THE JOURNAL OF CHEMICAL PHYSICS 140, 024705 (2014)

Solid phases of spatially nanoconfined oxygen: A neutron scattering study Danny Kojda,1,2 Dirk Wallacher,1 Simon Baudoin,3 Thomas Hansen,3 Patrick Huber,4 and Tommy Hofmann1,a) 1

Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, 14109 Berlin, Germany Freie Universität Berlin, 14195 Berlin, Germany 3 Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France 4 Technische Universität Hamburg-Harburg, 21073 Hamburg, Germany 2

(Received 1 November 2013; accepted 17 December 2013; published online 13 January 2014) We present a comprehensive neutron scattering study on solid oxygen spatially confined in 12 nm wide alumina nanochannels. Elastic scattering experiments reveal a structural phase sequence known from bulk oxygen. With decreasing temperature cubic γ -, orthorhombic β- and monoclinic α-phases are unambiguously identified in confinement. Weak antiferromagnetic ordering is observed in the confined monoclinic α-phase. Rocking scans reveal that oxygen nanocrystals inside the tubular channels do not form an isotropic powder. Rather, they exhibit preferred orientations depending on thermal history and the very mechanisms, which guide the structural transitions. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4860555] I. INTRODUCTION

Condensed matter on nanometer sized length scales behaves differently than in bulk form. Static and dynamic properties are altered by spatial restrictions, reduced dimensionality, and interfacial contributions to the systems free energy. Condensates embedded in nanometer wide vacancies of mesoporous substrates were exploited intensely to study the influence of these effects on known bulk properties of matter.1–19 Simple van der Waals systems as rare gases in confinement were in the focus of interest as well as more elaborate quantum liquids and solids like helium or hydrogen isotopes.9–12 Dioxygen O2 was also among the extensively studied pore condensates.13–19 It is the only elementary system, which can be physisorbed into porous substrates by simple vapor phase condensation to exhibit magnetic properties in its condensed bulk form.20 Dioxygen O2 is the most common allotrope of oxygen. Its importance for life on earth is well understood and has not to be discussed here. In bulk form, it is stable at moderate temperatures and pressures. It condenses in molecular form and exhibits an intriguing structural phase sequence.20 It forms a molecular liquid below its critical point (Tc = 154.59 K, Pc = 5.043 MPa). Depending on temperature T and pressure P, various solid phases appear below the solidification point of T = 54.38 K. Under solid-vapor equilibrium conditions, a cubic γ -phase forms below 54.38 K, an orthorhombic β-phase at temperatures lower than 43.8 K and a monoclinic α-phase below 23.8 K. High-pressure phases (δ-, ζ -, and -oxygen) exist beyond pressures of 9 GPa. Structural equilibrium transitions (liquid-γ , γ -β, β-α) are mainly caused by a complex interplay of isotropic dispersion forces and anisotropic quadrupolar and anisotropic magnetic interactions.20 The latter, strong antiferromagnetic exchange between O2 molecules, is due to unpaired eleca) [email protected]

0021-9606/2014/140(2)/024705/9/$30.00

trons, which combine to a total molecular spin of S = 1.20 Consequently solid phases of bulk O2 differ in their centerof-mass lattices as well as in their magnetic structures. The monoclinic α-phase exhibits long-range antiferromagnetic order.20, 21 Frustrated short-range order is evidently found in the triangular (001)β -planes of the orthorhombic β-phase20, 22 and there are some evidences for one-dimensional antiferromagnetic ordered spin chains in the cubic γ -phase along [001] directions.23 The alteration of bulk properties in confinement has been studied intensely in the past. Among the many techniques of choice to probe confined oxygen (cO2 ) in mesoporous hosts were elastic x-ray scattering, elastic and inelastic neutron scattering, SQUID and scanning calorimetry. Scattering studies revealed a phase sequence that readily depends on the pore size.19 Below a critical pore diameter of 8 nm, phase transitions known from the bulk (γ -β, β-α) were incomplete or entirely suppressed. Squid measurements implied not only temperature and pore size dependent magnetic properties of cO2 but also evidenced a radial variation of the magnetic characteristics inside the pores.18 Inelastic measurements revealed magnetic fluctuations in confined β-oxygen similar to corresponding ones in the bulk as precursor of the evolving antiferromagnetic long-range order in the α-phase.15 Calorimetric studies provided deeper insights into the freezing melting mechanism in the confinement.14 Studies so far employed dominantly monolithic substrates, e.g., vycor, gelsil, and xerogels, which exhibit random and interconnected pore networks of ill-defined size distributions and shapes14 or template grown substrates, e.g., SBA-15 and MCM-41 with well-defined pore geometries of narrow size distributions in form of powders.16 In all these studies, it was therefore inherently impossible to deconvolute directly a random orientation of the pores from a spatially anisotropic response of the confined system on the used probe. Only indirect arguments served as a resort to imply orientation dependent properties of the pore condensates inside the

