8Physical techniques in inorganic chemistry

All the structures of the molecules and materials to be covered in this book have been determined by applying one or more kinds of physical technique. The techniques and instruments available vary greatly in complexity and cost, as well as in their suitability for meeting particular chal- lenges. All the methods produce data that help to determine a compound’s structure, its composi- tion, or its properties. Many of the physical techniques used in contemporary inorganic research rely on the interaction of electromagnetic radiation with matter and there is hardly a section of the electromagnetic spectrum that is not used. In this chapter, we introduce the most important physical techniques that are used to investigate the atomic and electronic structures of inorganic compounds and study their reactions.

Diffraction methods

Diffraction techniques, particularly those using X-rays, are the most important methods available to the inorganic chemist for the determination of structures. X-ray diffraction has been used to determine the structures a quarter of a million different substances, in- cluding tens of thousands of purely inorganic compounds and many organometallic com- pounds. The method is used to determine the positions of the atoms and ions that make up a solid compound and hence provides a description of structures in terms of features such as bond lengths, bond angles, and the relative positions of ions and molecules in a unit cell. This structural information has been interpreted in terms of atomic and ionic radii, which then allow chemists to predict structure and explain trends in many properties. Diffraction methods are nondestructive in the sense that the sample remains unchanged and may be analysed further by using a different technique.

8.1 X-ray diffraction

Key points: The scattering of radiation with wavelengths of about 100 pm from crystals gives rise to diffraction; the interpretation of the diffraction patterns gives quantitative structural information and in many cases the complete molecular or ionic structure.

Diffraction is the interference between waves that occurs as a result of an object in their path. X-rays are scattered elastically (with no change in energy) by the electrons in atoms, and diffraction can occur for a periodic array of scattering centres separated by distances similar to the wavelength of the radiation (about 100 pm), such as exist in a crystal. If we think of scattering as equivalent to reflection from two adjacent parallel planes of atoms separated by a distance d (Fig. 8.1), then the angle at which constructive interference oc- curs (to produce a diffraction intensity maximum) between waves of wavelength is given by Bragg’s equation:

Diffraction methods

8.1 X-ray diffraction

8.2 Neutron diffraction

Absorption spectroscopy

8.3 Ultraviolet–visible spectroscopy

8.4 Infrared and Raman spectroscopy

Resonance techniques

8.5 Nuclear magnetic resonance

8.6 Electron paramagnetic resonance

8.7 Mössbauer spectroscopy

Ionization-based techniques

8.8 Photoelectron spectroscopy

8.9 X-ray absorption spectroscopy

8.10 Mass spectrometry

Chemical analysis

8.11 Atomic absorption spectroscopy

8.12 CHN analysis

8.13 X-ray fluorescence elemental analysis

8.14 Thermal analysis

Magnetometry Electrochemical techniques Computational techniques

FURTHER READING EXERCISES PROBLEMS

d

d sin2d sin n (8.1)

Figure 8.1 Bragg’s equation is derived bywhere n is an integer. Thus an X-ray beam impinging on a crystalline compound with anordered array of atoms will produce a set of diffraction maxima, termed a diffraction pat- tern, with each maximum, or reflection, occurring at an angle corresponding to a differ- ent separation of planes of atoms, d, in the crystal.

treating layers of atoms as reflecting planes. X-rays interfere constructively when the additional path length 2d sin is equal to an integral multiple of the wavelength .

225Diffraction methods

The effectiveness of powder X-ray diffraction has led to it becoming the major techniquefor the characterization of polycrystalline inorganic materials (Table 8.1). Many of thepowder diffraction data sets collected from inorganic, organometallic, and organic com-pounds have been compiled into a database by the Joint Committee on Powder Diffrac-tion Standards (JCPDS). This database, which contains over 50 000 unique powder X-raydiffraction patterns, can be used like a fingerprint library to identify an unknown materialfrom its powder pattern alone. Powder X-ray diffraction is used routinely in the investiga-tion of phase formation and changes in structures of solids. The synthesis of a metal oxide

8 16

Diffract

(b)

24ion ang

32le, 2 /°

40 can be verified by collecting a powder diffraction pattern and demonstrating that the dataare consistent with a single pure phase of that material. Indeed, the progress of a chemi- cal reaction is often monitored by observing the formation of the product phase at the

