Electronic states in valence and conduction bands of group-III nitrides --Experiment and theory

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INFORMATION No.INF02/70A Date:March 2003Product SM3000 Videographic RecorderManuals IM/SM3000Guidance on the use of ABB’s SM3000 Videographic Recorder forElectronic Record Keeping in FDA Approved ProcessesIntroductionOn August 20th 1997 the Food and Drug Administration made21 CFR Part 11 effective. This regulation is summarized asfollows:‘The Food and Drug Administration (FDA) is issuing regulationsthat provide criteria for acceptance by FDA, under certaincircumstances, of electronic records, electronic signatures, andhandwritten signatures executed to electronic records asequivalent to paper records and handwritten signaturesexecuted on paper. These regulations, which apply to all FDAprogram areas, are intended to permit the widest possible use ofelectronic technology, compatible with FDA’s responsibility topromote and protect public health. The use of electronic recordsas well as their submission to FDA is voluntary.’This guide provides details of the relevant sections of 21 CFRPart 11 and gives information on how the SM3000Videographic recorders can be used to meet these FDArequirements for the creation of electronic records in a closedsystem.FDA 21 CFR Part 11 Subpart B – Electronic Records, Section 11.10: Controls for Closed Systems‘Persons who use closed systems to create, modify, maintain, or transmit electronic records shall employ procedures and controls designed to ensure the authenticity, integrity and, when appropriate, the confidentiality of electronic records and ensures that the signer cannot repudiate the signed record as not genuine.’Process data can be archived in a binary encoded format which can be viewed only in a human-readable form through the use of ABB’s DataManager review software. The recorded data contains built-in data integrity checks for each block of data (maximum of 240 samples per block) in order to detect any corruption or attempted falsification of the record. The DataManager software checks the data against the built-in checksums to validate the integrity of the data and to warn the user of any invalid recordsFDA 21 CFR Part 11 Section 11.10 (a)‘Validation of systems to ensure accuracy, reliability, consistent intended performance and the ability to discern invalid or altered records.’Validation is a function usually performed by the end-user or a third party acting on behalf of the end-user. The SM3000 Videographic Recorders have been developed (including the design of the recorders software) and manufactured in ISO9001:1994 standard processes. Further details on the manufacturing and design practices applied to the SM3000 can be provided by ABB to assist the customer with the validation of the Videographic recorders. The accuracy of the recorder measurements can be ensured by exercising the system calibration procedures described in the User Guide. The SM3000 recorders have an encoded audit log feature which allows the identification of changes to the system by recording the nature, time/date and authorized user of the modification.FDA 21 CFR Part 11 Section 11.10 (b)‘The ability to generate accurate and complete copies of records in both human-readable and electronic form suitable for inspection, review and copying by the agency (FDA).’The SM3000 recorder can create process data files on SmartMedia or Compact Flash memory cards. These data files are created from secure records stored in internal flash memory. Error detection algorithms are employed to ensure that the stored data faithfully represents the actual raw measurements made by the recorder. Each write to the archive media is also verified to ensure the integrity of the data record. The archived process data files can be viewed using the DataManager review software. The data can be viewed and printed in tabular or graphical formats. Standard spreadsheet formats (e.g. Microsoft Excel) of the archived data files can be created for viewing by users who do not have the DataManager software.FDA 21 CFR Part 11 Section11.10 (c)‘Protection of records to enable their accurate and ready retrieval throughout the records retention period.’The SM3000 videographic recorder uses solid-state flash memory, in the form of Smartmedia and Compact Flash cards, for data storage. Data retention for these devices is specified as a minimum of 10 years. They provide zeropower data retention, i.e. the data integrity is not dependent on battery back-up. The data is not affected by magnetic fields. For even longer-term data storage the archive files can be copied to CDROM or to a network file server.FDA 21 CFR Part 11 Section11.10 (d)‘Limiting system access to authorized individuals.’The SM3000 Videographic Recorder provides the ability to limit access to the instruments configuration and critical operator functions. Two different security modes can be configured in the instrument:1) Password ProtectionUp to 15 users, each with a unique ID and password, can be created to control access to critical operator functions and configuration parameters.The ID can be alphanumeric and up to 20 characters in length.The passwords can be alphanumeric and the minimum number of characters allowable in a password can be set from 4 to 20 characters.To prevent password ageing a password expiry time can be set.To prevent illegal use of user ID’s a user can be de-activated after a configurable number of repeated wrong password entries.Users can be de-activated after a configurable period (7 days to 1 year) of inactivity.Different access privileges can be set for each user.One of four levels of configuration access can be assigned to a user:1)No access2)The ability to load existing configuration files only3)Limited access (read access plus the ability to adjustalarm trip values4)Full read/write access.In order to gain access to the configuration or critical operator parameters a valid operator ID and password combination has to be entered. The recorders do not have a secret override password.Any modification of the instruments’ configuration is recorded in the audit log identifying the user responsible for the change.2) Security Switch ProtectionAccess to the instruments’ configuration is protected by a physical internal switch. In order to gain access to the internal security switch it is necessary to remove the instruments inner chassis from the case. A tamper-evident seal can be fitted to the front of the instrument to prevent the inner chassis from being withdrawn without breaking the seal.In addition to these protection methods access to the archive media (i.e. Smartmedia or Compact flash card) can be protected by a mechanical lock, fitted as standard on all units to the media door on the front of the instrument.FDA 21 CFR Part 11 Section11.10 (e)‘Use of secure, computer-generated, time-stamped audit trails to independently record the date and time of operator actions that create, modify or delete electronic records. Record changes shall not obscure previously recorded information. Such audit trail documentation shall be retained at least as long as that required for the subject electronic records and shall be available for agency review and copying.’The SM3000 Videographic recorders automatically produce a time-stamped audit trail that includes disk insertion and removal, power failure and recovery, configuration changes, file deletions, system diagnostics and calibration changes. This information is stored in an audit log which can be automatically archived to a permanent file on Smartmedia or Compact flash. A separate alarm/event log automatically produces a time-stamped record of all alarm state changes and can also be automatically archived to a permanent file. Each time the configuration of the recorder is changed a new file is created which can be stored as a permanent file to Smartmedia or Compact flash. Each file is time-stamped to indicate the date and time when the change occurred. This allows the configuration at a previous time in the recorders history to be maintained and for the configuration before and after a change to be reviewed.The audit and alarm/event logs are stored in an encoded format with checksum protection to prevent the falsification of its contents.FDA 21 CFR Part 11 Section 11.10 (g)‘Use of authority checks to ensure that only authorized individuals can use the system, electronically sign a record, access the operation or computer system input or output device, alter a record or perform the operation at hand.’The recorder’s security system outlined in part d) limits access to the system to modify any configuration parameters.FDA 21 CFR Part 11 Section 11.10 (h)‘Use of device (e.g., terminal) checks to determine, as appropriate, the validity of the source of data input or operational instruction.’The analog inputs provided on the SM3000 Videographic recorder’s have built-in broken-sensor, over- and underrange detection. Indication of these conditions is provided on the recorder’s display and in the data files.FDA 21 CFR Part 11 Section 11.10 (i)‘Determination that the persons who develop, maintain or use electronic record/electronic signature systems have the education, training and experience to perform their assigned tasks.’Only suitably qualified people are employed in product design & development and their training is updated to meet advances in technology. Levels of competence and training needs are externally audited by the British Standards Institute (BSI) for our ISO9001 quality management system.FDA 21 CFR Part 11 Section 11.10 (k)‘Use of appropriate controls over systems documentation including:(1)Adequate controls over the distribution of, access to,and use of documentation for system operation andmaintenance.(2)Revision and change control procedures to maintain anaudit trail that documents time-sequenceddevelopment and modification of systemsdocumentation.’A design control system is used which is fully documented and traceable. This is externally audited by the British Standards Institute (BSI) for our ISO9001 quality management system. Documentation is provided for installation, configuration and operation in the instrument’s User Guide.FDA 21 CFR Part 11 Subpart B – Electronic Records, Section11.50: Signature manifestationsa)Signed electronic records shall contain informationassociated with the signing that clearly indicates all ofthe following:1)The printed name of the signer2)The date and time when the signature was executed3)The meaning (such as review, approval, responsibilityor authorship) associated with the signature.b)The items identified in paragraphs a) 1), a) 2), and a) 3)of this section shall be included as part of anyhumanreadable form of the electronic record (such aselectronic display or printout).The SM3000’s electronic signature is recorded with the operators username (up to 20 characters), the data and time at which the signature was activated and a 20-character message which the operator can use to indicate the purpose of the signature.FDA 21 CFR Part 11 Subpart B – Electronic Records, Section 11.70: Signature/record linkingElectronic signatures and handwritten signatures executed to electronic records shall be linked to their respective electronic records to ensure that the signatures cannot be excised, copied or otherwise transferred to falsify an electronic record by ordinary means.Electronic signatures are stored in the SM3000’s alarm/ event log. This log can be stored to archive media in an encoded format with checksum protection to prevent the falsification of its contents. The archived alarm/event log and channel data files both contain the instrument tag and unique instrument serial number. This can be used to ensure that the electronic signature and the associated data are securely linked.FDA 21 CFR Part 11 Subpart C – Electronic Signatures, Section11.100: General requirementsa)Each electronic signature shall be unique to oneindividual and shall not be reused by, or reassigned to,anyone else.The SM3000 does not allow the same username to be used by more than one operator. This function together with procedural controls can be used to meet this requirement.FDA 21 CFR Part 11 Subpart C – Electronic Signatures, Section11.200: Electronic signature components and controls.a)Electronic signatures that are not based uponbiometrics shall:1)Employ at least two distinct identificationcomponents such as an identification code andpassword.i)When an individual executes a series ofsignings during a single, continuous period ofcontrolled system access, the first signing shallbe executed using all electronic signaturecomponents; subsequent signings shall beexecuted using at least one electronic signaturecomponent that is only executable by, anddesigned to be used only by, the individual.ii)When an individual executes one or moresignings not performed during a single,continuous period of controlled system accesseach signing shall be executed using all of theelectronic signature components.2)Be used only by their genuine owners; and3)Be administered and executed to ensure thatattempted use of an individual’s electronic signature byanyone other than its genuine owner requirescollaboration of two or more individuals.To perform any electronic signing the SM3000 requires the operator to provide a valid username and password. The SM3000 does not have a security override code. The security can only be overridden by the use of an internal switch, access to which can be protected by a tamperevident seal.FDA 21 CFR Part 11 Subpart C – Electronic Signatures, Section 11.300: Controls for identification codes/passwords.Persons who use electronic signatures based upon use of identification codes in combination with passwords shall employ controls to ensure their security and integrity.The passwords can be alphanumeric and the minimum number of characters allowable in a password can be set from 4 to 20 characters. To prevent password ageing a password expiry time can be set. To prevent illegal use of user ID’s a user can be de-activated after a configurable number of repeated wrong password entries. Users can be de-activated after a configurable period (7 days to 1 year) of inactivity.FDA 21 CFR Part 11 Section 11.300 (a)Maintaining the uniqueness of each combined identification code and password, such that no two individuals have the same combination of identification code and password.The SM3000 does not allow the same username to be used by more than one operator.FDA 21 CFR Part 11 Section 11.300 (b)Ensuring that identification code and password issuances are periodically checked, recalled or revised (e.g., to cover such events as password ageing).To prevent password ageing a password expiry time can be set. To prevent illegal use of user ID’s a user can be deactivated after a configurable number of repeated wrong password entries. Users can be de-activated after a configurable period (7 days to 1 year) of inactivity. These features together with procedural controls can be used to meet these requirements.SummaryABB is an established world force in the design and manufacture of instrumentation. The quality, accuracy and performance of the Company’s products result from over 100 years experience. The products are manufactured and designed using ISO9000 approved processes.The SM3000 Videographic Recorders have been designed to meet the standards set out in 21 CFR part 11 and properly implemented they can be used as part of a validated system.1.All process data can be recorded in a binary encoded,tamper-proof format. The recorded data is further protected by error detection checks to ensure the authenticity of these records2.Solid state flash memory that is not reliant on battery back-up and which is not subject to magnetic fields is used to provide secure storage of data .3.DataManager review software provides the ability to viewthe data records and audit trails in a humanreadable form.4.Password and physical security systems are provided inthe recorder to limit access to authorized personnel.Provision is made to counter password ageing and attempted unauthorized access.5. A detailed audit log accompanies all process datarecorded by a SM3000 Videographic Recorder. All system events including configuration changes, memory card removal/insertions, power failures and instrument calibrations are logged. All entries are timeand date-stamped and include an operator ID where applicable. This log is encoded and protected by builtin error checks to prevent/detect tampering or data corruption.6. An electronic signature function provides a securealternative to a hand written signature. The integrity of the signature is protected by a unique username and password.I N F 02/70A I s s u e 1ABB LimitedHoward Road, St Neots Cambridgeshire PE19 8EU UKTel:+44 (0)1480 475321Fax:+44 (0)1480 217948ABB Inc.125 E. County Line Road Warminster PA 18974USATel:+1 215 674 6000Fax:+1 215 674 7183ABB has Sales & Customer Supportexpertise in over 100 countries worldwide The Company’s policy is one of continuous product improvement and the right is reserved to modify theinformation contained herein without notice.Printed in UK (03.03)© ABB 2003。

