverages of2.4–9.3l mol mà2,which is in excellent agree-ment with our estimate of the limit of adsorption based on the ETLM calculations in Fig.7a and b.

The predicted model speciation of arsenate on HFO sur-faces is given in Fig.7c and d for the highest and lowest sur-face coverages of Fig.7a,respectively.For both surface coverages,it can be seen that the bidentate-binuclear spe-cies dominate at pH values less than about8–https://www.doczj.com/doc/2812617617.html,paring Fig.7c with d,it can be seen that the importance of the mononuclear species increases with decreasing surface cov-erage,which is consistent with the trend indicated by EX-AFS spectroscopy of arsenate adsorption on poorly crystalline iron oxide(Waychunas et al.,1993).The proton-ated bidentate-binuclear species becomes important at low pH values,consistent with IR spectroscopy of phosphate adsorption on ferrihydrite(Arai and Sparks,2001).

3.3.Adsorption of arsenate on ferrihydrite from Jain et al. (1999)and Jain and Loeppert(2000)

A much greater variety of experimental data types are depicted in Fig.8a–c.These include proton surface charge in the absence and presence of arsenic(Fig.8a),proton coadsorption with arsenic at two?xed pH values (Fig.8b),and percent arsenic adsorption(Fig.8c).The pro-ton surface charge data in the presence of arsenic(Fig.8a) were obtained from a combination of the titration di?er-ence data and the proton surface charge data without ar-senic presented in Figs.2and5of Jain et al.(1999). Adsorption envelope data reported by the same research group(Raven et al.,1998)at lower and higher As loadings than those depicted in Fig.8c were not used because the lowest surface loadings all result in essentially100%adsorp-tion and the highest surface loading will be dominated by processes other than adsorption(see below).

Although the uniqueness of surface species for surface complexation modeling has been questioned when only macroscopic percent adsorption data are modeled(Hering and Dixit,2005),the great variety of types of data in Fig.8a–c provide strong constraints on the reaction stoichi-ometries of the arsenate surface species.The solid curves in Fig.8a–c represent regression calculations again using the

3732K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

three reactions in Fig.1and the site density used previously for arsenite calculations for this sample(Table1).Only data represented by the solid symbols were regressed in Fig.8b and c.Data at higher surface coverages presumably represent processes in addition to adsorption such as sur-face polymerization or precipitation(Raven et al.,1998; Jain et al.,1999;Jain and Loeppert,2000;Zhang and Stan-forth,2005;Jia et al.,2006,2007).For example,in Fig.8c, the adsorption data at the two highest As(V)loadings rep-resented by the open symbols are systematically underesti-mated by the dashed calculated curves at pH values less than about6.Similarly,it can be seen in Fig.8b that extrapolation of the calculated proton coadsorption curve for pH4.6will underestimate the data at surface coverages above about2.3l mol mà2.It is under acidic conditions that surface precipitation of ferric arsenate has been docu-mented(Jia et al.,2006,2007).Under other conditions,it can be seen that the solid curves represent a reasonable?t to the data in Fig.8a–c.

The dashed curves in Fig.8a represent the alternative approach of placing the arsenate on the0-plane,as de-scribed above for Fig.2e(see the footnotes to Table3).This approach is clearly inconsistent with the trends represented by the data.

The predicted surface speciation of arsenate on the sur-face of ferrihdyrite is given in Fig.8d for one surface cov-erage from Fig.8c.It is predicted that the deprotonated bidentate-binuclear species is dominant for most pH condi-tions.However,the importance of the mononuclear species is again predicted to increase with pH similar to HFO,con-sistent with EXAFS and IR spectroscopic results(Waych-unas et al.,1993;Arai et al.,2001).

3.4.Adsorption of arsenate on amorphous aluminum oxide (am?AlO)from Goldberg and Johnston(2001)

The data depicted in Fig.9a show arsenate adsorption envelopes on am?AlO as functions of pH,ionic strength

As(V)surface speciation on oxides3733

and surface coverage.The solid curves in Fig.9a represent regression calculations using the three reactions in Fig.1 and the same site density used previously for arsenite calcula-tions for this sample(Table1).The calculated curves provide a close description of the arsenate adsorption data.In addi-tion to the adsorption data,Goldberg and Johnston(2001) measured electrophoretic mobilities of am?AlO with and without arsenic to obtain the e?ect of arsenic on the isoelec-tric point.The experimental isoelectric points decrease from 9.4(no arsenic and0.01mM As)to6.5(1mM As).Using the extended triple-layer model,the isoelectric point is also pre-dicted to decrease,but from9.4to2.3.Although too large, the calculated shift is in qualitative agreement with the direc-tion of the experimental results.The calculated shifts can be sensitive to trace amounts of surface arsenic species not in-cluded amongst the three species used in the present study. More extensive sets of adsorption and electrokinetic data would be needed to calibrate more accurate calculation of the electrokinetic results.

