High resolution continuum source AAS the better way to do atomic absorption spectrometry

Spectral Line Profiles

Natural Line Width

When an atom is in an excited state, such as after absorbing a photon, it will eventually relax to a lower energy state within a finite time, typically between 10^-9 and 10^-8 seconds, even in the absence of interactions with other atoms or molecules This relaxation process involves the re-emission of the absorbed photon, leading the atom back to its ground state during resonance transitions The finite lifetime of the excited state introduces an uncertainty in energy, as described by Heisenberg's uncertainty principle, which states that the product of the uncertainty in energy (ΔE) and the lifetime (Δt) is equal to Planck's constant (h).

2πτ (2.1) in the energyEof the excited state Since the transition is associated with a photon energy ofhν 0 =E, the frequency of the photon is also uncertain: Δν = ΔE h = 1

When the lower state is not the ground state, it exhibits an energy uncertainty linked to its lifetime, resulting in a frequency uncertainty Δν that combines both contributions This frequency uncertainty, inversely related to the lifetime, creates a Lorentz-shaped line profile centered at ν₀ with a width of Δνₙ The natural line width Δλₙ can be determined using the formula Δλₙ = (λ²/c) Δνₙ, leading to a wavelength-dependent intensity distribution Iₙ(λ) for the area-normalized profile.

2 , (2.3) withλ 0=c/ν 0and a full width at half maximum (FWHM) of: Δλ N=λ 2 c

In Atomic Absorption Spectroscopy (AAS), the lifetime of an electron in an excited state typically lasts a few nanoseconds, leading to a wavelength uncertainty (Δλ N) of approximately 0.01 picometers This effect is minimal when compared to other broadening mechanisms present in AAS and is consequently disregarded in this discussion.

Doppler Broadening

Atomic emission and absorption involve the motion of free atoms, which impacts the radiation's frequency During emission, atoms moving towards the observer cause a frequency shift, resulting in symmetric broadening of the emitted line In absorption, the motion of atoms leads to further broadening of the incoming radiation's frequency Both effects arise from the Doppler effect, with the observed frequency being a combination of all contributions towards the observer When atoms are in thermodynamic equilibrium, their velocity distribution follows a Maxwellian profile, allowing the intensity distribution \( I_D(\lambda) \) observed to be represented by a Gaussian curve.

⎦ (2.5) Δλ D, the so-called Doppler line width, is the FWHM which is given by: Δλ D= 2√

If the massmof the atom is expressed by the molar massMgiven in g/mol, the width can be written as: Δλ D= 7.16ã10 −7 λ 0

Figure 2.1 illustrates how the wavelength dependence of Δλ D varies for different atomic masses at a temperature of 2600 K, typical of an air/acetylene flame In the critical wavelength range of 190 nm to 350 nm and atomic masses between 14 g/mol and 200 g/mol, Δλ D shows a variation from 0.5 pm to 3.5 pm.

Figure 2.1:Calculated FWHM values for Doppler broadening at 2600 K and different atom masses

Collision Broadening

Collisional effects significantly influence the broadening of spectral lines when absorbing atoms interact with other atoms or molecules Allard and Kielkopf have extensively discussed these complex collisional effects The resulting broadening mechanisms yield a Lorentz distribution as the line profile According to Larkins, the collisional broadening width (Δν C) in Hz can be expressed by the formula Δν C = (1/π)Nσ Cν.

In the context of thermal equilibrium, the mean relative velocity (ν) between colliding partners is expressed as ν = √(8k_B T / π), where N represents the density of the perturbing atom or molecule, and σ_C denotes the collisional cross-section measured in square meters (m²).

(2.9) m Aandm Bare the masses of the absorbing (A) and disturbing (B) atom, respectively For normal pressure, Equation 2.8 then transforms to: Δν C= 1.4ã10 16 σ C

Expressed in wavelength and by using molar massesM A,M B(g/mol), Equation 2.10 gives the FWHM for collisional broadening, the so-called collisional line widthΔλ C: Δλ C= 1.13ã10 21 λ 2 0 σ C

Larkins measured the collisional cross-sections for various elements in an air/acetylene flame, identifying a typical value of σ C ≈ 2 × 10^(-18) m² The wavelength dependence of Δλ C for this cross-section is illustrated in Figure 2.2, considering a temperature of 2600 K and different atomic masses, with nitrogen (N₂) as the perturbing particle, having a mass of M B = 28 This analysis focuses on the critical wavelength range of 190 nm to 350 nm and atomic masses from 14 g/mol.

200 g/mol, the variation ofΔλ C spans from 0.5 pm to 2 pm, which is comparable to the range of the Doppler broadening under the same conditions (refer to Figure 2.1).

The spectral line experiences both broadening and a shift, which can manifest as a blue shift towards shorter wavelengths or a red shift towards longer wavelengths, influenced by the collision partner In the notable instance of an adiabatic impact, Corney [19] established a predicted relationship between the shift and broadening, quantified as 0.36.

The spectral line profile typically exhibits a Voigt profile, which is a combination of Lorentz and Gaussian distributions rather than being purely one or the other This profile arises from the convolution of the Lorentz distribution, influenced by collision broadening (Δλ C), and the Gaussian distribution, affected by Doppler broadening (Δλ D), under the assumption that these broadening processes are independent Due to the complexity of the Voigt profile, it cannot be derived analytically, necessitating the use of numerical convolution methods for accurate characterization.

At a temperature of 2600 K and normal pressure within an air/acetylene flame, the calculated Full Width at Half Maximum (FWHM) values for collisional broadening reveal significant insights The perturbing particle in this scenario is nitrogen (N2), with a molecular weight (MB) of 28 The damping constant (α), a crucial parameter in this analysis, is defined by the formula α = √(ln2) * (ΔλC / ΔλD), where ΔλC and ΔλD represent specific wavelength changes.

The Full Width at Half Maximum (FWHM) of the Voigt profile, known as the Voigt line width (Δλ V), cannot be determined by merely adding the Doppler and Lorentz widths Instead, it can be approximated using an empirical formula, where Δλ V is approximately equal to Δλ C.

Figure 2.3 illustrates the Gauss and Lorentz profiles with equal area and full width at half maximum (FWHM), leading to the Voigt distribution In this distribution, the Lorentzian component predominantly influences the line wings, while the Gaussian component shapes the line core.

Figure 2.4 illustrates the line widths in a conventional air/acetylene flame, corresponding to the data presented in Figures 2.1 and 2.2 The Voigt profile widths are determined using Equation 2.13 In the critical wavelength range of 190 nm to 350 nm and for masses between 14 g/mol and 200 g/mol, the variation of Δλ V spans from 0.8 pm to 4.5 pm However, for longer wavelengths and lighter elements, widths exceeding 10 pm may be anticipated.

Figure 2.3:Comparison of Gauss (blue line) and Lorentz (green line) curves of equal area and same FWHM, and a Voigt (red line) profile produced by convoluting the other two curves

The calculated Full Width at Half Maximum (FWHM) values for Voigt profiles, influenced by Doppler and collisional broadening, were determined at a temperature of 2600 K and standard pressure within an air/acetylene flame, using nitrogen (N2) as the perturbing particle with a molecular mass (MB) of 28 The curve parameter is defined by the atomic mass (MA).

Voigt profiles accurately represent the true line shape in spectrometry; however, instrument transmittance profiles also influence the measured intensity distribution The geometric shape of the instrument profile is shaped by factors such as radiation wave diffraction, entrance slit geometry, and optical aberrations when focusing a monochromatic image onto the instrument's focal plane This profile can be mathematically described as the convolution of a sinc² profile with a rectangular shape and a typically non-symmetric aberration distribution The sinc² profile is defined by the observed wavelength (λ₀) and the relative aperture (k_en = f_en / D_eff), where f_en is the collimator focal length and D_eff is the effective collimator diameter The distance from the first sinc² minima to the central maximum is approximately 1.22λ₀ / k_en, while the full width at half maximum (FWHM) of the geometric sinc² shape is given by Δg_sinc = 1.1 λ₀ k_en.

In optical systems with real entrance slit widths and minimal aberrations, the geometric profile is determined by the convolution of a sinc² function with a rectangular function The entrance slit width, denoted as s_en, can be optimally selected as s_opt = 1.22λ₀/k_en to achieve the best geometric instrument profile, resulting in a full width at half maximum (FWHM) of Δg instr opt = 1.37λ₀/k_en.

To convert geometrical profiles into spectral profiles, the geometrical width must be multiplied by the reciprocal linear dispersion (δλ/δx) of the instrument This calculation yields the optimal instrument profile width (Δλ opt instr), represented by the formula Δλ opt instr = 1.37 λ 0 k en δλ/δx.

In Figure 2.5, Curve B represents a profile that closely resembles a Gaussian function As the slit widths increase, the profiles tend to become more rectangular, particularly when utilizing a multi-pixel photo detector in the focal plane, where the pixel width is considerably smaller than the entrance slit width These conditions are visually depicted in Figure 2.5.

Figures 2.6, 2.7, and 2.8 illustrate the effectiveness of various broadening mechanisms by comparing calculated and measured line profiles in a typical air/acetylene flame Initially, the Cu doublet at 324.754 nm was analyzed using a high-resolution echelle spectrometer.

