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A Three-modal Epitaxial Adsorption of Formamide (HO-C-NH
2) on the {111}
L. Pastero,
a,bD. Aquilano
aThe whole series of the face centred cubic (f.c.c) alkali halides, from to LiF to RbI, has been crystallized from
aqueous solutions in the presence of variable amounts of formamide (HO-C-NH
2). Scanning electron
microscope images show that the corresponding morphology of the grown crystals is not homogeneous, within
the whole crystal series, and that the {111} octahedron does appear and compete with the {100} cube only in
three separated crystal domains: (NaF), (LiBr, RbF, NaCl) and (KCl, NaI, RbCl, KBr). Starting from our preceding
finding about the formation of the NaCl/formamide anomalous mixed crystals and recollecting the peculiar
{100}+{111} habit change of NaCl growing from pure aqueous solution, we propose that formamide can be
adsorbed as 2D epitaxial layer on the {111} surfaces of the f.c.c. alkali halides according to a three-modal
distribution
1. Introduction
The morphological change of the f.c.c. alkali halides crystals grown from water/formamide (HO−C−NH2) solutions represents a long debated case study, and the {100}→{100}+{111}→{111} habit variations of NaCl is by far the most investigated.
Gille and Spangenberg1 first found this habit change when evaporating NaCl aqueous solutions containing formamide. Much later, in the Kern’s group, the stability domains of {100} and {111} forms (the so-called growth morphodrome) were identified as a function of two parameters: the initial solution supersaturation (β) with respect to NaCl and the formamide concentration.2-5 It was also shown that formamide, analogously to urea,3,4 lowers the critical supersaturation (βcr=1.004) at which the transition {100}→{111} occurs, with respect to that measured in pure aqueous solution (βcr=1.23). This was interpreted by considering that both urea and formamide, due to their similar steric hindrance, do occupy the vacant sites on the octopolar reconstructed {111} form, where the surface electric field reaches its highest value.The stability of the {111} form should further increase since the dipole moment of urea and formamide is definitely higher than that of the water molecule.
Recently, the Vlieg’s group 6(a-e) confirmed the previous observations by evaporating at room temperature NaCl aqueous solutions containing up to 30% of formamide and outlined that its enhances the quality of NaCl crystals. Moreover, through a surface X-ray diffraction (SXRD) on the {111} NaCl−liquid interface structure, it was ascertained that the crystal surface is not reconstructed and that the polar surface is stabilized through the formation of an electrochemical double layer. On this ground, the investigation was extended to the influence of formamide on the habit change of several other f.c.c. alkali halides. It was noticed that the {111} appearance is strictly related to the size of their unit cell parameter and that it ranges from NaF crystals (a0=4.62 Å) to KCl (a0=6.28 Å). 6c Thus, it was concluded that all alkali halide crystals with dimensions outside this range of unit cells crystallize as cubes and that the stable {111} surfaces are due to both volume and shape of “individually adsorbed” formamide molecules. Interestingly, formamide seems do not affect the growth morphology of LiF and KI (octahedron does not appear), since their unit cell size is either too small or too large with respect to that of NaCl. 6b
Starting from these results, Singh et al. studied the interaction of formamide with the LiF, NaCl and KI surfaces employing molecular modeling techniques to investigate the morphological importance of molecular size fitting of formamide on the lattice planes of interest.7 It followed that:
i)- the solvent influences the strength of formamide/ alkali halides interactions;
ii)- concerning NaCl, solvation strongly influences the relative strength of interactions with the various crystal planes, a strong preference being observed for the {111} form which accounts for its appearance.
From all the quoted investigations one could argue that the {001}{001}+{111}{111} habit change of the f.c.c. alkali halides growing from water/formamide solutions is attributed: i) either to the interaction of “randomly adsorbed single formamide molecules” with different adsorption sites (terraces, ledges, kinks) of atomically different substrates ii) or to the fit between the size of adsorbed formamide and that of the unit cell of the crystalline substrate
This is for sure a reasonable chemical way of thinking; actually, we are dealing with a kinetic competition between cube and octahedron and this cannot be explained through such qualitative approximations.
For more than ten years we investigated adsorption/absorption phenomena in the aqueous systems: calcite (CaCO3)/zabuyelite (Li2CO3),8-12 calcite/L-aspartic acid,13 NaCl/formamide,12,14 KCl/(PbCl2, PbCl(OH), KCl·PbCl2),15 and found that
the results play in favor of a more complex interaction mechanism acting between the adsorbed phase and the crystalline substrate. When analyzing only two examples:
i)- Some surfaces of the calcite crystals, growing from water/lithium solutions, intimately interact with the {101} form of the monoclinic zabuyelite; further, and even if the solution is unsaturated with respect to 3D-zabuyelite, Li2CO3 lamellae are captured in the bulk of growing calcite in such a way that epitaxy sets up between zabuyelite domains and the encompassing calcite structure.8-12
In fact, lithium carbonate is not only orderly adsorbed (as a 2D crystal phase) on calcite surfaces but
orderly absorbed as well into the calcite lattice during growth: accordingly, an “anomalous CaCO3/Li2CO3 mixed crystal” can form, in the sense of Gaubert,16
Seifert,17
Johnsen,18
Neuhaus,19
and Hartman,20
limited to the growth sectors of {00.1} and {10.4} forms of calcite (see ESI point A).
ii)- Anomalous NaCl/formamide “single” crystals form when NaCl grows from aqueous solutions in the presence of varying percentage of formamide (0-100%). In fact, the decomposition of XRPD diagrams proved that diffracting {-101} domains of formamide are epitaxially buried into the {111} sectors of the growing NaCl 10,12
(see ESI point B).
