Misfit driven azimuthal orientation of NaCl domains on Ag(1 0 0)

Misfit driven azimuthal orientation of NaCl domains on Ag(1 0 0)

Surface Science 603 (2009) 2434–2444 Contents lists available at ScienceDirect Surface Science journal homepage: www.elsevier.com/locate/susc Misfit...

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Surface Science 603 (2009) 2434–2444

Contents lists available at ScienceDirect

Surface Science journal homepage: www.elsevier.com/locate/susc

Misfit driven azimuthal orientation of NaCl domains on Ag(1 0 0) Eric Le Moal *, Mathias Müller, Oliver Bauer, Moritz Sokolowski Institut für Physikalische und Theoretische Chemie der Universität Bonn, Wegelerstrasse 12, 53115 Bonn, Germany

a r t i c l e

i n f o

Article history: Received 15 April 2009 Accepted for publication 12 May 2009 Available online 6 June 2009 Keywords: Insulating thin films NaCl Ag(1 0 0) SPA-LEED Azimuthal mosaicity Higher-order commensurability

a b s t r a c t We investigated the growth of thin NaCl films on Ag(1 0 0) by spot-profile-analysis low energy electron diffraction (SPA-LEED), varying extensively the growth temperature (200–500 K) and the film thickness (0.5–14 ML). The incommensurate growth of NaCl on Ag(1 0 0) yields (1 0 0)-terminated epitaxial NaCl domains, which are preferentially oriented with their [0 1 0] axis parallel to that of the substrate. At 300 K, the NaCl domains exhibit an azimuthal mosaicity by 14° around this orientation and the NaCl unit cell is laterally contracted in the first layers by 0.9% with respect to the bulk. At higher growth temperatures, the azimuthal mosaic distribution sharpens and additional distinct orientations appear, presumably due to a higher-order commensurability. The evolution of the azimuthal mosaic distribution with increasing temperature can be ascribed to both the NaCl thermal expansion and higher diffusion rates of NaCl on Ag(1 0 0). The best epitaxy, i.e. that with the highest selectivity of a specific azimuthal domain orientation, is achieved by growing NaCl films at low deposition rate (60.1 ML min1) on the Ag(1 0 0) substrate at constant high temperature (450–500 K). The observations made here can probably be applied more generally to other heterogeneous interfaces and, in particular, be used to improve the quality of thin insulating films. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Thin insulating films on conductive substrates have been widely used to study the electronic properties of the insulating surfaces themselves [1–3] or those of adsorbed nanostructures [4]. At sufficiently low film thickness, thin insulating films have the advantage over bulk insulators to avoid the accumulation of electric charges and thus to allow the use of standard characterization methods by electron diffraction and spectroscopy [5,6]. The epitaxial growth of thin insulating films, especially of alkali-halide (AH) materials, has also attracted much attention for their potential applications as high-quality insulating layers in miniaturized electronic devices, since they were found to exhibit a wide electronic band-gap from thickness as low as two atomic layers [7,8]. AH growth has notably been investigated in details on a number of fcc metals such as copper [6,8–14], silver [14–20], gold [21–23], nickel [13,14], palladium [24,25], platinum [25], and aluminium [26,27]. At room temperature (RT), the formation of compact (1 0 0)-terminated AH layers is the general rule; however, various epitaxial relationships are found depending on the mechanisms of growth. On stepped and facetted surfaces of these metals, strong electrostatic interactions between the ionic AH molecules and the corrugated distribution of charges at the substrate surface are able to stabilize commensurate AH superstructures with severe * Corresponding author. Tel.: +49 228733267; fax: +49 228732551. E-mail address: [email protected] (E. Le Moal). 0039-6028/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2009.05.019

lattice constraints [12,28]. Conversely, it has been reported that lattice matching is not the preponderant criterion on low-indexed surfaces (i.e. (1 0 0), (1 1 0), and (1 1 1)) of metals [13,18]. NaCl growth on Ag(1 0 0) has already been the subject of several experimental studies, conducted by reflection high-energy electron diffraction (RHEED) [13], low energy electron diffraction (LEED) [18] and scanning tunnelling microscopy (STM) [19,29]. However, these have led to partly contradictory conclusions concerning the epitaxy, as we will describe below. Fig. 1a and b shows Ag(1 0 0) and NaCl(1 0 0) surfaces with the centred (dashed line) and primitive (straight line) unit cells and the respective lattice constants at 298 K [30]. Two typical azimuthal orientations of the NaCl domains, namely azimuthally aligned or rotated by 45° with respect to the substrate, are illustrated in Fig. 1c. Because the first-nearest neighbour Ag–Ag and Na–Cl distances in the (1 0 0) plane differ by only 2.2%, one might expect that an azimuthal rotation of the NaCl lattice by 45° is energetically preferred at the NaCl/Ag(1 0 0) interface. Nevertheless, NaCl domains preferentially grow with their [0 1 0] axis parallel to that of the substrate [13,18,19]. Kiguchi et al. [13] proposed that the azimuthal epitaxy of NaCl on Ag(1 0 0) is related to the preferential orientations of the substrate steps. Due to high diffusion rates on Ag(1 0 0), NaCl molecules migrate to the step edges and the nucleation of NaCl domains starts there. Kramer et al. [18] reported on the azimuthal mosaicity of NaCl growth on Ag(1 0 0) and ascribed it to the natural deviation of the substrate steps from their main orientation. However, Pivetta et al. [19] revealed by STM measurements that

E. Le Moal et al. / Surface Science 603 (2009) 2434–2444

(c)

9 88 2.

4.086 Å

(a)

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Å



Ag

5.640 Å 8 98 3. Cl

[001]

[010]

Na

[0 11 ]

[010]

Å

45° [0 11 ]

(b)

[001]

