Anal. Chem. 1989, 6 1 , 1243-1248 (25) Kysllka, J.; Blchsel, S. E. In Proceedings of the 1984 Sugar Processing Research Conference, Oct. 16-18, New Orleans, LA; U S . Department of Agriculture, Agriculture Research Service ARS-49, 1986. (26) Felton, H. J . Chromatogr. Sci. 1969, 7 , 13-16. (27) Goodall, D. M.; Cross, M. T. Rev. Sci. Instrum. 1975, 4 6 , 391-397. (28) Clayton, G. B. Operational Ampifiers, 2nd ed.; Butterworths: London, 1979; p 76. (29) Alkemade, C. Th. J.; Snellman, W.; Boutllier, 0.D.; Pollard, B. D.; Wlnedorfer, J. D.; Chester, T. L.; Omnetto, N. Spectrochim. Acta 1978, 338,383-399. (30) Djerassi, C. J. Optical Rotatory Dispersion; McGraw-Hill: New York, 1960.
1243
(31) Knox, J. H.; Done, J. N.; Fell, A. F.; Gilbert, M. T.; Pryde, A,; Wall. R. A. High Performance Liquid Chromatography; Edinburgh University Press: Edinburgh, U.K., 1977.
RECEIVED for review July 5,1988. Accepted February 27,1989. This research was supported by the University of York’s Research and Innovation fund and by the British Technology Group, who have also made patent applications concerning this detector.
Relative Elemental Responses for Laser Ablation-Inductively Coupled Plasma Mass Spectrometry James W. Hager
S C I E X , 55 Glen Cameron Road, Thornhill, Ontario L 3 T 1P2,Canada
A method for determlnlng relative elemental response factors for laser ablation-Inductively coupled plasma mass spectrometry Is described. The model uses response factors determined from solution nebuilzatlon and modHles them based on the element-dependent volatillzation effIclencles, whlch can be calculated or determined empirically. Comparisons between observed and calculated relative responses for Qswltched and free runnlng laser ablatlon of steel, copper, and aluminum standards are presented. I n general, the agreement Is wlthln approximately f50 %. The implications of this approach for semiquantitatlve analysls of solids for which standards are not available are discussed.
INTRODUCTION The ability of focused laser radiation to volatilize virtually any material has provided the analytical chemist with a versatile method of direct solid sampling for subsequent analysis (1). Within the last several years laser solid sampling has been combined with analytical techniques such as atomic absorption (2),microwave-induced plasma atomic emision (3), dc plasma atomic emission (4-6), inductively coupled plasma atomic emission (7), and inductively coupled plasma mass spectrometry (ICP-MS) (49)with varying degrees of success. Because of the diversity of these atomic spectroscopic techniques and the wide range of laser characteristics employed, it has been difficult to assess the degree to which laser ablation competes with other techniques for direct solid analysis. A recent comparison by Arrowsmith (8)however suggests that laser sampling ICP-MS is characterized by comparable or better detection limits than several conventional techniques. The reasons behind the proliferation of laser ablation sampling are clear. Minimum sample preparation, a reduction of injected solvent, and microprobe capabilities have driven the development of this versatile technique. Furthermore, laser volatilization can be used to sample a wide variety of materials including conductors, semiconductors, superconductors, and dielectrics. Considering the good detection limits reported for laser ablation-ICP-MS and the range of solid types that can be sampled, it appears that laser solid sampling has secured a permanent place on the list of sample introduction techniques for atomic spectroscopy. There are, however, potential difficulties associated with laser ablation techniques. Previous investigators have shown
that the sensitivity of laser sampling with ICP-MS detection is dependent on the mode of operation of the laser (long or short pulse duration) and physical properties of the solid (8). A degree of elemental selectivity in the laser volatilization process, leading to relative elemental response factors differing significantly from unity, has also been observed (8). This presents the question: to what extent are the signals measured at the detector truly representative of the elemental composition of the solid? Ideally, one would like to be able to relate the analytical signals to the material properties, the elemental response factors determined from solution nebulization, and the laser sampling conditions in a comprehensive fashion. In this publication, a model of laser solid sampling is presented and used to explain some recent laser ablation ICP-MS experimental results. Such a model is potentially of great utility in helping to understand the important experimental parameters in the sampling step. Since the laser solid sampling in laser ablation-ICP-MS is separated from the atomization and ionization steps of the ICP, it is possible to characterize the efficiency and elemental selectivity of the sampling process itself and convolute these characteristics with those of the spectroscopic technique to obtain an overall picture of the analytical method. The goal is to obtain standardless full elemental analysis with a minimum of sample information.
