Kristal alanlarının, elektrik alan gradiyentlerinin ve faz geçişlerinin SbC13 ve K2ZnC14 de incelenmesi

Abstract

ÖZET Bu çalışmada Kristal Alan Teorisi ve Nükleer Kuvad- rupol Rezonans Teorisi teorik olarak gözden geçirilmiştir. Ayrıca Nükleer Kuvadrupol Rezonans Enerji durumları yeniden ve duyarlıklı hesaplanarak Asimetri Parametresinin daha du yarlıklı tayini örneklerle verilmiştir. Ayrıca bu parametre nin bir order parametresi olarak kullanımı önerilmektedir. Bu amaçla SbCl3 deki Sb121 ve Sb123 izotoplarının ve K2ZnCl4 deki Cl.35 izotopunun muhtelif sıcaklıklarda Nükleer Kuvadrupol Rezonansı Frekansları ölçülmüş ve bir bilgisayar yardımıyle Bayer katsayıları (a, b, c) daha duyarlıklı olarak bulunmuş tur. Asimetri Parametresi SbCl3 de Sbl23 izotopu için Rezo nans frekanslarının oranlarından 10-4 hassasiyetle hesaplan mıştır. Buna ek olarak SbCl3 de Sbl23 için Morino-Toyama metodu ile de asimetri parametresi hesaplanmıştır. Her iki yöntemle hata sınırları içinde aynı sonuçlar elde edildiği görülmüştür. Bu tezde ayrıca düzenli (commensurate) ve düzensiz (incommensurate) yapılarda faz geçişleri hakkında bilgi verilmiş, düşük ve yüksek sıcaklıklarda faz geçişleri ince lenerek bunlara ait örnekler verilmiştir. Enerji değerlerini veren sekuler denklemlerin çözümü bir bilgisayar programı ile hesaplanmış, spini 5/2, 7/2, 9/2, ve n 'nın 0, 0,5, 1 değerleri için bu sekuler denklemlerin gratikleri çizilmiş tir. IV. Bölümde Faz geçişleri teorik olarak incelenmiş, V. Bölümde ise deney yaptığımız Nükleer Kuvadrupol Rezonans Spektrometresi hakkında bir bilgi verilmiştir. V I. Bölümde ! ise yapmış olduğumuz denel çalışmalar verilmiştir. VII. Bölümde deney sonuçlarının tartışılması yapılmış ve bazı öneriler verilmiştir.

