授課教師: Professor 吳逸謨 教授 Warning: Copyrighted by textbook publisher. Do not use outside class.

Principles of Instrumental Analysis

Chapter 12 Atomic X-ray Spectrometry

1 X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.

2 Ｘ光機器被選為史上最佳的科學發明 • Ｘ光機器被選為史上最佳的科學發明，1928年問世的抗生素藥物盤尼西林（Penicillin） • 排名第二。

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• 由德國物理學家倫特根（William Roentgen）114年前發明的Ｘ光機器，獲得近1萬 張選票，高居榜首，倫特根本人並因為這項發明在1901年獲得諾貝爾物理獎殊榮。

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• 排名第10的是1837年發明的電報機（ElectricTelegraph），它縮短人類通訊的時間，掀起傳播 革命。 981104

X-ray: X-radiation to signify an “unknown type of radiation”.

X-ray is also called: Röntgen radiation, after Wilhelm Röntgen (a German physicist, who discovered this radiation. Atomic X-ray Spectrometry Atomic X-ray Spectrum Methods include: X-ray Emission method (Ｘ光發射分析) X-ray Absorption method (Ｘ光吸收分析) X-ray Fluorescence method (Ｘ光螢光發射分析) X-ray Diffraction method (Ｘ光繞射分析) [skipped]

12A. FUNDAMENTAL PRINCIPLE X-rays are short-wavelength (high-energy) electromagnetic radiation produced by the deceleration of high-energy electrons or by electronic transitions of electrons in the inner orbitals of atoms.

The wavelength range of X-rays is from about 10-5 Å to 100 Å; conventional X-ray spectroscopy is, however, largely confined to the region of about 0.1 Å to 25 Å (1 Å = 0.1 nm = 10-10 m).

4 12A-1 Emission of X-rays • For analytical purposes, X-rays are generated in four ways:

• (1) by bombardment of a metal target with a beam of high-energy electrons, [This is the most common source.] • (2) by exposure of a substance to a primary beam of X-rays to generate a secondary beam of X-ray fluorescence, • (3) by use of a radioactive source whose decay process results in X-ray emission, and • (4) from a synchrotron radiation source.

• Only a few laboratories in the United States (in the world) have facilities to produce X-rays from synchrotron radiation. For this reason, we will consider only the first three sources. - (Note: This is not true anymore. Many labs outside US now have synchrotron facilities, including one in Hsinchu, Taiwan. National Synchrotron Center)

Note: When the energy source is a synchrotron, the X-ray beam can be very small (microns) and very intense. 5 Note: Snychrotron For X-ray sources

Cyclotron

The electromagnetic radiation emitted when charged particles 6 are accelerated radially ( ) is called synchrotron radiation. X-ray sources produce only line and continuum emissions, but no bands.

X-ray sources, like ultraviolet and visible emitters, often produce both continuum and line spectra; both types are of importance in analysis. Continuum radiation is also called white radiation or bremsstrahlung. Bremsstrahlung means radiation that arises from retardation of particles; such radiation is generally a spectral continuum.

Lines – correspond to quantum energies of inner electrons. Continuum –radiation from retardation by particles.

Note: Characteristic X-rays were discovered by Charles Glover Barkla in 1909,[1] who later won the Nobel Prize in Physics for his discovery in 1917. Continuum Spectra from Electron Beam Sources In an X-ray tube, electrons produced at a heated cathode are accelerated toward a metal anode (the target) by a potential difference as great as 100 kV; when electrons collide with the anode, part of the energy of the beam is converted to X-rays. Continuum emission -radiation from retardation by particles – Continuous and not quantum.

Under some conditions, only a continuum spectrum [i.e., no lines] such as that shown in results; Figure 12-1 FIGURE 12-1 Distribution of continuum under other conditions, a line radiation from an X-ray tube spectrum is superimposed on the with a tungsten target. The numbers above the curves indicate the continuum (see Figure 12-2). accelerating voltages. 8 Bremsstrahlung – brake radiation Continuum X-ray

Bremsstrahlung (German pronunciation) from bremsen "to brake" and Strahlung "radiation", i.e. "braking radiation" or "deceleration radiation") is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus.

The moving particle loses kinetic energy, which is converted into a photon, thus satisfying the law of conservation of energy.

The term is also used to refer to the process of producing the radiation.

Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the 9 energy of the accelerated particles increases. Continuum X-ray

Strictly speaking, braking radiation is any radiation due to the acceleration of a charged particle, which includes synchrotron radiation, cyclotron radiation, and the emission of electrons and positrons during beta decay.

However, the term is frequently used in the more narrow sense of radiation from electrons (from whatever source) slowing in matter.

Bremsstrahlung emitted from plasma is sometimes referred to as free-free radiation. This refers to the fact that the radiation in this case is created by charged particles that are free both before and after the deflection (acceleration) that caused the emission.

10 – The continuum X-ray spectrum shown in the two figures is characterized by a well-defined, short-length limit (λ0), which depends on the accelerating voltage V but is independent of the target materials. [Left (Fig. 12-1): tungsten, Z=74; Right (Fig. 12-2): molybdenum, Z=42]

– Thus, λ0 (0.35 Å) for the spectrum produced with a molybdenum target at 35 kV (Figure 12-2) is identical to λ0

for a tungsten target at the same voltage (Figure 12-1). 11 X-ray emission

X-ray notation (K, L, M) of line emissions vs. atomic notation: “1s, 2s, 3p,”, etc., will be discussed later.

