Melting of alloy clusters: effects of aluminum doping on gallium cluster melting

Calorimetry measurements have been performed as a function of temperature for size-selected Ga(n-1)Al+ clusters with n = 17, 19, 20, 30-33, 43, 46, and 47. Heat capacities determined from these measurements are compared with previous results for pure Ga(n)+ clusters. Melting transitions are identified from peaks in the heat capacities. Substituting an aluminum atom appears to have only a small effect on the melting behavior. For clusters that show melting transitions, the melting temperatures and latent heats for the Ga(n-1)Al+ clusters are similar to those for the Ga(n)+ analogs. For Ga(n)+ clusters that do not show first-order melting transitions (n = 17, 19, and 30) the Ga(n-1)Al+ analogs also lack peaks in their heat capacities. The results suggest that the aluminum atom is not localized to a specific site in the solid-like Ga(n-1)Al+ clusters.     

Melting and glass transition for Ni clusters

The melting of NiN clusters (N = 29, 50-150) has been investigated by using molecular dynamics (MD) simulations with a quantum corrected Sutton-Chen (Q-SC) many-body potential. Surface melting for Ni147, direct melting for Ni79, and the glass transition for Ni29 have been found, and those melting points are equal to 540, 680, and 940 K, respectively. It shows that the melting temperatures are not only size-dependent but also a symmetrical structure effect; in the neighborhood of the clusters, the cluster with higher symmetry has a higher melting point. From the reciprocal slopes of the caloric curves, the specific heats are obtained as 4.1 kB per atom for the liquid and 3.1 kB per atom for the solid; these values are not influenced by the cluster size apart in the transition region. The calculated results also show that latent heat of fusion is the dominant effect on the melting temperatures (Tm), and the relationship between S and L is given.     

Thermal characterization of tetrafluoroethylene-perfluoroalkylvinylether copolymers: Melting behavior and low-temperature transitions

Differential scanning calorimetry has been used to study the melting and the low-temperature transitions of tetrafluoroethylene-perfluoroalkylvinylether copolymers (PFA). Melting is similar to that of PTFE in that it is subject to superheating, moreover the melt-crystallized samples show temperatures and heats of fusion lower than the native ones. At temperatures lower than room temperature, crystal-crystal transitions are observed for copolymers containing 2 mol % of perfluoromethyl-, perfluoroethyl-, and perfluoro-n-propylvinylether. In the case of perfluoromethylvinylether as a comonomer, low-temperature transitions are present only up to a content of 4 mol %. The effect on melting and low-temperature transitions of both the comonomer content and of the type of side groups has been investigated. The temperatures and heats of transitions show the expected dependence as a function of the comonomer concentration and have been found to be independent on the chemical nature of the side group. © 1994 John Wiley & Sons, Inc.     

Structural transitions and melting in LJ(74-78) Lennard-Jones clusters from adaptive exchange Monte Carlo simulations

Phase changes in Lennard-Jones (LJ) clusters containing between 74 and 78 atoms are investigated by means of exchange Monte Carlo simulations in the canonical ensemble. The replica temperatures are self-adapted to facilitate the convergence. Although the 74- and 78-atom clusters have icosahedral global minima, the clusters with 75-77 atoms have decahedral ground-state structures and they undergo a structural transition to icosahedral minima before melting. The structural transitions are characterized by quenching and by looking at the Q4 and Q6 orientational bond order parameters. The transition temperatures are estimated to be 0.114, 0.065, and 0.074 reduced units for LJ75, LJ76, and LJ77, respectively. These values, their ordering and the associated latent heats are compared with other estimates based on the harmonic superposition approach.     

Analysis by calorimetry

The last years have seen the development of differential calorimetry into a scanning technique for routine analysis. In order of ease of determination heats of fusion, heats of reaction, phase diagrams, purity analysis, heat capacity and similar heat effects are added to the list of quickly measurable quantities. Accuracies of the order of 1–5% of heats of fusion and heat capacity are obtainable under favorable conditions. Special topics which have been discussed are instrumentation, transition temperatures, heat capacities, glass transitions, heats of transitions, and phase diagrams.     

