This paper reviews the experimental studies of displacive phase transitions in solids. Primary emphasis is upon inelastic light scattering and neutron scattering; related infrared reflectivity measurements, as well as x-ray and EPR analyses are also summarized. Several prototype structures are considered in detail: (1) the rocksalt IV-VI semiconductors PbTe, SnTe, and GeTe; (2) the ferroelectric perovskites exemplified by PbTi${\mathrm{O}}_{3}$ and BaTi${\mathrm{O}}_{3}$; (3) perovskites which exhibit cell-doubling transitions, such as LaAl${\mathrm{O}}_{3}$, SrTi${\mathrm{O}}_{3}$, and KMn${\mathrm{F}}_{3}$; (4) crystals having the $\ensuremath{\alpha}$-quartz structure, including Ge${\mathrm{O}}_{2}$, Si${\mathrm{O}}_{2}$, and AlP${\mathrm{O}}_{4}$; (5) the "improper ferroelectrics" ${\mathrm{Gd}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$ and ${\mathrm{Tb}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$; (6) the V-VI-VII semiconductors typified by SbSI; (7) the hydrogen-bonded ferroelectrics of the K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ family; (8) Jahn-Teller systems such as DyV${\mathrm{O}}_{4}$ and RbCo${\mathrm{F}}_{3}$, in which structural distortions occur as secondary effects; (9) order-disorder systems such as NaN${\mathrm{O}}_{2}$ and the ammonium halides (N${\mathrm{H}}_{4}$Cl, N${\mathrm{H}}_{4}$Br), in which no "soft mode" occurs in the spectral region ($\ensuremath{\omega}g{10}^{11}$ Hz) probed by ir, Raman, and neutron spectroscopy; (10) $\ensuremath{\beta}$-tungsten ($A\ensuremath{-}15$) structures such as ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn, which exhibit high-temperature superconductivity. These crystal categories are used to illustrate several phenomena of current physical interest: Specifically, we discuss harmonic and anharmonic mode coupling; "critical exponents" $\ensuremath{\beta}$ differing from one-half in the temperature dependences of the order parameter $\ensuremath{\phi}(T)={\ensuremath{\phi}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$ and of the soft-mode frequency $\ensuremath{\omega}(T)={\ensuremath{\omega}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$; and the recently discovered "central" modes centered at zero frequency, which grow in intensity as the transition temperature ${T}_{0}$ is approached from above or below. The review covers the period 1940-1972. A few 1973 works are mentioned for which the author had preprints in 1972 or very early 1973. This review is in no sense a comprehensive survey of ferroelectricity. Readers are referred to the following earlier reviews on that subject: Silverman (1966, 1969), Cochran and Cowley (1967), Blinc (1968), Murzin et al. (1968), Nettleton (1970), and Blinc and Zaks (1972).

Soft-mode spectroscopy: Experimental studies of structural phase transitions

The co-operative Jahn-Teller effect is a phase transition which is driven by the interaction between localized orbital electronic states and the crystal lattice. The possible origins, symmetries and properties of the electron-lattice interactions and how they lead to possible hamiltonians for the coupled system are discussed. The relation of these interactions with quadrupolar interactions and magnetostriction is included. The methods of solution of the hamiltonians lead to an understanding of the electronic states, the phonon spectrum and the mixed normal modes. The wide variety of experimental techniques used on this problem are reviewed in detail and the results are compared with theoretical expressions whenever possible. The application of external stress and magnetic field is of particular significance in the case of the rare earth compounds, because they can product effects which are larger than the low-temperature spontaneous effects.

http://iopscience.iop.org/article/10.1088/0034-4885/38/1/001/pdf

Co-operative Jahn-Teller effects

List of contributors Preface Introduction 1 Crystal field splitting mechanisms D J Newman and Betty Ng 2 Empirical crystal fields D J Newman and Betty Ng 3 Fitting crystal field parameters D J Newman and Betty Ng 4 Lanthanide and actinide optical spectra G K Liu 5 Superposition model D J Newman and Betty Ng 6 Effects of electron correlation on crystal field splitting M F Reid and D J Newman 7 Ground state splittings in S-state ions D J Newman and Betty Ng 8 Invariants and moments Y Y Yeung 9 Semiclassical model K S Chan 10 Transition intensities M F Reid Appendix 1 Point symmetry D J Newman and Betty Ng Appendix 2 QBASIC programs D J Newman and Betty Ng Appendix 3 Accessible program packages Y Y Yeung, M F Reid and D J Newman Appendix 4 Computer package CST Cz Rudowicz Bibliography Index