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confinement. For instance, coherence lengths of (003)β Bragg reflections, which exceeded the average pore diameter in vycor, were interpreted in terms of a preferred orientation of the [001]-direction in β-nanocrystals along the pore axis.19 Porous membranes of anodized silicon (aSi) and anodized aluminum (aAl) are natural candidates for directional dependent studies on confined matter. These monolithic samples are characterized by regular arrays of co-linear, tubular channels and exhibit fairly narrow pore size distributions. Their use for the envisioned experiments with O2 on a 10 nm length scale however is by no means without obstacles. aSi is not suited at all for these investigations. Spontaneous explosive (!) chemical reactions between silicon and condensed oxygen make every experiment impossible and dangerous.24 Even in O2 atmosphere pre-oxized aSi (700 K, 6 h) with a more than 1 nm thick SiO2 passivation layer is not inert. It exhibits a heavy chemical reaction with cO2 close to its solidification point at T = 55 K probably due to strain induced cracking of the oxide layer. aAl, the other substrate under discussion, does not react with O2 but is not readily available with pore sizes less than 20 nm. In this paper we present a comprehensive structural study of cO2 phases by means of elastic neutron scattering techniques. We succeeded in synthesizing anodic alumina substrates with pore diameters of 12 nm and utilized its wellaligned pore topology to ascertain stable crystallographic phases in the confining environment as well as to discern preferred growth directions of nanocrystals inside the porous host. II. ANODIC ALUMINA MEMBRANES

An electrochemical anodization procedure25, 26 was employed to synthesize mesoporous aluminum oxide membranes. Therefore, aluminum foils (purity >99%) were anodized in sulfuric acid (c = 10 wt. %) at constant voltage U = 7 V and constant electrolyte temperature T = −2◦ C for 48 h. Hereby, the associated electrochemical reaction converted bulk aluminum in mesoporous aluminum oxide Al2 O3 .26, 27 The chosen anodization parameters caused the growth of a 15–20 μm thick porous Al2 O3 layer with 10–12 nm wide tubular nanochannels on top of residual aluminum. Scanning electron microscopy (SEM) and nitrogen (N2 ) sorption isotherms served as standard tools to characterize the morphology of the etched membranes. The SEM images in Fig. 1 show a representative membrane in a perspective from the top and the side. The top view exhibits directly the pore openings with diameters of about 12 nm. Their lateral arrangement at the surface of the membrane appears mostly arbitrary. But occasionally six neighbors surround a pore in the center. This particular arrangement is a precursor of long-range hexagonal 2d-lattices, which evolve in a selfassembling process when larger pores are synthesized.27 The side-view exhibits segments of spatially separated micrometers long nanochannels in a synthesized Al2 O3 layer. The pore size distributions of the etched membranes were probed by standard nitrogen (N2 ) sorption isotherms.28 An analysis of the recorded desorption data related the onset of capillary condensation in the pore center and pore radius via

J. Chem. Phys. 140, 024705 (2014)

FIG. 1. SEM images of anodized aluminum: Top-view of the pore openings, a rectangle marks a hexagonal arrangement of neighboring pores (top ), sideview on tubular nanochannels in a cracked alumina membrane (bottom).

the Kelvin equation.29 An average pore size of 12 nm with a mean deviation of roughly 20% was found in agreement with the SEM images. A porosity estimate of 10% for a single membrane bases also on sorption measurements. III. NEUTRON SCATTERING EXPERIMENTS

