22nd April 2013
, Accepted 9th July 2013First published on the web 9th July 2013Sets of self-consistent oxygen-rare earth (RE = La, Y, Lu, Sc) interatomic potential parameters are derived using a force-matching procedure and utilized in molecular dynamics (MD) simulations for exploring the structures of RE2O3–Al2O3–SiO2 glasses that feature a fixed molar ratio nAl/nSi = 1 but variable RE contents. The structures of RE aluminosilicate (AS) glasses depend markedly on the RE3+
field strength (CFS) over both short and intermediate length-scales. We explore these dependencies for glasses incorporating the
La3+, Y3+, Lu3+ and Sc3+, whose CFSs increase due to the concomitant shrinkage of the ionic radii: RLa & RY & RLu & RSc. This trend is mirrored in decreasing average RE3+ coordination numbers (RE) from La = 6.4 to Sc = 5.4 in the MD-derived data. However, overall the effects from RE3+ CFS elevations on the local glass structures are most pronounced in the O and {Al[4], Al[5], Al[6]} speciations. The former display minor but growing populations of O[0] (“free oxygen ion”) and O[3] (“oxygen tricluster”) moieties. The abundance of AlO5 polyhedra increases significantly from ≈10% in La-based glasses to ≈30% in their Sc counterparts at the expense of the overall dominating AlO4 tetrahedra, whereas the amounts of AlO6 groups remain &5% throughout. We also discuss the Si[4]/Al[p] (p = 4, 5, 6) intermixing and the nature of their oxygen bridges, where the degree of edge-sharing increases together with the RE3+ CFS.
Thanks to their beneficial (magneto)optical properties, rare-earth (RE) bearing silicate-based glasses have found applications as laser hosts and optical amplifiers in telecommunication. For optimal performance of such devices, it is desirable to introduce high amounts of uniformly dispersed RE3+ ions into
melts. Unfortunately, the RE2O3–SiO2 system manifests liquid immiscibility, which leads to RE-clustering at low RE2O3 contents of a few mol% and to macroscopic phase-separations for RE3+-richer compositions. The solubility may be increased by introducing RE3+ ions into a M2O–SiO2 based glass, or by exploiting the ternary RE2O3–Al2O3–SiO2 aluminosilicate (AS) system that generally admits the formation of homogeneous amorphous phases by standard melt-quench procedures/conditions, unless their RE2O3 and/or Al2O3 contents are too low (typically ?10 mol%, depending on the identity of the RE3+ ion).
Owing to their chemical inertness and favorable physical properties, e.g., high glass transition temperatures (Tg), high microhardness (HV) and low thermal expansion coefficients, lanthanide-bearing AS glasses are explored as model systems for storage of long-lived actinides, whereas Y–Al–Si–O glasses are exploited in radiotherapy for in situ cancer treatment. There is a strong correlation between many physical/mechanical features of RE2O3–Al2O3–SiO2 glasses and the RE3+
field-strength (CFS); the CFS is given by z/R2, where z and R denote the charge and radius of the ion, respectively. However, the detailed structure–property relationships of RE AS glasses are poorly understood, such as why the Tg-value of the glass strongly depends on the RE3+ CFS but is almost independent of its RE–Al–Si composition. While such peculiarities inarguably stem from the presence of RE3+ ions and most likely originate from their bearings on structural features over both short and intermediate length-scales ?1 nm, the currently incomplete structural insight hampers unambiguous rationalizations of many structure–property correlations of RE2O3–Al2O3–SiO2 glasses. We have recently demonstrated that the RE3+ effects on such relationships may be subtle, for example that the well-known enhanced microhardness for increasing RE3+ CFS originates from the accompanying elevated amounts of high-coordination AlO5/AlO6 polyhedra, whose populations are in turn dictated by the RE3+ CFS.
Hence, it is desirable to reach a more detailed structural picture that encompasses (i) the local RE3+ environments (coordination numbers and RE–O distances) and their distribution across the structure, as well as (ii) the speciations and intermixing of the various SiO4 and AlOp (p = 4, 5, 6) groups associated with the glass network. Data obtained from X-ray and
techniques constitute the primary information source for feature (i), whereas the hitherto most detailed insight into the network structures stem from 17O, 27Al, and 29Si solid-state
applied to AS glasses incorporating the diamagnetic (and thereby accessible to ) La3+, Y3+, Lu3+ and Sc3+ ions that are listed in the order of decreasing ionic radii and thereby increasing CFS. Besides including both end-members of the lanthanide series, this ion-set features a large CFS-span from 2.8 ?-2 for La3+ to 5.4 ?-2 for Sc3+, thereby allowing for the probing of structural variations across a wide range of field-strengths.
As the experimentally derived structural understanding is insufficient, molecular dynamics (MD) simulation is an attractive method for gaining complementary insight. However, such reports of RE2O3–Al2O3–SiO2 glasses are hitherto limited to the Y system, except in our recent modeling work on Lu and La AS glasses. The present contribution serves the dual purpose of (i) outlining the approach for deriving the RE–O (RE = La, Y, Lu) interionic potential parameters utilized by us in , as well as introducing new parameters for the Sc–O (ii) exploring the relationships between the local structural features and the nature of the RE3+ ion (RE = La, Y, Lu, Sc) in two series of RE–Al–Si–O RE(2.21) and RE(2.45). Their members feature equal Al and Si molar contents but distinct glass network
degrees of r = 2.21 and r = 2.45, respectively, with r = nO/(nAl + nSi),(1)where nE and xE denote the stoichiometric amount and molar fraction of species E, respectively (the latter out of the ): xE = nE/(nSi + nAl + nRE), with E = Si, Al, or RE.(2)The glass compositions correspond to those reported by Iftekhar et al.,i.e., 0.171RE2O3–0.276Al2O3–0.553SiO2 [RE(2.21)] or 0.238RE2O3–0.254Al2O3–0.508SiO2 [RE(2.45)] that are associated with {xSi = xAl = 0.381; xRE = 0.238} and {xSi = xAl = 0.340; xRE = 0.320}, respectively. Except for Sc(2.45), which is outside the glass-forming region attainable by a regular melt-quench procedure at 1650 °C and that has only been prepared with 20 at.% of Sc substituted by either Y or La, several physical properties and 27Al/ parameters are reported for all RE(2.21) and RE(2.45) specimens, as well as for related RE AS compositions.
