American Mineralogist, Volume 85, pages 543–556, 2000
0003-004X/00/0304–543$05.00
543
I NTRODUCTION
The importance of synthetic miconductors to chemical and industrial process has spurred a large rearch effort to understand the fundamentals of photochemical process and to develop new photocatalysts. For example, synthetic photocatalysts can promote process such as photodecompo-sition of organic and inorganic contaminants (Borgarello et al.1988; Brinkley and Engel 1998; Fox 1988; Pelizzetti et al. 1988;Serpone et al. 1988a, 1988b), photosynthesis of organic com-pounds from carbon dioxide and other inorganic substrates (Anpo et al. 1997; Inoue et al. 1979; Kanemoto et al. 1996),photodecomposition of water to hydrogen and oxygen (Lauermann et al. 1987; Reber and Meier 1984), and photore-duction of dinitrogen to ammonia (Augugliaro and Palmisano 1988; Bickley et al. 1988; Schrauzer and Guth 1977; Soria et al. 1991).
In contrast, there has been relatively little rearch on the photocatalytic properties of mineral micon
ductors. There is,however, a growing recognition of the role miconducting minerals may play as catalysts of redox reactions in natural environments and engineered systems designed to degrade haz-ardous chemicals (Schoonen et al. 1998; Selli et al. 1996;Stumm and Morgan 1995; Sulzberger 1990). Hence, the ques-
The absolute energy positions of conduction and valence bands of
lected miconducting minerals
Y ONG X U AND M ARTIN A.A. S CHOONEN *
Department of Geosciences, State University of New York at Stony Brook, Stony Brook, New York 11794-2100, U.S.A.
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The absolute energy positions of conduction and valence band edges were compiled for about 50each miconducting metal oxide and metal sulfide minerals. The relationships between energy levels at mineral miconductor-electrolyte interfaces and the activities of the minerals as a cata-lyst or photocatalyst in aqueous redox reactions are reviewed. The compilation of band edge ener-gi
es is bad on experimental flatband potential data and complementary empirical calculations from electronegativities of constituent elements. Whereas most metal oxide miconductors have valence band edges 1 to 3 eV below the H 2O oxidation potential (relative to absolute vacuum scale),energies for conduction band edges are clo to, or lower than, the H 2O reduction potential. The oxide minerals are strong photo-oxidation catalysts in aqueous solutions, but are limited in their reducing power. Non-transition metal sulfides generally have higher conduction and valence band edge energies than metal oxides; therefore, valence band holes in non-transition metal sulfides are less oxidizing, but conduction band electrons are exceedingly reducing. Most transition-metal sul-fides, however, are characterized by small band gaps (<1 eV) and band edges situated within or clo to the H 2O stability potentials. Hence, both the oxidizing power of the valence band holes and the reducing power of the conduction band electrons are lower than tho of non-transition metal sulfides.
tion aris of whether miconducting minerals could promote the same process. If so, the minerals could play an im-portant role in the fate of contaminants and the chemical com-positions of atmosphere and hydrosphere of the early earth. Although all the process mentioned above are photo-chemical process, there is also evidence for non-photolytic catalysis of redox reactions by s
emiconductors (Xu 1997; Xu and Schoonen 1995; Xu et al. 1996, 1999). Semiconductors can act as a conduit for electrons between the aqueous reac-tants. Becau no illumination is needed for non-photo cata-lytic process, this mechanism may be important beneath the photic zone in aquatic systems.
