
SHEMETOV YEVGENY. STUDIES OF PHASE TRANSITIONS IN THE UNITED A_{2}BX_{4} STRUCTURE βK_{2}SO_{4 }METHOD NUCLEAR QUADRUPOLE RESONANCE English abstract § 1.1 § 1.2 §1.3 § 1.4 § 2.1 § 2.2 §2.3 §2.4 § 3.1 § 3.2 § 3.3 § 3.4 § 4.1 § 4.2 § 4.3 § 4.4 Reference Template pdf abstract
§ 4.2. PT phase diagram of Rb_{2}ZnBr_{4}. In the beginning of this section briefly touch on issues of experimental measurements techniques not mentioned in Sec. 2. During the first stage, which was carried out in 198687, decided camping methodical task is to determine the possibility of equipment to record the "disproportionate" spectra at high pressures and determine increases or decreases the temperature range of the existence of Jc structure to such impacts [136,137]. This problem was originally solved by a hightemperature phase transition area using a titanium chamber NQR method and differential thermal analysis (DTA construct a cell for measurement is described in [74]). At temperatures below room used lowtemperature cell HPC1. And only later, after the production of the second stage HPC2 managed to meet the challenge of a detailed study of structural changes in the J_{c} phase. In the study technique was used isobaric and isothermal changes of PT parameters. The spectra were recorded with a temperature step of 510^{0}K and step pressure of 0.10.5 MPa. Frequency scanning range was from 55 to 78MGz. To control the sensitivity of the receiving path and to assess the impact of nonequilibrium processes in crystalline amplitude spectrum used NQR "frame". PT field of study in HPC2 was 170290^{0}K at pressures up to 0.4 GPa. Above these pressures and temperatures data obtained HPC1. Total about 20 isosections. tracked, recorded more than 300 spectra. The samples of high quality obtained with the growth of single crystals for NMR experiments. Due to the fact that data obtained in HPC2 far been published only in a succinct form, we elaborate on their description in this paper. On Fig.4.11 open circles marks the position of the differential thermal break in the temperature curve passing
Figure 4.11. DTA data (open circles) near T_{i}, dielectric [59] (dotted lines, Roman notation) and NQR (continuous lines) measurements in the PT region of the incommensurate phase of Rb_{2}ZnBr_{4}
PJc transition at different pressures. For comparison, in this figure, dotted line plotted PJc transition obtained later by Japanese researchers according dielectric measurements [59]. Note that the phase transition temperature T_{i} and DTA recorded at atmospheric pressure. differ by more than 5K. NQR measurements in the area of T_{i} conducted on highline absorption signal from nucleus ВrI. (Presented below is a purely technical information intended for trainees and specialists experimenters. Panoramic reader can omit these routine details and go to page 127 and then 139.) When isobaric changes in the phase transition observed "failure" in the intensity of this line, and at higher pressures, the line was not observable in a greater range of temperatures. These intentions have shown little promise HPC1 use design with a small diameter of the working channel for research NQR spectra near T_{i.} However, it was found that the temperature T_{i} with increasing pressure shifts to the high temperature region and the phase transition is smeared PI (Fig.4.11). Much more informative studies were NQR in the transition from the incommensurate to the ferroelectric phase. At low pressures 100MPa) near Jc, there was a marked increase in the intensities of the NQR lines of type N. With increasing pressure, the temperature region where these lines appear in the spectrum, expanding that recorded by changes in relative intensities of the "clean" lines of type N, NJ overlapped and FN and F types of spectral lines. The relative intensities of the course is illustrated by the example of Fig.4.12 lines F10 and N10. In the pressure range up to 250MPa. The spectral lines of these types coexist in the incommensurate phase. Intensities of the lines of type N increases gradually and at pressures higher than 250MPa spectrum consists of 14 discrete lines, which were correlated with the existence in this pressure commensurate phase N. In isobaric measurements at проходах 200MPa with decreasing temperature, a phase transition to the ferroelectric structure, which is characterized by intense 12 discrete absorption NQR (line Fl  F12). With increasing temperature above 210^{0}K spectra intensity gradually decreases. Area of PT parameters (where the overall intensity of the spectra decreases) designated by us Jc symbol on Fig.4.11 can be roughly separated from the rest of the lowtemperature region of the incommensurate phase. During the measurements, it was also found that the isobaric passages corresponding to high pressures from the incommensurate phase transitions (Jc) in the N phase and ferroelectric phase strongly blurred. Changes in the intensities F, N and overlain
Fig.4.12 The relative intensity of the spectral lines NQR F10 and N10 at different pressures.