This paper is organized as follows: Section 2 describes our general MD simulation procedures, whereas Section 3 outlines our implementation of the three-step force-matching procedure of Ercolessi and Adams, which was employed to derive new Born–Mayer RE–O interionic potential parameters for RE = La, Y, Lu, Sc. These are subsequently evaluated in Section 4, where the modeled short-range features of RE2O3–Al2O3–SiO2 glasses—as well as the energy-optimized lattice parameters of several RE-bearing
and aluminate structures—are compared with experimental literature data. Section 5 explores the dependence of local and intermediate-range structures of the RE(2.21) and RE(2.45) glass series on variations of each of the four RE3+ ions and their respective contents, where we examine the RE and O speciations, the
constellations at the various O environments, as well as the Si–Al intermixing and the nature of their shared bridging oxygen (BO) sites.
The classical MD simulations emulating a melt-quench procedure were performed for an NVT ensemble in a cubic box with periodic boundary conditions. The computations were carried out with the DLPOLY3 package for ≈3300 atoms and a cubic box-length in the range 3.33–3.54 nm. These parameters were adjusted slightly to match the experimental density and composition of each RE AS glass, using the previously reported values for the La, Y, Lu and Sc bearing samples. The experimental densities ranged between 2.93 g cm-3 for Sc(2.21) and 5.05 g cm-3 for Lu(2.45). The melt-quench simulation started from a structure equilibrated at 3500 K for 100 ps, followed by a 10 ps step-wise decrease of 10 K ps-1 down to 300 K, where equilibration was performed during 200 ps, of which the trajectory during the last 150 ps was used for the structural analysis. For each glass composition, this protocol was completed twelve times with distinct initial ion configurations, each generated by a random distribution subject to the constraint of a 50 pm minimum distance in any ion-pair. The average value and uncertainty of each reported modeled structural feature was derived from these distinct trajectories.
For two ion species α and β with indices j and k separated at a distance Rjkα–β, the corresponding interaction energy included both long-range Coulombic (~zαzβ/[4πε0Rjkα–β], where zα represents the ionic charge), and short-range Buckingham terms. The latter is given by Ujkα–β(Rjkα–β) = Aα–βexp{-Rjkα–β/ρα–β} - Cα–β(Rjkα–β)-6,(3)except for the RE–O (RE = La, Y, Lu, Sc) interionic potentials derived herein that solely employed the repulsive Born–Mayer contribution: Ujkα–β(Rjkα–β) = Aα–βexp{-Rjkα–β/ρα–β},(4)i.e., for which C ≡ 0. The sets {Aα–β,ρα–β,Cα–β} are listed in . The Buckingham/Born–Mayer parameters employed partial charges of -1.2e for O, 2.4e for Si, and 1.8e for Al together with all RE species, where e is the elementary charge. A modified Buckingham potential was implemented to circumvent strong attractions at small interionic distances. were evaluated for all ion-pairs up to 0.8 nm, whereas the Coulombic interactions were calculated by a smoothed particle mesh Ewald summation with a 1.2 nm real-space cut-off and an accuracy of 10-6. These parameters provide sufficient accuracy and are standard for MD implementations for similar glass systems (e.g., see ). The equations of motion were integrated in time-steps of 2 fs by the velocity Verlet integrator approach, and a Berendsen thermostat with a 1.0 ps relaxation time constant.
Table 1 Buckingham potential parameters
Superscripts indicate values of the partial ionic charges according to van Beest et al.
Parameters from Du and Cormack.
The new parameters derived herein, corresponding to the set {A(3)RE–O,ρ(3)RE–O} of Section 3.
O1.2-–O1.2-
Al1.8+–O1.2-
Si2.4+–O1.2-
Y1.8+–O1.2-
La1.8+–O1.2-
Y1.8+–O1.2-
Lu1.8+–O1.2-
Sc1.8+–O1.2-
These parameters and methods were employed throughout all MD simulations, except for the optimization procedure of the new RE–O potential parameters in Section 3, which employed a smaller set of 113 atoms and box-lengths spanning 1.12–1.15 nm, whereas 0.53 nm and 0.55 nm cut-off radii were used for the Buckingham and Coulombic interactions, respectively. The restricted set of atoms originates from computer memory constraints in the ab initio calculations outlined below.
To verify that the sets of interionic potential parameters may also reproduce the experimental glass densities, we additionally performed NPT simulations for four distinct initial configurations of each composition. The modeled densities were consistently slightly lower than their experimental counterparts, but deviated only by ?3% and ?5% within each RE(2.21) and RE(2.45) series, respectively. The overall largest discrepancy (5.3%) was observed for the Y(2.45) composition, whereas essentially perfect matches resulted for the two La glass compositions (&1% relative error). The sets of simulations revealed a negligible spread within ±0.01 g cm-3 incidentally, this value is equal to the experimental uncertainty.
Current computer resources limit ab initio calculations to systems comprising less than a few hundred atoms over ?10 ps, and simulations of larger ensembles over long timescales can only be achieved by classical MD approaches that require a set of parameters for approximating the interaction energy in each ion-pair of a targeted structure. An “ideal” interaction potential should reproduce the experimentally assessed properties of the system, as well as providing reliable predictions over widely spanning sample compositions. Several strategies exist for constructing interatomic potentials, such as the reverse Monte Carlo, electronic density, and effective medium options.
We employed the iterative force-matching procedure of Ercolessi and Adams to obtain the parameters Aα–β and ρα–β of the Born–Mayer potential []; their values were selected so as to provide the closest possible match to ab initio-derived forces. Such a protocol is convenient for applications to amorphous phases where elastic constants or lattice parameters cannot be defined. It was carried out for the RE(2.21) composition of each RE–Al–Si–O (RE = La, Y, Lu, and Sc) glass. Every iteration step (n) involves three stages:
(1) For a given set of Buckingham parameters {Aα–β,ρα–β,Cα–β} of Si–O, Al–O and O–O interionic pairs (using the values of Du et al.) and Born–Mayer counterparts {A(n)RE–O,ρ(n)RE–O} for the RE–O pairs, a glass structure model was obtained using classical MD simulations (see Section 2) at the nth iteration stage. For the case of RE = Y, the initial set {A(0)Y–O,ρ(0)Y–O} was derived by mapping the Buckingham parameters of Du onto the Born–Mayer form [{AY–O,ρY–O,CY–O} → {A(0)Y–O,ρ(0)Y–O}] using a numerical fitting, whereas the A(0)RE–O starting values were scaled for the other RE–O contacts according to the ratios of their Shannon–Prewitt ionic radii (RRE/RY).
(2) The ion coordinates of each MD-derived glass structure were utilized in a density functional theory (DFT) full-potential linearized augmented plane wave (FP-LAPW) calculation to provide the interionic forces [(ab initio)]. The generalized gradient approximation of Perdew, Burke and Ernzerhof was used with the Wien2k package. One k-point of the irreducible Brillouin zone was computed by employing basis functions that obeyed the criterion KmaxRmin = 7.0, where Kmax represents the magnitude of the largest basis vector in the reciprocal space and Rmin is the smallest muffin-tin radius in the simulated cell. The latter values were fixed throughout all computations at 1.83 a.u., 1.66 a.u., 1.51 a.u., and 1.31 a.u. for the RE, Al, Si, and O species, respectively. We verified that the product KmaxRmin = 7.0 provides converged forces. The electronic band-states were separated by -8.1 Ry to include all contributions down to the 2p and 2s orbitals for Si and Al, respectively. The force convergence criteria for the self-consistent field (SCF) procedure were 0.5 mRy per a.u. During the last SCF-cycle, the total forces were calculated using Pulay's correction.