2

Dif

frac

tio

n in

tensi

ty

An atom or ion scatters X-rays in proportion to the number of electrons it possesses and the intensities of the measured diffraction maxima are proportional to the square of that number. Thus the diffraction pattern produced is characteristic of the positions and types (in terms of their number of electrons) of atom present in the crystalline compound and the measurement of X-ray diffraction angles and intensities provides structural information. Because of its dependence on the number of electrons, X-ray diffraction is particularly sensitive to any electron-rich atoms in a compound. Thus, X-ray diffraction by NaNO

3 displays all three nearly isoelectronic atoms simi-

larly, but for Pb(OH) the scattering and structural information is dominated by the

Sample

2

X-rays

Figure 8.2 A cone of diffraction that results from X-ray scattering by a powdered sample. The cone consists of thousands of individual diffraction spots from individual crystallites that merge together.

X-ray tube

Tube focus

Detector

Pb atom.There are two principal X-ray techniques: the powder method, in which the materi-

als being studied are in polycrystalline form, and single-crystal diffraction, in which the sample is a single crystal of dimensions of several tens of micrometres or larger.

(a) Powder X-ray diffraction

Key point: Powder X-ray diffraction is used mainly for phase identification and the determination of lattice parameters and lattice type.

A powdered (polycrystalline) sample contains an enormous number of very small crys- tallites, typically 0.1 to 10 μm in dimension and orientated at random. An X-ray beam striking a polycrystalline sample is scattered in all directions; at some angles, those given by Bragg’s equation, constructive interference occurs. As a result, each set of planes of atoms with lattice spacing d gives rise to a cone of diffraction intensity. Each cone consists of a set of closely spaced diffracted rays, each one of which represents diffraction from a single crystallite within the powder sample (Fig. 8.2). With a very large number of crystallites these rays merge together to form the diffraction cone. A powder diffractometer (Fig. 8.3a) uses an electronic detector to measure the angles of the diffracted beams. Scanning the detector around the sample along the circumfer-

(a)

Sampleplate 2

Measuring circle

ence of a circle cuts through the diffraction cones at the various diffraction maxima and the intensity of the X-rays detected is recorded as a function of the detector angle (Fig. 8.3b).

The number and positions of the reflections depend on the cell parameters, crystal system, lattice type, and wavelength used to collect the data; the peak intensities depend on the types of atoms present and their positions. Nearly all crystalline solids have a unique powder X-ray diffraction pattern in terms of the angles of the reflections and their intensi- ties. In mixtures of compounds, each crystalline phase present contributes to the powder diffraction pattern its own unique set of reflection angles and intensities. Typically, the method is sensitive enough to detect a small level (5 to 10 per cent by mass) of a particular crystalline component in a mixture.

Figure 8.3 (a) Schematic diagram of a powder diffractometer operating in reflection mode in which the X-ray scattering occurs from a sample mounted as a flat plate. For weakly absorbing compounds the samples may be mounted in a capillary andthe diffraction data collected in transmission mode. (b) The form of a typical powder diffraction pattern showing a series of reflections as a function of angle.

expense of the reactants.Basic crystallographic information, such as lattice parameters, can normally be

extracted easily from powder X-ray diffraction data, usually with high precision. The presence or absence of certain reflections in the diffraction pattern permits the determination of the lattice type. In recent years the technique of fitting the intensities of the peaks in the dif- fraction pattern has become a popular method of extracting structural information such as atomic positions. The analysis, which is known as the Rietveld method, involves fitting a calculated diffraction pattern to the experimental trace. The technique is not as powerful as the single-crystal methods, for it gives less accurate atomic positions, but has the advan- tage of not requiring the growth of a single crystal.

2

Counts

25.

362

7.5

0

36.

15

37

.01

37

.85

39.

28 41

.32

44.

14

53.

97

54.