The predicted model speciation of arsenate on the sur-face of am?AlO is given in Fig.9b–d for I=0.01and I=1.0for4g Là1as well as I=1.0for0.5g Là1from Fig.9a.It can be seen in Fig.9b–d that the bidentate-binu-clear species dominates for all pH values less than about10. It is noteworthy that the monodentate species appears to be much less important compared with iron oxides.

3.5.Adsorption of arsenate on b-Al(OH)3from Arai et al. (2001)

The adsorption data depicted in Fig.10a refer to arse-nate adsorption envelopes on b-Al(OH)3(Arai et al., 2001).The limited amount of data in Fig.10a can be?t using only the deprotonated bidentate-binuclear species in

3734K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

Fig.1.The other species were included in the model solely to place upper limits on their importance under the experimental conditions studied by Arai et al.(2001).

Consequently,the values of log K h

e>SOT2AsOOH and

log K h

>SOAsO

32àin Table2merely represent upper limits.

Arai et al.(2001)also measured a decrease of the isoelectric point with increasing arsenate concentrations from electro-phoretic mobility studies.The ETLM prediction again agrees with the direction of the shift,although the overall predicted shift is too large.

The predicted model speciation for arsenate on the sur-face of b-Al(OH)3is given in Fig.10b and c for the lowest and highest ionic strength of Fig.10a as well as a prediction of the surface speciation at a lower arsenate loading (0.07mM of arsenate)in Fig.10d.It can be seen that the bidentate-binuclear species is predicted to dominate in any of these conditions regardless of the pH and ionic strength.These predictions of surface speciation are consis-tent with the EXAFS and XANES spectroscopic results on the same sample(Arai et al.,2001),which showed only the bidentate-binuclear species regardless of pH and ionic strength.Our predictions in Fig.10d for even lower surface coverages than those investigated by Arai et al.(2001)indi-cate that the mononuclear species would become important only at very high pH values(e.g.>10),even when the sur-face coverages are very low.This is again a signi?cant dif-ference to the results discussed above for the iron oxides.

3.6.Adsorption of arsenate on a-Al(OH)3from Manning and Goldberg(1996)

The data depicted in Fig.11a show two arsenate adsorp-tion envelopes on a-Al(OH)3as a function of pH.The solid curves in Fig.11a represent regression calculations using the three species in Fig.1and a site density of 3.0 sites nmà2derived from work on arsenite adsorption on gibbsite(Sverjensky and Fukushi,2006b).With the excep-tion of data at the highest pH values,the calculated curves provide a close description of the arsenate adsorption over a wide range of conditions shown in Fig.11a.

The predicted model speciation of arsenate on the sur-face of a-Al(OH)3is given in Fig.11b–d.The surface coverages from Fig.11a are shown in Fig.11b and c, and a prediction of the surface speciation in lower ionic strength solutions(0.01M NaCl)is shown in Fig.11d. It can be seen in Fig.11b–d that the bidentate-binuclear species predominates at pH values up to about10.The predicted surface speciation at low pH is consistent with an EXAFS study of arsenate on a-Al(OH)3at pH5.5, which inferred an inner-sphere bidentate-binuclear species (Ladeira et al.,2001).As in Figs.9and10,the mononu-clear species is predicted to occur only at the highest pH values,and is little in?uenced by ionic strength(cf. Fig.11c and d).