(3) The DLPOLY3 package was employed to compute a set of forces {j(ARE–O,ρRE–O)}. A refined set of interionic potential parameters resulted from a least-square force-fitting procedure that minimized the function (5)where the index j runs over all RE3+ sites in the structure and ||?|| denotes the magnitude (norm) of the vector-difference. The Born–Mayer parameters were varied until the best match was found in . This provided a new set of values, {A(n+1)RE–O,ρ(n+1)RE–O}, extracted at the minimum of χ2(ARE–O,ρRE–O) and subsequently provided as input to the MD simulation stage (1) of the next, i.e., (n + 1)th iteration step.
Steps (1)–(3) of the protocol were repeated three times, resulting in the sets {A(n)RE–O,ρ(n)RE–O} with n = 1, 2, and 3.
lists the {A(3)RE–O,ρ(3)RE–O} values that were employed in all remaining calculations, as well as in our recent work. The parameters obtained at each iteration stage were used to compute the potential energy [URE–O(RRE–O)] from , as well as the respective radial distribution function [RDF; denoted gRE–O(RRE–O)]. The latter was evaluated for an ensemble of ≈3300 atoms, as described in Section 2. Fig. S1 of the ESI shows the results for the RE(2.21) glass composition and RE = {La, Y, Lu, Sc}.
The general validity of the new potential parameters for reproducing short-range structural features of RE2O3–Al2O3–SiO2 glasses was previously confirmed over large RE–Al–Si compositional ranges within each La, Y and Lu system. Focussing on the structural dependency on the identity of the RE3+ ion, we evaluate here the predictions of the MD simulations for the series of RE(2.21) and RE(2.45) specimens against experimental results from either
(Si and Al coordinations) or di the latter data on –oxygen distances were reported for Si-richer and RE-poorer compositions and may therefore only serve as general guides.
The MD simulations of the present glass compositions, as well as others previously reported, reveal that Si4+ is exclusively (&98.5%) present in tetrahedral coordination (Si[4]), which is in excellent agreement with experimental solid-state
data. For this reason, we henceforth do not explicitly indicate the coordination number of Si. All Al3+ ions (≥99.9%) coordinate either four (Al[4]), five (Al[5]) or six (Al[6]) oxygen atoms, also in full accordance with
results obtained from the present RE AS compositions as well as related ones.
Fourfold Al3+ coordinations dominate the three coexisting AlO4, AlO5 and AlO6 polyhedra. The amounts of higher-coordination species (mainly AlO5) grow primarily for increasing RE3+ CFS and secondly for decreasing xSi, in good agreement with experimental findings. These trends are witnessed in the average Al coordination number (Al) and fractional populations {x[p]Al} of the {AlOp} polyhedra listed in
for the two RE(2.21) and RE(2.45) series of specimens. As the CFS elevates between the La3+ and Sc3+ ions, the modeled Al values range over 4.14–4.43 for the RE(2.45) series, whereas its RE(2.21) counterpart displays nearly equal average Al coordination numbers ≈4.24 in the Y, Lu and Sc bearing structures. Minor variations are observed for each RE AS structure when xSi diminishes, i.e., for increasing the r-value of the glass. The elevation of Al stems primarily from a growth of the AlO5 population, whereas that for the AlO6 groups remains low throughout (x[6]Al & 0.05).
Table 2 Results of MD Simulations and
MD-derived RE3+ and Al3+ average coordination numbers (RE, Al) and fractional populations of AlOp groups (x[p]Al) obtained by MD simulations and . The latter data are given within parentheses and are reproduced from our recent work. The populations are associated with uncertainties of ±0.010 (MD) and ±0.015 (). The rightmost columns list the mean O coordination numbers (O) and the fractional population x[p]O of each O[p] (p = 0, 1, 2, 3) coordination, where only bonds to Si and Al are considered.
Results obtained by using the Y–O potential parameters of Du.
4.13(4.14)
0.872(0.877)
0.123(0.091)
0.005(0.022)
4.24(4.25)
0.773(0.776)
0.209(0.195)
0.018(0.029)
4.23(4.31)
0.782(0.718)
0.201(0.250)
0.017(0.032)
4.25(4.40)
0.767(0.649)
0.217(0.307)
0.016(0.044)
4.14(4.14)
0.871(0.884)
0.122(0.089)
0.007(0.027)
4.30(4.30)
0.729(0.746)
0.246(0.210)
0.025(0.044)
4.29(4.34)
0.739(0.698)
0.237(0.260)
0.024(0.042)
4.22(4.25)
0.795(0.776)
0.191(0.195)
0.014(0.029)
4.28(4.30)
0.738(0.746)
0.239(0.210)
0.023(0.044)
compares the modeled Al and {x[p]Al} results with their experimental counterparts obtained from solid-state
in . The x[p]Al values are plotted against the RE3+ CFS in . While excellent agreement is observed for all La and Y AS glasses, for the cases of Lu and Sc the MD simulations underestimate the AlO5 populations (and thereby Al), notably so for the Sc(2.21) glass. Despite the largest relative discrepancy between the MD and
derived Al-values being only ≈4% [for Sc(2.21)], the pronounced experimental trend of a monotonic elevation of Al for increasing RE3+ CFS is not reproduced well by the simulations of the Lu and Sc members, particularly for the r = 2.21 branch. Given the significantly faster quench-rate in the calculations relative to the physical samples, one expects the modeled x[5]Al and x[6]Al populations to be comparable to, or even higher, than their NMR-derived counterparts, as explained in detail in . Hence, the frequently observed underestimation of Al from the MD simulations is surprising (see ). We have no explanation for these effects but refer to Jaworski et al. for further discussions.
Fractional populations
as obtained from MD simulations (black symbols) and
experiments (grey symbols), plotted against the RE3+ CFS for the as-indicated RE(2.21) and RE(2.45) AS glasses for (a) p = 4; (b) p = 5 and p = 6.
–oxygen distances.
displays a selection of RDFs [i.e., gα–β(Rα–β)] for the four RE(2.21) glasses (RE = La, Y, Lu, Sc), whereas
lists a collection of average interionic distances (α–β), as well as the R-value where gα–β(Rα–β) is maximized (Rmaxα–β). Here we focus on the various –oxygen distances.
