Roughening Transition Research Articles

Nucleation of wavy growth modes in quantum well stacks of III–V compound alloys

The influence of strain and temperature on the development of 3D island growth patterns (wavy layer growth) and the establishment of a defined modulation period in epitaxially grown multiple quantum well structures of the III–V compound alloys is discussed. Experimental evidence for a previously derived theoretical roughening transition curve, which separates 2D monolayer from 3D island growth is presented. In this paper we furthermore derive the f 2 ∼ λ −1 relationship between misfit strain f and modulation wavelength λ, and give experimental evidence. Ultra-high resolution scanning transmission electron microscopy (STEM) analysis is performed in the above alloys to investigate the occurrence of alloy inhomogeneities. In parallel, highly dislocated regions in the multiple quantum well (MQW) stacks are systematically studied by transmission electron microscopy (TEM). The latter two investigations are undertaken in order to establish possible nucleation sites and to better understand the nucleation process for the 3D growth mode.

Morphological variations of quartz crystals as deduced from computer experiments

The crystal forms of double pyramidal quartz composed of faces, R, r and m, drawn by computer simulations are classified into 8-groups corresponding to 8-areas in the growth diagram which are characterized by the growth rate ratios of the faces, gr(r) gr(R) = p and gr(m) gr(R) = q within the ranges 1 ≦ p ≦2 and 0 < 1 ≦ 2. All crystal forms drawn were found in natural quartz specimens. The final crystal forms, independent of growth time, are under the control of the specific growth rate ratios in each growth area. The 8-areas are classified into two types, closed and open areas. In closed areas, the crystal forms are controlled by p and q. In open areas, the crystal forms are controlled by either p or q, defined by the closed direction in the area. Equi-temperature lines in the range from 200°C to 680°C are drawn in the growth diagram from a calculation based on a model process characterized by growth rates. The characters of the m-faces obtained from the computer simulations are discussed on the basis of their roughening transition.

A scanning tunneling microscopy study of epitaxial Ge growth

We report new findings on Ge homoepitaxy on the (110) face using molecular beam epitaxy techniques. Our in-situ scanning tunneling microscopy study reveals that low temperature growth ( T ∼ 300° C) followed by annealing at T ∼ 500° C produces superior surface morphology with long terraces (> 1 μm). High temperature growth ( T > 500° C), on the other hand, promotes the formation of facets and pits. A roughening transition occurs for growth temperatures < 300°C, where long and regularly spaced ridges form along the [1 1 0] direction.

Directional elastic peak and directional Auger electron spectroscopies — New tools for investigating surface-layer atomic structure

Intensities of elastically scattered electrons and Auger electrons emitted from a crystalline sample depend strongly on the direction of the primary electron beam with respect to the sample. Namely, distinct maxima of those intensities appear when the primary beam is parallel to one of the close-packed rows of atoms in the sample, In an RFA analyzer, the angular distribution of the elastically scattered electrons or Auger electrons is integrated over a large scattering angle and does not influence the dependence of intensities mentioned above on the primary beam incidence angle (DEPES or DAES polar profiles). Those profiles can be obtained simply by rotation the sample positioned in front of the RFA analyzer around the axis parallel to the sample surface, Maxima in DEPES and DAES polar profiles connected with the close-packed atom rows can be easily recognized because their position does not depend on the primary electron energy. Those maxima are the evidence for presence of the crystalline structure in the surface layer. They also enable characterization of this structure even for a crystalline layer composed of very small islands or maintained at temperatures too high to observe LEED patterns. This was shown for the Ag Cu (111) , Ag Cu (011) , and Ag Ni (111) adsorption systems. DEPES and DAES profiles are sensitive to the disorder in the surface layer. For example, the surface roughening transitions on the Ni(O11) and Cu(O11) faces was clearly demonstrated and the temperatures of these transitions in both cases were determined with the use of those methods. A background on which maxima of the DAES and DEPES profiles appear is calculated using a simplified model. It is indicated that the shape of this background should contain information about the sample composition profile.