In photochemical reactions, as well as the non-photochemi-cal mechanism outlined in our earlier work, the crucial step is the transfer of electrons between the miconductor and sorbed reactants. As pointed out by Morrison (1990), electrons can only be transferred between tho energetic states in the mi-conductor and the electrolyte that are at approximately the same energy level. The energy level of energetic states of sorbates undergoing an electron transfer can be approximated by the standard redox potential (E 0), whereas relevant energy levels for a miconductor are the top of the valence band (E V ) and the bottom of the conduction band (E C ). The relative energet-ics of E V and E C vs. E 0 is the fundamental property of an elec-trolyte/miconductor system that dictates whether an electron transfer between the miconductor and sorbate is feasible.Although band gap (E g ) is well known for most micon-ductors, unfortunately, E V and E C have not been determined ac-
*E-mail: mschoonen@notes.sunysb.edu
XU AND SCHOONEN: SEMICONDUCTING OXIDES AND SULFIDES
田园日记 歌词
544curately for most miconducting minerals. Furthermore, E V and E C values are often prented in ways that prevent a straight-forward comparison to the redox potentials of aqueous elec-trolytes. For example, in both the materials science and applied physics literature, it is customary to express the energy posi-tion of band edges with respect to the energy level midway in the band gap of the material (i.e., the Fermi level of the mate-rial), rather than on the absolute vacuum scale (AVS). In con-trast, geochemical and electrochemical literature typically reports standard redox potentials for aqueous redox couples with respect to the normal hydrogen electrode (NHE). To com-pare the energy levels of sorbates to the band edges of a mi-conductor, however, it is necessary to have all energy levels of interest (i.e., E 0, E C , E V ) expresd on a common energy scale,such as the absolute vacuum scale or the normal hydrogen elec-trode scale.
The objective here is to (1) provide a compilation of the absolute energy positions of valence and conduction band edges of miconducting metal oxide and metal sulfide minerals and (2) address the relationship between the energy positions and the catalytic activities of the minerals in various heteroge-neous electron transfer process. For tho minerals for which band edge energies have not been determined experimentally,the band edge energies were calculated using an
empirical re-lationship bad on the electronegativity of the elements (But-ler and Ginley 1978). More extensive reviews on the interactions between miconductor and electrolyte and photochemistry involving miconductors can be found elwhere (Balzani and Scandola 1989; Bockris and Khan 1993; Grätzel 1988; Kish 1989; Lewis and Ronbluth 1989; Mills and Le Hunte 1997;Nozik and Memming 1996; Morrison 1990; Nozik 1978; Smith
and Nozik 1997; Stumm and Morgan 1995; Stumm and Sulzberger 1992; Waite 1990).
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T HEORETICAL BACKGROUND
Energetics of miconductor/electrolyte interfaces For the purpo of this study we briefly review the elec-tronic band structure of miconductors and the energetics of the miconductor/electrolyte interface. Comprehensive treat-ments of this topic are by Bockris and Khan (1993), Grätzel (1989), Morrison (1990), and Nozik (1978).
The electronic structure of miconductors is characterized by the prence of a bandgap (E g ), which is esntially an en-ergy interval with very few electronic states (i.e., low density of states) between the valence band and the conduction band,which each have a high density of states (Borg and Dienes 1992). In the context of electron transfer between miconduc-tors and aqueous redox s
pecies, it is crucial to identify the high-est occupied and the lowest unoccupied electronic levels in the miconductor becau tho are the energy levels involved in the transfer. In most miconductors, all electronic levels in the valence band are occupied whereas the levels in the con-duction band are empty. Hence, the highest occupied electronic level coincides with the top of the valence band. The energy of valence band edge, E V , is a measure of the ionization potential,I , of the bulk material. The lowest unoccupied electronic level in most miconductors coincides with the bottom of the con-duction band. Where the band edge energy, E C , is a measure of the electron affinity, A , of the compound. The Fermi level or energy, E F , reprents the chemical potential of electrons in a miconductor. In esnce, the Fermi level is the absolute elec-tronegativity, –χ, of a pristine miconductor, a value which
F IGURE 1. (a ) Position of the conduction band edge (E C ), the valence band edge (E V ) and the intrinsic Fermi level (E F ) of a miconductor with respect to vacuum as the zero energy reference. A is electron affinity; χ is electronegativity; I is ionization energy; E g is band gap. (b )Position of energy levels at the interface of an n-type miconductor and an aqueous electrolyte on the absolute vacuum energy scale (AVS) and with respect to normal hydrogen electrode (NHE). The E CS and E VS reprent the conduction band edge and valence band edge at the interface;U ft is the flatband potential; V H is the potential drop of the Helmholtz layer; V B is the band bending; E F is the Fermi level of the system at equilibrium; ΔE F is the difference between the Fermi level and the conduction band edge; E 0F,redox , is the standard Fermi level of the redox couple; E unoc and E oc , are energies of unoccupied states and occupied states of the redox couple; and λ
is the reorganization energy.