THEORY The model described here is based on laser-induced heating of an opaque surface producing a phase change of the material. For even a simple treatment of such complex phenomena it is necessary to include properties of the laser radiation, the solid material, and the laser beam-solid interaction. A review of previous approaches can be found in ref 1. From the outset, it is assumed that the infrared laser light incident on the sample surface is not attenuation by any vaporized particulate matter or any laser-produced plasma. The absorbed energy is considered to be instantaneously converted into heat where the laser beam is incident on the sample. At infrared wavelengths this process occurs rapidly with respect to nanosecond or longer laser pulses (10). A further assumption is that local thermodynamic equilibrium is established during the pulse, consequently the concept of temperature is valid, and the usual heat flow equations can be applied. One can think of the laser as a heat source with a characteristic temporal and spatial extent with the amount of heat actually coupled into the solid being dependent on the
0003-2700/89/0361-1243$01.50/0 0 1989 American Chemical Society
1244
ANALYTICAL CHEMISTRY, VOL. 61,
NO. 1 1 , JUNE
1, 1989
absorbance of the sample at the laser wavelength. At the termination of the laser pulse, the thermal properties of the sample will dominate the model. Thus, the efficacy of the laser-induced volatilization in intimately related to the temperature rise of the affected volume within the sample (1&12). The solid sample will be considered to be a semiinfinite medium with a boundary at the plane z = 0. This is a reasonable assumption when the focused laser beam diameter is much smaller than the sample dimensions (10-12). It is also assumed that the thermal properties of the solid are temperature independent. The theoretical difficulties of including the true temperature dependence of the thermal properties have been discussed by Carslaw and Jaeger (13). Perhaps the largest simplification made here is that the absorbance of the sample material at the laser wavelength is independent of temperature and laser pulse characteristics. Even for nominally transparent solids such as sapphire, the initial portion of a microsecond duration laser pulse can transform the material from nonabsorbing to strongly absorbing (14). There is also evidence that the absorbance of metals is significantly enhanced near the end of free running laser pulse relative to the value measured during the early portion of the pulse (14). Previous investigators have employed a constant, average value of the absorbance which is significantly greater than the ambient value (10.12,15). For the purposes of the present investigation, absorbance values at the laser wavelength have been calculated by using the technique of Johnson and Cristy (16). The heat flow equation for radiation heating of a semiinfinite slab of material with a boundary at t = 0 is given by (13) -KVT(r,z,t)
dT + C-(r,t,t) dt
= Q(r,z,t)
(1)
where K and C are the material thermal conductivity and heat capacity per unit volume, respectively, T i s the position- and time-dependent temperature, and Q is the heat coupled to the material. The heating of the material initially takes place within a small volume and may be expressed to good approximation as (12) Q(r,z,t) = (1 - R)I(r,t)a exp(-at) (2) where R is the reflectivity of the material, Z(r,t) is the laser irradiance (W/cm2),and a is the absorption coefficient of the target. In order to construct a realistic picture of the effects of the laser beam-sample interactions, one must consider both the spatial and temporal extents of the laser pulse. The laser irradiance as a function of position and time may be approximated as (10) where I,, is the peak laser irradiance in W/cm2, p ( t ) is the normalized temporal shape of the laser pulse, d is the radius of the Gaussian laser spot, and r is the radial coordinate measured from the center of the spot. This leads to the following form of the heat flow equation:
aT at
-KV2T(r,z,t) + C-(r,z,t)
=
(3
(1- R ) I m a g ( t )exp -
LY
exp(-az) (4)