3.7.Adsorption of arsenate on a-Al2O3from Halter and Pfeifer(2001)

The data depicted in Fig.12a and b show proton surface titration without arsenate as well as arsenate adsorption envelopes on a-Al2O3as functions of pH and surface cover-age.The solid curves in Fig.12a represent regression of the data shown in order to generate values of the electrolyte adsorption equilibrium constants(Table1).The solid curves in Fig.12b represent regression calculations using the three reactions in Fig.1and a site density of 3.0

Table3

Predicted equilibrium constants(referring to site-occupancy standard states)for arsenate adsorption on oxides consistent with the extended triple-layer model a:

log K h

>SOAsO

32à

:>SOH

2

ttH3AsO4?>SOAsO

3

2àt3HttH2O

log K h

e>SOT2AsO

2à:2>SOH2

ttH3AsO4?e>SOT

2

AsO

2

àt3Htt2H2O

log K h

e>SOT2AsOOH :2>SOH

2

ttH3AsO4?e>SOT

2

AsOOHt2Htt2H2O

Solid e s b log K h

>SOAsO

42à

log K h

e>SOT2AsO2à

log K h

e>SOT2AsOOH

Fe3O41000 1.0 5.4 6.8

HFO1000 1.0 5.4 6.8

a-MnO21000 1.0 5.4 6.8

a-TiO21210.36 4.8 6.4 Ferrihydrite32à1.5 3.2 5.2

am.FeO32à1.5 3.2 5.2

b-TiO218.6à3.3 1.7 4.0

FeOOH15à4.30.81 3.4

Fe2O312à5.7à0.33 2.5

a-Al2O310.4à6.7à1.2 1.9

c-Al2O310.4à6.7à1.2 1.9

am?AlO10.3à6.8à1.2 1.9

b-Al(OH)310.3à6.8à1.2 1.9

a-Al(OH)38.4à8.5à2.80.66

a-SiO2 4.6à16.5à9.6à4.5

am?SiO2 3.8à20.0à12.6à6.7

a Calculated with Eqs.(33)–(35)and the dielectric constants tabulated.

b Dielectri

c constant of the soli

d from Sverjensky and Fukushi(2006b).

As(V)surface speciation on oxides3735

sites nmà2derived from work in progress on oxalate adsorption on corundum which refers to a very wide range of surface coverages.This site density is reasonable for sin-gly-coordinated oxygens on corundum.For example,the abundance of such oxygens that can participate in biden-tate-binuclear surface complexes varies from0to 3.3–8.2sites nmà2on the(0001),(10–10)and(01–12)faces, respectively.The calculated curves show excellent agree-ment with the experimental data over a wide range of pH values and the surface coverages shown in Fig.12b.

The predicted model speciation of arsenate on the sur-face of a-Al2O3is given in Fig.12c–e for the high and low surface coverage of Fig.12b,as well as a prediction of the surface speciation in solutions with higher arsenate (0.133mM)to give the same surface coverage as in Fig.11c for gibbsite.It can be seen in Fig.12c–e that the bidentate-binculear species dominates at pH values less than about8–9and that the mononuclear species contributes substantially to adsorption above these pH values.In this regard,the relative importance of the mononuclear species appears to be greater on corundum than on the other aluminas discussed above.However, when comparing the same surface coverage on corundum (Fig.12e)with that for gibbsite(Fig.11c),it can be seen that the arsenate surface speciation on the two aluminas is quite similar.

The predicted dominance of the bidentate-binuclear species at low pH values in Fig.12c–e is consistent with resonant anomalous X-ray re?ectivity(RAXR) studies of arsenate adsorption at pH5on the(012) surface of corundum which also established a biden-tate-binuclear type of species(Catalano et al., 2006a,b).If the current calculations can be extrapolated to single crystal surfaces,the results of the present study suggest that at high pH values the(012)surface of corundum should show a transition from predomi-nantly binuclear to mononuclear arsenate surface species (see below).

