High-f requency Electrodeless Plasma Spectrometry B. L. SHARP Macaulay Instatute for Soil Research Craagaebuckler Aberdeen Scotland A Bg 2Q J Contents Introduction Classification of plasma types Non-flame-like plasmas Flame-like plasmas Thermodynamic equilibrium Self-absorption Atom and molecule formation Emission spectrometry general considerations Nebulisers The The inductively-coupled radio-frequency plasma torch Mechanism of the r.f. plasma Temperature of the r.f. plasma The plasma generator Analytical development and applications of the r.f. plasma microwave plasma Mechanism of the microwave plasma Temperature of the microwave plasma Analytical significance of physical plasma parameters Microwave cavities A4nalytical development and application of the microwave plasma Conclusion References Addendum 3 38 SHARP Introduction A plasma may be defined as any luminous volume of gas having a fraction of its atoms or molecules in the ionised state.Many different types have been observed and numerous schemes for their generation have been described. Developments in the science of spectroscopy have largely been dependent on the existence of suitable plasma sources capable of exciting a wide range of spectral transitions. The potential application of plasmas in chemical analysis was realised at an early stage and this realisation has undoubtedly been one of the main motivating forces in their further development. The definition of a plasma encompasses a wide range of hot gases in which the energy of the atoms molecules or electrons is sufficiently high to cause significant ionisation and emission of radiation.Before describing in detail high-frequency electrodeless plasmas a general classification of types is useful since it will provide the background and historical development on which the modern work is based. Classification of Plasma Types Plasmas may usefully be divided into two types those which are ‘flame-like’ and those which are not. It should be pointed out that although the combustion flame conforms to the definition of a plasma the term is usually reserved for systems deriving their energy directly from electrical sources. Non-flame-like plasmas This description covers those discharges which are confined to a column joining the current-carrying electrodes.The d.c. arc a.c. arc and a.c. spark are examples of this type of plasma which historically was the first type t o be used in chemical analysis. A source for use in emission spectrometry should be capable of performing the functions of atomisation and excitation. It is a characteristic of the non-flame-like plasma that both these functions are achieved within the main column of the discharge and therefore spatial resolution of the effects is poor. Non-flame-like plasmas are the most widely used for chemical analysis and a substantial literature exists describing their properties and applications. It will suffice here to refer the reader to some of the principal texts dealing with the subject .1-5 Flame-like plasmas Flame-like plasmas are characterised by existing with a significant portion of the discharge external to the main core into which power is coupled.Their development has been occasioned largely by the desire to obtain spatial stability, spatial resolution of atomisation and excitation and ease of sample introduction ; characteristics which are not readily obtainable with the non-flame-like plasma sources. Historically two types of flame-like plasma have been developed the d. c. or low-frequency transferred plasma and the single-electrode high-frequenc HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 39 plasma. The high-frequency electrodeless systems which are the main subject of this review came as a later development of the single-electrode high-frequency plasma. Transferred plasmas.Transferred plasmas can be described as d.c. arcs having a portion of the plasma transferred away from the primary arc column. This is usually accomplished by a special design of the electrode configuration and by the application of vortex gas flows to the primary column. In order t o produce the flame-like portion of the plzsma ring electrodes and electrodes mounted at right angles to the arc axis have been employed. Such sources were described by Gerdien and Lotz6 in the 1920s and later in the 1950s by Peters Weisss and Giannini.g However it was not until Margoshes and ScribnerlO and independently, Korolev and Vainshteinll devised methods for the introduction of sample particu-lates into these plasmas that their analytical potential was realised. Following the early work many designs have been reported12-17 and their analytical character-istics discussed.It is apparent that the successful design (as measured by the detection limit and precision that can be attained) incorporates two facets. Firstly, considerable turbulence is required at the sample introduction point if the sample particulates are to penetrate the axial region of the d.c. arc where the highest temperatures are obtained (7000 to 9000 K). Secondly the intense recombination continuum emitted from arc discharges severely limits detection limits unless spatial separation of the primary column and the ‘tail flame’ is achieved. High-frequency single-electrode plasmas. The occurrence of flame-like plasmas or ‘brush’ discharges in high-frequency circuits was first reported in the 1 9 2 0 ~ .l ~ - ~ ~ Although studies describing their physical properties appeared in the literature from 1941 onwards,22-28 it was not until 1954 that Mavrodineanu and B o i t e ~ x ~ ~ first suggested that such plasmas could be used for the analysis of solutions and a further two years elapsed before practical analyses were reported.30 Following the early work many systems were de~cribed~l-~~ which were specifi-cally designed for analytical applications. In addition to r.f. plasmas operated at between 1 and 100 MHz single-electrode microwave plasmas operated at 2450 MHz have also been used as analytical s o ~ r c e s . ~ ~ ~ 3 5 ~ ~ 0 - ~ ~ F a ~ s e 1 ~ ~ has given an excellent review of the developments that have occurred in analytical plasma spectrometry and many of the systems referred to in this introduction are described in his paper.Looking retrospectively at the developments in plasma spectrometry it is possible to identify the difficulties that were encountered and thereby understand why the search for new plasma sources has continued until the present day. The plasma because of the attainable temperature offered the early spectroscopist a chance to study a much wider range of phenomena than had previously been possible. Once quantitative studies were undertaken stability both spatial and temporal became important. The advent of analytical spectrometry introduced the requirement of sensitivity which meant that the problems associated wit 40 SHARP introducing the samples into the plasma and those presented by the inherently high background emission of most discharges had to be overcome before acceptable analytical reproducibility could be obtained.In part the work on flame-like plasmas met the new requirements but many difficulties remained. The use of electrodes for power coupling presented problems because of wear and the resultant contamination of the source. The problem is particularly serious for samples that are solutions. The recent trend therefore has been to develop sources that combine the ease of sampling associated with flames with the high temperatures attainable in plasmas. Emission Spectrometry General Considerations* 'Edztorzal Note -Because the general theoretical basis of the techniques that make use of plasma sources is not widely reviewed the author was asked to include sections that are perti-nent to his review but that normally would be outside the scope of a review These sections have been printed in small type Emission spectrometry is based on the principle that an atom in an excited state k of energy Ek may spontaneously undergo a radiational transition to a lower energy state El with emission of a photon of energy hv = Ek - El where h is Planck's constant (6 6 x J s) When the lower of the two levels is the ground state (1 = 0 E = 0 ) the emitted spectral line is known as a resonance line The process was described by Einstein in terms of the transi-tion probability Akl which is the probability per second that an atom in state k will spon-taneously radiate its energy and return to a lower state Consider a small volume A V of plasma gas in which there are n,A V excited analyte atoms, (where nk is the number of excited atoms per cubic metre ) The power radiated P is given by where vo is the frequency of the emitted photons Detection systems are not generally capable of measuring the total power emitted but they view a given area AA of the source and accept radiation emitted into a given solid angle which is determined by the optical aperture The quantity which is of interest is therefore the power emitted per unit area per unit solid angle which is known as the brzghtness or radzance of the source Dividing A V by AA leaves L the depth (in metres) of the source along the line of viewing and recognizing that the radiation is emitted into all space z e into 4~ steradians of solid angle the brightness B, becomes P = hvonkA klAV (1) 1 4n B = -hv,nkAklL W m-2 sr-I The radiated photons are not monochromatic but are spread over a range of frequencies distributed about the central frequency v, The spectral profile of a line is usually expressed in the form of a normalized integral such that cc(v)dv is the fraction of photons having frequen-cies in the range v+ (v + dv) and a3 Jcc(v)dv = 1 0 (3) Thus the brightness as expressed above is the integrated output and this is the parametel of analytical importance since the measuring bandwidth (typically 0.1 nm) usually exceeds the width of the spectral line (typically 0.05 nm) Equation (2) expresses the radiance in terms of the excited-state population and it is neces-sary to relate this to the total free-atom concentration of the analyte element Assuming fo HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 41 the moment that all the conditions in the source approach thermodynamic equilibrium then the population of states for each kind of particle follows a Boltzmann distribution and hence where K is the Boltzmann constant T is the absolute temperature and gk is the statistical weight of the k’th state.The total concentration of atoms N is given by the sum of the concen-trations in each state thus i=l i = O where 1 is the highest state that must be considered in the summation. It is convenient to define a quantity that expresses the population of states as a function of temperature; this is known as the partition function viz nk c€ gk exp(- Ek/kT) (4) N = C n i i = l i = O Z ( t ) = Z gl exp(-Ei/kT) ( 5 ) Hence (6) - - n k gk exp(-Ek/kT) N - i = l Zgi exp (- Ei/k T ) i = O Substituting into equation (2) yields the required expression for B, 1 N B = -hv,-gkAkiLexp(-Ek/kT) w m-2 sr-I 4T Z ( t ) (7) Equation (7) is correct for the ideal model on which its derivation is based although i t represents little more than an approximation for all real plasma sources.It is therefore necessary to develop the theory further and to take into account the factors that have been omitted froin the simple treatment. Thermodynamic equilibrium The temperature of a plasma is the parameter which is of most importance to the spectro-scopist. The term is often used loosely for descriptive purposes without due reference to the fact that i t can only have significant meaning when related to a defined equilibrium.A mona-tomic gas may be characterised by four temperature^,^^ uiz.,-( a ) the electron temperature which is determined by the kinetic energy of the electrons; (b) the gas temperature which is determined by the kinetic energy of the atoms; (c) the excitation temperature which characterises the population of the various energy ( d ) the ionisation temperature which describes the population of the various ionisation For molecular gases temperatures are also assigned to the dissociation equilibria and the population of vibrational and rotational levels. If all the measured temperatures are equal, the system is said to be in thermodynamic or thermal equilibrium.The properties of the system are then identical t o those of a gas confined inside a backbody furnace of equal temperature, and the following hold true-( a ) the velocity distribution of all particles (atoms molecules electrons and ions) in all (b) the relative population of states for each kind of particle conforms to Boltzmann’s Law; (c) the ionisation equilibrium is defined by the Saha equation;54~659 (d) the chemical dissociation equilibrium is defined by the Law of Mass Action ; (e) the radiation density is given by Planck’s Law. (f) the conditions for ‘detailed balancing’ are realised so that the rate of population of a levels; states. energy states is Maxwellian 42 SHARP state by a given path is equalled by the rate of de-population by the converse path thus excitation collisions by atoms electrons or molecules (collisions of the first kind) are exactly balanced by quenching collisions with the same species (collisions of the second kind) and the absorption of radiation quanta is exactly balanced by spontaneous and stimulated emission It must be emphasised that practical sources cannot exist in complete thermal equilibrium because they suffer energy losses (by conduction convection and radiation) and these are not balanced by the existence of surroundings which are at the same temperature The resultant radial ‘temperature’ distribution appears to preclude establishment of a defined equilibrium However it has been shown that when the temperature change along a mean free path within a localised volume element is small compared with the mean temperature of that element, the equilibrium is only slightly affected Thus it is common to refer to ‘local thermal equzlzbrzum’ (LTE) existing in defined regioris of the source Referring to the model considered in equation (7) it was assumed that all the photons generated by spontaneous emission left the source the total power radiated being that due to the summed power of N separate emitters Such sources are said to be ‘optically thin,’ and it is a characteristic that the radiation density in them does not follow Planck’s Law z e the radiation is not pure ‘temperature radiation,’ but depends also on the atomic concentration It follows that the escaping photons cause the excited state to be slightly less populated than is predicted assuming a Boltzmann distribution Nevertheless the energy loss associated with radiation is very small ,and since in most sources a t atmospheric pressure the dominating mechanism for population and de-population of excited states is that of collision the assump-tion of equilibrium is often still justified The existence of radial temperature distributions in sources causes inhomogeneity of radiance along the line of viewing It is not therefore possible to describe the integrated optical depth by the simple linear distance L rather this should be replaced by an integral of the type L L’ = B(Z) dl (8) 0 Physical studies of plasmas usually involve determination of the radial temperature distribu-tion Lateral scanning of the plasma does not produce this directly since the observed output represents a series of samples of integrals such as the one given in equation (8) The true radial distribution is obtained from the data by use of the Abel transform integral (see p 135 of Boumans’ book’) Self -absorption In a gaseous cloud containing more than one atom there is a finite probability that emitted photons will be absorbed by atoms of the same kind This phenomenon is termed ‘self-absorp-tion ,’ it decreases the relative radiance of the source so destroying the proportionality between radiance and atomic concentration and also causes an apparent broadening of the spectral line This broadening should not be confused with the processes of Doppler Lorentz natural, Holtzmark and Stark br~adening,~’ which determine the physical line profile and are referred to in the derivation of equation (7) Consider a homogeneous cloud of atoms of depth L , absorbing radiation from a continuum source of radiance B W m-2 sr-l per unit frequency interval Let the absorptzopz coeficzent a t the frequency v be k (m-l) then the radiance of the transmitted beam a t the frequency v is given by The absorbed power is therefore The ratio of the absorbed power to the incident power is generally known as the absorptzvzty and is given the symbol A, thus B(v) = B,exp(-kk,L) (9) (10) B (v) = B,[1 - exp(-k,L)] A = 1 - exp(-k,L) (no units) (11 HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 43 B(v) = AVBB(v) (12) The absorptivity occurs in the Kirchhoff Law of Radiation and it describes to what extent a source a t a given temperature approaches a blackbody a t the same temperature.Thus where BB(v) is the brightness of a blackbody a t the temperature T. Equation (12) can be used to develop an expression for the radiance of a spectral line under conditions where self-absorp-tion is present. Obtaining &(v) from Planck’s Law and recognising that A v varies across the spectral profile the spectral radiance of the line a t the frequency v becomes 2hv3 B(v) = Av- exp(-Ek/kT) W m-2 sr-ls c2 (13) where c is the velocity of light and the 1 occurring in the denominator of Planck’s formula has been neglected in comparison to the exponential term. For the reasons stated previously the integrated output is required; as v remains relatively constant over the spectra1 line width (v+vo) i t may be taken outside the integral sign and the required expression is 2hv 3 a, = s[1 - exp(-k,L)]dv-$ exp(-Ek / k T ) W m-2 sr-1 (14) The quantity 00 AT = (1 - exp-k,,L)dv s-l 0 is known as the total absorption factor.From the Einstein theory of radiation and Milne’s treatment (p.95 of Mitchell and Zemansky’s i t can be shown that This equation is of fundamental importance since it shows that the integrated absorption coefficient has a constant value that is independent of the shape of the spectral line. When kv is small [i.e. N (the total number of atoms) is not large] and the source depth L is not too great AT approximates to the integral in equation (16). Hence W m-2 sr-1 which is identical with equation (7) [in this equation a simple two-level model is assumed and hence gi appears in place of .Z(t)].Under these conditions self-absorption is minimal and the analytical growth curve of log B nersus log N is a straight line with a slope of unity. The integrated area AT grows linearly with N but the spectral half-width remains approximately cons tan t . At high atomic concentrations or when extended sources are encountered the approximation made previously no longer holds and for a line having a mixed Doppler-Lorentz profile i.e., a Voigt profile,57 i t can be shown 58$59 that where AVD is the Doppler half-width and a = (In ~)*AvI,/AQ where AVL is the Lorentz half-width Hence equation (14) becomes s-l s-l Thus self-absorption degrades the proportionality between radiance and atomic concentration to a square-root relationship.Winefordner et aZ.so have shown that under these conditions A at the line centre reaches its limiting value of unity and the radiation a t that frequency is equivalent to that from a blackbody a t the same temperature being independent of atomic 44 SHARP concentration Further emission can only occur in the line wings where the absorption is weaker hence an apparent broadening of the line occurs resulting in an increase of AT in proportion to (NL) Referring to the previous discussion of thermal equilibrium it is apparent that conditions a t the line centre more closely approach equilibrium (z e the radiation density is consistent with Planck’s Law) than do those in the line wings Analytical growth curves for the conditions of (2) no self-absorption (zz) a Lorentz profile with integrated radiance measured (zzz) a Lorentz profile with line centre measured and (zv) a Doppler profile with integrated radiance measured have been established for many years 58 The curves begin with a straight portion having a slope of unity but except for conditions of no self-absorption all then deviate considerably from rectilinearity The straight portion of the curve with unity slope is of most importance analytically since it provides the maximum precision of measurement The existence of radial temperature profiles in practical sources was discussed previously in relation to the establishment of thermal equilibrium A further result is the distortion of observed line profiles by inhomogeneous self-absorption this effect is known as ‘self-reversal,’ for reasons that will become apparent The spectral profile of atoms in the outer regions of a plasma is somewhat narrower than that of atoms in the core because the lower temperature results in lessened Doppler and collisional half-widths Nevertheless the integrated absorption coefficient remains approximately constant (ignoring the different populations of the excited states) and therefore the absorption a t the line centre by the cooler atoms is greater than that of atoms in the high-temperature region The net result is that the centre of the emitted profile shows a ‘dip,’ hence the term ‘self-reversal ’ The product of the total number of atoms and the optical length L and also the temperature gradient determine the degree of self-reversal