12 Cont’d – Continuum in X-ray emission

• The continuum radiation from an electron beam source results from collisions between the electrons of the beam and the atoms of the target material. At each collision, the electron is decelerated and a photon of X-ray energy is produced. • The energy of the photon is equal to the difference in kinetic energies of the electron before and after the collision. • Generally, the electrons in a beam are decelerated in a series of collisions; the resulting loss of kinetic energy differs from collision to collision. Thus, the energies of the emitted X-ray photons vary continuously over a considerable range

(continuum). [Fig. 12-1, next page, again] 13 The high velocity electrons collide with a metal target, the anode, creating the X-rays.[17]

-In medical X-ray tubes the target is usually tungsten (W, Z=74) or a more crack-resistant alloy of rhenium (5%) and tungsten (95%), but sometimes molybdenum (Mo, Z=42) for more specialized applications, such as when softer X-rays are needed as in mammography [Note: low-energy X-rays (usually around 30 kV) to examine the human breast].

-In crystallography, a copper target is most common [Kα =1.54A is used.]

Characteristic X-ray emission lines for some common anode materials.[15][16] Photon energy Wavelength Anode Atomic [keV] [nm] material number Kα1 Kβ1 Kα1 Kβ1 W 74 59.3 67.2 0.0209 0.0184 Mo 42 17.5 19.6 0.0709 0.0632 Cu 29 8.05 8.91 0.157 0.139 Ag 47 22.2 24.9 0.0559 0.0497

Ga 31 9.25 10.26 0.134 0.121 14 In 49 24.2 27.3 0.0512 0.455 Conversion[edit] X-ray notation is a method of labeling atomic orbitals that grew out of X-ray science. It is still traditionally used with most X-ray spectroscopy techniques including AES and XPS.  In X-ray notation, every principal quantum number is given a letter [K, L, M, etc.] associated with it.

Therefore, the X-ray notation (K, L, M) is different from atomic notation: “1s, 2s, 3p,”, etc., used in the atomic spectroscopy discussed earlier.

Conversion[1][2] Quantum Numbers Atomic Notation X-ray Notation (n l s j)

1 0 ±1/2 1/2 1s(1/2) K1

2 0 ±1/2 1/2 2s(1/2) L1

2 1 -1/2 1/2 2p(1/2) L2

2 1 +1/2 3/2 2p(3/2) L3

3 0 ±1/2 1/2 3s M1

3 1 -1/2 1/2 3p1/2 M2

3 1 +1/2 3/2 3p3/2 M3 3 2 -1/2 3/2 3d M 3/2 4 15 3 2 +1/2 5/2 3d5/2 M5 Duane-Hunt law – energy transfer - electron to photon The maximum photon energy generated corresponds to the instantaneous deceleration of the electron to zero kinetic energy in a single collision. For such an event, we can write:

E=hνo =hc/λo = V e (12-1)

where V e, the product of the accelerating voltage and the charge on the electron, is the kinetic energy of all of the electrons in the beam; h is Planck's constant; and c is the velocity of light. The quantity ν0 is the maximum frequency of radiation that can be produced at voltage V, and λ0 is the low wavelength limit for the radiation.

This relationship is known as the Duane-Hunt law. (Note that Equation 12-1 provides a direct means for the highly accurate determination of Planck’s constant.) 16 Cont’d - Duane-Hunt law When we substitute numerical values for the constants and rearrange, Equation 12-1 becomes:

λo=12,398/V (12-2)

where λo and V have units of angstroms and volts, respectively.

[λ0, as discussed, is the low wavelength limit for the radiation. - Note that not all radiations have this same wavelength. Radiations (after metal bombardment) have a continuous distribution equal or lower than this values.] 17 Line Spectra from Electron Beam Sources • As shown in Figure 12-2, bombardment (35kV) of a molybdenum (Z=42) target produces intense emission lines (K-lines) at about 0.63 and 0.71 Å; an additional simple series of lines occurs in the longer- wavelength range of 4 to 6 Å (L-lines, not shown in this figure).

18 Cont’d. – line emission p. 304~305 • The emission behavior of molybdenum (Mo, Z=42) is typical of all elements having atomic numbers larger than 23; the X-ray line spectra are remarkably simple when compared with ultraviolet emission and consist of two series of lines.

• The shorter-wavelength group is called the K series (from 1s orbital) and the other the L series (from 2s or 2p) . Elements with atomic numbers smaller than 23 produce only a K series. • Even longer-wavelength (longer than L lines) is called “M-series”.

• Table 12-1 presents wavelength data for the emission spectra of a few elements. 19 TABLE 12-1 Wavelengths in Angstroms of the More Intense Emission Lines for some Typical Elements p. 305

20 Ch12 Atomic X-ray Spectrometry P.305 21 Cont’d - Line Spectra from Electron Beam Sources p.305 A second characteristic of X-ray spectra is that the minimum acceleration voltage required for the excitation of the lines for each element increases with atomic number. Thus, the line spectrum for molybdenum (atomic number = 42) disappears if the excitation voltage drops below 20 kV. [Fig. 12-2]

As shown in Figure 12-1 (right), bombardment of tungsten (W, atomic number = 74) produces no lines in the region of 0.1 to 1.0 Å, even at 50 kV.

Characteristic K lines appear at 0.18 and 0.21 Å, however, if the voltage increases to 70 kV. 22 Figure 12-3 illustrates the linear relationship between the square root of the frequency for a given (K or L) line and the atomic number (Z) of the element responsible for the radiation. This property was first discovered by English physicist H. G. J. Moseley in 1914.

FIGURE 12-3 Relationship between X- ray emission frequency and atomic number for Kα1 and Lα1 lines.

23 K and L series X-ray lines • X-ray line spectra result from electronic transitions that involve the innermost atomic orbitals. • The short-wavelength K series is produced when the high- energy electrons from the cathode remove electrons from those orbitals (1s) nearest the nucleus of the target atom.

• The collision results in the formation of excited ions, which then emit quanta of X-radiation as electrons from outer orbitals undergo transitions to the vacant orbital.

• As shown in Figure 12-4 (next page), the lines in the K series arise from electronic transitions between higher energy levels and the K shell.

