Abstract
The lowenergy structures (LESs) of adatom clusters on a series of metal facecentered cubic (fcc) (110) surfaces are systematically studied by the genetic algorithm, and a simplified model based on the atomic interactions is developed to explain the LESs. Two different kinds of LES group mainly caused by the different next nearestneighbor (NNN) adatomadatom interaction are distinguished, although the NNN atomic interaction is much weaker than the nearestneighbor interaction. For a repulsive NNN atomic interaction, only the linear chain is included in the LES group. However, for an attractive one, type of structure in the LES group is various and replace gradually one by one with cluster size increasing. Based on our model, we also predict the shape feature of the large cluster which is found to be related closely to the ratio of NN and NNN bond energies, and discuss the surface reconstruction in the view of atomic interaction. The results are in accordance with the experimental observations.
PACS: 68.43.Hn; 68.43.Fg.
Keywords:
supported cluster; structure; shape; metal surfaceIntroduction
In the nextgeneration microelectronics and ultrahighdensity recording, the fully monodispersed nanostructures are believed to be one of the most promising materials [1]. In order to fabricate such nanostructures, knowledge of the morphology of nanoclusters on surfaces becomes enormously important. So far, numerous experimental observations and theoretical investigations into structures of clusters have been reported on transition and noble fcc metal surfaces, e.g., fcc(111), fcc(100), and fcc(110) surfaces [210]. However, such studies mainly focus on the lowestenergy structures. For the structures with energy close to the lowest one, which are named lowenergy structures here, investigations and discussions are far from enough. At the usual experimental temperature, besides the lowestenergy structure, the lowenergy ones also appear frequently owing to thermal effect and usually play significant role in many surface thermodynamic processes [11]. In earlier publications, the lowenergy structures of adatom cluster on fcc(111) have been systematically studied, and it has been shown how the atomic interactions determine the equilibrium structures and shapes of the supported clusters [10]. In order to get a global view on the morphology of supported homoepitaxial clusters, here we investigate further a series of metal homoepitaxial clusters on fcc(110) surfaces, whose structure characteristics are far different from those of fcc(111).
Calculation method
Four metal homoepitaxial systems are investigated: Ni, Cu, Pt, and Ag. The atomic interactions are described by semiempirical potentials. The semiempirical potential might not be as accurate as the firstprinciple method in describing atomic interaction, but it enables us to study systematically clusters in a large size range, which is quite expensive for the latter one. Considering of the shortcoming of the semiempirical method, here we focus on the relationship between the atomic interaction and the structure of cluster, which is not sensitive to the accuracy of potential. However, we still choose the potentials carefully that nicely describe the surface diffusion [12,13]. For Ni and Cu, the atomic interactions are described by the embeddedatom method (EAM) potential given by Oh and Johnson [14] and the potential developed by Rosato, Guillopé, and Legrand (RGL) on the basis of the secondmoment approximation to the tightbinding model [15,16], respectively. While, for Pt and Ag, the atomic interactions are all modeled by the surfaceembedded atom method (SEAM) potential given by Haftel and Rosen for the surface environment [17,18].
Clusters are put on a slab containing 12 atom layers in Z direction, in which three bottoms of them are fixed to simulate a semiinfinite slab, while the atom numbers in X and Y directions vary with the cluster size n. Periodic boundary conditions are applied in X and Y directions. The clusters with size n = 2 to 39 are studied. Structures are optimized according to their energy by the genetic algorithm (GA), which has been described in detail in our previous publications [7,8].
Results and discussion
In the present work, we investigate the structures whose energy differences with the lowest one are smaller than 0.12 eV. These structures are defined as the lowenergy structures (LESs). According to the Boltzmann distribution, the probability of finding a structure whose energy is 0.12 eV higher than the lowest one is less than 1% at room temperature. Under the definition of LES above, we see that the lowenergy structures obtained by our genetic algorithm are all twodimensional on the surfaces studied here, i.e., threedimensional structures are excluded from the LES group for their higher energy. However, on the different surface, the structure features are different as expected. On Ni(110), Ag(110), and Cu(110) surfaces, various types of structures are included in the LES group. In Figure 1, for example, the lowenergy structures of cluster n = 15 obtained by our genetic algorithm on Cu(110) and Pt(110) are given. On Cu(110) surface, as shown in Figure 1a, both the linear chain and twodimensional islands appear. The energy of linear chain is lower than that of threerow islands and higher than those of short tworow islands. While on Pt(110) surface, as shown in Figure 1b, there is only one structure type in the LES group, i.e., the linear chain along the []. For other cluster sizes, the results are similar to those of cluster n = 15 on Ni(110), Ag(110), Cu(110), and Pt(110), i.e., the structure types of LES on Ni(110), Ag(110), and Cu(110) surfaces are various and change with the cluster size, while on Pt(110) surface, only one type of structure is included in LES group.