Elastic scattering of thermal neutrons (λ = 2.420 Å ± 0.004 Å) was employed at powder diffractometer D2030 of the Institute Laue-Langevin in Grenoble (France) to elucidate structural properties of solid oxygen confined in 12 nm wide alumina nanochannels. Equipped with a multistripe He3 detector, scattering intensities could be probed simultaneously up to scattering angles 2θ of 153◦ . A standard orange cryostat controlled the temperature of the sample in the range from 70 K to 2 K. A sample stick equipped with a stainless steel capillary and a semi-automatic sorption apparatus (Hiden Isochema) as provided by ILLs department for sample environment were used to fill the pore volume in situ at D20 with liquid O2 at T = 70 K by means of a controlled volumetric sorption technique. A stack of about 100 porous membranes (10 mm× 20 mm) in an aluminum sample cell accumulated in total a pore volume of 0.18 cm3 and guaranteed sufficient scattering volume for the experiments. A fragment of a single crystalline (001) silicon wafer added to the membrane stack allowed ascertaining the orientation

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FIG. 2. Scattering geometry: Incident and scattered neutrons define the scattering angle 2 . The orientation of the sample with respect to the incident neutron direction is given by ω. The angle φ characterizes the orientation of the wave vector transfer Q with respect to the pore axis. Depicted Si reflections help to define the sample orientation.

of the amorphous alumina foils with respect to the incoming neutron beam by locating prominent Si-Bragg reflections in the scattering pattern. Pore axis and the (004) Si-reflection were parallel and resided both in the scattering plane. Scattering intensities were recorded as function of scattering angle 2θ , the angle ω between pore axis and incoming neutron beam (Fig. 2), temperature T, and thermal history. The studied temperature range between 70 K and 2 K allowed ascertaining structural phase transitions in cO2 that are liquid-solid as well as solid-solid transitions. At selected temperatures (T = 45 K, 25 K, 2 K) rocking scans (ω-scans) over 180◦ in steps of ω = 1◦ ascertained preferred growth directions of nanocrystals inside the channels. The influence of thermal history on the structural characteristics was studied in rocking scans at the discussed temperatures after repeatedly cycling through the solid-solid transitions. Scattering contributions from the sample cell and empty membranes were recorded similarly as background to facilitate a quantitative data analysis.

IV. THERMODYNAMICS

A sorption isotherm of oxygen in aAl (Fig. 3) was recorded at a temperature of T = 70 K at which the bulk material is liquid under equilibrium pressure. The isotherm relates the O2 uptake f = N/N0 in the pores and relative pressure p = P/P0 of the coexisting vapor. N is the number of molecules physisorbed in the substrate and N0 the number of molecules required to fill the pores completely. P represents the vapor pressure of the pore condensate and P0 the saturation pressure of the bulk system. The sorption data itself resemble the typical shape of isotherms known from van der Waals systems as argon, nitrogen, or carbon monoxide.31 Pore condensed oxygen is thermodynamically stable in the confining environment below its bulk saturation point p = 1. At low relative vapor pressures p, the condensate physisorbs on the pore walls only as the pore center remains empty.32 Capillary condensation of liquid oxygen in the pore center occurs at higher pressures p in the hysteretic regime.10, 32 Only this quasi-bulk like part of the condensate is expected to exhibit structural transitions as function of temperature.10

FIG. 3. Oxygen isotherm in aAl at T = 70 K: Adsorption and desorption branches are marked by arrows. Insets depict the geometric distribution of pore condensed oxygen in the nanochannels depending on relative pressure p = P/P0 . An horizontal arrow marks the filling fraction f = N/N0 ≈ 0.9 employed for the scattering experiments.

V. STRUCTURE

Fig. 4 shows selected scattering data from cO2 recorded at temperatures of 45 K, 25 K, and 2 K for an arbitrary chosen sample orientation. Scattering contributions from sample cell and porous host have been subtracted as background. Evident Bragg reflections confirm the existence of a crystalline solid in the confinement. Three different crystallographic phases appear depending on temperature. The corresponding bulk system adapts at these temperatures its γ -, β-, and α-phase. Drumsticks labeled with miller indices mark reflections of these bulk phases.33 They are always located at scattering angles close to the found reflections from the pore-confined solid. As a consequence evident Bragg reflections can be readily assigned to a γ -, β-, and α-phase in confinement. No novel oxygen structures appear. Rather the structural phase sequence from the bulk is reproduced on the nanometer sized length scale, although with slightly increased lattice constants (see below). Liquid oxygen starts to freeze at 50 K as can be seen by the onset of intensity in the (210)γ reflection and completes freezing at T = 46 K as the (210)γ reflection becomes most intense (Fig. 5). The cubic to orthorhombic transitions occurs between 40 K and 34 K as indicated by the disappearance of the (210)γ reflection and the appearance of the (110)β reflection. The intensity-temperature relationship for (020)α implies a transition region from 22 K to 16 K for the orthorhombic to monoclinic transition. The mean phase transition temperatures that are the inflection points of the I(T) curves in Fig. 5 are Tliquid→γ = 50 K, Tγ →β = 38 K, and Tβ→α = 18.5 K. These temperatures are significantly reduced in confinement with respect to their bulk counterparts. This suppression of phase transitions is expected for pore condensates as cO2 and scales with the pore size.19 Based on reference data19 the relative suppression of the γ - and β-phase predicts a pore size of roughly 11 nm in fairly good