Figure 2.5:Calculated instrument profiles for three different entrance slit widthss en; A:s en = 0

(pure sinc 2 profile); B: profile A convoluted by a rectangular profile withs en =s opt; C: profile A convoluted by a rectangular profile withs en = 5s opt; wavelength unit: FWHM of sinc 2 profile (A)

Instrument Profile

Voigt profiles accurately represent true line shapes; however, spectrometer measurements are influenced by the instrument's transmittance profile This profile is shaped by the diffraction of radiation waves, the geometry of the entrance slit, and optical aberrations when focusing a monochromatic image onto the instrument's focal plane It can be defined as a convolution of a sinc² profile and a non-symmetric aberration distribution The sinc² profile is characterized by the observed wavelength (λ₀) and the relative aperture (k_en = f_en / D_eff, where f_en is the collimator focal length and D_eff is the effective collimator diameter) The first minima of the sinc² profile are separated from the central maximum by approximately 1.22λ₀ / k_en, while the full width at half maximum (FWHM) of the geometric sinc² shape is given by Δg_sinc = 1.1 λ₀ k_en.

For optimal geometric instrument profiles with minimal aberrations, the entrance slit width (s_en) should be set to s_opt = 1.22λ_0/k_en This configuration results in a geometric profile derived from the convolution of the sinc² function with a rectangle, yielding a full width at half maximum (FWHM) of Δg_instr_opt = 1.37λ_0/k_en.

To convert geometrical profiles into spectral profiles, the geometrical width must be multiplied by the reciprocal linear dispersion (δλ/δx) of the instrument This calculation yields the optimal instrument profile width (Δλ opt instr), represented by the formula: Δλ opt instr = 1.37 λ 0 k en δλ/δx.

In Figure 2.5, Curve B represents a profile that closely resembles a Gaussian function As the slit width increases, the profiles become more rectangular, particularly when utilizing a multi-pixel photo detector in the focal plane, where the pixel width is considerably smaller than the entrance slit width These conditions are visually demonstrated in Figure 2.5.

Figures 2.6, 2.7, and 2.8 illustrate the comparison between calculated and measured line profiles, validating the broadening mechanisms discussed Initially, the Cu doublet at 324.754 nm was observed using a high-resolution echelle spectrometer in a typical air/acetylene flame.

Figure 2.5:Calculated instrument profiles for three different entrance slit widthss en; A:s en = 0

(pure sinc 2 profile); B: profile A convoluted by a rectangular profile withs en =s opt; C: profile A convoluted by a rectangular profile withs en = 5s opt; wavelength unit: FWHM of sinc 2 profile (A)

The comparison of the Cu doublet line profile, obtained from a hollow cathode lamp (HCL), is illustrated in Figure 2.6 It features two distinct profiles: A represents the lamp emission profile at a current of 5 mA, while B depicts the corresponding Doppler profile at a temperature of 2600 K, characterized by a full width at half maximum (FWHM) of 1.4 pm.

ELIAS II (LTB Lasertechnik Berlin GmbH, Berlin, Germany), having an instrument pro- file width of 0.13 pm (FWHM), which is negligible compared to the line width The mea- sured profiles were used to determine the line positions and intensities of the Cu dou- blet For these values Gauss profiles with 1.4 pm FWHM were calculated, representing the Doppler broadening for Cu at 2600 K.

The synthetic copper profiles were adjusted using a Lorentz profile with a full width at half maximum (FWMH) of 1.1 picometers, which accounts for collisional broadening in a flame at 2600 K under normal pressure This adjustment is based on an assumed collisional cross-section of 2 x 10^-18 m², as illustrated in Figure 2.2.

The convolution of the synthetic Doppler profile, as depicted in Figure 2.6, with a Lorentz profile at 2600 K and normal pressure, results in a Voigt profile This process involves using a collisional cross-section of 2 × 10^-18 m², where the Doppler profile is represented as A, the Lorentz profile with a full width at half maximum (FWHM) of 1.1 pm is represented as B, and the final Voigt profile is shown as C.

The final profile was modified using a Gauss function with a 0.9 pm FWHM, reflecting the instrument profile of the SuperDEMON spectrometer at 324 nm This calculated profile was then compared to the absorbance profile obtained from an air/acetylene flame measurement with the SuperDEMON The comparison revealed a strong agreement between the calculated and measured profiles.

Using a numerical deconvolution procedure aligned with the previously demonstrated convolution method, we determined the Voigt widths for several measured analytical lines The findings are summarized in Table 2.1, where they are compared with the calculated values derived from Equations 2.7, 2.11, and 2.13.

The convolution of the synthetic Voigt profile with a Gaussian profile, which represents the instrument function of SuperDEMON, is illustrated in Figure 2.8 The Voigt profile (A) is combined with a Gaussian profile that has a full width at half maximum (FWHM) of 0.9 pm (B), resulting in a convolution output (C) This convolution is compared to the measured absorbance profile in an air/acetylene flame (D).

Table 2.1: Comparison of measured with calculated FWHM values for Lorentz profiles

Element Wavelength MeasuredΔλ V CalculatedΔλ V Ratio

/ nm / pm / pm measured / calculated

Element Wavelength MeasuredΔλ V CalculatedΔλ V Ratio

/ nm / pm / pm measured / calculated

Element Wavelength MeasuredΔλ V CalculatedΔλ V Ratio

/ nm / pm / pm measured / calculated

Figure 2.9 presents a comparison of measured and calculated Voigt profiles, with calculated line widths shown alongside the molar mass (M A) as a parameter The measured values are categorized by the masses of the absorbing atoms, indicated by distinct colors: black for M A = 7, green for M A = 23 to 40, blue for M A = 52 to 79, cyan for M A = 88 to 128, and magenta for higher values.

The measured values of M A, ranging from 192 to 207, exhibit notable deviations from the calculated values, primarily resulting in larger line widths due to non-resolvable line splitting Nevertheless, for most lines, the agreement between measured and calculated values is satisfactory, highlighting the effectiveness of the proposed approximations.

Figure 2.9 illustrates a comparison between the measured (represented by dots) and calculated (depicted by curves) Voigt widths for the absorption lines listed in Table 2.1 These results are organized according to atom masses, which were utilized as parameters for the calculated curves.

Atomic Absorption with a Continuum Source

General Principle of Absorption

The basic description of the attenuation of radiation by passing an absorbing volume is given by Beer’s law: φ=φ 0 e − k l (2.17)

The transmitted radiant power decreases exponentially with both the absorption coefficient and the length of the absorbing layer When a beam from a continuum radiation source passes through an absorption cell filled with a mono-atomic gas that has an absorption line at wavelength λ₀, the transmitted radiant power φₗ becomes wavelength-dependent, as illustrated in Figure 2.10.

Figure 2.10: Continuum spectrum with a single absorption line

The transmitted radiant power spectrum reveals the absorption line of gaseous atoms at the central wavelength λ₀ According to Beer’s law, the absorption coefficient is influenced by the wavelength, represented by the equation φ(λ) = φ₀ e^(-k(λ)l).

The shape of k(λ) is influenced by Doppler and collisional broadening effects According to classical radiation theory, there is a correlation between k(λ) and N, where N represents the volume concentration of absorbing atoms in their ground state The relationship can be expressed as k(λ)dλ = (πe²/λ₀²)fN/mc², which indicates that k(λ) is approximately proportional to N.

The factor \( f \) denotes the oscillator strength derived from quantum mechanics, while \( e \) and \( m \) represent the electron charge and mass, respectively To achieve a result that is directly proportional to the number of atoms, it is essential to measure the radiant power absorbed at the absorption line in Atomic Absorption Spectroscopy (AAS) This involves determining both the incident radiant power (\( \phi_0 \)) and the transmitted radiant power (\( \phi_\lambda \)) The equation can be adjusted accordingly to reflect these measurements.

The dimensionless number known as absorbance (A), or optical density, is defined as a function of wavelength (k λ) It is directly proportional to the concentration of absorbing atoms (N) within a given volume and the length (l) of the path through which light passes.

This section explores how the spectrometer's design impacts absorbance measurement results, focusing on minimum detectable absorbance and sensitivity with varying entrance slit widths A virtual instrument model is proposed, featuring an entrance slit with adjustable widths and a linear multi-pixel photo detector It is assumed that the pixel width is less than the entrance slit width and that all pixels are illuminated simultaneously, resulting in fully time-correlated signals The instrument profile is simplified to a rectangular shape, excluding the sinc² component from diffraction effects A diagram of this virtual CS AAS spectrometer is provided for clarity.

For low concentrations of absorbing atoms near the limit of detection (LOD), measuring φ 0 and φ λ simplifies to determining a small reduction in a large signal Numerous studies have addressed this challenge, with a significant contribution from Snelleman in 1968, who developed algorithms that clearly outline how lamp properties and spectrometer characteristics influence Δλ instr φ 0.

The virtual CS AAS spectrometer, illustrated in Figure 2.11, showcases a rectangular instrument profile that highlights the impact of shot noise It is noted that the absorbance signal-to-noise ratio (SNR) remains unaffected by the spectrometer bandwidth The radiant power (φ λ) detected by a monochromator, when effectively imaging a continuum source, is quadratically related to the bandwidth This relationship indicates that the absorbance noise, dominated by shot noise, is inversely proportional to the bandwidth These principles are mathematically expressed by the equation φ λ = L λ τΔλ instr s en h en D eff f en 2

The radiance of the CS is denoted by L λ, while τ represents the instrument's transmittance, and s en and h en indicate the entrance slit’s width and height, respectively In Section 2.1.5, parameters such as D eff, f en, and Δλ instr are defined By utilizing the angular dispersion δβ/δλ of the dispersive optical element, typically a grating, the entrance slit width can be expressed as s en = Δλ instr f en δβ/δλ.