Figure 1. Lowenergy structures of cluster n = 15 (a) on Cu(110) and (b) on Pt(110) surface. From structures 1 to 7, the energy is increasingly higher. The nearestneighbor (NN), next nearestneighbor (NNN), and third nearestneighbor (TNN) bonds are indicated in (c).
In order to understand the results on Ni(110), Ag(110), Cu(110), and Pt(110) surfaces, and give a general relationship between the structure and the atomic interaction, we try to give a simplified or approximated model in the following for describing the energy of the system, which is based on only the twobody atomic interaction. We decompose the total internal energy E of the system into three parts:
where E_{aa}, E_{as}, and E_{slab }refer to the energies contributed by the adatomadatom interaction, the adatomsubstrate interaction, and the bare slab internal interaction, respectively. For E_{aa}, we consider the nearestneighbor (NN), next nearestneighbor (NNN), and third nearestneighbor (TNN) interactions, and then E_{aa }can be written as:
where C_{nn}, C_{nnn}, and C_{tnn }refer to the numbers of NN, NNN, and TNN bonds, respectively. E_{nn}, E_{nnn}, and E_{tnn }are the energies of NN, NNN, and TNN bonds, respectively. As shown in Figure 1c, one NNN bond generally corresponds to two TNN bonds, i.e., C_{tnn }≈ 2C_{nnn}. Therefore, the last two terms in the right side of Equation 2 can be written as C_{nnn}E_{nnn}+C_{tnn}E_{tnn}=C_{nnn}(E_{tnn+}2E_{tnn}). For convenience, we set (E_{nnn }+ 2E_{tnn}) as , i.e., . Considering the number of TNN bonds has fixed proportion with that of NNN bonds, and the TNN atomic interaction is much weaker than the NNN atomic interaction, we regard as the effective bond energy of NNN bond. Therefore, Equation 2 can be written as:
The values of E_{nn }and can be obtained by comparing the cohesive energies of structures with different C_{nn }and C_{nnn }[8]. For the adatomsubstrate interaction, our calculation shows that it is not sensitive to the configuration of cluster and thus E_{as }can approximately be viewed as a linear function of cluster size n, i.e., , where refers to the cohesive energy contributed by adatomsubstrate interaction of one adatom. Then, Equation 1 can be written as:
Considering that the energy contributed by the bare slab internal interaction, i.e., E_{slab}, can be approximately viewed as invariant, we then get the energy difference ΔE between the two structures as following:
Equation 5 shows that the energy difference of two structures results from the different nearestneighbor and effective next nearestneighbor adatomadatom interactions.
By examining the structure feature of cluster on fcc(110) surface, one can see the numbers of NN and NNN bonds satisfy:
in which r and l are the numbers of rows and lines of the cluster, respectively. For example, structure 1 in Figure 1a, r = 2 and l = 8, then C_{nn }= 13 and C_{nnn }= 7. With Equations 4 and 6, total internal energy can be written as:
where . In Equation 7, only one term is relevant to the structure. We denote as structure factor Φ, i.e.,
With this simplified model Equation 7, for different structures of a cluster, we can predict their energy sequence just by comparing the values of Φ, which can be easily obtained by counting the numbers of rows and lines. Note that the bond energy E_{nn }is always positive, the larger structure factor Φ then means the higher energy of the structure, and vice versa. In other words, the lowestenergy structure should have the smallest structure factor Φ.
On Pt(110) surface, our calculation shows that the bond energy is negative, which means the effective next nearestneighbor adatomadatom interaction is repulsive, and then the parameter . According to Equation 8, when r is minimized and l is maximized, i.e., r = 1 and l = n, structure factor Φ reaches the minimum and the corresponding structure has the lowest energy. The r = 1 and l = n suggest that the cluster has the linear chain structure. Therefore, the linear chain is always the lowestenergy structure on Pt(110). In Figure 2, we give the relative energy distribution of linear chain, broken chain, and tworow island. For the broken chain and tworow island, only their lowest energies are shown for simplification. As shown in Figure 2, there are obvious gaps among the tworow island and