International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.8, pp. 177-186

Section 2.8.3. Examples

H. Ehrenberg,a* M. Hinterstein,a A. Senyshynb and H. Fuessc

aInstitut für Angewandte Materialien (IAM-ESS), Karlsruhe Institut für Technologie (KIT), Eggenstein-Leopoldshafen, Germany,bTechnische Universität München, Garching b. München, Germany, and cTechnische Universität Darmstadt, Darmstadt, Germany
Correspondence e-mail:  helmut.ehrenberg@kit.edu

2.8.3. Examples

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2.8.3.1. In situ studies of ferroelectrics in an external electric field

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The function of ferroelectrics as stress sensors, high-frequency microphones, medical injectors or large strain actuators is based on electric poling. A polycrystalline material exhibits a zero net polarization. When an electric field is applied to the sample, the spontaneous electric polarization of the ferroelectric material is reoriented along the electric field vector. This occurs by a reorientation of domains. Additional polarization is obtained by an increase of the spontaneous polarization induced by the applied electric field. With in situ experiments, the field-induced changes in the powder diffraction reflections are measured. Fig. 2.8.1[link] is a schematic representation of some in situ sample geometries. The electric field is applied via electrodes on the sample surface.

[Figure 2.8.1]

Figure 2.8.1 | top | pdf |

Sample geometries for in situ experiments with an applied electric field. Samples are poled via an applied voltage (U) at the sample electrodes (grey). Different sample geometries are necessary to account for different beam sizes, absorption and detector concepts. Yellow indicates the irradiated sample volume. (a) Flat-plate samples for X-ray experiments with strip detectors, limiting photon energies to around 30 keV. (b) Bar-shaped samples for high-intensity neutron powder diffraction (NPD) or high-energy X-ray diffraction (XRD). (c) Cylinder-shaped samples for high-resolution neutron diffraction with fixed detector collimators.

Many of these ferroelectric materials crystallize in a structure derived from the cubic perovskite type, but in a crystal system with lower symmetry and with a non-centrosymmetric space group. The most widely used material is lead zirconate-titanate (PbZr1−xTixO3, PZT), which exhibits the highest strain response at the so-called morphotropic phase boundary with a composition of about 50% for Ti and Zr. It is generally accepted that the phase on the Ti-rich side of the PZT phase diagram has a tetragonal structure with space group P4mm. On the rhombohedral Zr-rich side, two ferroelectric phases can be identified, with space groups R3m for high and R3c for low temperatures. A considerable amount of work has been devoted to the elucidation of the crystal structure of the material close to the morphotropic phase boundary. Neutron and synchrotron diffraction detected monoclinic symmetry at low temperatures and nanometre-sized regions (the so-called polar nanoregions) were inferred from diffuse scattering (Noheda et al., 2000[link]; Hirota et al., 2006[link]). Alternative interpretations explained the new reflection found in the pattern between the 111C and 200C reflections (where the subscript `C' corresponds to the cubic archetype structure) as diffuse scattering from diffuse incoherent scattering by small domains (Jin et al., 2003[link]).

Unique information on structural changes during poling is obtained from in situ studies in applied external electric fields (Hoffmann et al., 2001[link]). Fig. 2.8.2[link] displays two groups of powder reflections (Schönau, Schmitt et al., 2007[link]) observed by synchrotron X-ray diffraction. They are directly compared with the domain structure from TEM observations (Schmitt et al., 2007[link]) for a range of compositions near the morphotropic phase boundary. One group of reflections is derived from the cubic 111C reflection, the other from the archetype 200C reflection. The transition from the rhombohedral splitting to the tetragonal one with increasing Zr content is correlated with the forms of ferroelectric domains in TEM. Close to the morphotropic phase boundary, nanodomains (ranging in width from 20 to 200 nm) are observed in addition to the well known microdomains. The nanodomains react immediately under the influence of an electric field to become microdomains. Fig. 2.8.3[link] shows the intensity changes observed for the 110C group of reflections. The changes under an electric field are pronounced and depend on the c/a ratio (Schönau, Knapp et al., 2007[link]), the formation and disappearance of nanodomains, and the local symmetry of these domains.

[Figure 2.8.2]

Figure 2.8.2 | top | pdf |

(a), (b) High-resolution synchrotron X-ray powder diffraction patterns and TEM imaging of PZT with a varying Zr/Ti ratio. An increase in broadening is seen in changes in shape and width of the 002T reflection between the samples PZT 45/55, 52.5/47.5 and 54/46. The asymmetry and width of the tetragonal 101T reflection not only change, but also evolve into a new peak between 101T and 110T in sample PZT 54/46, which gains in intensity towards PZT 57.5/42.5. This rise is accompanied by a decrease in intensity of the visible 110T reflection, which then seems to be absent or overlapped in sample PZT 56/44. The domain structure changes from a lamellar tetragonal configuration via nanodomains to a rhombohedral herringbone structure. Reproduced with permission from Schönau, Schmitt et al. (2007) [link]. Copyright (2007) by the American Physical Society.

[Figure 2.8.3]

Figure 2.8.3 | top | pdf |

Diffraction patterns of the tetragonal 101T /110T reflection pairs of PZT 52/48, PZT 53/47, PZT 54/46, PZT 55/45 and PZT 56/44 recorded in situ under an electric field for the first poling cycle of up to 4 kV mm−1. Reproduced with permission from Schönau, Knapp et al. (2007) [link]. Copyright (2007) by the American Physical Society.