Since it adversely affects growth-curve linearity self-reversal should be avoided if possible Atom and molecule formation The steps involved in producing the emitting species from the original sample material are probably the least understood aspect of emission spectrometry.The preparation of calibration curves from matched standards permits analyses to be performed accurately without the need for comprehension of the whole process. However since the mechanisms involved are vital in determining the ‘analytical signal’ it is appropriate that some consideration of them be given. Solution samples are the most commonly encountered and provided that a sufficient volume is available (e.g. 1 ml) nebulisation is usually employed as the first step in the atomisation process.The droplets produced undergo de-solvation either in a pre-heated chamber or in the plasma itself to produce salt particles of the type (MX)n. Vaporisation of the dry particulate mass yields individual MX units which are then dissociated to a degree dependent on the equilibrium constant for the reaction MX + M + X at the plasma temperature. The free-atom popula-tion thus produced is excited by collisional energy exchange and an emission signal results. Unfortunately the free-atom population may be suppressed by further chemical reaction to produce molecular species that are stable at the source tem-perature (particularly in flames in which stable oxygen-containing species may be formed). For a theoretical consideration of the phenomena of dissociation and ionisation and their effects on the radiance of the spectral lines reference may be made to Boumans’ contribution to Grove’s text.HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 45 Nebulisers Two types of nebuliser have been used in plasma emission spectrometry pneumatic nebulisers (as in atomic absorption spectrometry) and ultrasonic nebulisers. Several authors61-71 have investigated nebuliser design and performance ; attempts to predict mathematically the sample uptake rate and the droplet size tend to produce erratic results probably because of the difficulty of manufacturing a nebuliser that conforms in minute detail to the theoretical model on which the calculations are based. Most practical nebulisers have performances which fall in a range having an uptake rate of 0.03 to 8 ml per minute at flow rates of 0.8 to 4 litres per minute.72 Droplet sizes are generally between 50 and 1 pm although many commercial nebulisers occasionally produce droplets far in excess of this size.Large droplets must be avoided if possible; their atomisation efficiency is poor and in plasmas they may be a source of instability producing high flicker noise on the emission signal. Generally the droplet fraction below 5 pm is suitable for introduction into plasmas and therefore impact beads,61 baffle chambers73 and de-sol~ators~~ are employed both to further reduce the size and to select the smallest fraction from the size distribution. Unfortunately the losses involved in using these devices are high and the efficiency of the combined system rarely exceeds 10 per cent.Nebuliser-auxilliary chamber systems are extremely sensitive to changes in the viscosity of the solution gas flow rate and temperature and every effort should be made to control these parameters closely in experimental systems. Ultrasonic n e b u l i s e r ~ ~ ~ ~ ~ overcome some of the difficulties associated with pneumatic designs. They produce finer droplets (less than 2 pm) and the gas flow rate can be varied independently of the solution uptake rate an important factor in use with plasmas where flow rates tend to be more critical than in flames. Most designs employ a curved ceramic transducer (or plane transducer plus epoxy-resin lens) to focus ultrasonic energy in the range 1 to 5 MHz on to a thin film coupled to the transducer by a liquid medium e.g.water. The analyte solution is fed on to the film for example with a syringe or a peristaltic pump and the ultrasonic energy produces capillary waves77 on the surface which then rupture to produce a mist of fine droplets. Although it is accepted that superior results are obtained7* with this type of nebuliser no preferred design has emerged in the literature. A difficulty arising in design is to reconcile the production of a uniform and small flow of solution on to the film whilst preserving the ease of sample changing. This factor together with the cost probably accounts for the lack of a standard commer-cially accepted system. De-solvation commences as soon as the droplets are formed and progresses quite rapidly because of the high ratio of surface area to volume of the spheroids.Comple-tion of the de-solvation process may occur either in the plasma or previously in a heated spray chamber. The smaller sizeof the dry particulatematter is an advantage in plasma work where sample rejection problems are encountered. Vaporisation occurs within the source and progresses in a somewhat simila 46 SHARP fashion to de-solvation. Although plasma temperatures are high enough to vaporise most substances the thermal conductivity of the gas is low and therefore a finite residence time is required for the process to reach completion. Slow or incomplete vaporisation of the sample particulate matter may adversely affect the magnitude, spatial homogeneity and noise characteristic of the emission signal.Two types of high-frequency electrodeless plasma are currently being used for analytical spectrometry the inductively coupled radio-frequency (5 to 40 MHz) plasma torch and the microwave (2450 MHz) plasma. The I nductively-coupled Radio-f requency Plasma Torch The inductively-coupled radio-frequency plasma torch was first described in 1961 by Reed79@981 and since then has been the subject of considerable study and development as a source for emission spectrometry. Reed’s torch was operated at 5 MHz and the resultant plasma was used for growing crystals. Before looking at the analytical development of the system a consideration of the mechanism of the r.f. plasma is necessary. 1.5mrn-9 mm-id. L ,Codant 40 rnm I -4mm i.d.7mm ad. *’8/9 Ball joint ‘-Aeroso[ inlet Fig. 1. A typical radio-frequency plasma torch (FasseIs2 HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 47 Mechanism of the r.f. plasma Consider a typical torch (see Fig. 1) ; a gas usually argon is introduced tangentially into the annular gap between the two outer quartz tubes (typically 18mm and 13 mm in diameter). The resulting vortex flow produces a low-pressure region a t the end of the inner tube where the plasma is ultimately located and the high velocity of the flow cools and physically separates the outer tube from the plasma core. Gas is also introduced into the inner tube and produces a low-velocity laminar flow the ‘plasma flow,’ on which the plasma operates. For analytical applications a third tube is added the ‘injector tube,’ which is tapered to produce a high-velocity flow for ‘punching’ the sample into the centre of the plasma.The induction coil typically two or three turns of 6 mm 0.d. water-cooled copper pipe is coupled to an r.f. generator giving 2 to 30 kW of output at 5 to 40 MHz. When the power is switched on an alternating magnetic field is established having field lines running axially through the coil. No plasma results however as there are no charged particles to which power can be coupled. It is therefore necessary to ‘seed’ the plasma with electrons; this may be accomplished either with a Tesla coil, or by introducing a graphite rod (suitably insulated) into the coil which is induc-tively heated and produces thermal electrons.The free electrons are accelerated by the field and rapidly reach ionising energies so causing further breakdown in the gas. Equilibrium is reached when the rate of energy loss from the plasma is equalled by the power input. The magnetic field induces the ions and electrons to flow in closed circular horizontal paths around the field lines so producing eddy currents. The neutral argon is heated by collisional energy exchange with the charged particles. Macroscopically the process is equivalent to the heating of a conductor by an r.f. field the resistance to eddy-current flow producing joule heating. The field does not penetrate the conductor uniformly and therefore the largest currents flow in the periphery of the plasma; this is the so-called ‘skin effect.’ The existence of the phenomenon fundamentally influences the shape of the plasma and its analytical potential.Fa~se1’~ has given a mathematical treatment of the effect which is presented below. The skin depth is given by the relationship s = 5*03/(puv)* cm (19) where p is the relative permeability and and is defined as the depth at which the eddy currents drop to l / e of their surface ~ a l u e . * ~ ~ * The inside portion of the plasma is heated indirectly resulting in a low-temperature channel running through the centre. This fact more than any other influences the analytical applications of the source as i t permits efficient sampling into the plasma tail flame. The power-coupling efficiency and total energy absorbed can be described in terms of a Bessel function of the ratio r/s where r is the plasma radius.The function when plotted against r / s shows a ‘knee’ a t r / s = 2-25 with little increase in the coupling efficiency for greater values. In order to obtain a high temperature in the axial channel r / s should be as small as possible and therefore on balancing the two considerations 2.25 is considered to be the optimal value. Substituting this value into o is the specific electrical conductivity (0-1 cm-1) v is the frequency of the applied field in MH 48 SHARP equation (19) yields the radius given that the function o ( T ) z e the variation of u with temperature is known Hence The temperatureIfrequency conditions for a number of plasma radii have been derived by Fassel and co-workers 73 Assuming quasi-adiabatic conditions for the plasma that is to say that energy is only lost from the core region by the forced transport of the hot gas it is possible to calculate a minimum power requirement The enthalpy of gas which has passed through the core region is VY2 = 128/pu (20) H = JCpdT (21) where Cp is the heat capacity a t constant pressure (cal mol-l K-l) Cp IS equal to 512 R (where R is the gas constant 1.986 cal mol-l K-l) for argon a t atmospheric pressure and for T less than 10 000 K If the flow rate through the plasma is 4 then the power P required to heat the gas to a temperature T IS P = 0.015cj5T W (22) The temperature is an average value and does not indicate the nature of the radial temperature distribution which is a function of flow rate torch design and skin-depth effect According to Fa~se11,~~ to operate a plasma a t 7250 K a t 27 MHz with a radius of 0 8 cm and a gas flow of 10 litres per minute requires a minimum power of about 1.1 kW Normally more power than this would be required to overcome energy losses associated with radiation conduction con-vection and expansion However even allowing for these factors generators of no more than 2 kW should provide adequate power for satisfactory plasma operation The metallic-cylinder model for the plasma is over-simple and therefore the calculations are approximate in nature.For example it is clear that plasma radius and the temperature cannot be regarded as independent variables and recent work84,85 has indicated that the true independent variables are the geometrical parameters of the torch design and gas flow rates.A more advanced discourse on plasma heating by r.f. induction may be found in the work of Miller.S6 Temperature of the r.f. plasma Several ~ 0 r k e r ~ ~ ~ ~ ~ 8 ~ - ~ ~ have reported on plasma temperatures using a variety of methodsg1 and most have assumed the existence of ‘local thermal equilibrium’ (LTE) in their calculations. Without proof of the assumption serious doubts about the validity of the results are raised. However Johnstong21g3 has carried out an extensive study of the r.f. plasma and concludes that it closely approaches ‘local thermal equilibrium.’ In this work the temperature of the plasma was measured by various methods (a) using the relative intensities of the 3p44s-3p54p and 3p54s-3p55p argon lines (b) using the ratio of relative line (425.9 mm) and the continuum intensities and (c) using the line-reversal technique.All the methods yielded similar results indicating an off-axis maximum of about 9000 K. The electron density of the plasma was then measured from the Stark broadening of the spectral lines and the results together with the temperature measurements were used in applying the Griem1S7 criteria to the plasma. These criteria involve calculations that show that the population of states by collisional processes exceed those due to radiational mechanism ten-fold. For excited state HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 49 a close approach to LTE was found and for the ground state which is subject to high radiational transition rates the deviation from LTE was found to be less than 10 per cent.The establishment of LTE in a plasma depends on a balance between the rates of energy exchange between the various particles in the plasma. Both ions and electrons gain similar energies from the field. However in an elastic collision the exchange of energy takes place in proportion to the ratio 2m/M where m and M are the masses of the colliding particles. Thus an ion is ‘thermalised’ in a few collisions, whereas an electron requires about 5 x lo4 collisions. The collision frequency for electrons in argon at 9000 K is about 7-5 x 1O1O s-l which means that about 6.6 x lO-’s are required for thermalisation of the electrons. For a field frequency of 20 MHz the energy exchange cycle between the field and electrons occurs in about 2.5 x 10-8 s ; therefore the electron temperature would be expected to rise Fig.2. Radio-frequency plasma isotherms ( JohnstonQ3 50 SHARP above that of the other particles. The apparent establishment of LTE suggests that this does not happen. In part this may be due to the presence of molecular impurities in the cylinder gas e.g. nitrogen water or oxygen. Such species have frequent inelastic collisions with electrons of all energies and can therefore rapidly redistribute the electron energy. Fig. 2 shows a typical set of isotherms; the origin of the description ‘doughnut plasma’ is clear. Formation of the ‘doughnut’ ring is essential for efficient sampling; particulate matter injected at the base of the plasma is channelled into the low-temperature axial region by the high temperature of the core.Injection velocities of about 0.13 m s-1 are required to ensure penetration. The temperature in the axial channel and hence that experienced by the sample73 is about 5000 K. A d.c. plasma of this temperature would exhibit a high sample-rejecton factor due to the aero-dynamic barrier set up by radial expansion of the discharge gas. It is therefore apparent that the geometry of the r.f. plasma is ideally suited to the requirements of emission spectrometry. The plasma generator Much of the work with r.f. plasmas has been performed using r.f. heaters based on either the Hartley or Colpitts type of self-oscillator circuit. With these circuits the power leads andthe plasma are part of theresonant circuit, with the result that changes in the plasma impedance due for example to sample loading alter both power dissipation and frequency.Where this results in variation in the spectral output from the plasma some re-tuning of the circuit is necessary. A tuning facility is always provided in order to accommodate the change in impedance of the plasma gas following initiation. Fortunately with the ‘doughnut’ plasma the effects of sample loading are minimal since the sample is heated indirectly and does not therefore interfere with the coupling process. Recently a new type of generator that employs a fixed-frequency crystal oscilla-tor to feed a power amplifier has appeared.’3 The output from the amplifier is fed to a standard 50 R transmission line and then variable capacitors are used to match the impedance of the plasma (typically about 2 a) to the cable.This ensures efficient power transfer from source to load and should also minimise r.f. leakage which presents a problem with the older type of generator. Care is always required in shielding the load coil from the detection electronics. The normal method adopted is to place the torch inside an aluminium cabinet and to fit the service holes with tubes whose length is at least four times their diameter. The modern generators provide fixed-fequency output e.g. 27 MHz at powers of up to 2 kW and are ‘bench-top’ size. This is an improvement on the valve-type r.f. heaters which are usually quite bulky and emit considerable amounts of heat into the laboratory. Analytical development and applications of the r.f.plasma The first analytical application of the r.f. plasma torch was reported by Greenfiel HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 51 et al. in 1964.87 In this work a 36 MHz 2.5 kW generator was used to produce an annular plasma into which a number of samples were introduced. Results were reported for samples introduced by nebulisation and it was stated that direct injection of liquids slurries and solid powders was also possible. In 1965 a second paper appeared this time by Wendt and Fassel,9* describing a 3.4 MHz 5 kW plasma into which solutions were introduced by an ultrasonic nebuliser. The lower frequency of the Fassel system produced a ‘tear drop’ shaped plasma having no cool axial channel. Such geometry results from the increased skin-depth which in turn yields a greater uniformity of heating throughout the plasma gas.It is now known that whilst frequencies in excess of 20 MHz assist in producing an annular plasma correct selection of gas flows can produce similar geometry at much lower frequencies. Solution Analysis. Following the initial papers several author^^^-^^^ have reported on the application of the r.f. torch to solution analysis. Most work on solutions has been carried out using nebulisers for sample introduction. Plasmas, unlike flames cannot tolerate large amounts of sample as the drain on the avail-able power can disrupt the ionisation equilibrium that sustains the discharge. Practically the limiting sampling rate for aqueous samples in about 0.2 ml per minute which allowing for a 10 per cent.efficiency in the expansion-de-solvation chamber requires a nebuliser uptake rate of 1 ml per minute usually achieved at a gas flow of about 1 to 1.5 litres per minute. When solutions with a high salt content are being sprayed blockage of the injection tube may occur; however this can be overcome by d e - s ~ l v a t i o n . ~ ~ ~ ~ . Results have also been reported for the introduction of micro-samples into the plasma. Greenfield et aLg7 used a cross-flow nebuliser in a heated chamber to carry out analyses on 25 pl samples of fuel oil, organophosphorus compounds and blood samples. Fassel et al,lo9 have described work with 100 p1 samples vaporised from a tantalum boat and introduced into the plasma. The effective temperature of the r.f.plasma varies from about 5000 K to ambient temperature along a vertical and horizontal profile of the tail flame. Taking into account the excitation energy the partition function and the degree of ionisation, each spectral line has an optimal temperature a t which its radiance reaches a maximum for a given atomic concentration. If one adds to this the consideration of atomisation it is found that the optimal viewing height in the plasma varies from element to element. A practical limit to the viewing height is set by the turbulence in the upper regions of the tail flame caused by entrainment which results in high flicker noise on the emission signal. Generally for neutral atom lines those with excitation energies above 4 eV are best observed in the low region of the plasma, h.5 to 20 mm above the coil. Those elements with lines below 4 eV usually have peak emissions in the 20 to 40 mm region. The results are weighted by the other effects particularly ionisation. The alkali and alkaline-earth metals are quite highly ionised by the plasma and ion lines are usually preferred for their measure-ment; this of course leads to lower optimal heights of observation 52 SHARP The changing plasma conditions both lateral and axial pose particular problems for multi-element analysis and also the selection of internal standards. The traditional criteria for choosing line pairs with similar behaviour are that the excitation and ionisation energies should be similar. This works fairly well for uniform sources but as Fassel et al.observe,s8 when large temperature changes and spatial inhomogeneity of the sample distribution are encountered other factors have to be considered. In particular the ionisation equilibrium constant is a more reliable parameter than the ionisation energy since it takes into account the effect of the free electron concentration. In a plasma with extremely steep temperature gradients the partition function should be considered as well as the excitation energy in estimating radiance/temperature behaviour. Self-absorption also plays a part in the careful selection of a reference line especially where the sample is unevenly distributed throughout the source. The factors listed above have repercussions when the plasma is required for simultaneous multi-element analysis.Fortunately the optimal viewing regions