linear and broken chains, and these gaps generally keep unchanged with cluster size increasing. For the broken chain, we have r = 2 and l = n, and for the tworow island, r = 2 and l ≤ n − 1. According to Equation 7, the energies of broken chain and tworow island are much higher than that of linear chain; the energy differences with linear chain are, respectively, E_{nn }and ≥(). Based on our calculation, both E_{nn }and () are much larger than 0.12 eV, the energy difference for defining the lowenergy structure here. Therefore, both the tworow island and broken chain are always excluded from the LES group. As to islands with more than two rows, their energies are even much higher than that of tworow island because they have more NNN and less NN bonds, and they are also not included in the LES group. That is to say, the simplified model Equation 7 explains well the result of GA optimization on Pt(110) surface, where only one structure type, i.e., the linear chain appears in the LES group.
Figure 2. The relative energy distribution. For simplification only the lowest energies of liner chain (solid squares), broken chain (open squares), and tworow island (dots) on Pt(110) surface are given. The structures of cluster n = 15 as an example are shown in the right. The number in the bracket means the number of NN and NNN bonds, respectively.
On Ni(110), Cu(110), and Ag(110) surfaces, different from the case on Pt(110), the calculation shows that the bond energy is positive. Then, , which means, according to Equations 7 and 8, the structures with low energy on Ni(110), Cu(110), and Ag(110) surfaces should have proper numbers of rows and lines to ensure low structure factor Φ. For example, n = 15 on Cu(110) as shown in Figure 1a, the proper values include r = 2, l = 8; r = 1, l = 15; r = 3, l = 6, etc., because the structures with these values have low energy and all of them are included in the LES group. If the structures with the same row are classified as one structure type, then the LES group on Cu(110), also on Ni(110) and Ag(110) surfaces, contains several types of structures. When the cluster size increases, it is easy imaginable that the structure types will change for keeping the proper values of r and l. It is indeed true as shown in our GA optimization results and closely related to the type change of the lowestenergy structure, the details of which are described later.
In our previous work [8], we reported the type change of the lowestenergy structure at critical size . Here, with the model Equation 7, we can further give the explicit expression for . When the lowestenergy structure changes from R rows to R + 1 rows, the number of lines will change from L to (L − dl) correspondingly, where dl is the decrement of number of lines. The change of the structure type at , according to Equation 7, means that the configuration with (R + 1) rows and (L − dl) lines instead of R rows and L lines has the lowest Φ. Namely R+L/ξ>R+1+(Ldl)/ξ, i.e., dl>ξ. The dl should be an integer, and then dl>ξ means
For example, on Cu(110) surface, our calculation gives the ratio of E_{nn }and , which is ξ = 5.26, and then dl = 6. In Figure 3, we give some structures of Rrow and (R + 1)row types (R = 2) whose energies are the lowest in their own type. At the critical cluster size , Rrow structure changing to (R + 1)row structure also means that their energy difference reaches minimum. According to our model Equation 7, in which only NN and NNN bonds are considered, the most probability for these two structures is that they are all perfect rectangle as shown in Figure 3 at size n = 36. Therefore, we have . Then whether n = RL = (R+1)(Ldl) is just the critical size ? We see cluster n = 35, at which Equation 9 is also satisfied, i.e., dl = Int(ξ)+1 = 6, and the relationship
Figure 3. The lowestenergy structures with two and three rows for cluster n = 34, 35 and 36, respectively.
is still valid. If we continue to subtract one atom, i.e., n = 34, the Rrow structure with oneless line comparing with that of n = 36 appears, as shown in Figure 3, because such structure can keep the energy being lowest according to the model Equation 7. As a result, from Rrow structure to R + 1 one at n = 34, dl = 5 no longer satisfies Equation 9. Therefore, on Cu(110) surface, the critical size for tworow type changing to threerow one should be , and it can be written in general form,
With Equations 9 and 10, we can finally fix the critical size, which satisfies:
Therefore, according to Equation 11, we can predict the type change of the lowestenergy structure. Still take Cu(110) as an example (ξ = 5.26), from Equation 11, the change of the lowestenergy structure from one linear chain to tworow island will occur at , and tworow island to threerow one at , these predictions for the lowestenergy structure are in accordance with our GA optimization result. In Figure 4, we further give the relative energy distribution of the four structure types on Cu(110), the crossing of the lines means the change of the structure type, which just appears at the cluster sizes as Equation 11 given, i.e., at n = 12 and 35. On Ni(110) and Ag(110) surfaces, the and are also obtained from Equation 11 and given in Table 1, which are consistent with GA optimization results. On Ag(110) for example, ξ is 37.56 and then and , which are much larger than those on Cu(110) (see Table 1). Accordingly, as shown in Figure 5, the type change of the lowestenergy structure is much slower than that on Cu(110) with the cluster size increasing.