The different poling mechanisms can be studied in transmission geometry, which allows variation of the angle between the electric field vector E and the direction of the incident X-ray beam k from 0° to about 45° (Fig. 2.8.4[link]) (Hinterstein et al., 2011[link]). Two sputtered electrodes (Ag, Pt) were used for polarization.

[Figure 2.8.4]

Figure 2.8.4 | top | pdf |

In situ transmission geometry developed by Schönau, Schmitt et al. (2007[link]) with the electric field vector perpendicular to the flat-plate sample surface. The electric field results from an applied voltage U between two opposing sputtered electrodes (Ag, Pt) with a thickness of about 15 nm. (a) ω = 0° and (b) ω = 45°.

An extensive study under an electric field has been carried out on the commercially available sintered PZT material named PIC, in which Ti is partially replaced by Ni and Sb [Pb0.99Zr0.45Ti0.47(Ni0.33Sb0.67)0.08O3], in transmission geometry. The angle between the electric field perpendicular to the flat sample surface and the incident beam was varied between 0 and 45°. The effect of domain switching in tetragonal symmetry mainly affects the {h00}C reflections, whereas the piezoelectric effect predominantly influences the {hhh}C reflections. Thus, the reflection pair 111C and 200C are the only reflections analysed in most studies. Fig. 2.8.5[link] displays just these reflections, with 200C split into 002T and 200T, where the subscript `T' refers to the tetragonal distorted cell, which is translationengleich to the cubic one (i.e. they have the same group of translations). The shift to higher angles of 111C under an applied field indicates a decrease in volume. This is explained by the large angle between the electric field vector and the vector of spontaneous polarization for the unit cells contributing to 111C. This induced compression remains in the remanent state.

[Figure 2.8.5]

Figure 2.8.5 | top | pdf |

111C and 200C reflections of the unpoled, remanent and applied field state of PIC 151 at ω = 0°. Owing to the piezoelectric effect, the 111C reflection is shifted. The preferred orientation of the 200C reflection indicates tetragonal 90° domain switching.

While analysis of single reflections or orientations can yield valuable information on textured functional materials, a more sophisticated approach involves coupling the Eulerian angles to the diffraction patterns and modelling all observable mechanisms within a single refinement. By applying this method to a technically applied actuator material, Hinterstein, Hoelzel et al. (2015[link]) could quantify all strain mechanisms and calculate the macroscopic response to an applied electric field with a structure model at the atomic scale.

The function of piezoceramics is related to periodic cycling of the polarization, accompanied by periodic changes of macroscopic strain. Fatigue in piezoceramic materials means that this strain is reduced as a result of the cycling; this has been studied with respect to the underlying structural changes (Hinterstein et al., 2011[link], 2014[link]).

Whereas strain is related to texturing, no preferred orientation is observed in fatigued samples. The orientation of nanodomains is demonstrated in different patterns: in Fig. 2.8.6[link] the two reflections are shown for the remanent state (0 kV mm−1) at different diffraction angles and in Fig. 2.8.7[link] for values of the external field ranging from 0 to 2 kV mm−1.

[Figure 2.8.6]

Figure 2.8.6 | top | pdf |

111C and 200C reflections of bipolar fatigued PIC 151 (50 Hz, 107 cycles) in the remanent state (0 kV mm−1 at ω = 0°, 15°, 30° and 45°).

[Figure 2.8.7]

Figure 2.8.7 | top | pdf |

111C and 200C reflections of bipolar fatigued PIC 151 (50 Hz, 107 cycles) at ω = 45° with 0.0, 0.72, 1.41 and 2.0 kV mm−1.

The diffuse scattering between the split 200C reflections in the fatigued sample is reduced and the texturing increases after static poling for a few seconds. Thus, the fatigued samples show a more tetragonal appearance after cycling. The energy of the electric field induces a transition of well oriented nanodomains with preferred orientation along the field vector, leading to texturing for ω = 0°. At a certain point the system will no longer respond to the electric field because of crack formation and a decrease in the volume of switchable nanodomains. From that point, the diffraction pattern recorded under a field is no different to the diffraction pattern recorded without a field.

Cyclic loading with high frequencies is required in real applications of ferroelectric ceramics. Exposure times in the range of seconds are necessary to ensure sufficient statistics for single diffraction experiments in the subsecond regime. Stroboscopic measurements can be used to achieve this.

Absolutely reversible processes are necessary for a successful stroboscopic analysis. The stability of the system is achieved by pre-cycling circa 105 times. Time resolutions in the range of several tens of milliseconds are possible with modern X-ray detectors. By repeating the excitation and summing the intensities, proper statistics can be achieved (Choe et al., 2015[link]; Hinterstein et al., 2014[link]).

The use of the stroboscopic data-collection technique and cyclic fields in neutron diffraction experiments enabled a direct measurement of non-180° domain wall motion during the application of subcoercive cyclic electric fields (Fig. 2.8.8[link]) (Jones et al., 2006[link], 2007[link]; Jones, 2007[link]; Daniels et al., 2007[link]). It was shown that the non-180° domain switching contributes 34% of the macroscopically measured strain during cycling with half of the coercive field.