Chapter7Chemical ChangeThe magic of chemistry comes with thrills and excitement,flashy reactions andfireworks,with colour and sound.It is not bonding and structure that grab the imagination,but spectacle and change.Here is the topic that tells the real story of chemistry.Chemical change,more than anything,happens in a crowded environment.Factors of importance are the state of aggrega-tion,material concentration,temperature and pressure,collectively known as thermodynamic conditions.Students of chemistry,even at the elementary level,should be familiar with thermodynamic models of chemical reactivity. For a concise revision refer to[15].A brief summary follows.7.1Thermodynamic PotentialsThe fundamental assumption of thermodynamics is the conservation of en-ergy,also during its conversion from one form into another.In chemical applications it is cumbersome to account for total energy in all its forms and the problem is avoided by focussing on differences in energy rather than absolute values.As the basis of calculation a convenient energy zero is arbi-trarily defined and energy,relative to this state,is called the thermodynamic energy,consisting of three components:U=T S−P V+ µj N j(7.1) or alternatively,∆U=q+w+tdefining heatflux,mechanical work and matterflow.The parameters T,S, P,V,µand N represent temperature,entropy,pressure,volume,chemical potential and mole number,respectively.By discounting one or more of these249250CHAPTER7.CHEMICAL CHANGE terms the zero point moves to a new level and alternative potential functions are defined,such as:Enthalpy:H=U+P V=T S+ µj N jFree energy:F=U−T S=−P V+ µj N jFree enthalpy:G=H−T S= µj N jThese formulae explain the common terminology for one-component closed systems:H=q P,heat contentF=w T,work functionG/N=µ,partial molar free enthalpyThe differential form of the potential expressions shows that chemical poten-tial is defined by afirst derivative of each potential:µ= ∂U∂N S,P= ∂F∂N T,PChemical reactivity,depending on the reaction conditions,can be described equally well in terms of any of these thermodynamic potentials and no effort will be made to differentiate between them in the following discussion.7.2Chemical ReactivityIt is possible to gain significant insight into chemical reactivity from a few simple principles,without getting involved with the abstract ideas of statis-tical thermodynamics.A chemical reaction occurs as the material composition of a reaction mixture changes.Should this process happen spontaneously,chemical energy is released.Alternatively,supply of energy from an external source drives the chemical change.The energy produced during spontaneous change does not necessarily cause an increase in temperature as most of it may be dissipated as increased entropy.The course of a chemical reaction can therefore be followed by mapping changes in the energy of a system.As a general principle the propensity for chemical change in a mixture is considered to be a function of a potential-energyfield,created by the mass ratios or amounts of substance7.2.CHEMICAL REACTIVITY251 in the mixture.Thisfield is related to the quantum potential of the system and is said to reflect the chemical potential of the reaction mixture.The chemical potential of an atom has been shown to depend on its elec-tronegativity,or quantum potential,in the valence state.For a molecule, such a measure,although more difficult to estimate,still has the same mean-ing.In the case of a pure substance the chemical potential is an intensive property of the system,independent of the amount of material,but sensi-tive to thermodynamic changes in the environment.The quantity that varies with amount of substance is an energy,u=nµ.The dimensionless variable n is conveniently expressed in moles of substance,definingµas a molar energy. In a reaction mixture the chemical potential of each componentµi=u/n i is equivalent to its partial molar energy.The observed energy of reaction depends on the thermodynamic condi-tions and the choice of zero point.The useful index in chemical reactions is therefore not the absolute value of the energy,but the change in energy during the course of the reaction.This change drives the reaction and is responsible for changing the supply of reactant by an amount∆n:∆u=µ∆n.The quantity∆u=αis also known as the affinity of the reaction.In a reaction mixture consisting of several reactants and a number of reaction products,all of these components contribute to the affinity at any time during the course of the reaction:α=∆u= i n iµi products− j n jµj reactantsSpontaneous chemical change occurs when∆u<0and ceases when∆u=0. Chemical reaction therefore proceeds in the direction that minimizes the affinity and depends on the rate at which affinity changes.Because of their variable thermodynamic state and concentration each reactant or product is characterized at any instant by an intrinsic activity, a i,and the interplay between these activities defines the chemical action A, at that instant.The action changes at a rate proportional to A and to the change in affinity,as summarized by the linear homogeneous equation:d Ad A=βA dαor252CHAPTER7.CHEMICAL CHANGE yieldsln A f(a j)n jreactants (7.2) Both chemical potential and affinity depend on the choice of a standard state.A convenient choice is A i=1.The action relative to the standard state(⊖) is given by:ln A f=β iµi∆n i=β ∆u f−∆u⊖1∆u f=∆u⊖+ln a i(7.4)βActivities,as yet undefined,must,by definition,be proportional to the con-centration,or mole fraction,of each reactant in the mixture,i.e.a i=γi X i. The activity coefficientγi→1as X i→1.Equations(7.3)and(7.4)are well-known thermodynamic expressions.A reaction reaches equilibrium as the affinity approaches zero,henceQ=e−β∆u⊖≡K,known as the equilibrium constant.The elementary form of the equilibrium constant of the reaction:a A+b B⇌c C+d Dis readily derived in terms of equilibrium molar concentrations as[C]c[D]dK=7.3.THE BOLTZMANN DISTRIBUTION253 7.3The Boltzmann DistributionThe inverse argument shows how a chemical potentialfield imposes a partic-ular energy distribution on units of matter.Consider a quantizedfield with discrete energy levels,each occupied by a characteristic number of molecules.These numbers can be thought of as representing relative activities during the course of a hypothetical reaction that starts with n i molecules at the initial energy level u i and reaching equi-librium with n j molecules of thefinal product at the level u j.Intermediate levels are occupied by secondary products.As beforeln A fA i =n jn i 2∆u f−∆u i=u j−u i−Nk=j u k+N l=i u l=2(u j−u i) Hence,by(7.5)2ln n j254CHAPTER7.CHEMICAL CHANGE where n0and u0refer to the ground level.Finallyn in0( ∞i=0e−u i/kT·e u0/kT)e−u i/kT=kTThe quantized energyǫj can be of electronic,vibrational,rotational or trans-lational type,readily calculated from the quantum laws of motion.In a macrosystem the sum over all the quantum states for the complete set of molecules,the sum over states defines the canonical partition function:Z= states e−E i/kT7.4EntropyEntropy production during chemical change has been interpreted[7]as the result of resistance,experienced by electrons,accelerated in the vacuum.The concept is illustrated by the initiation of chemical interaction in a sample of identical atoms subject to uniform compression.Reaction commences when the atoms,compacted into a symmetrical array,are further activated into the valence state as each atom releases an electron.The quantum potentials of individual atoms coalesce spontaneously into a common potentialfield of non-local intramolecular interaction.The redistribution of valence electrons from an atomic to a metallic stationary state lowers the potential energy, apparently without loss.However,the release of excess energy,amounting to ∆u=µval−µmet per atom,into the environment,requires the acceleration of electronic charge from a state of rest,and is subject to radiation damping [99].Emitted radiation carries offenergy,momentum and angular momentum and so must influence the subsequent motion of the charged emitters.These reactive effects are usually considered of negligible importance and therefore7.5.CHEMICAL REACTION255 neglected in most cases.The effect of radiation damping on elementary quantum transitions is immeasurably small and therefore ignored on account of Occam’s razor.The laws of quantum mechanics are therefore considered to be strictly time-reversible.However,when charges at rest are suddenly accelerated for a short time the effect becomes appreciable.Redistribution of charge during chemical reaction represents situations of exactly this type.The most general chemical reaction can be reduced to the process of mak-ing and breaking bonds through the rearrangement of valence electrons and atomic cores to minimize the electronic energy.This motion in molecular space is not frictionless and some energy is lost irretrievably to the radiation field.It is this universal friction that renders processes irreversible and cre-ates the arrow of time.The time-irreversible second law of thermodynamics, like the exclusion principle,is thereby identified as an emergent property of macrosystems.For book-keeping purposes the production of entropy during chemical change is considered as reducing the useful energy of the system by disorderly dispersion.In many cases this waste can be calculated statistically from the increase in disorder.To be in line with other thermodynamic state functions, any system is considered to be in some state of disorder at all temperatures above absolute zero,where entropy vanishes.Thermodynamics is the workhorse of chemical engineering,but less im-portant as a theory to elucidate the mechanism of chemical reactions. 7.5Chemical ReactionThe quantum-mechanical formulation of the progress of a reaction such asA+B→C+Dstarts[7]from a stationary product stateψA.ψB of mixed reactants and proceeds via the entangled valence stateψABCD towards thefinal product stateψC.ψD.There is no obvious mechanism for such events in terms of traditional quantum theory.In Bohmian formalism it may be argued that the reaction system,con-sidered closed,is described at all times by an equation HΨ=EΨin the time-dependent wave functionΨ(A,B,C,D).The product statesψA.ψB andψC.ψD,as well as the valence state are special solutions of this equa-tion under different boundary conditions.All rearrangements and transfor-mations that determine thefinal outcome happen in the valence state.The256CHAPTER7.CHEMICAL CHANGE valence state is not unique and is conditioned by thermodynamic factors.Un-der stormy conditions the reactants may be fragmented into smaller units, A→na i,B→mb j,etc.The number and nature of possible reaction prod-ucts will depend critically on the degree of fragmentation.Fragmentation itself is brought about by electronic,vibrational and rotational transitions, with rates linked to the ambient conditions.The valence state may therefore be formulated in terms of variables,characteristic of either molecular frag-ments,atoms,nuclei,electrons and/or photons.It may be either holistic or partially holistic,with matching quantum potential.The extent of non-local interaction depends on the quantum potential and may be a factor limiting the extent of possible intramolecular rearrangement during chemical reaction. The traditional argument does not contemplate instantaneous transitions be-tween states and intramolecular rearrangement becomes a complete mystery.Real chemical reactions are violent affairs and not likely to proceed as smoothly as an ideal metalization.Reacting units have translational kinetic energy but only a fraction of activating encounters leads to binding.The final product is unlikely to incorporate all of the atoms promoted into a va-lence state;smaller fragments are more likely to separate before reaction has spread homogeneously through the entire system and all nuclei have moved into place.Formation of intermediate fragments represents relaxation to an energy well below the valence state and leads to cessation of further chemical interaction.In an atomic medium diatomic fragments are expected to be the major product.If these emerge in or near their valence states,further reaction may cause formation of oligomers.In complex reaction mixtures the course of reaction depends on the relative promotion status of the various constituents,which may be atoms,small molecules or ions.Although each individual reaction therefore has a specific course that depends on the com-position of the reaction mixture and on environmental factors,it is of interest to identify the common principles that may influence reaction mechanisms.It has been argued[7]that secondary interactions between primary frag-ments should normally result in a new non-local equilibrium situation in-volving all constituent atoms of an oligomer and their quantum potentials. However,this is not the soup of individually promoted atoms.It is more likely that interacting primary fragments would reach their own promotion state,which does not require sequestration of all cohesions established be-fore.Any chemical process that occurs over a series of steps is thus predicted to yield diverse products dependent only on environmental conditions during each step.Certain fragments remain intact during rearrangement.These fragments,rather than their constituent atoms,contribute to the quantum7.5.CHEMICAL REACTION257 potential of the whole and the shaping of a new product.The extent to which the molecular quantum potential dictates a robust three-dimensional shape depends on a wave function that remains localized on the molecule.It is only the electronic wave function of an isolated free hydrogen atom that can conceivably be considered to extend indefinitely in a void.For any other situation,including the real world,local potential barriers must restrict it to a much smaller region.The more crowded the environment,the more closely is the wave function–and therefore the effect of the quantum potential–confined.Only when environmental crowding promotes the atom into its valence state does the wave function start penetrating into a larger region that covers the chemically interacting neighbourhood.As the primary reaction products separate,the total wave function factorizes into a product stateψT=φM1φM2···φM n.