3736K.Fukushi,D.A.Sverjensky/Geochimica et Cosmochimica Acta71(2007)3717–3745

工程测试技术试题及答案

工程测试技术试题及答案Last revision on 21 December 2020

复习总结 一、概念题 1.测试过程中，若所测试的信号不随时间变化或变化非常缓慢，称这种测试称为静态 测试。如果所测试的信号随时间周期变化或变化很快，这种测试称为动态测试。 2.传感器是把被测量转换成易于变换、传输和处理的一种器件或装置。 3.按构成原理分类，电阻应变片、热敏电阻、压电晶片属物性型传感器。 4.按构成原理分类，电容传感器、自感型电感式传感器属结构型传感器。 5.为提高和改善传感器的技术性能，可采取以下技术措施：差动技术、平均技术以及 补偿与修正技术。 6.传感器的定度曲线（或标定曲线）与拟合直线之间的偏离程度称为传感器的线性 度。 7.传感器的灵敏度是指稳态时，输出变化量与输入变化量之间的比值。 8.对于一阶传感器系统，当其时间常数（或τ）越小，其频率响应特性越好。 9.激波管标定系统中，激波管的作用是一种动态标定设备，能产生阶跃压力信号输 出。 10.金属电阻应变片的规格一般以面积（或长×宽）和初始阻值表示。 11.用电阻应变片测量构件的变形，影响电阻应变片电阻变化的因素有：应变片的灵敏 度和初始阻值、被测构件的应变量、以及应变片沿构件的粘贴方向。（因为：△R=KεR，K为灵敏度，R为应变片初始阻值，ε被测构件的应变量） 12.将电阻丝绕成应变片后，由于存在横向效应，其灵敏系数一般会减小。 13.在电桥测量中，由于电桥接法不同，输出电压的灵敏度也不同，全桥接法可以得到 最大灵敏度输出。 14.应变片的温度误差补偿方法通常可分为：桥路补偿法、应变片自补偿法。 15.根据工作原理，变气隙型自感式传感器的灵敏度具有理论上的非线性。 16.电涡流接近开关结构简单，根据其工作原理，不可用来进行类似如玻璃瓶、塑料零 件以及水的液位的检测。 17.在差动式自感传感器中，若采用交流桥路为变换电路，常出现零点残余电压现象， 该现象使传感器灵敏度下降，灵敏阈值增大，非线性误差增大。

中考必会几何模型：8字模型与飞镖模型

8字模型与飞镖模型模型1：角的8字模型 如图所示，AC 、BD 相交于点O ，连接AD 、BC ． 结论：∠A ＋∠D ＝∠B ＋∠C ． O D C B A 模型分析 证法一： ∵∠AOB 是△AOD 的外角，∴∠A ＋∠D ＝∠AOB ．∵∠AOB 是△BOC 的外角， ∴∠B ＋∠C ＝∠AOB ．∴∠A ＋∠D ＝∠B ＋∠C ． 证法二： ∵∠A ＋∠D ＋∠AOD ＝180°，∴∠A ＋∠D ＝180°－∠AOD ．∵∠B ＋∠C ＋∠BOC ＝180°， ∴∠B ＋∠C ＝180°－∠BOC ．又∵∠AOD ＝∠BOC ，∴∠A ＋∠D ＝∠B ＋∠C ． （1）因为这个图形像数字8，所以我们往往把这个模型称为8字模型． （2）8字模型往往在几何综合题目中推导角度时用到． 模型实例 观察下列图形，计算角度： （1）如图①，∠A ＋∠B ＋∠C ＋∠D ＋∠E ＝________； 图图① F D C B A E E B C D A 图③ 2 1O A B 图④ G F 12 A B E 解法一：利用角的8字模型．如图③，连接CD ．∵∠BOC 是△BOE 的外角， ∴∠B ＋∠E ＝∠BOC ．∵∠BOC 是△COD 的外角，∴∠1＋∠2＝∠BOC ． ∴∠B ＋∠E ＝∠1＋∠2．（角的8字模型），∴∠A ＋∠B ＋∠ACE ＋∠ADB ＋∠E ＝∠A ＋∠ACE ＋∠ADB ＋∠1＋∠2＝∠A ＋∠ACD ＋∠ADC ＝180°． 解法二：如图④，利用三角形外角和定理．∵∠1是△FCE 的外角，∴∠1＝∠C ＋∠E ．