[Figure 2.8.8]

Figure 2.8.8 | top | pdf |

Diffracted intensities of the pseudo-cubic 002 reflections as a function of 2θ and time during application of a square, bipolar electric field waveform of frequency 1 Hz and amplitude of plus or minus half the coercive field. The timescale is described using eight steps. The positive (P) state of the electric field is applied between 0.25 and 0.75 s, which is bounded on either side by the negative (N) field state. The diffraction vectors 002 and 200 are parallel to the applied electric field. Reproduced with permission from Jones et al. (2006[link]). Copyright (2006) AIP Publishing.

The highest time resolutions are obtained in a pump–probe setup. Under the influence of an electric field of 2 kV mm−1, the switching kinetics can be investigated directly. With a time resolution of 1 ms only one intermediate step is observed (Fig. 2.8.9[link]a). With a time resolution of 250 µs a significant number of intermediate steps can be studied (Fig. 2.8.9[link]b). The commercially available soft-doped PZT material EC-65 has also been observed under the application of an electric field and mechanical stress. Lattice strains were measured under cyclic electric fields at times as short as 30 µs (Pramanick et al., 2010[link]).

[Figure 2.8.9]

Figure 2.8.9 | top | pdf |

Pump–probe measurements of the 200C reflection at ω = 45°. Cycling switching between the remanent and the applied field state at 2 kV mm−1 with 50 Hz and a time resolution of (a) 1 ms and (b) 250 µs. Only a time resolution of 250 µs results in sufficient intermediate steps between the remanent and the poled state to study the processes during poling.

The use of lead-containing materials may in the future be banned because of environmental concerns, hence considerable efforts are being made to find materials with properties similar to PZT. Only a few elements (Ba, Bi, Na, K, Nb, Ti) seem to be suitable. Nevertheless, a combination of the relevant oxides of these leads to a large variety of potential materials. (Bi0.5Na0.5)­TiO3–BaTiO3 (BNT–BT) (Hinterstein, Schmitt et al., 2015[link]), (Bi0.5Na0.5)TiO3–(Bi0.5K0.5)TiO3 (BNT–BKT) (Levin et al., 2013[link]), BNT–BT–K0.5Na0.5NbO3 (BNT–BT–KNN) (Schmitt et al., 2010[link]), BNT–BKT–KNN (Anton et al., 2012[link]) and BNT–KNN (Liu et al., 2017[link]) are the focus of most attention. The materials in the (1 − x − y)BNT–xBT–yKNN system exhibit remarkable piezoelectric properties over a narrow composition range 0.05 ≤ x ≤ 0.07 and 0.01 ≤ y ≤ 0.03 (Zhang et al., 2007[link]). Daniels et al. (2010[link]) proposed a combinatorial approach to studying a range of compositions in a single sample, where different stoichiometries created a compositional gradient in the sample. A limited number of bulk homogeneous samples were prepared for comparison. Microfocus X-ray beams from a synchrotron allowed investigation of the gradient material under a field.

Fig. 2.8.10[link] displays the diffraction patterns under an external electric field up to 5.5 kV mm−1. Data analysis was performed by fitting the data of the pseudo-cubic 002 reflection to distorted pseudo-cubic and tetragonal symmetry for each composition and electric field. Whereas in the 0.86BNT–0.14KNN composition only a distorted pseudo-cubic behaviour is observed above a threshold of 0.5 kV mm−1, a very pronounced distortion is observed for 0.93BNT–0.07BT, which eventually above 2 kV mm−1 develops into a tetragonal structure. In addition to the combination of various compositions, the authors simultaneously measured the X-ray fluorescence spectra, thus confirming the actual composition.

[Figure 2.8.10]

Figure 2.8.10 | top | pdf |

The pseudo-cubic 002 reflection of (a) 0.93BNT–0.07BT end member, (b) 0.938BNT–0.053BT–0.009KNN, (c) 0.932BNT–0.045BT–0.023KNN and (d) 0.86BNT–0.14KNN end member as a function of electric field from the initial zero-field state (top) to an applied field of 5.5 kV mm−1 (bottom). The sample orientation is such that the scattering vector is parallel to the electric field. Reproduced with permission from Daniels et al. (2010[link]). Copyright (2010) Elsevier.

Fig. 2.8.11[link] depicts a Rietveld refinement of a lead-free ferroelectric material with the composition 0.92Ba0.5Na0.5TiO3–0.06BaTiO3–0.02K0.5Na0.5NbO3. New superstructure ref­lections (Fig. 2.8.11[link]b, arrows) and a lattice distortion (Fig. 2.8.11[link]b, circled) were observed due to a transition from space group P4bm to R3c (Hinterstein et al., 2010[link]).

[Figure 2.8.11]

Figure 2.8.11 | top | pdf |

Rietveld refinement based on different patterns of 0.92Bi0.5Na0.5TiO3–0.06BaTiO3–0.02K0.5NbO3 (a) in the unpoled and (b) in the applied field state at 6 kV mm−1. Experimental data are shown by grey crosses, black lines denote calculated profiles, and the lower plot shows their difference. Calculated positions of Bragg reflections are shown by vertical tick marks, where the different rows correspond to the initial tetragonal phase with space group P4bm (1) and the field-induced rhombohedral phase with space group R3c (2). Arrows mark superlattice reflections of type ½{ooe} and the circle highlights the rhombohedral split 331C reflection.

In an overview, Jones summarized the use of diffraction techniques. Along with the importance of microdiffraction, diffuse scattering and texture effects, the importance of time-resolved studies including stroboscopy was acknowledged (Jones, 2007[link]).