XU AND SCHOONEN: SEMICONDUCTING OXIDES AND SULFIDES 545
corresponds to the energy halfway between the conduction and valence band edges (Fig. 1a). The relationship between band edge energies and electronegativity can be expresd as:E C = –A = –χ + 0.5 E g (1a)
and
E V = –I = –χ –0.5 E g
(1b)Incorporation of impurities in the structure of a miconductor leads to the prence of electron acceptor state levels and/or donor state levels within the bandgap. The prence of donor or acceptor state levels changes the position of E F so that E F lies just above E V for p -type miconductors (prence of ac-ceptor states) and E F lies just below E C for n -type miconduc-tors (prence of donor states) (Morrison 1990).
The next step is to define the energy levels of sorbates. Aque-ous redox species exchanging electrons with a miconductor mineral can either accept (A + e – → A –) or donate (D → D + + e –)electrons. Upon electron transfer from or to an aqueous species,the electronic structure of the species changes. Upon the accep-tance of an electron, a previously unoccupied electronic level becomes occupied, whereas upon electron donation an elec-tron is removed from an occupied level. For an electron accep-tor (A/A –), it is the energy level of the lowest unoccupied level,E unoc , that is of importance, whereas for an electron donor (D/D +)the highest occupied energy level, E oc , is of importance. Becau of the polar nature of water molecules, H 2O dipoles in the solva-tion shell of a
redox species will re-orientate when there is a change in the charge of the redox species. The re-orientation of the solvation shell will result in an addition energy gain or loss when an electron is transferred from or to an aqueous redox spe-cies. The free energy change associated with this re-orientation process is known as reorganization energy (λ). V alues for λ range from a few tenths of an eV up to 2 eV . Furthermore, thermal fluctuation of the solvation structure cau a corresponding ther-mal distribution of the energy levels of both E oc and E unoc , e Figure 1b (Bockris and Khan 1993; Grätzel 1989; Morrison 1990). Whereas the energy distributions are difficult to quan-tify, it is helpful to make u of the notion that the redox poten-tial, E redox , of a redox couple undergoing a one-electron transition (e.g., A/A – or D/D +) lies midway between the maxima in E oc and E unoc for the species. The Fermi level of electrons of a redox couple (E F,redox ) is equivalent to the redox potential of aqueous redox couples (E redox ) on the absolute energy scale; hence, this can be expresd as:
E E E T a a F,A/A A/A A/A o
A A
R −−−−==+ln(
)
(2a)E E E T a a F D/D D/D D/D o D D
the hurt locker
R +,ln(
)
+++==+(2b)
where E 0 is the standard redox potential of the aqueous redox couple with respect to the Normal Hydrogen Electrode (NHE).The Fermi level of NHE at 25 °C is –4.5 eV with respect to the vacuum level (Bockris and Khan 1993).
The distribution of energy states in a redox couple (Fig. 1b)becomes more complicated if the redox couple undergoes a multi-electron tranfer, becau each one-electron step has a
population of two energy states (E oc and E unoc ) associated with
it. Instead of standard redox potential of the overall reaction,the standard potential of each one-electron steps should be con-sidered for a multi-electron transfer reaction. So for a two-elec-tron tran
sition, such as CO 2 + 2e – + 2H + = HCOOH, the standard potentials of the CO 2/CO 2·– and CO 2·–/HCOOH redox couples should be ud (CO 2·– reprents a CO 2 radical group with a charge of –1). The standard redox potentials for the one-elec-tron steps are mostly unavailable becau the intermediate prod-ucts are often unstable. Using E 0 for the overall reaction invariably leads to a misleading comparison of energy levels between miconductor and aqueous species. This aris from the fact that E 0 for the overall reaction does not lie midway between the maximum of E oc and E unoc populations associated with each of the one-electron transitions. For example, E 0 for
CO 2/CO 2
·–
is estimated to lie at –2 V (NHE), whereas E 0 for CO 2/HCOOH equals –0.61 V(NHE) (Tributsch 1989).