Multiple structural transformations in Lennard-Jones clusters: generic versus size-specific behavior

The size-temperature "phase diagram" for Lennard-Jones clusters LJn with sizes up to n=147 is constructed based on the analysis of the heat capacities and orientational bond order parameter distributions computed by the exchange Monte Carlo method. Two distinct types of "phase transitions" accompanied by peaks in the heat capacities are proven to be generic. Clusters with Mackay atom packing in the overlayer undergo a lower-temperature melting (or Mackay-anti-Mackay) transition that occurs within the overlayer. All clusters undergo a higher-temperature transition, which for the three-layer clusters is proven to be the 55-atom-core-melting transition. For the two-layer clusters, the core/overlayer subdivision is ambiguous, so the higher-temperature transition is better characterized as the breaking of the local icosahedral coordination symmetry. A pronounced size-specific behavior can typically be observed at low temperatures and often occurs in clusters with highly symmetric global minima. An example of such behavior is LJ135, which undergoes a low-temperature solid-solid transition, besides the two generic transitions, i.e., the overlayer reconstruction and the core melting.     

Etude de la cristallinite de derives n-octadecyliques de l'alcool polyvinylique obtenus par greffage chimique

Differential scanning calorimetry has been used to study the heats of fusion and melting transitions of n-octadecyl derivatives of polyvinyl alcohol. These derivatives were obtained by grafting paraffinic chains on polyvinyl alcohol, at various proportions. The melting transitions are independent of the degree of substitution; the heats of fusion are proportional to the fraction of crystallizable units. Using Flory's equilibrium crystallization theory, it is possible to interpret these results assuming, as demonstrated previously, that the chemical grafting is sequential with two unreacted hydroxyl groups between two adjacent paraffinic side-chains.     

Metal clusters that freeze into high energy geometries

Heat capacities measured for isolated aluminum clusters show peaks due to melting. For some clusters with around 60 and 80 atoms there is a dip in the heat capacities at a slightly lower temperature than the peak. The dips have been attributed to structural transitions. Here we report studies where the clusters are annealed before the heat capacity is measured. The dips disappear for some clusters, but in many cases they persist, even when the clusters are annealed to well above their melting temperature. This indicates that the dips do not result from badly formed clusters generated during cluster growth, as originally suggested. We develop a simple kinetic model of melting and freezing in a system consisting of one liquidlike and two solidlike states with different melting temperatures and latent heats. Using this model we are able to reproduce the experimental results including the dependence on the annealing conditions. The dips result from freezing into a high energy geometry and then annealing into the thermodynamically preferred solid. The thermodynamically preferred solid has the higher freezing temperature. However, the liquid can bypass freezing into the thermodynamically preferred solid (at high cooling rates) if the higher energy geometry has a larger freezing rate.     

Intermediates in the melting transitions of aluminum nanoclusters

The author uses heat capacity data for aluminum cluster ions, Aln+, obtained in the laboratory of Breaux et al. [Phys. Rev. Lett. 94, 17340 (2005)] to determine whether or not intermediate species are present in the transition from the solidlike form of the clusters present at low temperatures to the liquidlike form present at high temperatures. He gives a general method on how to test for the presence of such intermediates and how to calculate their probabilities and thermodynamics as a function of temperature. In addition he uses energy distribution functions, using the maximum-entropy method that he developed previously, to substantiate the presence or absence of intermediates. As examples of the method he treats n=53 and n=79 clusters both of which exhibit marked maxima in the temperature dependence of their heat capacity curves, indicating strong order-disorder transitions. He find that in the melting transition n=53 clusters have no intermediates while the melting of n=79 clusters is dominated by intermediate species.     

Melting, freezing, sublimation, and phase coexistence in sodium chloride nanocrystals

Calorimetry measurements, performed by multicollision induced dissociation, have been used to probe the melting of a number of (NaCl)nNa+ clusters with n=22-37. The clusters anneal at 225-325 K and melt at 750-850 K. (NaCl)22Na+ and (NaCl)37Na+, which can adopt geometries that are perfect fragments of the bulk lattice melt at around 850 K. The other clusters, which (except for n=31) must have defects, melt at temperatures which are up to 100 K lower than the perfect nanocrystals. The internal energy distributions become bimodal near the melting temperature. This is the signature of slow dynamic phase coexistence where clusters spontaneously jump back and forth between the solid and liquid states with an average period that is longer than required for thermal equilibration. The jump frequency must be between 10(4) and 10(7) s(-1) for the bimodal distribution to be observable in our experiments. The (NaCl)nNa+ clusters can dissociate by an unusual thermally activated process where melting and freezing raise the internal energy to generate hot solid clusters that can sublime before they cool to the ambient temperature.     