∵∠2是△GBD 的外角，∴∠2＝∠B ＋∠D ． ∴∠A ＋∠B ＋∠C ＋∠D ＋∠E ＝∠A ＋∠1＋∠2＝180°． （2）如图②，∠A ＋∠B ＋∠C ＋∠D ＋∠E ＋∠F ＝________． 图② F D C B A E 312图⑤ P O Q A B F C D 图⑥ 2 1 E D C F O B A （2）解法一： 如图⑤，利用角的8字模型．∵∠AOP 是△AOB 的外角，∴∠A ＋∠B ＝∠AOP ． ∵∠AOP 是△OPQ 的外角，∴∠1＋∠3＝∠AOP ．∴∠A ＋∠B ＝∠1＋∠3．①（角的8字模型），同理可证：∠C ＋∠D ＝∠1＋∠2．② ，∠E ＋∠F ＝∠2＋∠3．③ 由①＋②＋③得：∠A ＋∠B ＋∠C ＋∠D ＋∠E ＋∠F ＝2（∠1＋∠2＋∠3）＝360°． 解法二：利用角的8字模型．如图⑥，连接DE ．∵∠AOE 是△AOB 的外角， ∴∠A ＋∠B ＝∠AOE ．∵∠AOE 是△OED 的外角，∴∠1＋∠2＝∠AOE ． ∴∠A ＋∠B ＝∠1＋∠2．（角的8字模型） ∴∠A ＋∠B ＋∠C ＋∠ADC ＋∠FEB ＋∠F ＝∠1＋∠2＋∠C ＋∠ADC ＋∠FEB ＋∠F ＝360°．（四边形内角和为360°） 练习： 1．（1）如图①，求：∠CAD ＋∠B ＋∠C ＋∠D ＋∠E ＝ ； 图 图① O O E E D D C C B B A A 解：如图，∵∠1=∠B+∠D ，∠2=∠C+∠CAD ， ∴∠CAD+∠B+∠C+∠D+∠E=∠1+∠2+∠E=180°． 故答案为：180° 解法二：

传感器与检测技术考试试题及部分答案(DOC)

全国2001年10月自学考试传感器与检测技术试卷 课程代码：02202 第一部分选择题（共24分） 一、单项选择题（本大题共12小题，每小题2分，共24分）在每小题列出的四个选项中只有一个选项是 符合题目要求的，请将正确选项前的字母填在题后的括号内。错选、多选和未选均无分。 1．下列被测物理量适合于使用红外传感器进行测量的是（C ） A．压力B．力矩C．温度D．厚度 2．属于传感器动态特性指标的是（D ） A．重复性B．线性度C．灵敏度D．固有频率 3．按照工作原理分类，固体图象式传感器属于（A ） A．光电式传感器B．电容式传感器 C．压电式传感器D．磁电式传感器 4．测量范围大的电容式位移传感器的类型为（ D ） A．变极板面积型B．变极距型 C．变介质型D．容栅型 5．利用相邻双臂桥检测的应变式传感器，为使其灵敏度高、非线性误差小（C ）A．两个桥臂都应当用大电阻值工作应变片 B．两个桥臂都应当用两个工作应变片串联 C．两个桥臂应当分别用应变量变化相反的工作应变片 D．两个桥臂应当分别用应变量变化相同的工作应变片 6．影响压电式加速度传感器低频响应能力的是（ D ） A．电缆的安装与固定方式B．电缆的长度 C．前置放大器的输出阻抗D．前置放大器的输入阻抗 7．固体半导体摄像元件CCD是一种（ C ） A．PN结光电二极管电路B．PNP型晶体管集成电路 C．MOS型晶体管开关集成电路D．NPN型晶体管集成电路 8．将电阻R和电容C串联后再并联到继电器或电源开关两端所构成的RC吸收电路，其作用是 （D ）A．抑制共模噪声B．抑制差模噪声 C．克服串扰D．消除电火花干扰 9．在采用限定最大偏差法进行数字滤波时，若限定偏差△Y≤0.01，本次采样值为0.315，上次采样值为0.301，则本次采样值Y n应选为（ A ） A．0.301 B．0.303 C．0.308 D．0.315 10．若模/数转换器输出二进制数的位数为10，最大输入信号为2.5V，则该转换器能分辨出的最小输入电压信号为（ D ） A．1.22mV B．2.44mV C．3.66mV D．4.88mV 11．周期信号的自相关函数必为（A ） A．周期偶函数B．非周期偶函数 C．周期奇函数D．非周期奇函数 12．已知函数x(t)的傅里叶变换为X（f），则函数y(t)=2x(3t)的傅里叶变换为（D ） A．2X(f 3) B．2 3 X(f 3 ) C．2 3 X(f) D．2X(f) 第二部分非选择题（共76分） 二、填空题（本大题共12小题，每小题1分，共12分）不写解答过程，将正确的答案写在每小题 的空格内。错填或不填均无分。 13．对传感器进行动态的主要目的是检测传感器的动态性能指标。 14．传感器的过载能力是指传感器在不致引起规定性能指标永久改变的条件下，允许超过的能力。 15．传感检测系统目前正迅速地由模拟式、数字式，向方向发展。 16．已知某传感器的灵敏度为K0，且灵敏度变化量为△K0，则该传感器的灵敏度误差计算公式为r s= 。

第四章 景观模型制作

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D C B A M D C B A O 135E F D C B A 105O O 120 D C B A 模型2 角的飞镖模型 如图所示，有结论： ∠D=∠A+∠B+∠C 。 模型分析 飞镖模型往往在几何综合 题目中推导角度时用到。 模型实例 如图，在四边形ABCD 中，AM 、CM 分别平分∠DAB 和∠DCB ，AM 与CM 交于M 。探究∠AMC 与∠B 、∠D 间的数量关系。 热搜精练 1．如图，求∠A+∠B+∠C+∠D+∠E+∠F= ； 2．如图，求∠A+∠B+∠C+∠D = 。

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工程测试技术试题及答案

1.