are sufficiently diffuse and the sensitivity high enough to make multi-element work a t high sensitivity possible. For any given group of elements and by appropriate selection of lines it is usually possible to achieve adequate sensitivity with a compromise viewing height .lo6 The multi-element capability of the source is greatly enhanced by the long rectilinear ranges obtained and its freedom from chemical interference. The freedom from self-absorption effects even at quite high concentrations is attributable to the fact that for a given sample input the product NL (number of atoms multiplied by the optical length) is relatively small. The dimensions of the plasma the confinement of the sample to the axial regions and the decreased population of the ground state afforded by the high temperature all contribute in maintaining a linear relation between N and the total absorption factor AT.The freedom from chemical interference has been noted by several workers;87,98, loS in particular no interference has been reported for the calcium/phosphate or aluminium/calcium systems. In an early paper Veillon and Margoshe~'~ reported an enhancement effect with the calcium/phosphate system that is difficult to interpret. However in their system a 4.8 MHz 'tear-drop' plasma was used and the sample was simply drifted up the plasma tube which undoubtedly resulted in most of it going round the outside of the plasma core. It is apparent from the reported observations that the temperature experienced by the sample is sufficient to dissociate even the most thermally stable compounds and this together with the inert nature of the plasma gas accounts for the very high sensitivity exhibited for elements forming stable oxides (see Table I).The most serious source of inter-ference encountered with the r.f. plasma is ionisation and its suppression by con-comitant matrix elements.lo6 Unfortunately no detailed study of this aspect has yet been reported but it is clear that the viewing position must be carefully considered in this context since both the magnitude of the phenomenon and the relative effect of suppressants will be related to it. (See additional references. HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 53 TABLE I COMPARATIVE DETECTION LIMITS FOR THE R.F.AND MICROWAVE PLASMAS R. F . Plasma Miwowave Plasma Wave- Wave- Detection length/ Sampling Detection length/ Com- Sampling limit ; Species nm method limit Ref nm pound method Sensitivity Ref 2 As B Ba Be Bi Br C c2 cc1 CH CN cs Ca Cd Ce c1 c o Cr c u Fe Ga Ge H Hf Hg I In La Li Mn Mo Mg 2 328.07 396.15 278.02 193.69 249.77 249.77 455.4 I1 455.4 I1 234.86 234.86 306.77 393.37 I1 326.1 1 226.50 418.66 345.35 425.43 327.4 371.97 417-21 265.12 339.98 253.65 253.65 408.67 670.78 279.55 I1 403.07 257.61 379.82 588.99 Ta F N N Ta F N Ta F N Ta F N Ta F Ta F N N Ta F N N N N N N N N N Ta F N N N N Ta F N N 0~0001 109 0.001 73 0.360 106 0.01 109 0.080 106 0*0001 109 0~0001 0.0000003 109 0-0004 106 0~00002 109 0.002 109 0.0005 0.003 0.006 0.002 0.004 0.001 0.1 0.0003 0.0006 0.004 0.010 0.001 0.002 73 106 106 73 73 106 106 106 106 78 106 109 0.0004 106 0.0003 106 0.00005 106 0.00006 106 0.00003 109 0.2 106 0.0003 106 328.07 396.15 193-7 228-8 235.0 249.8 249.8 234.86 472.26 478.55 CBr, 247.9 EtOH 516.52 CH, 516.52 278.8 CHCl, 431.42 CH, 388.34 CH, 393.37 I1 228.8 228.8 247.9 co2 479.45 Lindane 240.7 217.89 371.99 248.32 486.1 H, 253.65 253.65 253.65 206.16 533.82 CH212 303.94 279.55 I1 337.13 N2 N N N Pt F cv N Pt F Pt F N GC GC GC DI GC Gc DI DI N N Pt F GC N WF N Pt F GC N Pt F cv Pt F GC N N DI 0.005 1.0 0.03 4 x 10-11 0.028 0.01 1 x 10-10 1 x 10-10 1.0 2 x 10-11 2 x 10-11 8 x 10-l1 0.1a 8 x 10-lo 0.28 0.058 0.01 0.0004 3 x 10-14 2 x 10-13 5 x 10-11 0.06 1 x 10-10 1.0 3 x 10-10 2 x 10-9 0.003 2 x 10-11 0.001 78 5 x 10-11 0.1 1 x 10-9 0.5 0-78 136 136 161 157 160 161 157 157 136 144 149 149 155 125 125 155 155 136 161 157 144 161 157 136 157 125 161 157 159 157 144 136 136 15 SHARP 54 Nb Ni OH P P b S Sb Se Sn Sr Ta Te Th Ti T1 U V W Y Yb Zn Zr 405.89 341.48 253.56 213-62 405.78 405.78 182.04 259.81 231.15 196.03 196.03 303.4 317.51 407.77 301.25 214.27 401.91 334.90 I1 535.05 409.01 437.92 400.87 371.03 I1 369.42 213.86 343.82 I1 N 0.010 N 0.003 N 0.070 Ta F 0.020 N 0.008 Ta F 0.003 N 1.7 N 0.2 Ta F 0.001 N 0.1 Ta F 0.006 N 0.030 Ta F 0.02 N 0.00002 N 0.070 Ta F 0.007 N 0.003 N 0-005 Ta F 0.003 N 0.030 N 0.002 N 0.001 N 0.0006 N 0.00004 N 0.01 N 0.0004 78 73 306-72 308.9 106 253.57 109 73 405.78 109 261.41 108 545.38 78 231.15 109 252.85 73 196.03 109 203.98 106 242.95 109 78 78 109 78 216.9 H,O DI H,O GC Phosdrin GC N Pt F DMSO GC SO DI N Pt F N Pt F N 0.1a 2 x 10-6 9 x 10-12 0.005 1 x 10-10 5 x 10-1' 0.1 5 x 10-10 0-04 4 x 10-10 1.0 2.6 x 155 125 144 161 157 144 135 136 157 161 157 136 73 334.90 I1 N 0.1 136 109 78 73 437.92 N 0.08 161 106 73 106 73 213.86 N 0.0006 161 213.86 Pt F 8 x 10-l1 157 106 KEY The sampling method and appropriate detection units are N Nebulisation; detection limit in pg ml-l F Filament of metal X; absolute detection limit in g CV Cold vapour technique; detection limit in pg ml-1 GC Gas chromatography; sensitivity in g s-l DI Direct injection; detection limit in p.p.m.by volume Detection limits marked a are the minimum background levels found in the sample. Solids analysis. Potentially one of the most important assets of the r.f.plasma is that it will allow the direct analysis of solids. Many industrial processes e.g., cement manufacture routinely produce samples consisting of finely divided powders having particle sizes in the 0 to 100 pm range. Although many of these samples are refractory in nature the 5000 to 6000 K effective temperature of the plasma is sufficient to achieve complete vaporisation provided that a sufficiently long resi-dence time is achieved. Unfortunately residence time is not readily variable as there is a general transport rate required for plasma operation and more important, the injection velocity has a lower limit set by the need to penetrate the plasma annulus. In practice samples in the 5 to 50 pm range can be used although the atomisation efficiency for the larger particles is probably low.The limited progress reported for the analysis of solids can be attributed to the difficulty of designing a universally applicable sample-introduction system. Such HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 55 device must be capable of producing a uniform gas-powder dispersion and de-livering about 50 mg per minute or less to the plasma. This alone is not difficult: however if it is to be achieved without sample segregation occurring the problem is more formidable. Dagnall et aZ.lfl used a fluidised-bed device to introduce alumina and magnesium oxide samples into a plasma and succeeded in determining boron and beryllium in the matrix. This system certainly produces severe segregation with the finer fraction being removed first followed by the larger particles.A total-consumption approach is necessary to achieve representative sampling. Other studies were carried out on the same materials with admixtures of elements such as phosphorus, sulphur iodine and bromine.1l2 Another design113 used a conventional nebuliser with the sample placed on a rotating table so that it just brushed the tip of the uptake capillary. Obvious difficulties arise here with the uniformity of sample uptake rate. The use of a nebuliser could possible help solve the segregation problem, although blockage of the uptake capillary is difficult to avoid. When using nebulisers for powder work the flow characteristics of the powder are imp~rtant.'~ Powders such as alumina and magnesium oxide tend to form fairly uniform spheroids which can flow easily.A suitably dimensioned nebuliser can handle this type of powder quite satisfactorily particularly if the particles are coarse i e . about 60 pm. Powders containing large fractions of smaller particles whose sizes are below about 1 pm and those having irregular particle shape e.g. a natural clay are far more difficult to handle because they stick to surfaces and agglomerate quite readily. The injection of a powder slurry was reported in the early work>6 but the method has not been followed up by other workers. Fassel et aZ.lo9 reported the use of an ultrasonic nebuliser employing a 20 kHz probe dipped into a molten alloy from which it produced 12-pm particles at 1 to 10 mg per minute. Other devices have been described for powder i n t r o d u ~ t i o n ~ ~ ~ ~ ~ ~ and it may be that these have characteristics compatible with r.f.plasmas. However, generally no preferred design has emerged and undoubtedly more work is required in this area. Other applications. The r.f. plasma is an excellent atomiser and therefore potentially an atom reservoir for other techniques such as atomic absorption spectrometry. Both Greenfield et aLg6 and Fassel et aL88 have reported absorption measurements. The former studied the determination of copper in the plasma, and then reversed the system using the plasma as a source of magnesium or calcium lines and an air-acetylene flame as the reservoir. There seems to be little point in trying to use the torch in this manner since the sensitivity obtained with the emission technique is adequate for most analyses.The latter paper described the use of atomic absorption studies for determining free-atom distributions in the plasma and certainly useful information can be gained in this manner. Atom reservoirs specifically designed for atomic absorption using r.f. heating have also been rep0rted.10~J~~9118 Argon is the most convenient gas for analytical work although other gases hav 56 SHARP been studied. Molecular species require more power input since the molecular bonds require considerable amounts of energy to break them. However thermal equilibrium in the plasma is more easily established with molecular gases and the increased enthalpy of the system might be advantageous in high sample loading applications e.g.solids work. The excitation of gasesllg in an r.f. plasma has been investigated by Alder and Mermet120. The species studied included sulphur dioxide hydrogen sulphide carbon tetrachloride chlorine phosphorus trichloride and sulphur hexafluoride in argon. Excitation temperatures from the argon lines and C rotational temperatures were reported for mixed-gas plasmas. The Microwave Plasma Early work with microwave plasmas was mainly concerned with the production of spectral sources :121p122 the discharges were generally of low pressure and were operated in sealed bulbs. These studies have progressed and today the electrodeless discharge lamp (EDL)123 is a fairly common source for atomic absorption and fluorescence spectrometry. The development of EDLs has been reviewed