In this paper we moved along three steps, having considered that no observation has been shown about the behavior of f.c.c. crystals ranging from NaI to RbI, all having lattice parameters larger than 6.28Å:
i)- The complete f.c.c. series, from LiF (the smallest) to RbI (the largest unit cell) has been crystallized from water/formamide solution.
ii)- The structure of formamide crystal was investigated to find if there is a {hkl} form showing a compactness able to yield self-consistent 2D deposits on given crystalline substrates;
iii)- Lastly, we searched for lattice coincidences between the {100} and {111} surfaces of all f.c.c. alkali halides (host) and formamide (guest) to find the necessary conditions to set up guest/host epitaxial relationships.
Furthermore, it is worth remembering that we confirmed the reliability of the findings of the Kern’s School 2,3,5
and showed that the {111} NaCl octahedron can appear in the growth morphology even in pure aqueous solution, within specific domains of temperature and supersaturation. 21
Finally, owing to the small difference ( 2.5 °C) in the crystallization temperature of formamide and water, we do infer that not only formamide can affect the {111} form of selected alkali halides but that also water could work as formamide if the substrate surfaces offer the suitable adhesion conditions. Then, remembering the trigonal symmetry of the outmost {111} surface structures of alkali halides, we will search for 2D epitaxy of a water layer organized like the {00.1} form of the hexagonal ice. On this ground, we will try to find if a competition can set up between water and formamide on the fresh {111} surfaces of the crystallizing alkali halides.
2. Experimental
Growth experiments were performed both by evaporation and cooling of saturated solutions. All reagents were Sigma-Aldrich analytical grade and ultrapure 18.2 MΩ water was used as solvent, pure or mixed with formamide. A first fact-finding series of growth runs, was performed by saturating a pure (100%) formamide solution with each salt of the f.c.c. alkali halides series. The equilibrium between a water/formamide solution and its salt (saturation) was reached when, after adding the salt to the stirred solution at a given T (saturation temperature), a salt deposit maintains at the bottom of the vessel. Once saturated, the solution was filtered in order to avoid the presence of nuclei favouring the heterogeneous nucleation. The concentration of the salt in solution does depend, obviously, on the chemical nature of the salt.
When crystallization was obtained by evaporation the solvents were allowed to evaporate in oven at 100°C. During this kind of experiments, both supersaturation with respect to the salt and salt/formamide concentration ratio vary. In particular, a competition takes place between the supersaturation rise, due to the evaporation of the solvent, and its simultaneous decrease due to the salt precipitation. Describing the system becomes quite complicated, from the chemical point of view. Consequently, the evaporation experiments were replaced by the rapid-cooling experiments in which the supersaturation decreases with crystal nucleation and growth, and then the competition between precipitation and evaporation is avoided. Crystals obtained by evaporation were filtered and slowly dried at room temperature in order to avoid the rapid nucleation of a secondary generation of crystals. Following this procedure, the contamination of the samples by secondary grown crystals has been avoided; further, washing of the samples is inadvisable due to the high solubility of the alkali halides in water. The rapid-cooling experiments were carried out starting from solutions saturated at 25°C. The equilibrium between a given solution and its salt was reached, at 25°C, in the same way as for the evaporation experiments. The solvent was a formamide/water mixture in which the concentration of formamide was kept constant respectively at 0, 20, 40 and 60 % w/w with respect to water. As in evaporation experiments, after saturation the solution was filtered in order to avoid the presence of foreign nuclei that may act as a substrate for nucleation. Then, the solution was cooled at -10°C in order to reach the supersaturation and precipitate the salts.
At low temperature the nucleation process can be slow: the supersaturated solutions could linger metastable for a while and a little mechanical shock is sometimes necessary in order to trigger the nucleation. Crystals obtained were filtered and dried at -10°C in order to avoid dissolution by humidity condensation on crystals surfaces and the coverage by small secondary grown crystals. Imaging of gold-coated crystals was performed by using a Cambridge S360 scanning electron microscope. Typical working conditions were: EHT 25 kV, probe current 100 pA and working distance 5 mm. In Figure 1, SEM images of NaF, NaCl and KBr crystals are shown. Their morphology is composed by the {100} and {111} forms, with the octahedron dominating as much as the formamide concentration increases. This crystal habit is sensibly representative of the three domains in which the whole alkali halides series (made by 17 species) is divided. In fact, the octahedron appears in the growth habit in the following crystals: NaF, (NaCl, RbF) and (NaI, RbCl, KBr) while, in the remaining 11 crystal species the octahedron has been hardly detected.
