NH4 CI faz geçişi yakınlarında frekans kaymalarının hesaplanması
Başlık çevirisi mevcut değil.
- Tez No: 75483
- Danışmanlar: PROF. DR. HAMİT YURTSEVEN
- Tez Türü: Yüksek Lisans
- Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
- Anahtar Kelimeler: Faz geçişleri, Frekans kayması, Kristaller, Phase transitions, Frequency shift, Crystals
- Yıl: 1998
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Fizik Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Fizik Mühendisliği Bilim Dalı
- Sayfa Sayısı: Belirtilmemiş.
Özet
NH4CI FAZ GEÇİŞİ YAKINLARINDA FREKANS KAYMALARININ HESAPLANMASI ÖZET Bu çalışmada NH4CI kristal sistemindeki X- faz geçişi yakınlarında değişik basınçlar altında sıcaklığın bir fonksiyonu olarak kristalin ultrasonik frekansları ile hacim değişimleri arasındaki bağıntılar verilmektedir. Bu bağıntılar ultrasonik frekanslar kullanılarak NH4CI için q [1 T 0], q [1 10] ve q [100] modlan için oluşturuldu. Önce her mod için y Grüneisen parametresinin değeri belirlendi. Ardından her bir mod için tek bir y Grüneisen parametresini kullanarak faz geçiş bölgesi boyunca ultrasonik frekanslar belirlendi. Bu analizlerde NBUCPün birinci, üçlü kritik ve ikinci faz geçiş bölgelerindeki ultrasonik frekanslar ve boy-değişim verileri için literatürdeki veriler kullanıldı. Sonuçlar gösteriyor ki birinci geçiş bölgesinde q [1 T 0] ve üçlü geçiş bölgesinde q [110] modları için literatürdeki gözlemlenen frekanslar ile hesaplanan frekanslar arasında oldukça iyi bir uyum bulunmaktadır. İkinci faz geçiş bölgesinde q [100] modu için hesapladığımız frekanslar gözlemlerdeki gibi kritik bir davranış sergilemektedir. IX
Özet (Çeviri)
NH4CI for zero pressure. For this calculation the pressure dependent term A(P) was first determined by using the observed values of Vi=388 kHz and V/Vi at T=260 K. This temperature was chosen to get a constant value of A(P=0)=0. We then fitted our calculated frequencies to those observed [5], which gave us Ap as a function of AT at and below T% for P=0. As the order-disorder contribution to the ultrasonic frequencies of the q[l 1 0] mode of NH4CI, the values of Ap are given in Table 2.2. Our calculated and those observed frequencies [5] for the q[l 1 0] ultrasonic mode of NH4CI are given at various temperatures for P=0 in Fig. 2. 1. We calculated the frequencies using the observed ultrasonic frequencies for the q[l 10] mode [5] for the tricritical phase region (P=1.5 kbar) of NH4CI. For this phase region the frequencies were calculated within the temperature interval of 260 K<T<280 K, which is well above the transition temperature (Tr=256 K). With in this interval we got the slope value of (âv/â£)p = -0.0166 kHz/K, from which we had the value of vi=207 kHz at T=296 K (P=1.5 kbar). This then gave us the value of the isobaric mode Grüneisen parameter as yp=0.68 for the q[110] ultrasonic mode of NH4CI (P=1.5 kbar) by means of Eq. (2.3). For this phase region we used the value of oHS.SxMy4 K“1 for the thermal expansivity of NH4CI, that was also deduced from the length-change data [6]. The ultrasonic frequencies were then calculated for the q[110] mode of NH4CI according to Eq. (2.4). For this calculation the pressure dependent term A(P) was first determined for the pressure of P=1.5 kbar using the observed values of Vi=207 kHz and V/Vi at T=267 K. At this temperature which is well above the transition temperature (Tx=256 K), we obtained the value of A(P)=1.3 kHz for P=1.5 kbar. We then fitted our calculated frequencies to those observed [5], which gave us Ap as a function of AT at and below Ta,. Our calculated and those observed frequencies [5] for the q[110] ultrasonic mode of NH4CI are given at various temperatures for P=1.5 kbar in Fig. 2.8. The ultrasonic frequencies for the q[100] mode were calculated using the observed frequencies [5], which varied linearly with temperature in the interval of 264 K< T < 294 K. Within this temperature interval which is well above the transition temperature ( Tx=261.76K, P=2.15 kbar), the slope value was obtained as (âv/âT)p = 0.1263 kHz/K. This gave us the value of vi=308.33 kHz at T=296 K for P=2.15 kbar. Using Eq. (2.3), we obtained the isobaric mode Grüneisen parameter as Yp=1.05 for the q[100] mode. For this value, the value of a=-4.15xlO_4K~: was used for the thermal expansivity that was deduced from the length-change data [6]. Then, by means of Eq. (2.4) the pressure dependent term A(P) was obtained using the observed values of vi=318 kHz and V/Vi at T=274 K. Since this temperature is far away from the transition temperature (Tx=261.76 K, P=2.15 kbar), we were then able to obtain A(P)=11.98 kHz as a constant value. Our calculated frequencies were then fitted to the observed frequencies [5], which gave us the order-disorder contribution to the q[100] mode, Ap as a function of AT at and below Tx for P=2. 