Figure 4. The relative energy distribution. The energies of liner chain (solid squares), broken chain (open squares), tworow islands (dots), and threerow islands (open circles) are given on Cu(110) surface. Only the lowest energies are considered as before.
Table 1. The energies of NN and effective NNN bonds and their ratio on metal surfaces
Figure 5. The relative energy distribution. Same as Figure 4, but for Ag(110) surface.
Corresponding to the type change of the lowestenergy structure, the lowenergy structures studied here show an interesting stepwise replacement in type with the cluster size increasing. For example, on Cu(110), there is only linear chain in the LES group for n ≤ 5. At n = 6, the tworow island appears in the LES group. Our GA optimization shows that when the cluster size n increases, the energy of tworow island is increasingly lower than that of the linear chain, and at n = 12, as mentioned above, the tworow island becomes the lowestenergy structure of the cluster. When the size increases further, the linear chain gradually disappears from the LES group, meanwhile the threerow island appears. The tworow island maintains in the group. At n = 16, there is no linear chain in the LES group. When the cluster size becomes much larger than 16, similar to the case of linear chain, the energy of tworow island is increasingly higher than that of threerow island. At n = 35, as mentioned above, the threerow island becomes the lowestenergy structure. When cluster size increases further, the tworow islands are gradually excluded from the LES group, meanwhile the fourrow island appears in the LES group. At that time, the threerow island maintains in the group. In one word, when the cluster size increases, the structures with more rows replace the ones with fewer rows step by step. The stepwise replacement of the lowenergy structures also appears on Ag(110) and Ni(110) surfaces, the difference is only the speed of the replacement owing to the different ratio ξ and then . For example, on Ag(110) surface, the speed of the replacement with the cluster size increasing is much slower than that on Cu(110) like Figures 4 and 5 for the change of the lowestenergy structure.
In terms of NN and NNN atomatom interactions, we give a simple model Equation 7 to describe the energy of the cluster adsorbed on fcc(110) surface. In the above, we see that the model explains well the distinguishing features of the lowenergy structures obtained by our GA optimization, including structure type varying with the surface species and cluster size, which suggest that the model is reasonable. The most important is that based on our model Equation 7, we can further explore the equilibrium shape of large islands on fcc(110) surfaces, which is difficult to be obtained directly by GA optimization owing to the heavy computation. For numbers of rows and lines in cluster, we have
where d is the number of atoms needed for the cluster to form a complete r × l rectangular island, and it satisfies 0 ≤ d < l. For example, the structure (7) in Figure 1a has d = 3. When the cluster size n increases, the value of d linearly oscillates from 0 to (l − 1). Considering that the problem we are interested in here is the general shape of the lowenergy islands in equilibrium state, we take the average value of d in Equation 12, i.e., d = l/2. Note that r and l need to have proper values to minimize the energy of cluster, i.e., minimize Φ Equation 8, and then with Equation 12 and d = l/2, we have:
If the right side of Equation 13 is not an integer, then the close one which minimizes Φ is taken as the value for r or l. Then, we obtain the aspect ratio A of the equilibrium island:
where a is distance between two nearest neighbor atoms. Note that we have used for large clusters and assumed that each NN bond has the same length in Equation 14. Therefore, the equilibrium shape of large cluster only relates with ξ, i.e., the ratio of NN and NNN bond energies. If the cluster has large ξ, the aspect ratio A is small, and then the equilibrium shape is long in [] direction and narrow in [001] direction. If the ξ is small, then the equilibrium shape with large aspect ratio A appears short and wide. For clusters on Ag(110), as shown in Table 1, our calculation shows that A is small, only 0.038. Such aspect ratio suggests the equilibrium shape of large clusters on Ag(110) is striplike in [] direction, and it is consistent with the experimental observation in general [19].
