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Graphene to fluorographene and fluorographane: A theoretical study

Paupitz, R.; Autreto, P. A S; Legoas, S. B.; Srinivasan, S Goverapet; Van Duin, A. C T; Galvão, D. S.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
65.83%
We report here a fully reactive molecular dynamics study on the structural and dynamical aspects of the fluorination of graphene membranes (fluorographene). Our results show that fluorination tends to produce defective areas on the graphene membranes with significant distortions of carbon-carbon bonds. Depending on the amount of incorporated fluorine atoms, large membrane holes were observed due to carbon atom losses. These results may explain the broad distribution of the structural lattice parameter values experimentally observed. We have also investigated the effects of mixing hydrogen and fluorine atoms on the graphene functionalization. Our results show that, when in small amounts, the presence of hydrogen atoms produces a significant decrease in the rate of fluorine incorporation onto the membrane. On the other hand, when fluorine is the minority element, it produces a significant catalytic effect on the rate of hydrogen incorporation. We have also observed the spontaneous formation of new hybrid structures with different stable configurations (chair-like, zigzag-like and boat-like) which we named fluorographane. © 2013 IOP Publishing Ltd.

Calculation of the continuum--lattice HQET matching for the complete basis of four--fermion operators: reanalysis of the $B^{0}$-$\bar{B}^{0}$ mixing

Gimenez, V.; Reyes, J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.89%
In this work, we find the expressions of continuum HQET four-fermion operators in terms of lattice operators in perturbation theory. To do so, we calculate the one--loop continuum--lattice HQET matching for the complete basis of $\Delta B=2$ and $\Delta B=0$ operators (excluding penguin diagrams), extending and completing previous studies. We have also corrected some errors in previous evaluations of the matching for the operator $O_{LL}$. Our results are relevant to the lattice computation of the values of unknown hadronic matrix elements which enter in many very important theoretical predictions in $B$--meson phenomenology: $B^{0}$-$\bar{B}^{0}$ mixing, $\tau_{B}$ and $\tau_{B_{s}}$ lifetimes, SUSY effects in $\Delta B=2$ transitions and the $B_{s}$ width difference $\Delta \Gamma_{B_{s}}$. We have reanalyzed our lattice data for the $B_{B}$ parameter of the $B^{0}$-$\bar{B}^{0}$ mixing on 600 lattices of size $24^{3}\times 40$ at $\beta=6.0$ computed with the SW-Clover and HQET lattice actions. We have used the correct lattice--continuum matching factors and boosted perturbation theory with tadpole improved heavy--light operators to reduce the systematic error in the evaluation of the renormalization constants. Our best estimate of the renormalization scale independent $B$--parameter is $\hat{B}_{B} = 1.29 \pm 0.08 \pm 0.06$...

Spontaneous CP violation on the lattice

Laine, M.; Rummukainen, K.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/08/1999
Relevância na Pesquisa
45.74%
At finite temperatures around the electroweak phase transition, the thermodynamics of the MSSM can be described by a three-dimensional two Higgs doublet effective theory. This effective theory has a phase where CP is spontaneously violated. We study spontaneous CP violation with non-perturbative lattice simulations, and analyse whether one could end up in this phase for any physical MSSM parameter values.; Comment: 3 pages; talk at LATTICE99(electroweak), Pisa, Italy, and EPS-HEP99(non-perturbative), Tampere, Finland

Approximate Actions for Lattice QCD Simulation

Irving, Alan C.; Sexton, James C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/08/1996
Relevância na Pesquisa
45.76%
We describe a systematic approach to generating approximate actions for the lattice simulation of QCD. Three different tuning conditions are defined to match approximate with true actions, and it is shown that these three conditions become equivalent when the approximate and true actions are sufficiently close. We present a detailed study of approximate actions in the lattice Schwinger model together with an exploratory study of full QCD at unphysical parameter values. We find that the technicalities of the approximate action approach work quite well. However, very delicate tuning is necessary to find an approximate action which gives good predictions for all physical observables. Our best view of the immediate applicability of the methods we describe is to allow high statistics studies of particular physical observables after a low statistics full fermion simulation has been used to prepare the stage.; Comment: 34 pages, 5 postscript figures, uses revtex and psfig