Equation 2.21 can now be written as follows: φ λ =L λ τΔλ 2 instr h en D eff f en δβ δλ (2.23)

The established proportionalities for radiant power measured with a CS indicate that the mean photon flux per second, represented as n = φ λ λ/(hc), has a statistical nature The standard deviation of n, observed over a time interval t, is calculated as √(n t) Consequently, the minimum detectable reduction in n during the observation time t, which corresponds to a measurable decrease in radiant power, is defined as Δn min = C√.

Here,C is the reliability factor, which is usually assumed to equal three The factor√

Each absorbance measurement requires two independent intensity measurements The minimum detectable fraction of absorbed incident radiant power, denoted as α min, is defined by the equation α min = Δn min / n t = 3√.

According to the relationship betweennandφ λ , Equation 2.25 can be written as follows: α min= 3√

On the other hand, the relative radiant power reductionαgenerated by volume absorption liable to Beer’s law can be written as: α φ 0 dλ − φ 0 e − k λ l dλ φ 0dλ (2.27)

Ifφ 0is constant over the measuring intervalΔλ instrand if (−k λ l) is small compared to one, the integration overΔλ instrresults in: α= Δλ instr −

, (2.28) and in a next step one gets: α=l k λ dλ Δλ instr

Using equation 2.19, the following proportionality is achieved: α∼ l N Δλ instr

The concentration N min at the shot-noise dominated LOD can be calculated from Equations 2.23 and 2.26 by settingα=α min:

Equation 2.31 exemplifies that the shot-noise dominated LOD for an absorbing atom con- centration can be reduced only by an enhanced radiance of the lamp, an enlarged transmit- tance and geometrical conductance of the spectrometer, an increased angular dispersion of the dispersing optical component, and/or an increased measuring time All these improve- ments, however, produce square-root effects only.

This analysis explores the impact of a narrower instrument profile on absorbance measurements, specifically for small Δλ instr values A virtual spectrometer was utilized to model the absorbance of a Voigt-shaped line, which combines Gaussian and Lorentzian profiles with equal full width at half maximum (FWHM) To reflect realistic measurement conditions, a stray light level of 3% was incorporated The resulting transmittance curves for various peak absorbance values are illustrated in Figure 2.12.

Figure 2.12:Calculated transmittance profiles for Voigt-shaped absorption lines with maximum absorbance values of (A) 0.03, (B) 0.3, and (C) 3, assuming 3 % stray light level

The computer simulation results for the virtual CS AAS measurement, depicted in Figure 2.13, illustrate the relationship between integrated absorbance and maximum absorbance across various widths of a symmetrical rectangular instrument profile The maximum absorbance is calculated assuming no stray light and an infinitesimal instrumental width, utilizing Voigt functions as line profiles The instrumental width, Δλ instr, is expressed in multiples of the FWHM of the normalized Voigt curves Notably, for Δλ instr = 0.2 FWHM, the averaged absorbance values align with the line center values up to a stray light level of 3%, corresponding to an absorbance of 1.5 However, at Δλ instr = 2 FWHM, the sensitivity in the low absorbance range decreases to approximately half of the ideal sensitivity Furthermore, for values greater than 2 FWHM, the impact of the instrumental width on curve shape becomes evident, exhibiting a hyperbolic characteristic as previously predicted by Harnly and colleagues.

The relationship between the minimum amplitude (A min) and instrumental width (Δλ instr) is influenced by the signal-to-noise ratio (SNR) and shot noise By calculating α numerically and applying Equation 2.26, which shows the inverse proportionality between shot noise and α min, we can derive how A min is connected to Δλ instr, given that A min is defined as A min = -log(1 - α min).

Instrument Effects

ifη Qdenotes the quantum efficiency of the detector:

The uncertaintyΔIofIis principally determined by three effects: detector read-out noiseΔI det =constant, radiant power flicker-noise ΔI flick ∼ I, and shot-noise of the signalΔI shot =√

I The resulting noiseΔI resis given by the well-known operation: ΔI res 2 = ΔI det 2 + ΔI flick 2 + ΔI shot 2 (2.33)

Modern solid-state detectors, such as CCD arrays, exhibit read-out noise levels ranging from 5 to 30 electrons per read-out When the signal exceeds 2000 electrons, the ΔI det becomes insignificant compared to shot noise Additionally, the influence of flicker noise can be minimized by considering time-correlated signal generation, allowing the detector to simultaneously capture a spectral line and its surrounding area, thereby providing optimal monitoring of flicker effects.

Consistent exploitation of this advantage in absorbance calculations renders flicker noise negligible, resulting in ΔI res equating to ΔI shot Consequently, 1/√η Q emerges as an additional factor in Equation 2.31.

Structure of Molecular Spectra

Electronic Transitions

Energy in molecules can be categorized into three types: electronic energy (E el), vibrational energy (E vib), and rotational energy (E rot), ranked by their energy content Electronic energy arises from the Coulomb interaction between nuclei and electrons, while vibrational and rotational energies stem from the internal motion of the nuclei Although vibrational and rotational contributions are relatively small compared to electronic energy, they will be further explored in Sections 2.3.2 and 2.3.3.

In a stable molecular configuration, overlapping outer atomic orbitals form molecular orbitals that are partially filled with electrons The energy differences between these orbitals are comparable to atomic energies, leading to molecular electronic transitions and corresponding electron excitation spectra at energies or wavelengths similar to atomic transitions, typically within the UV or visible range This often results in overlapping spectra of both molecular and atomic origins, as illustrated by the diatomic molecule scheme in Figure 2.15, which depicts an electronic transition to a higher energy orbital triggered by photon absorption at wavelength λ.

An electronic molecular transition is characterized by key attributes of the initial and final electronic states For diatomic molecules, which are significant in Atomic Absorption Spectroscopy (AAS), this labeling typically includes: (i) the energetic order of the electronic state, (ii) the total spin of the electrons, (iii) the total angular momentum of the electrons relative to the molecular axis, and (iv) the symmetry properties of the electronic wave function, which indicates the probability of locating the electrons within the molecule Thus, a typical electronic state can be effectively labeled to convey essential information.

The leading letter is either ‘X’ for the lowest electronic state (ground state) or ‘A’, ‘B’,

In the context of electronically excited states, the notation changes to small letters for electronic states with a total spin \( S > 0 \) Here, \( S \) represents the total spin values (0, 1/2, 1, etc.), while \( \Lambda \) denotes the total angular momentum, which is represented by capital Greek letters such as Σ, Π, Δ, etc., for \( \Lambda = 1 \).

The optional subscript ‘g’ or ‘u’ applies exclusively to homo-nuclear diatomic molecules, indicating how the electronic wave function behaves during inversion at the molecular center, regardless of whether its sign changes Additionally, the superscript ‘+’ or ‘−’ further characterizes these wave functions.

‘−’ denotes the behavior of the wave function in the case of reflection at a plane including the molecular axis (with or without changing its sign). hc/ e -

Figure 2.15:Scheme of a diatomic molecule undergoing an electronic transition by absorption of a photon with energyhc/λ

Figure 2.16 illustrates the absorbance spectrum nomenclature of PO as observed in a flame, highlighting key electronic transitions to excited states D, A, and B within the critical wavelength range of 200 nm to 350 nm Additionally, the distinct substructure of these transitions is noteworthy and will be explored in subsequent sections.

In typical conditions, electronic states possess energies around a few electron volts (eV), while the thermal energy of the absorber is approximately 0.2 eV As a result, most atoms stay in their ground electronic state, leading to the conclusion that nearly all observable electronic transitions initiate from the X- state.

Figure 2.16:Nomenclature of the electronic transitions demonstrated for the absorbance spectrum of the diatomic molecule PO observed in a flame

Vibrational Spectra

Molecules possess internal energy arising from the vibrations of their nuclei around an equilibrium configuration This vibrational energy, denoted as E_vib, is generally one to two orders of magnitude lower than the electronic energy, E_el Consequently, pure vibrational transitions are primarily detected in the infrared (IR) region, which is the foundation of classical IR spectroscopy Thus, the total energy, E_tot, of a molecule can be roughly represented as the sum of its vibrational and electronic energies.

Diatomic molecules exhibit vibrational motion primarily through the stretching of the intra-nuclear axis This behavior is illustrated in Figure 2.17 In the case of purely harmonic motion of the nuclei, the vibrational energy (E vib) can be accurately described.

Equation 2.35 shows that the allowed vibrational energies are equally spaced and sepa- rated byhν The amount of the latter is specific to the nuclei and the strength of their coupling The number v is called the vibrational quantum number It denotes the amount of vibrational excitation energy in the respective molecular state.

Figure 2.17: Stretching vibration of a diatomic molecule

In an electronic transition, both the initial and final states can have extra vibrational energy, as indicated by equation 2.34 This leads to an absorbance spectrum featuring substructures due to allowed vibrational transitions, represented by Δv = v(A) - v(X) = 0, 1, 2, for transitions from state X to state A A singular vibrational transition from v(X) to v(A) is termed a band, while multiple bands with a consistent Δv value are collectively known as a sequence.