Fig. 1. (a and b) Schematic representation of Ag(1 0 0) and NaCl(1 0 0) surfaces. The unit cell and the primitive cell are indicated by dashed and straight lines, respectively. (a) Purple spheres are silver atoms. (b) Large red spheres and small green spheres are chloride and sodium ions, respectively. The main directions in the (1 0 0) plane are referred to as [0 1 0] and [0 0 1] with respect to the axes of the bulk fcc crystals. The lattice constant of the primitive unit cell equals 2.889 Å for Ag(1 0 0) and 3.988 Å for NaCl(1 0 0) at 298 K [30]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

epitaxially aligned NaCl domains nucleate both at step edges and on terraces, and azimuthal mosaicity was also observed for NaCl islands on terraces. Moreover, 45°-oriented domains were found to nucleate at step edges, but never on terraces. Hence the origin of the azimuthal mosaicity in thin NaCl films on Ag(1 0 0) is not yet fully understood. In this paper, we report a detailed investigation by spot-profileanalysis low energy electron diffraction (SPA-LEED) on the structure of thin NaCl layers, ranging from 0.5 to 14 monolayers (ML) in nominal thickness, grown on Ag(1 0 0) at substrate temperature varying between 200 K and 500 K. We focused on two main aspects, namely the lateral contraction of the NaCl lattice constant and the influence of the substrate temperature on the azimuthal mosaic distribution. Our results provide new insight into the understanding of NaCl growth on Ag(1 0 0). In particular, the appearance of well-defined and energetically favoured domain orientations for high growth temperatures might be explained by higher-order commensurability and indicates the important role of the NaCl/Ag(1 0 0) interface energy for the growth scenario. Strategies for an optimization of the epitaxy will be discussed. 2. Experimental The sample preparation and the structural characterization were carried out in a UHV-chamber at a base pressure of 3  1010 mbar. The chamber is equipped with SPA-LEED apparatus manufactured by Omicron NanoTechnology GmbH. Differing from the original Omicron setup, a channeltron aperture of 300 lm was used to achieve higher counting rates. For NaCl deposition control, a mass spectrometer and a quartz-microbalance were used. The sample was mounted on a manipulator cooled by liquid nitrogen. Our setup allows to cool the sample down to 130 K and to heat it up to 900 K by a tungsten filament or electron bombardment. SPA-LEED measurements were performed at a sample current of about 1 nA in order to limit charging effects and to exclude dissociation of NaCl upon electron bombardment. Radial or azimuthal spot profiles were obtained by measuring the LEED signal along either a straight line crossing a spot of interest and

the specular reflection, or along an arc of a circle centred on the specular reflection, respectively. k// values were computed on the basis of k0 = 2p/k. Most of the LEED data were recorded at incident electron beam energy of 95 eV. With respect to single steps of NaCl, this electron energy corresponds to the in-phase scattering conditions for NaCl (±1, 0) and (0, ±1) diffraction spots. Under this condition, electron waves diffracted from different terraces interfere constructively and hence the radial widths of these spots only depend on the mean size of the NaCl domains and on the instrumental resolution, and it is not influenced by the surface roughness of the NaCl domains. The Ag(1 0 0) single crystal was prepared by cycles of sputtering with Ar+ ions of about 900 eV kinetic energy at an ion current of 4 lA on the sample and subsequently annealing at about 723 K for 60 min. NaCl of 99.999% purity was purchased from Sigma–Aldrich. NaCl deposition on the Ag(1 0 0) crystal was performed by thermal evaporation from a home-made Knudsen-cell at a cell temperature of 680–720 K and a deposition rate of 0.05– 0.65 ML min1, typically. The Ag(1 0 0) substrate was held at temperatures ranging from 200 K to 500 K during NaCl growth. For a very accurate internal calibration of diffraction vectors, we also prepared a commensurate monolayer of perylene-3,4,9,10-tetracarboxylic acid dianhydride (PTCDA) on the same Ag(1 0 0) substrate. The PTCDA layer was grown on Ag(1 0 0) at room substrate temperature and then annealed at 443 K for 5 min [31]. 3. Results and interpretations 3.1. Growth at room temperature Fig. 2a1 shows an experimental LEED pattern of a 1 ML thick NaCl film grown on Ag(1 0 0) at 300 K, at a deposition rate of 0.1 ML min1. In the superimposed simulation of the LEED pattern, the (0,0) specular reflection and the first-order diffraction spots for

1 For interpretation of colour in Figs. [2,3,7–9] the reader is referred to the web version of this article.

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Ag(0,1)

(1,1)

(0,1)

-45

Azimuthal angle (°) -15 0 15

30

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Signal (cps)



NaCl (1,0) spot

Azimuthal profile Radial profile

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0°-oriented domains

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-1

ΔK// (Å ) Fig. 2. (a) LEED pattern of a 1 ML thick NaCl film grown at RT, measured at incident electron beam energy of 95 eV. LEED pattern simulation of a (1 0 0)-terminated NaCl layer on Ag(1 0 0) with two different azimuthal epitaxial orientations, namely NaCl [0 1 0]//Ag [0 1 0] (red) and NaCl [0 1 0]//Ag [0 1 1] (blue). Inset: colour 3D-plot of a detail of the  0Þ spot of the 45°-oriented NaCl domains besides the much larger ð1;  1Þ spot of the 0°-oriented domains. (b) Azimuthal (black line) and LEED pattern showing the small ð1;  0Þ spots of 0°- and 45°-oriented domains. Note that the azimuthal profiles have been offset to ease the comparison with radial (red line) spot profiles, measured on the NaCl ð1; the radial profiles. The x-scale has been centred on the diffraction spot of the 0°-oriented NaCl domains and is expressed both in terms of reciprocal length (Dk//) and azimuthal angle (U[rad] = Dk///k//, where k// is the relative position of the diffraction spot with respect to the specular reflection, and U[°] = 180/p U[rad]). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the Ag(1 0 0) surface (black circles) and the NaCl(1 0 0) film (red and blue circles) are marked. The two sets of unit vectors (red and blue) in Fig. 2a correspond to the two domain orientations schematized in Fig. 1c, respectively. In Fig. 2a, we mainly observed the epitaxial growth of azimuthally aligned NaCl(1 0 0) domains, i.e. with the [0 1 0] axis of NaCl parallel to that of the metal crystal. The diffraction spots of 45°-oriented domains (with the NaCl [0 1 0] axis parallel to the Ag [0 1 1] axis) were also detected with however about 40 times less intensity. The presence of these two domains with different azimuthal orientations, one predominating over the other, is in good agreement with the STM measurements by Pivetta et al. [19]. Note that the LEED simulation, shown in Fig. 2a, does not take into account the azimuthal elongation of the NaCl spots, which is due to the rotational mosaicity of the NaCl domains in the (1 0 0) plane (so-called in-plane or azimuthal mosaicity). Fig. 2b shows azimuthal (black line) and radial (red line) spot profiles, measured under the same conditions as the LEED pattern  0Þ spots of the 0°- and 45°-oriented doin Fig. 2a, on the NaCl ð1; mains. Both azimuthal and radial profiles were plotted with the same length scale in k-space, which can alternatively be expressed in terms of azimuthal angles for the azimuthal profiles. Remarkably, the azimuthal spot profile of the 0°-oriented NaCl domains in Fig. 2a does not exhibit a typical Lorentzian shape. In particular, the profile seems to be split into two secondary peaks. It is noteworthy that both the general shape of the profile and the position of these secondary peaks were found to be reproducible on a number of samples (without exception) under the same conditions of preparation and were observed independently of the incident electron beam energy (from 34 eV to 110 eV). These fine features in the azimuthal spot profiles are discussed in details in Section 3.3. Table 1 presents the azimuthal and radial widths (full widths at half maximum, FWHM) of the NaCl spots, which were obtained by fitTable 1  0Þ spots of the 0°- and 45°Azimuthal and radial widths (FWHM) of the NaCl ð1; oriented domains of a 1 ML thick NaCl film grown on Ag(1 0 0) at 300 K. Domain orientation