When a miconductor is placed in a solution containing redox species, electrons will be transferred across the mi-conductor/electrolyte interface until the chemical , Fermi levels, of electrons in the solid and the solution are equalized. The interfacial electron transfer generates a space charge layer in the miconductor, and conduction and valence band edges are bent such tha
t a potential barrier is established against further electron transfer across the interface. As a re-sult, the energies of conduction and valence band edges at the miconductor/electrolyte interface, (E CS and E VS , respectively),deviate from their bulk values (E C and E V ). The difference be-tween E CS and E C or E V and E VS is known as band bending, V B (Fig. 1b). The thickness of the space charge layer typically ranges from 100 Å to veral microns depending on the con-ductivity of the miconductor and the amount of band bend-ing. On the solution side of the interface, the Helmholtz double layer will develop due to the sorption of counter-ions onto the charged surface of the miconductor. The thickness of the Helmholtz layer is typically on the order of 1 Å (Morrison 1990). The Helmholtz layer results in an additional potential drop inside the miconductor space charge layer so that the band bending adjusts to make the net rate of electron transfer across the interface equal to zero at equilibrium. Hence, the band edge positions of the miconductor at the interface can-not be determined unless the additional potential drop associ-ated with the Helmholtz layer is quantified (Morrison 1990).To link the energy levels of the miconductor and the elec-trolyte, an experimentally measurable quantity, flatband po-tential (U ft ), is esntial. U ft is the electrode potential measured with respect to a reference electrode (e.g., normal hydrogen electrode, NHE) in an electrolyte/miconductor system when the potential drop across the space charge layer becomes zero.U ft can be expresd as (Nozik 1978):U ft (NHE) = A + ΔE F + V H + E 0
( 3)
where ΔE F is the difference between the Fermi level and ma-jority carrier band edge (E C for a n-type miconductor, and E V for a p-type miconductor), V H is the potential drop across the Helmholtz layer, and E 0 is the scale factor relating the refer-ence electrode redox level to the A VS (E 0 = –4.5 V for NHE,Bockris and Khan 1993). Becau U ft is determined not only
XU AND SCHOONEN: SEMICONDUCTING OXIDES AND SULFIDES 546
by intrinsic properties of the miconductor (A andΔE F), but also by the electrolyte (V H), U ft is a property of the interface.
Note that V H is fixed and independent of both the externally applied voltage across the miconductor-electrolyte interface and the changes in redox condition of the system, provided the composition changes associated with electron transfer do not affect the equilibrium distribution of ions adsorbed onto the miconductor. The independence of V H on the interfacial charge transfer is caud by the high charge density and small width of the Helmholtz layer relative to the miconductor space charge layer (Morrison 1990). As a result, the potential drop across the interface caud by the electron transfer occurs pre-dominantly within the miconductor space char
ge layer, whereas the V H remains esntially constant. Conquently, at a given electrolyte composition and miconductor, U ft is a characteristic parameter independent of the electron transfer process. On the other hand, the potential drop within the Helmholtz layer depends on the adsorption/desorption equi-librium of electrolyte ions at the miconductor surface. When the net adsorbed charge within the Helmholtz layer is zero, i.e., at the zero point of charge, (pH ZPC), V H is also zero. The flatband potential at the pH ZPC (U ft0) equals the intrinsic Fermi level of the miconductor, and is the only meaningful flatband potential. Under conditions other than pH ZPC, flatbands are not really flat but contain the band bending induced by the Helmholtz layer. Hence, band edge energies can be calculated from U ft0measurements combined with E g data and an inde-pendent estimate of ΔE F (Nozik 1978).