• The L series of lines results when an electron is lost from the second principal quantum level (), either as a result of ejection by an electron from the cathode or from the transition of an L electron to the K level that accompanies the production of a quantum of K radiation. 24 K has lower energy than K α β, The main transitions are given which is lower than K γ names:

an L→K transition is

traditionally called Kα, an M→K transition is called Kβ, An NK: called Kγ.

an M→L transition is called Lα, and so on…..

FIGURE 12-4. Partial energy level diagram showing common transitions producing X- rays.

The most intense lines are indicated by the wider arrow.

25 Ch12 Atomic X-ray Spectrometry P.306 the principal quantum numbers n=1, 2, and 3, correspond to the K-, L-, and M-edges, respectively.

For instance, excitation of a 1s electron occurs at the K-edge, while excitation of a 2s or 2p electron occurs at an L-edge (Figure 1).

Note: K level is split into α, β, γ; while L level is split into I, II, III.

26 Post notes to Fig. 12-4 • It is important to appreciate that the energy scale in Figure 12-4 is logarithmic. Thus, the energy difference between the L and K levels is significantly larger than that between the M and L levels. The K lines therefore appear at shorter wavelengths.

• It is also important to note that the energy differences

between the transitions labeled α1 and α2 as well as those between β1 and β2 are so small that only single lines are observed in all but the highest- resolution spectrometers (see Figure 12-2).

[i.e., Kα1 and Kα2, etc., cannot be resolved, and merge into one single line.]

27 Cont’d - Energy level diagram in Figure 12-4 p.305

• The energy level diagram in Figure 12-4 is applicable to any element with sufficient electrons to permit the number of transitions shown.

• The differences in energies between the levels increase regularly with atomic number because of the increasing charge on the nucleus; • therefore, the radiation for the K series appears at shorter wavelengths for the heavier elements (see Table 12-1).

• The effect of nuclear charge is also reflected in the increase in minimum voltage required to excite the spectra of these elements.

28 Cont’d – Chemical/physical states and X-ray lines p.306 • It is important to note that for all but the lightest elements, the wavelengths of characteristic X-ray lines are independent of the physical and chemical state of the element because the transitions responsible for these lines involve electrons that take no part in bonding.

Thus, the position of the Kα lines for molybdenum is the same regardless of whether the target is the pure metal, its sulfide, or its oxide.

29 Note: Covalent bonds in compounds use only the outer orbital electrons.

X-ray spectra • Emission – previous sections • Absorption • Fluorescence • Diffraction

Absorption: Atom absorbing X-ray - Core electron is ejected.

30 X-rays with photon energies above 5–10 keV (below 0.2–0.1 nm wavelength) are called hard X-rays, while those with lower energy are called soft X-rays.[4]

Due to their penetrating ability, “hard X-rays” are widely used to image the inside of objects, e.g., in medical radiography and airport security Since the wavelengths of hard X-rays are similar to the size of atoms they are also useful for determining crystal structures by X-ray crystallography. 31 12A-2 Absorption spectra P307-P310 When a beam of X-rays is passed through a thin layer of matter, its intensity, or power, is generally diminished as a result of absorption and scattering. The effect of scattering for all but the lightest elements is ordinarily small and can be neglected in those wavelength regions where appreciable absorption occurs. As shown in Figure12-5 (next page), the absorption spectrum of an element, like its emission spectrum, is simple and consists of a few well-defined absorption peaks. Here again, the wavelengths of the absorption maxima are characteristic of the element and are largely independent of its chemical state.

“Absorption edge” in X-ray spectra: A peculiarity of X-ray absorption spectra is the appearance of sharp discontinuities, called absorption edges, at wavelengths immediately beyond absorption maxima. 32 牙科 X-光 (absorption): Teeth appear lighter because less radiation penetrates them to reach the film. Dental caries, infections and other changes in the bone density, and the periodontal ligament, appear darker because X-rays readily penetrate these less dense structures.

Digital x-rays, which replace the film with an electronic sensor, are becoming widely used in dentistry as the technology evolves.

They may require less radiation and are processed much quicker than 33 conventional radiographic films, often instantly viewable on a computer. The Absorption Process -mechanism • Absorption of an X-ray quantum causes ejection of one of the innermost electrons from an atom, which results in the production of an excited ion.

• In this process, the entire energy hν of the X-ray radiation is partitioned between the kinetic energy of the electron (the photoelectron) and the potential energy of the excited ion.

• The highest probability for absorption occurs when the energy of the quantum is exactly equal to the energy required to remove the electron just to the periphery of the atom (that is, as the kinetic energy of the ejected electron approaches zero).

34 FIGUER 12-5 X-ray absorption spectra for lead and silver. X-axis: wavelength (A) vs. photon energy (eV)

35 Ch12 Atomic X-ray Spectrometry P.308 36 • The absorption spectrum for lead (blue spectrum), shown in Figure 12-5, exhibits four peaks, the first occurring at 0.14 Å. • The energy of the quantum corresponding to this wavelength exactly matches the energy required to just eject the highest- energy K electron of the element. • At wavelengths just larger than this wavelength, the energy of the radiation is insufficient to bring about removal of a K electron, and an abrupt decrease in absorption occurs. • At wavelengths shorter than 0.14 Å, the probability of interaction between the electron and the radiation gradually diminishes; this results in a smooth decrease in absorption. In this region, the kinetic energy of the ejected photoelectron increases continuously with the decrease in wavelength. 37 Cont’d – absorption for lead (Pb) • The additional peaks at longer wavelengths correspond to the removal of an electron from the L energy levels of lead. • Three sets of L levels, differing slightly in energy, exist (see Figure 12-4); three maxima are, therefore, observed. • Another set of lines, arising from ejections of M electrons, are located at still longer wavelengths.