44

Table 8.1 Application of powder X-ray diffraction

Application Typical use and information extracted

Identification of unknown materials Rapid identification of most crystalline phases

Determination of sample purity Monitoring the progress of a chemical reaction occurring in the solid state

Determination and refinement of Phase identification and monitoring structure as a lattice parameters function of composition

Investigation of phase diagrams/ Mapping out composition and structure new materials

Determination of crystallite size/stress Particle size measurement and uses in metallurgy

Structure refinement Extraction of crystallographic data from a known structure type

Ab initio structure determination Structure determination (often at high precision) is possible in some cases without initial knowledgeof the crystal structure

Phase changes/expansion coefficients Studies as a function of temperature (cooling or heating typically in the range 100–1200 K). Observation of structural transitions

E X A M P L E 8 .1 Using powder X-ray diffraction

Titanium dioxide exists as several polymorphs, the most common of which are anatase, rutile, and brookite. The experimental diffraction angles for the six strongest reflections collected from each of these different polymorphs are summarized in the table in the margin. The powder X-ray diffraction pattern collected using 154 pm X-radiation from a sample of white paint, known to contain TiO

2 in

Rutile Anatase Brookite

27.50 25.36 19.34

36.15 37.01 25.36

39.28 37.85 25.71

41.32 38.64 30.83polymorphic forms, showed the diffraction pattern in Fig. 8.4. Identify the TiO

2 polymorphs present.

Answer We need to identify the polymorph that has a diffraction pattern that matches the one observed.44.14

54.44

48.15

53.97

32.85

34.90The lines closely match those of rutile (strongest reflections) and anatase (a few weak reflections), so the paint contains these phases with rutile as the major TiO

2 phase.

Self-test 8.1 Chromium(IV) oxide also adopts the rutile structure. By consideration of Bragg’s equation and the ionic radii of Ti4 and Cr4 (Resource section 1) predict the main features of the CrO powder X-raydiffraction pattern.

(b) Single-crystal X-ray diffraction

Key point: The analysis of the diffraction patterns obtained from single crystals allows the full deter- mination of the structure.

Analysis of the diffraction data obtained from single crystals is the most important method of obtaining the structures of inorganic solids. Provided a compound can be grown as a

20 30 40 50 602 /°

Figure 8.4 A powder diffraction pattern obtained from a mixture of

TiO2

polymorphs (see Example 8.1).

229Absorption spectroscopy

Sample

X-ray beam

2

Detector

crystal of sufficient size and quality, the data provide definitive information about molecular and extended lattice structures.

The collection of diffraction data from a single crystal is normally carried out by using a four-circle or area-detector diffractometer (Fig. 8.5). A four-circle diffractometer uses a scintillation detector to measure the diffracted X-ray beam intensity as a function of the angles shown in the illustration. An area-detector diffractometer uses an image plate that is sensitive to X-rays and so can measure a large number of diffraction maxima simultane- ously; many new systems use this technology because the data can typically be collected in just a few hours (Fig. 8.6).

Analysis of the diffraction data from single crystals is formally a complex process in- volving the locations and intensities of many thousands of reflections, but with increasing advances in computation power a skilled crystallographer can complete the structure de- termination of a small inorganic molecule in under an hour. Single-crystal X-ray diffraction can be used to determine the structures of the vast majority of inorganic compounds when they can be obtained as crystals with dimensions of about 50 50 50 μm or larger.

Figure 8.5 The layout of a four-circle diffractometer. A computer controls the location of the detector as the four angles are changed systematically.

Figure 8.6 Part of a single-crystal X-ray diffraction pattern. Individual spots arise by diffraction of X-rays scattered from different planes of atoms within the crystal.

O CsH C O

Figure 8.7 An ORTEP diagram of caesium oxalate monohydrate, Cs

2C

2O

4.H

2O. The ellipsoids correspond to

a 90 per cent probability of locating the atoms.

Positions for most atoms, including C, N, O, and metals, in most inorganic compounds can be determined with sufficient accuracy that bond lengths can be defined to within a fraction of a picometre. As an example, the S S bond length in monoclinic sulfur has been reported as 204.7 0.3 pm.

A note on good (or at least conventional) practice Crystallographers still generally use the ångström (1 Å 10−10 m 10−8 cm 10–2 pm) as a unit of measurement. This unit is convenient because

bond lengths typically lie between 1 and 3 Å. The S S bond length in monoclinic sulfur would be reported as 2.047 ± 0.003 Å.