(7.7) Non-local connections between these molecular units are much feebler than within the molecules and vary with the state of aggregation.This conclusion seems to agree with conventional thinking in chemistry.7.5.1AtomicReactionsEnergyFigure7.1:Schematic drawing to illustrate promotion to the valence state and formation of a diatomic molecule.A characteristic degree(energy)of uniform compression is required to promote an atom into its valence state.In a compressed monatomic medium all atoms enter the valence state simultaneously.At this point the valence258CHAPTER 7.CHEMICAL CHANGE electrons have quantum potential energy only,but they are free to move away from their atomic cores.The barrier between actual atoms is never as uniform and impervious as in the simulation.Valence electrons gain ki-netic energy and percolate into interatomic voids where they encounter other valence electrons with which they interact through the field effects of their quantum torque.In this fashion electrons become delocalized across the neighbourhood defined by those promoted atoms in close proximity;inter-acting via the quantum potential field.The reaction neighbourhood may consist of only two atoms that end up equally sharing the pair of valence electrons.This condition is the prototype of a covalent bond.A schematic diagram to illustrate the course of reaction is shown in figure7.1.The energy level of the valence state corresponds to the promotion of two atoms involved in the reaction.The energy of the system drops as the valence electrons spread out across the larger accessible space surrounding the atomic cores.Holistic interaction between the two valence electrons and the cores stabilizes the molecule by an amount D e .According to the classical model this corresponds to an internuclear distance r e .E n e r g yFigure 7.2:Activation and interaction of a heteronuclear pair of atoms.Red dots indicate the activation levels of homonuclear diatomics.Because of the difference in polarity formation of the heteronuclear molecule is favoured.The idea of a chemical bond between two atoms in a molecule is akin to the classical model of a diatomic molecule,and its formation can be dis-7.6.CHEMICAL KINETICS 259cussed along the same lines.The first assumption is that a pair of neigh-bouring atoms can be identified and isolated for study,well knowing that this action sacrifices all knowledge pertaining to overall intramolecular entangle-ment.The next approximation is to clamp the nuclei at classically variable coordinates.This approximation still allows freedom to study the electron density quantum-mechanically.However,in view of the nature of the va-lence state developed here there is nothing to gain by attempting all-electron calculations.The predicted course of reaction between a heteronuclear pair of atoms is shown in Figure 7.2.Promotion is once more modeled with isotropic com-pression of both types of atom.The more electropositive atom (at the lower quantum potential)reaches its valence state first and valence density starts to migrate from the parent core and transfers to an atom of the second kind,still below its valence state.The partially charged atom is more readily com-pressible to its promotion state,as shown by the dotted line.When this modified atom of the second kind reaches its valence state two-way delo-calization occurs and an electron-pair bond is established as before.It is notable how the effective activation barrier is lowered with respect to both homonuclear (2V q )i barriers to reaction.The effective reaction profile is the sum of the two promotion curves of atoms 1and 2,with charge transfer.7.6ChemicalKineticsReaction CoordinateE n e r g y In a molar-scale diatomic reaction mixture (R =kL )the number of reactants in the valence state,at a given temperature,is given by an equation such as (7.6)with u i =(2V q )eff ≡E a ,called the activation energy .The mole260CHAPTER7.CHEMICAL CHANGE fraction(concentration)n a/N=Ze E a/RT(7.8) of activated reactants determines the chemical action at temperature T.The well-known equationk=Ae E a/RTthat defines reaction rate constant as a function of temperature,first obtained empirically by Arrhenius,clearly defines the same relationship as(7.8).In the case of a complex reaction the rate constant is the product of rate constants for several elementary steps.The progress of such reactions is usually presented along a reaction coordinate–a hypothetical parameter that depends on all internuclear distances of relevance to the mechanism whereby reactants are converted into products.The forward and reverse reactionsk1=A1e−(E a)1/RTk−1=A−1e−(E a)−1/RThave different activation energies that define the thermodynamic equilibrium constant,K=k1/k−1∝e−∆H/RT.All theories of chemical kinetics and reaction mechanisms are based on eqn.(7.8)by an estimation of the relevant partition function.。

PHYSICAL REVIEW B84,035406(2011)Energetics and electronic structure of semiconducting single-walledcarbon nanotubes adsorbed on metal surfacesYoshiteru Takagi1and Susumu Okada21Graduate School of Pure and Applied Sciences,University of Tsukuba,1-1-1Tennodai,Tsukuba305-8571,Japan 2Japan Science and Technology Agency,CREST,5Sanbancho,Chiyoda-ku,Tokyo102-0075,Japan (Received11April2011;revised manuscript received30May2011;published19July2011) We investigated the electronic structure of semiconducting single-walled carbon nanotubes(CNTs)adsorbed on the(111)surfaces of Au,Ag,Pt,and Pd and on the(0001)surfaces of Mg byfirst-principles calculations. Our calculations show that the electronic structure of the CNTs adsorbed on the metal surfaces strongly depends on the metal species.We found that on Pd surfaces,the characteristic one-dimensional electronic structure of the CNTs is totally disrupted by the strong hybridization between theπstate of the CNTs and the d state of the Pd surfaces.In sharp contrast,on the Au surfaces,the CNTs retain the one-dimensional properties of their electronic structure.The distribution of the total valence charge of the CNTs on the Pd surfaces also shows a strong covalent nature between the CNTs and the surfaces.Our calculations show the importance of metal electrodes in designing CNT electronic devices.DOI:10.1103/PhysRevB.84.035406PACS number(s):73.20.At,73.40.Ns,61.48.DeI.INTRODUCTIONMiniaturization in semiconductor technology requiresfind-ing and predicting nanometer scale materials that incorpo-rate or substitute for conventional materials in silicon-based electronic devices.Among them,carbon nanotubes(CNTs) (Refs.1and2)remain important as they have various intere-sting electronic properties that depend on tiny differences in atomic arrangements.3,4Their peculiar electronic properties allow for the possible fabrication of superior nanometer scale electronic devices that consist of nanotube and conventional material hybrids.For instance,it has been demonstrated that individual semiconducting nanotubes can function as field-effect transistors(FETs)(Refs.5–16)in which nanotubes can be placed on the insulating substrates and thus form contacts with various metal surfaces such as Pt,Au,Ca,Al, and Pd.5,6It has been reported that the FETs have different properties depending on the contact metal species;e.g.,they exhibit n-type and p-type properties for Ca and Pd electrodes, respectively.13,14This experimental evidence indicates that nanotubes and other conventional material hybrids are essen-tial in these devices and they play a crucial role in determining their fundamental properties.However,little is known about the fundamental properties of the hybrid structures compared with current semiconductor technology.17–21In particular,the stability and properties of the interface between the nanotubes and the metals are most important for the next generation of semiconductor technology.The purpose of this work was to unravel the interplay between the tube-origin and the surface-origin electronic states in determining the stability and properties of the nanotubes attached to metal surfaces.We used single-walled carbon nanotubes(CNTs)that were adsorbed onto metal surfaces and this is considered to be a structural model of the contact between CNT and the metal electrodes. Ourfirst-principles total energy calculation was based on density functional theory and we determined the geometric structures and properties of the nanotube-metal contact,which strongly depended on the metal species.The Fermi level of metal/CNT hybrid system is proportional to the work function of the metal species.This is in sharp contrast to conventional semiconductor-metal contacts in which the Fermi level is virtually pinned.22–24A detailed analysis of the local density of states(LDOS)of the CNTs revealed that the LDOS on the C atoms at the interface region loses the characteristics of semiconducting CNTs for all the metals. At the opposite side of the CNTs for Mg,Ag,and Au,the CNTs repair their inherent density of states(DOS)near the Fermi level.In sharp contrast,on the Pd and Pt surfaces, the LDOS of the CNTs still exhibit substantial hybridization between the CNTs and the metal surfaces.II.CALCULATION METHODSIn this work,we used the TAPP(Refs.25and26)code to study the geometric and electronic structures of(10,0) nanotube adsorbed on metal surfaces.All the calculations were performed using density functional theory.27,28To express the exchange-correlation energy between electrons,we used a functional formfitted to the Monte-Carlo results for a homoge-neous electron gas.29,30Ultrasoft pseudopotentials were used to describe the electron-ion interaction.31The valence wave functions were expanded in terms of the plane-wave basis set with a cutoff energy of30Ry.The conjugate-gradient minimization scheme was used for the electronic structure calculation and for geometry optimization.The lattice param-eters werefixed during the structural optimization.For the optimized geometry,the atoms were subjected to a force of less than0.002hartree/a.u.32Integration over the two-dimensional Brillouin zone was carried out using eight k points.For this calculation,we assumed the structure shown in Fig.1to simulate the contact between the CNTs and the metal electrode.We chose the(111)surfaces of Pd,Pt,Ag,and Au as substrates for CNTs.We also chose the(0001)surfaces of the Mg substrate.The surfaces were simulated by repeating slab models withfive atomic layers.Each slab was separated by 22˚A vacuum regions to determine the optimized geometries, electronic states,and energetics of the CNTs adsorbed on the surface.We therefore placed semiconducting(10,0)nanotubesYOSHITERU TAKAGI AND SUSUMU OKADA PHYSICAL REVIEW B84,035406(2011)(34 634 6FIG.1.Structural model of the CNTs on a metal surface.(a)Top view and(b)side view of a CNT on the(111)surface of fcc structure.(c)Top view and(d)side view of a CNT on the(0001)surface of HCP structure.The open circles and the closed circles represent carbon atoms and metal atoms,respectively.The indexes in(b)and(d)denote the atomic position in terms of the metal surface.on the metal surfaces.Each nanotube was separated in the lateral direction by7˚A or more to simulate the characteristics of individual nanotubes on metal surfaces.We imposed a commensurability condition between the one-dimensional periodicity of the nanotube and the lateral periodicity of the metal surface.Consequently,the unit cell along the tube axis parallel to the surfaces contains double periodicity because of the zigzag nanotube.The commensurability results in the lattice constant of the nanotube on the metal surface becoming elongate by around3%.III.RESULTS AND DISCUSSIONA.Energetics of CNTs on the metal surfacesFigure2shows the optimized structures of the CNTs adsorbed on metal surfaces.As shown in Fig.2(b),substantial structural relaxation was found for both the CNT and the topmost subsurface of the Pd substrate.The CNT is slightly deformed along the direction normal to the Pd surface.The Pd atoms at the topmost layer are shifted slightly downward. The equilibrium distance between the wall of the CNT and the Pd surfaces is2.2˚A.Substantial structural relaxation was also found to occur for the CNT on the Pt surface.In this case,the CNT is elongated along the direction normal to the Pt surface.On the other hand,the topmost layer of the Pt surface is protruded,resulting in a decrease in interunit spacing.The optimum spacing between the wall of the CNTs and the surfaces was found to be2.2˚A and this is the same as for the CNTs on Pd surfaces.In sharp contrast to Pd and Pt surfaces,the CNT and the metal atoms on the substrate do not exhibit structural relaxation on Au,Ag,and Mg surfaces. The CNTs adsorbed on the Au,Ag,and Mg surfaces retain their cylindrical shape.Furthermore,these metal surfaces also retain their planar structure.In this case,the optimum distance between the walls of the CNTs and the surfaces are2.9,2.5, and2.9˚A for the Mg,Ag,and Au surfaces,respectively.The local potential of the CNT/metal hybrid structure averaged along the normal to the surfaces is shown in Fig.2. Among the metal surfaces studied,Pd and Pt seem to be the preferred electrodes for CNTs that possess good contact properties because there is no potential barrier between the CNTs and the Pd/Pt surfaces.Therefore,the electrons are injected smoothly from the metal electrode into the CNT. These experiments show that Pd is a good electrode for carbon-based electronic devices.7,8Besides the Pd surface,no potential barrier exists between the CNTs and the Ag surface. As shown later,however,the electronic structure of the CNTs on the Ag surface is very different from that of CNTs on Pd/Pt surfaces.In sharp contrast,Au and Mg seem to be unfavorable candidates for metal electrodes which form ohmic contact with CNTs.Substantial barriers exist between the CNTs and the metal surfaces.These potential barriers may scatter the electrons that are transferred from the metal to the CNT.It should be noted that the local potential profiles in the metal region depend on the metal species.This dependency comes from the configuration of valence electrons in each metal atoms.Configurations of valence electrons are(3s)2,(4d)10, (4d)10(5s)1,(5d)9(6s)1,and(5d)10(6s)1for Mg,Pd,Ag,Pt,and Au,respectively.The local potential profile of Mg comprising only of s orbital is the most simple and has local minimum values at atomic layers.In contrast,the local potential profile of Pd comprising only of d orbital is bumpy and has some local minima due to the characteristic distribution of d orbital.The local minima are not only at atomic layers but also at middle points of atomic layers.For the other metal surface possessing d orbitals,the slopes of the local potential profile are more easier than that of Pd,because of the presence of s orbital.B.Electronic structure of the CNTs on the metal surfacesFigure3shows the total DOS of CNT/metal hybrid structures.Substantial DOS emerge near the Fermi level, which conceals the CNT spectrum from the total DOS. However,we can assign thefirst van Hove singularity of the CNTs on Mg,Ag,and Au,by comparing with LDOS for these systems.As will be mentioned later,the E11gap clearly exits in LDOS for the CNTs on Mg,Ag,and Au.It is clear that electrons are injected into the CNTs from the Mg surface since the lowest unoccupied state of the CNT is located below the Fermi level.In sharp contrast,for the Ag and Au surfaces, a charge transfer does not occur.On the Ag surfaces,the Fermi level is located just below the lowest unoccupied state of the CNTs.These facts indicate that the CNTs on the Ag surfaces can potentially be an n-type channel as for the Mg electrode. On the Au surfaces,the Fermi level is located just above theENERGETICS AND ELECTRONIC STRUCTURE OF ...PHYSICAL REVIEW B 84,035406(2011)(b)(d)z (Angstrom)z (Angstrom)z (Angstrom)z (Angstrom)z (Angstrom)av. Vlocal(z) (eV)av. Vlocal(z) (eV)av. Vlocal(z) (eV)av. Vlocal(z) (eV)av. Vlocal(z) (eV)FIG.2.Optimized structure (left panel)and plane-averaged local potential (right panel)for the CNTs on (a)Mg,(b)Pd,(c)Pt,(d)Ag,and (e)Au substrates.In the left panels,the open circles and the closed circles represent carbon atoms and metal atoms,respectively.In the right panels,the black dots represent the position of carbon atoms or metal atoms.Equilibrium distance separation between the wall of the CNT andthe Mg,Pd,Pt,Ag,and Au surfaces is 2.9,2.2,2.2,2.5,and 2.9˚A,respectively.highest occupied state of the CNT.Therefore,the CNTs withAu electrodes may exhibit a p -type character.In sharp contrast to the Ag,Au,and Mg surfaces,it is difficult to assign the peaks in the spectra that originate from the CNTs on the Pt and Pd surfaces.This fact indicates that the πstates of the CNT are substantially hybridized with the d states of surface Pd and Pt atoms.It is thus important to investigate how the local electronic structure of a CNT is modulated by the adsorption of CNTs onto the metal surfaces.In particular,it is important to determine if the semiconducting CNTs on the metal surfaces retain their semiconducting properties on the surfaces.To obtain theoretical insight into this issue,we investigated the LDOS on each C atom along the circumference of a CNT.Figures 4,5,and 6show the LDOS of the CNTs adsorbed on the Mg surface,the Ag surface,and the Au surface,respectively.As shown in these figures,all the C atoms in the CNTs retain the characteristic nature of a CNT.For each atomic site,the peaks that originate from the first van Hove singularities are present in the spectra.In particular,at the atomic sites facing the vacuum region,the two peaks associatedYOSHITERU TAKAGI AND SUSUMU OKADA PHYSICAL REVIEW B 84,035406(2011)-4-3-2-101e n e r g y (e V )DOS (states/eV)FIG.3.Density of states for the CNTs on Mg,Pd,Pt,Ag,and Au substrates.The Fermi level is at 0eV .The arrows represent the E 11band gap of the CNTs,respectively.