Figure 1. SEM pictures of NaF crystals grown at the bottom of the crystallizing vessel from aqueous solution in the presence of
40% formamide (top, left). The corresponding drawing with face indexes (top, right). NaCl cube-octahedra (middle, left) obtained from slow evaporating solution (formamide 80%). Growth of macro-layers on a {111} NaCl form (middle, right). {111} and {100} forms of a KBr crystal obtained from evaporating solution (bottom, left; formamide 50%). Iso-oriented growth islands on a {111} KBr form (bottom, right).
3. The choice of the d101 layer of formamide: searching for epitaxies between formamide and the
alkali halides series
Formamide crystal is monoclinic (S.G. P21/n), its lattice parameters (in Å) being: a0=3.69; b0=9.18; c0=6.87; =98°, at the temperature of 223 K.22 The 3D cells, measured at different temperatures are reported in Table 1.
Temperature (K) [number of the reference] 90 [22] 108 [23] 223 [24] Extrapolated at 0°C Space group P21/n P21/n P21/n a0 (Å) 3.604 3.613 3.69 3.732 b0 (Å) 9.041 9.053 9.18 9.267 c0 (Å) 6.994 6.979 6.87 6.816 (°) 100.50 100.42 98 95.80 Volume (Å3 ) 224.07 224.51 230.45 234.55
Table 1. Lattice parameters of the formamide crystal as a function of temperature, as resulting from the structures quoted in
references [22], [23], [24]. Parameters at 108K have been converted to the S.G. P21/n from the S.G. P21/c, as published in the original paper [ref. 23].
Besides, one can find the cell extrapolated just below the melting point ( 2,5°C). Its structure is made by adjacent sheets of molecules separated by the spacing d101 (3.133 Å at 0°C). Within the sheets, pairs of molecules associate to form almost coplanar dimers. Puckering of the sheets results from the tilt of the bimolecular units relative to one another. N H···O bonds of two types cross-link the chains forming each sheet: H-bonds (), 2.93 Å long, link monomers to form dimers, while H-bonds (), 2.88 Å long, link dimers together. In the light of the Hartman-Perdok theory, [25] we found that three PBCs run within the layers of thickness d101: the two symmetry equivalent PBCs: [
´1
11] and [´1 ´1
1], both made by and -bonds and the PBC [010], developing along the 21 axis and made by alternating half segments of the [´1
11] and [´1 ´1
1] PBCs (Figure2).
Figure 2. Projection of the formamide structure along the direction [301], perpendicular to the face (101) which lies in the
plane of the figure. The two symmetry equivalent PBCs: [
´1
11] and [´1 ´1
1] are drawn along with the PBC [010] which is composed by alternating segments equal to the half of [´1
11] and [´1 ´1
1] PBCs. The smallest 2D-cell is made by the orthogonal vectors [010]F and [10´1
]F.Hence, the {101} pinacoid has a strong flat (F) character. Further, one can see that no other flat forms can exist in the [010] zone (Figure 3).
Figure 3. The formamide structure viewed along the [010]A2 axis. The dashed highlighted slices: d101, d200, d002 and
d
10 ´1are allowed by the extinction rules of the space group P21/n. Stepped (S) forms:{
´1 01
}, {100} and {001}. The d101 slices, limiting the flat (F) form {101}, are the only ones containing H-bonds within the slice, while no bond exists between contiguous d101 slices.As a matter of fact, the PBCs [010] are not connected within the slices of thickness
d
10 ´1 , d200 and d002 which are allowed by the extinction rules of the space group P21/n (h0l: h+l=2n; 0k0: k=2n; h00: h=2n; 00l: l=2n). Thus, the three pinacoids {100}, {001} and {´1
01} must have stepped (S) character.Summing up and remembering that no H-bonds can be found outside the d101 layers (Figure 3), one can consider the {101} pinacoid as the most important F form of the crystal; thus, the theoretical crystal habit (at least from vapor phase) should be {101} platy.
A symmetry 010 plane cuts in two parts the formamide platelets, according to its monoclinic symmetry; further, from a deeper observation of the lattice, it follows that the 101 plane shows a strong pseudo-hexagonal symmetry. In fact, a hexagonal supercell can be obtained with two sides coincident with the lattice vectors: [020]F=18.534 Å and the four symmetry equivalent [
´2
12]F, [21´2
] F=18.633 Å. The small deviation from the hexagonal shape is well represented by two internal angles of 120.17° and four of 119.82°. The area of the reduced 2D cell corresponds to one third of the hexagonal cell, being determined by the vectors : [020]F and [21´2
] F ; its multiplicity is 4 times the area of the elementary cell of the 101 lattice plane (Figure 4).Figure 4. The pseudo-hexagonal lattice symmetry of the {101} form of formamide. The misfit between the length of the two
sides [020] and the four equivalent <
´2
12> is lower than 0.6%, while the misfit between the two kinds of angles is only 0.35°. The reduced cell shows an area of 300.16 Å2, corresponding to 4 elementary cells of the 101 plane of formamide.Due to this quasi-hexagonal symmetry, it should be reasonable to hypothesize that the (101)-formamide 2D-lamellae could fit with some of the alkali halides which always show the rigorous trigonal symmetry of their {111} form.