2.8.3.2. In situ studies of electrode materials and in operando investigations of Li-ion batteries

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Rechargeable energy sources in mobile electronics are mainly based on lithium-ion batteries. Their application relies on the mobility of the small Li ions, which move from the cathode through an electrolyte to the anode during charge and back during discharge. Intensive research is underway to improve the performance of such energy-storage technology. High gravimetric and volumetric energy and power densities are required. Other additional challenges are safety, lifetime, the temperature range of stable operation and production costs per unit energy at the battery level. Knowledge of the correlation between the electrochemical functionality and the structure of the electrode materials during Li exchange is essential in order to interpret the underlying mechanisms and degradation processes and to find a promising approach to better materials. The high reactivity of the cell components and the very strong interactions between materials inside an electrochemical cell require studies on complete operational devices by non-invasive in operando methods. So-called electrochemical `half cells' are often studied to follow structural changes in electrode materials. These are complete operational cells, but the electrode is cycled against an Li-metal counter electrode. Such half-cell studies are sometimes described as in situ studies. Limitations might occur with respect to fatigue studies and at very high charge and discharge rates, when the performance is determined by the Li-metal electrode. The classification of in situ and in operando methods is not unambiguous in structural studies on battery materials. Sometimes the term quasi in situ is used for studies where specific states of the materials are prepared electrochemically and handled in an Ar atmosphere with complete protection against humidity and air, but actually investigated ex situ (Oswald et al., 2009[link]).

Some early in situ setups have been described for neutron diffraction (Bergstöm, Andersson et al., 1998[link]) and transmission X-ray diffraction (Bergström, Gustafsson & Thomas, 1998[link]), and also at elevated temperatures (Eriksson et al., 2001[link]). Today, for example, good-quality full diffraction patterns can be obtained with exposure times well below 100 ms using synchrotron radiation (Herklotz et al., 2013[link]). Capillary-based micro-battery cells allow for in situ X-ray powder diffraction studies on one single electrode (Johnsen & Norby, 2013[link]). Even spatially resolved neutron diffraction studies are possible on commercial cylindrical Li-ion batteries (Senyshyn et al., 2015[link]).

The mechanism of Li extraction and insertion differs for different types of electrodes. In intercalation-type electrodes the topology of the host structure remains mainly unchanged, and suitable sites in the structure are either occupied by Li or are vacant in the delithiated state. This use of intercalation chemistry for electrochemical energy storage was established for a battery based on Li metal as the negative electrode and TiS2 as the positive electrode (Whittingham, 1976[link]). In commercial cells today the negative electrode is also based on intercalation and consists of layered graphite, which hosts Li during the charge cycle up to the composition LiC6. Another working mechanism for negative electrodes is electrochemical alloying with Li. The most promising examples involve Si, Al and Sn. These electrode concepts suffer from extreme volume changes: 100% for Al → LiAl or even 300% for Si → Li21Si5. In combination with the brittleness of these materials, the particles break down and become amorphous during successive charging and discharging, accompanied by contact losses and resulting pronounced fade in capacity. Two other mechanisms have also received considerable attention as they allow higher specific capacities. In a replacement reaction, one transition metal is replaced by Li while the topology of the structure is mainly preserved. During a conversion or displacement reaction the initial structures of transition-metal compounds, for example nanometre-sized oxides (Poizot et al., 2000[link]) or other binary compounds (Cabana et al., 2010[link]), are believed to be destroyed completely by either amorphization or phase transitions. The transition-metal ions are reduced to metallic nanoparticles, which are embedded in a complex network of Li2O and reaction products from the electrolyte. In spite of the loss of long-range order, an important short-range structure remains. This has been shown in detail for ternary Cu–Fe oxides (Adam et al., 2013[link]). The reduction of Cu2+ from CuO takes place through the formation of a Cu2O/Li2O composite, in which Cu2O reacts further to form Cu metal and Li2O. Spinel-type CuFe2O4 and CuFeO2 react to form α-LiFeO2 with the extrusion of metallic Cu and Fe nanoparticles. At even lower potentials against Li+/Li between 0.8 and 1.0 V, α-LiFeO2 is further reduced into metallic Fe nanoparticles and Li2O. While most of these displacement reactions suffer from very poor reversibility, good cycling stability was shown for Cu2.33V4O11 (Morcrette et al., 2003[link]). During cell discharge Li penetrates into the well crystallized copper vanadate, forming a solid solution up to an Li content of x = 0.6, when Bragg peaks of metallic copper were observed. The end result was a composite electrode of an amorphous Li–V–O matrix with dispersed metallic copper. The essential point is the reversibility, with the disappearance of the metallic copper and the recrystallization of the initial Cu2.33V4O11.