In vibrational transitions, the likelihood decreases as the change in vibrational quantum number (Δv) increases, limiting observable transitions to low Δv values Additionally, since the thermal energy of the absorber is similar to the vibrational energy at the ground state (v = 0), only vibrational states with small quantum numbers are populated, further constraining the observable vibrational transitions.

Figure 2.18 illustrates an electronic transition spectrum featuring a distinct vibrational structure, displaying six sequences ranging from Δv = +3 to Δv = −2 The transitions with constant Δv exhibit strong overlap due to the equal spacing of vibrational energies, resulting in well-aligned consecutive sequences The next section will discuss the clearly visible substructure within these band systems.

Figure 2.18:Example of vibrational transitions with equidistant energy spacing within the same electronic transition (PO molecule, refer to Figure 2.16)

In polyatomic molecules, the number of potential vibrations significantly increases, allowing thermal energy to populate a greater variety of vibrational states This results in a higher number of observable bands during electronic transitions.

Rotational Spectra

Molecular rotation is a significant form of internal energy, particularly for non-linear molecules that can rotate around three perpendicular axes intersecting at their center of mass The rotational energies (E_rot) are typically two to three orders of magnitude lower than vibrational energies (E_vib), with pure rotational spectra detectable in the far-infrared or microwave regions This highlights the relationship between the various types of molecular energy.

Equation 2.34, describing the total molecular energy, may now be expanded to:

For diatomic and linear polyatomic molecules, rotational motion is restricted to an axis perpendicular to the molecular longitudinal axis A corresponding diagram is shown in

Figure 2.19 The rotational energy is given by:

The rotational energy levels of a diatomic molecule are quantized and defined by the equation E_rot = B J(J + 1), where J represents the rotational quantum number ranging from 0 to positive integers Unlike vibrational energy levels, which are evenly spaced, the rotational energy values increase quadratically with J, leading to distinct multiples of the rotational constant B.

Figure 2.19: Rotational motion of a diatomic molecule

Every vibrational state has a substructure made up of numerous rotational states, as indicated by Equations 2.37 and 2.38 The high thermal energy of the absorber allows for the population of many of these rotational states, resulting in vibrational bands that contain a multitude of rotational lines An example of this can be seen in Figure 2.20, which illustrates a rotational spectrum within a vibrational band The spectral distance between consecutive rotational lines demonstrates that the rotational structure of diatomic molecules can produce a significantly modulated absorbance signal within a narrow spectral range of approximately 10 pm.

Larger and nonlinear polyatomic molecules exhibit rotational motion around three axes, leading to a significant increase in the number of rotational states As the molecular moments of inertia rise, the rotational constants that influence the energy spacing of these states decrease This results in an increase in both the spectral density and the number of rotational lines observed.

Under normal pressure and temperature conditions, the rotational transitions in a vibrational band of the PO molecule become less distinct, with the spacing between adjacent lines shrinking below their widths This results in the modulation of observable absorbance fading away, leading to diffuse, non-structured bands that have no impact on High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS).

Dissociation Continua

When molecules absorb radiation with quantum energy exceeding their dissociation energy, they transition to a state that is not a discrete energy level, resulting in a spectral continuum devoid of fine structure This phenomenon parallels the ionization limit observed in atomic spectra, which signifies the energy required to completely remove a valence electron from an atom.

Massmann and colleagues conducted in-depth studies on spectral types in graphite furnaces, focusing on the dissociation continua of various molecules, including alkali halides This continuous background absorption does not pose a challenge for High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) and can be effectively corrected by all Background Correction (BC) systems utilized in Line Source (LS) AAS, provided that the background absorption does not change too rapidly or exceed established correction limits For further information, refer to Reference [150].

Instrumentation for HR-CS AAS 31

Radiation Source

A continuum source (CS) is a type of radiation source that produces a continuous spectral distribution across a wide range of wavelengths, unlike a line source (LS) CS can function in either continuous or pulsed modes, making it versatile for various applications For a comprehensive overview of CS in common spectroscopic applications, refer to the review by Ingle and Crouch [71].

High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) can utilize incandescent sources like quartz-halogen lamps and various arc lamps filled with deuterium or xenon The key factor in choosing a radiation source is its spectral radiance in the far-ultraviolet region, particularly down to 190 nm To achieve detection limits comparable to those of Line Source Atomic Absorption Spectroscopy (LS AAS), the spectral radiance per picometer bandwidth of a continuum source must be at least ten times greater than that of hollow cathode lamps, due to the significantly lower geometrical conductance of HR-CS AAS spectrometers.

GLE (Berlin, Germany) has developed an enhanced version of the traditional xenon short-arc lamp, commonly utilized for stadium lighting, which features increased UV emission This improved lamp type has been employed for all measurements discussed in this book (refer to Figure 3.16 in Section 3.4).

The lamp, resembling a traditional arc lamp, has been enhanced for 'hot-spot mode', which features a tiny plasma spot near the cathode surface instead of the usual diffuse arc seen in standard xenon lamps This plasma contraction is effectively achieved through the use of advanced materials for the anode and cathode rods, a minimal electrode distance of less than 1 mm, and elevated xenon pressure.

Figure 3.1:Photo of a xenon short-arc lamp operating in hot-spot mode (left) and diffuse mode

In optimized electrode geometries, the lamp operates at a pressure of 17 bar in cold conditions, which increases to 3-4 times during operation This process creates a hot-spot with a diameter of less than 0.2 mm and achieves a plasma temperature of approximately 10,000 K.

The lamp is operated with a nominal power of 300 W (typically 20 V and 15 A) using a DC power supply An additional circuit to produce a short high-voltage pulse of about

30 kV realizes the ignition To maintain a tolerable operating temperature, the lamp is mounted in a water-cooled housing, which is integrated in a closed water loop with air cooling.

Figure 3.2 illustrates the wavelength-dependent spectral radiance of the hot-spot xenon lamp at varying distances from the cathode, highlighting key emission lines of hollow cathode lamps Furthermore, Figure 3.3 provides a comparison of this spectral radiance with that of a commercial xenon lamp in diffuse mode and a traditional D2 lamp.

The spectral radiance of a xenon short-arc lamp varies with wavelength and is measured at various distances from the cathode, particularly in the hot-spot area This data is compared to specific emission lines from hollow cathode lamps, highlighting the differences in light emission characteristics.

The spectral radiance comparison illustrates the differences in wavelength performance among three light sources: (a) the xenon short-arc lamp in hot-spot mode (XBO 301, 300 W, GLE Berlin, Germany), (b) a commercial xenon lamp functioning in diffuse mode (L 2479, 300 W, Hamamatsu, Japan), and (c) a conventional D2 lamp (MDO 620, 30 W, Heraeus, Germany).

The small size and erratic movement of the hot plasma zone necessitate rapid stabilization of the spot image relative to the spectrometer entrance slit for optimal illumination This is achieved through a lightweight plane folding mirror positioned near the lamp, which is controlled by piezo-electric or magneto-mechanical actuators The mirror's adjustments are guided by signals from a four-quadrant detector, illuminated by the lamp via partial reflection from a thin quartz plate placed in front of the spectrometer slit The illumination control unit operates continuously throughout the entire AAS recording cycle, effectively compensating for hot-spot jitter, thermal drift, and displacement caused by periodic replacement of the xenon lamp.

Over time, the brightness of a lamp diminishes due to the darkening of its bulb However, after approximately 1,000 hours of use, the light output remains significantly above the 25% threshold This indicates that, even under shot-noise limitations, the reduction in light output degradation (LOD) stays within a factor of two.

Research Spectrometers with Active Wavelength Stabilization

The HR-CS AAS spectrometer demands significantly higher instrumental resolving power—approximately two orders of magnitude greater than that of conventional LS AAS—to achieve comparable sensitivity for various elements while minimizing spectral interferences from line overlap Adequate geometrical conductance and diffraction efficiency are essential for attaining a high signal-to-noise ratio (SNR) and low limits of detection (LOD), particularly in the far-UV range Additionally, the ability to simultaneously measure any analytical line along with its spectral vicinity is crucial for precise background correction Finally, precise control over absolute wavelength and dispersion at the femtometer scale is vital for ensuring analytical reliability and utilizing reference spectra stored in the computer effectively.

Classical spectrometers, utilizing concave or plane gratings, are recognized for their ability to generate low order spectra, making them valuable in techniques like LS AAS While they provide notable features for applications requiring low to medium spectral resolution, only specially designed echelle spectrometers with internal or external order separation, paired with modern solid-state detectors, can fulfill the high-resolution requirements for High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS).

Echelle gratings, also known as ladder gratings, were first characterized by Harrison in 1949 For additional insights into the theory and applications of echelle gratings, refer to the works of Schroeder and Boumans & Vrakking.

Echelle gratings, characterized by a ruling structure of 30 to 300 grooves per mm and diffraction angles exceeding 45°, serve as a bridge between classical echellette gratings and Michelson’s echelon The mechanical ruling of these gratings remains a complex and time-consuming task, resulting in a limited availability of copies from only a handful of manufacturers.

Figure 3.4 illustrates the shape of an echelle grating and the propagation of principal rays, which typically operate near the auto-collimation mode Echelle gratings are known for producing high order numbers ranging from 20 to 120 due to their large step-shaped grooves They achieve maximum grating efficiencies of up to 70% and maintain high dispersion across a wide spectral range by diffracting overlapping orders close to the high blaze angle, perpendicular to the small facet of the step.