RDFs of the (a) Si–O, (b) Al–O, (c) RE–O, and (d) O–O pairs for each of the RE(2.21) glasses with RE = {La, Y, Lu, Sc}, the identity of which is identified by the legend in (a).
Table 3 Average interatomic distances and bond angles
Pair α–β (R)
The distances Rmaxα–β (in pm) and bond angles θmaxα–β–γ (in degrees) were estimated from the maximum of the radial distribution function (RDF) and the angular distribution function (ADF), respectively. The corresponding average distance (α–β) or bond angle (α–β–γ) over each respective distribution is given within parentheses.
The cutoff distance Rcut corresponds to the first minimum of the RDF, which varied depending on the RE3+
identity {La, Y, Lu, Sc} as follows: {315, 303, 289, 275} pm for the RE–O {434, 415, 405, 395} pm for Si–RE; {465, 434, 425, 400} pm for Al–RE and {495, 480, 465, 430} pm for RE–RE.
Results obtained by the potential parameters of Du.
260.3(310.0)
260.7(309.1)
261.1(308.9)
260.5(309.1)
260.9(309.0)
260.3(312.0)
261.1(310.1)
262.1(309.7)
261.1(309.9)
261.3(308.5)
159.3(160.1)
159.3(160.2)
159.1(160.3)
159.3(160.2)
159.1(160.2)
159.3(160.0)
159.1(160.1)
159.1(160.2)
159.1(160.1)
158.9(160.1)
176.7(180.3)
176.9(181.9)
176.9(181.8)
176.9(181.9)
176.9(182.1)
176.5(180.5)
177.1(182.3)
176.9(182.6)
176.9(182.4)
177.5(183.6)
175.9(178.3)
175.9(178.3)
175.6(178.6)
175.9(178.4)
175.6(178.5)
176.1(178.0)
176.1(178.0)
175.9(178.2)
175.9(178.1)
175.6(178.1)
179.9(190.9)
179.9(190.3)
179.6(190.8)
179.9(190.5)
179.6(190.4)
180.9(190.6)
180.9(190.0)
180.9(190.2)
179.6(190.0)
180.1(189.6)
185.6(199.5)
181.9(198.8)
186.1(199.4)
182.4(198.4)
182.9(198.5)
181.6(200.2)
184.9(198.3)
185.9(198.7)
185.4(198.3)
185.4(197.7)
234.3(250.9)
224.3(239.6)
228.9(240.9)
216.3(229.3)
204.9(217.6)
233.7(249.7)
224.7(238.9)
228.9(240.3)
216.5(228.8)
205.5(217.9)
312.9(309.3)
312.5(308.9)
312.9(308.8)
312.7(308.7)
313.1(308.7)
313.5(309.5)
311.3(308.3)
312.9(308.5)
312.7(308.4)
312.1(308.8)
320.3(316.2)
318.9(315.6)
318.1(315.8)
320.3(315.5)
321.1(315.6)
315.9(316.0)
315.9(315.3)
318.1(315.6)
314.9(315.3)
316.7(315.1)
363.5(366.2)
352.9(355.1)
354.1(353.1)
349.5(349.5)
342.1(343.0)
360.9(365.2)
351.7(354.1)
351.9(353.0)
346.9(348.6)
338.7(342.1)
314.7(317.6)
315.1(316.9)
314.3(317.5)
312.9(316.4)
315.5(315.8)
315.1(318.6)
314.7(317.1)
313.9(318.4)
313.1(316.7)
314.9(316.0)
359.5(370.3)
352.5(356.1)
313.3(354.5)
343.8(349.3)
338.7(339.1)
360.5(370.3)
350.5(356.1)
356.7(354.9)
346.7(349.7)
338.7(338.7)
370.7(405.9)
352.3(390.3)
352.3(391.5)
337.9(378.0)
360.9(360.0)
369.5(405.2)
353.5(389.4)
352.9(390.6)
340.3(377.8)
355.1(359.3)
Triplet α–β–γ (θ)
Si4+ exhibits the highest CFS of all : it arranges well-ordered SiO4 environments, reflected in a sharp peak of the gSi–O(RSi–O) function [see ] and consequently essentially equal values of RmaxSi–O and Si–O, amounting to 159 pm and 160 pm, respectively (). These Si–O distances are independent of the RE3+ identity and display good agreement with the value RSi–O = (162 ± 3) pm reported in
by deconvolution of X-ray and
into Gaussian peaks for Si-rich and RE-poor (RE = La, Y, Sc) AS glasses.
The Al3+ ion that features the second largest CFS also manifests essentially identical RDF peak maxima ≈177 pm among the various RE- see
and . However, for a given RE AS glass, minor differences are now observed between RmaxAl–O and Al–O: the latter values (180–184 pm) are slightly larger than their RmaxAl–O counterparts, with the Al–O–RmaxAl–O separation increasing together with the RE3+ CFS along the series La3+ & Y3+ & Lu3+ & Sc3+. This trend is expected from the concomitant population-elevations of the high-coordination (AlO5, AlO6) polyhedra and the accompanying lengthened Al[p]–O distances for increasing p; compare the Al[4]–O, Al[5]–O and Al[6]–O bond-lengths with their aggregate “Al–O” value in . The values RmaxAl–O ≈ 177 pm and Al–O ≈ 182 pm accord well with the experimental diffraction data of
that yielded Al–O distances in the range 180–184 pm (±3 pm) for La, Y and Sc glasses.
We next consider the oxygen distances to the RE3+ species, i.e., the lowest field-strength
in each glass structure. The first peak-maximum of the respective gRE–O(RRE–O) function [] becomes more diffuse as the CFS decreases along the series Sc3+ & Lu3+ ? Y3+ & La3+. This translates both into progressively lengthened RE–O distances [from 218 pm for the Sc(2.21) structure to 251 pm for La(2.21)] and RmaxRE–O [205 pm for Sc(2.21) to 234 pm for La(2.21)] in , as well as into steadily increased RE–O–RmaxRE–Odifferences [from 13 pm for Sc(2.21) to 17 pm for La(2.21)] as the RE3+ CFS diminishes. The RmaxRE–O-values of
compare very well with their corresponding diffraction-derived data, where the latter values are stated within parentheses (or ranges of values in the case of several data-points): 234 pm (234–238 pm) for La; 224 pm (220–226 pm) for Y, and 205 pm (212 pm) for Sc. The largest discrepancy (≈3%) is observed for Sc, although it may partially originate from widely differing
compositions between our Sc(2.21) glass and that analyzed by Sadiki et al.; the latter corresponds to r = 1.87, xAl/xSi = 0.58 and xSc ≈ 0.03 in our sample nomenclature. While both the Y–O interionic parameters derived herein and those of Du provide RmaxY–O values in good accordance with experimental , slightly better predictions are observed from the present {ARE–O,ρRE–O} set. Experimental Lu–O bond-lengths are not reported from Lu–Al–Si–O glasses. Yet, as shown below in Section 4.2, our interionic Lu–O potential parameters provide excellent predictions of Lu–O-values and lattice-parameters for some crystalline Lu-bearing phases.