Two more examples belong to the class of intercalation materials: graphite as used for the negative electrode, and LiNiO2 as a candidate for the positive electrode. `Positive' and `negative' electrodes are the preferred terms for secondary batteries instead of `cathode' and `anode', because anode and cathode reactions match only for discharge (interchange between the two electrodes occurs for the charge process). A comprehensive summary of structure reports on lithiated graphite can be found in Johnsen & Norby (2013[link]). From the voltage plateau in cyclovoltammograms four distinct lithiated graphite phases have been postulated. However, only for two of them have complete structure models been reported and confirmed. The first is LiC12, P6/mmm (space group No. 191), a = 4.29, c = 7.03 Å, with C on the 12n site with x = 0.33 and z = 0.25 and Li on the 1a site; the second is LiC6, also P6/mmm, a = 4.31, c = 3.70 Å with C on the 6k site with x = 0.33 and Li again on the 1a site. According to the number of graphene layers that are needed for the smallest unit repeated by translational symmetry along the sixfold rotation axis, these structures are described as stage-II (LiC12) and stage-I (LiC6) compounds, like graphites intercalated with other alkaline elements. Note that in these phases the graphene layers are not shifted with respect to each other (AA sequence), in contrast to graphite (AB sequence). For a lower Li content, a much more complex structural behaviour was observed, including incommensurate Li distributions between the graphene layers, which were described as twisted bilayers (Senyshyn et al., 2013[link]). Higher-order reflections were observed for these phases and allowed indexing with a propagation vector (α, α, 0). Different structure models were discussed, but a complete description of the Li distribution is still lacking. Therefore, it is still an open question as to where the Li atoms in lithiated graphite are at low Li contents (below 1 Li per 12 C).

LiNiO2 is considered to be a promising positive electrode material (Ohzuku et al., 1993[link]). However, it has some limitations, which are directly linked to the underlying structure. A high degree of cation disorder, i.e. Li on the Ni site and vice versa, hinders Li transport within the layers. Furthermore, Li and Ni exchange takes place rather easily, in contrast to LiCoO2, because of a more favourable transport process through a tetrahedral interstitial site for Ni than for Co. In the cases of Li excess, Li1+δNiO2, or Ni excess, (Li1−δNiδ)NiO2, some Ni2+ ions exist, which have a very similar ionic radius to that of Li+. Therefore, it is nearly impossible to prepare stoichiometric LiNiO2 with perfect separation of Li and Ni onto distinct layers. The best samples with respect to cation order are obtained from NaNiO2 by successive Na → Li ion-exchange reactions. These drawbacks have prevented the commercial application of LiNiO2, and more complex materials like Li(Ni,Co,Al)O2 (NCA) and Li(Ni,Co,Mn)O2 (NCM) are increasingly replacing LiCoO2. Fig. 2.8.12[link] shows the structural changes in LiNiO2 during the first charge and discharge. The detailed experimental conditions are the same as those described by Nikolowski et al. (2005[link]) for Li(Ni0.8Co0.2)O2. One of the most characteristic features of the structural response to Li extraction and insertion is the pronounced change in the lattice parameters, shown by the changes in the c/a ratio for the rhombohedral structure. During Li extraction the c parameter increases, because there are fewer Li ions between (repulsive) O-atom layers. However, at lower Li contents, some of the O ions become oxidized, and the repulsion between the O-atom layers is weaker, resulting in shorter c-axis parameters. As a general rule, all layered oxides LiMO2, with M = Mn, Co and/or Ni, become intrinsically unstable in the highly de­lithiated states beyond the maximum in the c/a ratio. Note that the as-prepared material has a very high degree of cation dis­order (9.3% Ni on the Li site) and very poor capacity retention in the second cycle. The initial phase (A) gradually disappears and apparently transforms into a second phase (B) with a much lower degree of cation disorder (less than 3%). Note that this phase sequence does not necessarily reflect equilibrium conditions, but depends strongly on the chemical composition (Li or Ni excess), microstructure (size and strain) and the experimental conditions (charge rate, temperature, electrode formulation and more).

[Figure 2.8.12]

Figure 2.8.12 | top | pdf |

Li1+δNiO2 during charge and discharge. From about 210 complete diffraction patterns [a small section is shown below (λ = 0.499366 Å)], the structural response to Li extraction and insertion was monitored. In addition to changes in the unit-cell metric, the distribution of Li and Ni onto layers becomes more ordered during the first highly charged state. A pronounced capacity loss is observed during discharge after a holding time of 3 h in this overcharged state. A, B and C are three successively appearing phases. SOC = state of charge.

Such in situ studies are very important for elucidating the working mechanism and degradation processes for intercalation electrodes (Senyshyn et al., 2012[link]). Nevertheless, complementary methods are also essential for providing all the necessary information, especially about the surface near-interface region between the electrode and electrolyte, which has to be studied with surface-sensitive and local methods.

2.8.3.3. Diffraction under a magnetic field

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2.8.3.3.1. General remarks

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The majority of synchrotron and neutron experiments are currently limited to superconducting magnets with fields of 5–16 T. When higher fields are required there are essentially two possible solutions: pulsed resistive or steady-field resistive (or hybrid: resistive inner coil, superconducting outer coil) magnets. Pulsed fields are often used when signals are strong and the signal-to-noise ratio is good, whereas steady fields are primarily used for techniques with relatively long counting times and many data points. The relatively short pulse duration (from microseconds to milliseconds) along with the rather large sample volume required severely limit the use of pulsed magnetic fields in powder diffraction applications as well as more exotic methods of achieving high magnetic fields, e.g. magnetic flux compression or single-turn coils (Schneider-Muntau et al., 2006[link]). Furthermore, because of the large stresses, the lifetime of a resistive/pulsed magnet is finite: pulsed magnets have typical lifetimes of 500 shots at 95% of the design field, and their lifetimes are virtually independent of pulse duration.