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(420) (421)

(400) (410) (411) (330)

(015)

(110)

(006)

a

(113)

(310)

(222) (320) (321) (104)

(012)

(101)

(003)

-O2 T=45K

intensity [a.u.]

-O2 T=25K

c FIG. 5. Temperature dependent intensities I(T) of representative reflections of solid cO2 phases as recorded in the first cooling run.

(-312) (310)

(-311) (021)

(110) (-201) (-111)

(-202)

(200)

(111) (002) (-112) (020) (201)

a

(001)

intensity [a.u.]

(220)

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(210) (211)

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b

scattering angle 2 [°] FIG. 4. Diffractograms of cO2 in the solid state: γ -phase in confinement at T = 45 K (top), β-phase in confinement at T = 25 K (middle), α-phase in confinement at T = 2 K (bottom). Drumsticks mark the position of bulk reflections according to Krupskii et al.33 Their lengths scale expected powder intensities. Insets illustrate the crystallographic unit cells of the various phases with their respective lattice parameters that are side lengths and angles.

agreement with the analysis of the sorption isotherms and the SEM images of the porous host. The finite temperature range of the transitions is owned to the pore size distribution of the alumina membranes. Transitions occur in larger pores at higher temperatures than in smaller ones. This causes sizeable coexistence regions for the various phases. Heating data are not shown in Fig. 5. They exhibit thermal hysteresis compared to the cooling data as expected for first order phase transitions. As a consequence, transition temperatures in a heating run seem not to differ more than 1 K from the known bulk values. We refer to available literature10, 19 for a detailed discussion of the origin of the hysteresis effect. Tables I–III list lattice parameters and thermal expansion coefficients for cO2 as obtained from the first cooling run (liquid-γ -β-α). No significant dependence of presented parameters on thermal history was observed in succeeding

cooling-heating cycles. Provided values do not claim accuracy up to the last digit rather shall illustrate temperature trends as well as statistical uncertainties of our analysis. The cubic γ -phase (Pm3n) is characterized by one lattice parameter (Fig. 4) the cube length aγ . Bragg reflections (hkl) as in Fig. 4 provide sufficient data to predict aγ with high precision as function of temperature T (Table I). In the pore confined system, the cube length is 0.679 nm right after freezing at T = 50 K. It contracts with decreasing temperature to reach 0.676 nm before onset of the γ -β transition. The absolute values of the lattice parameter are at given temperatures about 0.5% to 1% larger than in the bulk state.33 Such increased lattice parameters were earlier attributed to defects in the confined solid,19 which increase the molar volume of the condensate compared to the bulk system. One might also speculate that concave solid-vapor interfaces of the capillary

TABLE I. Lattice parameter and thermal expansion coefficients in the cubic γ -phase as function of temperature T. Values are given for confined (c-) as well as bulk (b-) system. Available bulk data are taken from Krupskii et al.33 Thermal expansion coefficients for confined systems are calculated by means of a polynomial fit of the lattice parameters dependence on temperature.

T [K]

c-aγ [nm]

b-aγ [nm]

c-α γ [10−4 K−1 ]

b-α γ [10−4 K−1 ]

38 39 40 41 42 43 44 45 46 47 48 49 50

0.675(7) 0.676(0) 0.676(2) 0.676(6) 0.676(9) 0.677(1) 0.677(4) 0.677(7) 0.678(0) 0.678(3) 0.678(6) 0.678(9) 0.679(2)

... ... ... ... ... ... 0.6727 0.6732 0.6737 ... 0.6747 ... 0.6757

4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3

... ... ... ... ... ... ... 7.4 7.4 ... 7.5 ... 7.6

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TABLE II. Lattice parameter and thermal expansion coefficients in the orthorhombic β-phase as function of temperature T. Values are given for confined (c-) as well as bulk (b-) system. Available bulk data are taken from Krupskii et al.33