Azimuthal width (Å1)

(°)

(Å1)

Radial width

0° 45°

0.392 ± 0.005 0.046 ± 0.001

14.3 ± 0.2 1.66 ± 0.04

0.043 ± 0.001 0.042 ± 0.001

Azimuthal mosaic spread 14° 1°

ting the entire profiles with one Lorentzian curve. This evaluation ignores the abovementioned splitting in the case of the 0°-oriented domains. Assuming an isotropic density of steps of the NaCl films, the azimuthal and radial widths are expected to be identical in the absence of azimuthal mosaicity. This is almost the case (within 10%) for the 45°-oriented domains (see Table 1), which indicates that the NaCl [0 1 0] axis is almost perfectly parallel to the Ag [0 1 1] axis. (Hence a value 1° is estimated for the azimuthal spread of the 45°-oriented domains and given in Table 1). Conversely, the 0°-oriented domains exhibit an azimuthal profile about 9-times wider, with a width of about 14°. Of course, the azimuthal width that we are considering here is only a rough and effective parameter. An accurate calculation of the azimuthal mosaic spread (FWHM of the azimuthal mosaic distribution) requires a deconvolution of the azimuthal profile by the instrumental response and the broadening due to step density. Nevertheless, we consider the azimuthal width (14°) to be an acceptable approximation of the actual mosaic spread, because the azimuthal mosaicity is the predominant source of broadening here. We further analysed the NaCl spot profiles of a 5 ML thick NaCl film grown on Ag(1 0 0) at RT. We examined the variation of their radial and azimuthal widths with the incident electron beam energy, from 34 eV to 110 eV. From the energy dependence of the widths [32], we inferred a mean step height of 2.75 ± 0.03 Å (consistent with monoatomic NaCl steps), a mean terrace size of 100 ± 30 Å and a mean size of the coherently scattering domains (effective transfer width) of 500 ± 200 Å. We found the azimuthal width of the NaCl spots of the 0°-oriented domains to vary from 12° to 14° within the investigated energy range. These results indicate that the broadening due to steps contributes less than 20% to the azimuthal width here. Remarkably, 1 ML and 5 ML thick NaCl films grown at RT exhibit comparable mosaic spreads, which indicates that azimuthal mosaicity is not limited to ultrathin films. Our assessment of the azimuthal mosaic spread is in relatively good agreement with that previously reported in literature [18,19] for the 0°-oriented domains. Kramer et al. [18] measured an azimuthal width of about 18° for a 1.6 ML thick NaCl layer grown on Ag(1 0 0) at RT. Pivetta et al. [19] have calculated a mosaic spread of 14° from the statistical analysis of STM images for a 1 ML thick NaCl film grown on Ag(1 0 0) at RT. We suggest that the slightly larger mosaic spread found by Kramer et al. may be related

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to differences in the substrate preparation or, more likely, in the assessment method. It might also be that the higher NaCl deposition rate (0.3 ML min1) in the experiments by Kramer et al. yielded a broader azimuthal mosaic distribution. The influence of the deposition rate is discussed below in Section 3.5. 3.2. Lattice contraction at room temperature  0Þ spot, measured for Fig. 3a shows radial profiles of the NaCl ð1; NaCl films ranging from 1.2 ML to 14 ML in nominal thickness. Here we considered the spots of the 0°-oriented NaCl domains, exclu 0Þ spot shifts with sively. As can be seen in Fig. 3a, the NaCl ð1; increasing film thickness and hence the NaCl lattice constant varies with film thickness. To calculate the absolute position of the NaCl spots, we used the diffraction pattern of thepPTCDA on ffiffiffi pmonolayer ffiffiffi  Ag(1 0 0), which exhibits a commensurate ð4 2  4 2ÞR45 super 0Þ spot is compared to structure [31]. The position of the NaCl ð1;  3Þ  spot, with the aim of enhancing the that of the near PTCDA ð3; measurement accuracy. The lattice constant of NaCl bulk is known from X-ray diffraction measurements to be a = 5.6402 Å at 298 K [30], hence the size a100 of the primitive unit cell in the (1 0 0) plane p is 3.988 Å (a100 = a/ 2). We used this value to evaluate the variation of NaCl lattice constant in thin films at RT. The results are plotted as a function of film thickness in Fig. 3b, together with results from previously reported LEED measurements by Kramer et al. [18] (blue triangles) and ab initio calculations for unsupported NaCl films by Hebenstreit et al. [26] (red dots). Experimentally we found a100 to amount to 3.952 ± 0.008 Å and 3.957±0.008 Å for 1.2 ML and 3.5 ML thick NaCl films, respectively. It corresponds to contractions of the NaCl lattice constant by 0.9 ± 0.2% and 0.8 ± 0.2%. The effect tends to vanish at higher thickness; a100 equals 3.981 ± 0.008 Å at 14 ML. The deviation from the bulk value almost falls within the error there. The latter was defined with respect to the confidence interval, when fitting a spot profile with a Lorentzian curve to find its centre position. We still measured a significant contraction of the NaCl lattice constant at 7 ML, namely by 0.6 ± 0.2%, presumably partly because the electrons penetrate deeper into the film than the top NaCl layer and the measurement hence samples also contributions from layers closer to the interface. To sum up, a lateral contraction of NaCl unit cell by about 0.9% with respect to bulk NaCl is measured for the first few layers and then a relaxation of the constraint is observed. Kramer et al. [18]