• Figure 12-5 also shows the K absorption edge for silver, which occurs at 0.485 Å. The longer wavelength for the silver peak reflects the lower atomic number (Z=47) of the element compared with lead (Z=82). 38 The Mass Absorption Coefficient • Beer's law is as applicable to the absorption of X- ray radiation as to other types of electromagnetic radiation; thus, we may write

ln(Po/P) = µx

• where x is the sample thickness in centimeters and P and P0 are the powers of the transmitted and incident beams, respectively. • The constant µ is called the linear absorption coefficient and is characteristic of the element as well as the number of its atoms in the path of the beam. 39 Beer’s law for X-ray analysis A more convenient form of Beer’s law is

ln(Po/P) = µΜρx (12-3)

where ρ is the density of the sample and µM is the mass absorption coefficient, a quantity that is independent of the physical and chemical state of the element.

Thus, the mass absorption coefficient for bromine has the same value in gaseous HBr as in solid sodium bromate.

Note that the mass absorption coefficient carries40 unit of cm2/g. Absorption of multiple elements Mass absorption coefficients are additive functions of the weight fractions of elements contained in sample. Thus,

• µM = µA WA + µB WB + µC Wc (12-4)

where µM is the mass absorption coefficient of a sample containing the weight fractions WA, WB, Wc of elements A, B, and C. The terms µA, µB and µC are the respective mass absorption coefficients for each of the elements. - Tables of mass absorption coefficients for the elements at various wavelengths are found in many handbooks, monographs, and research papers and on the web. 41 12A-3 X-ray Fluorescence The absorption of X-rays produces electronically excited ions that return to their ground state by transitions involving electrons from higher energy levels. Thus, an excited ion with a vacant K shell is produced when lead absorbs radiation of wavelengths shorter than 0.14 Å (Figure 12-5); after a brief period, the ion returns to its ground state via a series of electronic transitions characterized by the emission of X-radiation (fluorescence) of wavelengths identical to those that result from excitation produced by electron bombardment. 42 X-ray Fluorescence vs. absorption

The wavelengths of the fluorescence lines are always somewhat greater than the wavelength of the corresponding absorption edge, because absorption requires a complete removal of the electron (that is, ionization), whereas emission involves transitions of an electron from a higher energy level within the ion.

For example, the K absorption edge for silver occurs at , but the K emission lines for the element 0.485 Å 43 have wavelengths at 0.497 Å and 0.559 Å (doublets). EXAMPLE – X-ray absorption vs. exciting a fluorescence emission of a same element When K-line fluorescence is to be excited by radiation from an X-ray tube, the operating voltage must be sufficiently great so that the cutoff wavelength λ0 (Equation 12-2) is shorter than the K-absorption edge of the element whose spectrum is to be excited.

Thus, to generate the K lines for silver (K- edge=0.485A), the tube voltage would need to be (from Equation 12-2) 12,398V ⋅ Å V is greater than 25.6 kV V ≥ = 25,560V 0.485⋅ Å

The wavelength of this fluorescent radiation can be calculated from Planck's Law: 44

45 X-ray absorption edge energy vs. atomic number

46 47 FIGURE 12-4 Partial energy level diagram showing common transitions producing X-rays.

The most intense lines are indicated by the wider arrow. 48 Ch12 Atomic X-ray Spectrometry P.306 X-ray Fluorescence

X-ray Fluorescence spectrum

49 12A-4 Diffraction of X-rays

• Like other types of electromagnetic radiation, when X-radiation passes through a sample of matter, the electric vector of the radiation interacts with the electrons in the atoms of the matter to produce scattering. • When X-rays are scattered by the ordered environment in a crystal, constructive and destructive interference occurs among the scattered rays because the distances between the scattering centers are of the same order of magnitude as the wavelength of the radiation. •  Diffraction is the result. 50 Bragg's Law

• When an X-ray beam strikes a crystal surface at some angle θ, part of the beam is scattered by the layer of atoms at the surface. The unscattered part of the beam penetrates to the second layer of atoms where again a fraction is scattered, and the remainder passes on to the third layer (Figure 12-6), and so on. • The cumulative effect of this scattering from the regularly spaced centers of the crystal is diffraction of the beam in much the same way as visible radiation is diffracted by a reflection grating (Section 7C-2).

• The requirements for X-ray diffraction are: (1) the spacing between layers of atoms must be roughly the same as the wavelength of the radiation and (2) the scattering centers must be spatially distributed in a highly regular way. 51 Bragg’s law

From derivation demonstrated in textbook: nλ = 2dsinθ (12-6) Equation 12-6 is the fundamentally important Bragg equation. Note that X-rays appear to be reflected from the crystal only if the angle of incidence satisfies the condition: Sinθ = nλ/2d

At all other angles, destructive interference occurs.

52 Instrument Components - X-ray analysis p. 310

X-ray instruments are available in:

• Absorption method, • Emission method, • Fluorescence method, • Diffraction method.

Components differ among the different methods 53 12B INSTRUMENT COMPONENTS Absorption, emission, fluorescence, and diffraction of X- rays are all applied in analytical chemistry.

Instruments for these applications contain components that are analogous in function to the five components of instruments for optical spectroscopic measurement; these components include a source, a device for restricting the wavelength range of incident radiation, a sample holder, a radiation detector or transducer, and a signal processor and readout.

These X-ray components differ considerably in detail from the corresponding optical components.

Their functions, however, are the same, and the ways they combine to form instruments are often similar to those shown in Figure 7-l (Chap. 7).

54 Components in X-ray instrument (repeat)

• Source of X-ray • Devices for restricting the wavelength range (Filters, or Monochromators), • Sample holder. • Detector/Transducers. • Signal processor/Readout.

55 12-B Wavelength-dispersive vs. energy-dispersive p.310

As with optical instruments, both X-ray photometers and spectrophotometers are encountered, the first using filters and the second using monochromators to transmit radiation of the desired wavelength from the source.

In addition, however, a third method is available for obtaining information about isolated portions of an X-ray spectrum. Here, isolation is achieved electronically with devices that discriminate among various parts of a spectrum based on the energy rather than the wavelength of the radiation.

Thus, X-ray instruments are often described as wavelength- dispersive instruments or energy-dispersive instruments, depending on the method by which they resolve spectra.