1 5 kbar. Our calculated frequencies are plotted at various temperatures with those observed frequencies [5] for the q[100] mode of NH4CI for P=2. 15 kbar in Fig. 2. 13. XUlIn this study we calculated the ultrasonic frequencies for the q[l 1 0] mode (P=0 kbar), the q[110] mode (P=1.5 kbar) and the q[100] mode (P=2.15 kbar) using the observed frequencies from the literature [5]. For this calculation we first determined the mode Griineisen parameter for each mode. The value of the isobaric mode Griineisen parameter is nearly yp=l for the q[lT 0] and q[110] modes and it is -2 for the q[100] mode, as given in Tables 1-29. These values of yp can be compared with our values of yp =3.1 for the ViTAm(93 cm”1) and of YP =2.1 for the VsTOm(144 cm"1) Raman modes of NH4CI [1]. Our values of yp =1 for the q[l 1 0], q[l 10] and yp =-2 for the q[100] mode can also be compared with our values of yp = 2.5 for the v5TOr (174 cm'1) Raman mode of NH4CI and of yp =1.59 for the vsTOm (134cm yp ) Raman mode of NKjBr [3]. Using our values of yp given in Tables 2.2, 2.17 and 2.28, we calculated the ultrasonic frequencies for each mode. For calculating the frequencies, the A(P) and Ap terms were employed according to Eq. (2.4). The values of A(P) increased as the pressure was increased, as given in tables. With our values of yp and A(P), and the temperature dependent function Ap, the ultrasonic frequencies calculated here are in quite good agreement with the experimentally observed frequencies for the q[l 1 0] and q[110] modes in the first order (P=0) and in the tricritical (P=1.5 kbar) phase regions, as seen in Figs. 2.1 and 2.8, respectively. For the q[100] mode agreement is not that good between our calculated frequencies and the observed frequencies from the literature for the second order phase region (P=2.15 kbar) as also seen from Fig. 2.13. Above the transition temperature (Tj=261.8 K) our calculated frequencies seem to agree with those observed for the interval of about 10 K (270 K<T<280 K). As the temperature increases further, there occurs the discrepancy between our calculated frequencies and those observed. Below T^., this discrepancy becomes more apparent. If one is able to extrapolate the observed and calculated frequencies starting from the low temperatures, say from about 250 K up to 260 K, both frequencies would coincide nearly at the transition temperature as seen in Fig. 2.13. In fact, the critical behavior of this mode is rather different, when compared with that of the q[ll 0] and q[110] modes, as we can see from Figs. 2.1, 2.8 and 2.13. That difference between the q[100] mode and those modes of q[l 1 0] and q[l 10] occurs firstly in their slopes, the positive slope for the former and the negative slope for the latter (see Table 1). As far as the isobaric mode Griineisen parameter is concerned, there happens to be the same value of yp=l for all the three modes. We also note here that the first order character of the phase.transition in NH4CI is exhibited by the observed and calculated frequencies of the q[l 1 0] mode for P=0, as seen from Fig. 2.1. For this mode the frequency jump at the transition temperature (Tx=242.9 K) is about Av= 3 kHz (Fig. 2.1), whereas this jump is nearly Av =1 kHz for the q[110] mode for the pressure of P=1.5 kbar (Fig. 2.8). This decrease of the frequency jump as the pressure increases, is an indication that the first order phase transition (P=0) changes its character towards the tricritical one (P=1.5kbar) in NH4CI. Finally, the (dP/dT)x slope values of [110] ultrasonic modes of NH4CI at P=0 Kbar and P=1.5 Kbar were calculated. It can be shown that those results are close to the literature data [13] and [14]. XIV
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