found a contraction by 2% for a 1.6 ML thick NaCl film grown on Ag(1 0 0) at RT and no change of the lattice constant with increasing film thickness up to 4 ML. The deviation from the here reported trend may be due to experimental reasons. Hebenstreit et al. [26] predicted lateral contractions by 5.7% and 3.4% for 1 ML and 3 ML thick free standing NaCl films. In accordance with Pivetta et al. [19], we assume that the influence of the Ag(1 0 0) substrate partly counteracts the lateral contraction expected for the free standing thin NaCl film. Furthermore, the actual contraction by 0.9 ± 0.2% that we report here is in good agreement with the contraction by 0.8% that Pivetta et al. [19] obtained from STM measurements for the 45°-oriented NaCl domains. 3.3. Influence of the growth temperature Fig. 4a shows an experimental LEED pattern of a 0.5 ML thick NaCl film grown at 400 K, juxtaposed with a simulated LEED pattern. At this temperature, we mainly observed the epitaxial growth of azimuthally aligned NaCl(1 0 0) domains, the diffraction spots of the 45°-oriented domains being almost undetectable. We verified up to thickness of 10 ML that the absence of 45°-oriented domains at 400 K is not connected to the thickness of the NaCl film. In the following, we only consider the thinnest NaCl films because these provide major information on the growth mechanisms. In Fig. 4b, the azimuthal profile of the NaCl (1,0) spot is plotted for 0.5 ML thick NaCl films grown at different temperatures ranging from 200 K to 500 K. All measurements were conducted under the same conditions of observations. First of all, the fine analysis of the azimuthal profiles reveals interesting fine structures, shoulders or satellite peaks at all considered temperatures of growth. Hereby, the profiles undergo a gradual transformation upon increasing growth temperature. A sharpening of the azimuthal width is observed, namely by more than a factor 2.5 when comparing the NaCl films grown at 200 K and 500 K. However, one can hardly define an azimuthal mosaic spread for the NaCl films grown at or above 400 K, because the azimuthal spot profiles cannot be reliably fitted with a single Lorentzian curve. Much more, the presence of additional peaks, symmetrically positioned around a central peak, becomes obvious at these temperatures. It reveals the existence of distinct preferred domain orientations. The central peak is associated with a perfect azimuthal alignment of the NaCl domains with respect to the Ag(1 0 0) substrate,

3

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bulk

-1 -2 this work LEED measurements by Kramer et al. ab initio calculations for NaCl films without substrate by Hebenstreit et al.

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 0Þ diffraction spot, measured for NaCl layers of various thickness deposited on Ag(1 0 0) at RT and a monolayer of PTCDA directly Fig. 3. (a) Radial profiles of the NaCl ð1;  0Þ spot is compared to the ð3;  3Þ  spot of the commensurate superstructure of grown on Ag(1 0 0), at incident electron beam energy of 34 eV. The position of the NaCl ð1;  0Þ spot enhances the PTCDA/Ag(1 0 0) [31], which is known precisely from the superstructure to be at k// = 1.631 Å1. Using this spot instead of the more distant Ag ð1; measurement accuracy, which is usually limited by the inherent distortion of the diffraction pattern in its peripheral areas. All measurements were conducted rigorously under the same experimental conditions. (b) Relative variation of the NaCl lattice constant in NaCl films deposited on Ag(1 0 0) at RT as a function of their nominal thickness. Our experimental results (black squares) are compared to other LEED measurements on NaCl/Ag(1 0 0) by Kramer et al. [18] (blue triangles) and to ab initio calculations for unsupported NaCl films by Hebenstreit et al. [26] (red dots). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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(a)

Ag(0,1)

(1,1)

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0.5 ML NaCl grown at



2

200 K 308 K 323 K

1

400 K 450 K 0 -30

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0

10

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500 K 30

Azimuthal angle (°) Fig. 4. (a) LEED pattern of a 0.5 ML thick NaCl film grown at 400 K; LEED pattern simulation. (b) Azimuthal profiles of the NaCl (1, 0) spot for 0.5 ML thick NaCl films grown at substrate temperatures from 200 K to 500 K. The intensity (count rate) of the LEED signal has been normalized to unity for each profile and plotted as a function of the azimuthal angle. LEED pattern and profiles were measured at incident electron beam energy of 95 eV.

whereas the satellite peaks correspond to well-defined deviations from this orientation. We analysed each azimuthal profile by fitting a set of several Lorentzian curves to it. In Fig. 5, we report the angular position of the main peaks for different temperatures of growth. Examples of fitted sets of peaks are given in the upper part of Fig. 5. In the low temperature range (from 200 K to 323 K), fitting is often ambiguous and different peak positions can be found depending on the fitting parameters, e.g. the predefined number of components. Only in the high temperature range (from 400 K to 500 K), the azimuthal profiles are clearly composed by a set of at least five peaks, the positions of which seem to con-

verge towards well-defined angular values. Besides a central peak at 0°, we found peaks at ±3.0° and ±5.7°. One can note, both in Figs. 4b and 5, the presence of two small supplementary peaks at ±13.5° for growth temperatures between 323 K and 450 K. However, these two peaks were not detected at 500 K, presumably because the associated domain orientations are not stable above 450 K. To sum up, the temperature of the Ag(1 0 0) substrate during the growth of thin NaCl films has a strong influence on the azimuthal mosaic distribution. However, it is not clear yet if this distribution is determined only by the substrate temperature at the very first steps of growth or if it plays a role throughout the growth process and even afterwards. Therefore we examined the effect of annealing treatments on thin NaCl films grown at low temperature.

500 K

3.4. Influence of annealing

400 K 308 K 200 K

15

Azimuthal angle (°)

10 5 0 -5 -10

Peak position

-15 200

300

400

500

Temperature (K) Fig. 5. Peak analysis of azimuthal NaCl spot profiles, measured for 0.5 ML thick NaCl films grown at different temperatures, at incident electron beam energy of 95 eV. The peak positions were found by fitting the profiles with a set of several Lorentzian profiles. Angular peak positions are plotted as a function of the growth temperature. Insets: fitted profiles at growth temperature of 200 K, 308 K, 400 K and 500 K, from left to right.

Fig. 6 shows two experimental LEED patterns of a very thin, only 0.5 ML thick NaCl film, as grown at 200 K (a) and after an additional annealing step at 450 K (b). Calculated LEED patterns were added for clarity. The annealing consisted in slow heating and cooling ramps from 200 K to 450 K and backwards at rates of ±1 K s1, and holding the sample at 450 K for 30 min. Fig. 7a displays two azimuthal scans, measured along a 180°-wide arc of a circle on the LEED patterns of Fig. 6a and b. The radius of this circle was chosen to fall onto the (1,0) spot of NaCl. In these azimuthal scans, one can observe the (1,0) and (0,1) spots of azimuthally aligned NaCl domains, at 0° and 90°, and those of azimuthally rotated domains at 45° and 45°, respectively. Two obvious differences can be seen in Fig. 6a and b. Firstly, the signature of the 45°-oriented NaCl domains is observed only prior to the annealing, whereas it is almost undetectable afterwards (see also Fig. 7a). Secondly, unusual arcs of circles are only present before the annealing but not afterwards. Remarkably, these arcs of circles are centred on the first and second order diffraction spots of Ag(1 0 0) and not on the specular reflection (0,0), and they have the same radii and the same azimuthal widths as the NaCl spots. In Fig. 6a, we have drawn a circle, centred on (0,0) and crossing the NaCl (0,1) spot. As shown by a simple geometrical construction, four of the unusual arcs around the (0,0) spot are recovered by centering this circle on the Ag (±1,0) and (0,±1) spots. Four other unusual arcs around the (0,0) spot can be built from a larger (0,0)-centred circle crossing the NaCl (1,1) spot, by moving it to the Ag (±1,±1) spots (this construction is not shown in Fig. 6). From these observations, we

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centred on Ag(0,1) ↓

Ag(0,1)

(a)

(1,1)

(0,1)

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° 45

centred on Ag(1,0) ↓



Ag(0,1)

(b)

(1,1) (1,1)



centred on Ag(0,1) ↑ Fig. 6. LEED patterns and simulations of a 0.5 ML thick NaCl film (a) as grown at 200 K and (b) annealed 30 min at 450 K after growth at 200 K. The LEED patterns were measured at incident electron beam energy of 95 eV (see details in the text).