2.对于一阶传感器系统，当其时间常数（或τ） 越小，其频率响应特性越好。 3.激波管标定系统中，激波管的作用是一种动态 标定设备，能产生阶跃压力信号输出。 4.金属电阻应变片的规格一般以面积（或长× 宽）和初始阻值表示。 5.用电阻应变片测量构件的变形，影响电阻应变 片电阻变化的因素有：应变片的灵敏度和初始阻值、被测构件的应变量、以及应变片沿构件的粘贴方向。（因为：△R=KεR，K为灵敏度，R为应变片初始阻值，ε被测构件的应变量） 6.将电阻丝绕成应变片后，由于存在横向效应， 其灵敏系数一般会减小。 7.在电桥测量中，由于电桥接法不同，输出电 压的灵敏度也不同，全桥接法可以得到最大灵敏度输出。 8.应变片的温度误差补偿方法通常可分为：桥 路补偿法、应变片自补偿法。

9.根据工作原理，变气隙型自感式传感器的灵 敏度具有理论上的非线性。 10.电涡流接近开关结构简单，根据其工作原 理，不可用来进行类似如玻璃瓶、塑料零件以及水的液位的检测。 11.在差动式自感传感器中，若采用交流桥路为 变换电路，常出现零点残余电压现象，该现象使传感器灵敏度下降，灵敏阈值增大，非线性误差增大。 12.差动变压器式位移传感器是将被测位移量 的变化转换成线圈互感系数的变化，两个次级线圈要求反向串接。 13.电容传感器的转换电路包括：交流电桥、变 压器电桥、调频电路、运算放大器电路。14.压电式传感器是一种可逆型传感器，即可将 机械能转换为电能。也可反之实现逆向变换。 15.压电传感器中压电晶片的等效电路，可以看 作是一个电荷源与一个电容器的并联。 16.压电传感器测量电路常接电压或电荷放大

模型制作方法

动画精度模型制作与探究 Animation precision model manufacture and inquisition 前言 写作目的：三维动画的制作，首要是制作模型，模型的制作会直接影响到整个动画的最终效果。可以看出精度模型与动画的现状是随着电脑技术的不断发展而不断提高。动画模型走精度化只是时间问题，故精度模型需要研究和探索。 现实意义：动画需要精度模型，它会让动画画面更唯美和华丽。游戏需要精度模型，它会让角色更富个性和激情。广告需要精度模型，它会让物体更真实和吸引。场景需要精度模型，它会让空间更加开阔和雄伟。 研究问题的认识：做好精度模型并不是草草的用基础的初等模型进行加工和细化，对肌肉骨骼，纹理肌理，头发毛发，道具机械等的制作更是需要研究。在制作中对于层、蒙版和空间等概念的理解和深化，及模型拓扑知识与解剖学的链接。模型做的精，做的细，做的和理，还要做的艺术化。所以精度模型的制作与研究是很必要的。 论文的中心论点：对三维动画中精度模型的制作流程，操作方法，实践技巧，概念认知等方向进行论述。 本论 序言：本设计主要应用软件为Zbrsuh4.0。其中人物设计和故事背景都是以全面的讲述日本卡通人设的矩阵组合概念。从模型的基础模型包括整体无分隔方体建模法，Z球浮球及传统Z球建模法（对称模型制作。非对称模型制作），分肢体组合建模法（奇美拉，合成兽），shadow box 建模和机械建模探索。道具模型制作，纹理贴图制作，多次用到ZBURSH的插件，层概念，及笔刷运用技巧。目录： 1 角色构想与场景创作 一初步设计：角色特色，形态，衣装，个性矩阵取样及构想角色的背景 二角色愿望与欲望。材料采集。部件及相关资料收集 三整体构图和各种种类基本创作 2 基本模型拓扑探究和大体模型建制 3 精度模型大致建模方法 一整体无分隔方体建模法 二Z球浮球及传统Z球建模法（对称模型制作。非对称模型制作） 三分肢体组合建模法（奇美拉，合成兽） 四shadow box 建模探索和机械建模 4 制作过程体会与经验：精度细节表现和笔刷研究 5 解剖学，雕塑在数码建模的应用和体现（质量感。重量感。风感。飘逸感）

