^.fazgeçiti yakınında NH4 Br ve NH4CI'ün kritik davranışının incelenmesi
Analysis of critical behaviour of NH4 Br and NH4CI near ^. point
- Tez No: 46157
- Danışmanlar: PROF.DR. HAMİT YURTSEVEN
- Tez Türü: Yüksek Lisans
- Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 59
Özet
ÖZET Bu tez, amonyum halojenlerinden NH4Br ve NH4CI'ün çeşitli modlarının Raman spektroskopik deneysel verilerinden yararlanarak, A,-faz geçişlerine yakın noktalarda yapılan analizleri kapsamaktadır. Literatürden özellikle H.yurtseven'in NH4Br ve NhfyCI'ün çeşitli modları için elde ettiği sıcaklığa bağlı frekans verileri ile : (a) Faz geçişi yakınında hacim değişimi ve frekans kaymalarını birbirine bağlayan Mod Grûneisen parametresinin hesaplanması (b) Pippard bağıntıları aracılığı ile özgül ısının Raman frekans kaymalarından hesaplanması (c) Çeşitli frekanslarda Ising-fonon çiftlenim sistemi olarak kabul edilen Nh^Br'ün kritik davranışlarının incelenmesine (d) Özgül ısının Ising ve Einstein-Debye modeline göre hesaplanmasına olanak vermiş, çeşitli fitler yapılarak deneysel değerler ile hesapladığımız değerler karşılaştırılmıştır. V
Özet (Çeviri)
SUMMARY ANALYSIS OF CRITICAL BEHAVIOUR OF NH4Br AND NH4CI NEAR Â-POINT In this thesis we concentrated on the experimental aspects of phase transition in ammonium halides. y-relations are introduced for some second order or weakly first order phase transitions. The general thermodynamic funcions can be derived using the quasi-harmonic approximation for vibrations of crystaline system. This approximate treatment correlates these functions with vibrational frequencies through thermodynamic relations. The vibrational frequencies are in general volume dependent. This dependedence is given by the Grunisen parameter. Y = -d In v/d InV y, Grunisen parameter, can be used to measure anharmonicity, since the anharmonic effects are due to the volume dependent of vibrational frequencies. A considerable amount of work has been devoted to obtain the Grunisen parameter well away from the phase transitions. These studies showed that y, the Grüneisen parameter would be temperature and volume dependent. Two mode Grunisen parameter are defined as isothermal and isobaric. These are expressed in terms of thermodynamic quantities which are isothermal copressibility and thermal expansion constant. These relations are given as = 1 V(dv^ 71 Pv[dV VIl V(dv~\ »'«»br) Near a transition point, the critical behaviour of thermodynamic quantities determines the order of the transition. Acording to Ehrenfest clasification, first order is due to the discontinuity in a first derivative of free energy of a system, ie, entropy ör volume. Second order phase transitions are due to discontinuity in second derivative of free energy ie, specific heat, compressibility ete. Ehrenfest classification can be used to describe the type of phase transition to which we applied our y-relations. it is assumed that for second order phase transitions, changes in the mode frequencies are due to volume change contributions only. A, transitions are of second order. A large number of material show X type phase transition. We have studied ammonium halides and in particular NH4Br and NH/tCI. NH^CI has been studied by H.YURTSEVEN. He concluded that NFfyCI show X type phase transition. The mode Grunisen parameters yT and y? can De determined using the observed Raman frequency and volume data for the disordered phase well away from phase transitions. Then using these values in the follovving relations.0= Ap+a)! exp[-yj\n(V/VJ ]P=0 \)=Ap+A(p)+ D^pt-yp InfV/V^ ] P=0 where Ap= {*0 TTC we can obtain frequenencies as a function of V. The above expressions relate the frequency to volume as a function of pressure and as a function of temperature respectively. Ap can be defined as a order-disordered contribution. viiPhase in lattice system are usually described in terms of critical behaviour of various thermodynamic quantities of the system. Among these quantties specific heat and compressibilitiy are particular important. Classical teories predict a finite, discontinous anomaly for specific heat near the transition poînt. Also the approximate calculations for Ising model indicate that specific heat tends to diverge to infinity as the transition point is approached. in ammonium halides phonon branches, namely, the optical and acoustical, may be represented by the Einstein and Debye models ör in a combined form of these models. The lattice specific heat for the Einstein model can be given as o A /T A /T o CVE=3Nnk((8E/T) e°E/1/ eÖE/i-ir) where 9^=hi)E/k in Debye model specific heat can be given as CVD=9Nnk (T/9D)3 oJ9D/T xV / (ex-1) where x=hi)/kT and 6D is the characteristic temperature. it is assumed that the thermodynamic functions due to the lattice vibrations, remain finite and show no anomaly near transition. Thus as the crystal system undergoes a phase transition the spin(lsing) part of thermodynamic functions becomes dominant. So, spin (Ising) part should be added to the thermodynamics functions for the total system. The thermodynamic quantities then describe the critical behaviour of Ising model superimposed on an Einstein and/or Debye model. in order to be able to calculate the specific heat due to the spin intereactions near the transition for the NH4Br system, we consider the povver -law formula given by Cyp-^a-a ) (2-a ) lel 'a ı». viiiThe derivation of the Pippard relations which correlate thermodynamic quantities in the vicinity of the phase transitions of the X type is shovvn. Pippard relations apply to the systems for vvhich the frequency shifts can be correlated with volume change through a constant Y, the Grûneisen parameter. Pippard proposed linear relationship betvveen specific heat Cp, thermal expansion a and isothermal compressibility p in the vicinity of X point. He arrived at the approximate relations C, (dP\.. (dP\ - = - uVa+ - u T Ur; Ur; (dP\ 0 ( l VdV} o-l3rHvJbr} We can get the spectroscopic modification of the above relations, by a susbtution of our y- relations. Then above relations become _ KVA l fdv} Cf =-- U+constanf YP V\dT) a = - Î^VA-f-^ |r+constanr T v\dT) The length-change datas were used to calculate the frequencies through the following relation in vvhich the Yİ Grûneisen parameter is constant in the vicinity of the A,-point. YP =(~~f' nere (dı>/dT)p is W ı/ \ d Â. J determined from the best fitted line on the D vs T curve by the help of the computer and a is taken from literatüre. The calculated frequencies are listed on the tables and the graph of these frequences are dravvn with respect to temperature. The calculated frequencies are compared with the experimental frequency values. We attempted to calculate the (dP/dT)x of v(177 cm“1) and.ü (134 cm”) Raman modes of by Pippard relations, from the Cp vs -(d In-u/dt) plot vvhich gives the slope -(1/YP) Txvx (dp/dT)x- ixThe critical exponent“a”is calculated for the o>(177 cm“ ) Raman mod by the help of InCv/DjJsB l e l ^ ~a' relation. The slope of ln(ln(x>A)x)) vs in l e l plot gives us 1-a. Two different ”a“ is calculated for TT\. The specific heat CVE values were calculated acording to Einstein model for the -u(177 cm ) Raman mode frequency which is equivalent to the Einstein frequency % at 246 K. The specific heat CVD values were calculated acording to Debye model for the i)(177 cm”) Raman mode. A small computer program is vvritten for this purpose. The CVI values vvhich are the Ising contribution to Cv near the A,-point were calculated. Finally, the (dP/dT\ slope values of u(174 cm“1) and i)(1708 cm”1) Raman modes of NH4.CI at P=1.6 kbar and P=2.8 kbar were calculated. The (dP/dT)x vs P(kb) graphs were drawn.
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