Phase structure for lattice fermions with flavored chemical potential terms

Misumi, Tatsuhiro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.92%
We discuss the chiral phase diagram in the parameter space of lattice QCD with minimal-doubling fermions, which can be seen as lattice fermions with flavored chemical potential terms. We study strong-coupling lattice QCD with the Karsten-Wilczek formulation, which has one relevant parameter $\mu_{3}$ as well as gauge coupling and a mass parameter. We find a nontrivial chiral phase structure with a second-order phase transition between chiral symmetric and broken phases. To capture the whole structure of the phase diagram, we study the related lattice Gross-Neveu model. The result indicates that the chiral phase transition also exists in the weak-coupling region. From these results we speculate on the $\mu_{3}$-$g^{2}$ chiral phase diagram in lattice QCD with minimal-doubling fermions, and discuss their application to numerical simulations.; Comment: 34 pages, 9 figures; extended discussion on Lorentz symmetry for general values of parameters, two figures added, references added, version to appear in JHEP

Remarks on left-handed lattice fermions

Gattringer, Christof; Pak, Markus
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/10/2007
Relevância na Pesquisa
45.82%
We study whether applying lattice projectors on a vector-like Ginsparg-Wilson Dirac operator is the only way to construct left-handed lattice fermions. Using RG transformations we derive an equation for the generating functional on the lattice, obtained by blocking from the continuum. We analyze how symmetries of the continuum theory manifest themselves in this lattice generating functional and how anomalies emerge. The formalism is applied to left-handed continuum fermions and we derive two equations that characterize the corresponding lattice symmetries. To analyze possible solutions, we directly block a parameterized action for free continuum fermions to obtain the corresponding lattice action. Subsequently we study parameter values where the continuum action corresponds to left-handed fermions.; Comment: Contribution to Lattice 2007, based on two presentations by the authors

On Scale Determination in Lattice QCD with Dynamical Quarks

De, Asit K.; Harindranath, A.; Maiti, Jyotirmoy
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/01/2009
Relevância na Pesquisa
35.88%
Dependence of a/r_c (inverse Sommer parameter in units of lattice spacing a) on am_q (quark mass in lattice unit) has been observed in all lattice QCD simulations with sea quarks including the ones with improved actions. How much of this dependence is a scaling violation has remained an intriguing question. Our approach has been to investigate the issue with an action with known lattice artifacts, i.e., the standard Wilson quark and gauge action with beta=5.6 and 2 degenerate flavors of sea quarks on 16^3 times 32 lattices. In order to study in detail the sea quark mass dependence, measurements are carried out at eight values of the PCAC quark mass values am_q from about 0.07 to below 0.015. Though scaling violations may indeed be present for relatively large am_q, a consistent scenario at sufficiently small am_q seems to emerge in the mass-independent scheme where for a fixed beta, 1/r_0 and sqrt{sigma} have linear dependence on m_q as physical effects similar to the quark mass dependence of the rho mass. We present evidence for this scenario and accordingly extract the lattice scale (a = 0.0805(7) fm, a^{-1} = 2.45(2) GeV) by chiral extrapolation to the physical point.; Comment: 7 pages, 5 figures, Talk given at the XXVI International Symposium on Lattice Field Theory (LATTICE 2008)...

Perturbative renormalization factors and O(a^2) corrections for lattice 4-fermion operators with improved fermion/gluon actions

Constantinou, Martha; Dimopoulos, Petros; Frezzotti, Roberto; Lubicz, Vittorio; Panagopoulos, Haralambos; Skouroupathis, Apostolos; Stylianou, Fotos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/11/2010
Relevância na Pesquisa
35.92%
In this work we calculate the corrections to the amputated Green's functions of 4-fermion operators, in 1-loop Lattice Perturbation theory. One of the novel aspects of our calculations is that they are carried out to O(a^2) (a: lattice spacing). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients. While our Green's function calculations regard any pointlike 4-fermion operators which do not mix with lower dimension ones, we pay particular attention to DF=2 operators, both Parity Conserving and Parity Violating (F: flavour). We compute the perturbative renormalization constants for a complete basis of 4-fermion operators and we study their mixing pattern. For some of the actions considered here, even O(a^0) results did not exist in the literature to date. The correction terms which we calculate are essential ingredients for minimizing the lattice artifacts which are present in non-perturbative evaluations of renormalization constants with the RI'-MOM method. Our perturbative results...

The phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential

Kaczmarek, O.; Karsch, F.; Laermann, E.; Miao, C.; Mukherjee, S.; Petreczky, P.; Schmidt, C.; Soeldner, W.; Unger, W.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/11/2010
Relevância na Pesquisa
35.89%
We determine the chiral phase transition line in (2+1)-flavor QCD for small values of the light quark chemical potential. We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. To do so we extend earlier studies of the magnetic equation of state in (2+1)-flavor QCD to finer lattice spacings, aT=1/8. We use these universal scaling properties of the chiral order parameter to extract the curvature of the transition line at two values of the cut-off, aT=1/4 and 1/8. We find that cut-off effects are small for the curvature parameter and determine the transition line in the chiral limit to leading order in the light quark chemical potential. We obtain Tc(\mu_q)/Tc(0) = 1 - 0.059(2)(4) (\mu_q/T)^2 +O(\mu_q^4).; Comment: 11 pages, 4 EPS files

The effect of material parameter values on the relation between the energy gap width and the scatterer symmetry in two-dimensional phononic crystals

Silwa, I.; Krawczyk, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/02/2005
Relevância na Pesquisa
45.99%
The phononic band structures of two-dimensional solid phononic crystals with different lattice and scatterer symmetry are studied numerically, with three types of lattice (square, triangular and rectangular) and four different scatterer shapes (circle, hexagon, square and rectangle) considered. XY and $Z$ vibration modes are investigated separately. Two types of phononic crystal are considered: one composed of high-density rods embedded in a low-density matrix, the other of low-density rods in a high-density matrix. In the former case, lattice type and polarization being fixed, the broadest gaps are obtained when the symmetry of the rods corresponds to that of the lattice (the shape of a rod is identical with that of the first Brillouin zone); the largest gap width values are observed in triangular lattice-based crystals (compared to those based on square and rectangular lattices), the shape of the corresponding first Brillouin zone being closest to a circle. These rules do not apply to structures in which the density of the rod material is lower than that of the matrix. In this case, when the symmetry of the rods corresponds to that of the lattice, gaps either fail to appear at all, or are much narrower than in other configurations. The effect of other material parameter values (such as the longitudinal and transversal velocity values) on the considered relation proves much lesser.; Comment: 13 pages...

Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case

Blum, T.; Chen, P.; Christ, N.; Cristian, C.; Dawson, C.; Fleming, G.; Mawhinney, R.; Ohta, S.; Siegert, G.; Soni, A.; Vranas, P.; Wingate, M.; Wu, L.; Zhestkov, Y.; Collaboration, RBC
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.9%
We report the results of a calculation of the K --> pi pi matrix elements relevant for the $\DIhalf$ rule and $\epe$ in quenched lattice QCD using domain wall fermions at a fixed lattice spacing $a^{-1} \sim 2$ GeV. Working in the three-quark effective theory, where only the u, d and s quarks enter and which is known perturbatively to next-to-leading order, we calculate the lattice K --> pi and K --> |0> matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield K --> pi pi matrix elements, which we then normalize to continuum values through a non-perturbative renormalization technique. For the ratio of isospin amplitudes |A_0|/|A_2| we find a value of $25.3 \pm 1.8$ (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10-20% below the experimental values. For $\epe$, using known central values for standard model parameters, we calculate $(-4.0 \pm 2.3) \times 10^{-4}$ (statistical error only) compared to the current experimental average of $(17.2 \pm 1.8) \times 10^{-4}$. Because we find a large cancellation between the I = 0 and I = 2 contributions to $\epe$, the result may be very sensitive to the approximations employed. Among these are the use of: quenched QCD...

On Scale Determination in Lattice QCD with Dynamical Quarks

De, Asit K.; Harindranath, A.; Maiti, Jyotirmoy
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/03/2008
Relevância na Pesquisa
35.98%
Dependence of $a/r_c$ (inverse Sommer parameter in units of lattice spacing $a$) on $am_q$ (quark mass in lattice unit) has been observed in all lattice QCD simulations with sea quarks including the ones with improved actions. How much of this dependence is a scaling violation has remained an intriguing question. Our approach has been to investigate the issue with an action with known lattice artifacts, i.e., the standard Wilson quark and gauge action with $\beta=5.6$ and 2 degenerate flavors of sea quarks on $ 16^3 \times 32 $ lattices. In order to study in detail the sea quark mass dependence, measurements are carried out at eight values of the Wilson hopping parameter $\kappa$ in the range 0.156 - 0.158 corresponding to PCAC quark mass values $am_q$ from about 0.07 to below 0.015. We analyze the static potential by fitting to the familiar phenomenological form and extract $a/r_c$. Though scaling violations may indeed be present for relatively large $am_q$, a consistent scenario at sufficiently small $am_q$ seems to emerge in the mass-independent scheme where for a fixed $\beta$, $1/r_0$ and $\sqrt{\sigma}$ have linear dependence on $m_q$ as physical effects similar to the quark mass dependence of the rho mass. We present evidence for this scenario and accordingly extract the lattice scale $a$ by chiral extrapolation to the physical point. Care has been exercised to determine optimal values of all fitting parameters and accuracy of the chiral extrapolation. An independent determination of the scale $a$ by chiral extrapolation of the rho mass is consistent with the scale obtained above ($a$ = 0.08041(12)(77) fm...