groups of lines are so gentle that above 150MPa definition phase transitions becomes difficult. Fig.4.11 on the phase diagram based on the results of isobaric studies [116,118,136,137]. Experimental data suggest the possibility of a more complex structural changes in the N phase. These assumptions were confirmed by us in isothermal studies CPH2 [111,112,116], for a detailed exposition of which we proceed. Increased pressure in the F phase (isotherm 173, 183 and 188K) possible to observe the following transformations NQR spectra: Fig.4.13, 4.14 and 4.16. Pressures up to 90110MPa observed only 12 lines of F type. Traces type lines N, due to the lower sensitivity in a bomb than a heat chamber, is not recorded. The above values range complemented weak spectral lines of type N (shaded areas on the spectrum Fig.4.13 and 4.14). Their intensity increases with increasing pressure to ~ 150MPa, and further in the range of DP ~ 60¸30MPa stabilized. With further increase of pressure changes in the spectrum are characterized by the disappearance of the lines of type F, increase the intensity of the N lines and the appearance of lines corresponding phase H: Hlines. Intensity increases dramatically past a narrow range of pressures above 250¸280MPa and at higher pressures there is powerful resonance lines 14, two of which, at frequencies 65.8 MHz and 66.7 have twice the strength. On Fig.4.15 presented as an illustration of the baric stroke frequency of the NQR spectrum of Rb_{2}ZnBr_{4} at T = 183K. In the phase transition region the slope of the frequency of moves and jumps NQR frequencies. Features isothermal evolution of the spectrum in the PT field is an extension of Pinterval overlap (coexistence) lines of type F and N with increasing temperature isotherm. So at 189^{0}K coexistence region F and N spectral lines is about 30MPa at 188^{0}K 40MPa and at 173^{0}K  £10MPa. However, the transition to the isobaric change in temperature in the range 160200MPa, the coexistence lines of type F, N and H extends over a wide temperature range over 40^{0}K and 200MPa isobar on phase transitions in H or F phase was not observed up to 150K. These data indicate that the region of coexistence the phases dependent on the direction of change of the parameters P T in relation to the PTphase lines.
Fig. 4.13. Full Br NQR spectrum in RZB at T = 183^{0}K and different pressures.
Fig.4.14. Changing of the NQR spectrum with increasing pressure at T = 183^{0}K.
Fig. 4.15. Baric stroke line frequencies of the NQR spectrum at T = 183^{0}K.
As the pressure decreases from phase H hysteresis of phase transitions. To move H ↔ N DР 20 ¸40MPa, the transition F ↔ N DР from 30 to 6OMPa where value increases with increasing temperature. Thus isothermal method at low temperatures clearly recorded two phase transitions F↔N and N↔N. Multiplicity NQR spectrum varies from 12 lines of singlet type F, through no less than 20 spectral lines of N type to sixteen NQR lines, corresponding to the high pressure phase N. Both phase transitions in classical featured are firstorder transitions. Phase transition line F↔N is negative ∂Р/∂T Phase transition H↔N at high temperatures observed at higher pressures (∂Р/∂T = 2,86 MPa/K) with a character transformation spectra NQR does not change significantly at temperatures up to 210K. Isothermal studies in the field of lowtemperature incommensurate phase (from 189^{0}K to 200^{0}K) were performed in detail with step 10¸ pressure 50MPa. Let us consider the general patterns observed in the NQR spectra in this area. On Fig.4.16 and 4.17 for example isotherms T = 198^{0}K and T = 190^{0}K presented baric Frequency spectrum lines. Due to the fact that in this area of PT observed spectral distribution with a complex change in intensity on the pressure dependence (Fig.4.17), except for specifying the frequency of the peak of each distribution, a closed oval contour scheduled spectral distributions that reflect their intensity and area of overlap. On Fig.4.26 and 4.27 are graphs of peak intensities. With increasing pressure, the overall intensity of the spectra increases and decreases the halfwidth frequency distributions. At a certain pressure, in the absence of frequency overlap, have seen the emergence of new lines (for example N8^{+,} N8^{,} N11^{+} )Fig.4.17. PT boundary area of occurrence of these lines at high temperatures is shifted to higher pressures and the phase diagram it is possible to compare a certain PT line at = 150MPa and 200^{0}K (Fig.4.24). When crossing this line is also measured the change in peak intensities most NQR signals. With decreasing, the pressure indicated
Fig. 4.16. Baric move NQR frequencies at T = 190^{0}K.