56 12B-1 Sources of X-ray p.310

• Three or four types of X-ray sources are used:

• 1. X-ray tubes (most common sources) • 2. radioisotopes • 3. Secondary fluorescence sources • 4. (Synchrotron radiation -同步幅射) – if available

57 FIGURE 12-7 Schematic of an X-ray Tube (vacuum tube).

Metals: Cu, Fe, Pt, W, Mo, etc.

58 Ch12 Atomic X-ray Spectrometry P.310 Other X-ray sources: p. 311 • Radioisotopes.

- Radioactive materials may be used as sources in X-ray fluorescence and absorption methods. - must be encapsulated to prevent contamination. (Table 12-2) - produce line and continuum emissions.

• Secondary Fluorescent sources. • Advantage: continuum is avoided. - For example, X-ray tube with a tungsten (W, z=74) target (Fig. 12-1, with continuum only) can be used to excite Kα and Kβ lines of molydenlum (Mo, z=42). - The fluorescent source spectrum from Mo would be similar to that in Fig. 12-2, except that the continuum is absent.

59 12B-2 Filter for X-ray p. 311

USE of a filter to filter out undesired radiation. - Characteristics in Fig. 12-8 (next page) • Emission intensity vs. wavelength. • Proper voltage and target must be used. (Mo is used in Fig. 12-8) • Emission Spectrum Continuum + line emissions (Kα, Kβ) • Short wavelength limit (λo, depending on V). (λo=0.38 A, from which V of X-ray tube can be estimated.)

• Filter with a suitable absorption edge. To restrict a certain line emission that is not desired.

[Zr (Z=40) is used as filter, whose K-absorption edge = 17,998 eV. (λ(edge) = 12,398/17,998=0.689 A). This is ideal to filter out all but Kα line of Mo X-ray emission.

 See next page. 60 FIGURE 12-8 USE of a filter to produce monochromatic radiation.

Note to Zr (Z=40) as a filter:

Absorption peak for Zr (from Table): K= 17.998 eV.

From E=hν, (Planck’s equation),

Or λ = 12,398/V λ = 12,398/17,998 = 0.689A

The process is extremely inefficient with 99% of the energy of the beam being dissipated as heat in the target. 61 Ch12 Atomic X-ray Spectrometry P.311 In the laboratory, a filament is heated to produce electrons which are then accelerated in vacuum by a high electric field in the range 20-60 kV towards a metal target, which being positive is called the anode.

What about the intensity of the Kβ radiation? Again considering a copper anode, the intensity of the Kα lines is approximately 5 times that of Kβ. Hence, all instrumental setups are optimized around the Kα radiation, and preferably around Kα1 when high resolution monochromators are used as part of the X-ray optics. 62 The diagram below show the electronic energy levels for a copper atom:

The splitting of the 2p orbitals in copper, i.e. the splitting of

the energy levels LII and LIII, is very small (0.020 keV) and

so the two wavelengths Kα1 (= 1.54056 Å) and Kα2 (= 1.54439 Å) are very similar.

Anode Kα Kβ Cu 1.54184 Å 1.39222 Å Mo 0.71073 Å 0.63229 Å 63 Example: Zr as a filter for Mo target X-ray emissions

- electron bombardment produces continuum, Kα, and Kβ lines. - how to remove the continuum and the Kβ line in Fig. 12-8?

Find a material with proper absorption edge: • K-absorption edge for Zr ((Z=40) from table of X-ray absorption edges for the elements) = 17,998 eV.

From Duane-Hunt law: λedge = 12,398/V (A)

λedge = 12,398/17,998 = 0.689 A (for Zr)

 Any emissions (line or continuum) in the X-ray tube with wavelength lower than 0.689 A will be removed (absorbed by Zr). 64 12B-3 X-ray Monochromator Fig. 12-9 p. 311-312 • Figure 12-9 shows the essential components of an X- ray spectrometer.

• The monochromator consists of a pair of beam collimators, which serve the same purpose as the slits in an optical instrument, and a dispersing element. The latter is a single crystal mounted on a goniometer, or rotatable table, that permits variation and precise determination of the angle θ between the crystal face and the collimated incident beam.

• From Equation 12-6, it is evident that, for any given angular setting of the goniometer, only a few wavelengths are diffracted (λ, λ/2, λ/3,....,λ/n, where λ =2dsinθ). 65 p. 312

• To produce a spectrum, it is necessary that the exit beam collimator and the detector be mounted on a second table that rotates at twice the rate of the first (Incidenc X-ray beam);

• That is, as the crystal rotates through an angle θ, the detector must simultaneously move through an angle 2θ. Clearly, the interplanar spacing d for the crystal must be known precisely (Equation 12-6).

• Many modern X-ray monochromators have computer- controlled motors to drive the crystal and the detector independently without a gear-based mechanical connection. • These units are capable of scanning at very rapid rates (ca. 240o/min), or very low speed (1o/min). 66 FIGURE 12-9 An x-ray monochromator and detector. Note that the angle of the detector with respect to the beam (2θ) is twice that of the crystal face.

For absorption analysis, the source is an X-ray tube and the sample is located in the beam as shown.

For emission measurements, the sample becomes a source of X-ray fluorescence as shown in the insert.

67 Ch12 Atomic X-ray Spectrometry P.312 12B-4. X-ray transducers and signal processors p.313 In early days, X-ray instruments employed photography films for detection and measurement of radiation.

For convenience, speed, and accuracy, however, modern instruments are usually equipped with transducers that convert radiation (photon) into an electrical signal.

There are three kinds of transducers to be discussed: -1. Gas-filled transducer, (Fig. 12-10) -2. Scintillation counters  X-ray striking phosphor, or sodium iodide (NaI) crystal, etc. -3. Semiconductor transducers. (Fig. 12-12)

Photon counting. • Before considering the function of each of these devices, it is worthwhile to discuss photon counting, a signal-processing method that is often used with X- ray transducers as well as detectors of radiation from radioactive sources (Chapter 32).