At present, the maximum field for technical superconductors is 23 T and modern developments in superconductor design along with robust magnet manufacturing techniques have made possible high-flux-density magnets for neutron scattering studies up to 16 T. For resistive magnets, there are in principle no limitations to the generation of the highest continuous fields apart from economics, as approximately 1 MW of electric power is consumed per 1 T field strength. Therefore, in order to reduce the running costs (i.e. the required power per unit magnetic field), hybrid magnets are becoming increasingly popular. In this context we mention the joint developments between the National High Magnetic Field Laboratory (Tallahassee, FL, USA), the Spallation Neutron Source (Oak Ridge, TN, USA) and Helmholtz-Zentrum Berlin (Germany) in the development of high-steady-field (25 T with a 4 MW resistive insert, 30 T with an 8 MW resistive insert) hybrid magnets for neutron scattering (Bird et al., 2009[link]). A high-field magnet has been installed and is in routine user operation (Fig. 2.8.13[link]) at the Extreme Environment Diffractometer (HFM-EXED) of Helmholtz-Zentrum Berlin (Prokhnenko et al., 2015[link]).

[Figure 2.8.13]

Figure 2.8.13 | top | pdf |

The High Magnetic Field Facility for Neutron Scattering at the Helmholtz-Zentrum Berlin has two main components: the High Field Magnet (HFM) and the Extreme Environment Diffractometer (EXED). Courtesy of Dr O. Prokhnenko.

On the other hand, it is quite simple to produce magnetic flux density uniformity or homogeneity over the required sample volume down to the p.p.m. level with a solenoid magnet. However, the majority take the form of split-pair solenoids. With this setup, the access to the sample environment (along the magnetic axis) can be orthogonal to the beam-access plane. The split-coil setup is the most popular in neutron scattering, but the geometry constraints imposed by the neutron aperture make the creation of very uniform flux density much more difficult. In general, for a typical neutron-scattering sample volume of 1 cm3, the magnetic field homogeneity is normally limited to the range 0.1 to 5%. As the available current density for a given conductor decreases with increasing flux density, the flux density seen by the superconductor inside the magnet windings is greater than the `nominal' central value. This is particularly the case for split-pair magnets, where the ratio of the two can be large, e.g. for a central value of 9 T, a ratio of 1.6 gives a maximum flux density of 14.3 T (Brown, 2010[link]).

As already pointed out, diffraction studies under a magnetic field are almost always performed with neutrons. However, Mitsui et al. (2009[link]) have developed a device that includes a cryo-cooled split-pair NbTi superconducting magnet and a sample furnace, for high fields and temperatures above room temperature, respectively, which can be installed on a laboratory X-ray diffractometer. The magnetic field generated goes up to 5 T at the centre of a 50 mm vertical and 10 mm horizontal bore, with a field homogeneity of 0.1%. The first results of studies on the martensitic phase transition in the shape memory system Ni40Co10Mn34Al16 in a field of 5 T and at temperatures up to 473 K have been reported for powders (Mitsui et al., 2009[link]).

Synchrotron radiation can be used to study specific properties such as orbital contributions and their separation from the spin values. Diffraction studies with unpolarized neutrons are common at a constant field to elucidate simple magnetic structures: no confident conclusion about the spin direction can be obtained if the configurational symmetry is cubic, and in the case of uniaxial symmetry (either tetragonal, hexagonal or rhombohedral) only the angle with the unique axis of the magnetic structure can be defined (Shirane, 1959[link]). The sensitivity of non-polarized neutron powder diffraction (the magnetic detection limit) is by a few orders of magnitude less than that of superconducting quantum interference device (SQUID) magnetometry, muon spin rotation or magnetic dichroism spectroscopy. In an antiferromagnetically ordered system the determination of magnetic moments below 0.1 µB per magnetic atom presents severe challenges, which become even more pronounced for the localization of weak ferromagnetic components. Less frequent are in situ investigations to determine magnetic phase diagrams. The use of powder samples at high magnetic fields is often limited by the redistribution of grains and texture effects.

Experiments with polarized neutrons are normally performed with single crystals. Out of the variety of compounds that have been studied, we have chosen materials with particular properties and report on in situ studies of them under magnetic fields.

2.8.3.3.2. Frustrated magnetic systems

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Multiferroic systems (or more precisely magnetoelectric materials) have gained considerable attention because of their potential applications in devices. In fact, the efficient control of magnetism by an electric field allows magnetic information to be written electrically (with low energy consumption) and read magnetically. A real application, however, requires both phenomena to occur at room temperature. There are very few compounds that fulfil this requirement; examples include BiFeO3 and β-NaFeO2.

Magnetoelectric properties have been observed in many compounds with different structures and chemical compositions. However, they all have a geometrical magnetic frustration in common, which induces competition among multiple magnetic ground states. Furthermore, a magnetic phase transition is thought to be an essential ingredient for realizing a non-linear colossal response in the electric properties. In the colossal effect, the two properties not only coexist but couple strongly in their order parameter. Most novel multiferroic materials exhibit a cycloidal component to the magnetic structure; this has been considered as a guiding principle for tailoring new materials based on the non-collinearity of the spins. Many cycloidal compounds exhibit a small ferromagnetic component in their antiferromagnetic order, giving rise to the Dzyaloshinskii–Moriya interaction. We shall concentrate here on two systems linked by frustration in the magnetic ordering, namely ortho­vanadates and the manganites of the rare earths.