Figure 3.4:Echelle grating (α: angle of incidence,β: angle of diffraction,θ: blaze angle,2δ: angle between incident and diffracted ray at blaze maximum,W: ruled grating width)

To describe the unique characteristics of an echelle grating, two fundamental equations are essential At the blaze maximum for each order, the angles of incidence (α) and diffraction (β) relate to the small angular difference (δ) from the blaze angle (θ), expressed as α=θ+δ and β=θ−δ Assuming cosδ≈1, the universally applicable grating equation simplifies to m λ=2W sinθ.

In an echelle spectrometer, the relationship between the order number (m), wavelength (λ), ruled width of the grating (W), and total number of grooves (N) is crucial for calculating center wavelengths in each echelle order The product of m and λ serves as a fundamental value for this calculation Additionally, the difference in center wavelengths between adjacent orders, known as the free spectral range (FSR), is represented by F(λ) = λ/m, which typically spans only a few nanometers.

According to the Rayleigh criterion, the theoretical resolutionΔλ theor, which could be produced by a spectrometer, is given by the theoretical diffraction-limited resolving powerR theor:

Using Equations 3.1 and 3.2 the simple formula:

The equation R theor = 2W sinθ λ (3.3) indicates that the optimal resolving power of an echelle spectrometer is attained by utilizing a large grating with a significant blaze angle Under ideal conditions, this setup can achieve a resolving power of several million for large echelles.

A similar formula could be obtained for the angular dispersionδβ/δλdifferentiating the grating Equation 3.1: δβ δλ = 2tanθ λ (3.4)

The angular dispersion of an echelle grating at a specific wavelength is solely determined by its blaze angle In typical experimental settings, where the slit width significantly exceeds the diffraction limit, the instrumental resolving power (λ/Δλ) of an echelle spectrometer remains constant for each detector pixel at the center wavelength across different orders.

High-quality echelle gratings are now available with blaze angles reaching up to 79°, offering significantly higher angular dispersion—approximately an order of magnitude greater than traditional echellette gratings used in their first or second order This enhanced angular dispersion allows for high linear dispersion at the detector when paired with a compact echelle spectrometer As a result, this technology leads to improved thermal and mechanical stability, increased transportability, and reduced manufacturing costs.

The echelle grating causes all diffraction orders to overlap, making it difficult for a spectrometer's detector to differentiate them Therefore, incorporating an additional dispersing element is crucial for accurate wavelength identification.

The preferred method for sequentially detecting spectral fractions smaller than single echelle orders involves external pre-selection before an echelle monochromator, which produces a one-dimensional spectrum Conversely, to simultaneously capture a wider spectral range, internal order separation is necessary within an echelle spectrograph that utilizes a two-dimensional array detector By employing a cross-dispersing prism, multiple orders can be focused side by side, maximizing detector efficiency Thus, optimizing the size and quality of the echelle spectrum image is crucial and can be achieved through advanced spectrometer design.

Becker-Ross and colleagues at the ISAS – Institute for Analytical Sciences in Berlin, Germany, developed various research spectrometers for high-resolution spectroscopy applications starting in the early 1990s This innovative equipment was systematically utilized for foundational studies in High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) During this time, two PhD theses were presented by Weiòe and Schỹtz, focusing on specific topics related to the research This article will briefly outline the general considerations and technical features of these spectrometers.

The spectrometer design at ISAS prioritizes the coupling of an echelle monochromator with a linear detection system, primarily due to the lengthy read-out times and high costs associated with large image detectors This sequential spectrometer approach allows for the detection of a limited spectral window at any desired wavelength within a broad range Key advantages of this design include high resolving power, excellent geometrical conductance, low stray light levels, precise spectral accuracy, and rapid peak hopping times between wavelengths.

The initial version of the resulting Double Echelle Monochromator (DEMON) was introduced by Florek et al in 1993 at the XXVIV CSI in York This model featured a prism monochromator for order pre-selection, paired with a simple echelle monochromator, and was utilized for High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) An enhanced version of this instrument, demonstrating the arrangement principle of the concept, is depicted in Figure 3.5.

Figure 3.5:HR-CS AAS setup with DEMON spectrometer (1 xenon short-arc lamp, 2 hollow cath- ode lamp (optional), 3 elliptical mirrors, 4 atomizer, 5 entrance slit, 6 parabolic mirrors,

7 prism, 8 folding mirrors and intermediate slit, 9 echelle grating, 10 CCD detector)

Detector

The high-resolution spectrometer's radiation detector requirements are intricate to fully leverage the potential of HR-CS AAS While some criteria are met, others remain critical or involve trade-offs, and enhancements in detector parameters are still sought after The CS AAS detector must provide high quantum efficiency across the far-UV to NIR spectrum, fast and low-noise read-out, substantial saturation capacity, and high spatial resolution with flexible two-dimensional pixel configurations, all at a reasonable cost Consequently, advancements in detector technology significantly shape the evolution of CS AAS.

In the early stages of CS AAS work, data generation began with the use of a photoplate, a real ‘multichannel’ photon detector that provided high spatial resolution and broad spectral sensitivity However, this early technology became obsolete due to its poor dynamic range and low repetition rate, stemming from the lengthy chemical development and spectrum evaluation processes The photo-multiplier tube (PMT), while an excellent single-channel detector capable of shot-noise limited measurements across various photon fluxes, was not a viable alternative due to its limitation of sequentially registering spectral intervals, rendering it and similar dissector tubes unsuitable for CS AAS applications.

The advent of solid-state array detectors has combined the benefits of photoplates and photomultiplier tubes (PMTs), resulting in an innovative 'electronic' photoplate Notably, photodiode arrays (PDA) and charge-coupled devices (CCD) enable precise registration of spatially and temporally resolved intensity distributions, as detailed by Harnly and Fields Today, various configurations of these array detectors, known for their exceptional mechanical accuracy and photometric performance, along with advancements in electronic signal processing, facilitate the development of high-resolution continuum source atomic absorption spectroscopy (HR-CS AAS) spectrometers for routine analytical applications.

In this section some detector considerations are discussed, which were of some relevance for the design of the different research spectrometers mentioned in this book.

The performance of array detectors, including those used in Continuous Source Atomic Absorption Spectroscopy (CS AAS), is primarily characterized by their 'dynamic range.' This dynamic range defines the operational area of the detector where absorbance measurements are constrained by shot noise It is influenced by fundamental detector parameters and is determined by the ratio of the saturation capacity to the square of the read-out noise.

A large dynamic range is crucial for accurate measurements, especially in scenarios with significant background absorption and when capturing data across a broad spectral range In this context, CCD arrays are the preferred choice for optimal performance.

CS AAS detectors were chosen for the research spectrometers due to their impressive specifications, featuring a saturation capacity ranging from 600,000 to 800,000 electrons per pixel With a read-out noise between 5 to 30 electrons, these detectors achieve a shot-noise limited dynamic range of 600 to 800, making them highly suitable for AAS applications.

The adoption of back-thinned CCD technology overcomes the sensitivity limitations found in traditional front-illuminated and UV-coated CCDs This advanced method utilizes substrates with ultra-thin silica layers, significantly boosting quantum efficiency in the UV spectrum to as high as 0.9 electrons per photon Additionally, specialized anti-reflection coatings on the detector surface further enhance efficiency for specific spectral bands.

The read-out process for a CCD array detector is truly simultaneous when restricted to a small number of pixels (m) perpendicular to the read-out direction During illumination, electrons generated in each pixel well are rapidly and simultaneously shifted to the read-out register following each accumulation interval.

The 'binning' procedure allows for the collection of electrons representing the same wavelength within a column into a single register increment, facilitating detection of small linear spectral intervals by a CCD spectrometer, even with substantial slit heights and without a mechanical shutter This feature is particularly beneficial for echelle spectrometers of the DEMON type.

Figure 3.14: Read-out scheme of a CCD array detector

Echelle spectrographs of the ARES type require large CCD detectors with millions of pixels to capture a wide spectral range during each read-out cycle However, in the case of simultaneous high-resolution continuum source atomic absorption spectrometry (HR-CS AAS), implementing smart 'on-chip' binning routines is impractical This is due to the variable tilt of successive echelle orders, which does not align with the rectangular pixel pattern of the detector, leading to significant cross-talk between integrated detector areas before analog-to-digital conversion Consequently, individual pixel read-out is necessary, resulting in a slower repetition rate when a high dynamic range is needed.

While this limitation is not critical for basic investigations, particularly in simultaneous HR-CS FAAS, the choice of an appropriate detector remains an open question Designing an instrument with specifications that match competitive analytical methods will be further explored in Chapter 9.

The contrAA 300 from Analytik Jena AG

The atomic absorption spectrometer contrAA 300 from Analytik Jena AG is the pioneering commercial instrument for high-resolution continuum source atomic absorption spectroscopy (HR-CS AAS), closely linked to the DEMON research spectrometers detailed in Section 3.2.2 As of this writing, the contrAA 300 supports only flame atomization and chemical vapor generation techniques, as illustrated in Figure 3.15 However, the manufacturer has indicated plans to release a combined flame and graphite furnace version soon.