These are the reason why we chose the {101} formamide ({101}F, hereinafter) as the best candidate for the epitaxy between the d101 slices of formamide and the {111} surfaces of the growing alkali halides.
4. Lattice coincidences between the {101} -formamide and {111} form of the f.c.c. alkali halides
4.1 The “NaF mode” of the lattice coincidences: from LiF to LiCl.
Searching for lattice coincidences at the interface between the 101 lattice plane of formamide and the 111 plane of the three alkali halides with the lowest lattice parameters, i.e.: LiF, NaF and LiCl, we found that NaF exhibits two interesting lattice fits. The first one is illustrated in Figure 5a.
Figure 5a. The best 2D-coincidence cell between the {111}NaF (left side) and {101}formamide (right side). The 2D supercell of formamide, defined by the vectors: 2[10
´1
]F and [11´1
]F, overlaps with the NaF supercell through a clockwise rotation of 109° around any lattice point of the 101 plane of formamide.The linear misfits of the coincidence 2D cell are not particularly small, but they work in opposite sense, being one positive and the other one negative: thus, the misfit of the coincidence cell areas is exceptionally good (0.70%). This means that the relaxation occurring at the NaF111 / formamide101 interface could further improve the fit between the adsorbed phase and the substrate. Our experience shows that when the absolute area misfit marea < 5% a very good epitaxy could occur, while for 5%<
marea <10% the epitaxy probability rapidly decreases and for marea > 10%, an epitaxy is hardly probable. Thus, we should like to
take this opportunity to propose a new criterion for evaluating, on reticular basis, the epitaxy probability: lower is the percent
misfit between the coincidence cells of the host and guest crystals, higher will be the probability for the epitaxy to occur.
Accordingly, we will name the just found epitaxy as the “NaF mode”. A further quality of this coincidence lattice consists in the low multiplicity of the coincidence cell, which corresponds to an area of only 4 cells of the 111NaF lattice plane. As concerns the possibility that the adsorbed layers of formamide can be buried into the growing {111}NaF form, the compatibility between the 2D elementary layers is not good, owing to the sensible difference between their related thicknesses (d111-NaF=2.227Å and d101-formamide=3.133 Å). Nevertheless, if the (111) face of NaF should grow by spiral mechanism, three growth layers of NaF111 could reasonably bury two formamide 101 adsorbed layers. All these features are summarized in Table 2a. The second coincidence cell for the couple NaF111/formamide101, which has multiplicity 6, is illustrated in the ESI (Figure ESI_1).
Host crystal {111}NaF Guest crystal {101}F Misfit m (%) 2D cell multiplicit y Notes 2D-cell vectors (Å) [2
´3 1
] = 17.337 2´1 ´1
] = 11.350 2[10´1
]= 16.165 [11´1
]= 12.296 7.25 +8.34 Low and opposi te linear misfits 2D-cell Area (Å2) 148.754 149.804 0.70 4{111}NaF Very low area misfit, low 2D cell multipl icity Layer thickne ss (Å) 5d111= 13.38 4d101= 12.53 6.74 Low compa tibility for 2D absorp tionTable 2a. 2D- Lattice coincidences for the 111NaF /101formamide interface. Structural data of formamide have been extrapolated at T=0°C, according to Table 1.
The just quoted coincidence cell does not work so well when dealing with the {111} forms of LiF and LiCl crystals. As a matter of fact, the misfit of the 2D coincidence cell areas reaches the value of 33.33 and 22.18% for LiF and LiCl, respectively. The detailed data can be found in the ESI (Table ESI_1, ESI_1a).
4.2 The “NaCl mode” of the lattice coincidences: from LiCl to KCl.
Figure 5b. The 2D-coincidence cell between the {111}NaCl (left side) and {101}F (right side). 2D-cell vectors of the host (NaCl) and guest (formamide) are quoted in Table 2a. The coincidence cell has the multiplicity of 4 elementary 2D-(111)NaCl cells, corresponding to a multiplicity of 3 elementary 2D-(101)F cells.
Here, we are dealing with a rectangular cell, its low multiplicity (4 {111}NaCl cells) coming out from the very low linear misfits of the 2D-cell vectors (Table 2a). The low percent misfit, between the areas of the coincidence cell of NaCl and formamide
(marea=1.96 %) has to be specially considered as the best indicator of a possible 2D-epitaxy.