From the distinguishing features of the structures in LES group and the simplified atomic interaction model Equation 7, we can further discuss the surface reconstruction qualitatively. On Pt(110), as mentioned above, there is only linear chain in the LES group, the reason is that the effective next nearestneighbor atomic interaction in cluster is repulsive. The islands are all excluded from the LES group. The result suggests that the Pt adatoms on Pt(110) do not tend to form closepacked configuration but prefer the loose one which is continuous in [] direction but discontinuous in [001] direction, e.g., structure (a) in Figure 6, where two types of structures for large adatom cluster on fcc(110) are shown. The calculation shows that the energy of loose configuration as the structure (a) in Figure 6 is indeed much lower than that of the compact one as the structure (b) in Figure 6, and thus the former configuration has much higher frequency to occur than the latter one. When the cluster size increases, the compact configuration like the island (b) in Figure 6 forms the regular unreconstructed surface, while the loose configuration as structure (a) will form the surface with (1 × 2) reconstruction. Therefore, on Pt(110) surface, the (1 × 2) reconstruction has much higher frequency to occur than the regular unreconstructed arrangement. In other words, the (1 × 2) reconstruction would occur naturally on Pt(110), which in view of atomic interaction is caused by the repulsive NNN atomic interaction. According to the FIM observation, Pt(110) is indeed naturally form (1 × 2) reconstruction at room temperature [20].
Figure 6. Two types of structures for large adatom cluster on fcc(110) surface. Loose (a) and compact (b) configurations of cluster n = 126.
For cluster on other surfaces, e.g., Cu(110) and Ag(110), different from the case on Pt(110), the compact configuration has much lower energy than the loose one because the effective next nearestneighbor adatomadatom interaction is attractive as mentioned above. Then, on Cu(110) and Ag(110) surfaces, the compact structure such as island (b) in Figure 6 has much higher frequency than structure (a). Therefore, contrary to Pt(110) surface, the Cu(110) and Ag(110) surfaces are unlikely to occur (1 × 2) reconstruction naturally, which are in good agreement with the observation of Zhang et al. [21]. These accordant results including the shape of large islands and the surface reconstruction reflect that our model Equation 7 really works although it is just based on the simplified twobody interaction.
Conclusion
Groups of lowenergy structures are obtained for clusters adsorbed on Ag(110), Ni(110), Cu(110), and Pt(110) surfaces by the genetic algorithm based on the EAM, SEAM, and tightbinding potentials. In order to explain or understand the lowenergy structures, we give a model based on the simplified atomatom interactions. The result shows that the difference of the lowenergy structure on different surface is due to the effective NNN adatomadatom interaction although it is very weak comparing to the NN atomic interaction. For a repulsive NNN atomic interaction, e.g., on Pt(110), there is only one type of structure in the LES group, i.e., linear chain. For an attractive NNN atomic interaction, e.g., on Ag(110), Ni(110), and Cu(110) surfaces, the structure type in the LES group is various, and when the cluster size increases the structure type with fewer rows will be gradually excluded from the LES group and replaced by the new one with more rows. The speed of replacement with the cluster size is determined by the ratio of the NN and NNN bond energies ξ. Based on our model, we also discuss the aspect ratio of the large island and the surface reconstruction on fcc(110) in the view of atomic interaction. It is shown that the aspect ratio is inversely proportional to ξ. On Ag(110) surface, for example, owing to large ξ, the equilibrium shape of the large island is striplike in [] direction. The surface reconstruction is related to the NNN atomic interaction. On Pt(110) surface, the surface is likely to reconstruct naturally at room temperature because of the repulsive NNN atomic interaction. On other surfaces, e.g., Cu(110), however, owing to the attractive NNN atomic interaction, the natural surface reconstruction is unlikely to occur. These results are basically in accordance with the experimental observations.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
PZ, LXM, HZS, and JHZ wrote the computer program together, and PZ also performed the simulations and other calculations. WXZ, XJN, and JZ corrected the program and developed the algorithm. PZ and JZ give the model and explained the results. All the authors participated in the revision and approval of the manuscript.
Acknowledgements
The calculations are performed at the National High Performance Computing Center of Fudan University and Shanghai Supercomputing Center. This work is supported by Chinese NSF (no. 11074042), Major State Basic Research Development Program of China (973 Program) (no. 2012CB934200), and Innovation Program of Shanghai Municipal Education Commission (no. 10ZZ02).
References