Normalized intensity

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grown at 200 K and annealed at 450 K

(c)

as grown at 450 K -1 at 0.10 ML min

-1

at 0.65 ML min

0 -30

0

30

Azimuthal angle (°)

Fig. 7. (a) Azimuthal LEED scans from the LEED patterns of Fig. 6a and b, namely for 0.5 ML thick NaCl films grown at 200 K before (straight black line) and after annealing 30 min at 450 K (dashed red line). The (1, 0) and (0, 1) spots of the azimuthally aligned NaCl domains appear at 0° and 90°. Black arrows point at the (1, 0) and (0, 1) spots of the 45°-rotated NaCl domains, which almost disappear upon annealing at 450 K. (b) Azimuthal profile of the NaCl (0, 1) spot of 0.5 ML thick NaCl films grown at 200 K and subsequently annealed 30 min to 450 K (dashed red line) and directly grown at 450 K (dotted blue line). (c) Azimuthal profiles of the NaCl (0, 1) spot of 0.5 ML thick NaCl films grown at 450 K at deposition rates of 0.10 ML min1 (dotted blue line) and 0.65 ML min1 (dotted grey line). All measurements were conducted at incident electron beam energy of 95 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

concluded that these unusual arcs are due to multiple-scattering of the electrons by the Ag(1 0 0) substrate and the NaCl film. It is noteworthy that neither the annealed 0.5 ML thick NaCl films nor those directly grown at 450 K exhibited these multiple-scattering circles. The disappearance of the multiple-scattering circles upon annealing could possibly indicate a transition in the NaCl film from single-layered to double-layered islands. This explanation is discussed in details in Section 4.1. Fig. 7b shows the azimuthal profile of the NaCl (0,1) spot of the 0.5 ML thick NaCl film grown at 200 K and after subsequent annealing for 30 min at 450 K (red dots), and the profile of a 0.5 ML thick NaCl film directly grown at 450 K (blue dots). As it can be seen in Fig. 7a and b, annealing the NaCl film grown at 200 K at 450 K modifies the azimuthal mosaic distribution, but it does not yield the same distribution as that of the NaCl film di-

rectly grown at 450 K. The two profiles in Fig. 7b exhibit major differences. In the case of the annealed film, two preferred domain orientations at about ±6° dominate the distribution, whereas for the film directly grown at 450 K the azimuthal alignment (i.e. 0°orientation) is the prevailing domain orientation. Moreover, the annealed film exhibits a significantly broader profile, possibly due to the existence of many secondary favoured orientations in the azimuthal mosaic distribution. We also investigated the influence of the film thickness (from 0.5 ML to 5 ML) at a given growth temperature (400 K). We observed a homogeneous broadening of the azimuthal mosaic distribution (by about 40%), although the preferred domain orientations basically remain unchanged. Besides, for a 10 ML thick NaCl film grown at 200 K we did not observe significant modifications upon annealing at 450 K.

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E. Le Moal et al. / Surface Science 603 (2009) 2434–2444

3.5. Role of the deposition rate

observed a sharpening of the azimuthal profiles and the disappearance of the non-0° azimuthal peaks in the azimuthal mosaic distribution for increasing growth temperature or decreasing deposition rate. For the thinnest NaCl films grown at high temperature (see Fig. 4b), it can be seen that the azimuthal profiles grown at 450 K and 500 K exhibit very similar shapes. Both of them are mainly composed of a central peak at 0° and two pairs of satellite peaks, centred on ±3.0° and ±5.7°, respectively. From the integrated intensities, we found these five components to have roughly (to about 10%) the same relative weights in both distributions, namely 30% for the central peak, 60% for the satellites at ±3.0° and 10% for those at ±5.7°. This resemblance presumably indicates that the azimuthal mosaic distribution at 450 K is already close to the most stable equilibrium state that can be achieved at this thickness (0.5 ML) and this deposition rate (0.10 ML min1). By thermal desorption spectroscopy, we found that NaCl starts to desorb from the Ag(1 0 0) surface around 580 K. In other words, this stable equilibrium state of the azimuthal mosaic distribution is achieved at a growth temperature approaching the desorption threshold, where a high surface diffusion of the NaCl molecules can be expected.

Fig. 7c shows azimuthal profiles of the NaCl (0,1) spot of two 0.5 ML thick NaCl films grown at 450 K at different deposition rates, namely 0.10 ML min1 (blue dots) and 0.65 ML min1 (grey dots). We found both azimuthal profiles to be mainly composed of seven peaks, with almost identical angular positions (to less than 5%), namely ±13.6°, ±5.8° and ±2.9° with respect to the central peak at 0°. Nevertheless, the two azimuthal profiles differ in respect of the width of these seven peaks and in their relative amplitudes. At the largest rate of deposition, a general broadening of the peaks is observed in the azimuthal profile, by up to 50% for those at ±2.9°, together with a diminution in the relative amplitude of the central peak. Hence the azimuthal mosaic distribution looks less sharp and less well-defined. In particular, the domain orientations at ±13.6° are more pronounced in the distribution at 0.65 ML min1 than at 0.10 ML min1. Remarkably this component of the distribution has roughly the same weight at 450 K/ 0.65 ML min1 and 400 K/0.10 ML min1 (see Fig. 4b), whereas it can hardly be observed at 450 K/0.10 ML min1 and is simply undetectable at 500 K/0.05 ML min1 (see Fig. 4b). To sum up, we

NaCl Ag

Signal (cps)

(a) 10 10

(1,0) (1,0)

(0,0) 300 K 350 K 400 K 450 K 500 K 550 K

5

4

-2

-1

0

1

(e)

2

-1

k// (Å )

Signal (cps)

(b) 10 10

5

Ag(1,0)

4

-1

10

(f)