Kinetic Roughening of Interfaces and Mixing in Alloys Under Shear or Irradiation

AbstractBoth irradiation and plastic deformation can induce the stabilization of non-equilibrium phases in alloys. A simple kinetic atomistic model is used for describing these two situations, when the external forcing is acting in competition with thermally activated diffusion. Monte Carlo simulations are performed on alloys with positive heats of mixing. Both situations share common features : random solid solutions are stabilized at high enough forcing intensity (i.e. irradiation flux or shearing rate), while at moderate forcing intensities interfaces exhibit kinetic roughening. However, major differences are observed : alloys under irradiation undergo dynamical transitions between steady-states, such as a dynamical roughening transition at interfaces and a precipitation-dissolution transition in the bulk ; in alloys under shear such transitions are not observed ; instead the steady-state microstructure of a two-phase alloy is continuously refined on increasing the shearing rate. These differences originate from the size of the perturbation induced by the external forcing : the perturbation is of microscopic size for alloys under irradiation, while it is of macroscopic size for alloys under shear. Results obtained for the shearing case provide a rationalization scheme of ball milling experiments showing chemical mixing of immiscible elements. The fact that such systems consist of nanograins should also contribute to prevent the existence of 1st order phase transitions on varying the milling conditions.

Reconstruction and disordering on (110) fcc metal surfaces

Due to the large number of possible defects available to disorder the fcc metal (110) 2x1 missing row reconstruction, there is a particularly rich variety of possible disordered phases. The five distinct disordering scenarios that have been predicted for this reconstruction depend on the relative energy cost to generate the different defects that can form on this surface. Recent high resolution LEED measurements on the clean and alkali covered Pd(110) surfaces have explored a few of these phases. For clean Pd(110), a surface consisting of semi-ordered islands has been demonstrated to exist up to 950 K. The periodic island structure can be predicted by a simple model that includes step-step interactions and strain relaxation in the islands. Subsequent alkali adsorption destroys the island structure and forms the 2x1 missing row reconstruction. Diffraction results will be presented as a function of alkali coverage that show that the Pd(110)+K 2x1→1x1 transition is an example of deconstruction to the “even” flat phase. The existence of this intermediate phase has important implications to the growth of the missing row reconstruction and the range of the alkali-substrate interaction. In addition to these observations, higher potassium coverage data demonstrates that the Pd(110)+K work function minimum is correlated with a surface roughening transition.

Temperature effects in directional elastic peak electron spectroscopy for the Cu(011) face: observation of the surface roughening transition

Polar profiles of directional elastic peak electron spectroscopy (DEPES) and directional Auger electron spectroscopy (DAES) were measured for the Cu(011) face in the vicinity of particular close-packed directions in the sample and for sample temperatures of 400< T<1200 K. For all directions investigated, the ln C versus T curve, where C is the contrast: C = 2(I max−I max) (I max + I max) for a particular maximum in the polar profile, is composed of three linear parts. The slope of this particular part is different for the different maxima investigated but the breaks between the linear parts occur always at the temperatures T 1 ≈ 700 K and T 2 ≈ 1000 K. The former break is ascribed to the appearance of anharmonic thermal vibrations while the latter one indicates the surface roughening transition. DEPES was applied for the first time in the investigation of the surface roughening transition and it was found to be a very convenient and effective method. The surface roughening temperature T R ≈ 1000 K was found for the Cu(011) face, in an excellent agreement with theoretical predictions.

DISORDERING MECHANISMS OF THE Cu(110) SURFACE

We review recent theoretical work on the various disordering mechanisms of the Cu(110) surface. In these studies the properties of the surface, from the onset of enhanced anharmonicity in surface vibrations up to bulk melting point T M , have been studied using molecular dynamics and lattice-gas Monte Carlo methods with many-body interactions derived from the effective medium theory. Well after the onset of enhanced out-of-plane surface vibrations, clustering of surface defects is found to induce a roughening transition at T≈0.81T M , and surface premelting is found to occur at T≈0.97T M . These results suggest, that these transitions can both appear at Cu(110). The general picture of disordering as reported here for Cu(110), is expected to be valid also for other unreconstructed (110) surfaces of fcc metals.