-0.8-0.400.40.81.2LDOS (states/eV)e n e r g y (e V )FIG.4.Local density of states (LDOS)around C 1,C 2,C 3,C 4,C 5,and C 6,which are shown in Fig.1,for the CNTs on a Mg (0001)surface.The Fermi energy is at 0eV .The arrow represents the E 11band gap of the CNTs,respectively.-0.8-0.40.40.81.2LDOS (states/eV)e n e r g y (e V )FIG.5.Local density of states (LDOS)around C 1,C 2,C 3,C 4,C 5,and C 6,which are shown in Fig.1,for the CNTs on a Ag (111)surface.The Fermi energy is at 0eV .The arrow represents the E 11band gap of the CNTs,respectively.-0.8-0.40.40.81.2LDOS (states/eV)e n e r g y (e V )FIG.6.Local density of states (LDOS)around C 1,C 2,C 3,C 4,C 5,and C 6,which are shown in Fig.1,for the CNTs on an Au (111)surface.The Fermi energy is at 0eV .The arrow represents the E 11band gap of the CNTs,respectively.-0.8-0.400.40.81.2C 1C 2C 3C 4C 5C 6LDOS (states/eV)e n e r g y (e V )FIG.7.Local density of states (LDOS)around C 1,C 2,C 3,C 4,C 5,and C 6,which are shown in Fig.1,for the CNTs on a Pd (111)surface.The Fermi energy is at 0eV .with the E 11gap are clear in the spectra and the LDOS are absent between these two peaks.Upon approaching the metal surfaces,metal-induced gap states appear 23,24and give small but substantial DOS in the band gap of the CNTs.It should be noted that the peak position weakly depends on the atomic site.This shift should correspond with band bending in the semi-conductor at the interfaces with the metal surfaces.The CNTs on the Ag,Au,and Mg surfaces mostly retain their electronic structures except for the above-mentioned differences.In contrast to the Ag,Au,and Mg surfaces,the electronic structure of the CNTs is drastically modulated upon their adsorption onto Pd and Pt surfaces.The LDOS of a CNT on Pd and Pt surfaces is shown in Figs.7and 8,respectively.As shown in these figures,the characteristic feature of the DOS of CNT is absent and a finite DOS emerges around the Fermi level.For the C 6atoms facing the Pd/Pt surfaces,a large DOS without significant structure emerges at the Fermi level.Furthermore,a small but finite DOS emerges around the Fermi level even on C atoms facing the vacuum region.This modulation is due to strong hybridization between the πstate of the C atoms and the d states of the Pd/Pt surfaces.The LDOS of the CNTs on the Pd/Pt surfaces indicates that the CNTs lose their original character,at least in the nanometer range.Finally,we focused on the Fermi level of our CNT/metal hybrid system as a function of the work function of the metal species.It is well known that the Fermi level of conventional semiconducting materials such as Si and GaAs is pinned at a certain energy.However,the Fermi level is not pinned in the CNT/metal hybrid system.As shown in Fig.9,the Fermi level E f of the CNT/metal hybrid system measured from the vacuum level is almost proportional to the work function of the metal species.For CNTs on Mg whose work function is the-0.8-0.400.40.81.2C 1C 2C 3C 4C 5C 6LDOS (states/eV)e n e r g y (e V )FIG.8.Local density of states (LDOS)around C 1,C 2,C 3,C 4,C 5,and C 6,which are shown in Fig.1,for the CNTs on a Pt (111)surface.The Fermi energy is at 0eV .ENERGETICS AND ELECTRONIC STRUCTURE OF ...PHYSICAL REVIEW B 84,035406(2011)3456−E fwork function (eV)(e V )FIG.9.Fermi level of CNT/metal system as a function of the work function of the metal substrate.E f is the Fermi level measured from the vacuum level.Here,the work functions of the metal species are calculated values.smallest among the metals studied here,−E f is the shallowest.With increasing the work function,−E f also monotonically increases.Therefore,the Fermi level of the CNT/metal hybrid system strongly depends on the work function of metal surface.The fact indicates the possibility that the height of the Schottky barrier between CNT and metal surface is tunable by selecting metal species.This agrees well with experimental results,which showed that CNTs can function as p -type and n -type channels depending on the metal electrode species.14IV .CONCLUSIONWe investigated the electronic structures of CNTs on (111)surfaces of Ag,Au,Pd,and Pt,and the (0001)surfaces of Mg by performing first-principles total-energy calculations.Our calculations show that the electronic structure of the CNTs adsorbed on metal surfaces strongly depends on themetal species.For Ag,Au,and Mg surfaces,the CNTs mostly retain their pristine electronic structures upon adsorption.In particular,for the C atoms far from the metal surfaces,the characteristic DOS for the CNTs are found to emerge around the Fermi level.On the other hand,for the C atoms that face the metal surfaces,metal-induced gap states appear and give small but substantial DOS in the band gap of the CNTs.In sharp contrast,the characteristic electronic feature of the CNTs is totally disrupted after adsorption onto Pd and Pt surfaces due to the hybridization between the πstate of the CNTs and the d orbital of the metal surfaces.Our analysis of the total valence charge clearly shows that CNTs form covalent bonds with the Pd surface and the Pt surface.Finally,our calculations indicate that the metal-induced gap states and the interface states caused by hybridization between the πstate of the CNTs and the d orbital of the metal surfaces do not pin the Fermi level in the CNT/metal hybrid system.The Fermi level at the CNT/metal interface is proportional to the magnitude of the work function of the metal species.ACKNOWLEDGMENTSThis work was supported by CREST,Japan Science and Technology Agency,and a Grant-in-Aid for Scientific Research from the Ministry of Education,Culture,Sports,Sci-ence and Technology of putations were performed on an NEC SX-8/4B at the University of Tsukuba,on an NEC SX-9at the Institute for Solid State Physics,The University of Tokyo,on an NEC SX-9at the Information Synergy Center,Tohoku University,and on an NEC SX-9at the Cybermedia Center,Osaka University.1S.Iijima,Nature 354,56(1991).2M.S.Dresselhaus,G.Dresselhaus,and P.C.Eklund,Science of Fullerenes 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CHAPTER3ATOMIC COLLISIONS3.1BASIC CONCEPTSWhen two particles collide,various phenomena may occur.As examples,one or both particles may change their momentum or their energy,neutral particles can become ionized,and ionized particles can become neutral.We introduce the funda-mentals of collisions between electrons,positive ions,and gas atoms in this chapter, concentrating on simple classical estimates of the important processes in noble gas discharges such as argon.For electrons colliding with atoms,the main processes are elastic scattering in which primarily the electron momentum is changed,and inelas-tic processes such as excitation and ionization.For ions colliding with atoms,the main processes are elastic scattering in which momentum and energy are exchanged, and resonant charge transfer.Other important processes occur in molecular gases. These include dissociation,dissociative recombination,processes involving negative ions,such as attachment,detachment,and positive–negative ion charge transfer,and processes involving excitation of molecular vibrations and rotations. We defer consideration of collisions in molecular gases to Chapter8.Elastic and Inelastic CollisionsCollisions conserve momentum and energy:the total momentum and energy of the colliding particles after collision are equal to that before collision.Electrons and fully stripped ions possess only kinetic energy.Atoms and partially stripped ions have internal energy level structures and can be excited,de-excited,or ionized, Principles of Plasma Discharges and Materials Processing,by M.A.Lieberman and A.J.Lichtenberg. ISBN0-471-72001-1Copyright#2005John Wiley&Sons,Inc.43corresponding to changes in potential energy.It is the total energy,which is the sum of the kinetic and potential energy,that is conserved in a collision.If the internal energies of the collision partners do not change,then the sum of kinetic energies is conserved and the collision is said to be elastic.Although the total kinetic energy is conserved,kinetic energy is generally exchanged between particles.If the sum of kinetic energies is not conserved,then the collision is inelas-tic.Most inelastic collisions involve excitation or ionization,such that the sumof kinetic energies after collision is less than that before collision.However,super-elastic collisions can occur in which an excited atom can be de-excited by acollision,increasing the sum of kinetic energies.Collision ParametersThe fundamental quantity that characterizes a collision is its cross section s(v R), where v R is the relative velocity between the particles before collision.To define this,we considerfirst the simplest situation shown in Figure3.1,in which aflux G¼n v of particles having mass m,density n,andfixed velocity v is incident on a half-space x.0of stationary,infinitely massive“target”particles having density n g.In this case,v R¼v.Let d n be the number of incident particles per unit volume at x that undergo an“interaction”with the target particles within a differential distanced x,removing them from the incident beam.Clearly,d n is proportional to n,n g,and d x for infrequent collisions within d x.Hence we can writed n¼Às nn g d x(3:1:1)where the constant of proportionality s that has been introduced has units of area and is called the cross section for the interaction.The minus sign denotes removal from the beam.To define a cross section,the“interaction”must be specified,for example,ionization of the target particle,excitation of the incident particle to a given energy state,or scattering of the incident particle by an angle exceeding p=2.Multiplying(3.1.1)by v,wefind a similar equation for theflux:d G¼Às G n g d x(3:1:2) FIGURE3.1.Aflux of incident particles collides with a population of target particles in the half-space x.0.44ATOMIC COLLISIONSFor a simple interpretation of s,let the incident and target particles be hard elastic spheres of radii a1and a2,and let the“interaction”be a collision between the spheres.In a distance d x there are n g d x targets within a unit area perpendicular to x.Draw a circle of radius a12¼a1þa2in the x¼const plane about each target.A collision occurs if the centers of the incident and target particles fall within this radius.Hence the fraction of the unit area for which a collision occurs is n g d x p a212.The fraction of incident particles that collide within d x is thend G G ¼d nn¼Àn g s d x(3:1:3)wheres¼p a212(3:1:4)is the hard sphere cross section.In this particular case,s is independent of v.Equation(3.1.2)is readily integrated to give the collidedfluxG(x)¼G0(1ÀeÀx=l)(3:1:5) with the uncollidedflux G0eÀx=l.The quantityl¼1n g s(3:1:6)is the mean free path or the decay of the beam,that is,the distance over which the uncollidedflux decreases to1=e of its initial value G0at x¼0.If the velocity of the beam is v,then the mean time between interactions ist¼lv(3:1:7)Its inverse is the interaction or collision frequencyn;tÀ1¼n g s v(3:1:8)and is the number of interactions per second that an incident particle has with the target particle population.We can also define the collision frequency per unit density,which is called the rate constantK¼s v(3:1:9)3.1BASIC CONCEPTS45and,trivially,from (3.1.8)and (3.1.9)n ¼Kn g(3:1:10)Differential Scattering Cross SectionLet us consider only those interactions that scatter the particles by u ¼908or more.For hard spheres,taking the angle of incidence equal to the angle of reflection,the 908collision occurs on the x ¼458diagonal (see Fig.3.2),therefore having a cross section s 90¼p a 2122,(3:1:11)which is a factor of two smaller than (3.1.4).Of course,multiple collisions at smaller angles (radii larger than a 12=ffiffiffi2p )also eventually scatter incident particles through 908.This indeterminacy indicates that a more precise way of determining the scat-tering cross section is required.For this purpose we introduce a differential scatter-ing cross section I (v ,u ).Consider a beam of particles incident on a scattering center (again assumed fixed),as shown in Figure 3.3.We assume that the scattering force is symmetric about the line joining the centers of the two particles.A particle incident at a distance b off-center from the target particle is scattered through an angle u ,as shown in Figure 3.3.The quantity b is the impact parameter and u is the scattering angle (see also Fig.3.2).Now,flux conservation requires that for incoming flux G ,G 2p b d b ¼ÀG I (v ,u )2p sin u d u (3:1:12)FIGURE 3.2.Hard-sphere scattering.46ATOMIC COLLISIONS3.1BASIC CONCEPTS47FIGURE3.3.Definition of the differential scattering cross section.that is,that all particles entering through the differential annulus2p b d b leave through a differential solid angle d V¼2p sin u d u.The minus sign is because an increase in b leads to a decrease in u.The proportionality constant is just I(v,u), which has the dimensions of area per steradian.From(3.1.12)we obtainI(v,u)¼bsin ud bd u(3:1:13)The quantity d b=d u is determined from the scattering force,and the absolute value is used since d b=d u is negative.We will calculate I(v,u)for various potentials in Section3.2.We can calculate the total scattering cross section s sc by integrating I over the solid angles sc¼2p ðpI(v,u)sin u d u(3:1:14)It is clear that s sc¼s for scattering through any angle,as defined in(3.1.2).It is often useful to define a different cross sections m¼2p ðp(1Àcos u)I(v,u)sin u d u(3:1:15)The factor(1Àcos u)is the fraction of the initial momentum m v lost by the incident particle,and thus(3.1.15)is the momentum transfer cross section.It is s m that is appropriate for calculating the frictional drag in the force equation(2.3.9).For asingle velocity,we would just have n m¼s m v,where s m is generally a function of velocity.In the macroscopic force equation(2.3.15),n m must be obtained by aver-aging over the particle velocity distributions,which we do in Section3.5.We illustrate the use of the differential scattering cross section to calculate thetotal scattering and momentum transfer cross sections for the hard-sphere modelshown in Figure3.2.The impact parameter is b¼a12sin x,and differentiating, d b¼a12cos x d x,so thatb d b¼a212sin x cos x d x¼12a212sin2x d x(3:1:16)From Figure3.2the scattering angle u¼pÀ2x,such that(3.1.16)can be written asb d b¼À1a212sin u d u(3:1:17)48ATOMIC COLLISIONSSubstituting(3.1.17)into(3.1.13),we haveI(v,u)¼14a212(3:1:18)Using the definitions of s sc and s m in(3.1.14)and(3.1.15),respectively,wefinds sc¼s m¼p a212(3:1:19) for hard-sphere collisions.In general,s sc=s m for other scattering forces.For electron collisions with atoms the electron radius is negligible compared to the atomic radius so that a12%a,the atomic radius.Although the value of a% 10À8cm gives s sc¼s m%3Â10À16cm2,which is reasonable,it does not capture the scaling of the cross section with speed.In the following sections of this chapter,we consider collisional processes in more detail.Except for Coulomb collisions,we confine our attention to electron–atom and ion–atom processes.After a discussion of collision dynamics in Section3.2,we describe elastic collisions in Section3.3and inelastic collisions in Section3.4.We reserve a discussion of some aspects of inelastic collisions until Chapter8,in which a more complete range of atomic and molecular processes is considered.In Section3.5,we describe the averaging over particle velocity distri-butions that must be done to obtain the collisional rate constants.Experimental values for argon are also given in Section3.5;these are needed for discussing energy transfer and diffusive processes in the succeeding chapters.A more detailed account of collisional processes,together with many results of experimental measurements,can be found in McDaniel(1989),McDaniel et al.(1993),Massey et al.