溴化钾团簇相变的分子动力学研究

众所周知，团簇的尺寸介于原子或分子与大块物质之间。由于它有较大的表面／体积比而有独特的物理化学性质。团簇在成核，晶体生长，材料科学和纳米器件加工等领域起了至关重要的作用。近年来，计算机模拟已成为物理，化学，生物，天文，地质等领域的重要研究工具。计算机模拟不仅可以     

Nanosolids, slushes, and nanoliquids: characterization of nanophases in metal clusters and nanoparticles

One of the keys to understanding the emergent behavior of complex materials and nanoparticles is understanding their phases. Understanding the phases of nanomaterials involves new concepts not present in bulk materials; for example, the phases of nanoparticles are quantum mechanical even when no hydrogen or helium is present. To understand these phases better, molecular dynamics (MD) simulations on size-selected particles employing a realistic analytic many-body potential based on quantum mechanical nanoparticle calculations have been performed to study the temperature-dependent properties and melting transitions of free Al n clusters and nanoparticles with n = 10-300 from 200 to 1700 K. By analyzing properties of the particles such as specific heat capacity (c), radius of gyration, volume, coefficient of thermal expansion (beta), and isothermal compressibility (kappa), we developed operational definitions of the solid, slush, and liquid states of metal clusters and nanoparticles. Applying the definitions, which are based on the temperature dependences of c, beta, and ln kappa, we determined the temperature domains of the solid, slush, and liquid states of the Al n particles. The results show that Al n clusters ( n or= 19, diameter of more than 1 nm) do have a melting transition and are in the liquid state above 900-1000 K. However, all aluminum nanoparticles have a wide temperature interval corresponding to the slush state in which the solid and liquid states coexist in equilibrium, unlike a bulk material where coexistence occurs only at a single temperature (for a given pressure). The commonly accepted operational marker of the melting temperature, namely, the peak position of c, is not unambiguous and not appropriate for characterizing the melting transition for aluminum particles with the exception of a few particle sizes that have a single sharp peak (as a function of temperature) in each of the three properties, c, beta, and ln kappa.     

First-principles investigation of finite-temperature behavior in small sodium clusters

A systematic and detailed investigation of the finite-temperature behavior of small sodium clusters, Na(n), in the size range of n=8-50 are carried out. The simulations are performed using density-functional molecular dynamics with ultrasoft pseudopotentials. A number of thermodynamic indicators such as specific heat, caloric curve, root-mean-square bond-length fluctuation, deviation energy, etc., are calculated for each of the clusters. Size dependence of these indicators reveals several interesting features. The smallest clusters with n=8 and 10 do not show any signature of melting transition. With the increase in size, broad peak in the specific heat is developed, which alternately for larger clusters evolves into a sharper one, indicating a solidlike to liquidlike transition. The melting temperatures show an irregular pattern similar to the experimentally observed one for larger clusters [Schmidt et al., Nature (London) 393, 238 (1998)]. The present calculations also reveal a remarkable size-sensitive effect in the size range of n=40-55. While Na(40) and Na(55) show well-developed peaks in the specific-heat curve, Na(50) cluster exhibits a rather broad peak, indicating a poorly defined melting transition. Such a feature has been experimentally observed for gallium and aluminum clusters [Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004); Breaux et al., Phys. Rev. Lett. 94, 173401 (2005)].     

Ion calorimetry: Using mass spectrometry to measure melting points

Calorimetry measurements have been used to probe the melting of aluminum cluster cations with 63 to 83 atoms. Heat capacities were determined as a function of temperature (from 150 to 1050 K) for size-selected cluster ions using an approach based on multicollision-induced dissociation. The experimental method is described in detail and the assumptions are critically evaluated. Most of the aluminum clusters in the size range examined here show a distinct peak in their heat capacities that is attributed to a melting transition (the peak is due to the latent heat). The melting temperatures are below the bulk melting point and show enormous fluctuations as a function of cluster size. Some clusters (for example, n = 64, 68, and 69) do not show peaks in their heat capacities. This behavior is probably due to the clusters having a disordered solid-like phase, so that melting occurs without a latent heat.     

二元贮冷水合盐熔解热的差示扫描量热法研究

用差示扫描量热法（differential scanning calorimetry)对二元贮冷水合盐的相变温度与熔解热进行了研究，实验结果对认识多元贮冷水合盐的相变过程的相变机理及选配贮冷水合盐材料，具有重要意义。     

Thermodynamics on the nanoscale

Classical thermodynamics is applied to the melting of nanometer-sized Sn particles with radii in the range 5-50 nm. Such particles display a depression of both the melting point and the latent heat of fusion depending on the particle size. The size dependence can be explained with the formation of a structurally perturbed layer at the particle surface. The experimental measurement of both melting temperatures and latent heats of fusion allowed for estimation of the thickness of the perturbed layer. This permitted in turn the evaluation of the excess Gibbs free energy associated with the perturbed layer at melting and the determination of its variation with particle size and temperature.     