This equation consists of terms incorporating characteristics of the solid, the laser pulse, and the laser-solid interaction. Since the absorption coefficients of metals are on the order of lo5 to lo6 cm-‘, it is reasonable to assume that the heat is produced initially-only a t the surface (10-12). Under these conditions, the solution of the heat flow equation, and thus
the temperature a t time t within the solid, can be expressed as (10) T(r,z,t) = AIrnaxd’ :)2 p ( t - t’) d t ’
(
1
K
W(4K
&
+ d2)
- 4 ~ r2 t+ ’ d2
1
(5)
Here, the thermal diffusivity K has been introduced (K= K/C). In general, eq 5 must be integrated numerically once the spatial and temporal characteristics of the laser pulse have been determined. In the present investigation, only laser ablation using pulsed Nd:YAG lasers operating at 1064 nm is considered. Consequently, two limiting types of behavior are treated Q-switched and free running laser operation. The laser pulse shapes used for the purposes of these calculations are smooth Gaussian distributions with full widths a t half height of 8 ns and 120 ws for $-switched and free running operation, respectively. For the sake of simplicity, relaxation oscillation structure commonly observed for free-running laser pulses has been omitted. Once the temperature of the material has been determined, the next step in the construction of the model is to obtain an approximate expression for the elemental number density in the laser-produced vapor as a function of the temperature of the solid. Under the assumption of phase equilibria, the time rate of change of the number of atoms (n,) of a particular element in the solid is given by (10, 17) dn, _ d t -- *on’ex’
(
--
L:T)
where vo is the Debye frequency, M is the atomic weight, L is the amount of energy required to volatilize the element per unit mass, No is Avogadro’s number, k is Boltzmann’s constant, and T i s the temperature of the solid. Thus, the number of atoms of a given element in the vapor (n,) is related to the number in the solid by the relationship (10, 17)
n,
-
n, exp( NokT E
)
(7)
Equation 7 suggests that one may observe a degree of elemental enrichment in the vapor relative to the concentration of that element in the solid sample depending on the material temperature. Considering two elements in the solid with equivalent concentrations but different characteristic energies required to produce vapor phase atoms ( L ) ,the vapor concentration of an element with the lower value of L will be greater than that of an element with a higher value. Only at infinitely high temperatures do the elemental concentrations in the vapor directly reflect those in the solid sample. One should recall at this point that the temperature of the solid sample will be a function of the laser pulse Characteristics, the thermal properties of the material, and the absorbance of the sample at the laser wavelength. Furthermore, the temperature of the solid will be both position- and time-dependent. The spatial dependence is determined by the focused laser spot size and the thermal conductivity of the material. The temporal dependence is determined by the laser pulse width and the thermal diffusivity of the sample. In what follows, this thermal model is used to explain the element selectivity observed in recent laser ablation-ICP-MS experiments. To a larger extent, elemental response factors for a variety of sample materials can be predicted by use of this model, allowing for rapid semiquantitative analysis.
EXPERIMENTAL SECTION The apparatus employed in the experiments reported here is an advanced prototype laser ablation-ICP-MS instrument. The
ANALYTICAL CHEMISTRY, VOL. 61, NO. 11, JUNE 1, 1989
Nd:YAG laser (Quantel YG660A-20) was operated at the fundamental wavelength of 1064 nm and a repetition rate of 20 Hz. Since optimum ion signal was obtained at less than full laser power, the pulse energy was reduced from the maximum value of 400 mJ to 200 mJ via the flashlamp voltage control and neutral density filters. The laser beam was focused onto the target material with a 75 mm focal length “best form” singlet lens. In order to reduce the laser-produced plasma formed above the sample during Q-switched operation, the laser beam was slightly defocused by placing the lens 70 mm above the sample. The measured crater diameters with this configuration are approximately 150-200 pm. The