The positions of H atoms can be determined for inorganic compounds that contain only light atoms (Z less than about 18, Ar), but their locations in many inorganic compounds that also contain heavy atoms, such as the 4d- and 5d-series elements, can be difficult or impossible. The problem lies with the small number of electrons on an H atom (just 1), which is often reduced even further when H forms bonds to other atoms. Other tech- niques, such as neutron diffraction (Section 8.2), can often be applied to determine the positions of H in inorganic compounds.

Molecular structures obtained by the analysis of single-crystal X-ray diffraction data are often represented in ORTEP diagrams (Fig. 8.7; the acronym stands for Oak Ridge Thermal Ellipsoid Program). In an ORTEP diagram an ellipsoid is used to represent the volume within which the atomic nucleus most probably lies, taking into account its ther- mal motion. The size of the ellipsoid increases with temperature and, as a result, so does the imprecision of the bond lengths extracted from the data.

(c) X-ray diffraction at synchrotron sources

Key point: High-intensity X-ray beams generated by synchrotron sources allow the structures of very complex molecules to be determined.

Much more intense X-ray beams than are available from laboratory sources can be obtained by using synchrotron radiation. Synchrotron radiation is produced by electrons circulating close to the speed of light in a storage ring and is typically several orders of magnitude more intense than laboratory sources. Because of their size, synchrotron X-ray sources are normally national or international facilities. Diffraction equipment located at such an X-ray source permits the study of much smaller samples and crystals as small as 10 10 10 μm can be used. Furthermore, data collection can be under- taken much more rapidly and more complex structures, such as those of enzymes, can be determined more easily.

8.2 Neutron diffraction

Key point: The scattering of neutrons by crystals yields diffraction data that give additional informa- tion on structure, particularly the positions of light atoms.

Diffraction occurs from crystals for any particle with a velocity such that its associated

229Absorption spectroscopy

wavelength (through the de Broglie relation, h/mv) is comparable to the separations

of the atoms or ions in the crystal. Neutrons and electrons travelling at suitable velocities have wavelengths of the order of 100–200 pm and thus undergo diffraction by crystalline inorganic compounds.

Neutron beams of the appropriate wavelength are generated by ‘moderating’ (slowing down) neutrons generated in nuclear reactors or through a process known as spallation, in which neutrons are chipped off the nuclei of heavy elements by ac- celerated beams of protons. The instrumentation used for collecting data and ana- lysing single-crystal or powder neutron diffraction patterns is often similar to that used for X-ray diffraction. The scale is much larger, however, because neutron beam fluxes are much lower than laboratory X-ray sources. Furthermore whereas many chemistry laboratories have X-ray diffraction equipment for structure characteriza- tion, neutron diffraction can be undertaken only at a few specialist sources world- wide. The investigation of an inorganic compound with this technique is therefore much less routine and its application is essentially limited to systems where X-ray diffraction fails.

The advantages of neutron diffraction stem from the fact that neutrons are scattered by nuclei rather than by the surrounding electrons. As a result, neutrons are sensi- tive to structural parameters that often complement those for X-rays. In particular, the scattering is not dominated by the heavy elements, which can be a problem with X-ray diffraction for most inorganic compounds. For example, locating the position of a light element such as H and Li in a material that also contains Pb can be impos- sible with X-ray diffraction, as almost all the electron density is associated with the Pb atoms. With neutrons, in contrast, the scattering from light atoms is often similar to that of heavy elements, so the light atoms contribute significantly to the intensities in the diffraction pattern. Thus neutron diffraction is frequently used in conjunction with X-ray diffraction techniques to define an inorganic structure more accurately in terms of atoms such as H, Li, and O when they are in the presence of heavier, electron- rich metal atoms. Typical applications include studies of the complex metal oxides, such as the high-temperature superconductors (where accurate oxide ion positions are required in the presence of metals such as Ba and Tl) and systems where H atom posi- tions are of interest.

Another use for neutron diffraction is to distinguish nearly isoelectronic species. In X-ray scattering, pairs of neighbouring elements in a period of the periodic table, such as O and N or Cl and S, are nearly isoelectronic and scatter X-rays to about the same extent, therefore they are hard to tell apart in a crystal structure that contains them both. How- ever, the atoms of these pairs do scatter neutrons to very different extents, N 50 per cent more strongly than O, and Cl about four times better than S, so the identification of the atoms is much easier than by X-ray diffraction.