2.8.3.3.2.1. Kagomé staircase systems

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Among the orthovanadates of 3d metals, Co3V2O8 and Ni3V2O8 have been identified as kagomé staircase magnetic structures, which exhibit a considerable number of phase transitions at low temperature. Their crystal structure was determined by Fuess et al. (1970[link]) as orthorhombic (space group Cmca). Ferromagnetic order was found for the cobalt compound and an indication of antiferromagnetism for the nickel compound at 4.2 K. The crystal structure is characterized by edge-sharing CoO6 octahedra forming buckled layers of corner-sharing triangles, called kagomé staircases, separated by VO4 tetrahedra. The magnetic ions (Co or Ni) are situated at the corners of triangles, thus leading to spin frustration. Therefore, if a small amount of energy is supplied by an external magnetic field, a whole sequence of magnetic phase transitions can be introduced. The previously determined ferromagnetic order as the ground state for Co3V2O8 was confirmed by Wilson et al. (2007[link]). They also reported field-dependent neutron powder diffraction studies under a field of 8 T at 2 and 9 K (Fig. 2.8.14[link]). At 9 K the system has an incommensurate magnetic structure. At a field as low as 0.5 T, new magnetic peaks indexed in a commensurate structure occur, accompanied by a shift in the position of others. The incommensurate ordering disappears completely at a higher field and a purely ferromagnetic behaviour is observed, similar to the low-temperature ground state at zero field. At 2 K and 8 T no additional magnetic reflections are observed but changes in the intensity of several existing ones are seen. The refinement of the magnetic structure based on these data indicated a change of the spin direction in the ferromagnetic arrangement as compared with the zero-field low-temperature structure. Furthermore, the magnetic moments on the two different Co sites in the structure are aligned under the field and reach the same value of 3.15 µB on both sites, which is similar to the spin-only moment of cobalt.

[Figure 2.8.14]

Figure 2.8.14 | top | pdf |

Neutron powder diffraction data for Co3V2O8 at 9 K (left) and 2 K (right) under magnetic fields of 0, 0.5, 1.5, 2.5, 4.0 and 8.0 T. Data from a bank of detectors situated at the scattering angle 35° are shown. The arrows indicate the changes between the data at different fields. Individual curves are offset arbitrarily for display purposes. Reprinted with permission from Wilson et al. (2007[link]). Copyright (2007) by the American Physical Society.

The reorientation of spins and the complete magnetic field versus temperature (HT) phase diagram of the multiferroic Ni3V2O8 has been reported (Kenzelmann et al., 2006[link]). The inversion symmetry of space group Cmca is broken at low temperature and a commensurate phase is observed. Thus, over a narrow temperature range a macroscopic polar vector leads to a multiferroic behaviour. As this study was based on single-crystal neutron measurements, no further details are given here. Frustrated triangular-lattice Ising antiferromagnets have degenerate magnetic ground states, which give rise to very complex magnetic structures. As there are only small differences in the competing exchange interaction in such frustrated triangular-lattice compounds, a sequence of phase transitions is introduced by changes in temperature or magnetic field. The compound Ca3Co2O6 is another example of a frustrated system. Field-dependent powder diffraction patterns were reported for the doped system Ca3Co1.8Fe0.2O6 by Yusuf et al. (2013[link]). They distinguished the short-range magnetic order (SRO), reflected in the half-width of the Bragg reflections (Fig. 2.8.15[link]), from the long-range order as given by the Bragg positions. They stated that even under magnetic fields up to 4 T the broadening of Bragg reflections indicates the persistence of SRO. In a field of 2 T, the observed change in the structure from incommensurate to commensurate indicates a reduction of spin frustration. In fields of 4 T, a ferrimagnetic system is introduced, followed by a ferromagnetic one above 5 T.

[Figure 2.8.15]

Figure 2.8.15 | top | pdf |

The observed Bragg reflection 100 (open circles) under an applied field of (a) 0 T, (b) 2 T and (c) 4 T at 4.2 K and (d) 0 T, (e) 2 T and (f) 4 T at 16 K (taken from Yusuf et al., 2013 [link]). Copyright IOP Publishing. Reproduced with permission. All rights reserved.