Fig. 4.17. Baric move NQR frequencies at T = 198^{0}K.
hysteresis in the position marked abnormalities ΔР 40MPa. Thus, all indications in phase N, a phase transition from a phase existing near atmospheric pressure to a phase N4, the previous highsymmetry phase N. A detailed analysis of the spectral data (see § 4.3) shows that the evolution of the NQR spectrum in the PT region is represented by a more complex way than the coexistence of spectral lines F, N, NJ HN or type. At pressures of ~ 260MPa, clearly observed phase N↔H transition. We now describe the data in isothermal studies CHP2 in the middle region of the incommensurate phase (above 200K). The characteristic form of NQR spectra in this area is presented in Fig.4.18. Fig.4.19 on the example shows a typical isotherm 219^{0}K baric frequency dependence of NQR lines, and change Fig.4.20 peak intensity spectral component at the frequency J14  67.3 MHz, which is characteristic for the other lines of the spectrum. At atmospheric pressure, the shape of the spectrum is represented by a small number of resolved components (Fig.4.18a). This form is maintained until the pressure 200MPa, where there is the first anomaly. So blurred spectral distribution at frequencies 69¸ 66,5 MHz (line group conventionally designated J13J16) above 200MPa varies considerably (Fig.4.18b). Shape of the spectral distribution J5J6 and J7J8 also converted by increasing the circuit under their new spectral components. Group lines J1J4, at atmospheric pressure characterized by a continual distribution between edge peaks above 200MPa proceeds to the frequency resolution of the form M1  M4. Absorption signals at frequencies 7070,5 MHz observed only above 200MPa, and at high temperatures in all of high pressures. Also noticeable transformation of the spectrum shape (Fig.4.18a and 4.18b) measured the change in the halfwidth distributions and their peak intensities (Fig.4.20). Thus, a phase transition from a phase of Jc to a new phase marked by us symbol M1. With increasing temperature recorded overall reduction ratio S/N Features characterizing the anomaly Jc↔M1 becoming less distinct and isotherm 250^{0}K completely blurred. When the pressure is reduced there is a significant hysteresis of the phase transition Jc↔M1 about DP 160MPa. Fig.4.24. Marked change in the slope of the phase transition to negative ∂Р/∂T = 75Pa/K.
Fig.4.18.Change NQR spectrum at T = 190K
Fig.4.19. Baric move NQR frequencies at T = 218K.
Рис.4.20аг. Барическое изменение интенсивности линий спектра ЯКР типа J4М14 при разных температурах.
Fig.4.20ag. Baric change in the intensity of the spectral lines NQR type J4M14 at different temperatures.