工程测试技术试题及答案

复习总结 一、概念题 1.测试过程中，若所测试的信号不随时间变化或变化非常缓慢，称这种测试称为 静态测试。如果所测试的信号随时间周期变化或变化很快，这种测试称为动态测试。 2.传感器是把被测量转换成易于变换、传输和处理的一种器件或装置。 3.按构成原理分类，电阻应变片、热敏电阻、压电晶片属物性型传感器。 4.按构成原理分类，电容传感器、自感型电感式传感器属结构型传感器。 5.为提高和改善传感器的技术性能，可采取以下技术措施：差动技术、平均技术 以及补偿与修正技术。 6.传感器的定度曲线（或标定曲线）与拟合直线之间的偏离程度称为传感器的线 性度。 7.传感器的灵敏度是指稳态时，输出变化量与输入变化量之间的比值。 8.对于一阶传感器系统，当其时间常数（或τ）越小，其频率响应特性越好。 9.激波管标定系统中，激波管的作用是一种动态标定设备，能产生阶跃压力信号 输出。 10.金属电阻应变片的规格一般以面积（或长×宽）和初始阻值表示。 11.用电阻应变片测量构件的变形，影响电阻应变片电阻变化的因素有：应变片的 灵敏度和初始阻值、被测构件的应变量、以及应变片沿构件的粘贴方向。（因为：△R=KεR，K为灵敏度，R为应变片初始阻值，ε被测构件的应变量） 12.将电阻丝绕成应变片后，由于存在横向效应，其灵敏系数一般会减小。 13.在电桥测量中，由于电桥接法不同，输出电压的灵敏度也不同，全桥接法可以 得到最大灵敏度输出。 14.应变片的温度误差补偿方法通常可分为：桥路补偿法、应变片自补偿法。 15.根据工作原理，变气隙型自感式传感器的灵敏度具有理论上的非线性。 16.电涡流接近开关结构简单，根据其工作原理，不可用来进行类似如玻璃瓶、塑 料零件以及水的液位的检测。

初中数学优质专题：8字模型与飞镖模型

1 O D C B A 图1 2图E A B C D E F D C B A O O 图12图E A B C D E D C B A 第一章 8字模型与飞镖模型 模型1 角的“8”字模型 如图所示，AB 、CD 相交于点O ， 连接AD 、BC 。 结论：∠A+∠D=∠B+∠C 。 模型分析 8字模型往往在几何综合 题目中推导角度时用到。 模型实例 观察下列图形，计算角度： （1）如图①，∠A+∠B+∠C+∠D+∠E= ； （2）如图②，∠A+∠B+∠C+∠D+∠E+∠F= 。 热搜精练 1．（1）如图①，求∠CAD+∠B+∠C+∠D+∠E= ； （2）如图②，求∠CAD+∠B+∠ACE+∠D+∠E= 。

2 H G E F D C B A D C B A M D C B A O 135 E F D C B A 2．如图，求∠A+∠B+∠C+∠D+∠E+∠F+∠G+∠H= 。 模型2 角的飞镖模型 如图所示，有结论： ∠D=∠A+∠B+∠C 。 模型分析 飞镖模型往往在几何综合 题目中推导角度时用到。 模型实例 如图，在四边形ABCD 中，AM 、CM 分别平分∠DAB 和 ∠DCB ，AM 与CM 交于M 。探究∠AMC 与∠B 、∠D 间的数量关系。

3 105O O 120 D C B A O D C B A 热搜精练 1．如图，求∠A+∠B+∠C+∠D+∠E+∠F= ； 2．如图，求∠A+∠B+∠C+∠D = 。 模型3 边的“8”字模型 如图所示，AC 、BD 相交于点O ，连接AD 、BC 。 结论：AC+BD>AD+BC 。