4

1.010

1.005

1.000 350

400

450

500

550

1.395

NaCl(1,0)

1.390 (1)

-1

NaCl/Ag lattice ratio

Signal (cps)

1.015

Temperature (K)

-1.5

k// (Å )

Signal (cps)

1ML NaCl film on Ag(100) NaCl bulk Ag(100) surface Ag bulk

-2.1

k// (Å )

-1.6

(d)

1.020

300

-2.2

(c)

Relative variation of the lattice constant

Ag NaCl (1,0) (1,0)

10 10 10

6

(0,0) 5

1.385

(2)

1.380

(3)

bulk NaCl / bulk Ag (4)

1.375

(5)

1.370 1.365 1ML NaCl film / Ag(100)

4

1.360

-0.1

0.0

0.1

300

350

400

450

500

550

Temperature (K)

-1

k// (Å ) Fig. 8. (a) Radial LEED scans, measured on 1 ML thick NaCl film grown on Ag(1 0 0) at 300 K and after subsequent annealing up to 550 K (see details in the text), at incident  0Þ and (c) NaCl ð1;  0Þ diffraction spots and (d) the specular reflection (0, 0). (e) electron beam energy of 95 eV. (b–d) Zoom-in on Fig. 8a to see the radial profiles of (b) the Ag ð1; Relative variation of the NaCl lattice constant, measured for a 1 ML thick NaCl film on Ag(1 0 0) in this work by SPA-LEED (black squares) and measured for NaCl bulk as found in the literature [33] (black dash-dot line). Relative variation of the Ag lattice constant, measured in this work (red dots) and taken from the literature [33] (red dash-dot–dot line). (f) Ratio between the lattice constants of the thin NaCl film and the Ag(1 0 0) substrate (aNaCl/aAg) as a function of the temperature, as calculated from our experimental results shown in (e). The ratio between Ag and NaCl bulk lattice constants at 298 K [33] is indicated on the left side of the graph (red dot). Horizontalpdashed lines, numbered ffiffiffiffiffiffi pffiffiffiffiffiffi fromp (1) toffi (5), indicate the theoretically calculated /aAg ratios required to achieve the following commensurable structures: (1) ð 25  25ÞR tan1 ð4=3Þ; pffiffiffiffiffiffi pffiffiffiffiffiffi aNaCl pffiffiffiffiffiffi pffiffiffiffiffiffi higher-order ffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi ffi 1 1 1 (2) ð 117  117ÞR tan ð6=9Þ; (3) ð 61  61ÞR tan ð5=6Þ; (4) ð11  11Þ and (5) ð 17  17ÞR tan ð4Þ. Details about these structures are given in Table 2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

E. Le Moal et al. / Surface Science 603 (2009) 2434–2444

Therefore, we conclude that the increase of NaCl diffusion rates plays an important part in the sharpening of the azimuthal mosaic distribution at high growth temperatures. 3.6. Thermal lattice expansion of NaCl and Ag Fig. 8 shows radial spot profiles, measured on a 1 ML thick NaCl film grown on Ag(1 0 0) at 300 K and after subsequent stepwise heating to different temperatures ranging from 350 K to 550 K. The sample was heated with a rate of 0.3 K s1 and held at a constant temperature during the measurements. All the profiles were measured along the same direction, namely along a line crossing  0Þ and (1, 0) spots. In Fig. 8a, one can see the Ag and NaCl the Ag ð1; (±1, 0) spots, and the specular (0, 0) spot at the centre. The radial  0Þ, NaCl ð1;  0Þ and (0, 0) spots can be seen in profiles of the Ag ð1; details in Fig. 8b–d. The annealing was performed in front of the LEED apparatus and the LEED measurements were conducted after each annealing step without changing the sample position, at the identical electron energy and focus settings. In Fig. 8b and c, the diffraction spots of Ag and NaCl can be seen to shift towards the (0, 0) spot with increasing the temperature, indicating a lateral expansion of both Ag and NaCl lattices. In Fig. 8e, we plotted the relative variation of the Ag (red dots) and NaCl (black squares) lattice constants as a function of temperature with respect to their values at 300 K. We compared our experimental results by SPALEED with both experimental and theoretical data from the literature on the thermal expansion of Ag and NaCl bulk. In the temperature range 300–550 K, we measured for the Ag lattice constant a mean coefficient of linear thermal expansion of (2.08 ± 0.04)  105 K1, in good agreement with experimental data from the literature [33] (red dash-dot–dot line). Interestingly, our results on the thermal expansion of a 1 ML thick NaCl film on Ag(1 0 0) differ from both experimental [33] (black dash-dot line) and calculated data [34] for NaCl bulk. Above 400 K, we measured for the 1 ML thick NaCl film on Ag(1 0 0) a mean coefficient of linear thermal expansion of (9.1 ± 0.3)  105 K1, which is almost twofold higher than that of NaCl bulk in the temperature range 400–550 K [33]. The thermal expansion coefficients of thin films are known to be sensitive on both the film thickness and the presence of structural defects in the films, which are inherent of thin film growth by vacuum-deposition techniques [35–37]. On the basis of the relative variation of the Ag and NaCl lattice constants (Fig. 8e), we calculated the ratio between the two lattice constants as a function of the temperature (Fig. 8f). The value of the Ag lattice constant at 300 K was adapted from the literature [30]; for the value of the NaCl lattice constant at 300 K we used the experimentally determined value (0.9 ± 0.2% contracted). As a result of the heterogeneous thermal expansion of NaCl/Ag(1 0 0), the NaCl/Ag lattice constant ratio increases with the temperature, by up to 1.2 ± 0.5% at 550 K with respect to its value at 300 K. The possible influence of this phenomenon on the azimuthal mosaic distribution of NaCl films grown on Ag(1 0 0) will be discussed below. 4. Discussion 4.1. Growth of the first single/double NaCl layer In the case of 0.5 ML thick NaCl films grown at 200 K, we observed additional arcs due to multiple-scattering (see Fig. 6a), a phenomenon which generally occurs in the case of ultra thin layers, typically one monolayer in actual thickness. We observed these arcs neither for thicker NaCl films (10 ML in thickness) grown at 200 K nor for 0.5 ML thick NaCl films grown at higher temperatures (300 K and above). From earlier studies in the field, it is