Barth JV, Costantini G, Kern K: Engineering atomic and molecular nanostructures at surfaces.
Nature (London) 2005, 437:671679. Publisher Full Text

Wang SC, Ehrlich G: Equilibrium shapes and energetics of iridium clusters on Ir(111).
Surf Sci 1997, 391:89100. Publisher Full Text

Wang SC, Ehrlich G: Diffusion of large surface clusters: direct observations on Ir(111).
Phys Rev Lett 1997, 79:42344237. Publisher Full Text

Roy HV, Fayet P, Patthey F, Schneider WD, Delley B, Massobrio C: Evolution of the electronic and geometric structure of sizeselected Pt and Pd clusters on Ag(110) observed by photoemission.
Phys Rev B 1994, 49:56115620. Publisher Full Text

Yin C, Ning X, Zhuang J, Xie Y, Gong X, Ye X, Ming C, Jin Y: Shape prediction of twodimensional adatom islands on crystal surfaces during homoepitaxial growth.
Appl Phys Lett 2009, 94:183107183109. Publisher Full Text

Fernandez P, Massobrio C, Blandin P, Buttet J: Embedded atom method computations of structural and dynamical properties of Cu and Ag clusters adsorbed on Pd(110) and Pd(100): evolution of the most stable geometries versus cluster size.

Zhuang J, Kojima T, Zhang W, Liu L, Zhao L, Li Y: Structure of clusters on embeddedatommethod metal fcc (111) surfaces.

Sun Z, Liu Q, Li Y, Zhuang J: Structural studies of adatom clusters on metal fcc(110) surfaces by a genetic algorithm method.

Zhang P, Xie Y, Zhang W, Ning X, Zhuang J: Different magic number behaviors in supported metal clusters.
J Nanopart Res 2011, 13:18011807. Publisher Full Text

Zhang P, Xie Y, Ning X, Zhuang J: Equilibrium structures and shapes of clusters on metal fcc(111) surfaces.
Nanotechnology 2008, 19:255704255714. PubMed Abstract  Publisher Full Text

Wang SC, Kürpick U, Ehrlich G: Surface diffusion of compact and other clusters: Irx on Ir(111).
Phys Rev Lett 1998, 81:49234926. Publisher Full Text

Zhuang J, Liu L: Global study of mechanisms for adatom diffusion on metal fcc(100) surfaces.
Phys Rev B 1999, 59:1327813284. Publisher Full Text

Xie Y, Ma L, Zhang P, Cai X, Zhang W, Gan F, Ning XJ, Zhuang J: Reversible atomic modification of nanostructures on surfaces using directiondepended tipsurface interaction with a trimerapex tip.
Appl Phys Lett 2009, 95:7310573107. Publisher Full Text

Oh DJ, Johnson RA: Simple embedded atom method model for fcc and hcp metals.
J Mater Res 1988, 3:471478. Publisher Full Text

Rosato V, Guillopé M, Legrand B: Thermodynamical and structural properties of fcc transition metals using a simple tightbinding model.
Philos Mag A 1989, 59:321336. Publisher Full Text

Cleri F, Rosato V: Tightbinding potentials for transition metals and alloys.
Phys Rev B 1993, 48:2223. Publisher Full Text

Haftel MI: Surface reconstruction of platinum and gold and the embeddedatom model.
Phys Rev B 1993, 48:26112622. Publisher Full Text

Haftel MI, Rosen M: Moleculardynamics description of early film deposition of Au on Ag(110).
Phys Rev B 1995, 51:44264434. Publisher Full Text

Morgenstern K: Direct observations of the (1 × 2) surface reconstruction on the Pt(110) plane.
Phys Rev Lett 1985, 55:21682171. PubMed Abstract  Publisher Full Text

Robinson IK, Eng PJ, Romainczyk C, Kern K: Xray determination of the 1 × 3 reconstruction of Pt(110).
Phys Rev B 1993, 47:1070010705. Publisher Full Text

Zhang JM, Li HY, Xu KW: Reconstructed (110) surfaces of FCC transition metals.
J Phys Chem Solids 2006, 67:16231628. Publisher Full Text