• As was mentioned earlier (Section 7F-1), photon counting is also used in ultraviolet and visible spectroscopy. – Photomultiplier Tube (PMT) 68 Photon Counting • X-ray detectors (transducers) are usually operated as photon counters.

• Individual pulses of charge are produced as quanta of radiation are absorbed by the transducer and are counted. The power of X-ray beam is then digitally recorded as the number of counts per unit time.

• Photon counting requires rapid response times for the transducer and signal processor so that the arrival of individual photons may be accurately transduced and recorded.

• In addition, the technique is applicable only to

beams of relatively low intensity. 69 Cont’d • For weak sources of radiation, photon counting generally provides more accurate intensity data than are obtainable by measuring average currents.

• Photon counting is used in X-ray work because the power of available sources is often low.

• In addition, photon counting permits spectra to be acquired without using a monochromator.

70 Type-1: Gas-filled Transducers (detector) - Fig. 12-10 p.314 • When X-ray passes through an inert gas such as argon (xenon, etc), interactions produce a large number of positive gaseous ions and electrons (ion pairs) for each X-ray quantum.  As a result, conductivity is enhanced for each X-ray photon.

71 FIGURE 12-10 Cross section of a gas-filled detector. Gas-filled transducers – cont’d • Fig. 12-11 shows effect of applied potential (V) on the number of electrons that reach the anode of a gas- filled transducer for each entering X-ray-photon. (amplification of photon via electrons produced:  102 ~1010 electrons per X-ray photon.)

• Three types of gas-filled transducers: Fig. 12-11, next page, depending on the applied voltages (100~1500 V).

- Ionization chamber region (low voltages, V1~V2). - Proportional counters region (medium voltages). - Geiger counter region (operated at high voltages, V5~V6). 72 FIGURE 12-11 Gas amplification for various types of gas-filled detectors.

73 Ch12 Atomic X-ray Spectrometry P.314 FIGURE 12-11x- Gas amplification. Note only the intermediate range is used. 74 Type-2: Scintillation counters (sparks, flash) • The luminescence produced when radiation strikes a phosphor represents one of the oldest methods of detecting radioactivity and X- ray. • ------• Most widely used modern scintillation detector consists of a transparent crystal of sodium iodide (NaI) that has been activated by introducing 0.2% thallium iodide.

• The crystal (NaI) is shaped as a cylinder ~10 cm in dimension. 75 Type-3: Semiconductor Transducer P316 • Semiconductor transducers have assumed major importance as detectors of X-radiation.

• These device are sometimes called lithium-drifted silicon detectors, Si(Li), or lithium-drifted germanium detectors, Ge (Li).

• Figure 12-12 illustrates one form of a lithium-drifted detector, which is fashioned from a wafer of crystalline silicon. There are three layers in the crystal: a p-type semiconducting layer that faces the X-ray source, a central intrinsic zone, and an n type layer. The outer surface of the p-type layer is coated with a thin layer of gold for electrical contact; often. It is also covered with a thin beryllium window that is transparent to X-rays. The signal output is taken from an aluminum layer that coats the n- type silicon; this output is fed into a preamplifier with a gain of about 10. The preamplifier is frequently a field-effect transistor that is fabricated as an integral part of the detector. 76 FIGURE 12-12 Vertical cross section of a lithium-drifted silicon detector for X-rays and radiation from radioactive sources. 77 Ch12 Atomic X-ray Spectrometry P.316 12C X-RAY FLUORESCENCE (XRF) METHODS P317-319 Although it is feasible to excite an X-ray emission spectrum by incorporating the sample into the target area of an X-ray tube, this approach is extremely inconvenient for many types of materials. Instead, excitation is usually accomplished by irradiating the sample with a beam of X-rays from an X-ray tube or a radioactive source. In this method, the elements in the sample are excited by absorption of the primary beam and emit their own characteristic fluorescence X-rays.

This procedure is thus properly called an X-ray fluorescence, [or X- ray emission method]. X-ray fluorescence (XRF) is a powerful tool for rapid, quantitative determinations of all but the lightest elements.

In addition, XRF is used for the qualitative identification of elements having atomic numbers greater that of oxygen (Z>8) and is often used for semiquantitative or quantitative elemental analyses.

A particular advantage of XRF is that it is nondestructive, in contrast to most other elemental analysis techniques.

78 X-ray fluorescence

The X-ray “emission” following absorption of X-ray is called “fluorescence”, as long as the atoms are excited by x-ray.

Thus, for X-ray fluorescence analysis, the sources are always “X-ray tubes”.

79 12C-1 Instrument of X-ray fluorescence (XRF) p.319 Three types of XRF:

• 1. Wavelength dispersive type of XRF: -always employs X-ray tubes as sources. -Single-channels (usually with two X-ray sources), and multi- channels (for simultaneous determination of as many as 24 elements.) Detector: photomultiplier, a detector similar to a Geiger counter.

• 2. Energy dispersive type of XRF: Fig. 12-13 [Next page] -Polychromatic sources (i.e., multi-energies) Sources: X-ray tubes or radio-active materials. Detectors: solid-state detectors (PIN diode, Si(Li), Ge(Li), or Silicon Drift Detector SDD) are used.

• 3. Non-dispersive type XRF: For routine determination of sulfur (S) and lead (Pb) in gasoline. 80 energy dispersive analysis vs. wavelength dispersive analysis

Each element has electronic orbitals of characteristic energy, meaning the energy is “unique to the element”.

The fluorescent radiation can be analysed either by sorting the energies of the photons (energy-dispersive analysis) or by separating the wavelengths of the radiation (wavelength-dispersive analysis).

Once sorted, the intensity of each characteristic radiation is directly related to the amount of each element in the material [quantitative analysis].

This is the basis of a powerful technique in analytical chemistry by X-ray.