elsewhere, and therefore it is intended in this review to concentrate on free-flowing plasmas as used for emission spectrometry.In 1965 Cooke et aZ.125 reported the application of a low-wattage microwave plasma for the spectral identification of eluents from a gas chromatograph. This publication marked the beginning of the development of the microwave plasma emission source. Mechanism of the microwave plasma The microwave plasma draws its energy from a standing electromagnetic wave resonating in a confining cavity The most commonly used frequency is 2450 MHz m hich is the band allocated for the operation of microwave diathermy units The power to the cavity is supplied by a magnetron valve and the total dissipation is usually in the range 0 to 200 W Consider the establishment of the ionisation equilibrium following ‘seeding’ of the gas with a Tesla coil Each electron is accelerated by the field for a short period of time until either the field changes direction or it collides with an atom (assuming an atomic gas) The collision changes the direction of motion of the electron but does not seriously alter its velocity the energy exchange occurring in proportion to 2m/M This process continues with the electron gaining energy in steps from the field and losing energy by elastic collisions Once the energy exceeds that of the first excited state there is a finite probability that an inelastic collision will occur returning the electron energy to zero Provided that the electric field strength is high enough a few electrons will reach the ionisation energy and thus produce further breakdown, leading to the establishment of equilibrium A similar process occurs in a d c plasma and therefore it is necessary to consider further the effect of the high field frequency An electron accelerated by the field will move off in a particular direction and since both voltage and electron current are initially in phase will present a resistive load to the generator The energy exchange between the field and the electron then approaches 100 per cent efficiency When the field changes direction the force on the electron is reversed but the direction of motion does not change abruptly (assuming no collisions occur) so that a phase lag develops between voltage and current and the loading becomes partially reactive The electron decelerates and loses energy which it passes back to the field After HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 57 few cycles a steady phase lag develops say 8 and the power dissipation can be represented in the usual manner as where Vrms and I,, are the root mean square voltage and current respectively.The value of 8 depends both on the frequency of the applied field and on the electron collision frequency, as collisions interupt the out-of-phase motion thereby promoting efficient energy exchange. At very low pressures the phase lag may approach go" leading to zero power transfer and thus i t may appear that higher pressures are most suitable for plasma operation. This is not so, since the elastic-collision energy damping becomes more important as the collision frequency goes up with the result that an optimal breakdown pressure occurs.P = Vrms Irma COSO Some recent work illustrates the problem. For example MacDonald has shownlZ6 that there is an optimal breakdown pressure of about 4 torr in argon a t 2-8 GHz whereas at 994 MHz the pressure drops to about 1-5 torr.12' It is interesting to note the closeness of these values to the experimentally determined optimal pressures for EDL operation. Assuming for the moment a temperature of 5000 K for the electrons and atmospheric pressure the collision frequency is about 5 x 1O1os-l (see p.20 of MacDonald's booklZ8). The normally used field frequency is 2.45 GHz and therefore approximately 20 collisions per field cycle can be expected which would indicate an efficient energy transfer.In the lower pressure range i.e. 1 to 10 torr the collision frequency is considerably less being similar to that of the driving field. The establishment of the ionisation equilibrium depends on the following processes : Ar + e* -f Ar+ + e + e (23) Ar+ + e + Ar + Iav (24) Ar+ + e + e + A r + e (25) which describe ionisation radiative recombination and three-body recombination, respectively. The asterisk in the equation denotes the energetic particle in the reaction. Under conditions of low electron density the occurrence of three-body collisions is rare and equations (23) and (24) principally descirbe the equilibrium. It has been ~ u g g e s t e d ~ ~ ~ ~ ~ ~ that two separate groups of electrons can exist in the system a high-energy low-density group and a low-energy high-density group.The equilibrium is then a balance between the ionisation caused by the energetic electrons and the rate of electron loss by recombination and diffusion. Kentyl31 had shown earlier that radiative recombination cross-sections decreased with increasing energy and therefore it was to be expected that the high-energy electrons would be lost mainly by diffusion and the low-energy group by recombination. The two-group model is most likely to exist at low pressures where the damping effect of collisions is less. One of the most important but perhaps least investigated aspects of analytical plasma studies is the role of impurities in the carrier gas. The presence of the impurities introduces two additional and important ionisation mechanisms.Firstly, the ionisation energy of the impurity is often much lower than that of the carrier gas (e.g. that of oxygen is 13.62 eV; that of hydrogen is 13.60 eV) and therefor 58 SHARP the impurity becomes a major source of free electrons. Secondly the existence of long-lived metastable levels in the rare gases provides the conditions under which Penning ionisation128 occurs. This can be represented by the equation Armeta + M -+ Ar + M+ + e where Armeta is the metastable argon atom and M is a concomitant gas species whose ionisation energy is less than that of the metastable level of the argon. A metastable level having a lifetime measurable in milliseconds experiences several thousands of collisions in that period and therefore the probability of collision with a trace constituent is high.Another mechanism for Penning ionisation has been suggest ed,132 However the probability of such a collision must be low. The net effect of the additional ionisation mechanisms is to lower the effective ionisation potential of the carrier gas. This phenomenon is well understood and is used in microwave breakdown studies to produce gases of varying ionisation poten-tial. For example ‘Heg’ gas (a mixture of He ‘doped’ with Hg described on p.74 of MacDonald’s book12*) exhibits an ionisation potential of 19.8 eV which is equivalent t o the energy of the first helium metastable level (ionisation energy 24.5 eV). The free electron is produced by Penning ionisation of the mercury (ionisation energy 10.4 eV).Armeta + Armeta + Ar+ + €3 + Ar Temperature of the microwave plasma Defining a meaningful temperature for the microwave plasma is more difficult than for the r.f. plasma because simple observation of the source indicates that it in no way approaches LTE. The energy-exchange process between field and electron occurs in a very short period with the result that the electrons are not thermalised and therefore attain energies far in excess of those of the neutral atoms or ions. The high velocity collision rate and excitation cross-section of the electrons causes them to play the dominant role in determining the spectroscopic properties of the microwave plasma. This is true of most non-LTE sources and under these con-ditions the concept of ‘partial LTE’ is employed.(The term ‘partial’ is used to indicate that the equilibrium is related only to that species which is dominating the collisional population of states.) Application of the Griem criteria13’ is instructive in determining whether the spectroscopically determined ‘excitation temperature,’ which is a measure of the population of states is indeed yielding the ‘electron temperature,’ defined as the temperature describing the kinetic energy of the free electrons. Winefordner et ~ 1 . ~ 3 3 reported excitation temperatures in an atmospheric-pressure argon plasma as 4980 K by using the relative-intensity method and 6560 K by using the absolute intensity of the 425.94 nm argon line. Ionisation temperatures of 5050 K and 4980 K were calculated by measuring the relative intensities of the Sr(I1) 407.77 nm/Sr(I) 460.73 nm and Ca(I1) 396.8 nm/Ca(I) 422.67 nm line-pairs respectively.The electron density was measured independently fro HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 59 the Stark broadening of the H/3 line and yielded a value of 18 x 1015 ~ r n - ~ . The plasma was operated at 100 W input and 30 W reflected power and the total gas flow was 1.2 litres per minute. Other workers have found similar excitation temperatures; for example Sharp134 obtained a value of 5680 K from the relative intensity method Sk~gerboel~~ reported a temperature of 4850 K calculated by the same method and Kawaguchi et aZ.136 reported a temperature of 5650 K from the relative intensity of the Cu 515.324 nm and Cu 510.554 nm lines.The Griem ~riteria13~ for collision-dominated equilibria are for excited states that ne 7 x 10" - 2 7 x (g)* cm-3 ,1712 where 2 is the effective charge and E the ionisation energy, and for the ground state that n is the principal quantum number where Ek is the excitation energy of the first excited state. Substituting a temperature of 5680 K and consideringlevels of n > 4inequation (26) yields Comparing this with the measured value of 1-8 x 1015 indicates that the excited-state population is in partial equilibrium with the free electrons and therefore the excitation temperatures reflect the electronic temperature. Substituting the appropriate values into the condition for equilibrium of the ground state yields ne > 1 0 1 3 ~ ~ - 3 ne > 1.2 x 1017 cm-3 However it has been showns3 that for argon self-absorption tends to decrease the effective radiational rate of population of the ground state with the result that the above condition can be relaxed by a factor of 10.A comparison of the measured and required values shows that the electron concentration is normally insufficient to guarantee that the ground state is in collisional equilibrium with the free elec-trons. Rather the ground-state population is controlled jointly by collisional and radiational mechanisms placing it in a state somewhere between the extremes of thermal and coronal eq~i1ibrium.l~' The absence of complete LTE is indicated by measurements of the neutral-gas temperature which can be accomplished quite readily with a thermocouple.Values of 873 K135 and 963 K134 