(1969–1974),Smirnov(1981),and Raizer(1991).3.2COLLISION DYNAMICSCenter-of-Mass CoordinatesIn a collision between projectile and target particles there is recoil of the target as well as deflection of the projectile.In fact,both may be moving,and,in the case of like-particle collisions,not distinguishable.To describe this more complicated state,a center-of-mass(CM)coordinate system can be introduced in which projec-tiles and targets are treated equally.Without loss of generality,we can transform to a coordinate system in which one of the particles is stationary before the collision. Hence,we consider a general collision in the laboratory frame between two particles having mass m1and m2,position r1and r2,velocity v1and v2;0,and scattering angle u1and u2,as shown in Figure3.4a.We assume that the force F acts along the line joining the centers of the particles,with F12¼ÀF21.3.2COLLISION DYNAMICS49The center-of-mass coordinates may be defined by the linear transformationR ¼m 1r 1þm 2r 2m 1þm 2(3:2:1)andr ¼r 1Àr 2(3:2:2)with the accompanying CM velocityV ¼m 1v 1þm 2v 2m 1þm 2(3:2:3)and the relative velocityv R ¼v 1Àv 2(3:2:4)v 2´m 1m R center(a )(b )FIGURE 3.4.The relation between the scattering angles in (a )the laboratory system and (b )the center-of-mass (CM)system.50ATOMIC COLLISIONSThe force equations for the two particles are:m1_v1¼F12(r),m2_v2¼F21(r)¼ÀF12(r)(3:2:5) Adding these equations we get the result for the CM motion that_V¼0,such that the CM moves with constant velocity throughout the collision.Now dividing thefirst of (3.2.5)by m1and the second by m2,and using the definition in(3.2.4)we havem R_v R¼F12(r)(3:2:6) which is the equation of motion of a“fictitious”particle with a reduced massm R¼m1m2m1þm2(3:2:7)in afixed central force F12(r).Thefictitious particle has mass m R,position r(t), velocity v R(t),and scattering angle Q,as shown in Figure3.4b.This result holds for any central force,including the hard-sphere,Coulomb,and polarization forces that we subsequently consider.If(3.2.6)can be solved to obtain the motion,includ-ing Q,then we can transform back to the laboratory frame to get the actual scattering angles u1and u2.It is easy to show from momentum conservation(Problem3.2)thattan u1¼sin Q(m1=m2)(v R=v0R)þcos Q(3:2:8a)andtan u2¼sin Qv R=v0RÀcos Q(3:2:8b)where v R and v0R are the speeds in the CM system before and after the collision, respectively.For an elastic collision,the scattering force can be written as the gradient of a potential that vanishes as r¼j r j!1:F12¼Àr U(r)(3:2:9) It follows that the kinetic energy of the particle is conserved for the collision in the CM system.Hence v0R¼v R,and we obtain from(3.2.8)thattan u1¼sin Q1=m2þcos Q(3:2:10)3.2COLLISION DYNAMICS51and,using the double-angle formula for the tangent,u2¼1(pÀQ)(3:2:11) For electron collisions with ions or neutrals,m1=m2(1and we obtain m R%m1 and u1%Q.For collision of a particle with an equal mass target,m1¼m2,we obtain m R¼m1=2and u1¼Q=2.Hence for hard-sphere elastic collisions against an initially stationary equal mass target,the maximum scattering angle is908.Since the same particles are scattered into the differential solid angle 2p sin Q d Q in the CM system as are scattered into the corresponding solid angle 2p sin u1d u1in the laboratory system,the differential scattering cross sections are related byI(v R,Q)2p sin Q d Q¼I(v R,u1)2p sin u1d u1(3:2:12)where d Q=d u1can be found by differentiating(3.2.10).Energy TransferElastic collisions can be an important energy transfer process in gas discharges,and can also be important for understanding inelastic collision processes such as ioniz-ation,as we will see in Section3.4.For the elastic collision of a projectile of mass m1 and velocity v1with a stationary target of mass m2,the conservation of momentum along and perpendicular to v1and the conservation of energy can be written in the laboratory system asm1v1¼m1v01cos u1þm2v02cos u2(3:2:13)0¼m1v01sin u1Àm2v02sin u2(3:2:14)1 2m1v21¼12m1v012þ12m2v022(3:2:15)where the primes denote the values after the collision.We can eliminate v01and u1 and solve(3.2.13)–(3.2.15)to obtain1 2m2v022¼12m1v214m1m2(m1þm2)2cos2u2(3:2:16)Since the initial energy of the projectile is12m1v21and the energy gained bythe target is12m2v022,the fraction of energy lost by the projectile in the laboratory52ATOMIC COLLISIONSsystem isz L¼4m1m2(m12)cos2u2(3:2:17) Using(3.2.11)in(3.2.17),we obtainz L¼2m1m2(m1þm2)2(1Àcos Q)(3:2:18)where Q is the scattering angle in the CM system.We average over the differential scattering cross section to obtain the average loss:k z L l Q¼2m1m2(m1þm2)2Ð(1Àcos Q)I(v R,Q)2p sin Q d Q ÐI(v R,Q)2p sin Q d Q¼2m1m2 (m1þm2)2s ms sc(3:2:19)where s sc and s m are defined in(3.1.14)and(3.1.15).For hard-sphere scattering of electrons against atoms,we have m1¼m(electron mass)and m2¼M(atom mass),and s sc¼s m by(3.1.19),such that k z L l Q¼2m=M 10À4.Hence electrons transfer little energy due to elastic collisions with heavy particles,allowing T e)T i in a typical discharge.On the other hand,for m1¼m2,we obtain k z L l Q¼12,leading to strong elastic energy exchange among heavy particles and hence to a common temperature.Small Angle ScatteringIn the general case,(3.2.6)must be solved to determine the CM trajectory and the scattering angle Q.We outline this approach and give some results in Appendix A. Here we restrict attention to small-angle scattering(Q(1)for which the fictitious particle moves with uniform velocity v R along a trajectory that is practi-cally unaltered from a straight line.In this case,we can calculate the transverse momentum impulse D p?delivered to the particle as it passes the center of force at r¼0and use this to determine Q.For a straight-line trajectory,as shown in Figure3.5,the particle distance from the center of force isr¼(b2þv2R t2)1=2(3:2:20)where b is the impact parameter and t is the time.We assume a central force of the form(3.2.9)withU(r)¼C(3:2:21)3.2COLLISION DYNAMICS53where i is an integer.The component of the force acting on the particle perpendicu-lar to the trajectory is (b =r )j d U =d r j .Hence the momentum impulse isD p ?¼ð1À1b r d U d r d t (3:2:22)Differentiating (3.2.20)to obtaind t ¼r v R d r(r 2Àb 2)1=2substituting into (3.2.22),and dividing by the incident momentum p k ¼m R v R ,we obtainQ ¼D p ?p k ¼2b m R v R ð1b d U d r d r (r 22)(3:2:23)The integral in (3.2.23)can be evaluated in closed form (Smirnov,1981,p.384)to obtainQ ¼AW R b (3:2:24)where W R ¼12m R v 2R is the CM energy andA ¼C ffiffiffiffip p G ½(i þ1)=2 (3:2:25)FIGURE 3.5.Calculation of the differential scattering cross section for small-angle scattering.The center-of-mass trajectory is practically a straight line.54ATOMIC COLLISIONSwith G ,the Gamma function.ÃInverting (3.2.24),we obtainb ¼A W R Q1=i (3:2:26)and differentiating,we obtaind b ¼À1i A W R 1=i d Q Q (3:2:27)Substituting (3.2.26)and (3.2.27)into (3.1.13),with sin Q %Q ,we obtain the differ-ential scattering cross section for small angles:I (v R ,Q )¼1i A W R 2=i 1Q 2þ2=i (3:2:28)The variation of s ,n ,and K with v R are determined from (3.2.28)and the basic definitions in Section 3.1.If (3.2.28)is substituted into (3.1.14)or (3.1.15),then we see that a scattering potential U /r Ài leads to s /v À4=i R and n /K /v À(4=i )þ1R .These scalings are summarized in Table 3.1for the important scattering processes,which we describe in the next section.3.3ELASTIC SCATTERINGCoulomb CollisionsThe most straightforward elastic scattering process is a Coulomb collision between two charged particles q 1and q 2,representing an electron–electron,electron–ion,or ion–ion collision.The Coulomb potential is U (r )¼q 1q 2=4pe 0r such that i ¼1and TABLE 3.1.Scaling of Cross Section s ,Interaction Frequency n ,and Rate Constant K ,With Relative Velocity v R ,for VariousScattering Potentials UProcessU (r )s n or K Coulomb1/r 1/v R 41/v R 3Permanent dipole1/r 21/v R 21/v R Induced dipole1/r 41/v RConst Hard sphere 1/r i ,i !1Const v RÃG (l )¼(l À1)!¼l G (l À1)with G (1=2)¼ffiffiffiffip p .3.3ELASTIC SCATTERING 55we obtainA¼C¼q1q2 4pe0from(3.2.25).Using this in(3.2.28),wefindI¼b0Q2(3:3:1)whereb0¼q1q240W R(3:3:2)is called the classical distance of closest approach.The differential scattering cross section can also be calculated exactly,which we do in Appendix A,obtaining the resultI¼b04sin(Q=2)2(3:3:3)However,due to the long range of the Coulomb forces,the integration of I oversmall Q(large b)leads to an infinite scattering cross section and to an infinitemomentum transfer cross section,such that an upper bound to b,b max,must beassigned.This is done by setting b max¼l De,the Debye shielding distance for a charge immersed in a plasma,which we calculated in Section2.4.For momentumtransfer,the dependence of s m on l De is logarithmic(Problem3.5),and the exact choice of b max(or Q min)makes little difference.For scattering,s sc pl2De, which is a very large cross section that depends sensitively on the choice of b max. However,we are generally not interested in scattering through very small angles, which do not appreciably affect the discharge properties.The cross section for scattering through a large angle,say Q!p=2,is of more interest.There are two processes that lead to a large scattering angle Q for a Coulombcollision:(1)a single collision scatters the particle by a large angle;(2)the cumu-lative effect of many small-angle collisions scatters the particle by a large angle.Thetwo processes are illustrated in Figure3.6;the latter process is diffusive and,as wewill see,dominates the former.To estimate the cross section s90(sgl)for a single large-angle collision,we inte-grate(3.3.3)over solid angles from p=2to p to obtain(Problem3.6)s90(sgl)¼14p b2(3:3:4)To estimate s90(cum)for the cumulative effect of many collisions to produce a p=2deflection,wefirst determine the mean square scattering angle k Q2l1for a 56ATOMIC COLLISIONSsingle collision by averaging Q 2over all permitted impact parameters.Since the col-lisions are predominantly small angle for Coulomb collisions,we can use (3.2.24),which is Q ¼b 0=b .Hencek Q 2l 1¼1p b 2max ðb max b min q 1q 24pe 0W R 22p b d b b 2(3:3:5)The integration has a logarithmic singularity at both b ¼0and b ¼1,which is cut off by the finite limits.The singularity at the lower limit is due to the small-angle approximation.Setting b min ¼b 0=2is found to approximate a more accurate calcu-lation.The upper limit,as already mentioned,is b max ¼l De .Using these values and integrating,we obtaink Q 2l 1¼2p b 20p b 2max ln L (3:3:6)where L ¼2l De =b 0)1.The number of collisions per second,each having a cross section of p b 2max orsmaller,is n g p b 2max v R ,where n g is the target particle density.Since the spreadingof the angle is diffusive,we can then writek Q 2l (t )¼k Q 2l 1n g p b 2max v R tSetting t ¼t 90at k Q 2l ¼(p =2)2and using (3.3.6),we obtain (see also Spitzer,1956,Chapter 5)n 90¼t À190¼n g v R 8p b 20lnLFIGURE 3.6.The processes that lead to large-angle Coulomb scattering:(a )single large-angle event;(b )cumulative effect of many small-angle events.3.3ELASTIC SCATTERING 57Writing n90¼n g s90v R,we see thats90¼8p b 2ln L(3:3:7)Although L is a large number,typically ln L%10for the types of plasmas we are considering.Comparing s90(sgl)to s90,we see that due to the large range of the Coulomb fields,the effective cross section for many small-angle collisions to produce a root mean square(rms)deflection of p=2is larger by a factor(32=p2)ln L. Because of this enhancement,it is possible for electron–ion or ion–ion particle col-lisions to play a role in weakly ionized plasmas(say one percent ionized).Another important characteristic of Coulomb collisions is the strong velocity dependence. From(3.3.2)we see that b0/1=v2R.Thus,from(3.3.4)or(3.3.7)s90/1v4R(3:3:8)such that low-velocity particles are preferentially scattered.The temperature of the species is therefore important in determining the relative importance of the various species in the collisional processes,as we shall see in subsequent sections.Polarization ScatteringThe main collisional processes in a weakly ionized plasma are between charged and neutral particles.For electrons at low energy and for ions scattering against neutrals, the dominant process is relatively short-range polarization scattering.At higher energies for electrons,the collision time is shorter and the atoms do not have time to polarize.In this case the scattering becomes more Coulomb-like,but with b max at an atomic radius,inelastic processes such as ionization become important as well.The condition for polarization scattering is v R.v at,where v at is the charac-teristic electron velocity in the atom,which we obtain in the next section.Because of the short range of the polarization potential,we need not be concerned with an upper limit for the integration over b,but the potential is more complicated.We determine the potential from a simple model of the atom as a point charge of valueþq0,sur-rounded by a uniform negative charge sphere(valence electrons)of total chargeÀq0,such that the charge density is r¼Àq0=43p a3,where a is the atomic radius.An incoming electron(or ion)can polarize the atom by repelling(or attracting) the charge cloud quasistatically.The balance of forces on the central point charge due to the displaced charge cloud and the incoming charged particle,taken to have charge q,is shown in Figure3.7,where the center of the charge cloud and the point charge are displaced by a distance d.Applying Gauss’law to a sphere 58ATOMIC COLLISIONSof radius d around the center of the cloud,4pe0d2E ind¼Àq0d3 awe obtain the induced electricfield acting on the point charge due to the displaced cloudE ind¼Àq0d 4pe0a3The electricfield acting on the point charge due to the incoming charge isE appl¼q 4pe0rFor force balance on the point charge,the sum of thefields must vanish,yielding an induced dipole moment for the atom:p d¼q0d¼qa3r2(3:3:9)The induced dipole,in turn,exerts a force on the incoming charged particle:F¼2p d q4pe0r3^r¼2q2a34pe0r5^r(3:3:10)FIGURE3.7.Polarization of an atom by a point charge q.3.3ELASTIC SCATTERING59Integrating F with respect to r,we obtain the attractive potential energy:U(r)¼Àq2a38pe0r4(3:3:11)The polarizability for this simple atomic model is defined as a p¼a3.The relative polarizabilities a R¼a p=a30,where a0is the Bohr radius,for some simple atoms and molecules are given in Table3.2.The orbits for scattering in the polarization potential are complicated(McDaniel, 1989).As shown in Figure3.8,there are two types of orbits.For impact parameter b.b L,the orbit has a hyperbolic character,and for b)b L,the straight-line trajec-tory analysis in Section3.2can be applied(Problem3.7).For b,b L,the incoming particle is“captured”and the orbit spirals into the core,leading to a large scattering angle.Either the incoming particle is“reflected”by the core and spirals out again,or the two particles strongly interact,leading to inelastic changes of state.The critical impact parameter b L can be determined from the conservation of energy and angular momentum for the incoming particle having mass m and speed v0,with the mass of the scatterer taken to be infinite for ease of analysis.In cylindrical coordinates(see Fig.3.8a),we obtain1 2m v2¼12m(_r2þr2_f2)þU(r)(3:3:12a)m v0b¼mr2_f(3:3:12b)TABLE3.2.Relative Polarizabilities a R5a p/a03ofSome Atoms and Molecules,Where a0is the Bohr RadiusAtom or Molecule a RH 4.5C12.N7.5O 5.4Ar11.08CCl469.CF419.CO13.2CO217.5Cl231.H2O9.8NH314.8O210.6SF630.Source:Smirnov(1981).60ATOMIC COLLISIONSAt closest approach,_r¼0and r ¼r min .Substituting these into (3.3.12)and elimi-nating _f ,we obtain a quadratic equation for r 2min:v 20r 4min Àv 20b 2r 2min þa p q 240m¼0Using the quadratic formula to obtain the solution for r 2min ,we see that there is noreal solution for r 2min when(v 20b 2)2À4v 20a p q 20 0Choosing the equality at b ¼b L ,we solve for b L to obtains L ¼p b 2L ¼pa p q 2e 0 1=21v 0(3:3:13)which is known as the Langevin or capture cross section.If the target particle has a finite mass m 2and velocity v 2and the incoming particle has a mass m 1and velocity v 1,then (3.3.13)holds provided m is replaced by the reduced mass m R ¼m 1m 2=(m 1þm 2)and v 0is replaced by the relative velocity v R ¼j v 1Àv 2j .We (a )(b )FIGURE 3.8.Scattering in the polarization potential,showing (a )hyperbolic and (b )captured orbits.3.3ELASTIC SCATTERING 61。