Then, we compared the {101}F -2D cell with those of the other alkali halides, from LiCl to KCl, having the same cell vectors as NaCl (with different lengths, obviously). A detailed Table can be seen in the ESI (Table ESI_2). Confining our attention to the percent area misfit, marea (%), of the coincidence cells, we found from LiCl to KCl:
LiCl (+22.77), KF (+13.47), LiBr (+7.20), RbF (+1.54), NaCl (+1.96), NaBr (−10.14), CsF (−11.50), LiI (−12.04) and KCl (−22.10). Hence, one can see that RbF and NaCl behave as the optimal epitaxial hosts for {101}formamide; LiBr is placed on the edge of the epitaxial adhesion, while LiCl, KF, NaBr, CsF, LiI and KCl are unable to work as templates for {101}formamide. Even if RbF shows the best coincidence lattice with formamide, we would like to name as “NaCl mode” the epitaxy based on the 2D-cell vectors: 3[010]F, [10
´1
]F, only because the 2D-epitaxy NaCl/formamide has been the first to be demonstrated both experimentally and theoretically.194.3 The “KBr mode” of the lattice coincidences: from KCl to RbI.
Besides the “NaCl mode” a third 2D-coincidence cell can be found between the guest {101}F and the host {111} surfaces of the remaining alkali halides: NaI, KBr, RbBr, KI and RbI. This coincidence is shown in Figure 5c, where the 2D lattices of {111}KBr and {101}F are compared.
Figure 5c. The 2D-coincidence cell between the {111}KBr (left side) and {101}F (right side). 2D-cell vectors of the host (KBr) and guest (formamide) phase are quoted in Table 2b. One can see that the coincidence cell has the multiplicity of two elementary 2D-(111)KBr cells, corresponding to a multiplicity of two elementary 2D-(101)F cells.
At variance with the NaCl mode, the 2D-cell vectors limiting the coincidence cell are: [11
´2
]KBr and [1´1
0] KBr, which have to be compared to 2[10´1
]F and [010] F, respectively (Table 2b).Host crystal NaCl {111} Guest crystal formami de {101} Misfit m (%) 2D cell multiplicit y Notes 2D-cell vectors (Å) 2[11
´2
]= 27.632 [1´1
0 ]= 7.976 3[010]= 27.802 [10´1
]= 8.083 + 0.62 +1.68 Very low and cooper ating linear misfits 2D-cell Area (Å2) 220.393 224.723 + 1.96 4{111}NaCl Low 2D cell multipl icity Layer thickne ss (Å) d111= 3.256 d101= 3.133 3.92 Very good compa tibility for 2D absorp tionTable 2b. 2D- Lattice coincidences for the 111NaCl /101formamide interface. The 2D cell vectors and areas are differently chosen with respect to those published in: Aquilano, D.; Pastero, L. Cryst. Res. Technol. Special Issue 2013, 48, 819-839. 12
The multiplicity of the coincidence cell is one half of that referred to the “NaCl mode”, which means that formamide could be adsorbed, as an epitaxial 2D-layer, even better than in the just examined cases. In the ESI (Table ESI_3) a detailed Table illustrates the comparison of the 2D cell of {101}F with those of the other alkali halides, from LiI to RbI. Concerning the percent misfit of the 2D- cell areas, marea (%), one finds:
LiI (+20.09), KCl (+10.03), NaI (+3.21), RbCl (0.15), KBr (0.735), RbBr (8.92), KI (14.60) and RbI (23.72).
Accordingly, we should obtain three very good epitaxies between formamide and KBr, RbCl, NaI, respectively and a border line adhesion of 2D adsorbed KCl and RbBr layers. Conversely, LiI, KI and RbI could be surely excluded as useful substrates for formamide deposits.
Figure 6 summarizes the results obtained for the lattice coincidences that come out from “NaF, NaCl and KBr modes”, so
making clear what we mean with “three-modal distribution” of the epitaxy between formamide and the {111} octahedron of the f.c.c. alkali halides.
Figure 6. Three-modal distribution of the coincidence lattices between the {111} form of the f.c.c. alkali halides and the {101}F. The absolute values of the percent misfit, marea (%), between the areas of the coincidence cells in formamide and in the alkali
halides are represented on the ordinates of the histogram. In the diagram, truncated at marea = 25%, the limiting values marea =
5% and 10% are drawn.
A preliminary conclusion should be pointed out: experimental observations show that the presence of the {111} form on the crystals f.c.c. alkali halides grown from water/formamide solutions is not a monotonic function of the lattice parameter (a0) of the alkali halides. Besides, the histogram drawn in Figure 6 reveals a strict correlation between the occurrence frequency of the octahedron and the possible epitaxial coincidences between the {101} form of adsorbed formamide and the underlying surfaces of the {111} form of the complete series of the f.c.c. alkali halides.