2.8.3.3.2.2. Manganite systems

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Like the vanadates, in the class of rare-earth manganites of the type RMn2O5 successive magnetic phase transitions between commensurate (CO) and incommensurate phases (ICP) can occur. Intensive investigations have been undertaken to understand the relationship between their magnetic and dielectric properties. The spontaneous electric polarization is induced by a magnetic transition. Thus the primary order parameter is magnetic rather than structural. Among the rare-earth compounds, those containing Nd or an element lighter than Nd do not exhibit ferroelectricity. In all these materials a broken magnetic symmetry at lower temperatures leads to a polar symmetry group. In addition, a cycloidal component indicates a common underlying mechanism. The Mn3+ and Mn4+ ions are fully charge-ordered. Neutron diffraction studies of these phases have been performed by Radaelli & Chapon (2008[link]), who also analysed the possible exchange pathways. In TbMn2O5 the HT phase diagram of the commensurate–low-temperature–incommensurate (CO–LT–ICP) magnetic transitions shows an upward jump in the transition temperature from ∼25 K at zero field to 27 K at 9 T. The low-temperature ICP phase is stabilized under an external field for TbMn2O5 and the dielectric constant is enhanced. It was concluded that Tb and Mn order independently, implying the absence of coupling terms between them. Strong support for this suggestion was provided by an in-field neutron study on the analogue YMn2O5. Neither the positions nor the intensities of the magnetic Bragg reflections were affected by the magnetic field (Fig. 2.8.16[link]). The magnetic low-temperature ICP phase in the Tb compound was stabilized under a magnetic field. This is in contrast to observations on HoMn2O5 by Kimura et al. (2007[link]), using single crystals. In both cases, however, the neutron data correlate directly with the results obtained by dielectric measurements under a magnetic field. The difference in the behaviours is thus confirmed. The two studies also reveal different magnetic order at low temperatures. The same magnetic sequence at low temperatures as for Tb was observed in YMn2O5, which does not contain a magnetic rare-earth element. Under fields up to 8 T the positions and the intensities of the magnetic Bragg reflections remained unchanged, showing that the antiferromagnetic structure of the manganese sublattice is extremely stable. As in the vanadates, the main reason for the sequence of magnetic structures is frustration of the manganese spins. Without going too deeply into the details of the different exchange pathways and orbital occupancies, one factor behind this behaviour is the Jahn–Teller effect of the Mn3+ ion, which is also relevant in the multiferroic TbMnO3 as part of the RMnO3 family (Kimura et al., 2003[link]). Another feature often found in multiferroic systems is the small ferromagnetic component caused by small spin canting due to Dzyaloshinskii–Moriya interactions. This property strongly influences the low-temperature magnetism in RMn2O5 (Kimura et al., 2009[link]).

[Figure 2.8.16]

Figure 2.8.16 | top | pdf |

Time-of-flight diffraction patterns of YMn2O5 at 1.6 K under magnetic fields between 0 and 8 T (taken from Radaelli & Chapon, 2008 [link]). Copyright IOP Publishing. Reproduced with permission. All rights reserved.

2.8.3.3.3. Additional systems and scattering techniques

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Information about the anisotropy of the local magnetic susceptibility at different magnetic sites has been extracted from diffraction patterns for a Tb2Sn2O7 powder measured using polarized neutrons under magnetic fields of 1 and 5 T (Gukasov & Brown, 2010[link]). No magnetic contribution to the diffracted intensities was observed at 2 K in the absence of an external field. However, applying a field led to considerable changes in the diffraction pattern (Fig. 2.8.17[link]). At 100 K and 5 T, the intensities of the reflections that are allowed for the cubic space group [Fd{\overline 3} m] increase considerably. Furthermore, they were found to depend strongly on the polarization of the incoming neutrons, as shown by the difference pattern in Fig. 2.8.17[link]. At a field of 1 T, new reflections appear (Fig. 2.8.17[link]a) that are forbidden for the occupied sites in [Fd{\overline 3} m] symmetry, such as 200, 222 and 240. The intensities of these new reflections do not change with the polarization of the neutrons, as demonstrated in the difference plot, hence they are purely magnetic. In conclusion, information on local anisotropic magnetic susceptibility at different sites can be obtained by using a combination of unpolarized and polarized neutron powder patterns. This demonstrates the usefulness of polarized neutron scattering, even for polycrystalline samples.

[Figure 2.8.17]

Figure 2.8.17 | top | pdf |

Polarized neutron diffraction patterns for Tb2Sn2O7 at 2 K and 1 T (a) and 100 K and 5 T (b). I+ and I are the intensities for spin-up and spin-down neutrons, respectively. Taken from Gukasov & Brown (2010) [link]. Copyright IOP Publishing. Reproduced with permission. All rights reserved.

We now return to X-ray investigations of magnetic materials. A laboratory device for fields up to 5 T and temperatures above room temperature was mentioned in Section 2.8.3.3.1[link]. The corresponding low-temperature apparatus (Koyama et al., 2013[link]) has produced results on magneto-caloric compounds of MnFeP-type materials. Substitution of P in MnFeP1−xZx with Z = As or Ge produces materials that exhibit a large magneto-caloric effect and thus allows control of the Curie temperature by chemical composition. Studies under magnetic fields are mandatory, as the refrigerants are working under a field. For two different compositions of the As compound the lattice parameters change drastically and the cell volume decreases with increasing magnetic field strength. In MnFeP0.78Ge0.22 a field-induced ferromagnetic phase was observed near the Curie temperature at 280 K. This phase is, however, not identical to the low-temperature ferromagnetic one (Koyama et al., 2013[link]).

2.8.3.3.4. Concluding remarks

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Despite some shortcomings, powder diffraction studies as a function of magnetic fields are valuable for the qualitative and sometimes even quantitative interpretation of magnetic materials. Unpolarized neutrons are used in most experiments, but the additional information from polarized neutrons has also been exploited. X-rays do not interact directly with the magnetic moments, but structural changes as a consequence of magnetic phase transitions have been observed in several cases. In situ powder diffraction under magnetic fields reaching 4 T on an X-ray diffractometer with a rotating anode revealed details of lattice parameters and atomic positions in rare-earth alloys with a higher precision than that accessible by neutron diffraction (Pecharsky et al., 2007[link]). Furthermore, the two test-case compounds studied, Gd5Ge4 and DyCo2, contain the rare-earth elements Gd and Dy with the highest absorption cross sections for neutrons in their natural isotope abundance. The data were used to refine the underlying structure models by Rietveld analysis. Advances in X-ray and neutron sources and optics delivered higher resolution and flux to the samples, which in combination with rapid computing made real-time experiments feasible.

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