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known that the growth of NaCl films on single-crystalline surfaces starts by the formation of either single-layered [22,26] or doublelayered islands [5,38], namely by assembling NaCl ion pairs that lie flat or stand up on the surface, depending on the substrate nature. Moreover, it has been reported that additional NaCl layers can start to form on top of the first single or double layer before its completion [26]. In a recently published STM study on NaCl/ Ag(1 0 0), Ploigt et al. [29] found that NaCl submonolayers are double-layered with a great majority at room and high temperature (up to 473 K) and that growth temperature mainly influences the shape and the size of NaCl islands. It has also been reported that mono-layered LiF dendrites can form on Ag(1 1 1) at low temperature (77 K) [15,16]. Therefore, we suggest that mono-layered NaCl islands preferentially form on Ag(1 0 0) at low growth temperature. These mono-layered islands are presumably metastable and a transition to the more stable double-layered islands can be induced by heating. This scenario would be consistent with our observation of the disappearance of the multiple-scattering circles in LEED patterns upon annealing of the thinnest films grown at 200 K, and the absence of the multiple-scattering effects for thicker films grown at 200 K or thin films grown at 450 K. 4.2. Origin of the azimuthal mosaicity As previously reported by Pivetta et al. [19], we find NaCl growth on Ag(1 0 0) at RT to yield rotational mosaics with two main azimuthal orientations, namely with the NaCl unit cell azimuthally aligned or rotated by 45° with respect to that of Ag(1 0 0). Since NaCl growth on Ag(1 0 0) is incommensurate, the origin of this preference for the 0°- and 45°-orientations is not obvious. Actually, the large (38%) lattice mismatch between NaCl(1 0 0) and Ag(1 0 0) is unfavourable for a strict commensurate growth of azimuthally aligned NaCl layers. On the contrary, 45°-rotated NaCl domains are predestined for a commensurate c(2  2) superstructure on Ag(1 0 0), provided that an expansion of the NaCl lattice by only 2.2% occurs. However, such an expansion was experimentally excluded. Pivetta et al. [19] analysed the Moiré effect on STM images of 45°-oriented NaCl islands and concluded to a contraction of NaCl lattice constant by 0.8% with respect to the bulk. Although a strict commensurate growth of NaCl on Ag(1 0 0) is not observed, higher-order commensurability may occur, namely the existence of NaCl superstructures with a commensurate supercell much larger than the primitive unit NaCl cell. Such NaCl superstructures can be found not only at 0°- and 45°-orientations but potentially at any azimuthal domain orientation. To determine the azimuthal angles at which higher-order commensurability is susceptible to occur, we used a simple geometric approach (see Fig. 9). We superimposed a model of the Ag(1 0 0) surface (black dots) with a model of the NaCl lattice (big red and small green circles) and we gradually rotated the latter with respect to the former. Each time that we recognized a possibility to achieve higher-order commensurability, we optimized the lattice constant of NaCl in this way. Fig. 9 illustrates this method with examples of 3.2°and 5.2°-orientations of the NaCl lattice. Table 2 describes the first higher-order commensurate superstructures that we identified by this method, with the associated orientations of NaCl unit cell, the matrices that define the unit vectors of the NaCl supercells from those of the primitive unit cell of Ag(1 0 0), the sizes of the NaCl supercells, and finally the NaCl/Ag lattice constant ratios (aNaCl/ aAg) that are required for these superstructures to occur. The NaCl/Ag lattice constant ratios in Table 2 are to be compared with the experimental values of Fig. 8f, e.g. aNaCl/aAg = 1.368 ± 0.003 at 300 K. Five horizontal dashed lines have been added to Fig. 8f to that purpose, each of them indicating the aNaCl/aAg ratio theoretically associated with a higher-order commensurable structure of

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E. Le Moal et al. / Surface Science 603 (2009) 2434–2444

pffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi Fig. 9. Models for (a) ð 25  25ÞR tan1 ð4=3Þ and (b) ð 61  61ÞR tan1 ð5=6Þ higher-order commensurate structures on NaCl of Ag(1 0 0). The superstructures require azimuthal rotations of the primitive NaCl unit cell by 3.2° and 5.2° with respect to that of Ag(1 0 0), and aNaCl/aAg ratios of 1.387 and 1.381, respectively. Black dots, small green and large red circles indicate the positions of silver atoms and sodium and chlorine ions in the (1 0 0) plane. Straight and dashed black lines define the primitive Ag and NaCl unit cells and the supercell of the NaCl superstructures, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2 Structural parameters of possible higher-order commensurate NaCl superstructures on Ag(1 0 0). Noted are the azimuthal rotation of the primitive unit cell of NaCl with respect to that of Ag(1 0 0) and the NaCl/Ag lattice constant ratio (aNacl/aAg) that is required for commensurability. The experimentally observed domain orientations are given in the last column, together with the intervals of growth temperature within which they have been observed. Rotation of the primitive unit cell

Supercell matrix 

0°    45° 3.2° 5.2°

  

6.1°  8.2°  14.0°

4 0 7 0

0 4 0 7

aNaCl/aAg

Experimental observations

11.6  11.6

(4  4)

1.333

0° observed at all growth temperatures

20.2  20.2

(7  7)

1.400

31.8  31.8

(11  11)

1.375

4.09  4.09

pffiffiffi pffiffiffi  c(2  2) or ð 2  2ÞR45

1.414

45°

14.4  14.4

pffiffiffiffiffiffi pffiffiffiffiffiffi ð 25  25ÞR tan1 ð4=3Þ

1.387

200–450 K 3.0°

22.6  22.6

pffiffiffiffiffiffi pffiffiffiffiffiffi ð 61  61ÞR tan1 ð5=6Þ

1.381

400–500 K 5.7°

31.3  31.3

pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi ð 117  117ÞR tan1 ð6=9Þ

1.385

400–500 K

9.14  9.14

pffiffiffiffiffiffi pffiffiffiffiffiffi ð 10  10ÞR tan1 ð1=3Þ

1.414

Not observed

11.9  11.9

pffiffiffiffiffiffi pffiffiffiffiffiffi ð 17  17ÞR tan1 ð4Þ

1.374

13.5° 323–450 K



0 11

1 1

1 1

3 4

4 3

6 5

5 6

9 6

6 9

4 1

Conventional Wood’s superstructure



11 0

3 1

Supercell size (Å  Å)

1 3 1 4



     

Table 2. The lattice of the NaCl films expands stronger than that of the Ag(1 0 0) surface; therefore the adsorbate–substrate epitaxial relationship is expected to change. Hence one may expect that some of the superstructures in Table 2 are favourable within given intervals of temperature, which would explain the evolution of the azimuthal mosaic distribution shown in Fig. 4b. The three first higher-order commensurate NaCl structures that we identified for azimuthally aligned NaCl domains are (4  4), (7  7) and (11  11) superstructures. According to the required aNaCl/aAg ratio (see Table 2) and Fig. 8f, one would expect none of them to occur at RT and only the (11  11) superstructure is likely to exist at higher temperatures. Besides, structures with higher-order commensurability were found for azimuthal orientations of 3.2°, 5.2°, 6.1°, 8.2° and 14°, providing aNaCl/aAg ratios ranging from 1.374 to 1.414, which also excludes any of them to be achieved at