Absorption spectroscopy

The majority of physical techniques used to investigate inorganic compounds involve the absorption and sometimes the re-emission of electromagnetic radiation. The fre- quency of the radiation absorbed provides useful information on the energy levels of an inorganic compound and the intensity of the absorption can often be used to provide quantitative analytical information. Absorption spectroscopy techniques are normally nondestructive as after the measurement the sample can be recovered for further analysis.

The spectrum of electromagnetic radiation used in chemistry ranges from the short wavelengths associated with - and X-rays (about 1 nm), to radiowaves with wave- lengths of several metres (Fig. 8.8). This spectrum covers the full range of atomic and molecular energies associated with characteristic phenomena such as ionization, vibra- tion, rotation, and nuclear reorientation. Thus, X- and ultraviolet (UV) radiation can be used to determine the electronic structures of atoms and molecules and infrared (IR) radiation can be used to examine their vibrational behaviour. Radiofrequency (RF) radiation, in nuclear magnetic resonance (NMR), can be used to explore the ener- gies associated with reorientations of the nucleus in a magnetic field, and those ener- gies are sensitive to the chemical environment of the nucleus. In general, absorption

229Absorption spectroscopy

1 m 1 d

m

1 cm 1 m

m

1 µm

700

nm

420

nm 1

nm

1 p

m

Wavelength, λ/m

1 10–1 10–2 10–3 10–4 10–5 10–6 10–7 10–8 10–9 10–10 10–11 10–12 10–13 10–

14

Figure 8.8 The electromagnetic spectrum

Radio Microwave Far infrared Near

infrared

Vacuum ultraviolet

X-ray γ-ray Cosmic

rays

Visible Ultravioletwith wavelengths and techniques that makeuse of the different regions.

NMR EPR Rotational spectroscopy

Vibrational spectroscopy

UV/Visible spectroscopy

Photoelectron spectroscopy

Mössbauer spectroscopy

Table 8.2 Typical timescales of some common characterization methods

X-ray diffraction 10–18 s

Mössbauer 10–18 s

Electronic spectroscopy 10–15 sUV–visible

Vibrational spectroscopy 10–12

sIR/Raman

NMR c.10–3–10–6

s

EPR 10–6 s

spectroscopic methods make use of the absorption of electromagnetic radiation by a molecule or material at a characteristic frequency corresponding to the energy of a transition between the relevant energy levels. The intensity is related to the probability of the transition, which in turn is determined in part by symmetry rules, such as those described in Chapter 6 for vibrational spectroscopy.

The various spectroscopic techniques involving electromagnetic radiation have differ- ent associated timescales. This variation can influence the structural information that is extracted. When a photon interacts with an atom or molecule we need to consider fac- tors such as the lifetime of any excited state and a how a molecule may change during that interval. Table 8.2 summarizes the timescales associated with various spectroscopic techniques discussed in this section. Thus IR spectroscopy takes a much faster snapshot of the molecular structure than NMR, for a molecule may have time to reorientate or change shape in a nanosecond. The temperature at which data are collected should also be taken into account as molecular reorientation rates increase with increasing temperature.

■ A brief illustration. Iron pentacarbonyl, Fe(CO)5, illustrates why consideration of such

timescales is important when analysing the spectra to obtain structural information. Infrared spectroscopy suggests that Fe(CO)

5 has D

3h symmetry with distinct axial and equatorial carbonyl

groups whereas NMR suggests that all the carbonyl groups are equivalent. ■

8.3 Ultraviolet–visible spectroscopy

Key points: The energies and intensities of electronic transitions provide information on electronic structure and chemical environment; changes in spectral properties are used to monitor the progress of reactions.

Ultraviolet–visible spectroscopy (UV–visible spectroscopy) is the observation of the absorption of electromagnetic radiation in the UV and visible regions of the spec- trum. It is sometimes known as electronic spectroscopy because the energy is used to excite electrons to higher energy levels. UV–visible spectroscopy is among the most widely used techniques for studying inorganic compounds and their reactions, and most laboratories possess a UV–visible spectrophotometer (Fig. 8.9). This section describes only basic principles; they are elaborated in later chapters, particularly Chapter 20.