Oblique correction in a walking lattice theory

DeGrand, Thomas
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/06/2010
Relevância na Pesquisa
45.74%
I compute the difference of vector and axial vector current correlators in the weak coupling phase of (lattice-regulated) SU(3) gauge theory with two flavors of symmetric-representation dynamical fermions. This is a walking theory at the bare parameter values chosen for the simulation. Otherwise, it is not a conventional technicolor candidate. The correlator difference shows scaling behavior in the fermion mass, and vanishes in the fermion zero mass limit. Consequences for the phenomenology of similar systems which might be candidates for beyond Standard Model physics are discussed. I check my methodology against ordinary QCD, by computing the Gasser-Leutwyler coefficient L_10 and the charged - neutral pion mass difference from an approximate parameterization of the correlator.; Comment: 18 pages, 12 figures

Precise determination of the lattice spacing in full lattice QCD

Davies, C. T. H.; Follana, E.; Kendall, I. D.; Lepage, G. Peter; McNeile, C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/10/2009
Relevância na Pesquisa
35.94%
We compare three different methods to determine the lattice spacing in lattice QCD and give results from calculations on the MILC ensembles of configurations that include the effect of $u$, $d$ and $s$ sea quarks. It is useful, for ensemble to ensemble comparison, to express the results as giving a physical value for $r_1$, a parameter from the heavy quark potential. Combining the three methods gives a value for $r_1$ in the continuum limit of 0.3133(23)(3) fm. Using the MILC values for $r_0/r_1$, this corresponds to a value for the $r_0$ parameter of 0.4661(38) fm. We also discuss how to use the $\eta_s$ for determining the lattice spacing and tuning the $s$-quark mass accurately, by giving values for $m_{\eta_s}$ (0.6858(40) GeV) and $f_{\eta_s}$ (0.1815(10) GeV).; Comment: 15 pages

Superconductivity in Organic Compounds with Pseudo-Triangular Lattice

Kondo, Hisashi; Moriya, Tôru
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/01/2004
Relevância na Pesquisa
35.92%
We study spin fluctuation (SF) mediated superconductivity (SC) in a half-filled square lattice Hubbard model with the transfer matrices -t between nearest neighbor sites and -t' between a half of next nearest neighbor sites neighboring along only one of the <1,1> directions, considering application of this model to organic kappa-(BEDT-TTF)2X compounds. Varying the t'/t value from 0 to 1, one can interpolate between a square and an equilateral triangular lattice, the latter giving frustration to antiferromagnetically (AF) coupled spin systems. Within the fluctuation exchange (FLEX) approximation, we calculate chi(q,omega), Tc and the SC order parameter for various model parameter values and find that both AF and SC are suppressed as one approaches the frustration geometry or |(t'/t)-1| \to 0. The SC phase, however, extends beyond the AF phase boundary fairly close to t'/t=1 for realistic U/t values. The order parameter is of x2-y2-type for t'/t<1 and of xy-type for t'/t>1.; Comment: 4 pages, 5 eps figures, to appear in J. Phys. Soc. Jpn

Investigation of Lattice QCD with Wilson fermions with Gaussian Smearing

De, Asit K.; Harindranath, A.; Maiti, Jyotirmoy
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/12/2007
Relevância na Pesquisa
35.88%
We present a detailed study of pion and rho mass, decay constants and quark mass in Lattice QCD with two flavors of dynamical quarks. We use Wilson gauge and fermion action at $\beta=5.6$ on $ 16^3 \times 32 $ lattice at eight values of the Wilson hopping parameter in the range 0.156 - 0.158. We perform a detailed investigation of the effect of gaussian smearing on both source and sink. We determine the optimum smearing parameter for various correlators for each value of the Wilson hopping parameter. The effects of smearing on observables are compared with those measured using local operators. We also investigate systematic effects in the extraction of masses and decay constants using different types of correlation functions for pion observables. We make interesting observations regarding chiral extrapolations and finite volume effects of different operators.; Comment: 25 pages, 19 figures

The three-loop beta-function of SU(N) lattice gauge theories with overlap fermions