laser could be operated in either Qswitched (8 ns pulse duration, fwhm) or free-running (150 ps duration) mode. The laser irradiance for these two operating conditions was 8 X 1O’O W/cm2 (Q-switched)and 4 X lo6 W/cm2 (free-running). The ablation events were monitored collinearly with the laser beam with a closed circuit television (Hitachi KP-130) and 9-in. monitor (Hitachi VM 920) with a variable magnification of up to approximately 300X. Since the various sample types examined were of different heights, this viewing system proved to be critical for correctly positioning the samples in the vertical dimension. Initially, the image was focused at the vertical position of the first sample. Thereafter, the vertical stage was adjusted until the image of the surface of subsequent samples came into focus. In this manner, the distance between the laser focusing lens and the sample could be maintained precisely without any actual measurement. The sample cell employed here is designed for a 90° ablation geometry but is otherwise similar to that reported earlier (8). The window is high transmission quartz and is slightly angled in order to minimize damage to the optics from back reflections. The microparticulate transfler line is also similar to that in an earlier publication (8). The ICP-MS instrumentation is a standard Perkin-Elmer SCIEX ELAN 500. For all of the studies described here the forward power was 1.25 kW, the outer argon gas flow was 12.0 L/min, and the auxiliary argon flow was 1.2 L/min. The sampler to load coil separation was maintained at 16 mm. For the laser ablation measurements, the transport gas flow was regulated at 1.80 L/min with a mass flow controller. For the solution nebulization work, a Meinhard TR30-C3 nebulizer was used with a nebulizer flow of 0.85 L/min and a sample uptake rate of 0.60 mL/min. The spray chamber was maintained at room temperature. The voltages to the ion lenses were optimized in the usual way with a multielement standard solution to give equal response for 100 ppb Li and U and maximal response for 100 ppb Rh. Once set, these voltages were not altered between laser ablation and solution nebulization. When operation was at laser repetition rates greater than 1 Hz, the ion signal at the detector was found to be steady in time allowing conventional data acquisition software to be employed. Operation of the mass spectrometerwas in the peak hopping mode which involves repeated measurements among a set of preselected masses. The measurement process involved 100 repeats with a measurement time of 0.100 s for a total measurement time of 10 s/peak. Signal optimization was carried out as published earlier (8).
Solution standards were prepared in dilute nitric acid with trace element concentration in the 10-100 ppb range and the major element concentration at 1000 ppm.
RESULTS AND DISCUSSION In order to assess the degree to which the elemental concentrations in the laser-induced vapor reflect the true concentrations in the solid sample, a series of homogeneous metal standard reference materials have been examined by laser ablation sampling-ICP-MS. An internal standardization technique was employed to correct for sample-to-sample variations in the amount of material ablated and, thus, the absolute ion signals. The results are reported in terms of a relative element-dependent response which is defined as
-N-E ) R(IS)
I(E) ---
C(IS) C(E) I(IS)
(8)
1245
where E and IS refer to the element of interest and the internal standard, respectively, I is the measured ion intensity, and C is the concentration of the element in the solid. All of the relative elemental responses have been normalized to 100% isotopic abundances. The values of R(E)/R(IS) are, in effect, measures of the relative efficiencies for laser ablation, material transport to the ICP, ionization by the ICP, transmission of the ions from the ICP to the electron multiplier, and detection. The most important of these processes in determining any element selectivity for a homogeneous sample are likely to be volatilization by the laser, ionization, and ion transmission. Furthermore, since the sample generation technique and ionization are separated in laser ablation-ICP-MS, these processes can be considered independently, i.e.