The new RE–O potentials were further evaluated by energy minimizations at zero absolute temperature by applying the GULP program to the set of crystalline
they correspond to the La2O3, Y2O3, Lu2O3, and Sc2O3 oxides, some RE-bearing aluminates (LaAlO3, Y3Al5O12, Lu3Al5O12, ScAlO3) and scandium disilicate (Sc2Si2O7). Each representative XRD-derived structural parameter-set (obtained from the inorganic crystal structure database) was used as the initial input to the minimization procedure with the interionic potentials evaluated up to 2.0 nm. The space-group symmetry of each structure was preserved throughout.
Table 4 Parameters for energy-optimized structures
Results of using the interionic potential parameters of
in lattice-energy calculations that assumed fixed (α, β, γ) unit-cell angles, and leading to the calculated (Calc.) cell dimensions (a, b, c) and volume (V). Values within parentheses represent relative deviations from the XRD-derived experimental (Exp) data.
Average RE–O distance, except for the data on α-quartz and α-Al2O3 that reports Si–O and Al–O, respectively.
Obtained from the Y–O potential parameters of Du.
The β-value was optimized to β = 104.08°, which may be compared with the -derived result of β = 102.77°.
Obtained by using the Si–O or Al–O potential parameters of
La2O3 (γ = 120°)
382.5 (-2.9%)
603.2 (-1.7%)
0.0764 (-7.3%)
247.5 (-2.4%)
LaAlO3 (γ = 120°)
537.0 (0.09%)
1309.2 (-0.14%)
269.1 (0.34%)
1060.3 (-0.04%)
1.1921 (-0.11%)
228.4 (-0.09%)
1059.3 (-0.13%)
1.1887 (-0.40%)
228.1 (-0.22%)
239.7 (0.84%)
237.8 (0.04%)
1032.3 (-0.65%)
1.1001 (-2.0%)
222.5 (-0.49%)
236.8 (1.6%)
216.4 (2.0%)
504.0 (2.1%)
526.0 (0.54%)
742.7 (3.1%)
232.8 (2.7%)
658.2 (1.2%)
851.1 (0.15%)
482.1 (3.0%)
219.0 (3.1%)
α-SiO2 (γ = 120°)
493.1 (0.59%)
544.2 (0.78%)
158.9 (-1.5%)
494.0 (0.78%)
544.8 (0.89%)
160.1 (-0.74%)
504.5 (2.9%)
552.0 (2.2%)
161.8 (0.31%)
α-Al2O3 (γ = 120°)
476.7 (0.15%)
192.5 (0.63%)
The resulting lattice parameters (a, b, c), cell volume (V) and average RE–O distance (RE–O) within the unit cell are listed in
and compared with their experimental counterparts obtained using single crystal . An acceptable agreement is observed: the relative deviations among the (a, b, c) parameters and the volume of the unit cell generally stay below 2% and 4%, respectively. For both the RE2O3 and aluminate structures, the data derived from the new Y–O and Lu–O potential parameters accord very well with their experimental counterparts, where the largest discrepancies in the cell-lengths, volumes and average RE–O distances amount to 0.8%, 2.2% and 1.6%, respectively, while the agreement is overall significantly lower for La and Sc.
also compares the results of using the Y–O interionic potential parameters of Du et al. with those derived herein. Overall, the two options display comparable qualities in their st the present {AY–O,ρY–O} parameters perform favorably for the case of Y2O3, whereas those of
give better agreement with the experimental lattice parameters of Y3Al5O12.
The La–O and Sc–O interionic potentials offer the weakest predictability. While the LaAlO3 lattice parameters calculated by the new La–O potential give excellent agreement with the experimental data (), the globally largest discrepancy among all structures is observed for La2O3, for which the calculated values of V and La–O are underestimated by 7.3% and 2.4%, respectively. However, the three Sc-bearing structures manifest the overall weakest agreement between calculated and experimental lattice parameters, where discrepancies over the ranges of 1.2–2.1%, 3.8–5.8% and 2.0–3.1% are observed for the values of (a, b, c), V, and Sc–O, respectively.
Nevertheless, our new RE–O potential parameters that were optimized directly on amorphous phases, display a good transferability to crystalline structures, except for La2O3 and the Sc-based phases. For instance, the observed deviations between calculated and
are not substantially larger than the analogous results of Pedone et al. obtained by a Morse-based potential that was optimized directly on crystalline
and subsequently evaluated on several multicomponent structures.
also verifies acceptable values of the energy-minimized lattice parameters of α-quartz and α-Al2O3, which originated from solely employing the O–O, Si–O, and Al–O interionic parameters of Du and Cormack (see ); hence, the validity of our RE–O Born–Mayer parameters is confirmed by the comparable quality in the structural predictability observed both in their presence and absence. Moreover, the herein utilized Si–O and O–O parameters from
compare favorably with the Beest–Kramer–Santen (BKS) and Carré–Horbach–Ispas–Kob (CHIK) potentials when evaluated for the case of α-SiO2 (see ).
field-strength effects on RE2O3–Al2O3–SiO2 glass structures
plots the average number of oxygen species coordinated by each RE3+ ion (RE) against its corresponding Shannon–Prewitt radius, the latter value relevant for REO6 groups. Indeed, all MD-derived mean coordination numbers scatter around RE ~ 6; they elevate either for increasing RE3+ radius (i.e., decreasing CFS) or for growing r-value of the glass. The latter observation may be rationalized from the dependence of RE on the glass composition, where both RE and Al increases for decreasing
content (i.e., increasing xRE), as demonstrated in .
verifies our claimed correlation between RE and Al for the present glasses.
(a) MD-derived average RE3+ coordination numbers (RE) plotted against the respective Shannon–Prewitt ionic radius (assuming sixfold coordinations) for each RE(2.21) and RE(2.45) series. (b and c) Fractional populations x[p]RE plotted versus the coordination number p for the (b) RE(2.21) and (c) RE(2.45) series of glasses.
The underlying distribution of RE[p] populations (x[p]RE) are conveyed by
for the RE(2.21) and RE(2.45) series. Coordination numbers are observed in the range 4 ≤ p ≤ 8, although the fourfold and eightfold populations are only significant for the smallest (Sc3+) and largest (La3+) , respectively. Except for Sc3+ ions that primarily form ScO5 polyhedra, p = 6 coordinations dominate the {RE[p]} distributions of the RE3+ , where REO7 polyhedra constitute the second most abundant species for La3+ and Y3+, whereas &30% of the (small) Lu3+
assume fivefold coordinations. The MD-modeled RE-values around six accord semi-quantitatively with the X-ray absorption spectroscopy results of RE = 6 ± 0.5 observed throughout the lanthanide-ion series when RE3+ is present in a low amount (5 wt% RE2O3) in a Na2Si2O5 based glass, as well as with several MD reports on RE-bearing (alumino)silicate glasses.