81 FIGURE 12-13 Energy-dispersive X-ray fluorescence spectrometer. Excitation by X-rays from (a) an X-ray tube and (b) a radioactive substance (curium-244, a 5.81 MeV alpha particle and X-ray source) as shown in the sensor head for the Mars alpha proton X-ray spectrometer. The X-ray detector is a new room-temperature type. 82 Ch12 Atomic X-ray Spectrometry P.319 Wavelength-dispersive X-ray spectroscopy (WDXRF or WDS) is a method used to count the number of X-rays of a specific wavelength diffracted by a crystal

Wavelength-dispersive spectroscopy X-ray (WDS): -Unlike the related technique of energy-dispersive X-ray spectroscopy (EDS), WDS reads or counts only the X-rays of a single wavelength at time, not producing a broad spectrum of wavelengths or energies simultaneously.

WDS is mainly used in chemical analysis, in an X-ray fluorescence spectrometer, in an electron microprobe, and may be used in a scanning 83 electron microscope. FIGURE 12-16 Spectrum of an iron sample obtained with an energy- dispersive instrument with a Rh anode X-ray tube source. The numbers above the peaks are energies in keV. [See Page 37 F-chart] 84 Ch12 Atomic X-ray Spectrometry P.322 Energy dispersive X-ray (EDX) spectroscopy (fluororescence): It relies on an interaction of some source of X-ray excitation and a sample. Its characterization capabilities are due in large part to the fundamental principle that each element has a unique atomic structure allowing unique set of peaks on its X-ray emission spectrum

85 The XRF phenomenon is widely used for elemental analysis and chemical analysis, particularly in the investigation of metals, glass, ceramics and building materials, and for research in geochemistry, forensic science and archaeology.

86 Some advantages vs. disadvantages of X-ray Fluorescence (XRF) Methods p.325 Advantages (in comparison to optical atomic methods): • XRF – spectra are simple; thus, no interference. • X-ray methods are non-destructive. (good for paintings, jewelry, etc). • Speed, convenience, accuracy.

Disadvantages: • Not good for lighter atoms (atomic # < 8 becomes difficult). [Lighter atoms do not emit X-ray.] • Not as sensitive as optical atomic methods. (A few ppm at most). • High costs of instrument (more expensive than AA).

87 12D. X-ray absorption p. 325 • In contrast to optical atomic spectroscopy, where absorption methods are of prime importance, X-ray absorption applications are quite limited.

• Absorption methods are analogous to optical absorption, in which absorption lines of X-ray serve as analytical variables.

• Owing to the breadth of X-ray absorption bands, absorption methods are useful only when a single element (with high atomic number) in a matrix of lighter elements is to be characterized. (Examples: Lead in gasoline).

-The X-ray absorption experiment is usually performed at synchrotron radiation sources, which provide intense and tunable X-ray beams. -Samples can be in the gas-phase, solution, or condensed matter (i.e. solids).88 X-ray absorption Edges: K, L, M

Correspondence: K-edge: from 1s to loss of electron.

L-edge: from 2s/2p to loss of electron.

M-edge: from 3s/3p to loss of electrons.

Where letters (K, L, M) are related to different orbitals.

But subscripts (1,2,3..) are related to splits in same orbitals.

Note: There is only one K-edge in absorption, as 1s orbital does not spilt. But there are three L-edges (I, II, III) of absorption (2s, and 2p split). 89 X-ray absorption spectroscopy (XAS) usually is applied to specialized fields (for probing local state in orbitals). Thus, usually high-intensity synchrotron beams are used as X-ray sources for absorption (to ensure strong signal intensity).

XAS methodology can be broadly divided into four experimental categories : Metal K-edge, metal L-edge, ligand K-edge, and EXAFS [Extended X-ray Absorption Fine Structure]. XAS is a technique used in different scientific fields including molecular and condensed matter physics, materials science and engineering, chemistry, earth science, and biology.

In particular, its unique sensitivity to the local structure, as compared to x-ray diffraction, have been exploited for studying: -Amorphous solids and liquid systems; Solid solutions, -Doping and ion implantation materials for electronics, -Local distortions of crystal lattices, -Organometallic compounds, -Metalloproteins, -Metal clusters, -Catalysis, -Ions in solutions, 90 -Speciation of elements, etc…… 12E. X-ray Diffraction (XRD) Methods p. 325 • Determination of arrangement and spacing of atoms in crystals.

• Understanding of physical properties of polymers, metals, and other solids.

• It is the only analytical method for qualitative identification of crystalline compounds. •  e.g. X-ray powder method is capable of determining the percent of KBr and NaCl in a solid mixtures of these two compounds. • Other methods can only determine percent of K+, Cl-, Na+, Br-.

 Analysis is based on the fact that X-ray diffraction pattern is unique for each crystalline solid. 91 12D-2 Identification of Crystalline Compounds p.326 Sample Preparation For analytical diffraction studies, the crystalline sample is ground to a fine homogeneous powder. In such a form, the enormous number of small crystallites are oriented in every possible direction; thus, when an X-ray beam passes through the material, a significant number of the particles are oriented in such ways as to fulfill the Bragg condition for reflection from every possible inter- planar spacing.

Samples are usually placed in a sample holder that uses a depression or cavity to mount the sample. These mounts are commonly made of aluminum, bronze, Bakelite, glass, or Lucite. 92 Automatic Diffractometers • Diffraction patterns are generally obtained with automated instruments similar in design to that shown in Figure 12-9 (shown earlier, again in next page). • In this instrument, the source is an X-ray tube with suitable filters. The powdered sample, however, replaces the single crystal on its mount.

• In some instances, the sample holder may be rotated to increase the randomness of the orientation of the crystals. The diffraction pattern is then recorded by automatic scanning in the same way as for an emission or absorption spectrum.

• Instruments of this type offer the advantage of high precision for intensity measurements and automated data reduction and report generation.