Within the framework of the theoretical treatment presented earlier, the element dependence of the laser sampling is primarily determined by two factors: the temperature to which the affected area of the sample is heated by the laser radiation and the potential energy wells in which the individual elements find themselves a t the solid surface. By use of eq 7 the contribution of the laser-induced volatilization to the overall response is given by
where TA is the “ablation temperature”. The value of TA may be calculated by integrating eq 5 assuming that the relevant details of the laser, the material, and the absorbance of the material a t the laser wavelength are known. The element-dependent ionization efficiency of the ICP and ion transport to the detector can be determined empirically by measuring the relative elemental responses for nebulization of a multielement standard solution
Inserting eq 10 and 11 into eq 9 yields the overall relative elemental response equation
(””)
R(lS)
= TOTAL
Of course, this relationship is only expected to be approximately correct for several reasons. Equal transport efficiencies from the vaporization to the ionization regions have been assumed for all elements. This assumption will break down when the vapor contains inhomogeneous particulate matter for which transport efficiency from the sample to the ICP is low or that is too large to be atomized and ionized efficiently. In addition, any mass-dependent discrimination effects in the ion transmission efficiency (18) from the plasma to the detector have been assumed to be the same for solution nebulization and laser sampling. Despite these approximations however, the most important factors influencing the relative elemental responses, namely the laser solid sampling and the ionization by the plasma, are specifically included. At this point it is important to note that the only quantity in eq 12 that has not been explicitly specified or is not a value determined by experiment is TA. The element-dependent values of L used here are readily available from tabulations of the heats of formation of gaseous atoms from elements in
1246
ANALYTICAL CHEMISTRY, VOL. 61, NO. 11, JUNE 1, 1989
Table I. Relative Elemental Responses for Standard Steels R(E)/R(Ti)
fit to eq 13 element
IP, eV
L , eV
observed $-switched
Mg
7.64 6.82 6.74 6.76 7.43 7.86 7.72 9.39 9.81 6.84 6.88 7.10 7.57 7.34 8.64 5.60 7.88 7.98 9.22 7.42 7.29
1.52 4.87 5.33 4.13 2.94 4.44 3.50 1.35 3.14 6.31 7.48 6.82 2.95 3.13 2.74 4.38 8.10 8.81 3.82 2.03 2.17
2.35 1.oo 0.96 1.20 0.75 0.25 0.62 0.12 0.06 0.84 0.45 0.32 0.67 0.90 0.72 5.30 0.10 0.10 0.16 1.92 2.10
Ti
v
Cr Mn co
cu
Zn As Zr Nb Mo
&
Sn Sb Ce Ta W Au Pb Bi
their standard states, derived from vapor pressure data (19). It should also be noted that the source of the matrix dependence of the relative vaporization efficiencies in this model is the vaporization temperature TA,not the values of L(E), which are constants. A least-squares fit of the experimentally determined (R(E)/R(IS))TOTALvalues to an equation of the form
will determine the value of T A and, in turn, provide important information regarding the laser sampling step. The relative elemental response factors measured for both Q-switched and free-running laser ablation-ICP-MS of NBS standard steels (SRM 661-665) are presented in Table I. Both sets of response factors were obtained by using the 4sTi+ion intensity as the internal standard and normalizing the data for 100% isotopic abundances. With the exception of the mode of operation of the laser, these two sets of values were obtained with the same laser energies, with the same focusing conditions, and under identical ICP-MS operating parameters. Within this context, the significant differences between Qswitched and free-running performance are striking. The measured relative elemental response factors shown here for Q-switched laser ablation-ICP-MS are much closer to unity than those obtained with a free-running laser. In the Qswitched results the lowest response factors were obtained for As (0.06) and the highest for Ce (5.3). As can be seen from the first ionization potentials also listed in Table I, this is what one might have expected if the ionization step dominated the elemental responses. For ablation with a free-running laser, the range of experimental relative response values is considerably wide, e.g. 0.005 for W and 20.4 for Pb. One should note from Table I that tungsten has one of the highest values of L and lead has one of the lowest values. There is little correlation between the relative responses and the respective ionization potentials. Thus, in changing the nature of the laser pulse in the laser ablation-ICP-MS, the relative elemental responses go from exhibiting a strong dependence on the ionization step (Q-
( T = 26000 K) Q-switched
observed free running
2.70 1.oo 0.81 1.05 0.71 0.37 0.55 0.29 0.07 0.78 0.47 0.51 0.70 0.99 0.63 5.60 0.14 0.10 0.29 2.13 2.01
32.10 1.00 0.50 1.80 3.42 0.50 1.47 4.29 0.21 0.20 0.10 0.08 3.10 3.90 4.15 10.40 0.007 0.005 0.58 20.40 18.52
fit to eq 13 ( T = 9000 K) free running 37.20 1.00 0.57 2.05 3.72 0.56 1.80 5.89 0.30 0.24 0.06 0.18 3.72 4.46 3.94 4.41 0.009 0.003 0.73 24.07 20.35