Detector

Sample

SourceReference

Beam combiner

Grating

Figure 8.9 The layout of a typical UV–visible absorption spectrometer.

589

nm

Vi ible

Abso

rban

ce,

AA

bso

rban

ce,

A

30 0

00

25 0

00

20 0

00

15 0

00

10 0

00

0

(a) Measuring a spectrumThe sample for a UV–visible spectrum determination is usually a solution but may also be a gas or a solid. A gas or liquid is contained in a cell (a ‘cuvette’) constructed of an opti- cally transparent material such as glass or, for UV spectra at wavelengths below 320 nm, pure silica. Usually, the beam of incident radiation is split into two, one passing through the sample and the other passing through a cell that is identical except for the absence of the sample. The emerging beams are compared at the detector (a photodiode) and the absorption is obtained as a function of wavelength. Conventional spectrometers sweep the wavelength of the incident beam by changing the angle of a diffraction grating, but it is now more common for the entire spectrum to be recorded at once using a diode array detector. For solid samples, the intensity of UV–visible radiation reflected from the sample is more easily measured than that transmitted through a solid and an absorption spectrum is obtained by subtraction of the reflected intensity from the intensity of the incident radi- ation (Fig. 8.10).

The intensity of absorption is measured as the absorbance, A, defined as

A log⎛

I

0 ⎞

10 I ⎠⎟ (8.2)750 675 600 500 450 375

where I is the incident intensity and I is the measured intensity after passing through the Wavelength, λ/nm

sample. The detector is the limiting factor for strongly absorbing species because the meas- urement of low photon flux is unreliable.

■ A brief illustration. A sample that attenuates the light intensity by 10 per cent (so I0

/I 100/90) has an absorbance of 0.05, one that attenuates it by 90 per cent (so I

0 /I

100/10) has an absorbance of 1.0, and one that attenuates it by 99 per cent (so I0 /I 100/1)

an absorbance of 2.0, and so on. ■

The empirical Beer–Lambert law is used to relate the absorbance to the molar concentra- tion [J] of the absorbing species J and optical pathlength L:

Figure 8.10 The UV–visible absorption spectrum of the solid ultramarine blue Na

7[SiAlO

4]

6(S

3).

A ε[ J]L (8.3)

where ε (epsilon) is the molar absorption coefficient (still commonly referred to as the‘extinction coefficient’ and sometimes the ‘molar absorptivity’). Values of ε range fromabove 105 dm3 mol–1 cm–1 for fully allowed transitions, for example an electron trans-ferring from the 3d to 4p energy levels in an atom (∆l 1), to less than 1 dm3 mol–1

cm–1 for ‘forbidden’ transitions, such as those with ∆l 0. Selection rules also exist for transitions between molecular orbitals, although in complex molecules they are frequently broken (Chapter 20). For small molar absorption coefficients, the absorbing species may be difficult to observe unless the concentration or pathlength is increased accordingly.

Figure 8.11 shows a typical solution UV–visible spectrum obtained from a d-metal compound, in this case Ti(III), which has a d1 configuration. From the wavelength of the radiation absorbed, the energy levels of the compound, including the effect of the ligand environment on d-metal atoms, can be inferred. The type of transition involved can oftenbe inferred from the value of ε. The proportionality between absorbance and concentrationprovides a way to measure properties that depend on concentration, such as equilibriumcompositions and the rates of reaction.

E X A M P L E 8 . 2 Relating UV–visible spectra and colour

Figure 8.12 shows the UV–visible absorption spectra of PbCrO4

and TiO2. What colour would you

expectPbCrO

4 to be?

Answer We need to be aware that the removal of light of a particular wavelength from incident white light results in the remaining light being perceived as having its complementary colour. Complementary colours

s

Figure 8.11 The UV–visible spectrum of3

are diametrically opposite each other on an artist’s colour wheel (Fig. 8.13). The only absorption fr [Ti(OH2)6]

(aq). Absorbance is given as afunction of wavenumber.