have been reported. This is not surprising as enthalpy calculations of the type described for the r.f. plasma indicate that a thermal temp-erature of 5000 K is unlikely from a source which can be sustained on powers down to 20 W. Rotational temperature measurements made on the OH m 0 1 e c u l e ~ ~ ~ ~ ~ ~ have yielded values intermediate between the neutral-gas and electronic temperatures, z.e. in the range 1900 to 2400 K. It is considered that this is a further indicatio 60 SHARP of the absence of equilibrium and it suggests that the cross-section for electron excitation of rotational transitions is low. Low-pressure plasmas have also been the subject of physical studies; the most comprehensive work is that of Busch and Vi~kers.l~~ Generally slightly lower excitation temperatures have been found e.g.4300 K suggesting a somewhat lower electron temperature. This is at variance with the assumption that elastic collisional damping quenches electron energies at high pressure. Furthermore it has been established that low-pressure plasmas can be operated on air or helium (ionisation energy 24-58 eV) which appear to demand more energetic conditions, whereas only argon (ionisation energy 15.76 eV) can support a plasma at atmos-pheric pressure. It may be that these apparent contradictions are in part accounted for by the establishment of the two-electron-group system under low-pressure operation. V i ~ k e r s l ~ ~ sampled the high-energy electrons using the double-probe t e c h n i q ~ e ~ ~ ~ ? ~ ~ ~ and reported a temperature of 32 000 K in argon and 52 000 K in helium.However it remains to be proved whether these temperatures represent the mean of a Maxwellian distribution independent of that observed from excitation measurements. It is interesting to note the ubiquity of the excitation temperature which appears to fall in the range 4500 to 5500 K for a remarkably wide range of conditions. A possible explanation for this lies in the energy-dependent collisional cross-section for electrons in argon. The above temperatures yield a kT value of about 0.4 eV, and it is found that argon is almost transparent to electrons of this energy. This is known as the Ramsauer efect (see MacDonald’s book ~ . 1 8 ) . l ~ ~ For energies above this level the cross-section rises steeply thereby tending to dampen further energy increase.Analytical significance of physical plasma parameters The non-equilibrium state of the microwave plasma makes discussion of its properties extremely complex. The generalisations that apply in equilibrium conditions can no longer be made and it becomes necessary to treat each process individually which can lead to apparent contradictions. It is therefore helpful to clarify the position by considering the analytical significance of the various measurements. The total enthalpy of the microwave plasma is low as is shown by the relatively low temperature of the most prominent species the neutral argon atoms. Thermal vaporisation of particulate samples is therefore inefficient and the low degree of ionisation (about 0.02 per cent.) means that sputtering cannot be relied upon to improve the situation to a significant extent.In atmospheric-pressure free-flowing plasmas it is found that small quantities of molecular gases e.g. about 5 per cent. of nitrogen quench the plasma. These considerations lead to the conclusion that sampling is of critical importance in determining the application of the source for emission spectrometry. If possible the sample should be presented to the source in a pre-atomised condition and ready for excitation and whilst it is possible t HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 61 introduce fine particulate material etc. the loading must be small and even so, interferences are likely to occur. Given that a satisfactory sampling procedure exists the microwave plasma is an efficient excitation source that possesses a sufficient number of high-energy elec-trons to excite a t even quite energetic levels.For example a spectral plot of the plasma emission between 275.0 nm and 440.0 nm shows the presence of the nitrogen second-positive system which originates from a level 11.1 eV above the ground state. A number of possible excitation mechanisms exist. These are (28) (29) e* + M -+ M* + M + h v e* + M -+ M+ + e -+ M + hv Collisional excitation Radiative recombination Ar,,t + M -+ Ar + M+ + e -+ M + IZV Armeta + M -+ M* + Ar -+ M + hv Radiative recombination Collision exchange excitation (30) (31) Vickers13* has proposed that the mechanism of equation (29) dominates at low pressure.Also processes such as those of equations (30) and (31) are more important at low pressure when the number of metastable species is greater.13* At atmospheric pressure it is to be expected that direct collisional excitation will become more important. The balance between the various processes depends not only on the plasma conditions but also on the excitation and ionisation potentials of the species in question. At present there are insufficient systematic experimental data to determine the exact nature of the excitation under all conditions. Micro wave cavities The function of the microwave cavity is to act as a resonant structure at the Discharge tube r .-:* $2 Tuning adjustment I Air hose connect ion 1 *- Inch Scale Fig.3. The three-quarter-wave ‘Broida cavity 62 SHARP applied frequency thereby yielding a higher field strength and containing the field to a well defined region. Various cavities have been employed all following the designs described by Fehsenfeld et a1.,l4l of which the most commonly used types are the ‘foreshortened &wave coaxial’ type the ‘Broida’ cavity and the ‘foreshortened $-wave coaxial’ type the ‘Evensen’ cavity (see Figs. 3 and 4). Section A - A ______ 3 A Dis\charge L B cap Section B - B Inch Fig. 4. The quarter-wave ‘Evensen cavity’ 1 tube Scale A simplified equivalent circuit for the cavity and input leads comprises a conduct-ance g, representing the transmission line in series with a complex impedance, itself made up of conductive inductive and capacitive components in parallel (values g I and c respectively) representing the cavity.The conductance gs makes allowance for the losses in the transmission line due to the imperfect nature of the conductors. The cavity has a resonant angular frequency of w,. The lumped impedance of the line and circuit as ‘seen’ by the generator is 1 1 gs z = - + g + j ( w c - 1/ 4 which at resonance reduces to 1 1 z= - + -gs g Unfortunately operation of a plasma in the cavity changes both the impedance and resonant frequency of the device with the result that tuning is necessary to restore the power-coupling efficiency. A wave travelling down the transmissio HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 63 line is partially absorbed in the cavity (by the plasma) and partially reflected, thus setting up a standing wave.When the impedances are matched no reflected wave occurs and all the power is dissipated in the load. The process of tuning therefore amounts to minimising the magnitude of the reflected wave and this is accomplished by inserting a directional coupler in the line which enables the forward and reverse powers to be measured simultaneously. The impor-tance of tuning is found to depend very much on the cavity design. The &wave cavities appear to be quite insensitive to tuning adjustment whereas the &wave devices require critical adjustment for optimal operation. A well tuned $-wave cavity appears to give a stronger field than the %-wave type and it is a charac-teristic that the field appears to ‘peak’ opposite the central tuning electrode.The smaller dimensions of the former type permit greater access to the plasma, although the tube being exposed to the atmosphere is less thermally isolated from the environment. To date no experimental evidence has been reported to suggest that significantly greater analytical sensitivities are obtained with any particular type of cavity. Analytical development and application of the microwave plasma The original paper by Cooke et aZ.125 described the application of an atmospheric-pressure argon plasma operated as an emission detector for compounds eluted from a gas chromatograph. The species measured included CN C, CH I CS P PO, PS CC1 and F (as SiF,). Using a flow rate of 20 ml per minute and a gas input temperature of 373 K sensitivities in the range 2 x 10-l6 g s-l to 5 x 10-lo g s-l were reported.The effect of power on the emission signal was investigated and was found to vary considerably depending on the species under observation. The authors commented on the possibility of structural elucidation from the fragmenta-tion pattern and in doing so succeeded in anticipating some of the later studies. Immediately following Cooke et al. Bache and Lisk14 described a similar system in which the P 253.56 nm atomic line was used to determine organophos-phorus residues in crops. The samples were extracted into acetone or ether and sensitivities of 1.4 x 10-l2 to 3.3 x 10-l1 g s-l were obtained. Column splitting was employed to vent the solvent in order to prevent extinguishing the plasma.Later papers by the same authors described modifications to the system and further applications. Use of a low-pressure plasma a t 200 torrlg3 yielded an increase in sensitivity of one order of magnitude for phosphorus determinations. A further improvement was made by changing to low-pressure helium as the carrier gas144 and operating the plasma in a thick-walled (8.0 mm 0.d. ; 1.5 mm i.d.) tube. The thick-walled tube had a longer life than the thin-walled type and facilitated the thermostatic control of the plasma. The system was applied to the determination of drug compounds and of pesticide residues. More recently the determination of organomercury in fish in the range 0-05 to 1.0 p.p.m. has been r e ~ 0 r t e d . l ~ ~ Other workers have studied the use of the microwave detector for gas chromato-g r a p h ~ .