switched operation) to being determined largely by volatility considerations (free-running operation). The relative responses obtained by the fit of eq 13 to the experimental values are also presented in Table I. Recall that there is only one independent parameter involved in the fit, TA. In both instances, Q-switched and free-running operation, the correlation between the experimental results and the model is very good and provides a measure of the ablation temperature for the two modes of laser operation. The temperature of ablation determined by the fit for the Q-switched laser is 26 000 K and that for the free running laser is 9000 K. The average temperature rise of steel by laser heating has also been calculated by making use of eq 5. Average temperatures were obtained by numerically integrating eq 5 over the respective laser pulse duration and spatially averaging the results over the volume of the material heated above the boiling point of the target material. The results for laser heating of steel give a calculated average temperature rise of 35 000 K for the Q-switched laser and 11000 K for the freerunning laser in reasonable agreement with the best fits to the experimental results. This implies that the thermal model of laser sampling is indeed a reasonable approach for gaining insight into this complex phenomenon. It should be noted that the ablation temperatures under discussion here are higher than those normally associated with the heating of metals. As has been discussed by Ready (IO), laer heating of metals often results in temperatures greater than 10 000 K. Vaporization by a Q-switched laser leads to the production of a small amount of “blowoff”material early in the laser pulse. There is an associated recoil pressure exerted upon the irradiated target that effectively raises the boiling point of the material above the conventional vaporization temperature. In addition, the blowoff material itself can absorb a significant portion of the incoming laser light. This material may become thermally ionized and reradiate back to the target surface. The result is a high-temperature laser-produced plasma with an electron density as high as 1018-1019cm-3 (20, 21) that can lead to additional sample heating. These points are treated in considerable detail in ref 10. Relative elemental responses have also been determined for copper and aluminum standards. Table I1 presents the
ANALYTICAL CHEMISTRY, VOL. 61, NO. 11, JUNE 1, 1989
Table 11. Relative Elemental Responses for Standard Coppers
R(E)/R(Ag) fit to eq 13 fit to eq 13 observed (T= 9000 K) observed (T= 3750 K) element Q-switched Q-switched free running free running Cr Mn co
Fe Ni Zn
As Ag Sn Sb Au Pb Bi
0.47 0.94 0.17 0.22 0.25 1.61 0.08 1.00 1.24 1.20 0.15 4.95 5.12
0.55 1.00 0.15 0.18 0.14 1.58 0.08 1.00 1.02 1.06 0.20 6.47 5.47
0.05 0.56 0.006 0.009 0.008 14.6
0.04 1.00 0.27 0.99 0.03 18.4 10.2
0.03 0.45 0.003 0.003 0.003 16.4
0.03 1.00 0.39 0.73 0.02 17.3 11.3
observed and calculated relative responses for NBS copper standards (SRM 498 and 500) for both Q-switched and freerunning laser ablation-ICP-MS. In both cases, elemental responses display wider variation than the corresponding steel results. The best fit of eq 13 yields TA values of 9000 K (Q-switched) and 3750 K (free running). These two temperatures are significantly less than those determined for the steel standards probably due to the different thermal properties and the lower absorbance of copper at the laser wavelength. Although the heat capacities and densities of copper and steel are similar, the thermal conductivity of copper is significantly greater than that of steel. Consequently, heat conduction away from the interaction zone into the interior of the sample occurs much more readily for copper than for steel. Furthermore, the normal reflectivity of copper surfaces at 1064 nm is about 10 times greater than for steel (15). Thus, for a given laser irradiance, less energy is initially deposited and more heat is conducted away from the laser spot for copper relative to steel. Integration of eq 5 for the average temperature rise in a copper sample yields values of 6500 K for a Q-switched laser pulse and 2600 K for a free-running laser pulse. Again, despite the considerable differences in the two approaches for determining the material temperature, the agreement is encouraging. A set of in-house aluminum standards has also been examined by laser ablation-ICP-MS. The relative elemental responses are presented in Table 111. The ablation temperatures obtained from the fits to eq 13 are TA = 16 500 K for Q-switched operation and T A = 5900 K for the free-running laser. These values fall between those characterizing the same