Results for aliovalent doping of CeBr3 with Ca2+Paul Guss, Michael E. Foster, Bryan M. Wong, F. Patrick Doty, Kanai Shah, Michael R. Squillante, Urmila Shirwadkar, Rastgo Hawrami, Joshua Tower, and Ding YuanCitation: Journal of Applied Physics 115, 034908 (2014); doi: 10.1063/1.4861647View online: /10.1063/1.4861647View Table of Contents: /content/aip/journal/jap/115/3?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inHomogeneous carbon doping of magnesium diboride by high-temperature, high-pressure synthesisAppl. Phys. Lett. 104, 162603 (2014); 10.1063/1.4871578Improvement of LaBr3:5%Ce scintillation properties by Li+, Na+, Mg2+, Ca2+, Sr2+, and Ba2+ co-dopingJ. Appl. Phys. 113, 224904 (2013); 10.1063/1.4810848Theoretical and experimental characterization of promising new scintillators: Eu2+ doped CsCaCl3 and CsCaI3 J. Appl. 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Phys. 130, 174710 (2009); 10.1063/1.3123527Results for aliovalent doping of CeBr 3with Ca 21Paul Guss,1,a)Michael E.Foster,2Bryan M.Wong,2F .Patrick Doty,2Kanai Shah,3Michael R.Squillante,3Urmila Shirwadkar,3Rastgo Hawrami,3Joshua Tower,3and Ding Yuan 41Remote Sensing Laboratory –Nellis,P.O.Box 98521,Las Vegas,Nevada 89193-8521,USA2Materials Chemistry Department,Sandia National Laboratories,California,P.O.Box 969,Livermore,California 94551-0969,USA 3Radiation Monitoring Devices,Inc.,44Hunt Street,Watertown,Massachusetts 02472,USA 4National Security Technologies,LLC,Los Alamos Operations,P.O.Box 809,Los Alamos,New Mexico 87544-0809,USA(Received 20August 2013;accepted 23December 2013;published online 17January 2014)Despite the outstanding scintillation performance characteristics of cerium tribromide (CeBr 3)and cerium-activated lanthanum tribromide,their commercial availability and application are limited due to the difficulties of growing large,crack-free single crystals from these fragile materials.This investigation employed aliovalent doping to increase crystal strength while maintaining the optical properties of the crystal.One divalent dopant (Ca 2þ)was used as a dopant to strengthen CeBr 3without negatively impacting scintillation performance.Ingots containing nominal concentrations of 1.9%of the Ca 2þdopant were grown,i.e.,1.9%of the CeBr 3molecules were replaced by CaBr 2molecules,to match our target replacement of 1out of 54cerium atoms be replaced by a calcium atom.Precisely the mixture was composed of 2.26g of CaBr 2added to 222.14g of CeBr 3.Preliminary scintillation measurements are presented for this aliovalently doped scintillator.Ca 2þ-doped CeBr 3exhibited little or no change in the peak fluorescence emission for 371nm optical excitation for CeBr 3.The structural,electronic,and optical properties of CeBr 3crystals were studied using the density functional theory within the generalized gradient approximation.Calculated lattice parameters are in agreement with the experimental data.The energy band structures and density of states were obtained.The optical properties of CeBr 3,including thedielectric function,were calculated.VC 2014AIP Publishing LLC .[/10.1063/1.4861647]I.INTRODUCTIONCerium-activated and cerium-based crystals appear to be particularly promising fast scintillators.1,2The discovery of cerium-doped lanthanum tribromide (LaBr 3:Ce)and cerium-doped lanthanum trichloride (LaCl 3:Ce)3–5and the characterization of their outstanding scintillation performance sparked an interest in the lanthanide trihalide family of scin-tillators as candidates for replacing thallium-activated sodium iodide (NaI:Tl),the industry standard since its discovery in 1948.6,7Since then,numerous derivatives of this family of scintillators have been explored,including undoped,self-activated cerium tribromide (CeBr 3).8Although the scintillation performance of these cerium-doped and cerium-based crystals is outstanding,their mechanical prop-erties are not generally conducive to growth of large single crystals.2,9,10The CeBr 3material was chosen here,as previous work 8showed that it compared well with LaBr 3:Ce,but without the self-activity associated with the natural radioactivity of 138La.The energy resolution was good for CeBr 3,so this ma-terial was chosen for this study.The intent here was to estab-lish methods to model and fabricate the material for better fracture strength in a way that degrades the energy resolution as little as possible.However,our resulting crystal,based onspecifications calculated using a methodical density func-tional theory (DFT)approach to be described,had a superior energy resolution,for this cerium bromide material,of 3.2%.The intent of this work was to report not only this final result but also the methods that led us to this result,and the approach used.Cerium trihalides possess excellent scintillation proper-ties,as do most rare-earth trihalide scintillators,such as high light output,fast decay time,and excellent energy resolu-tion.8Therefore,they are widely used in various fields such as high-energy physics and positron emission tomography,as well as some chemical processes involved in the nuclear industry.11The structural,electronic,and optical properties of many lanthanum trihalides,as well as cerium trifluoride (CeF 3),have been extensively investigated using both exper-imental and theoretical methods.12–21CeBr 3shows prefera-ble optical and scintillation properties;for example,it has a higher light yield than NaI:Tl as well as many other inor-ganic scintillators.8,22CeBr 3is a self-activated lanthanide scintillator that has received considerable recent attention 8due to its linearity of light output with photon energy;also,its high energy resolu-tion for gamma spectroscopy is far superior to that of NaI:Tl.Because the material possesses no intrinsic radioactivity,CeBr 3has high potential to outperform scintillators such as LaBr 3:Ce or lanthanum-based Elpasolites,23making it an excellent candidate for gamma-ray spectroscopy.24,25a)Electronic mail:gusspp@.0021-8979/2014/115(3)/034908/10/$30.00VC 2014AIP Publishing LLC 115,034908-1JOURNAL OF APPLIED PHYSICS 115,034908(2014)However,due to its hexagonal crystal structure(space group P63/m,prototype structure UCl3),pure CeBr3can fracture during crystal growth,detector fabrication,and subsequent field use.Because the crystal fractures easily,manufacturing yield is low,and the reliability of large crystals is questionable.26 Therefore,significant gains in the practical scale for CeBr3 scintillators will be realized by increasing fracture toughness of the crystals.2Aliovalent substitution in which a host ion is replaced with an ion of different valence(e.g.,Ca2þfor Ce3þin CeBr3)is a more potent method of strengthening compared to isovalent substitution(i.e.,replacing a fraction of ions with like-valence ions).In this approach,the forma-tion of intrinsic defects necessary to maintain charge neutral-ity results in complexes with long-range interactions in the crystal.The resulting increase in hardening rate can be explained in terms of elastic interaction with dislocations.27 Because CeBr3already exhibits superior scintillation characteristics,8the alloying element(s)used to strengthen the crystal must not degrade the scintillation properties. Aliovalent alloying provides more strengthening than isova-lent ing a basic approximation,solid solution strengthening based on lattice distortions due to some small concentration of dopant can be estimated as2s¼cÁGc12;(1) where G is the shear modulus,c is the concentration of solute in atomic fraction,and c is a proportionality constant.2,28For spherically symmetric distortions,such as those found in iso-valent alloying,c typically takes on values that are signifi-cantly smaller than unity,on the order of10À4to10À6.For tetragonal lattice distortions,such as those created from sol-ute atoms of a different valence,c can be nearly unity. Therefore,aliovalent alloying is more effective for a given concentration of solute.2Electronic valence effects exert a powerful influence on material and optical properties.In particular,aliovalent sub-stitution(making dilute alloys by substituting atoms of a dif-ferent valence)has improved a variety of technological applications such as gadolinium titanate(Gd2Ti2O7)ion con-ductors for solid fuel cells;29–32gallium indium oxide (GaInO3)transparent conductors for solar cells;33,34 rechargeable batteries;35,36thermoelectric devices;37lead zirconate titanate(Pb[Zr(x)Ti(1–x)]O3)or piezoelectric, ceramics;38–41and cubic zirconium dioxide(ZrO2) crystals.42–44These improvements,however,are far from optimal because the fundamental aliovalent mechanisms are largely unknown.Within the arena of scintillating materials, CeBr3single crystals have shown superior scintillating prop-erties,and large CeBr3crystals critically enable improved identification of radioisotopes.Unfortunately,CeBr3crystals are very prone to fracture.Fracture during device testing and implementation leads to catastrophic failures.Fracture dur-ing synthesis complicates the growth of CeBr3crystals in sizes large enough to be used to identify radioisotopes,and it accounts for the high production cost that is preventing large-scale deployment required by homeland security efforts.Aliovalent substitution was found to strengthen the material without significantly degrading the scintillating properties.2An optimized material design,however,has not been achieved due to a large number of possible aliovalent combinations.Most empirical atomistic simulations can approximately account for charge variation but not electronic valence effects.These simplistic simulations cannot cor-rectly reveal aliovalent phenomena such as the valence-compensating interstitials or vacancies.From a theoretical point of view,one would like to explore a computational design beforehand to predict the effect of aliovalent doping on the mechanical and optical properties of these materials before they are used in experi-ments.Indeed,in previous theoretical studies,45,46it was shown thatfirst-principles-based approaches were necessary to accurately predict effects due to defects and radiation. Although there has been great progress in resolution-of-the-identity techniques for computationally intensive coupled cluster methods(described briefly in the Theoretical Background section,below),these wavefunction-based approaches are still computationally much more demanding than DFT methods.Our DFT results for both the pure CeBr3 primitive cell and the(divalent)calcium-doped“supercell,”which includes200atoms and well over1000electrons, were based on spin-polarized,generalized gradient approxi-mation(GGA)methods47–49using Projector-Augmented-Wave(PAW)pseudopotentials.50,51During this study,it was discovered that the inclusion of a Hubbard U DFT correc-tion,52,53often denoted as DFTþU,was essential for obtain-ing accurate band structures and band gaps.Within the Hubbard DFT approach,an onsite penalty function is placed on the f electrons for each of the Ce atoms to prevent spuri-ous over-delocalization of the electrons.II.THEORETICAL BACKGROUNDIn this work,state-of-the-art DFTþU approaches, beyond those of standard DFT,were carried out for obtaining electronic and optical properties for a Ca2þ-doped CeBr3 bulk material.The intent is not to resolve the many open questions regarding how best to formulate exchange-correlation functionals or provide universal benchmarks for universal material systems.Rather,the calculations are pre-sented to demonstrate that the DFTþU formalism offers an efficient and accurate approach for describing the electronic and optical properties in these novel scintillating materials.In this work,aliovalent strengthening and the optical properties of Ca2þ-doped CeBr3using state-of-the-art,large-scale,quantum mechanical simulations were explored.These simulations go far beyond the current state of the art by incor-porating valence and variable charge effects for both the cohe-sive energies and optical properties of this doped compound. The work leads to an understanding that affects a wide spec-trum of materials of U.S.Department of Homeland Security (DHS)and the U.S.Department of Energy National Nuclear Security Administration interests,as mentioned above.In par-ticular,it leads to a systematic design criterion that can opti-mize the radiation detection materials explored by DHS.Over the last few decades,DFT has made tremendous progress in the accurate description of electronic and opticalproperties of molecules and materials.Based on the Hohenberg–Kohm theorem,54which relates electron den-sities with the external electrostatic potential,DFT can,in principle,be applied to any quantum-mechanical situation. Despite the overwhelming success of DFT for predicting mo-lecular and bulk properties,it is well-known that an accurate description of electronic band structure and optical proper-ties provides a significant challenge for the DFT formalism. This shortcoming is not a failure of DFT itself nor is it a breakdown of the Hohenberg–Kohm theorem(which is for-mally an exact theory).As is the case for all DFT formal-isms,i.e.,for both orbital-free DFT and the Kohn–Sham orbital-dependent approach used here,55,56this limitation arises from approximations to the(still unknown)exact exchange-correlation functional.As shown by several groups including ours,the use of conventional exchange-correlation functionals results in severely underestimated band gaps and incorrect asymptotic potential energy surfaces resulting from electron-transfer self-interaction.22,46An alternative to DFT methods is the use of wave-function based methods which directly calculate the3N-dimensional wavefunction(as opposed to the3-dimensional electron density).The conventional approach for handling these systems(at least for molecules)is to use Møller-Plesset perturbative theory(MP2)57in conjunction with highly correlated coupled-cluster singles and doubles plus perturbative triples methods(CCSD(T))to estimate elec-tronic energies.However,the computational cost of CCSD(T)methods58is too high for routine application to molecules larger than about30atoms.DFT,on the other hand,scales efficiently with size and is the method of choice for studying large material systems.Unfortunately,the accu-rate description of band gaps has been a traditional failure of most current density functionals,and the development of new methods for properly treating these electronic properties is still a topic of active research.Recognizing the shortcomings of conventional function-als,major methodological progress has been made in DFT techniques,which incorporate a strong intra-atomic interac-tion in a(screened)Hartree–Fock like manner,as an on-site replacement of the GGA.47–49This approach is commonly known as GGAþU or Hubbard DFT methods.52,53,59The DFT results for both the pure CeBr3primitive cell and the(divalent)Ca2þ-doped supercell were based on spin-polarized,GGA methods using PAW pseudopoten-tials50calculated by the Vienna Ab-initio Simulation Package(VASP).60It was found that the inclusion of a Hubbard DFT correction,DFTþU,was essential for obtain-ing accurate band structures and band gaps.61This novel DFTþU method was used to support experimental efforts in understanding both the structural and electronic properties of aliovalently doped CeBr3materials.This formalism is essen-tial for the Ce-based materials studied here,as conventional GGAs fail to describe systems with localized(strongly corre-lated)d and f electrons,which manifests itself in the form of unrealistic one-electron energies due to spurious self-interaction.This approach has been further modified and applied in many forms by Liechtenstein62and Dudarev.63In this work,the rotationally invariant approach by Dudarev is used because the effective on-site Coulomb and exchange parameters(U and J)do not enter separately,and only their difference(UÀJ)is required.The Dudarev approach is denoted here as just“DFTþU”unless otherwise specified. III.CALCULATIONSDFT calculations were performed to discern the optical properties of the Ca2þ-doped CeBr3compound.Introducing the Ca2þdopant(Figure1(a))resulted in calculations that provided valuable insight to the increase in crystal strength. These calculations may be used to compare the differences of doping with different dopants or their concentrations and to calculate the optical properties of the resultant crystals. One must account for the electron densities over the space of the crystal.To do this accurately,the calculations were made for a“supercell”of200atoms with well over1000electrons (Figure1).In addition,the electron density of states was cal-culated.If there is a crystal defect,or an atomic substitution, then the electron density of states will change,leading to dif-ferent results.The presence of a Ca2þdopant can signifi-cantly affect electronic properties by distorting the electronic charge density near the Ca2þatom(Figure2).Our DFT results for both the pure CeBr3primitive cell and the(divalent)calcium-doped supercell were based onthe FIG.1.