T [K]

c-aβ [nm]

b-aβ [nm]

c-cβ [nm]

b-cβ [nm]

c-α aβ [10−4 K−1 ]

b-α aβ [10−4 K−1 ]

c-α cβ [10−4 K−1 ]

b-α cβ [10−4 K−1 ]

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

0.330(0) 0.330(2) 0.330(2) 0.330(2) 0.330(3) 0.330(4) 0.330(5) 0.330(5) 0.330(6) 0.330(7) 0.330(8) 0.330(9) 0.331(3) 0.331(5) 0.331(7) 0.332(0) 0.332(3) 0.332(5)

... ... ... ... 0.3272 0.3274 0.3277 ... 0.3281 ... 0.3286 ... 0.3291 ... 0.3297 ... 0.3303 ...

1.12(92) 1.12(86) 1.12(97) 1.13(05) 1.12(94) 1.13(12) 1.13(20) 1.12(71) 1.12(95) 1.12(98) 1.12(75) 1.13(02) 1.13(04) 1.12(79) 1.13(13) 1.12(89) 1.12(85) 1.12(45)

... ... ... ... 1.1295 1.1293 1.1292 ... 1.1289 ... 1.1285 ... 1.1281 ... 1.1277 ... 1.1273 ...

0.1 0.6 1 1.5 2.1 2.6 3.0 3.6 4.1 4.5 5.0 5.6 6.1 6.5 7.0 7.6 8.2 8.5

... ... ... ... ... 7.5 7.0 ... 7.0 ... 7.6 ... 8.2 ... 8.8 ... 9.5 ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... −0.74

... ... ... ... ... −1.2 −1.3 ... −1.5 ... −1.6 ... −1.7 ... −1.7 ... −1.8 ...

condensate cause a tensile effect34, 35 in cO2 . But an estimate similar to the one presented by Morishige and Yasunaga35 for confined solid krypton predicts an effect at least one order of magnitude too small. Artifacts in the analysis, for instance, due to systematic errors in the wavelength estimation cannot be ruled out entirely. They are at least of the order of several tenth of a percent and might account to some extent for the reported difference in the lattice constants. The thermal expansion coefficients α however are less affected by such systematic errors. They appear quite different ( α/α ≈ 40%) in confined and bulk solid likely due to a high defect density in the confined system. The orthorhombic β-phase (R-3m) is characterized by two lattice parameters (Fig. 4) that are the next nearest neighbor distance aβ in triangular netplanes and the distance between equivalent triangular planes cβ . The determined lattice parameters are again up to 1% larger than in the corresponding bulk system by a similar reasoning as above (Table II).

The in-plane distance aβ varies continuously from 0.333 nm to 0.330 nm between 37 K and 20 K (Table II). In the same temperature range cβ increases slightly with a temperature average of cβ T = 1.129 nm. Similar to the bulk, the plane-toplane distance exhibits a negative thermal expansion coefficient, which has been attributed to the bond axes in the oxygen molecules. They supposedly precess at higher temperatures around the c-axis and so effectively reduce the plane-to-plane distance.36 The found quantitative differences in thermal expansion between bulk and confined solid however must not be overanalyzed given the fairly poor statistics associated with cβ . The temperature dependence of aβ deviates significantly from the bulk behavior. Respective thermal expansion coefficients are at the highest temperatures smaller by a margin of 15%–20%. Close to the β-α transition at 18.5 K, the respective lattice parameter seems to be even pinned around a value of 0.33 nm resulting in a very low thermal expansion coefficient. In contrast, the bulk system exhibits a more linear relationship between lattice constant and temperature. The origin

TABLE III. Lattice parameter and thermal expansion coefficients in the monoclinic α-phase as function of temperature T. Values are given for confined (c-) as well as bulk (b-) system. Available bulk data are taken from Krupskii et al.33

T [K]

c-bα [nm]

b-bα [nm]

c-cp [nm]

b-cp [nm]

c-α bα [10−4 K−1 ]

b-α bα [10−4 K−1 ]

c-α cp [10−4 K−1 ]

b-α cp [10−4 K−1 ]

2 4 6 8 10 12 14 16 18 20

0.343(0) 0.341(1) 0.342(7) 0.343(2) 0.341(5) 0.342(3) 0.342(5) 0.343(1) ... ...

... ... ... 0.3424 0.3425 0.3425 0.3426 0.3426 0.3426 0.3426

0.376(9) 0.376(1) 0.376(6) 0.376(5) 0.376(5) 0.376(5) 0.376(5) 0.376(3) ... ...