Helium crystals as a probe in materials science

We review here a number of properties of helium crystals which are paradoxically classical, not quantum. We believe that the study of these properties are of general interest in materials science. Among them are the roughening transition and other properties of steps and terraces on hcp helium 4 crystals. We also describe the stress induced instability of helium crystal surfaces. We eventually mention other general problems whose study is interesting in helium because its extreme purity and quasi-infinite thermal conductivity offer unique opportunities for an accurate control of the relevant physical parameters.

Step capillary waves and equilibrium island shapes on Si(001).

From low-energy electron microscopy measurements of step fluctuations and equilibrium 2D island shapes on Si(001), We determine the temperature dependence of the ${S}_{A}$ and ${S}_{B}$ step edge stiffnesses, free energies, and mobilities. A capillary wave analysis of step stiffnesses is in quantitative agreement with the 2D island shapes, demonstrating the direct relation between equilibrium thermal fluctuations and equilibrium structure. The analysis also suggests that step free energies vanish at \ensuremath{\sim}1200\ifmmode^\circ\else\textdegree\fi{}C, providing direct evidence for a roughening transition. The combined exploration of step dynamics and equilibrium island shapes yields new insight into the basic thermodynamics of Si(001).

Inverse roughening transition in the staggered body-centered solid-on-solid model.

The F model and inverse F model in a staggered electric field are examined by using transfer matrices and finite-size scaling. It is shown that such a field induces a Kosterlitz-Thouless transition in the inverse F model, corresponding to an ``inverse'' roughening transition in the body-centered solid-on-solid representation: a crystal facet appears above a certain temperature. It disappears again in the limit of infinite temperature. We find the location of this phase transition as a function of staggered field and for a specific choice of this field we estimate the facet size as a function of temperature.

Equilibrium shape of bcc crystals: Thermal evolution of the facets.

The equivalence between the body-centered solid-on-solid model and the asymmetric six-vertex model is used to study the surface free energy and the equilibrium shape of bcc crystals in the solid-on-solid approximation. The thermal evolution of the (001)- and (011)-type facets is investigated analytically and illustrated for different values of the anisotropy of the next-nearest-neighbor couplings. It is shown that the (001) facet undergoes a roughening transition of the Kosterlitz-Thouless universality class and that the asymptotic regime below the critical point T=${\mathit{T}}_{\mathit{R}}$ is large. The occurrence of a universal jump in surface stiffness at the point where this facet vanishes at ${\mathit{T}}_{\mathit{R}}$ is reconfirmed.

SURFACE MELTING AND SURFACE ROUGHENING OF Pb(110) STUDIED BY LOW ENERGY ION SCATTERING

The Pb(110) surface undergoes two phase transitions. At about 400 K a roughening transition is observed. At 580 K, i.e. about 20 K below the bulk melting point, surface melting is found, The surface develops point defects at rather low temperatures. The roughening is connected with the generation of steps or the reduction of terrace size. There is also evidence for anisotropy of the roughening transition. Low energy ion scattering experiments in the temperature range from 160 to 590 K are used to study the structural changes of the Pb(110) surface.

The equilibrium crystal shape and the roughening transition on metal surfaces

The surfaces of metals at thermal equilibrium are characterized by a variety of defects which are thermally activated and entropically favored. In the last 10 years surface roughening transitions have been shown to exist on a large number of low-symmetry surfaces. For a given surface the transition temperature is known to scale with bulk properties. While a good deal of theoretical work has paralleled the experimental effort, direct comparisons between model potentials and experimental data are still lacking. The roughening transition on these surfaces is discussed in terms of competition with other processes such as facetting. Our work in this area is discussed and more recent developments in the field are reviewed. Unresolved problems in applying the theoretical framework to specific systems are also discussed.