(a)Ca dopant shows the(divalent)Ca2þ-substituted atom(near the lower left corner).(b)A CeBr3cross section showing the CeBr3supercell that was optimized and calculated using the Hubbard-U correction(i.e.,DFTþU).White and red dots represent cerium and bromine atoms,respectively,and the green dot represents the Ca2þ-substituted atom.Perdew-Burke-Ernzerhof (PBE)GGA functional using PAW pseudopotentials.The PBE GGA 48–51is used for the exchange and correlation correction.During our study,we found that the inclusion of a Hubbard DFT þU correction for the f -electrons on Ce was essential for obtaining accurate band structures and band gaps.Within the Hubbard DFT approach,an on-site penalty function is placed on the f -electrons for each of the cerium (Ce)atoms to prevent spurious over-delocalization of the electrons.Based on benchmarks for Ce 3þions,the Hubbard value (U)for our DFT studies was set at 4.5eV.For the initial study of the primitive cell,a very high cutoff energy of 400eV was used for the plane-wave basis set,and the Brillouin zone 64was sampled using a dense 8Â8Â8gamma-centered Monkhorst–Pack grid.65In addition to spin-polarization and dispersion effects,a relativistic spin-orbit coupling treatment was used for the valence electrons in the bulk-lattice calculations.Geometry optimizations of both the ions and the unit cell were carried out.Since the Ca-defect calculations require the use of larger supercells and significantly more atoms (>200atoms),a smaller 300eV cutoff energy is currently used for these cal-culations.For this same reason,we did not include spin-orbit effects in these large supercell systems,as we found this effect to be minimal in our initial calculations for the primi-tive cell described above.In the point-defect calculations,a large 3Â3Â3supercell was used and,therefore,a smaller 2Â2Â2Gamma-centered Monkhorst–Pack grid was used.Due to the extremely large size of these systems,these calcu-lations were carried out on a new massively parallelized supercomputer (located at Sandia National Laboratories headquarters in Albuquerque,NM)consisting of state-of-the-art Intel Sandy Bridge processors,QLogic Infiniband communication hardware,and a customized Linux software environment.This unique computing resource is the newest computing cluster at Sandia for high-performance capacity computing work and is necessary for solving the self-consistent,coupled Kohn–Sham equations with a large plane-wave basis.Unconstrained geometry optimizations of both the ions and the unit cell were carried out.Upon conver-gence,we found that the Ca atom was slightly displaced within the CeBr 3crystal lattice (Figure 1).However,the Ca 2þatom substitutes for Ce 3þatom and basically stays atthe Ce 3þsite when it is incorporated in the matrix.The results of the DFT modeling performed at Sandia National Laboratories suggested that a 1.9%substitution would result in a suitable combination of crystalline structural properties,increased strengthening of the lattice,and metrics for optical properties and emission spectra.The Fermi levels that result at different points in the lattice are also different because of the aliovalent substitution.Using the converged geometry,we then evaluated the cohesive energy of the Ca-doped CeBr 3material.The cohe-sive energy is defined as the energy required to break the atoms of the solid into isolated atomic species,a measure of the strength of the material.More specifically,the cohesive energy E coh is given byE coh ¼E solid ÀXiE atom i;(2)where the summation index,i ,represents all the differentatoms that constitute the solid.For the Ca-doped 3Â3Â3CeBr 3supercell,we obtained a cohesive energy of À3.66eV/atom.In order to further understand the electronic and structural properties due to the dopant,we also visual-ized the electron density of the entire supercell.Interestingly,we found that the presence of a Ca-dopant can significantly affect electronic properties by distorting the electronic charge density near the Ca atom (see Figure 2).The distortions in charge density associated with Ca-dopant site are in part from variations in energy transfer dynamics,electronic transitions around the dopant atom,and the effects of chemical modification on optical emission.The electronic structures and optical properties of both the undoped and the Ca-doped CeBr 3crystal may be derived using a k -point grid generated according to the Monkhorst–Pack scheme,65for the sampling of the Brillouin zone.The optical properties of CeBr 3can be determined by the frequency-dependent dielectric function e (x )¼e 1(x )þi e 2(x )that is mainly connected with the electronic struc-tures.The imaginary part e 2(x )of the dielectric function e (x )may be calculated from the momentum matrix elements between the occupied and unoccupied states within selection rules and given by22FIG.2.(a)Side view of electron charge density (red lobes)in a Ca 2þ-doped CeBr 3scintillating material.The electron density is significantly modified and accumulates near the Ca atom (blue).(b)Top-down view of electron charge density (red lobes)in a Ca-doped CeBr 3scintillating material.The calcium (blue)lies underneath a Ce atom in the left corner of the primitive unit cell.e2xðÞ¼½2e2p=ðX e0Þ Xk;v;cjh w c k j^uÁr jh w v k ij2Ád E c kÀE v kÀEÀÁ;(3)where x is the light frequency and e is the electronic charge.w c k and w v k are the conduction and valence band(VB)wave-functions at k,respectively.The real part e1(x)of the dielec-tric function e(x)can be derived from the imaginary part e2(x)using the Kramers–Kronig dispersion equation.All other optical constants can be derived from e1(x)and e2(x).22,66IV.STRUCTURE DETERMINATIONAND ELECTRONIC PROPERTIESCeBr3has a hexagonal structure with space groupP63/m,where the cerium and the halide occupy2(a)in(1/3, 2/3,1/4)and6(h)in(0.375,0.292,1/4)sites,respec-tively.22,67,68Our structures are in reasonable agreement with experiments.67–70Figure3shows the Brillouin zone.64 The electronic structures of CeBr3at their equilibrium struc-tures were calculated using this Brillouin zone formulation for context.We have carried out a series of DFT calculations taking into account both ferromagnetic and antiferromag-netic behaviors.We also performed a high-level calculation (using the HSE06hybrid functional71,72)to understand and predict the band gap of this material.Our high-level calcula-tions allow an accurate assessment of other CeBr3dopants in larger systems,which we will study in the near future.The energy band structure of CeBr3calculated at equi-librium is shown in Figure4.The energy band structure is calculated along the path that contains the highest number of high-symmetry points of the Brillouin zone,namely,C!A !H!K!C!M!L!H.The zero energy is arbitra-rily taken at the Fermi level.73The lowest bands around À36eV consist of5s states of Ce.The Ce5p states are located at aroundÀ19eV.The bands aroundÀ16eV are derived from the4s states of bromine(Br).The energy bands in the range fromÀ6toÀ2eV correspond to the4p states of Br that decide the top of the valence band.These results are in agreement with CeCl3experimental data.22Above the Fermi level,the conduction band(CB)consists of the4f and 5d states of Ce.The4f states have a sharp peak due to the strong localization character of the4f states.If the4f electron is kept in the core,the calculated result agrees with other experiments.22,74In addition,a partlyfilled f band situated right at the Fermi level was found.This discrepancy from an experiment by Park11,70may arise from the different treatment method of the4f states of Ce.If the4f electron is kept in the core,the calculated result was found to be in agreement with the ex-perimental results.74Otherwise,because of the localized character of the f states,the unpaired electron cannot lead to metallic behavior,with its effective mass tending toward in-finity.75Therefore,CeBr3is an insulator.22In order to understand how the defect influences the electronic density of states(DOS),we also evaluated the DOS for both the pure,undoped CeBr3material and the Ca-doped supercell(Figures5and6).Comparing Figures5and6,we notice that several peaks near2and À18eV disappear for the Ca-doped compound.These differ-ences are undoubtedly due to the presence of the Ca atom and its distortion of the electronic environment around this dopant.Finally,using the converged DOS results,we com-puted the optical properties of these compounds by evaluat-ing the real parts of the frequency-dependent dielectric tensor(Figures7and8).FIG.3.CeBr3Brillouin zone.Hex path:C–M–K–C–A–L–H–A–j L–M j–K–H.FIG.4.Band structure of CeBr3in a hexagonal crystal lattice.The bandstructure corresponds to the Brillouin zone for the CeBr3hexagonal crystallattice.The Fermi energy level is shifted to the valence band maximum atzero.FIG.5.The energy band structure and electronic partial density of statesaround the Fermi level for the3Â3Â3pure CeBr3supercell are displayed.The lowest bands aroundÀ36eV consist of5s states of Ce.The Ce5p statesare located at aroundÀ18eV.The bands aroundÀ16eV are derived fromthe4s states of Br.The energy bands in the range fromÀ6toÀ2eV corre-spond to the4p states of Br that decides the top of the valence band.Thereare more peaks near2andÀ18eV for the pure CeBr3supercell.Although the optical response in Figures 7and 8are similar,there are noticeable differences at 5and 20eV with a much stronger variation near 5eV for the pure CeBr 3mate-rial.We note,in passing,that these effects would probably be more significant if a higher Ca-doping level were used (i.e.,1Ca atom for every 4Ce atoms).Furthermore,under-standing how to modulate this distortion in electron density (which results in other spectroscopic observables)with other types of dopants would enable us to maximize their theoreti-cal energy resolution for advanced spectroscopy applica-tions,using a rational experimental approach guided by predictive modeling.Future studies will explore this factor.To summarize,these new simulations demonstrate a capability for predicting properties of doped CeBr 3materials that is unavailable elsewhere but is critically needed to study the property-limiting valence phenomena in ionic com-pounds.The model may also begin to enable realistic simula-tions of chemical reactions where the electronic valence effects of different atoms may dynamically vary (e.g.,differ-ent oxidation states or even different dopant atoms).It can be applied to improve properties and perform life-cycle anal-ysis of ionic materials and enhance our ability to respond to emerging mission critical problems.Examples of the appli-cations that are directly relevant include radiation detection,photovoltaics,thermoelectrics,solid fuel cells,rechargeable batteries,super-capacitors,piezoelectric ceramics,micro-electronics,photonics,micro-electro-mechanical systems (MEMS),and nano-electro-mechanical systems (NEMS).V.RESULTS AND ANALYSIS A.DetectorsIn 2012,in support of a Nevada National Security Site (NNSS)Directed Research and Development (SDRD)pro-ject,Dynasil Radiation Monitoring Devices,Inc.(RMD)was commissioned by the Remote Sensing Laboratory (RSL)to build a CeBr 3crystal alloy detector with 2%substitution using the Ca 2þcation.RMD grew a 1-in.-diameter CeBr 3crystal with 1.9%calcium dibromide (CaBr 2),as requested.The vertical Bridgman was used as the crystal growth tech-nique.Materials were purified prior to crystal growth.The charge composition was 222.14g of CeBr 3and 2.26g of CaBr 2.The resulting crystal is polycrystalline whitebutFIG.6.The energy band structure and electronic partial density of states around the Fermi level for the 3Â3Â3Ca 2þ-doped CeBr 3supercell are dis-played.The lowest bands around À36eV consist of 5s states of Ce.The Ce 5p states are located at around À18eV.The bands around À16eV are derived from the 4s states of Br.The energy bands in the range from À6to À2eV correspond to the 4p states of Br that decides the top of the valence band.There are fewer peaks near 2and À18eV for the Ca 2þ-doped CeBr 3supercell.FIG.7.Real parts e 1(x )of the dielectric tensor for the 3Â3Â3pure CeBr 3supercell,where e (x )¼e 1(x )þi e 2(x )and x is the light frequency.The dielectric function of CeBr 3is calculated based on its electronic structure.e 1(x )is a function of the photon energy.The imaginary part e 2(x )of the dielectric function is connected with the energy band structure but correlates with the real part e 1(x )of the dielectric function.The first peak at 1eV observed for the pure CeBr 3supercell is not evident for the Ca 2þ-doped CeBr 3supercell.The peak at 3eV corresponds to the transition 4f 1!5d 0of Ce.The main peaks of about 4eV may be ascribed to the transition from the Br 4p VB to the Ce 5d CB.The peaks near 20eV correspond mainly to the transition of inner electron excitation from Ce 5p VB to CB.22FIG.8.Real parts e 1(x )of the dielectric tensor for the 3Â3Â3Ca 2þ-doped CeBr 3supercell,where e (x )¼e 1(x )þi e 2(x )and x is the light frequency.The dielectric function of Ca 2þ-doped CeBr 3is calculated based on its electronic structure.e 1(x )is a function of the photon energy.The imaginary part e 2(x )of the dielectric function is connected with the energy band structure but correlates with the real part e 1(x )of the dielectric func-tion.The first peak at 1eV observed for the pure CeBr 3supercell is not evi-dent for the Ca 2þ-doped CeBr 3supercell.The peak at 3eV corresponds to the transition 4f 1!5d 0of Ce.The main peaks of about 4eV may be ascribed to the transition from the Br 4p VB to the Ce 5d CB.The peaks near 20eV correspond mainly to the transition of inner electron excitation from Ce 5p VB to CB.22。

2020年加利福尼亚州隐私权法的英文2020 California Privacy Rights ActIntroductionThe California Privacy Rights Act (CPRA) is a comprehensive privacy law that was approved by California voters in November 2020. Building on the existing California Consumer Privacy Act (CCPA), the CPRA strengthens and expands privacy protections for California residents. It introduces new requirements for businesses, enhances consumer rights, and establishes a dedicated enforcement agency.Key ChangesThe CPRA introduces several key changes to the existing privacy laws in California. Some of the main provisions include:1. Expansion of Consumer Rights: The CPRA expands the rights of consumers in relation to their personal information. For example, consumers now have the right to request that their personal information be corrected or deleted, as well as the right to know how their information is being used.2. Creation of a Dedicated Enforcement Agency: The CPRA establishes the California Privacy Protection Agency, which willbe responsible for enforcing privacy laws in the state. This agency will have the authority to investigate violations, issue fines, and take legal action against businesses that fail to comply with the law.3. Enhanced Data Protection Requirements: The CPRA introduces new requirements for data protection, including the establishment of data minimization and retention policies. Businesses will also be required to conduct regular risk assessments and audits to ensure compliance with privacy laws.4. Increased Transparency: The CPRA requires businesses to provide consumers with more information about how their personal information is being collected, used, and shared. Businesses must also obtain consent before collecting sensitive personal information, such as health or financial data.5. Restrictions on Data Sharing: The CPRA limits the sharing of personal information between businesses, particularly in the case of data brokers. Businesses must now enter into contracts with third parties to ensure that personal information is only used for specific purposes.Impact on BusinessesThe CPRA will have a significant impact on businesses operating in California. Companies that collect and process personal information of California residents will need to make changes to their privacy practices to comply with the new law. Some of the key challenges for businesses include:1. Compliance Costs: Businesses will need to invest in new technology, staff training, and legal expertise to ensure compliance with the CPRA. The costs of implementing these changes can be significant, particularly for small andmedium-sized businesses.2. Data Management: The CPRA introduces new requirements for data management, including the need for data minimization and retention policies. Businesses will need to review their data practices and establish procedures for handling consumer requests for access, correction, and deletion of personal information.3. Increased Accountability: Under the CPRA, businesses will be held accountable for any violations of privacy laws. The California Privacy Protection Agency has the authority to impose fines and penalties on businesses that fail to comply with the law, which could have serious financial consequences.4. Consumer Trust: Compliance with the CPRA can help businesses build trust with consumers by demonstrating a commitment to protecting their privacy rights. Companies that prioritize privacy and data security are more likely to attract and retain customers in an increasingly competitive marketplace.ConclusionThe California Privacy Rights Act represents a major step forward in privacy protection for California residents. By expanding consumer rights, creating a dedicated enforcement agency, and introducing new data protection requirements, the CPRA aims to strengthen privacy laws and hold businesses accountable for how they handle personal information. Businesses operating in California should prepare for the changes introduced by the CPRA and take steps to ensure compliance with the law.。