... ... ... 0.3754 0.3755 0.3755 0.3756 0.3756 0.3757 0.3758

... ... ... ... ... ... ... ... ... ...

... ... ... 0.6 0.6 0.6 0.4 0.3 0.0 − 0.8

... ... ... ... ... ... ... ... ... ...

... ... ... 0.6 0.7 0.7 0.8 0.8 0.9 1.1

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of the quasi-isochoric behavior of the confined solid could be explained by the influence of an extremely rigid porous matrix. But we know little about the rigidity of aAl upon solidification of pore confined liquids and additional studies are needed to elucidate this effect. The monoclinic α-phase is the structure with the lowest symmetry group (C2/m) in this sequence. It must be described by four independent parameters (Fig. 4), which can be chosen as the three sides aα , bα , cα of a monoclinic unit cell and the corresponding angle β α . Although the monoclinic structure is clearly identified, there are not sufficient independent Bragg reflections in the probed 2 range resolved to ascertain all these parameters and only incremental information are obtained. The (001)α and (002)α reflections, for instance, can be exploited to calculate the distance between adjacent basal planes (cp = cα sin(β α )) as function of temperature T (Table III). With cp T = 0.377 nm, a value larger than in bulk is evident but its temperature dependence cannot be ascertained in the margin of error to be reliably compared with the bulk behavior.33 The (020)α reflection reveals the parameter bα T = 0.34 nm to be quite similar to the bulk.33 But aα cannot be ascertained without knowledge of β α based on the recorded data. The position of the (−311)α in confinement implies either a distortion along aα of the pore solid, a different angle β α than in bulk, or a combination of both. Here one should note that in a monoclinic setting the β-phase is characterized by a monoclinic angle of β β ≈ 116.8◦ right before onset of the β-α phase transition. An analysis of Bragg reflections in the α-phase which employs this particular angle approximates aα ≈ 0.55 nm to be 1%–2% larger than in the bulk. The reflection widths in the various phases provide direct access to the average crystallite size in the tubular channels. The Debye-Scherrer equation relates the resolution corrected widths directly to the coherence length of the crystals. In combination with the sample orientation ω, a spatially resolved size estimate for grown crystals is obtained. Perpendicular to the pore axis, crystal growth is limited by the diameter of the pores. As a consequence, crystals are not larger than 15 nm that is reasonably close to the higher limit of the pore size distribution. Along the pore axis crystals are found with a length of up to 24 nm exceeding the average pore diameter by factor of two. The simultaneous nucleation and growth of a multitude of nanocrystals in a spatially restricting environment likely prevents the formation of larger crystals even along the several micrometer long nanochannels. Coherence lengths of up to 40 nm as earlier reported19 could not be confirmed. Thermal cooling-heating cycles were used to ascertain textural anisotropies in the various oxygen phases depending on their thermal history. We performed rocking (ω-) scans at selected temperatures along the structural phase sequence liquid-γ -β-α-[β-γ ]5 to discern preferred growth directions for the nanocrystals in confinement as well as to elucidate the very mechanisms that trigger the solid-solid transitions. The phase sequence was aborted bona fide after the 5th iteration of the β-γ transition as structural properties already settled after the first heating run and no additional changes were observed in later cycles.

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Φ [°]

Φ [°] FIG. 6. Rocking scans for various reflections in γ - and β-phase depending on thermal history. Arrows mark reflex positions as expected for γ -crystals, which are aligned with their [111] direction parallel to the pore axis.

Fig. 6 shows a subset of performed rocking scans. It exhibits the modulation of intensity for selected Bragg reflections in γ - and β-phase depending on previous thermal history as function of the out-of-plane angle φ = − ω between pore axis and probed wave vector transfer Q (|Q| = 4π/λ sin( )). An additional intensity dependence on an inplane angle is not expected, as the heterogeneous pore walls exhibit no regular anisotropies on their own. The γ -phase right after freezing is the only system in the studied phase sequence that evolves out of a completely disordered system, a liquid phase. A multitude of random oriented seed crystals (nuclei) are expected to form at the onset of freezing and to increase in size upon solidification. Such a nucleation and growth scenario favors in tubular channels the formation of nanocrystals that align with their fastest growing direction along the pore axis.36 In cubic systems the body diagonal of the unit cell represents naturally this fast growing crystal direction. Therefore nuclei, which align with the [111] direction along the pore axis, form the dominating domain of crystals upon solidification in nanochannels.36 Unfortunately, extinction rules for γ -oxygen forbid to probe (111)γ reflections directly. But intensity modulations of the (200)γ , (210)γ , and (210)γ reflections right after freezing comply readily with the assumption that a majority of nanocrystals is aligned with the [111]-direction along the pore axis. Such a selective influence of the pore geometry on the evolution of crystal domains in confinement has been earlier compared to the Bridgman method that is routinely employed for single crystal growth.37, 38