As things stand now, we needn’t say that, when a supersaturated alkali halide aqueous solution (simultaneously unsaturated with respect to formamide) is driven to the crystallization, then a three-modal distribution of formamide /alkali halides 2D-epitaxies induces a three-modal occurrence of the octahedron on the shape of the growing crystals. At last, only six out of seventeen alkali halides can work as excellent templates for giving epitaxy with formamide: they belong to three separated domains: the first is restricted to the NaF crystal having the parameter a0=4.634Å, the second includes NaCl and RbF with a0 equal to 5.640 and 5.652, and a third one comprising NaI, RbCl and KBr, with a0 equal to 6.473, 6.581 and 6.600, respectively.
4.4 The possible occurrence of adsorption/absorption mechanism of formamide in the {111} sectors of growing crystals of alkali halides.
It is worth remembering that formamide layers can be buried within the {111} sectors of growing NaCl, so giving rise to anomalous mixed crystals,12,14
since the best constraints are simultaneously fulfilled for both 2D-epitaxy (marea = 1.96%) and
misfit between layer thicknesses (3.92%), as can be seen in Table 2a. The misfit between the d101 thickness of formamide and d111 layers of the alkali halides reaches very low values also for KF (1.46%), LiBr (1.38%) and RbF (4.15%). Besides, very good epitaxies could occur for RbF, while a doubtful 2D coincidences could exist for LiBr and KF is decidedly excluded from epitaxy occurrence. Hence, it follows that ordered d101 layers of formamide can be captured not only in {111} sectors of the NaCl, but
also in those of RbF, while LiBr would show a lower probability to give rise to anomalous mixed crystals LiBr/formamide.
5. The potential role of water in the {100}{111} habit change of alkali halides crystals
As already mentioned in the Introduction, the NaCl-type crystals can undergo the {100} {111} habit change when growing in a polar solvent,26, 5b when a critical value cr of the supersaturation is exceeded. It was also observed 5b that the cr value is not the same for all alkali halides considered; all this was explained in terms of growth rates of the {100} and {111}forms that, in turn, depend differently on the mother phase supersaturation. Previous explanations were given earlier by Kern,26 Hille, Jentsch and Stranski,27 whose interpretative models were grounded on a variation of the solvation of the faces with supersaturation. This kind of habit change was also observed when there is an excess of one of the ionic species in the mother phase, as it was found for NaCl crystals grown in aqueous HCl or NaOH solution, 28 and in calcite when one of the ionic species was present in excess.29 Later, the electrostatic field near the {100} and {111} faces of alkali halide crystals with NaCl structure was calculated and the results were used to recover the growth mechanisms of these faces. 30 Moreover, the solvent interaction with the kinks was assumed to determine the integration rate of growth units; in this way, van der Voort and Hartman explained the {100}{111} habit change occurring when the supersaturation is increased or when one of the ions is present in excess. In all the quoted cases the interpretations about the effect of water on the habit modification were grounded on the hypothesis that water molecules act independently one from another, i.e. without mutual correlation once they enter the different surface sites of growth (terraces, ledges, kinks).
In the following we will venture the conjecture that, as done by formamide, water could be adsorbed forming 2D epitaxial aggregates on the surfaces of the growing alkali halides crystal. In doing this, and having considered the strong molecular interaction between water and formamide in solution,31 we will recover a hypothesis we put forward in a previous work,14 were we proposed that not only formamide can be orderly adsorbed on the {111} NaCl form, but also water.
Hence, one can suppose that the {111} surfaces of alkali halides could act as templates for a temporary short-range ordering of water at temperatures slightly higher than that of the melting point.
5.1 Coincidence lattices between the {00.1} pinacoid of the hexagonal ice and the 111 surfaces of the f.c.c. alkali halides
Hexagonal ice (Ih hereinafter), the polymorph stable at room pressure and T= 0°C, crystallizes in the space group P63/mmc, with parameter a0=4.513 and c0=7.355 Å. Its {00.1} pinacoid exhibits a layered structure with flat character and thickness d00.2 =3.672 Å. The 2D lattice associated to the {00.1} form has hexagonal symmetry and hence it is likely that lattice coincidences can be found between {00.1}Ih and the trigonal symmetric 2D-{111} lattices of the f.c.c. alkali halides. Detailed Tables reported in the ESI (Table ESI_4, ESI_5 and ESI_6) show the potential epitaxies we found, in analogy with the examples quoted in Table
2a,b, when dealing with formamide. The 2D- lattice coincidences for the interface {111}NaF /{00.1}Ice-Ih are quoted in Table 3a, as an example. Host crystal NaF {111} Guest crystal hexagon al Ice (Ih) {00.1} Misfit m (%) 2D cell multiplicity Notes 2D-cell vectors 2 [10
´1
] = 13.106 2 [´1
10 ] = 13.106 3[100]= 13.539 3 [010]= 13.539 +3.30 +3.30 Low and cooper ating linear misfits2D-cell Area 148.754 158.746 + 6.72 4{111}NaF Low area misfit, low 2D cell multipli city Layer thicknes s (Å) 3d111 = 6.683 2d00.1 = 7.356 + 10.07 Very low compa tibility for 2D absorp tion
Table 3a. 2D- Lattice coincidences for the {111}NaF /{00.1}Ice - Ih interface.