化学常见术语英文说法BET 公式BET formula DLVO 理论DLVO theory HLB 法hydrophile-lipophile balance method pVT 性质pVT propertyZ 电势zeta pote ntial阿伏加德罗常数Avogadro'number阿伏加德罗定律Avogadro law阿累尼乌斯电离理论Arrhenius ionization theory 阿累尼乌斯方程Arrhenius equation 阿累尼乌斯活化能Arrhenius activation energy 阿马格定律Amagat law 艾林方程Erying equation爱因斯坦光化当量定律Einstein 's law of photochemical equivalence 爱因斯坦－斯托克斯方程Einstein-Stokes equation安托万常数Antoine constant安托万方程Antoine equation盎萨格电导理论Onsager's theory of condu ctance半电池half cell半衰期half time period饱和液体saturated liquids饱和蒸气saturated vapor饱和吸附量saturated extent of adsorption饱和蒸气压saturated vapor pressure爆炸界限explosion limits比表面功specific surface work比表面吉布斯函数specific surface Gibbs function 比浓粘度reduced viscosity 标准电动势standard electromotive force 标准电极电势standard electrode potential 标准摩尔反应焓standard molar reaction enthalpy标准摩尔反应吉布斯函数standard Gibbs function of molar reaction 标准摩尔反应熵standard molar reaction entropy标准摩尔焓函数standard molar enthalpy function标准摩尔吉布斯自由能函数standard molar Gibbs free energy function 标准摩尔燃烧焓standard molar combustion enthalpy标准摩尔熵standard molar entropy标准摩尔生成焓standard molar formation enthalpy标准摩尔生成吉布斯函数standard molar formation Gibbs function 标准平衡常数standard equilibrium constant标准氢电极standard hydrogen electrode标准态standard state 标准熵standard entropy 标准压力standard pressure 标准状况standard condition 表观活化能apparent activation energy 表观摩尔质量apparent molecular weight 表观迁移数apparent transference number 表面surfaces表面过程控制surface process control表面活性剂surfactants 表面吸附量surface excess表面张力surface tension表面质量作用定律surface mass action law波义尔定律波义尔温度Boyle lawBoyle temperature波义尔点Boyle point玻尔兹曼常数玻尔兹曼分布玻尔兹曼公式Boltzmann constant Boltzmann distribution Boltzmann formula玻尔兹曼熵定理Boltzmann entropy theorem玻色－爱因斯坦统计Bose-Einstein statistics 泊Poise不可逆过程irreversible process 不可逆过程热力学thermodynamics of irreversible processes不可逆相变化irreversible phase change 布朗运动brownian movement 查理定律Charle ' s law 产率yield敞开系统open system 超电势over potential 沉降sedimentation沉降电势sedimentation potential 沉降平衡sedimentation equilibrium 触变thixotropy粗分散系统thick disperse system催化剂catalyst单分子层吸附理论mono molecule layer adsorption单分子反应unimolecular reaction单链反应straight chain reactions 弹式量热计bomb calorimeter 道尔顿定律Dalton law道尔顿分压定律Dalton partial pressure law 德拜和法尔肯哈根效应Debye and Falkenhagen effect德拜立方公式Debye cubic formula 德拜－休克尔极限公式Debye- Huckel 's limiting equation 等焓过程isenthalpic process 等焓线isenthalpic line 等几率定理theorem of equal probability 等温等容位Helmholtz free energy 等温等压位Gibbs free energy 等温方程equation at constant temperature 低共熔点eutectic point 低共熔混合物eutectic mixture低会溶点lower consolute point 低熔冰盐合晶cryohydric 第二类永动机perpetual machine of the second kind第三定律熵third-law entropy 第一类永动机perpetual machine of the first kind缔合化学吸附association chemical adsorption电池常数cell constant 电池电动势electromotive force of cells 电池反应cell reaction 电导conductance 电导率conductivity 电动势的温度系数temperature coefficient of electromotive force电动电势zeta potential 电功electric work 电化学electrochemistry 电化学极化electrochemical polarization 电极电势electrode potential 电极反应reactions on the electrode 电极种类type of electrodes 电解池electrolytic cell 电量计coulometer 电流效率current efficiency 电迁移electro migration 电迁移率electromobility 电渗electroosmosis 电渗析electrodialysis 电泳electrophoresis 丁达尔效应Dyndall effect 定容摩尔热容molar heat capacity under constant volume定容温度计Constant voIume thermometer 定压摩尔热容molar heat capacity under constant pressure定压温度计constant pressure thermometer定域子系统localized particle system动力学方程kinetic equations 动力学控制kinetics control 独立子系统independent particle system 对比摩尔体积reduced mole volume对比体积reduced volume 对比温度reduced temperature 对比压力reduced pressure 对称数symmetry number 对行反应reversible reactions 对应状态原理principle of corresponding state 多方过程polytropic process 多分子层吸附理论adsorption theory of multi-molecular layers 二级反应second order reaction 二级相变second order phase change 法拉第常数faraday constant 法拉第定律Faraday ' s law反电动势back E.M.F. 反渗透reverse osmosis 反应分子数molecularity 反应级数reaction orders 反应进度extent of reaction 反应热heat of reaction 反应速率rate of reaction 反应速率常数c onstant of reaction rate范德华常数van der Waals constant范德华方程van der Waals equation范德华力van der Waals force 范德华气体van der Waals gases范特霍夫方程van' t Hoff equation范特霍夫规则van' t Hoff rule范特霍夫渗透压公式van' t Hoff equation of osmotic pressure非基元反应non-elementary reactions 非体积功non-volume work 非依时计量学反应time independent stoichiometric reactions菲克扩散第一定律Fick ' s first law of diffusion沸点boiling point 沸点升高elevation of boiling point费米－狄拉克统计Fermi-Dirac statistics 分布distribution 分布数distribution numbers分解电压decomposition voltage分配定律distribution law分散系统disperse system分散相dispersion phase分体积partial volume分体积定律partial volume law 分压partial pressure 分压定律partial pressure law 分子反应力学mechanics of molecular reactions 分子间力intermolecular force分子蒸馏molecular distillation 封闭系统closed system附加压力excess pressure 弗罗因德利希吸附经验式Freundlich empirical formula of adsorption 负极negative pole 负吸附negative adsorption 复合反应composite reaction盖吕萨克定律Gay-Lussac law 盖斯定律Hess law甘汞电极calomel electrode感胶离子序lyotropic series 杠杆规则lever rule高分子溶液macromolecular solution 高会溶点upper consolute point隔离法the isolation method 格罗塞斯－德雷珀定律Grotthus- Draoer 's law 隔离系统isolated system根均方速率root-mean-square speed 功work 功函work content 共轭溶液conjugate solution共沸温度azeotropic temperature构型熵configurational entropy 孤立系统isolated system固溶胶solid sol固态混合物solid solution 固相线s olid phase line光反应photoreaction光化学第二定律the second law of actinochemistry 光化学第一定律the first law of actinochemistry 光敏反应photosensitized reactions 光谱熵spectrum entropy 广度性质extensive property 广延量extensive quantity 广延性质extensive property 规定熵stipulated entropy 过饱和溶液oversaturated solution过饱和蒸气oversaturated vapor过程process 过渡状态理论transition state theory过冷水super-cooled water 过冷液体overcooled liquid 过热液体overheated liquid 亥姆霍兹函数Helmholtz function 亥姆霍兹函数判据Helmholtz function criterion亥姆霍兹自由能Helmholtz free energy亥氏函数Helmholtz function 焓enthalpy 亨利常数Henry constant 亨利定律Henry law 恒沸混合物constant boiling mixture 恒容摩尔热容molar heat capacity at constant volume恒容热heat at constant volume 恒外压constant external pressure 恒压摩尔热容molar heat capacity at constant pressure恒压热heat at constant pressure 化学动力学chemical kinetics 化学反应计量式stoichiometric equation of chemical reaction化学反应计量系数stoichiometric coefficient of chemical reaction化学反应进度extent of chemical reaction化学亲合势chemical affinity 化学热力学chemical thermodynamics 化学势chemical potential 化学势判据chemical potential criterion化学吸附chemisorptions 环境environment 环境熵变entropy change in environment 挥发度volatility 混合熵entropy of mixing混合物 mixture活度 activity活化控制 activation control 活化络合物理论 activated complex theory活化能 activation energy霍根 -华森图Hougen-Watson Chart 基态能级 energy level at ground state基希霍夫公式 Kirchhoff formula基元反应 elementary reactions 积分溶解热 integration heat of dissolution吉布斯－杜亥姆方程 Gibbs-Duhem equation 吉布斯－亥姆霍兹方程 Gibbs-Helmhotz equation 吉布斯函数 Gibbs function 吉布斯函数判据 Gibbs function criterion 吉布斯吸附公式 Gibbs adsorption formula 吉布斯自由能 Gibbs free energy吉氏函数 Gibbs function 极化电极电势 polarization potential of electrode 极化曲线 polarization curves 极化作用 polarization 极限摩尔电导率 limiting molar conductivity几率因子 steric factor 计量式 stoichiometric equation 计量系数 stoichiometric coefficient 价数规则 rule of valenceJoule-Thomson experimentJoule-Thomson coefficient Joule-Thomson effect 焦耳定律 Joule's law 接触电势 contact potential 接触角 contact angle节流过程 throttling process节流膨胀 throttling expansion 节流膨胀系数 coefficient of throttling expansion结线 tie line结晶热 heat of crystallization解离化学吸附 dissociation chemical adsorption 界面 interfaces界面张力 surface tension浸湿 immersion wetting浸湿功 immersion wetting work 精馏 rectify 聚（合）电解质 polyelectrolyte 聚沉 coagulation 聚沉值 coagulation value 绝对反应速率理论 absolute reaction rate theory绝对熵 absolute entropy 绝对温标 absolute temperature scale 绝热过程 adiabatic process 绝热量热计 adiabatic calorimeter 绝热指数 adiabatic index卡诺定理Carnot theorem 卡诺循环Carnot cycle 开尔文公式 Kelvin formula柯诺瓦洛夫－吉布斯定律 Konovalov-Gibbs law 科尔劳施离子独立运动定律Kohlrausch ' s Law of Independent Migration of Ions 可能的电解质 potential electrolyte 可逆电池 reversible cell 可逆过程 reversible process 可逆过程方程 reversible process equation 可逆体积功 reversible volume work 可逆相变 reversible phase change 克拉佩龙方程Clapeyron equation 克劳修斯不等式 Clausius inequality焦耳 Joule 焦耳 -汤姆生实验 焦耳 -汤姆生系数 焦耳 -汤姆生效应克劳修斯－克拉佩龙方程Clausius-Clapeyron equation控制步骤control step 库仑计coulometer 扩散控制diffusion controlled 拉普拉斯方程Laplace ' s equation拉乌尔定律Raoult law 兰格缪尔－欣谢尔伍德机理Langmuir-Hinshelwood mechanism兰格缪尔吸附等温式Langmuir adsorption isotherm formula雷利公式Rayleigh equation 冷冻系数coefficient of refrigeration 冷却曲线cooling curve 离解热heat of dissociation 离解压力dissociation pressure 离域子系统non-localized particle systems 离子的标准摩尔生成焓standard molar formation of ion 离子的电迁移率mobility of ions 离子的迁移数transport number of ions离子独立运动定律law of the independent migration of ions离子氛ionic atmosphere 离子强度ionic strength 理想混合物perfect mixture理想气体ideal gas 理想气体的绝热指数adiabatic index of ideal gases理想气体的微观模型micro-model of ideal gas理想气体反应的等温方程isothermal equation of ideal gaseous reactions理想气体绝热可逆过程方程adiabatic reversible process equation of ideal gase理想气体状态方程state equation of ideal gas理想稀溶液ideal dilute solution 理想液态混合物perfect liquid mixture粒子particles 粒子的配分函数partition function of particles 连串反应consecutive reactions 链的传递物chain carrier链反应chain reactions 量热熵calorimetric entropy 量子统计quantum statistics 量子效率quantum yield 临界参数critical parameter 临界常数critical constant 临界点critical point 临界胶束浓度critical micelle concentration 临界摩尔体积critical molar volume 临界温度critical temperature临界压力critical pressure临界状态critical state零级反应zero order reaction 流动电势streaming potential流动功flow work 笼罩效应cage effect路易斯－兰德尔逸度规则Lewis-Randall rule of fugacity 露点dew point 露点线dew point line 麦克斯韦关系式Maxwell relations 麦克斯韦速率分布Maxwell distribution of speeds 麦克斯韦能量分布MaxwelIdistribution of energy 毛细管凝结condensation in capillary 毛细现象capillary phenomena 米凯利斯常数Michaelis constant摩尔电导率molar conductivity 摩尔反应焓molar reaction enthalpy 摩尔混合熵mole entropy of mixing摩尔气体常数molar gas constant 摩尔热容molar heat capacity 摩尔溶解焓mole dissolution enthalpy 摩尔稀释焓mole dilution enthalpy 内扩散控制internal diffusions control 内能internal energy 内压力internal pressure 能级energy levels 能级分布energy level distribution 能量均分原理principle of the equipartition of energy 能斯特方程Nernst equation 能斯特热定理Nernst heat theorem 凝固点freezing point 凝固点降低lowering of freezing point 凝固点曲线freezing point curve 凝胶gelatin 凝聚态condensed state 凝聚相condensed phase 浓差超电势concentration over-potential 浓差极化concentration polarization 浓差电池concentration cells 帕斯卡pascal 泡点bubble point 泡点线bubble point line 配分函数partition function 配分函数的析因子性质p roperty that partition function to be expressed as a productof the separate partition functions for each kind of state 碰撞截面collision cross section 碰撞数the number of collisions 偏摩尔量partial mole quantities 平衡常数（理想气体反应）equilibrium constants for reactions of ideal gases平动配分函数partition function of translation 平衡分布equilibrium distribution 平衡态equilibrium state 平衡态近似法equilibrium state approximation 平衡状态图equilibrium state diagram平均活度mean activity 平均活度系统mean activity coefficient平均摩尔热容mean molar heat capacity 平均质量摩尔浓度mean mass molarity 平均自由程mean free path 平行反应parallel reactions 铺展spreading普遍化范德华方程universal van der Waals equation 其它功the other work 气化热heat of vaporization 气体常数gas constant气体分子运动论kinetic theory of gases 气体分子运动论的基本方程foundamental equation of kinetic theory of gases 气溶胶aerosol 气相线vapor line 迁移数transport number 潜热latent heat 强度量intensive quantity 强度性质intensive property亲液溶胶hydrophilic sol氢电极hydrogen electrodes 区域熔化zone melting 热heat热爆炸heat explosion热泵heat pump热功当量mechanical equivalent of heat 热函heat content热化学thermochemistry热化学方程thermochemical equation 热机heat engine热机效率efficiency of heat engine热力学thermodynamics热力学第二定律热力学第三定律热力学第一定律热力学基本方程the second law of thermodynamics the third law of thermodynamics the first law of thermodynamics fundamental equation of thermodynamics热力学几率thermodynamic probability热力学能thermodynamic energy热力学特性函数characteristic thermodynamic function热力学温标thermodynamic scale of temperature 热力学温度thermodynamic temperature 热熵thermal entropy热效应heat effect熔点曲线melting point curve熔化热heat of fusion溶胶colloidal sol溶解焓dissolution enthalpy溶液solution溶胀swelling润湿wetting润湿角wetting angle萨克尔－泰特洛德方程Sackur-Tetrode equation三相点triple point三相平衡线triple-phase line熵entropy熵判据entropy criterion熵增原理principle of entropy increase渗透压osmotic pressure渗析法dialytic process生成反应formation reaction升华热heat of sublimation实际气体real gas舒尔采－哈迪规则Schulze-Hardy rule松驰力relaxation force松驰时间time of relaxation速度常数reaction rate constant速率方程rate equations速率控制步骤rate determining step塔费尔公式Tafel equation态－态反应state-state reactions唐南平衡Donnan equilibrium淌度mobility特鲁顿规则Trouton rule特性粘度intrinsic viscosity体积功volume work统计权重statistical weight统计热力学statistic thermodynamics统计熵statistic entropy途径path途径函数path function外扩散控制external diffusion control完美晶体perfect crystalline完全气体perfect gas微观状态microstate微态microstate 韦斯顿标准电池Weston standard battery维恩效应Wien effect 维里方程virial equation 维里系数virial coefficient 稳流过程steady flow process 稳态近似法stationary state approximation 无热溶液athermal solution 无限稀溶液solutions in the limit of extreme dilution物理化学Physical Chemistry 物理吸附p hysisorptions吸附adsorption 吸附等量线adsorption isostere吸附等温线adsorption isotherm吸附等压线adsorption isobar吸附剂adsorbent 吸附量extent of adsorption 吸附热heat of adsorption 吸附质adsorbate 析出电势evolution or deposition potential 析因子性质property that partition function to be expressed as a product of the separate partition functions for each kind of state 稀溶液的依数性colligative properties of dilute solutions稀释焓dilution enthalpy系统system 系统点system point 系统的环境environment of system 相phase 相变phase change 相变焓enthalpy of phase change 相变化phase change 相变热heat of phase change 相点phase point 相对挥发度relative volatility 相对粘度relative viscosity 相律phase rule 相平衡热容heat capacity in phase equilibrium 相图phase diagram 相倚子系统system of dependent particles 悬浮液suspension 循环过程cyclic process压力商pressure quotient 压缩因子compressibility factor 压缩因子图diagram of compressibility factor 亚稳状态metastable state 盐桥salt bridge 盐析salting out 阳极anode 杨氏方程Young' s equation 液体接界电势l iquid junction potential液相线liquid phase lines 一级反应first order reaction 一级相变first order phase change 依时计量学反应time dependent stoichiometric reactions 逸度fugacity 逸度系数coefficient of fugacity 阴极cathode 荧光fluorescence 永动机perpetual motion machine 永久气体Permanent gas 有效能available energy 原电池primary cell 原盐效应salt effect 增比粘度specific viscosity 憎液溶胶lyophobic sol 沾湿adhesional wetting 沾湿功the work of adhesional wetting 真溶液true solution 真实电解质real electrolyte 真实气体real gas 真实迁移数true transference number 振动配分函数partition function of vibration 振动特征温度characteristic temperature of vibration 蒸气压下降depression of vapor pressure正常沸点normal point 正吸附positive adsorption 支链反应branched chain reactions 直链反应straight chain reactions 指前因子pre-exponential factor 质量作用定律mass action law 制冷系数coefficient of refrigeration 中和热heat of neutralization轴功shaft work转动配分函数partition function of rotation 转动特征温度characteristic temperature of vibration 转化率convert ratio 转化温度conversion temperature 状态state 状态方程state equation状态分布state distribution状态函数state function准静态过程quasi-static process 准一级反应pseudo first order reaction 自动催化作用auto-catalysis 自由度degree of freedom 自由度数number of degree of freedom 自由焓free enthalpy 自由能free energy 自由膨胀free expansion 组分数component number 最低恒沸点lower azeotropic point最高恒沸点upper azeotropic point 最佳反应温度optimal reaction temperature 最可几分布mostprobable distribution 最可几速率most propable speed。