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The intensity modulations of the discussed Bragg reflections are significantly reduced in subsequent heating cycles after visiting the lower symmetry phases. A more isotropic powder of nanocrystals is found in the γ -phase if it evolves out of the crystalline β-phase. This complies with the observation that γ - and β-phase do not share a group-subgroup relation and a complete lattice reconstruction accompanies the phase transition. No microscopic mechanism has been identified so far to guide the β-γ transition. The structural evolution of the β-phase along the probed phase sequence is more complicated and only partially understood. First we observe that no textural differences exist between β-O2 in the first cooling and very first heating run (Fig. 6). Visiting the α-phase between succeeding γ -β-γ transitions does not alter textural characteristics of the β-phase. This effect is readily explained by the very mechanisms that trigger the β-α transition (see below). The thermal history of the sample affects strongly the textural properties of β-O2 in nanoconfinement. If the orthorhombic phase evolves out of a more or less isotropic γ -phase, a preferred alignment of (110)β in-plane reflections along and (003)β reflections perpendicular to the pore axis become evident and reproducible. It implies either a preferred nucleation of triangular netplanes on the pore walls or identifies the [−110]β direction as the fastest growing direction in β-O2 . It cannot be ascertained, which of these scenarios applies. The latter however would mirror our observations for the liquid-γ transition where the fast growing direction defines the outcome of the nucleation process in tubular pores. Here, a correlated displacement of molecules that might accompany the solid-solid transitions can not be revealed by scattering experiments as the starting phase does not exist in textured form. Textural characteristics of β-O2 are quite different if the sample evolves out of the as-prepared γ -phase (liquid-γ -β), which exhibits strong textural characteristics itself. Again a significant amount of crystals are aligned with the [001] direction perpendicular to the pore walls and none parallel. But the rocking curve exhibits a maxima around ±50◦ . One can only speculate that this quite surprising angle results of a combination of nucleation phenomena as described in the previous paragraph and collective and correlated displacements of molecules during the cubic to orthorhombic phase transition. However, details of or even the existence of such a well defined γ − β transition mechanism on microscopic scales cannot be verified further by means of the available data. Presented data can only challenge the results of DeFotis39 that predict the absence of any correlations between γ −O2 and β −O2 reflections in bulk when the orthorhombic phase evolves out of a single crystalline cubic phase. The discussion of textural properties in the α-phase can be abridged. Barrett and DeFotis39, 40 identified a shear parallel to the (001)β plane along the [−1−20]β , [210]β , or [−110]β directions as prerequisite for the β-α transition. As a consequence, in textured samples (003)β must be parallel to (001)α and (020)α must be parallel to (−120)β , (2−10)β , or (110)β . This textural correlation is readily displayed in our data. A plot in reciprocal space with points of maximum intensity for named reflections (Fig. 7) provides direct proof for

J. Chem. Phys. 140, 024705 (2014)

Q|| [Å-1]

(110) (020) (003) (001) -1

Q [Å ]

FIG. 7. Position of maximum intensity in reciprocal space for selected reflections of β- and α-phase (circles, open squares). Q and Q⊥ are wave vector transfers parallel and perpendicular to the pore axis. Positions of intensity maxima are shown for the first cooling run.