Also in this case, linear misfits have been considered along with the misfit between the areas involved in the epitaxies. Three kinds of trigonal 2D-coincidence cells were found for the couples {00.1}Ih /{111} of the complete series of the f.c.c. alkali halides:
i)- The first cell, defined by the vectors 3[100]Ih and 3[010]Ih (Figure 7a) limits an area of 158.75 Å2, its multiplicity being 9 times that of the elementary cell of {00.1}Ih. We decided to associate this coincidence cell to the “NaF mode”, due to the low misfit (6.72%) between the areas of the 2D coincidence cell of {111}NaF and {00.1}Ih , as shown in Table 3a.
Figure 7a.The 2D cell of the {111}NaF (left side-up) and {00.1}Ih (right side-up). The 2D coincidence cell is drawn as well in both lattices.
ii)- The second, defined by the vectors [
´1
10] Ih and [210] Ih (Figure 7b) limits an area of 52.915 Å2, its multiplicity being three times that of the elementary cell of {00.1}Ih . We decided to associate this coincidence cell to the “ LiBr mode”.
Figure7b. The 2D cell of the {111}LiBr (left side-up) and {00.1}Ih (right side-up). The coincidence cell (bottom) has the multiplicity of one elementary 2D-LiBr-(111) cells. This corresponds to a multiplicity of 3 elementary 2D-(00.1) cells of the hexagonal ice (Ih) and is named “LiBr mode”
iii)- The third one, defined by the vectors 2[100]Ih and 2[010]Ih (Figure 7c), defines an area of 70.554 Å2
, with multiplicity 4. This coincidence cell is associated to the “KCl mode”.
Figure7c. The 2D cell of the {111}KCl (left side-up) and {00.1}Ih (right side-up). 2D-cell vectors of the host (KCl) and guest (hexagonal ice) phase are represented and quoted in Table 3b. The coincidence cell (bottom) has the multiplicity of one elementary 2D-KCl-(111) cell. This corresponds to a multiplicity of 4 elementary 2D-(00.1) cells of the hexagonal ice (Ih) and is named “KCl mode”
Here, we will focus again our attention on the area misfit, marea (%).
According to the “NaF mode” we found, from the lowest to the highest lattice parameter, the following marea (%) values: LiF
(−36.65), NaF (+6.72), LiCl (+15.46).
Concerning the “LiBr mode”: LiCl (−15.64), KF (−6.86), LiBr (−0.96), NaCl (+4.11), RbF (+4.55), NaBr (+16.93), CsF (+18.38) and LiI (+18.74).
Finally, for the “KCl mode”, one finds: LiI (−12.28), KCl (−2.87), NaI (+2.85), RbCl (+6.32), KBr (+6.94), RbBr (+16.49), KI (+22.57) and RbI (+32.5)
In analogy with what summarized for the epi-adsorption of formamide, one is allowed to say: - The first epi-domain is limited to the NaF crystal.
- The second multiple cell (LiBr mode) fits very well with LiBr and well with NaCl and RbF, all their area misfits being lower than 5%. Epitaxy with KF may also occur, but is less probable with respect to the just considered cases, since its area misfit reaches 6.44%. For LiCl, NaBr, CsF and LiI the misfit is largely higher than 10%.
- The third multiple cell (KCl mode) has good coincidences with KCl and NaI, the area misfit reaching 2.79 and 2.85%, respectively. For RbCl and KBr one can use the same reasoning as for KF. For LiI, this kind of multiple cell (4) does work better than the preceding one (3); nevertheless, the corresponding misfit remains higher than 10%. As concerns RbBr, KI and RbI, the misfits are so high that no epitaxial relationships can set up.
In Figure 8 the three-modal distribution of the coincidence lattices for all the couples {00.1}Ih /f.c.c. alkali halides, is represented.
Figure 8. Three-modal distribution of the coincidence lattices between the {111} form of the f.c.c. alkali halides and the {00.1}Ih.
5.2 A comparison between the coincidence lattices of {101}F and {00.1}Ih on the f.c.c. alkali halides.
Summing up, a 101 adsorbed 2D-layer of formamide and a 2D-layer of water molecules, adsorbed as an ordered d00.2 monolayer of hexagonal ice, practically behave in the same way with respect to the complete series of the alkali halides. Comparing Figure 6 and Figure 8, it follows that:
i)- The area misfit shows a three-modal distribution for both {101}F/{111} alkali halides and {00.1}Ih/{111}alkali halides lattice coincidences.
ii)- Except the shared case of NaF, the lowest values of the area misfit do not exactly coincide, for the two distributions. In fact, the best of the {00.1}Ih/{111}alkali halides coincidences are displaced towards the smaller alkali halides lattices. For ice, the area misfits of LiBr, NaCl and RbF are lower than 5% in the LiBr mode, while the couple (KCl, NaI) reaches the minimum in the KCl mode. Instead, for formamide, the minimum in the NaCl mode is related to the couple NaCl, RbF; while the misfit values lower than 5% of the KBr mode have been obtained for NaI (4%) and for the couple RbCl, KBr (near 1%).
iii)- There are three shared domains where no meaningful coincidence lattices occur for both the adsorbed formamide and hexagonal ice: a first domain of the smallest lattices (LiF, LiCl), a second one of intermediate lattices (NaBr, CsF,LiI) and, finally, a third domain characterized by the largest lattices (KI, RbI).