93 FIGURE 12-9 (Top) An x-ray monochromator and detector. Shown again for demonstration

FIGURE 12-17 (Right) Schematic of (a) a Debye-Scherrer powder camera; (b) the film strip after development. D2, D1, and T indicate positions of the film in the camera.

PS: Negative films are no longer used. 94 Instead, digital detectors are used for X-ray instrument. Ch12 Atomic X-ray Spectrometry P.327 Sample holder - x-ray-diffraction 

 Oriented polycrystalline PP – Not “O”, but “arc”. x-ray-diffraction - polycrystalline omikron (O)

 This is the x-ray diffraction pattern for polycrystalline gold film.

For artistic designs, etc……. 95 Note: Digital recording

• Films (negatives) were used in old days for recording the X-ray diffractions signals.

• Nowadays, the negative films are not used.

• Instead, the data in films are converted into digital signals, stored and processed by computers.

• The outputs can be either digital graphs or diffraction intensity vs. angle plots. • • (digital graphs for WAXD – see figure next page)

96 Crystal Structures analysis by WAXD

Poly(L-lactic acid) (PLLA) – a biodegradable semicrystalline polyester

Complex crystal - PLLA/PDLA (1:1 racemic mixture) [stereocomplex PLA]

15o WAXD profiles of PLLA and sc-PLA.＊ 18.5o 12o 22.5o

21o

24o

＊ Ref: K. Fukushima, Y. Kimura, Polym Int (2006), 55, 626

9797 98 99 12D-3 Interpretation of Diffraction Pattern p. 326 • The identification of a species from its powder diffraction pattern is based on the position of the lines (in terms of θ or 2θ) and their relative intensities. • The diffraction angle 2θ is determined by the spacing between a particular set of planes; with the aid of the Bragg equation, this distance d is calculated from the known wavelength of the source and the measured angle. • Line intensities depend on the number and kind of atomic reflection centers in each set of planes. 100 Cont’d Crystals are identified empirically. A powder diffraction database is maintained by the International Centre for Diffraction Data, Newtown Square, Pennsylvania. As of 2005, this file contained powder diffraction patterns for more than 477,000 reference materials. Because the file is so large, the powder data file has been broken down into subfiles that contain listings for inorganics, organics, minerals, metals, alloys, forensic materials, and others. The sub-databases are available on CD-ROM, and software is available for searching the databases using any combination of several search criteria. Each record in the database contains a wealth of information regarding the substances and materials, including name, formula (if appropriate), composition, color, line strengths, melting point, mineral classification, density, and a host of other characteristics of the materials as well as bibliographic information. A variety of presentation modes are available so that graphs and other important images may be101 viewed and printed. X-ray peaks for SiO2 (quartz) and two different forms of CaCO3

102 Determination of the percentage crystallinity of materials using X-ray p. 327 One very important application is the determination of the percentage crystallinity of materials.

• In the analysis of polymeric and fibrous materials, determining the crystalline-to-amorphous ratio has long been of importance, and X-ray powder methods have unique advantages in these determinations. • In the pharmaceutical area, the degree of crystallinity can influence the long-term stability of a formulation as well as its bioactivity.

• X-ray diffraction methods are being increasingly

applied to pharmaceuticals. 103 Cont’d Crystalline materials produce well-defined diffraction peaks whose widths are related to the crystalline "quality.“ High-quality materials produce sharp peaks, and poor-quality materials give rise to more diffuse diffraction peaks.

• Amorphous phases come in different forms depending on how they were formed. A glassy phase produces a diffraction signal that is the radial distribution of nearest neighbor interactions. • An amorphous phase derived from a crystalline phase usually corresponds to a poor-quality, or paracrystalline, material.

• Both glassy and paracrystalline (i.e., semicrystalline) specimens produce a low-frequency halo, which can appear as a broad background.

104 X-ray determination of Crystallinity in materials p. 327 • One approach to determining the crystalline-to- amorphous ratio (C/A) is to use conventional quantitative analysis methods. • Non-overlapped X-ray diffraction peaks are chosen for the phase to be analyzed. Either peak height or peak area is used for quantitative analysis. • Standards of known concentration are then used to prepare a calibration curve.

105 Crystallinity determination (%Cu) • In the Vainshtein approach, the amorphous phase is used as a normalizing factor for the integrated intensities of the crystalline peaks. This eliminates the effects of sample preparation and instrument drift. • Analysis is based on Vainshtein's law, which states that the diffracted intensity from a material is independent of its state of order within identical regions of reciprocal space. • To apply the law, a single standard (std) with a known percentage of crystallinity is used to establish the normalization ratio between the integrated crystalline peaks and the amorphous "background." • The same measurements are then made on the specimen of unknown crystallinity (u). • The percentage crystallinity of the unknown is then found from  (C / A)  %C = % C u (12-8) u std   106 (C / A) std  Note: X-ray diffraction vs. Electron diffraction Electron diffraction is most frequently used in solid state physics and chemistry to study the crystal structure of solids. Experiments are usually performed in a transmission electron microscope (TEM), or a scanning electron microscope (SEM) as electron backscatter diffraction.

In these instruments, electrons are accelerated by an electrostatic potential in order to gain the desired energy and determine their wavelength before they interact with the sample to be studied. Electron diffraction in TEM is subject to several important limitations. First, the sample to be studied must be electron transparent, meaning the sample thickness must be of the order of 100 nm or less. Careful and time consuming sample preparation may therefore be needed.

Furthermore, many samples are vulnerable to radiation damage caused by the incident electrons. However, the main limitation of electron diffraction in TEM remains the comparatively high level of user interaction needed. Whereas both the execution of powder X-ray (and neutron) diffraction experiments and the data analysis are highly automated and routinely 107 performed, electron diffraction requires a much higher level of user input. End of Chap. 12 – X-ray atomic spectroscopy

Next lectures: Molecular spectroscopy: UV-Vis spectroscopy – Chaps. 13+14

Mid-term exam – to be announced

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