the proposed transformation mechanism. As a consequence, the dependence of α-phase texture on the previous thermal history directly correlates to the structural properties of the β-phase. Theoretical studies by English41, 42 predict the stability of β-oxygen even at zero temperature if the magnetic interactions were absent in O2 . The monoclinic phase suffers from excess elastic energy, which can be only balanced by the antiferromagnetic exchange. Magnetic ordering is therefore a prerequisite for the formation of α-oxygen. In this sense the pure existence of the α-phase implies a magnetic superstructure in cO2 . Fig. 8 provides some proof for this magnetic structure. Magnetic scattering becomes evident in the diffractograms of the α-phase at T = 2 K after averaging over the probed ωrange and subtracting the scattering signal from β-O2 at T = 25 K as a background. It manifests in a weak and very broad signal in the 2 range between 25◦ and 37◦ . This scattering signal reflects residuals of (100) and (−101) magnetic reflections known from the bulk (Fig. 8). They are significantly broadened and indistinguishably merged in confinement. The coherence length of the magnetic order is significantly smaller than the reported nanocrystal sizes of up to 24 nm. The solid red line in Fig. 8 approximates the magnetic scattering under the assumption that (100) and (−101) reflections (dashed lines) contribute with a 3 : 1 intensity ratio similar to bulk powder to the observed magnetic signal. From this admittedly ad hoc but conservative approach, it can be interfered that magnetic coherence does not exceed 2 nm in the nanochannels. It is significantly smaller than the average pore diameter and accounts for not more than six units of bα . The magnetic ordering is likely impaired by finite crystal sizes

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intensity [a.u.]

(a) cO2

(1)+(2)

(2)

(b) bulk O2

(1)

(001)nuc

intensity [a.u.]

(100)mag (-101)mag

scattering angle 2Θ [°] FIG. 8. (a) Magnetic scattering in the α-phase. The scattering signal in the β-phase at T = 25 K was subtracted as background in the 2 range between 20◦ and 40◦ to visualize the increased magnetic scattering signal after the phase transition. The gap in the data is a consequence of the “imperfect” subtraction of (003)β and (001)α . Dashed lines (1) and (2) represent (100) and (−101) magnetic reflections (see text). (b) Magnetic reflections in bulk powder (recorded at E6, Helmholtz-Center Berlin).

as discussed above, defects in the nanocrystals, and reduced magnetic interactions due to increased molecular distances. The final goal to ascertain a T- and ω-dependence of the magnetic scattering signal could not be achieved due to the bad signal to noise ratio and the limited time available for the scattering experiments. Only the ω-averaging allowed us to convincingly visualize the magnetic scattering in the α-phase. Ascertaining the T-dependence is naturally a challenging task as even in the bulk system, the intensity of the magnetic reflections jumps to 65% of its saturation values at the transition point and changes only gradually with decreasing temperature.22 VI. CONCLUSION

Alumina membranes with highly oriented arrays of 12 nm wide tubular nanochannels were synthesized in an electrochemical anodization procedure. These mesoporous substrates hosted liquid and solid phases of oxygen to probe their

structural properties at very small length scales by means of elastic neutron scattering techniques. The three bulk structures α-, β-, and γ -oxygen could be readily ascertained in confinement. Suppression of transition temperatures between various phases scaled expectedly with the pore diameter. Defects in the nanocrystals caused by roughly 1% increased lattice constants compared to the bulk system. A magnetic structure was found in the monoclinic low temperature phase. Residuals of (100) and (−101) reflections in the diffractograms evidenced antiferromagnetic ordering of molecular spins along the b-axis of the monoclinic unit cell similar to the bulk system. The observed scattering signal appeared particular weak as it was impaired by lattice defects, finite sizes of the grown nanocrystals, and reduced magnetic interactions in confinement. The orientation of the nanocrystals in the three solid phases is by no means uncorrelated to the symmetry axis of the tubular pores. Thermal history, microscopic transition mechanisms, and fast growing crystallographic directions control the orientation of nanocrystals in the pores on a macroscopic scale. Fast growing crystallographic directions define textural characteristics after the liquid-γ and isotropic γ -β transitions. Textural similarities between β- and α-cO2 trace back to the mechanism that triggers the orthorhombic to monoclinic transition. The texture in the β-phase as evolved from an anisotropic γ -phase remains mysterious. It might appear as a convoluted result of nucleation and growth of the lower symmetry phase as well as molecular displacements that accompany the transition. In summary, one might say that structuralwise oxygen is maybe one of the most challenging systems so far studied in confinement. It exhibits three solid phases of different symmetry, which do not adapt necessarily well to the tubular pore geometry. Magnetic characteristics add an additional degree of complexity. Even if this work provides an additional puzzle piece in the understanding of this sophisticated system, further studies are required to close the books on oxygen in nanoconfinement.

ACKNOWLEDGMENTS

We deeply appreciated beamtime granted at powder diffractometer E6 of the Helmholtz-Center Berlin in Germany to perform very first experiments on pore-confined O2 in alumina membranes. These experiments provided the basis for subsequent ILL proposals and therefore for the presented results. We thank Dr. Wanderka for providing regular and uncomplicated access to a SEM for membrane characterization. 1 E.

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