/pdf/crystal-field-handbook-5enwtd2lao.pdf

Crystal Field Handbook

Raman spectra of anhydrous crystalline samples of all of the lanthanide orthophosphates (with the exception of PmP04) have been obtained. These data were interpreted in a systematic manner based on the known structures of these compounds. Assignments and correlations have been made for many of the observed bands. Accordingly, a series of investigations of the chemical and physical properties of the lanthanide (and related) orthophosphates is currently in progress. Single crystals of all of the lanthanide orthophosphates (except PmP0,) doped with small amounts of Gd3+ were prepared for the initial purpose of performing a series of electron paramagnetic resonance experiments. The availability of these samples made it possible to carry out a study of the Raman spectra for essentially the entire series of rare-earth orthophosphates. This study was directed toward the following objectives. First, baseline spectra were to be established that could be used as a basis of comparison with subsequent lanthanide orthophosphate crystals that would be doped with @-active actinides and, consequently, would be subjected to heavy-particle radiation damage. Second, a classification and correlation of the Raman spectra of the entire group of rare earth orthophosphates was desired. Yttrium orthophosphate was included in the present investigation because its properties are known to correlate well with those of the orthophosphates of the second half of the rare-earth series (i.e. TbP04 through LuP04) and also because YP04 is the analog of the natural mineral xenotime. In addition, a consider- able literature exists on the properties of YP04 that can be used for the purposes of verification and comparison with the lanthanide compounds. The lanthanide orthophosphates can be conveniently divided into two groups on the basis of the prevalent crystal structural form. The first group has the mono- clinic 'monazite' structure and consists of LaP04 through GdP04. The second group has the zircon struc- ture and consists of TbP04 through LuP04. Both YP04 and ScP04 also crystallize with the zircon structure and can be grouped with the orthophosphates formed by EXPERIMENTAL ~~~~ ~ ~

Raman spectra of the rare earth orthophosphates

Crystal field and Electron–Phonon Interaction in Rare-Earth Ionic Paramagnets

The rare-earth crystals DyVO 4 , DyAsO 4 and TbVO 4 undergo structural phase transitions at 14, 12 and 34 K respectively induced by a cooperative Jahn-Teller effect. An experimental investigation of the phase changes has been made using Raman scattering methods. For purposes of comparison, the Raman spectra of DyPO 4 , YVO 4 and GdVO 4 (which do not undergo phase transitions) have also been measured. A detailed theory of the phase transitions has been developed which accounts for the electronic and vibrational Raman spectra. The lowest four electronic levels of Dy 3+ and Tb 3+ are treated in a pseudospin formalism, and the theory is discussed in terms of mixed phonon and pseudo-spin excitations. The singly degenerate κ ≈ 0 optic phonons are not measurably affected by the transitions, but splittings of up to 20 cm -1 developed in the doubly degenerate E g phonon modes in the Raman spectra owing to anharmonic couplings with the electronic states. Splittings are also observed in the lowest electronic levels of the rate earth ions below the transition temperature; these electronic modes effectively constitute the soft mode which causes the transitions to occur. A molecular field model is first used in the theoretical analysis. The equations of motion of the coupled excitations are then found and the energies, line widths and dispersion of the mixed excitations are discussed. The connexion between the static strain and the acoustic phonon mode coupling is investigated, and a thermodynamic treatment of the elastic constants is given. From the Raman data, it appears that in TbVO 4 the acoustic mode coupling is stronger than the optic mode coupling.

Raman scattering and theoretical studies of Jahn—Teller induced phase transitions in some rare-earth compounds

The thermal conductivity between 0.4 and 4.2K and in magnetic fields up to 50 kOe of KMgF$\_{3}$ doped with Ni$^{2+}$ has been measured. The results are analysed to give values of the average spin-lattice coupling constants ($\scr{H}$ $\_{\text{SL}}$) for the Ni$^{2+}$ ion. These are in agreement with values calculated using the magneto-elastic constants (G$\_{11}$ and G$\_{44}$) derived from acoustic paramagnetic resonance (a.p.r.) experiments. Below 1 K the thermal resistivity as a function of magnetic field shows a number of anomalies, for which possible causes are discussed; it is concluded that they result from phonon interactions with exchange-coupled pairs of Ni$^{2+}$ ions. Such pairs are also observed in a.p.r. experiments.

R. T. Harley

Papers

Raman scattering and theoretical studies of Jahn—Teller induced phase transitions in some rare-earth compounds

The Thermal Conductivity of Ni$^{2+}$ doped KMgF$_{3}$ in a Magnetic Field at Low Temperatures: The Effect of Single Ions and Coupled Pairs