Coupled compositional and roughening phase transitions at the surface of a PbBiNi alloy

The co-segregation of BiNi to the surfaces of small crystals of a dilute PbBiNi alloy changes the crystalline equilibrium form in relation to that of pure Pb and leads to the reversible formation of {112} and {110} facets at roughening transition temperatures of 515 and 510 K, respectively. These roughening transition temperatures are higher than those in pure Pb, thus increasing the kinetics of equilibration to the point that the observation of the appearance and disappearance of facets at those orientations becomes possible. Most interesting is the fact that the appearance and disappearance of these new facets is coupled with a compositional surface phase transition which manifests itself as an abrupt change in the surface concentrations of the Bi and Ni solutes.

On the morphology of crystals of triclinic even normal alkanes: theory and observation

In this paper the morphology of crystals of triclinic even n-alkanes over a range of chain lengths with 10 ≤ n ≤ 36 is studied theoretically and experimentally. Using the Buckingham potential for C-C, H-H and C-H interatomic interactions between neighboring molecules, the overall interaction energies between n-alkane molecules are calculated. Five types of important lateral interactions and three vertical interactions are identified from the structure. From these, a crystal graph with primitive cell is obtained. Thirteen connected nets corresponding to thirteen F forms, {001}, {010}, {011}, {100}, {101}, {111}, {110}, {1 1 1}, {1 11 }, {1 1 0}, {121}, {122} and {120}, are derived from the crystal graph. The dimensionless roughening transition temperatures of the faces are calculated. It follows that a phase diagram of the relative roughening temperature in dependence of n is obtained. To predict the theoretical growth forms, several recipes inspired by Ising models, the Hartman-Perdok and the Donnay-Harker theory are applied to the n-paraffins series. It turns out that crystals of triclinic even n-paraffins have the shape of long flat needles and are bounded by large faces of the form {001} and the narrow, long side faces of {010}, with the small {100} faces at the top of the needle. Some experiments were carried out to study the morphology and the roughening transition of n-C 24 and n-C 16 crystals in n-hexane and other systems. The predicted and observed results agree quite well.

Monte Carlo simulation studies of dendritic instabilities with faceted tips

Using a three-dimensional Ising-like model with thermal diffusion and a first-order phase transition, we study the faceting found at the tips of dendritic instabilities driven by a thermal gradient. Our preliminary results are consistent with experimental evidence, as well as with theoretical descriptions of the dynamic roughening transition.

Curvature Effects in Alloy Dissolution

An elemental metal can dissolve at kink sites at low everpotentials producing no new interfacial area. When an ideal solid solution alloy undergoes selective dissolution, this situation is not possible owing to atomic‐scale disorder. Dissolution of the less noble constituent can proceed only by injection of regions of negative curvature into the solid surface, which increases the interfacial area. We present a thermodynamic analysis which accounts for these capillary effects in alloy dissolution. The phenomenon of the critical potential for macroscopic selective dissolution is analyzed in terms of a kinetic roughening transition. This transition results from a competition between curvature‐dependent dissolution and surface diffusion. An expression for the critical potential as a function of alloy composition is developed. The dealloying threshold corresponds to a critical composition on the line of critical potentials defining the roughening transition.

High-temperature crystalline effects in Auger electron spectroscopy: the possibility of observation of the surface roughening transition on the Ni(110) face

The Auger signal of the M 2,3VV (62 eV) transition is measured as a function of the primary beam incidence angle for the (001) and (110) nickel faces with the samples maintained at temperatures of 300–1500 K. From those measurements the contrast C = 2(I max − I min ) (I max + I min) is calculated for the direction normal to the surface and the dependence of In C on the sample temperature is presented. For the Ni(001) face two linear parts of this dependence are found in the whole temperature range used (with the smaller and larger slope below and above 740 K, respectively) while for the Ni(110) face ln C drops appreciably faster than linearly for T > 1300 K. The increased slope above 740 K observed for both samples is ascribed to the anharmonic effects, while the fast drop of ln C observed for the Ni(110) face for T > 1300 K is interpreted as a result of thermal roughening of this face. Thus, crystalline effects in AES can give information on the thermal roughening.

High-temperature crystalline effects in Auger electron spectroscopy: the possibility of observation of the surface roughening transition on the Ni(110) face

High-temperature crystalline effects in Auger electron spectroscopy: the possibility of observation of the surface roughening transition on the Ni(110) face