pH Dependence of band edges at miconductor/electro-lyte interfaces
For miconducting metal oxides, U ft varies with pH fol-lowing a linear relation known as the Nernstian relation (But-ler and Ginley 1978; Halouani and Deschavres 1982; Matsumoto et al. 1989; Morrison 1990):
U fb = U fb0 + 2.303R T/(pH ZPC – pH)F(4) where R is the gas constant, T is temperature, and F is t
he Fara-day constant. At 25 °C and 1 atm, the Nernstian relation leads to a variation of 0.059 V/pH (Fig. 2a). It is generally accepted that the Nernstian dependence indicates that H+ and OH– are potential determining ions (PDI) adsorbed on the solid surface within the Helmholtz layer (Butler and Ginley 1978).
For metal-sulfide miconductors, the pH dependence of U fb appears more complicated than that for metal-oxides, and has not been as thoroughly studied. One unresolved issue is which ions are PDIs. If ions other than H+ and OH– are PDIs, the specific sorption of the ions can affect V H. For example, Ginley and Butler (1978) showed that dissolved sulfide (H2S and HS–) is a PDI for CdS, whereas our rearch has shown that dissolved sulfide and dissolved ferrous iron are PDIs for iron sulfides (Bebié et al. 1998; Dekkers and Schoonen 1994). For CdS, the flat band shows a variation in pH dependence from 0 to 59 mV/pH (Ginley and Butler 1978), with the slope depending on the concentrations of metal ions and dissolved sulfide ions. Minoura et al. (1977) reported that U ft varies with crystal face. For FeS2 and ZnS, however, the pH dependence is reported to be consistent with the Nernstian relation (Chen et al. 1991; Fan et al. 1983). We speculate that U ft for metal sul-fide miconductors may follow the Nernstian pH dependence in aqueous solutions with low concentrations of metal ions and/ or dissolved sulfide, but that the pH dependence will switch to
non-Nernstian behavior when specific sorption of metal ions and sulfide becomes important. More rearch in the surface chemistry of metal sulfides is needed to resolve the apparent inconsistencies highlighted above.
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The pH-E H relationship defined by the Nernstian slope is characterized by a constant fugacity of hydrogen, as illustrated in Figure 2b:
log
.
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E F
T
H
H
2
pH
R
=−−
2
2
2303
(5a) or
log f pe
H
2
22
highprofile=−−
pH
(5b) The constant hydrogen fugacity defined by the Equations 5a or 5b indicates a constant redox state for a linear combination of pH and E H in the Nernstian slope. On a pH-E H diagram, it is the linear combination of E H(or pe) and pH that describes the re-dox state of an aqueous redox system and not E H (or pe) alone; e also Anderson and Crerar (1993). Hence, we believe that the pH dependence of miconductor flatband potential given by the Nernstian slope is consistent with a constant reducing
F IGURE 2. pH dependence of the conduction band edge and valence band edge of pyrite in an aqueous electrolyte solution described by (a), a pH-Eh diagram, and (b) a pH-log f H
2
diagram. The E C and E V follow the Nernstian relation, which has a variation of 0.059V/pH at 25 °C at 1atm, and lies parallel to the water stability limits.
XU AND SCHOONEN: SEMICONDUCTING OXIDES AND SULFIDES547 (oxidizing) power of the (photo)electrons (holes) in a mi-
conductor. It is noteworthy that the flat-band potentials for
miconductors are parallel to the stability limits of water in
an E H-pH diagram if they follow the Nernstian behavior. If
log f H
2 is ud as the parameter defining the redox condition
of a miconductor/electrolyte system, as shown in Figure 2b, both the band edges and water stability limits are inde-pendent of pH. Hence, a pH-E H pair can be replaced with a single variable, the fugacity of hydrogen, to define the redox condition of the system.