Fig.4.20d th. Baric change in the intensity of the spectral lines NQR type J14M14 at different temperatures
As the pressure increases in this temperature range by a second anomaly. It is characterized by changes in the forms of spectral distributions (Fig.4.186 and 4.18v), especially during the peak intensities of all lines (Fig.4.go), as well as a notable change in the frequencies of spectral peaks and slopes of the frequency dependencies (Fig.4.19). Transition into a new phase, which we denote by M_{2,} with increasing temperature isotherm is shifted to higher pressures with a positive slope with respect to the temperature axis ∂Р/∂Т ≈ 110Pa/^{0}K .At temperatures above 260^{0}K transition line M_{1}↔M_{2} is not tracked due to the excess of its intended position limit values HPC2 pressure, and in the case HPC1 not sufficient sensitivity of the apparatus. Hysteresis transition M_{2}↔ measured isotherm 211^{0}K is about 50MPa. When pressure rises above 400MPa width of the spectral distributions decrease at a certain pressure and intensity of the NQR lines increases sharply, then stabilized again (Fig.4.21 and 4.22). There is a new spectral line frequency offset with respect to the spectral lines of phase M_{2.} This spectral anomaly, we compared with the phase transition into the next phase of high pressure М_{3}. Position of the transition points determined from the inflection in the course of baric intensities of the NQR lines M12M16 (Fig.4.22). At high temperatures, the anomaly in the transition М_{2}↔М_{3} is fixed much clearer. The slope of the transition line between phases M_{2} and M_{3} is ∂Р/∂Т =*8MPa/K. Hysteresis transition ΔР ≈40MPa. Thus, when the pressure in the middle of the incommensurate phase observed sequence of phase transitions J↔ М_{1} ↔ М_{2} М_{2}↔М_{3} The decrease in the width of the spectral lines indicates the ordering of the incommensurate structure with increasing pressure. With increasing pressure above 500MPa, or with decreasing temperature below 250^{0}K in this P region, the shape of the NQR spectrum continues to change (Fig.4.23) and transformed to characteristic of phase N. Due to the large step measurements (510K, 50MPa) in the PT range, and the vagueness of the anomaly, the proposed line separating phase M_{3} and H is fixed with a large error.
Fig.4.21. Convert NQR spectrum in the phase transition M_{2 }↔ M_{3 } M_{3}↔ H.
Fig.4.22. Baric of the intensity of spectral lines M13 (M12) in the phase transition M_{2} ↔ M_{3} at different temperatures.
. Fig.4.23. Changing of the NQR spectrum in the phase transition M_{3 }↔ H at P = 500MPa.
Final step of transforming the structure of Rb_{2}ZnBr_{4} at high pressure is highly symmetric phase G, which is characterized by four powerful singlet absorption lines NQR radio nucleus BrI, BrII, BrIII and BrIV (Fig.4.18). Phase transition in phase G is a firstorder transition, because, although no hysteresis phenomena (up 5MPa), there is a region of coexistence of phases. End increases with increasing temperature, and this transition is independent of the direction of change of PT parameters. Measurements at pressures above the transition to the 6 were not conducted. PT phase diagram of Rb_{2}ZnBr_{4}  On Fig.4.24 shows the experimental PT phase diagram rubidium tetra zinc bromine in the 160300^{0}K at pressures up to 1.0 GPa, built on the results of our data. In addition to the wellstudied at atmospheric pressure paraelectric (P), incommensurate (Jc) and ferroelectric (F) phases, it was discovered or suspected the existence of several phases with different structures and symmetries. By type and nature of changes NQR spectra investigated PT range can be divided into two areas: 1) the area where the spectrum consists of a small number of intense singlet lines (phase F, G, F and H) and the structure of the phases described by one of the space groups simorfnyh; 2) The second area where the species and the evolution of the spectrum can be associated with the existence of more or less disordered structures (phase N, M and Jc). Paraelectric and the ferroelectric phase are known as spatial symmetry D_{2}^{16h} (Pnma), and C_{2}^{9V} (P2_{1}/n), respectively. With this in mind, using the symmetry transformation rules involving data from NQR, we can show that the phase of H must have a rhombic or monoclinic symmetry. Availability 14 NQR lines, two of which have double the intensity allows unequivocally enough to suggest that this phase is described by the point group symmetry P2_{1} quadruple unit cell volume (V = 4, Z = 16). Highly symmetric phase G, which is characterized by four nonequivalent positions in structure Br nucleus may have a monoclinic or triclinic symmetry with unit relative to the paraelectric phase, the unit cell volume (V = l).
Fig. 4.24. Phase diagram of Rb_{2}ZnBr_{4}, obtained by NQR.