Figure 3.15:ContrAA 300 – the first commercially available continuum source flame AA spec- trometer (Analytik Jena AG, Jena, Germany)

The DEMON design features a double monochromator that incorporates a prism pre-monochromator and an echelle monochromator, ensuring high resolution across a selected spectral interval with minimal modifications to its optical and analytical specifications It offers a usable wavelength range from 189 nm in the vacuum ultraviolet (VUV) to 900 nm in the near-infrared (IR), fully encompassing the range utilized in LS AAS Additionally, the wavelength distance per pixel is λ/140,000, matching the latest prototypes of DEMON spectrometers.

The CCD detector, developed in collaboration with Hamamatsu, is specifically designed for high-resolution continuum source atomic absorption spectroscopy (HR-CS AAS) It features 576 measurement pixels, enabling highly-resolved and simultaneous observation across a spectral range of nearly 1 nm The instrument can adjust wavelengths in approximately 2 seconds, including necessary corrections and optimizations Its vertical spectrometer design allows for a compact size of just 781 x 730 x 635 mm and a weight of about 85 kg.

The high-pressure xenon short-arc lamp, housed in a water-cooled brass casing, features a self-adjusting design for easy replacement of the radiation source This integral water cooling system ensures optimal performance, allowing the lamp to operate maintenance-free throughout its designated lifespan and to be ready for use immediately after ignition.

Figure 3.16: Photo of the high-pressure xenon short-arc lamp (GLE, Berlin, Germany)

The atomizer unit, gas control, automatic burner adjustment, and sample introduction systems, including micro-sample injection and automatic sample dilution, have been derived from advanced LS AAS technologies The operational requirements for HR-CS AAS, in terms of temperature range, gas supply, and electrical conditions, are comparable to those of traditional LS AAS, making it equally user-friendly.

The third unit of the system comprises the radiation source, spectrometer, and detector, along with the instrument control, which includes the operator interface as depicted in Figure 3.17 Optimal measurement conditions are verified and adjusted for each spectral range within milliseconds before each measurement When fully operational, the system captures data from 576 pixels simultaneously every millisecond during evaluation This data is pre-averaged before being transmitted to the application software for further processing.

Figure 3.17: Screen-shot of the operator surface of the contrAA 300 spectrometer

The application software is designed for both manual and fully automatic measurement modes, assisting analysts in developing and optimizing methods for High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) It features rapid wavelength and element changes for flame operation, enabling quick sequential multi-element determinations for up to 20 customizable elements with a consistent sample flow Additionally, the software allows analysts to visualize and evaluate the spectral environment during the measurement cycle.

Reference spectra are recorded at regular intervals to calculate absorbance values and mitigate fluctuations in radiation source intensity while identifying suitable pixels for simultaneous baseline correction (BC) The automatic baseline adaptation algorithm ensures reliable results without requiring analyst programming, although analysts can manually define the spectral range, analyte, and correction pixels if desired The software also allows for the re-processing of recorded data, and additional least-squares adaptation algorithms are available to address complex analytical challenges by eliminating known spectral interferences using reference spectra for correction.

The Modulation Principle

Talking about his early thoughts about AAS back in 1952, Walsh [147] remembers that

For several years before exploring atomic absorption, I utilized a commercial IR spectrophotometer with a modulated light source and synchronized detection system This system's design ensured that any radiation emitted by the sample did not generate a signal at the output, which likely helped eliminate any mental barriers regarding absorption measurements of luminous atomic vapors The modulation principle, involving either an AC-operated radiation source or a beam chopper paired with a selectively tuned amplifier, has since become standard in all commercial atomic absorption spectrometers This feature is a significant advantage of atomic absorption spectroscopy (AAS) over optical emission techniques, as it enhances the selectivity and specificity of measurements through the use of element-specific radiation sources.

In High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS), potential interferences from luminous atomic vapors or emissions from the atomizer are significantly minimized The radiation source in HR-CS AAS is 1 to 2 orders of magnitude more intense than that of conventional Line Source AAS (LS AAS), reducing the risk of emission interferences correspondingly Additionally, while LS AAS detectors integrate radiation over a broad spectral bandwidth, capturing any atomic emission, HR-CS AAS focuses solely on emissions that coincide with the analytical line, resulting in a much lower intensity of any broadband emission on the analytical pixel Consequently, any potential interference from emissions is negligible, especially when considering the higher lamp intensity Furthermore, in the rare event of intense emissions affecting the measured signal, background correction systems will effectively compensate for this interference, ensuring accurate results.

HR-CS AAS offers distinct advantages by eliminating the need for source modulation or selective amplifiers, thereby reducing potential noise sources Unlike LS AAS, which experiences noise from AC operation of hollow cathode lamps and mechanical choppers, HR-CS AAS ensures a cleaner signal Additionally, issues related to emission noise from the nitrous oxide/acetylene flame, commonly encountered in the determination of barium and calcium in LS AAS, are absent in HR-CS AAS due to the superior intensity of its primary radiation source and enhanced resolution.

Simultaneous Double-beam Concept

In LS AAS, spectrometers are categorized into single-beam and double-beam types A single-beam spectrometer transmits primary radiation directly through the absorption volume without splitting the beam, whereas a double-beam spectrometer divides the beam into two parts, allowing for simultaneous measurement of the sample and reference radiation.

In spectroscopic analysis, a sample beam is directed through an absorption volume, such as a flame or furnace, while a reference beam bypasses this area The separation and recombination of these beams can be achieved using a rotating chopper with a partially mirrored quartz disk or semi-transparent mirrors Typical modulation frequencies for this process range from 50 Hz to 100 Hz, ensuring precise measurement of absorption characteristics.

Single-beam spectrometers offer the benefit of fewer optical components, resulting in lower radiation losses and higher effective optical conductance In contrast, double-beam spectrometers are often praised for their long-term stability, as they can compensate for variations in source intensity and detector sensitivity However, this advantage may be overstated, as changes in radiant intensity and line profile occur during the warm-up phase, affecting sensitivity Additionally, double-beam systems cannot account for variations in the atomizer, such as flame drift While double-beam spectrometers are preferred for routine Flame Atomic Absorption Spectroscopy (FAAS) to minimize baseline drift and recalibration, single-beam spectrometers are advantageous in Graphite Furnace Atomic Absorption Spectroscopy (GF AAS), where baseline resetting occurs before each atomization, making their superior optical conductance more beneficial.

High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) utilizes optical single-beam spectrometers, eliminating the need for geometric beam splitting and recombining This technology features an advanced stabilization system that rivals the performance of traditional optical double-beam instruments while allowing for simultaneous operation rather than sequential measurements The CCD array detector in HR-CS AAS typically comprises several hundred pixels, each functioning as an independent detector with its own charge-collecting capacity, all illuminated by a common radiation source and read out simultaneously.

In atomic absorption measurements, only a limited number of pixels are utilized, while additional pixels can be employed to adjust for lamp intensity fluctuations, which are consistent across all pixels within a few hundred picometers Since all pixels are illuminated and read simultaneously rather than sequentially, this method ensures that even rapid changes in emission intensity are accurately corrected.

The atomizer's ability to adjust for any temporal changes in transmittance, such as those caused by flame gases, is a significant advantage over optical double-beam systems This capability is crucial for accurately measuring and correcting background absorption, a topic that will be explored in detail in Section 5.2.

Selection of Analytical Lines

In LS AAS, the most sensitive analytical line is typically utilized for element determination due to the method's focus on trace and ultra-trace analysis, which demands high sensitivity This approach allows for greater dilution in complex sample matrices, minimizing potential interferences However, there are instances where using the most sensitive line is not advisable, as it may not yield the best signal-to-noise ratio (SNR), exemplified by the 217.001 nm lead line Additionally, the presence of other lines in the lamp spectrum can lead to a significantly non-linear working curve, making lines such as 340.725 nm for cobalt, 232.003 nm for nickel, and 244.791 nm for palladium less suitable for accurate analysis.

Figure 4.1:Absorbance over time for 200 pg of lead in aqueous solution measured at the CP at

283.306 nm only, (a) without and (b) with the use of reference pixels to correct for lamp noise

HR-CS AAS overcomes the limitations of conventional LS AAS due to its high radiation intensity, which provides a significantly improved signal-to-noise ratio (SNR) even at wavelengths down to 200 nm The radiation intensity remains consistent across various lines, although it does slightly decrease in the far-ultraviolet range Additionally, the monochromator's resolution ensures that only about twice the full width at half maximum (FWHM) of the line is detected by the analytical pixel, which is always centered on the line This setup eliminates issues commonly associated with line sources, such as line shifts, self-absorption, and interference from other emitted lines.

Atomic Absorption Spectroscopy (AAS) is primarily recognized for trace analysis but is also effective for quantifying main components like calcium in cement, lead and tin in soft solders, and chromium, iron, and nickel in stainless steel Achieving the necessary precision in these applications is challenging; simply diluting the sample solution to fit within the working range of the most sensitive lines is inadequate Instead, employing less sensitive secondary lines with moderate dilution is essential, as excessive dilution can compromise the results significantly However, the availability of suitable low-sensitivity analytical lines is often limited due to the weak emission intensity from the Hollow Cathode Lamp (HCL), which may not deliver the signal-to-noise ratio (SNR) required for high-precision measurements.