~ ~ ~ - ~ ~ ~ Dagnall and co-~orkersl~~ reported the simultaneous measurement of the C 247.9 nm line with that of a hetero species from the molecule as a mean 64 SHARP of determining the ratios of the hetero-atoms to the carbon atoms. This technique has been developed and a commercial system is now available offering the simult-aneous detection of up to 15 species. Atmospheric detection of species such as NO, CO and CH has been studied,15* using an ion exchange column to produce molecular iodine which was subsequently measured at the iodine atomic line at 206.1 nm. Direct determination of impurities in cylinder gases has also been rep0rted.1~5 The detection and measurement of metallic species in a microwave plasma was first described by Runnels and G i b ~ 0 n .l ~ ~ Their system employed a $-wave cavity and atmospheric-pressure argon gas flowing at 300 ml per minute through a 1-mm bore quartz plasma tube. Volatile copper iron cobalt and chromium acetylaceto-nates were vaporised into the plasma from a resistively heated platinum loop and the various system parameters investigated. Increasing power yielded an increase in intensity from the Ar 430.0 nm line whereas emission from the Cu 324.75 nm line decreased. The authors gave no interpretation of this effect and do not appear to have carried out any further experiments to clarify the behaviour. This raises an important point regarding the effect of increasing power on the signal. I t i s observed that when the power to the plasma is increased the length of the plasma also increases.Add to this the fact that the emission intensity shows a steeply varying intensity along the discharge and it is apparent that change in spatial intensity has to be allowed for before effects such as ionisation can be considered. Systematic evidence for the effect of increasing power in atmospheric-pressure plasmas is scant although it is interesting to note that the intensities of argon (Ei = 15.8 eV) and zinc (Ei = 9.4 eV) lines have been reported to i n ~ r e a s e l ~ ~ l cadmium (Ei = 9.0 eV) is reported to stay approximately constantl57 and copper (Ei = 7.6 eV) is reported to decrease156 with increasing applied power. This may indicate that the degree of ionisation is partly responsible for these phenomena.Detection limits for the system were in the 10-11 to 10-12g absolute range and linearity over four orders of magnitude was obtained. A platinum-loop sampling technique was used in the determination of a range of metals in a plasma burning at the tip of a quartz ~api1lary.l~~ Skogerboe et aZ.13j had previously studied plasma conditions in relation t o the determination of pesticides and sulphur compounds. Both emission and absorption measurements were reported and the best results were obtained with a helium plasma operating at 3 torr. The cold-vapour generation technique,158 used in determining traces of elements such as mercury and arsenic by atomic absorption spectrometry has been successfully adapted to the microwave plasma source.159,160 Measurements at the 0-01 p.p.m.level yielded precisions of 10 to 12 per cent. and the sensitivity of the emission technique was claimed to be two orders of magnitude better than that obtained using the absorption method. Continuous nebulisation of solutions into the plasma has been reported by various a~thors.~33~~36~161 The sensitivity of the plasma to molecular species necessitates the use of de-solvation systems although Lichte and SkogerboelG1 reported that the tolerance level of the plasma could be considerably raised by mounting th HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 65 plasma tube axially and providing additional cavity tuning. Another improvement in this system was obtained by the ‘end-onJ viewing of the plasma thereby increasing the apparent optical depth of the emitting gas (see Fig.5). The high sensitivities reported (see Table I) were no doubt in part due to this geometry and to the use of the derivative technique162 of signal measurement. Linearity extending over three orders of magnitude is considered to indicate that self-absorp-tion was not too serious a problem with the relatively long optical path used. Microwave power i-l-Fine tuning stub r-l Argon sample Impedance matching - t adjustment Air coolant / Y Y + Fig. 5. Axially mounted plasma tube and tuning arrangement for quarter-wave cavity Chemical interference in the microwave plasma is common and is attributable to the low temperature of the gas in the source. The classical calcium/phosphate and aluminium/calcium interferences have both been ~ b s e r v e d .l ~ ~ l ~ ~ D e n t ~ n l ~ ~ has studied the microwave excitation of the tail-flame gases of a d.c. capillary arc, using the arc as a thermal atomiser prior to excitation. Interferences were still observed but an advantage of the system is that sample-loading capability is greatly increased being determined by the arc and not by the microwave plasma. The relatively low gas temperature of the plasma may lead to interference problems, but at the same time it makes sample introduction relatively easy. However the rod-like geometry of the plasma is not ideal for sample introduction and an LTE plasma of similar excitation temperature and geometry would exhibit severe sample rejection characteristics. Ionisation interferences are to be expected and indeed indications that they occur have been r e ~ 0 r t e d .l ~ ~ The effect however, has not been universally observed and Skogerboe could find no effect of increasing sodium concentrations on elements having ionisation potentials down to 6.7 eV. The adaptability of the microwave emissive detector is evident from the wide range of instrumental systems and compounds studied. The detection limits and sampling procedure for a range of species are shown in Table I. Unfortunately the different conditions reported in the various papers limit the extent to which com-parisons can be made and more work is required before a comprehensive under-standing of the properties of the source is possible 66 SHARP Conclusion The development of non-flame-like electrodeless plasmas is undoubtedly making an impact on analytical chemistry.The traditional advantages of the emission technique - sensitivity selectivity and multi-element capability - are increasingly demanded in analytical applications and the development of the new plasma sources has greatly extended the range of problems to which emission spectrometry can be applied. Over the last 10 years atomic absorption spectrometry has undergone a dramatic development and growth so that today it is one of the major techniques for elemental analysis. The sensitivities from both flame and non-flame methods (see, for example the review by LVinef~rdnerl~~) are now adequate for the majority of analyses and therefore some levelling-off in the development of the technique seems probable.Specific areas may yet see considerable advances for example in the field of automated analyses and instruments dedicated to a limited range of elements; but the most probable growth point seems to be in simultaneous multi-element analysis and in this respect atomic absorption has several inherent limitations that are difficult to overcome. If this new need is to be met the most promising alternatives are atomic fluores-cence or atomic emission. The technique generally adopted will for prosaic and pragmatic reasons be one for which reliable equipment is available. In the reviewers’ opinion atomic fluorescence will not be accepted unless a truly reliable multi-element source is found and in this area EDLs and lasers are the principal contenders.By the same argument emission spectrometry will not be adopted unless a fairly universal source is available. For the latter technique electrodeless plasmas are quite well advanced towards meeting the appropriate requirements, and therefore emission spectrometry appears to be the most probable area for expansion. This expansion will only occur if commercial instruments are made available since most analytical chemists are users rather than developers of equipment. Once the first instruments appear the trend is likely to be followed by others since manufacturers are unlikely to relish developing two instrumental systems with similar functions- and indeed the potential market might not support such diversification. Assuming that the predictions concerning the future of emission spectrometry are correct it remains to assess the role that electrodeless plasmas will play.The r.f. plasma torch is potentially the most versatile emission source available. Its sampling and spectroscopic characteristics are such that it can be applied to an extremely wide range of elements in almost any matrix and yield high sensitivity (p.p.b. range) relatively good precision (about 0.5 per cent.) good selectivity and multi-element analytical capability. Laboratories dealing with industrial products natural waters geological samples biological samples or clinical testing, all have requirements which could be met in part by such a system. It is therefore conceivable if the merits of the technique are widely acknowledged that many laboratories in the future will use r.f.plasmas and that these will in part replace and in part complement the role of the atomic absorption spectrophotometer HIGH-FREQUENCY ELECTRODELESS PLASMA SPECTROMETRY 67 It is true to say that the microwave plasma must be regarded as of more limted scope than the r.f plasma. 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Inductively Coupled Radio-frequency Plasmas 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 Kornblum G. R. and deGalan L. Spectrochim.Acta 1974 29B 249. Dreher G. B. and Frank C. W. Appl. Spectry. 1974 28 191. Fassel V. A. and Kniseley R. N. Anal. Chem. 1974 46 lllOA 1155.4. Runser D. J. and Frank C . W. Appl. Spectry. 1974 8 175. Kniseley R. N. Amenson H. Butler C. C. and Fassel V. A. Appl. Spectry. 1974, 28 285. Larson G. F. Fassel V. A. Scott R. H. and Kniseley R. N. Anal. Chem. 1975, 47 238. Kirkbright G. F. Proc. Anal. Div. Chem. SOG. 1975 12 8. Barnes R. M. and Schleicher R. G. Anal. Chem. 1975 47 724. Butler C. C. Kniseley R. N. and Fassel V. A. Anal. Chem. 1975 47 834. Greenfield S. Jones I. LL. McGeachin H. McD. and Smith P. B. Anal. Chim. Acta, 1975 74 225. Scott R. H. and Kokot M. L. Anal. Chim. Acta 1975 75 257. Mermet J . M. and Robin J. Anal. Chim. Acta 1975 75 271. Scott R. H. and Strasheim A. Anal. Chim. Acta 1975 76 71. Kaluicky J. Kniseley R. N. and Fassel V. A. Spectrochim. Acta 1975 30B 511. Barnes R. M. and Schleicher R. G. Spectrochim. Acta 1975 30B 109. Boumans P. W. J . M. and De Boer F. J. Spectrochim. Acta 1975 30B 309. Mermet J. M. Spectrochim. Acta 1975 30B 361. Greenfield S. McGeachin H. McD. and Smith P. B. Talanta 1976 23 1. Lapworth K. C. and Allnutt L. A. Inst. Phys. Conf. Ser. No. 26 1975. Microwave Plasmas 184 185 186 187 188 189 190 191 192 193 194 Nakashima R. Sasaki S. and Shibata S. Anal. Chim. Acta 1974 70 265. Van Sandwijk A. and Agterdenbos J. Talanta 1974 21 360. Middleboe V. Appl. Spectry.. 1974 28 274. Toda S . Aizawa K. Takahashi N. and Fuwa K. Anal. Chem. 1974 46 1150. Greenfield S. McGeachin H. McD. and Smith P. B. Talanta 1975 22 553. Kawaguchi H. and Vallee B. L. Anal. Chem. 1975 47 1029. Talmi Y. Anal. Chim. Acta 1975 74 107. Watling R. J. Anal. Chzm. Acta 1975 75 281. Brassem P. and Maessen F. J . M. J. Spectrochirn. Actn 1975 30B 547. Avni K. and Winefordner J . D. Spectrochim. Acta 1975 30B 281. Layman L. R. and Hieftje G. M. Anal. Chem. 1976 47 194