The latter assumption is supported by extensive, approximately 4fold, increase in the integral intensity of each of the four NQR lines. Reduction of vernix with increasing pressure and temperature indicating the approach to a particular TP point in the phase diagram. It also indicates the position of the PT phase line separating Jc and P and PJc blur transition with increasing pressure. Based on this and several other reasons, we assumed the existence of the Lifshitz point, which should be located at the intersection of PT lines separating highly symmetric phase G and P (Ris.4.35). Region of existence of the disordered structure can also be divided into three parts: 1) lowtemperature region N, where there is a welldefined frequency resolution and intense spectral components or groups. In this area, we can assume (with) the existence of longperiod nearly commensurate structures; 2) PT region Jc, where there are blurred spectral shape characteristic of the incommensurate phase (disordered structure of longperiod); 3) Field of phases M where NQR spectra have more or less frequency resolution basis. The degree of ordering of the structure is increased when approaching the phase transitions in lines H and G phase. Reduce the blurring and hysteresis transitions between phases M1, M2, M3 with increasing pressure, also indicates the nature of the structural transformations. As in most of incommensurate phases dielectrics family A_{2}BX_{4} and in compounds with CDW [63,96] hysteresis phenomena are global in nature, and there is a large range of variation of hysteresis phenomena in different surroundings investigated PT region, from 20 to 160MPa. Note also feature observed in passing phase transitions F↔ N↔H for different directions of change of PT parameters (Chapter 4 § 2). This behavior indicates a specific data type conversions, due to the presence of significant nonequilibrium phenomena. Registers significant blurring if the transition phase as it passes along the line, compared with the transverse passage. This is apparently due to a clearer and observation of phase transitions isothermal scan compared with isobaric. Thus as a result of these studies failed to establish the following: 1) With increasing hydrostatic pressure PT transition is shifted to higher temperatures; 2) At pressures above 250MPa and temperatures below 220^{0}K observed commensurate phase H presumably rhombic symmetry P2_{1} and quadruple volume; 3) Has a highly symmetrical above 500MPa phase G, with the same, relative to the paraelectric phase, the unit cell volume (V = 1) ; 4) Lowtemperature region of the existence of an incommensurate phase increases with increasing pressure up to 250MPa, phase transitions F ↔ N, N ↔ H in isobaric mode significantly eroded; 5) Close T_{C} observed a special PT area, increases with increasing pressure and is characterized by the coexistence of different groups of spectral lines; 6) In the middle region of the incommensurate phase in zoom mode pressure observed sequence of phase transitions Jc→ M_{1}→ M_{2 }→ M_{3 }→ G, Apparent to transform NQR spectra. Almost simultaneously with our studies were performed measuring the dielectric constant of RZB at different pressures [59]. Although this method is less sensitive than the NQR method, the author managed to watch some anomalies. Position of the phase transition points, tracked in this study was determined from the temperature dependence of the maxima e (T,P), which in most cases were observed strongly blurred. Comparison of the phase diagram Gezi (Fig.4.11) with our data shows that in the pressure 250MPa near T_{C}, where we tracked a special area of the phase diagram, the triple point (see details in § 4.3), by emeasurements also assumes the existence of a triple point. There is a clear coincidence PT lines between II (Jc) and V phases Gezi and PT line Р_{3}^{+} (M2↔M3 ) tracked in this study. However, other data show significant differences. First, there is no phase transition line between phases G ↔ H, ↔ M ↔ N and I ↔ M1 ↔ M2 observed using NQR. Secondly there is the PT phase line separating Jc in at atmospheric pressure (phase II and II' in the notation Gezi). In this case the author notes that the PT line between phases II'II and IVV are fixed and not very clearly in cooling mode only, and epeak between II(Jo) and IV phases smeared with increasing pressure. Data differences in our opinion due to the following. First, the significant influence of nonequilibrium processes, as we discovered the character structure transformation depends on the direction and rate of change of external influence. Secondly, impurities. Third, the difference polycrystalmonocrystal. It is therefore possible for a shift of the phase transition lines and their degree of fuzziness for samples of different states and crystallization. Taking these arguments, we can explain the discrepancy between some of the data as follows. The PT transitions between phases H↔N, I↔M_{1}↔M_{2} is not recorded in the emeasurements due to their small inclination to the isobaric directions of measurement. 2) Mild line between phases II and II'(Gezi observed in cooling mode only), correlates with the position of PT line P_{1} (M_{1}↔Jc ), recorded by us in reducing the pressure mode. The difference in the absolute position PT can be explained along with the above arguments, the difference in the determination of transition criteria.
English abstract § 1.1 § 1.2 §1.3 § 1.4 § 2.1 § 2.2 §2.3 §2.4 § 3.1 § 3.2 § 3.3 § 3.4 § 4.1 § 4.2 § 4.3 § 4.4 Reference Template pdf abstract