THE STUDY OF CRYSTAL FIELDS, ELECTRICAL FIELD GRADIENTS AND PHASE TRANSITIONS IN SbCl3 AND K2ZnCl4 SUMMARY In modern physics, a very important parts of the experimental methods depend on the Nuclear Resonances. The most sensitive one of that methods is the paramagnetic resonance. This method depending on the electron spin and the total orbital angular momentum, has been used by many physicist to the investigation of crystal field and the high temperature super conductors. Since the applications of the paramagnetic Resonance Spectrometers, are in high frequency and necessitate high field magnets that include it's difficulties and it's economical weights. The method of Nuclear Magnetic Resonance was widely used in Basic Physics, Chemistry, Industrial research, metallurgy, Biology and Medicine because that it is applied in rather low frequencies. Recently this method is applied to Medicine under the name of. Magnetic Resonance Imaging (MRI). It has the* advantage of radiation less for the health, can be used for different thickness of planes, also the selection of different isotopes such as C^, N^4, p31, Na2^ etc are possible. In this thesis, we used a Nuclear Quadrupole Resonance Spectrometer. This method has some specialities against the others. Some scientific knowledge which can not obtained by other methods may be found on molecular binding and Electrical Field gradients etc. by only this method. Recently the phase transitions of some crystals are also investigated by this metod. It is also possible to define new order parameter to understand theoretical aspects of the phase transitions from Quadrupolar theory. We investigated Crystal Fields and Electrical Field Gradients in general theoretically. In the first section an introduction and a short summary of the subject was given. The second section is about the theoretical aspects of the `Crystal Field Theory`. This starts with general Hamiltonian and static electrical potential in the crystals. The solution of this problem is rather easy and only some results are given for different crystal symmetries. Only the simplest solutions and crysatl structures was considered. These are: Six fold Cubic, Four fold cubic, Eight fold Cubic, Six fold Trigonal, Nine fold Trigonal, Six fold Tetragonal, Eight fold Tetragonal, Six fold orthorombik symmetries. Thean introduction and a short summary of the subject was given. The second section is about the theoretical aspects of the `Crystal Field Theory`. This starts with general Hamiltonian and static electrical potential in the crystals. The solution of this problem is rather easy and only some results are given for different crystal symmetries. Only the simplest solutions and crystal structures was considered. These are: Six fold Cubic, Four fold cubic, Eight fold Cubic, Six fold Trigonal, Nine fold Trigonal, Six fold Tetragonal, Eight fold Tetragonal, Six fold orthorombik symmetries. The expressions for the crystal potential fields are also given in carthesian coordinates for the symmetries of Tetragonal, Trigonal, Hexagonal, Rombic, Triclinic etc. The third section starts with the Quadrupolar Hamiltonian and secular equations was solved for spin 1=5/2, 7/2 and 9/2 since in the literatures these were given with some errors. From these secular equations Energy eigen with arid Resonance Frequencies are calculated for the some spin values but for the Asymmetry parameter values zero Jto are in step 0,1 f at first then step 0,01. To obtain T[ in higher precision this energy levels, Resonance frequencies and the ratio of the resonance f requencies ^re calculated for the values of Asymmetry parameter T/ = 0,160-0,190 in step of Arj= 0,001 for spin 1= 7/2. The result of these calculations are given at the end of the thesis in table C-l to C-9. These Tables are used to obtain the value of the Asymmetry parameter from experimental data. By this way we obtained the experimental value of the Asymmetry parameter with a precision of 10~4. In section 3. a short review of the Bayer theory which gives temperature depence of the Nuclear Quadrupole Resonance frequencies in first order, was also given. The Bayer coefficients calculated from experimental data are given in tables 6.1 to 6.3. At the same time, the theory of the pressure and volume dependence of the Nuclear Quadrupole Resonance frequencies was also given in the same section. (Modified Bayer Theory). At the end of section 3., some examples for the anormal temparature dependence and their theoretical explanations are given for KCUCI3 and K2MCİ5 type molecules, Section 4. is on the theories of the phase transitions. Here lowest developments are given and the importance of xiiithe order parameter is reemphasized. Firstly the review of the classical theories are given shortly. After that recent developments in the phase transition theories are considered. The universal critical behaviour models also explained shortly. From these we see that new order parameters can be defined for first and second order phase transitions. The application of the phase transition theory to the Nuclear Quadrupole Resonance Spectroscopy was also given in some details. From these result we deduced that Asymmetry parameter can be used as order parameter especially for the phase transitions from so called `incommensurate` to commensurate phases. Section 5. includes the general description of the Nuclear Quadrupole Resonance Spectrometer is what called ` Super regeneratif Oscillator` type and made by Decca Radar Company in England. The Block diagramm of the Spectrometer is given in Figure S-l. The central part of the spectrometer was a superregeneratif oscillator. The frequency of this oscillator can be swept between 6 to 100 MHz. by changing the radio frequency (RF) coil. The oscilations of this circuit was quenched by an external square wave generator (Q). Quenching frequency may be choosen between 25 KHz to 5 MHz. This frequencies can be locked to a Quartz Crystal oscillator which also used as marker generator (D). The radio frequency (RF) coil of the Superregeneratif Oscillator (SR0) is kept in a dewar during the measurements while inside temperature kept constant. To make more sensitive measurements, the SRO was frequency modulated in 50 Hz. and a phase sensitive detector used to get second derivative of the signal shape. The output of the detector may be observed on oscillas- cope or registered on the paper of a recorder. The marking of the frequency marker was also recorded on both sides of the same paper. By this method the frequency can be determined with a precision 10``7. In this spectrometer signal searching can be done by frequency modulation (I and II type) or by Zeeman modulation. Since the coherrence of the Superregeratif Oscillator (SRO) depend on the frequency an Automatic Gain Control circuit (E) also used. This circuit keeps the coherence constant for the whole radio frequency bands. xiv(B) PSU (C) Q. Gen. (E) AGC (D) Marker (A) SRO O (G) Zeeman Moclülasyonu n(N) t (F) Rekorder (HJ FM + PSD Figure S.l- The Block diagramm of the Nuclear Quadrupole Resonance spectrometer. Section 6. includes the experimental details and results of our work. In this section examples from the Ruclear Quadrupole Resonance spectra of Sb121 and Sfc>123, also CI35 in SbCl3 and Cl35 spectra in K2ZnCl4 are given as examples. Firstly we explained the preparation of the samples. Then in Tables 6.1 - 6.3 the Resonance Frequencies measured in different temparature for the isotopes of Sb121 and SbJ-23 in SbCİ3 are given. A new method was used to calculate recisely determine the Asymmetry parameter in these compounds. The temperature coefficients defined by Bayer xvtheory are calculated and given in the tables of the experimental results. Some of the results are in good agreement with other workers results but more precisely determined in this thesis. At the section 7. the results are discussed and some proposals are given for the future work on the some materials and subjects. At the end of the thesis some addendum are exists. These are two examples öf the computers programmes used in the calculations, some tables including the energy eigen values resonance frequencies and ratio of them used for the determination of the Asymmetry parameter with a precision of 10~4. The graphs of the secular equations was also given. In this work the phase transition for K2ZnCl/t was also investigated for the temperatures -30°C to 50oc. The results shows that for this interval there ;are several signals and they are very close to each others. Superregeneratif oscilator was not very suitable to determine the frenquency of all this signal. We decided that, it should be better to use a pulsed spectrometer for this work. Same examples of the measurements and the temperature dependence of the chlorine. Nuclear Quadrupole Resonance are given in section 6. of the thesis. xvi