Calorimetric studies of binary systems of 1,3,5-trinitrobenzene with naphthalene, anthracene and carbazole. I. Phase transitions and heat capacities of the pure components and charge-transfer complexes

The enthalpies and temperature of fusion and solid—solid transitions and the heat capacity curves for naphthalene (NAP), anthracene, carbazole, 1,3,5-trinitrobenzene (TNB) and charge-transfer complexes of TNB with these donors have been determined by using a Perkin-Elmer DSC-1B scanning calorimeter in the temperature range 180 K to just below the melting point.

Three modifications of TNB, one stable and two metastable, with melting points 398.4, 380.3 and 383.0 K, have been observed. Two phase transitions in the NAP—TNB complex, at 220 and 424.5 K, have been revealed. The probable nature of the phase transitions is discussed.

The quantity ΔC_p, where ΔC_p = C_p (complex) − C_p (donor) − C_p (TNB), is negative at higher temperatures, being equal to zero or positive at 180 K. This result is interpreted as an indication of a decrease in the complex stability in the solid state with decreasing temperature     

A molecular dynamics simulation of the melting points and glass transition temperatures of myo- and neo-inositol

The heat of sublimation, density, melting point, and glass transition temperature are calculated for myo- and neo-inositol, using the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field and molecular dynamics techniques. Our results show that the calculated heats of sublimation and density are very close to the experimental values for both compounds. Furthermore, our simulated melting temperatures for myo- and neo-inositol also compare very well to the experimentally obtained data. The glass transition temperatures for myo- and neo-inositol have been calculated to be ca. 494 K and ca. 518 K, respectively, and the shape of the volume versus temperature plots produced are typical for a glass transition. As a result, it is our view that the COMPASS force field suitably describes these two compounds in molecular simulations and that molecular dynamics techniques, combined with this force field, can be used to simulate the melt and glass transitions for such molecules.     

Molecular structures and energetics of the (TiO2)n (n = 1-4) clusters and their anions

The (TiO2)n clusters and their anions for n = 1-4 have been studied with coupled cluster theory [CCSD(T)] and density functional theory (DFT). For n > 1, numerous conformations are located for both the neutral and anionic clusters, and their relative energies are calculated at both the DFT and CCSD(T) levels. The CCSD(T) energies are extrapolated to the complete basis set limit for the monomer and dimer and calculated up to the triple-zeta level for the trimer and tetramer. The adiabatic and vertical electron detachment energies of the anionic clusters to the ground and first excited states of the neutral clusters are calculated at both levels and compared with the experimental results. The comparison allows for the definitive assignment of the ground-state structures of the anionic clusters. Anions of the dimer and tetramer are found to have very closely lying conformations within 2 kcal/mol at the CCSD(T) level, whereas that of the trimer does not. In addition, accurate clustering energies and heats of formation are calculated for the neutral clusters and compared with the available experimental data. Estimates of the titanium-oxygen bond energies show that they are stronger than the group VIB transition metal-oxygen bonds except for tungsten. The atomization energies of these clusters display much stronger basis set dependence than the clustering energies. This allows the calculation of more accurate heats of formation for larger clusters on the basis of calculated clustering energies.     

Specific heat and Lindemann-like parameter of metallic clusters: mono- and polyvalent metals

The Brownian-type molecular dynamics simulation is revisited and applied to study the thermal and geometric properties of four mono- and two polyvalent metallic clusters. For the thermal property, we report the specific heat at constant volume CV and study the solid-liquid-like transition by scrutinizing its characteristic. For the geometric property, we calculate the root mean square relative bond-length fluctuation delta as a function of increasing temperature. The thermal change in delta reflects the movement of atoms and hence is a relevant parameter in understanding the phase transition in clusters. The simulated results for the CV of alkali and aluminum clusters whose ground state structures exhibit icosahedral symmetry generally show one phase transition. In contrast, the tetravalent lead is quite often seen to exhibit two phase transitions, a premelting process followed by a progressive melting. In connection with the premelting scenario, it is found here that those (magic number) clusters identified to be of lesser stability (among other stable ones) according to the second energy difference are clusters showing a greater possibility of undergoing premelting process. This energy criterion applies to aluminum clusters nAl=28 and 38. To delve further into the thermal behavior of clusters, we have analyzed also the thermal variation of deltaT and attempted to correlate it with CV(T). It turns out that the premelting (if exist) and melting temperatures of the smaller size clusters (n less, similar 50) extracted from CV do not always agree quantitatively with that deduced from delta.