In Graphite Furnace Atomic Absorption Spectroscopy (GF AAS), the use of secondary lines is infrequent due to the ability of Flame Atomic Absorption Spectroscopy (F AAS) to accurately determine high analyte concentrations However, the demand for reduced sensitivity has emerged with the direct analysis of solid samples in GF AAS, as these samples cannot be easily diluted, and variations in sample mass are limited Consequently, utilizing alternate, less sensitive lines becomes a viable method for measuring higher concentrations This need for alternative lines is expected to grow with High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS), which is particularly effective for direct solid sample analysis In contrast, in Line Source Atomic Absorption Spectroscopy (LS AAS), the use of secondary lines is often discouraged due to their typically low emission intensity, which can compromise signal-to-noise ratio (SNR) and measurement precision Additionally, secondary lines are frequently under-researched, raising concerns about potential spectral interferences, leading to caution in their application.

In High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS), challenges commonly faced in other methods are largely absent due to the consistent and intense emission of the primary radiation source, ensuring a high signal-to-noise ratio (SNR) across all analytical lines regardless of their spectral origin The main factors influencing the results are the absorption coefficient and the population of low excitation levels when non-resonance lines are utilized Additionally, the high resolution of the monochromator allows for the clear visibility of the entire spectral environment surrounding the analytical line, enabling easy detection of potential spectral interferences, which typically do not affect the measurement unless there is a direct line overlap In such rare cases, HR-CS AAS offers effective solutions, as will be elaborated in Section 5.2.3.

Sensitivity and Working Range

In Atomic Absorption Spectroscopy (AAS), the correlation between the concentration (c) or mass (m) of the analyte in the measurement solution and the absorbance (A) or integrated absorbance (A int) is mathematically defined through calibration samples, typically calibration solutions This relationship is represented by the calibration function, which illustrates how absorbance relates to the concentration or mass of the analyte.

The slopeSof the calibration function is termed sensitivity, i.e.:

In Atomic Absorption Spectroscopy (AAS), the sensitivity of an analyte is quantified using the terms 'characteristic concentration' (c₀) and 'characteristic mass' (m₀) These metrics correspond to an absorbance of A = 0.0044 (1% absorption) or an integrated absorbance of A_int = 0.0044s Sensitivity is influenced by physical properties, such as the absorption coefficient of the analytical line and the features of the atomizer unit The characteristic mass can be calculated using the formula: m₀ [pg] = 0.0044 × c [μg/L] × V [μL].

, (4.3) wherecandV are the concentration and the volume of standard required for an integrated absorbance ofA Standard, andA Blankis the absorbance signal for the blank.

Smith and Harnly [136] introduced the concept of 'intrinsic mass' to facilitate the comparison of different Echelle monochromator and slit configurations Similar to characteristic mass, intrinsic mass represents the analyte mass needed to achieve an integrated absorbance of 0.0044 s per picometer of spectral bandwidth This is determined using the wavelength-integrated absorbance A λ (over n samples) and the spectral bandwidth Δλ.

I i , (4.4) wherebyI 0 is the reference intensity andI i the intensity of the individual pixel.

In HR-CS AAS, optimal linearity of the calibration function is achieved by evaluating the absorbance at the center pixel (CP) of the line core However, integrating absorbance over the CP±1, which includes portions of the line wings, can enhance sensitivity by approximately twofold, as will be elaborated later in this section.

A significant limitation of LS AAS is its short linear calibration range, typically spanning two to three orders of magnitude due to factors like stray radiation and the emission line width of the radiation source In contrast, CS AAS theoretically has no limit to its calibration range, with practical constraints arising from detector size, potential spectral interferences, and the need for atomizer cleaning after high analyte concentrations To address these limitations, Harnly and colleagues proposed two methods to extend the calibration range of CS AAS to approximately 5 to 6 orders of magnitude: the wavelength integrated absorbance (WIA) method for read-noise limited linear photodiode array detectors, and the wavelength selected absorbance (WSA) method for shot-noise limited CCD detectors.

The WIA approach utilizes large entrance slits to measure integrated absorbance by integrating over an increasing number of pixels The calibration curves produced resemble those of large quotients between the instrumental profile width and the absorption line FWHM, as theoretically predicted by Mitchell and Zemansky At low concentrations, absorbance exhibits a linear increase with concentration, resulting in linear plots with a slope of 1.0 when plotting the logarithm of absorbance against the logarithm of concentration As concentration rises, the absorbance at the peak center reaches a maximum due to stray radiation, causing the calibration curves for LS AAS to plateau However, with a continuum source, absorbance can also be measured in the wings of the profile, where it increases linearly with concentration Notably, the wings broaden with the square root of concentration, leading to a relationship where the wavelength integrated absorbance increases with the square root of concentration, resulting in a linear plot with a slope of 0.5 on a log-log scale.

The inflection point on the calibration curve, where the slope changes from 1.0 to 0.5, is influenced by the 'α-value' and the hyperfine splitting of the absorption profile This α-value is directly related to the ratio of the collisional width, playing a crucial role in determining the curve's characteristics.

Doppler width influences the absorption profile's width, varying by element and temperature Hyperfine splitting, resulting from electronic transition coupling, dictates the number of absorption profile components Elements with low α-values and fewer hyperfine components exhibit deeper, narrower profiles, while those with higher α-values and more hyperfine components display shallower, broader profiles Consequently, elements with deeper profiles reach the stray radiation limit more quickly and show inflection points at lower concentrations.

The practicality of the log-log calibration approach in analytical work raises several concerns Firstly, it is rarely utilized in standard analytical procedures Secondly, the inflection point, which marks the transition between linear regions, complicates the integration of dynamic signals in Graphite Furnace Atomic Absorption Spectroscopy (GF AAS), as noted by L’vov Additionally, using approximately 30 pixels for signal evaluation significantly increases the risk of spectral interferences Furthermore, this WIA method is primarily designed for Photodiode Array (PDA) detectors, which are not suitable for Continuous Source Atomic Absorption Spectroscopy (CS AAS) and are not employed in the instruments referenced in this book.

The WSA approach introduced by Harnly et al for CCD detectors offers a more practical solution, allowing for the use of narrower entrance slits This method focuses not only on the evaluation of the circular polarization (CP) but also on the analysis of the line core.

In evaluating absorbance, pairs of pixels such as +3 and -3 or +4 and -4 are utilized, focusing on the wings at a specific distance from the line center where absorbance increases linearly with concentration This method minimizes the influence of line broadening since it excludes measurements around the line center Consequently, this approach yields a series of linear calibration curves with a slope of 1.0 on a log-log scale.

Heitmann et al [62] showcased the capabilities of a high-resolution continuum source atomic absorption spectrometer (HR-CS AAS) for analyzing two elements: silver, detected at 328.068 nm with a narrow absorption line, and indium, observed at 303.936 nm, which spans over five pixels, as illustrated in Figure 4.2.

Using HR-CS AAS allows for signal registration not only at the central pixel mass (CPM), similar to traditional LS AAS, but also enables the utilization of the volume of the absorption peak by incorporating an increasing number of pixels, including side pixels.

N x only, as shown in Figure 4.3.

In peak volume registration, increasing the number of pixels for detection can enhance sensitivity based on peak width For narrow absorption lines, such as with silver, the sensitivity achieved using only the central pixel (CP) is comparable to that obtained with a hollow cathode lamp (HCL) Utilizing three pixels (CP±1) significantly boosts sensitivity and extends the linear working range; however, further increasing peak volume detection leads to a rapid signal drop, integrating mostly noise Conversely, for broader absorption lines like indium, sensitivity in high-resolution continuum source atomic absorption spectroscopy (HR-CS AAS) is notably lower than in low-resolution AAS when only the CP is utilized.

Figure 4.2:Typical line profiles of (a) silver at 328.068 nm and (b) indium at 303.936 nm; sample concentration: 1 mg/L, respectively

Figure 4.3:Definition of center pixel (M), peak volume (M x ) and side pixel (N x ) registration

Figure 4.4:Influence of the peak volume registration scheme on the sensitivity and working range in the case of (a) silver at 328.068 nm and (b) indium at 303.936 nm

Significant sensitivity enhancements in HR-CS AAS can be achieved by utilizing CP±1, and even more so by increasing the peak volume to CP±2.

CP±3 For exact comparison the LS AAS measurement was obtained with the same spec- trometer setup by replacing the xenon short-arc lamp with a conventional HCL (refer to Figure 3.5).

Signal-to-Noise Ratio, Precision and Limit of Detection

This section focuses solely on the 'noise' component of the discussed terms, as the 'signal' sensitivity has been thoroughly addressed in Section 4.4 It will specifically examine the contribution of instrumental components to the noise, excluding the 'analytical' aspects like sample introduction imprecision, flame noise, and sample inhomogeneity, which also significantly impact the overall noise.

The noise contribution of the detector, as discussed in Section 2.2.2, indicates that for CCDs, absorbance noise remains unaffected by spectral bandwidth, but relies on the measurement pixels (n_sam) being minimized and reference pixels (n_ref) being larger Additionally, the radiance (L_λ) of the radiation source significantly impacts noise, with the minimal detectable volume concentration of absorbing atoms (N_min) being inversely proportional to the square root of L_λ Given that the intensity of the source in CS AAS is substantially higher—by 1 to 2 orders of magnitude—than typical line sources in conventional AAS, improvements in signal-to-noise ratio (SNR) and limits of detection (LOD) by factors of 3 to 10 are anticipated, barring the influence of dominant factors like flame noise Table 4.1 demonstrates that this anticipated improvement in LOD has been achieved for most elements.