processes for copper and steel as might have been expected on the basis of thermal properties of these three materials. These results show several clear trends with respect to laser ablation sampling of metals. The volatilization efficiencies of elemental impurities can be described with reasonable accuracy with a simple thermal model. Similar models have recently been applied to other solids sampling techniques such as laser mass spectrometry (LMS) (17)and spark source mass spectrometry (SS-MS) (22) with less success. The most probable explanation of the better agreement between theory and experiment for laser ablation-ICP-MS is that the sampling and ionization steps are separated and can be treated independently in the current investiation. In both LMS and SS-MS the ablation and ionization processes are intimately iinked, introducing a higher order dependence of the elemental responses upon the laser characteristics or the sparking conditions. For laser ablation-ICP-MS, however, the ionization efficiencies are determined by the plasma alone and are, in general, well characterized and independent of the sampling technique. One result of the present investigation that is not terribly startling, but is important in applications of laser-solids sampling, is that a Q-switched laser pulse raises the metal surface to a considerably higher temperature than does a free-running laser pulse. For Q-switched operation this is reflected in relative elemental responses that are determined primarily by ionization efficiencies rather than volatilization efficiencies and, thus, more closely correspond to the responses for solution nebulization. This is a much more desirable situation for semiquantitative analysis of materials for which matrix-matched standards are not available since solution response factors are easily obtained. In this respect it is likely that Q-switched laser ablation will provide more accurate semiquantitative results than free-running operation. The trend observed in ablation temperatures is interesting with respect to the laser-induced heating and subsequent volatilization. For both Q-switched and free-running operation, the TA values can be ordered as follows: steel > aluminum > copper. This is the same ordering one would expect if the thermal conductivity of the material being irradiated determined the ultimate surface temperature. This is borne out by the reasonable agreement between the calculated temperatures and the experimental values of T A . These calculations are based on a classical heat flow treatment in which thermal properties and the duration of the laser material interaction define the rate of heat conduction from the initially heated zone and play the decisive role in determining the affected volume and the temperature distribution within the solid. Since the relative elemental responses are exponential functions of the ablation temperature, one cannot, in general, expect different materials to yield similar responses with a
Table 111. Relative Elemental Responses for Standard Alumin
element
observed Q-switched
Mg Ti
9.45
V
0.82 1.26 0.85 0.61 0.56 0.82 0.56 1.43 4.12 3.84
Cr Mn Fe
Ni cu Zn Sn
Pb Bi
1.00
1247
fit to eq 13 (T= 16500 K) Q-switched
observed free running
fit to eq 13 (T= 5900 K) free running
11.36 1.00 0.71 1.28 1.18 0.45 0.40 0.79 0.73 1.56 4.49 4.09
412.20 1.00 0.46 3.17 11.70 1.13 0.71 3.87 58.40 16.30 196.00 163.00
352.00 1.00 0.39 3.26 13.32 0.93 0.66 4.36 64.30 14.16 162.30 125.40
1248
ANALYTICAL CHEMISTRY, VOL. 61, NO. 11, JUNE 1, 1989
given set of laser ablation conditions. Even though the elemental responses are intimately related to the laser beam characteristics and the properties of the solid, one of the primary findings of the present study is that these responses can be modeled with surprisingly good accuracy. This fact suggests that semiquantitative analysis across the mass range may be possible. Within the framework of this thermal model, this requires either the knowledge of one analyte concentration and the ablation temperature or two or more analyte concentrations from which the value of TAcan be determined. Either approach would enable the calculation of the element- and matrix-dependent ablation efficiencies for virtually all other analytes using eq 13 with no external standards. There are several discrepancies between the calculated and measured relative response factors that may be due to differences in the degree of ionization of the dry plasma compared to that when water is present. Such a change in the plasma conditions will likely be reflected in altered ionization temperatures and electron densities. For elements of low first ionization potentials, these changes in the plasma may not lead to significantly different relative responses. However, for elements with higher ionization potentials (>9 eV) these differences may explain some of the deviations between the measured and calculated response factors. The results of further experiments aimed at understanding the fundamental differences between plasma conditions obtained with solution nebulization and laser ablation sample introduction will aid in the interpretation of these relative response factors. Many applications of laser ablation-ICP-MS are expected to focus on solids that are difficult to analyze via conventional techniques, such as new high-technology and ultrapure materials, and in these cases it is likely that matrix matched standards will not be routinely available. Consequently, the demands put upon semiquantitative analysis will become more stringent as more exotic materials emerge. It is believed that the current treatment of relative elemental responses can make a significant contribution to such semiquantitative approaches. Such a path toward rapid semiquantitative analyses is being followed in this laboratory, and the results will be reported in a future publication (23).