Conclusions
In this paper, it has been shown that a synergic action of both adsorbed formamide and water does modify the growth morphology of the whole series of the alkali halides belonging to the face centered cubic lattice. The growth morphology does progressively change from {100}{100}+{111}{111} with the increasing percentage of formamide in the growth solution. However, this behavior is not homogeneous with respect to the whole series of the alkali halides: in fact, three sharply separated reticular domains have been experimentally found where the octahedron does coexist with the cube. Here, it has been demonstrated that the distribution of these domains can be related to the existence of epitaxial 2D coincidence lattices between the {111} crystalline substrates and the ordered solvent adsorbates.
6.1 Consequences on the growth morphology of the f.c.c. alkali halides
Item iii) of section 5.2. means that solvent (water, formamide) adsorption on the {111}alkali halides does disorderly occur within three domains; accordingly, anions and cations populating the growth solution can freely compete with water and formamide on the octahedron surfaces of the alkali halides belonging to these domains. Consequently, the advancement rate of the octahedron shall not be particularly hindered by solvent adsorption, in the same way as it occurs for the cube faces.
On the contrary, in the domains where are fulfilled the geometrical constraints for 2D epitaxy to occur, the solvent adsorption can generate ordered or quasi-ordered 2D islands of both water and formamide on the octahedron surfaces. This should affect both the equilibrium and kinetic properties of the alkali halides octahedron:
a)- the adsorption of 2D islands of a foreign species (solvent), even if temporary, sensibly lowers the specific free energy of the octahedron which could compete with the cube and hence enter the equilibrium shape of the crystal;
b)- the 2D adsorbed islands statistically occupy a portion of the growing octahedron terraces, so partially hindering the feeding of anions and cations in the growth sites (ledges, kinks): then, the kinetics of the octahedron is lowered and, consequently, its morphological importance is enhanced, as much as the concentration of formamide increases in the mother solution.
6.2 The reason why water and formamide can be captured in separate domains of alkali halides.
We just hypothesized that water can be adsorbed as hexagonal-ice mono-layers of thickness d00.2=3.672 Å, the subsequent and contiguous water layers in the solution bulk being surely less ordered with respect to the adsorbed one. When comparing this thickness with the d111 layers of the growing alkali halides substrates, it results that the misfit between
d
00.2hex−ice andd
111alkali halides
is lower than 5% only for KCl, NaI, RbCl and KBr. Having considered that the lowest area misfits (< 5%) of the 2D coincidence lattices between ice and alkali halides is obtained for KCl and NaI, the best condition for the capture (absorption) of ordered water in the growing {111} sectors of alkali halides will be realized for KCl and NaI.
A completely different situation sets up for formamide absorption. Here, it is worth remembering that formamide is absorbed in the {111} sectors of growing NaCl, so giving rise to anomalous mixed crystals,12,14
since the best conditions are simultaneously fulfilled for both 2D-epitaxy (marea = 1.96%) and misfit between layer thicknesses (3.92%). The misfit between
the d101 thickness of formamide and d111 layers of the alkali halides reaches very low values also for KF (1.46%) LiBr (1.38%) and RbF (4.15%). So, one can expect that ordered d101 layers of formamide can be captured not only in {111} sectors of the NaCl growing crystals, but also in those of LiBr and RbF, while KF would show a lower probability to give rise to anomalous mixed crystals KF/formamide.
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2 M. Bienfait, R. Boistelle, R. Kern, in: Adsorption et Croissance Cristalline; Coll. Intern. CNRS n◦152; CNRS Ed. Paris, 577-594, 1965.
3 M. Bienfait, R. Kern, B. Mutaftschiev, Zeits. Krist. 1964, 120, 466. 4 J. B. L. Romé de l’Isle, Cristallographie, 2nd ed., 4 v.; Imprimerie de Monsieur: Paris, 1783.
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6 (a) N. Radenović, W. J. P. van Enckevort, J. Cryst. Growth 2002, 234, 589. (b) N. Radenović, W. J. P. van Enckevort, P. Verwer, E. Vlieg, Surf. Sci. 2003, 523, 307. (c) N. Radenović, W.J. P. van Enckevort, E. Vlieg, J. Cryst. Growth 2004, 263, 544. (d) N. Radenović, D. Kaminski, W. J. P. van Enckevort, S. Graswinckel, I. Shah, M. in ‘t Veld, R. Algra, E. Vlieg, J. Chem. Phys. 2006, 124, 164706. (e) N. Radenović, The role of impurities on the morphology of NaCl crystals − An atomic scale view. Ph.D. Thesis, Radboud University, Nijmegen (NL), 2006.
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