~o d u c t i o n and method Although NaN02 has been intensively studied after the discovery of its ferroelectricity by Sawada et al. /I/, its band structure has been only studied in few works /2 to 51. In addition the mentioned studies /2 to 5/ turned no attention to the electron velocity (v) and effective mass (m*).In this work we use our previous results of the band structure at different temperatures /4, 5/ besides detailed calculations near the phase transition region t o study the temperature dependence of the electron velocity as well as the electron effective mass for the valence and conduction bands. The calculations are performed using the equations -bwhere k is the wave vector, fi is Planck' s constant, E( Z ) is the electronic energy given from the band structure calculation, v' is the electron velocity, and m* is the electron effective mass. 1JResults and discussion The temperature dependence of the effective mass, mzz, at the bottom of the conduction band as well a s at the top of the valence band is shown in Fig. 1. From this figure, an irregular dependence withinthe temperature range from 160 to about 180 O C is shown. This may be due t o the formation of an intermediate phase which was reported before by Ivanova and Chisler /6/. Fig. 2 shows the $ dependence of the electron velocity and the effective mass in the conduction band at different temperatures. It is shown that as the temperature approaches the region of phase transition the effective mass shows an irregular $ dependence. At 160 OC, mzz shows some oscillations, which are not observed at temperatures far from the phase transition region. In 1 ) N a s r City, Cairo, Egypt.
The electronic band structure of NaNO, crystals is calcdlated. The band structure is studied in the temperature range from 20 to 245 "C in the principal directions as well as a t the high symmetry points inside the Brillouin zone. The temperature dependence of the minimum energy gap is also investigated. The calculations are carried out using a semiempirical LCAO method. The general features of the electronic energy bands a t various temperatures are similar to that a t 20 "C. The optical energy gap calculated a t 20 "C equals to 3.24 eV which is in good agreement with experimental results.Die Struktur der Energiebander eines NaN0,-Kristalls, sowie das Minimum der verbotenen Zone fur Temperaturen zwischen 20 und 245 "C werden berechnet. Die Berechnung wird mittels der halbempirischen LCAO-Methode fur Punkte hoher Symmetrie und fur die Hauptrichtungen der Brillouin-Zone durchgefuhrt. Das Ergebnis dieser Betrachtung ergibt eine gewisse Ahnlichkeit der allgemeinen Merkmale der bei verschiedenen Temperaturen berechneten Stnikturen der Energiebander, die sich kaum von denen bei 20 "C unterschieden, sowie, in Ubereinstimmung mit den Experimenten, fur den optischen Energieabstand bei 20 "C den Wert von 3,24 eV.
The effect of thermal expansion on the energy gap of NaNO, is studied. An attempt is made t o estimate the effect of thermal vibrations on the energy gap. The temperature dependence of the effective mass in the conduction and valence bands is also studied. The energy gap shows a nonlinearity near the phase transition region. A sudden change is also observed at about 3 K above T,. Both the effective masses show some oscillations in a wide range of temperature (from 2 140 t o -220 "C). The results of the energy gap and the effective mass give evidence that a new phase transition exists a t about 3 K above T,. They also give an interpretation for the deviation of the dielectric constant from the Curie-Weiss law.Es wird der EinfluR der thermischen Ausdehnung auf dip Energielucke eines NaN0,-Kristalls untersucht. Neben dem Versuch zur Abschatzung der Auswirkung der thermischen Schwingungen auf die Energielucke wird auch die Temperaturabhangigkeit der effektiven Massen im Leitfahigkeits-und Valenzband berechnet. Das Ergebnis dieser Untersuchung zeigt, daR im Bereich des bekannten Phasenuberganges eine Abweichung vom linearen Zusammenhang zwischen Temperatur und Energielucke existiert. Zusatzlich wird etwa 3 K oberhalb der Curietemperatur (T,) eine steile Anderung der Energielucke festgestellt. Fur die beiden effektiven Massen ergeben sich einige Oszillationen im Temperaturbereich zwischen 140 und 220 "C. Die so erhaltenen Resultate fur Energielucke und effektiven Massen deuten auf die Existenz eines neuen Phasenuberganges 3 K oberhelb T, hin, und konnen die Abweichung der Dielektrizitatskonstante vom Curie-WeissGesetz erklaren.
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