Table 4.1:Overview of the characteristic concentrations and LOD (3σ) obtained with the DEMON based HR-CS AA spectrometer in an air / acetylene flame

Element Wavelength Characteristic concentration LOD

The stability of the radiation source significantly impacts its performance, particularly in the case of unstable arcs, which produce a wavelength-independent 'white' noise across all CCD array pixels This noise can be effectively mitigated using reference pixels, as previously discussed in Section 4.2 Consequently, the minimum detectable absorbance signal is primarily influenced by statistical variations in intensity between neighboring pixels, known as shot noise Notably, increasing the illumination time or radiation intensity by a factor of four can reduce the absorbance noise by a factor of two, illustrating the relationship between intensity and noise reduction.

Increasing the illumination time from 5 seconds to 45 seconds for lead at 217.001 nm significantly impacts measurement quality, as illustrated in Figure 4.6 This enhancement reduces the noise level, measured as the standard deviation over three pixels, by a factor of 2.9, aligning closely with expectations for shot-noise limited measurements Consequently, the limit of detection (LOD) is also improved by the same factor.

0.002 absorbance (CP +/- 1): 0.004118 standard deviation: 0.000028 LOD: 4.1 μ g/l

0.003 absorbance (CP +/- 1): 0.004106 standard deviation: 0.000080 LOD: 12 μ g/l

Figure 4.6:Influence of the illumination time on the absorbance noise in HR-CS F AAS for lead at

217.001 nm; (a) illumination time: 5 s; (b) illumination time: 45 s

Figure 4.7 illustrates the impact of radiation intensity, highlighting that while the intensity distribution of the xenon short-arc lamp remains relatively uniform across the spectrum, significant losses in radiation intensity occur in the far-UV range, especially below 200 nm, which are unavoidable in any optical system.

0.004 absorbance (CP +/- 1): 0.006508 standard deviation: 0.000114 LOD: 86 μ g/l

0.004 absorbance (CP +/- 1): 0.001607 standard deviation: 0.000038 LOD: 1.2 μ g/l

The impact of radiation intensity on absorbance noise in High-Resolution Continuum Source Flame Atomic Absorption Spectroscopy (HR-CS F AAS) is illustrated in Figure 4.7, showcasing two key determinations: selenium at 196.026 nm with a sample concentration of 1000 μg/L, and cadmium at 228.802 nm with a sample concentration of 10 μg/L, both measured over an illumination time of 5 seconds.

At a wavelength of 196.026 nm, selenium exhibits an absorbance noise of just 0.000114 with an illumination time of 5 seconds In contrast, cadmium at 228.802 nm, still within the far-UV region, shows a significantly reduced noise level of 0.000038, which is three times lower, attributed to the increased radiation intensity reaching the detector This trend of decreasing noise levels continues with longer wavelengths, although the effect becomes less pronounced.

Multi-element Atomic Absorption Spectrometry

Harnly has explored the concept of simultaneous multi-element Atomic Absorption Spectroscopy (AAS), which merges high-resolution continuum source AAS capabilities with multi-element detection Instruments utilizing high-resolution echelle spectrometers and intense continuum sources, like xenon short-arc lamps, enable simultaneous multi-element AAS measurements For instance, the ARES spectrometer developed by Becker-Ross and colleagues was designed for structured background studies in Flame AAS (FAAS), though it has limitations, such as a 2-second read-out time per spectrum, resulting in lengthy measurement times While this might suffice for FAAS, it lacks the speed advantages of fast sequential techniques in conventional Longitudinal AAS (LS AAS) and is unsuitable for transient signals in Graphite Furnace AAS (GF AAS) However, spectrometers employing continuum sources with double monochromators and echelle gratings can achieve rapid line access in under 1 second, allowing for optimized conditions for each element and facilitating fast sequential multi-element determinations The high intensity of the xenon short-arc lamp enhances signal-to-noise ratios, enabling quick adjustments in flame conditions Consequently, the total time for changing wavelengths, adjusting flame parameters, and measuring absorbance can be condensed to a few seconds, streamlining the routine determination of multiple elements in similar sample solutions.

In HR-CS F AAS, the process begins with calibrating the instrument for all relevant elements, followed by the analysis of multiple samples sequentially Notably, for a limited range of 10 to 15 elements, the total analysis time for HR-CS F AAS can be shorter than that of simultaneous ICP OES measurements This efficiency is primarily due to the significantly shorter equilibration time needed for the AAS burner when switching sample solutions, in contrast to the longer equilibration times required for the spray chambers in ICP OES.

Another option that is available with HR-CS AAS to a much greater extent than with

LS AAS utilizes secondary, less sensitive analytical lines due to the uniform high signal-to-noise ratio (SNR) across all lines, eliminating the presence of 'weak lines.' While emission intensity and detector sensitivity decline below 220 nm, this method allows for the selection of two or three analytical lines with varying sensitivities in fast sequential mode This is particularly beneficial when analyte concentrations in samples are unknown and can vary significantly As a result, the analyte can be accurately measured within the optimal working range of an analytical line without the need for additional dilution, leading to substantial time savings and reducing the risk of dilution errors.

The fast sequential mode of operation in High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) introduces the ‘reference element technique’ or ‘internal standard’ method, which has been rarely documented in Low-Resolution Atomic Absorption Spectroscopy (LS AAS) Although a few papers from the 1970s discuss this technique, its application has been limited due to several factors Firstly, it necessitates a dual- or multi-channel spectrometer, which has been scarce in the market Secondly, while this technique effectively corrects for non-specific interferences, finding a suitable reference element for element-specific interferences poses challenges Lastly, the most prominent multi-channel LS AAS system, the Perkin-Elmer model SIMAA 6000, was primarily designed for Graphite Furnace AAS, a method that typically does not face non-specific interferences Consequently, the body of literature utilizing the reference element technique remains minimal.

In HR-CS AAS, although no simultaneous measurement of two elements is yet pos- sible, the reference element technique can be used essentially without compromises for

In Flame Atomic Absorption Spectroscopy (FAAS), non-specific interferences are prevalent, particularly transport interference resulting from viscosity changes in sample and calibration solutions Fast-sequential operation effectively manages these interferences as it remains consistent over time To mitigate interferences in Line Source FAAS (LS FAAS), matrix matching can be employed when the sample matrix is known and stable across multiple samples, while the analyte addition technique is used for unknown or variable matrices However, matrix matching requires high concentrations of ultra-pure chemicals to minimize blank values, and the analyte addition method is labor-intensive, limited to the linear portion of the calibration curve, and offers lower precision due to reliance on extrapolation In contrast, the reference element technique in FAAS eliminates these limitations, providing significant time savings and improved accuracy in the presence of non-specific interferences.

The reference element technique offers the significant benefit of identifying and correcting dilution errors by incorporating the reference element early in the sample preparation process, prior to final dilution This method allows for quantitative analysis to be performed without the need for precise dilution or volumetric flasks, leading to time savings and reducing the risk of errors during sample preparation.

Absolute Analysis

Atomic Absorption Spectroscopy (AAS) is fundamentally a relative technique that relies on calibration samples for quantitative results; however, the concept of 'absolute analysis'—calculating the analyte quantity directly from absorbance using physical constants—has been a topic of discussion since Walsh's 1955 paper Although the flame atomizer introduced significant variables that hindered absolute analysis, L’vov later laid the groundwork for modern Graphite Furnace AAS (GF AAS), suggesting its potential for achieving absolute methods Subsequent research by Slavin and Carnrick demonstrated that GF AAS, utilizing the STPF concept based on L’vov's theories, could yield determinations with an accuracy of 10-20% in complex matrices without calibration, referencing the characteristic mass (m0) L’vov et al also explored calculating m0 through a simplified model, identifying sensitivity variations primarily due to the age, characteristics of line sources, and operational conditions.

Gilmutdinov and Harnly [42] proposed that High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) is better suited for absolute analysis compared to Low-Resolution Atomic Absorption Spectroscopy (LS AAS) They emphasized that integrating absorbance is essential for accurate absolute measurements, which require resolution in wavelength, space, and time This method allows for simultaneous measurements using a continuum source, a high-resolution echelle spectrometer, and a solid-state array detector While this approach represents a significant advancement in achieving absolute analysis by reducing key variables, it has faced criticism from L’vov [99].

The characteristic mass (m0) is a vital control criterion in Graphite Furnace Atomic Absorption Spectroscopy (GF AAS) due to its remarkable stability, even in Low-Resolution Atomic Absorption Spectroscopy (LS AAS) In laboratory settings, m0 is essential for verifying instrument functionality and the appropriateness of selected parameters, as well as providing insights into method trueness during development and serving as a benchmark in interlaboratory trials It is anticipated that the stability of m0 will improve further with High-Resolution Continuum Source Atomic Absorption Spectroscopy (HR-CS AAS) Despite its acknowledged utility, the concept of 'absolute analysis' remains a contentious issue, primarily of academic interest, as laboratories cannot forgo calibration samples and solutions to validate m0 Additionally, regulatory requirements often mandate the use of specific calibration samples at regular intervals to ensure the accuracy of analytical results.

Measurement Principle in HR-CS AAS 77

The Individual Elements 91

Electron Excitation Spectra of Diatomic Molecules 147

Specific Applications 211