2021中考数学易错题飞镖模型8字模型探究试题

2021中考数学易错题飞镖模型8字模型探究试题模型一：角的飞镖模型基础 结论：C + ∠ ∠ = ∠ B + A BDC∠ 解答： ①方法一：延长BD交AC于点E得证 ②方法二：延长CD交AB于点F得证 ③方法三：延长AD到在其延长方向上任取一点为点G得证 总结： ①利用三角形外角的性质证明

模型二：角的8字模型基础结论：D ∠ ∠ = + + C B A∠ ∠

解答： ①方法一：三角形内角和得证 ②方法二：三角形外角【BOD 】的性质得证总结： ①利用三角形内角和等于 180证明 推出 ②利用三角形外角的性质证明

角的飞镖模型和8字模型进阶 【例1】如图，则= ∠E D B A + C + + ∠ ∠ ∠ + ∠ 解答： ①方法一：飞镖ACD得证 ∠E + D C A B ∠ ∠ = 180 ∠ + + ∠ +

②方法二：8字BECD得证 + ∠ ∠E B A + C D ∠ = + 180 + ∠ ∠ 【例2】如图，则= E ∠F + D C A B ∠ ∠ ∠ + + ∠ ∠ + + 解答：飞镖ABF+飞镖DEC得证 ∠F + ∠ E D B + A C ∠ = ∠ + 210 ∠ ∠ + + 【例3】如图，求= E D ∠F B A + C ∠ + ∠ + ∠ ∠ + ∠ + 解答：8字模型得证 ∠F + ∠ E D A B C + 360 + = ∠ ∠ ∠ + ∠ + 【例4】如图，求= ∠D C A + B ∠ + ∠ + ∠

解答：连接BD得飞镖BAD+飞镖DBC得证 + ∠D A ∠ C B = + ∠ 220 + ∠ 【例5】如图，求= ∠H G ∠ F + D A C + E B + ∠ + ∠ ∠ + + ∠ + ∠ ∠ 解答：飞镖EHB+飞镖FAC得证 ∠H ∠ + + ∠ G F A B C D E ∠ + + = 360 ∠ ∠ ∠ + + ∠ + 模型三：边的飞镖模型基础 结论：CD + > AC BD AB+

传感器与检测技术试题及答案

《传感器与检测技术》试题 一、填空：（20分） 1，测量系统的静态特性指标主要有线性度、迟滞、重复性、分辨力、稳定性、温度稳定性、各种抗干扰稳定性等。（2分） 2.霍尔元件灵敏度的物理意义是表示在单位磁感应强度相单位控制电流时的霍尔电势大小。 4.热电偶所产生的热电势是两种导体的接触电势和单一导体的温差电势组成的，其表达式为Eab （T ，To ）=T B A T T B A 0d )(N N ln )T T (e k 0σ-σ?+-。在热电偶温度补偿中补偿导线法（即冷端延长线法）是在连接导线和热电偶之间，接入延长线，它的作用是将热电偶的参考端移至离热源较远并且环境温度较稳定的地方，以减小冷端温度变化的影响。 5.压磁式传感器的工作原理是：某些铁磁物质在外界机械力作用下，其内部产生机械压力，从而引起极化现象，这种现象称为正压电效应。相反，某些铁磁物质在外界磁场的作用下会产生机械变形，这种现象称为负压电效应。（2分） 6. 变气隙式自感传感器，当街铁移动靠近铁芯时，铁芯上的线圈电感量（①增加②减小③不变）（2分） 7. 仪表的精度等级是用仪表的（① 相对误差 ② 绝对误差 ③ 引用误差）来表示的（2分） 8. 电容传感器的输入被测量与输出被测量间的关系，除（① 变面积型 ② 变极距型 ③ 变介电常数型）外是线性的。（2分） 1、变面积式自感传感器，当衔铁移动使磁路中空气缝隙的面积 增大时，铁心上线圈的电感量（①增大，②减小，③不变）。 2、在平行极板电容传感器的输入被测量与输出电容值之间的关 系中，（①变面积型，②变极距型，③变介电常数型）是线性的关系。 3、在变压器式传感器中，原方和副方互感M 的大小与原方线圈 的匝数成（①正比，②反比，③不成比例），与副方线圈的匝数成（①正比，②反比，③不成比例），与回路中磁阻成（①正比，②反比，③不成比例）。 4、传感器是能感受规定的被测量并按照一定规律转换成可用输 出信号的器件或装置，传感器通常由直接响应于被测量的敏感元件

模型的制作工艺及流程

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建筑模型制作流程

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