Temperature and pressure dependence of band edge energies拍马屁英文
Becau miconductors can catalyze non-photoreactions as well as photoreactions, their catalytic activity may extend to subsurface geochemical process, such as in hydrothermal systems. To evaluate the potential of miconductors as cata-lysts in subsurface environments, it is important to understand the effects of temperature and pressure on the band energies.
In contrast to aqueous redox couples, which often show a considerable temperature dependence for
E redox, the electronic structure of a miconductor undergoes little change with tem-perature and pressure provided that no pha transition occurs. For example, the measured bandgap changes over temperature (d E g/d T) for PbS and ZnO range from +4 × 10–4 eV/K to –9.5 ×10–4 eV/K, respectively (Gonzalez et al. 1995). For most mi-conductors, the variation of the bandgap with pressure is also very small in the pressure ranges of interest. The experimental determined variation rates (d E g/d P) are in the order of 0.01–0.1 eV/GPa (Gonzalez et al. 1995). Therefore, the reducing power of a (photo)electron and the oxidation power of a hole are esntially constant with temperature and pressure, unless the solid itlf undergoes a pha transition and changes the electronic structure altogether.
Although temperature and pressure have negligible effect on the bulk band structure of miconductors in the T-P ranges of interest, they may have a more pronounced effect on inter-facial energetics. As shown in Equation 4 the Nernstian slope is temperature dependent. Perhaps more importantly, the pH ZPC of miconductors is also temperature dependent. Schoonen (1994) estimated pH ZPC values for veral metal oxides up to 350 °C bad on extrapolation of low-temperature (<95 °C) experimental data. The calculations indicate that pH ZPC values shift down by 1 to 2 pH units as temperature ris from 25 °C to 200 to 300 °C, but beyond 200 to 300 °C the p
H ZPC shifts back to higher values. This general trend was confirmed experimentally for rutile up to 250 °C by Machesky et al. (1994). A 2-pH-unit decrea in pH ZPC between 25 and 250 °C would result in a shift of interfacial band edge energies to a higher energy level (with respect to vacuum) by about 0.25 eV. However, the exact tem-perature dependence of pH ZPC of miconductors is largely un-known and more experimental investigations are needed.
B AND EDGES OF SEMICONDUCTING OXIDE AND
SULFIDE MINERALS
The conduction band edges and bandgaps for common ox-ide and sulfide miconducting minerals are given in Tables 1 and 2. This compilation includes data obtained from two dif-ferent methods: photo-electrochemical measurements, and empirical calculation bad on electronegativity of constituent atoms. A comparison of experimental and empirically calcu-lated conduction band edges is shown in Figure 3. The trends in the energy positions of band edges for metal oxides and metal sulfides will be discusd below parately. Determination methods
Band edges can be derived experimentally from the flatband potential measurement using various (photo)electrochemical techniques. The classic method for flatband potential determi-nation, which is
still considered as the most reliable technique, is the Schottky-Mott method (Nozik 1978). Another common method is the determination of anodic photocurrent ont po-tential by evaluating the photocurrent-potential plot (Arico et al. 1990; Butler 1977). More recently, the photocurrent-volt-age measurements have been extensively ud in miconduc-tor particle systems with electrochemical charge-collection techniques. The advantage of this technique is that the varia-tion of the steady-state photocurrent can be measured as a func-tion of pH. This allows for the estimation of interfacial energetics of the particulate system (Chen et al. 1991; Leland and Bard 1987). It is noteworthy that colloidal particles have a larger bandgap than large crystals due to the quantum size ef-fect, which results in a higher energy position of the conduc-tion band edge (Ward and Bard 1982).
In the last two decades, quantitative quantum mechanical calculations have been carried out for a large number of
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miconductor minerals (Folkerts et al. 1987; Huang and Ching
celtic
F IGURE 3. Correlation between the empirically calculated conduction band edge energy and the measured flatband potential at pH ZPC for miconducting metal oxide and sulfide minerals in absolute vacuum scale. The sources of the experimental data are given in the Tables 1 and 2.