Constantinou, Martha; Panagopoulos, Haralambos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/11/2007
Relevância na Pesquisa
35.91%
We briefly report our calculation of the 2-loop coefficient of the coupling constant renormalization function Z_g in lattice perturbation theory. The quantity under study is defined through g_0 = Z_g g, where g_0 (g) is the bare (renormalized) coupling constant. The 2-loop expression for Z_g can be directly related to the 3-loop bare beta-function beta_L(g_0). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. Our results depend explicitly on the number of fermion flavors (N_f) and colors (N). Since the dependence of Z_g on the overlap parameter rho cannot be extracted analytically, we tabulate our results for different values of rho in the allowed range (0

Nambu monopoles in lattice Electroweak theory

Bakker, B. L. G.; Veselov, A. I.; Zubkov, M. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.88%
We considered the lattice electroweak theory at realistic values of $\alpha$ and $\theta_W$ and for large values of the Higgs mass. We investigated numerically the properties of topological objects that are identified with quantum Nambu monopoles. We have found that the action density near the Nambu monopole worldlines exceeds the density averaged over the lattice in the physical region of the phase diagram. Moreover, their percolation probability is found to be an order parameter for the transition between the symmetric and the broken phases. Therefore, these monopoles indeed appear as real physical objects. However, we have found that their density on the lattice increases with increasing ultraviolet cutoff. Thus we conclude, that the conventional lattice electroweak theory is not able to predict the density of Nambu monopoles. This means that the description of Nambu monopole physics based on the lattice Weinberg - Salam model with finite ultraviolet cutoff is incomplete. We expect that the correct description may be obtained only within the lattice theory that involves the description of TeV - scale physics.; Comment: LATEX

Spin-2 $N\Omega$ Dibaryon from Lattice QCD

Etminan, Faisal; Nemura, Hidekatsu; Aoki, Sinya; Doi, Takumi; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Ishii, Noriyoshi; Murano, Keiko; Sasaki, Kenji
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.79%
We investigate properties of the $N$(nucleon)-$\Omega$(Omega) interaction in lattice QCD to seek for possible dibaryon states in the strangeness $-3$ channel. We calculate the $N\Omega$ potential through the equal-time Nambu-Bethe-Salpeter wave function in 2+1 flavor lattice QCD with the renormalization group improved Iwasaki gauge action and the nonperturbatively $\mathcal{O}(a)$ improved Wilson quark action at the lattice spacing $a\simeq 0.12$ fm on a (1.9 fm)$^{3}\times$ 3.8 fm lattice. The $ud$ and $s$ quark masses in our study correspond to $m_{\pi}= 875(1)$ MeV and $m_{K}= 916(1)$ MeV. At these parameter values, the central potential in the S-wave with the spin 2 shows attractions at all distances.By solving the Schr\"{o}dinger equation with this potential, we find one bound state whose binding energy is $18.9(5.0)(^{+12.1}_{-1.8})$ MeV, where the first error is the statistical one, while the second represents the systematic error.; Comment: 14 pages, 6 figures. Minor corrections made and some references added. A published version in the Gerry Brown Memorial issue of Nucl. Phys. A (2014)

LATTICE PARAMETER VALUES AND PHASE TRANSITIONS FOR THE Cu2-II-IV-S4(Se4) (II=Mn, Fe, Co; IV=Si, Ge, Sn) MAGNETIC SEMICONDUCTOR COMPOUNDS

Quintero,Miguel; Moreno,Ekadink; Alvarez,Silvana; Marquina,Jesús; Rincón,Carlos; Quintero,Eugenio; Grima,Pedro; Heano,José-Antonio; Macías,Mario Alberto
Fonte: Universidad Simón Bolívar; ; Publicador: Universidad Simón Bolívar; ;
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2014 EN
Relevância na Pesquisa
65.93%
X-ray powder diffraction measurements, at 300 K, and differential thermal analysis (DTA) were made on sixteen polycrystalline samples of Cu2-II-IV-S4(Se4) (II: Mn, Fe, Co; IV: Si, Ge, Sn) magnetic semiconductor compounds. The diffraction patterns were analyzed to determine lattice parameter values. The results showed that ten have tetragonal stannite I42m structure, one has tetragonal pseudo-cubic P4 structure, four an orthorhombic wurtz-stannite Pmn21 and two an orthorhombic pseudo-cubic F222 structure. When the values of the effective parameter ae = (V/N)1/3 are plotted against its molecular weight W, it was found that the tetragonal and orthorhombic materials lie on the same straight line. The peaks on the DTA measurements were used to determine the type of melting as well as the melting temperature. The resulting data together with the Lindemann relation were used to estimate values for the Debye temperature θD as well as for the sound velocity in the material vs.