Mean Square Vibrational Amplitudes in PbTe

Abstract

X-ray diffraction experiments on single crystals and powder specimens are performed in order to obtain the values of the mean-square vibrational amplitudes of lead and tellurium atoms in PbTe. From both dependences of the integrated intensities on sin O/A and on temperature, the values <u&) = (2.33 f 0.15) x cm2 and <u'&> = (2.09 f 0.14) X x 10-1s omz are derived. The X-ray Debye temperature is found to be 0, = (107 3) OK.The analysis of the experimental data is given in detail. The results are discussed in relation t o previous works tending t o substantiate the Brooks-Yu theory on the temperature dependence of the energy band gap.On a effectue des experiences de diffraction de rayons-X sur des monocristaux ainsi que sur des poudres afin d'obtenir les valeurs des amplitudes vibrationelles quadratiques moyennes des atoms de plomb et de tellure dans le PbTe. En tenant en considkration les dkpendences des intensitbs integrbes de sin 013, aussi bien que de la tempbrature, on obtient les valeurs (uib> = (2,33 f 0,15) x lo-'* cm2 et <u&> = (2,09 f 0,14) x cm2. La temFkrature de Debye par les rayons-X est Onr = (107 * 3) OK. On donne une analyse des donhes experimentales; les r6sultats sont discutbes en tenant compte des travaux pr6c6dents, oh on visait 8. confirmer la theorie de Brooks-Yu sur la dependance de la temperature de la bande d'bnergie interdite.

Solvent Influence on Cellulose 1,4‐β‐Glycosidic Bond Cleavage: A Molecular Dynamics and Metadynamics Study

“…This can be explained by the disorder around the Pb atom, which is modeled by the ADP. The unit cells show remarkably similar near linear thermal expansion of 2.01(2) × 10 −5 K −1 and 1.98(2) × 10 −5 K −1 at 300 K for PbTe and PbS, respectively, in good agreement with previous studies 27–29. Since the lead chalcogenides are “simple” structures, the ADPs possibly can be modeled using the Debye expression,30–32 …”

“…A low Debye temperature (i.e., a large U iso ( T ) slope) signifies a low velocity of sound, and this leads to a low phonon mean free path and, correspondingly, a low lattice thermal conductivity 33. The fits to the ADPs of PbTe and PbS give Debye temperatures of 87(1) K and 172(1) K, respectively, which in both cases are slightly lower than previously reported values 29, 34. Above θ D , the ADPs should depend linearly on the temperature but, as observed in Figure 2, the ADPs exceed the linear increase, which indicates anharmonic vibration or structural disorder.…”

Lattice dynamics and structure of GeTe, SnTe and PbTe

“…As seen in Table 2, the atomic displacement parameter 〈 u 2 〉 of the cation increases for larger atomic weight, this behavior can be rationalized in terms of the specificities of the density of phonon states, see below. The thermal parameters of the Pb atoms were found to be larger than those of the chalcogen as also reported elsewhere 54, 55 and for other chalcogenide binaries 56–58. As the studied materials and their alloys are intended for thermoelectric applications which requires low thermal conductivity values, the large atomic displacement parameters are of interest and indicate significant phonon scattering in these compounds.…”

The mean square atomic displacements and enthalpies of vacancy formation in some semiconductors

“…(where K is the diffraction vector, I the intensity of proper reflection, @ ( K ) is an angular factor which depends on IKl only, f A , B the scattering function of A and B atoms) was plotted versus K 2 to control the absence of extinction on the intensity of reflections having an index sum which is a multiple of 4 (sphalerite crystal lattice) or an index sum which is a multiple of 2 (NaC1 crystal lattice). If there is no influence of the extinction on the intensity of the diffraction maxima, the above-mentioned dependence should be linear [23]. The Debye-Waller factor was calculated only from the magnitude of p(K).…”