Interestingly, the calculations predict significant fractions 0.09 ≤ x[4]Sc ≤ 0.17, suggesting that Sc3+ might partially assume a glass-network forming role in the guise of ScO4 groups, as reported previously for the similarly-sized Mg2+ ion. displays a typical Sc[4] environment in the Sc(2.21) glass. The potential network-forming capability of Sc requires further experimental studies, but may constitute the origin of previously reported anomalies in
shifts and unexpectedly low glass transition temperatures observed from Sc AS glasses.
Some typical fragments in the MD-derived glass structures. (a) A ScO4 tetrahedron (O atoms of which are set in black) in relation to the aluminosilicate network. (b) A SiO4 tetrahedron accommodating one NBO ion and sharing corners with each of a SiO4, AlO4 and AlO5 group. (c) A “tricluster moiety” featuring an AlO6 polyhedron connected to SiO4 and AlO4 groups via corner and edge-sharing, respectively.
We identify the coordination number p of an oxygen species O[p] in the RE–Al–Si–O glass according to its total number of bonds to Si and/or Al. Hence, O[1] and O[2] represent non-bridging oxygen (NBO) and BO species, respectively. They dominate the total O speciation, as follows from
that lists the fractional population {x[p]O} of each O[p] moiety (p = 0, 1, 2, 3) observed in the modeled data. The relative amounts of the BO and NBO environments depend predominantly on the r-value of the AS glass and hence its RE3+ nearly constant x[1]O fractions of ≈0.23 and 0.32–0.35 are indeed observed for the series of RE(2.21) and RE(2.45) specimens, respectively.
The MD-predicted non-negligible amounts of O[0] (“free O2- ion”) and significant O[3] (“oxygen tricluster”) moieties in the present (as well as previously reported) RE AS glasses that involve high-CFS trivalent modifier ions is the primary distinction between their corresponding O speciations in mono- or di-valent based glasses of otherwise com compare for instance our results with previous modeled data from Ca AS glasses. Whereas both the O[0] and O[3] populations grow slightly as the RE3+ CFS increases, they also depend on the RE3+content, with x[0]O increasing and x[3]O decreasing as the r-value of the glass elevates from 2.21 to 2.45, as revealed in . The minor growth of the O[0] populations for an increase in either the CFS or amount of the RE3+ ions suggests an enhanced RE–O–RE association.
Fractional populations of O[p] species with (a) p = 0, (b) p = 3, and (c and d) p = 2, plotted against the RE3+ CFS for the as-indicated RE(2.21) and RE(2.45) series of glasses. Note that whereas the lower and upper values vary among the plots in (a–d), their spans of vertical ranges are equal throughout. Grey lines represent best fits.
While the abundance of free O2- ions depends solely on the nature and amount of the glass modifiers, the O[3] population is additionally dictated by the nAl/nSi ratio of the glass composition. The O[3] sites predominantly connect Al-centered polyhedra, notably so high-coordination AlO5 and AlO6 groups (see Section 5.2.2). Because the latter populations grow together with both xAl and the RE3+ CFS, the highest x[3]O-values (?0.15) are observed for high-CFS Al-rich glasses associated with relatively low values of r ? 2.21, whereas x[3]O stay consistently below 0.10 in La–Al–Si–O structures. These trends may be verified from our previous reports on glasses featuring variable RE:Al:Si contents within each La, Y, and Lu system.
reveal that the O[3] moieties grow largely at the expense of their O[2] counterparts. Further, for a fixed RE:Al:Si stoichiometric ratio,
verifies a strong correlation between (i) Al, which elevates concurrently with x[5]Al, as the AlO6 population remains low throughout
(ii) O and (iii) x[3]O, all of which increase with the RE3+ CFS. However, whereas the Al/O/x[3]O correlations are evident within both RE AS r-branches, their concomitant elevations with the CFS is only transparent along the RE(2.45) series.
–O[p] contacts.
We now examine the various –oxygen contacts, initially from the viewpoint of each Si4+, Al3+, and RE3+cation. For simplicity, we treat all RE[p] coordinations collectively and only summarize the general trends observed throughout all MD-generated structures.
Si exhibits the least preference for any particular O[p] coordination, meaning that the relative number of Si–O[p] bonds roughly reflect each respective x[p]O-value in . Conversely, RE–O[1] contacts are strongly preferred over their RE–O[2] counterparts, approximately by a factor of 3 compared to the predictions from a statistical intermixing based on the x[1]O/x[2]O ratio.
plots the various RE–O[p] populations. The relative preferences among the various
to coordinate the less abundant O[1] and O[3] species constitute their main distinctions: the affinity for X–O[1] bond formation decreases along the series RE(10) >> Si(4) & Al[4](2) & Al[5] ? Al[6](1),(6)with the numbers within parentheses roughly conveying the relative preference of species X to coordinate O[1] compared to that of Al[6] that is least prone to accommodate NBO ions. Typically, ?60% of all NBO ions are located at the SiO4 groups, whereas ?30% and ?15% reside on AlO4 and AlO5/AlO6 polyhedra, respectively. In contrast, the affinity of a
X to coordinate O[3] moieties manifests the reversed trend: besides relatively sparse RE–O[3] contacts, the preference for forming X–O[3] bonds scale roughly as 1:3:5:7–10 for Si:Al[4]:Al[5]:Al[6]. As expected from bond-valence sums, O[3] moieties coordinate at most one Si atom and up to three Al[p] species, where generally at least one is a high-coordination AlO5/AlO6 polyhedron, as illustrated in . The strong preference for Al[p]–O[3] linkages implies a slight Al–Al self-association across the structure, as also noted previously by Christie and Tilocca.
Variation of the RE–O[p] fractional populations associated with (a) p = 0 or (b) p = 1 and p = 2 for each as-indicated series of RE(2.21) and RE(2.45) glasses. Solid and open symbols in (b) represent data for RE–O[1] and RE–O[2] contacts, respectively. Grey lines represent best-fit data.
Despite the ability of Si and Al[p] to accommodate each O[p] species being independent of the nature of the RE element in the glass, the corresponding abundance of each –oxygen contact scales with the relative {x[1]O, x[2]O, x[3]O} values, where the x[2]O/x[3]O ratio is dictated both by the RE3+ CFS and content, as highlighted above.