ACKNOWLEDGMENT The author thanks Peter Arrowsmith and David Polk for helpful comments and discussion. Further thanks are expressed to a reviewer for several useful comments. Registry No. Mg, 7439-95-4;Ti, 7440-32-6;V, 7440-62-2;Cr, 7440-47-3; Mn, 7439-96-5; Co, 7440-48-4; Cu, 7440-50-8; Zn, 7440-66-6; As, 7440-38-2; Zr, 7440-67-7; Nb, 7440-03-1; Mo, 7439-98-7; Ag, 7440-22-4; Sn, 7440-31-5; Sb, 7440-36-0; Ce, 7440-45-1; Ta, 7440-25-7; W, 7440-33-7; Au, 7440-57-5; Pb, 7439-92-1; Bi, 7440-69-9; Fe, 7439-89-6; Ni, 7440-02-0. LITERATURE CITED (1) Dittrich, K.; Wennrich, R. Prog. Anal. A t . Spectrosc. 1984, 7,
139-198. (2) Wennrich. R.; Dittrich. K. Spectrochim. Acta, Part B 1982. 378, 9 13-9 19. (3) Ishizuka, T.; Uwarnino, Y. Anal. Chem. 1980, 52, 125-129. (4) Mitchell, P. G.; Ruggles, J. A.; Sneddon, J. Anal. Left 1985, 18, 1723-1 732. (5) Mitchell, P. G.; Sneddon. J.; Radziemski, L. J. Appl. Spectrosc. 1987, 4 1 . 141-148. (6) Sneddon, J. Spectrosc. Lett. 1987, 2 0 , 423-430. (7) Carr. J. W.; Horlick, G. Spectrochim. Acta, Parts 1982, 3 7 8 , 1-15. (8) Arrowsmith, P. Anal. Chem. 1987, 59, 1437-1444. (9) Gray, A. L. Analyst(London) 1985, 110, 551-556. (IO) Ready, J. F. Effects of High Power Laser Radiation; Academic: New York, 1972; Chapters 3-4. (11) Afanas'ev, Yu. V.; Krockhin. 0. N. J . Exp. Theoret. Phys. (USSR) 1967, 52, 966-975. (12) Sparks, M. J . Appi. Phys. 1976, 4 7 , 837-849. (13) Carslaw, H. S.;Jaeger, J. C . Conduction of Heat in Solids, 2nd ed.; Clarendon: Oxford, 1959. (14) Kocher. E.; Tschdi, L.; Steffen, J.; Herziger, G. I€€€ J . Quantum Nec120-125. tron. 1972, (25-8, (15) Duley, W. W. I n Laser Surface Treatment of Metals; Draper, C. W., Mazzoldi, P.. Eds.: Martin Nijhoff: Dordecht, 1986; pp 1-16. (16) Johnson, P. B.; Cristy, R. W. Phys. Rev. B 1975, 1 1 , 1315-1325. (17) Ramendek, G. I.; Manzon, B. M.; Tyurin, D. A,; Benyaev, N. E.; Komleva, A. A. Talanta 1987, 34, 61-67. (18)Gillson, G. R.: Douglas, D. J.: Fulford, J. E.; Halligan, K . W.; Tanner, S. D. Anal. Chem. 1988, 6 0 , 1472-1474. (19) CRC Handbook of Chemistry and Physics, 65th ed.;Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1984; p F-181. (20) David, C. D. Appi. Phys. Lett. 1967, 1 7 , 394-396. (21) Bruce, C. W.; Deacon, J.; Vonderhaar. D. F. Appl. Phys. Lett. 1966, 9 , 164-166. (22) Vieth, W. Spectrochim. Acta, Part B 1987, 428, 1085-1092. (23) Hager, J. W., manuscript in preparation.
RECEIVED for review December 7,1988. Accepted March 1, 1989.