RT. However, most of them (excepted that corresponding to 8.2°orientation) are likely to exist at higher temperatures. Some of these theoretically derived domain orientations are very close to those experimentally observed at high growth temperatures. Notably, the 3.2°- and 5.2°/6.1°-orientations of Table 2 could be identified with the 3.0°- and 5.7°-orientations of Fig. 5, observed at 500 K. A correspondence may also exist between the 14°-orientation of Table 2 and the 13.5°-orientation of Fig. 5, observed at 450 K. Assuming that higher-order commensurability is energetically preferred at the NaCl/Ag interface, we may expect to be able to predict the temperature intervals of probable existence of the NaCl structures as well as the main trends in the azimuthal mosaic distribution, solely from the comparison of aNaCl/aAg ratios in Table 2 and those in Fig. 8f. For instance, we would expect 14°-oriented

E. Le Moal et al. / Surface Science 603 (2009) 2434–2444

domains to be observed between 350 K and 450 K. Above 450 K, 3.2°- and 5.2°/6.1°-oriented domains would be favoured at the expense of 14°-oriented ones. Finally, 8.2°- and 45°-oriented domains are not expected at all. Remarkably, this description sticks relatively close to our experimental observations. Furthermore, the emergence of a sharp and intense peak at 0° for growth temperatures above 400 K could coincide with the formation of a (11  11) superstructure. As shown in Table 2, this superstructure requires a aNaCl/aAg ratio of 1.375, which is achieved at a temperature between 400 K and 450 K (see Fig. 8f). Nevertheless, the existence of stable domain orientations other than 0° and 45° is intriguing because this feature seems not to be consistent with a scenario where the domain orientation is determined at the very first steps of growth. Once the critical, but still small, nucleus of a NaCl island has formed, the electrostatic interactions with the surface potential can possibly favour the 0° and 45°-orientations with respect to the substrate, but unlikely ±3.0° and ±5.7°-orientations. If the latter orientations actually correspond to higher-order commensurability, the NaCl domains need to be sufficiently large to provide enough points of coincidence between the adsorbate and substrate lattices to sufficiently reduce the interface energy, and thus stabilize the domain orientation (see supercell sizes in Table 2). Therefore, we suggest that the azimuthal mosaic distribution in NaCl films on Ag(1 0 0) is not determined at the very first steps of growth, but rather results from a mechanism of selection of the most stable domain orientations. This mechanism would be based on the diffusion of NaCl molecules on the substrate surface, namely within the uncovered areas between the NaCl islands. The adsorbed NaCl molecules at the edges of the most stable domains would less frequently diffuse away; therefore these domains would grow at the expense of the less stable ones. Since the diffusion rates of adsorbed molecules increase with the substrate temperature, such a mechanism is expected to be more efficient at 500 K than at 200 K. Similarly, the highest efficiencies are expected at the lowest deposition rates. This scenario is consistent with our experimental observations (see Figs. 4b and 7c). It would also explain the presence of metastable 45°-oriented domains at 200 K, for which no lattice coincidence with Ag(1 0 0) was found, and their disappearance upon annealing at 450 K (see Fig. 7a). Moreover, the mechanism of selection can influence the azimuthal mosaic distribution as soon as NaCl domains start to nucleate, and not only after the growth is completed. Therefore, holding the sample at high temperature during the entire growth process and annealing the sample after the growth are not expected to yield the same result, which has been found experimentally (see Fig. 7b). From these observations, we conclude that the highest selectivity of a specific azimuthal domain orientation is achieved by growing NaCl films at a deposition rate lower than 0.1 ML min1 on the Ag(1 0 0) substrate at a constant high temperature between 450 K and 500 K. Finally, it is noteworthy that the description given above allows to predict only the domain orientations for which higher-order commensurability can be identified. These orientations correspond to stable equilibrium states at given NaCl/Ag lattice constant ratios. No trivial higher-order commensurability with an acceptable aNaCl/ aAg ratio was found for the 45°-oriented domains. However, the presence of these likely (on the basis of the above noted geometric considerations) less stable domains was detected at higher growth temperatures than 200 K and even for NaCl films directly grown at 450 K. A perfect alignment of the NaCl [0 1 0] axis with the Ag [0 1 1] axis was observed for the 45°-oriented domains. Hence the 45°-orientation must also minimize the interface energy despite the absence of a higher-order commensurability. Therefore, we conclude that a complete description of the azimuthal mosaic distribution needs to be based on the calculation of the interface energy [39] and go beyond the simple geometric consideration given above.

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5. Conclusions The incommensurate growth of NaCl on Ag(1 0 0) yields rotational mosaics in the (1 0 0) plane. Most of the NaCl domains are oriented with their unit cell aligned with that of Ag(1 0 0), with a mosaic spread of less than 14° at RT. The NaCl unit cell is laterally contracted in the first layers by 0.9% with respect to the bulk. At higher growth temperatures, the azimuthal mosaic distribution sharpens and shows distinct orientations. Increasing the substrate temperature after growth can cause significant changes, but not in the same amount as a high temperature during the growth. For thick multilayered NaCl films, the azimuthal mosaic distribution seems to be definitive and cannot be modified by post-growth annealing treatments. We propose that the evolution of the azimuthal mosaic distribution at high temperatures of growth is due to the relative expansion of the NaCl lattice with respect to that of Ag(1 0 0) and the possibilities of a higher-order commensurability of the NaCl and Ag(1 0 0) interfaces that ensues from this expansion. Besides, we suggest that the molecular diffusion between the NaCl domains plays a crucial role in the selection of the most stable domain orientations. Hence the azimuthal mosaic distribution depends both on thermodynamics (the favoured domain orientations are those minimizing the interface energy) and the kinetics (the selection of these favoured orientations is driven by diffusion processes). To conclude, we provided new aspects to the understanding of NaCl growth on Ag(1 0 0), which can probably be applied more generally to other heterogeneous interfaces. In particular, our approach to optimize the NaCl/Ag(1 0 0) epitaxy may be of significant interest to improve the quality of thin insulating films on conductive substrates, both in fundamental and applicative purposes. Acknowledgements The authors wish to acknowledge valuable discussions with Dr. M. Pivetta (EPFL, Lausanne). This project is supported by the Alexander von Humboldt Foundation through a Post-doctoral fellowship and the DFG (Deutsche Forschungsgemeinschaft) Research Unit 557 ‘‘Light Confinement and Control with Structured Dielectrics and Metals”. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

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