We next focus on the various Si, Al, and RE
constellations around each O[p] site, denoted here as O[p][q], where q represents the total coordination number when also accounting for the q–p RE–O contacts. For both the O[1][q] and O[2][q] environments, the net coordination number q ranges between 2 and 4, implying that each O atom coordinates 0, 1, or 2 RE3+ . In contrast, the free O2- anions predominantly coordinate 3 ( 50–80%) or 4 ( 10–50%) RE species, where the abundance of the latter grows for increasing RE3+ content (xRE), but diminishes markedly across each RE(r) series as the CFS increases. For instance, O[0][4] groups constitute ≈50% and ≈20% of the O[0] speciation in the La(2.45) and Sc(2.45) structures, respectively. The O[3] moieties predominantly constitute O[3][3] groups devoid of linkages to any RE3+ species, with the O[3][4] population amounting to 5–12% and 10–18% for the RE(2.21) and RE(2.45) series, respectively.
The NBO environments are dominated by O[1][2] constellations involving Si and RE, as well as O[1][3] sites where O coordinates two RE
together with either of Si or Al[p]. The O[1][3] species represent altogether 60–70% of the entire O[1] population. The relative abundance of each O[1][3]–Si/Al[p] moiety is reflected by the relevant fractional population of the
species (see ), weighted by the respective affinity for X–NBO bond formation given by . Furthermore, there are minor contributions from numerous distinct O[1][4] structural fragments, in total representing 3–18% of the total O[1] speciation. For increasing RE3+ CFS, the q = 2 populations grow and those of q = 4 diminish, while the reverse trends are observed when the RE3+ content elevates from xRE = 0.24 [RE(2.21)] to xRE = 0.32 [RE(2.45)].
The same general CFS/xRE trends are observed in the number of O[2]–RE the O[2][4] moieties remain ?10% throughout all structures, whereas the lower formal charge of the O[2] atoms relative to their O[1] counterparts implies overall higher O[2][2] contributions, dominated by Si–O[2]–Si and Si–O[2]–Al[4] fragments. Most Si–O[2]–Si bridges constitute O[2][2] groups devoid of contacts with RE3+. Conversely, roughly equal amounts of O[2][2] and O[2][3] motifs contribute to the overall dominating Si–O[2]–Al[4] linkages. The O[2][3] species involve O[2] coordinated by one RE3+
together with any two members of the set {Si, Al[4], Al[5], Al[6]}. As expected from the accumulated negative charges associated with Al[4]–O[2]–Al[4] bridges, all such motifs require one RE3+
for stabilization, reflected in their sole presence as O[2][3] (as opposed to O[2][2]) groups. O[2][3] moieties are also encountered for the majority of all interpolyhedral bonds involving either of AlO5 or AlO6, such as Si–O[2]–Al[5]/Al[6] and Al[4]–O[2]–Al[5]/Al[6] bridges. Generally, the amounts of the various O[2][3] groups involving Si–O–Al[p] and Al[p]–O–Al[q] linkages with (p, q) = (4, 5, 6) roughly obey a statistical partitioning based on the products between the relative fractions {xSi, xAlx[p]Al} associated with each pair of Si/Al[p] species, as discussed in detail below. Throughout all glass structures, ≈75–80% of all O[2] sites constitute O[2][2](Si, Si), O[2][2](Si, Al[4]), O[2][3](Si, Al[4]), O[2][3](Al[4], Al[4]) and O[2][3](Si, Al[5]) moieties, where the two interlinked
are indicated within parentheses.
and AlOp–AlOq interpolyhedral connectivities
The MD-generated glass structures exhibit networks built by interconnected SiO4 and AlO4 tetrahedra, as well as network-associated AlO5 and AlO6 polyhedra. These groups link through O[2] and O[3] bridging oxygen species, both of which we henceforth collectively refer to as “BO” atoms.
The various SiO4/AlOp polyhedra manifest a non-preferential intermixing, leading to an MD-derived fractional population x(X–Y) of an XOp–YOq pair that is well-approximated by its corresponding product (7)Each of yX and yY represents the fractional population of the given species X and Y out of the total Si and Al speciation, which for the present glass compositions (that exhibit nSi/nAl = 1) corresponds to ySi = 0.5 and y[p]Al = yAlx[p]Al = 0.5x[p]Al, with x[p]Al listed in . Consequently, owing to the dominance of SiO4 and AlO4 groups followed by AlO5, the most frequently encountered pairs of structural building blocks represent SiO4–AlO4, SiO4–SiO4, AlO4–AlO4 motifs, and to a lesser extent SiO4–AlO5 and AlO4–AlO5.
plots the relative abundances of the various pair-connectivities. Note that owing to the small amounts of AlO6 polyhedra, all AlO6–XOp contacts remain low throughout all structures, with the highest fractions x(Si–Al[6]) ≈ x(Al[4]–Al[6]) ≈ 0.03 observed in the Sc(2.45) glass.
Fractional populations of the SiO4–SiO4, SiO4–AlO4, SiO4–AlO5, AlO4–AlO4, AlO4–AlO5, and AlO5–AlO5 interpolyhedral pairs encountered in each (a) RE(2.21) and (b) RE(2.45) glass structure. Each Al[p] coordination is for brevity labeled by its respective integer “p”. Data are not shown for pairs involving AlO6 groups as their populations remain &5% throughout.
We verified that the modeled x(X–Y) fractions closely obey a statistical intermixing, where the deviations between the MD-derived values and the predictions from
are readily explained by the relative preference of each {SiO4, AlOp} polyhedral type to accommodate NBO ions [see ]: the comparatively most abundant Si–NBO bond formation leads consistently to somewhat lower x(Si–Si) populations relative to those predicted by , whereas the reluctance of the AlOp groups to accommodate NBO ions implies the opposite trend for the x(Al[p]–Al[q]) values. In the context of La2O3–Al2O3–SiO2 glasses, a pronounced Si–Al disorder was verified experimentally for SiO4–AlO4 [] and AlOp–AlOq [] contacts, in the latter case by a direct connectivity-probing of the various AlOp–AlOq pairs by double-quantum .
As illustrated by , the Si/Al[p]-centered polyhedra merge by sharing corners or edges that constitute &85% and 5–15% out of the entire BO ensemble, respectively. The RE AS structures are devoid of face-shared SiO4 or AlOp groups. For increasing RE3+ CFS, a slight growth in the relative degree of edge-sharing is observed across each RE(r) glass series, which concerns both the O[2] and O[3] bridges [], particularly for the RE(2.45) members. Yet, the relative preferences of the BO species to participate in edge-sharing differ substantially: while ?95% of all O[2] atoms connect polyhedral corners [], 45–60% of the O[3] counterparts are involved in edge-sharing []. Note that while both the amounts of O[3] moieties (x[3]O) and their affinity for edge-sharing increases concurrently with the RE3+ CFS, the x[3]O values decreases with the r-value, as discussed in Section 5.2.1.
Fraction of bridging oxygen species participating in edge-shared SiO4/AlOp polyhedra, plotted against the RE3+ CFS and considering (a) the total BO speciation (i.e., sum over O[2] and O[3]), or solely each individual (b) O[2] and (c) O[3] population.
Striking differences further emerge when comparing the preferences among the various {SiO4, AlO4, AlO5, AlO6} groups to connect through corners or edges: the strong tendency of O[3] moieties to interlink the
by edge-sharing, coupled with the inherently distinct affinities of the
to form X–O[3] bonds, implies that the participation in edge-shared polyhedra grows along the series Si ? Al[4] << Al[5] & Al[6]. Altogether, the net abundance of edge-shared XOp–YOq polyhedra scales roughly as Si–Si(0%) ≈ Si–Al[4](&1%) & Al[4]–Al[4](&3%) & Si–Al[5](≈5%) & Si–Al[6](≈10%) & Al[4]–Al[5](10–20%) & Al[4]–Al[6](20–25%) << Al[5]–Al[5](≈50%) & Al[5]–Al[6](60–70%) & Al[6]–Al[6](?75%),(8)where the numbers within parentheses reflect the edge-sharing contribution, with the remaining constituting corner-shared polyhedra of the respective type. However, whereas a majority of the AlO5–AlO6 and AlO6–AlO6 linkages occur through edge-sharing, the total amounts of such structural motifs remain very low, as discussed above. Analogously to the relative preferences of each Al[p]–O[q] and Si–O[q] contact, no statistically ascertained variation is observed among the relative tendencies for corner/edge-sharing of the SiO4/AlOp groups when the RE3+ CFS alters.
illustrates a collection of structural fragments typically encountered in the RE AS glass structures.
Edge-shared XOp–YOq polyhedra translate into bond-angles θX–O–Y ≈ 90° that may be compared with their wider corner-shared analogs peaking in the ranges of 110–130° for Al–O–Al/Si and 140–160° for Si–O–Si linkages (see ). Hence, the abundance of edge-shared polyhedra may also be inspected from the plots of the MD-derived angle-distribution functions (ADFs) shown in
for each type of Si–O[p]–Si, Si–O[p]–Al and Al–O[p]–Al contact. The ADF amplitudes of the latter indeed increases markedly around θAl–O–Al = 90°, which is most transparent for the structures involving Sc (and Lu; not shown) that exhibit the largest AlO5/AlO6 populations and thereby the highest extent of edge-sharing.
(a) Si–O–Si, (b) Si–O–Al and (c) Al–O–Al bond-angle (θX–O–Y) distributions for the La(2.45) (left panel) and Sc(2.45) (right) glass structures. “Al” represents the entire {Al[4], Al[5], Al[6]} speciation. Grey and dotted traces reveal the respective θ(X–O[3]–Y) and θ(X–O[2]–Y) contributions (where {X, Y} = {Si, Al}) to the total ADF (black trace).
New RE–O interatomic potential parameters were optimized for RE = {La, Y, Lu, Sc} by a force-matching procedure involving ab initio derived forces in MD-generated RE–Al–Si–O glass structures. Overall they performed well both for reproducing diffraction-derived lattice parameters of crystalline RE-bearing /aluminate structures, as well as short-range features in RE AS glasses, such as previously reported RE–O distances and {Al[4], Al[5], Al[6]} speciations. These self-consistent RE–O potential parameters are expected to be useful for exploring the structures of other amorphous as well as well-ordered RE-bearing -based structures.
The MD-derived average Al coordination numbers (Al) typically reproduce their experimental counterparts within &2% deviation, with the largest discrepancy (3.5%) observed for the Sc(2.21) glass. Whereas Sc3+ mainly assumes Sc[5] coordinations and non-negligible amounts of Sc[4] species (up to ≈20%), all other (larger) RE3+ ions reveal {RE[p]} speciations peaked at p = 6, with La[7] and Lu[5] constituting the second most abundant coordinations for La3+ and Lu3+, respectively. The simulated structures exhibit essentially randomized connectivities among the various SiO4 and AlOp (p = 4, 5, 6) network (associated) polyhedra, a feature attributed to the high charge of the trivalent RE3+ ions, whose comparatively strong RE3+–O bonds (relative to their M+–O and M2+–O counterparts) perturb any Si/Al ordering and also promote otherwise energetically disfavored structural motifs, such as free O2- ions, Al[4]–O–Al[4] bridges, and Al–O[1] contacts. These trends are primarily reflected by the following structural alterations when the RE3+ CFS increases along the series La3+ & Y3+ & Lu3+ & Sc3+:
(i) An increase in the minor but non-negligible populations of free O2- ions (&3.5%) is observed, suggesting a stronger RE–O–RE self-association, where each O[0] site coordinates 3 or 4 RE3+ . The x[0]O values also increase with the RE3+ content.
(ii) Each of Al and O increases by elevating Al[5] and O[3] populations, respectively, at the expense of the dominating Al[4] and O[2] counterparts.
(iii) Whereas &85% of all SiO4 and AlOp polyhedra connect through corners, the degree of edge-sharing increases steadily from ≈5% in the La-based glasses to ≈15% in the Sc analogs. Owing to the strong affinity for Al[5]–O[3] and Al[6]–O[3] bond formation combined with the pronounced tendency of O[3] moieties to create edge-sharing, large fractions of all AlO5 and AlO6 linkages to other groups occur via edge-sharing.
Altogether, the structures of RE2O3–Al2O3–SiO2 glasses exhibit a pronounced disorder both in their distributions of O[p], Al[p] and RE[p] coordinations and how the various structural motifs combine. Effectively, (i) and (ii) imply partial O[1] → O[0] and O[2] → O[3] net conversions as the RE3+ CFS grows, thereby amounting in more complex O[p] speciations compared with the sole presence of O[1] and O[2] moieties expected from traditional theories of glass structures.
The present study corroborates and reinforces previous experimental and computational findings that the structures of RE2O3–Al2O3–SiO2 glasses are strongly influenced by the RE3+ CFS over both short and medium ranges. The large CFS-span across the set {La3+, Y3+, Lu3+, Sc3+}, coupled with the overall monotonic (and occasionally
see ) trends of several structural features against the field-strength, suggest the possibility of roughly assessing the corresponding feature in another RE–Al–Si–O glass that exhibits a similar
composition but a distinct RE3+ ion, based on its CFS-value relative to those considered herein.
This work was supported by the Swedish Research Council (contract VR-NT ) and the Faculty of Sciences at Stockholm University. We thank Jekabs Grins and Alexander Lyubartsev for discussions.
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