Ab Initio Molecular Dynamics Simulations and GIPAW NMR

Subscriber access provided by ORTA DOGU TEKNIK UNIVERSITESI KUTUPHANESI

Article

Ab initio Molecular Dynamics Simulations and GIPAW NMR Calculations of a Lithium Borate Glass Melt Takahiro Ohkubo, Eiji Tsuchida, Takafumi Takahashi, and Yasuhiko Iwadate J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b00381 • Publication Date (Web): 24 Mar 2016 Downloaded from http://pubs.acs.org on March 29, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Ab initio Molecular Dynamics Simulations and GIPAW NMR Calculations of a Lithium Borate Glass Melt Takahiro Ohkubo,∗,† Eiji Tsuchida,‡ Takafumi Takahashi,¶ and Yasuhiko Iwadate† †Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho Inage-ku, Chiba 263-8522, Japan ‡National Institute of Advanced Industrial Science and Technology (AIST), Centeral-2, Umezono 1-1-1, Tsukuba 305-8578, Japan ¶Advanced Technology Research Laboratory, Nippon Steel and Sumitomo Metal Corporation (NSSC), 20-1 Shintomi, Futtsu City, 293-8511, Japan E-mail: [email protected] Phone: +81 (0)43 2903435. Fax: +81 (0)43 2903435

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 31

Abstract The atomic structure of a molten 0.3Li2 O–0.7B2 O3 glass at 1250 K was investigated using ab initio molecular dynamics (AIMD) simulations. The gauge including projector augmented wave (GIPAW) method was then employed for computing the chemical shift and quadrupolar coupling constant of

11 B, 17 O,

and 7 Li from 764 AIMD derived

structures. The chemical shift and quadrupolar coupling constant distributions were directly estimated from the dynamical structure of the molten glass.

11 B

NMR param-

eters of well-known structural units such as the three-coordinated ring, non-ring, and four-coordinated tetrahedron were found to be in good agreement with the experimental results. In this study, more detailed classification of B units was presented based on the number of O species bonded to the B atoms. This highlights the limitations of

11 B

NMR sensitivity for resolving

obtained spectra only. The

17 O

11 B

local environment using the experimentally

NMR parameter distributions can theoretically resolve

the bridging and non-bridging O atoms with different structural units such as non-ring, single boroxol ring, and double boroxol ring. Slight but clear differences in the number of bridging O atoms surrounding Li that have not been reported experimentally were observed in the theoretically obtained 7 Li NMR parameters.

Introduction The structure and properties of alkali borate glasses have been extensively studied in the past 100 years. However, fundamental questions about the structural properties of borate glass are still unresolved because of the variety and complexity of borate bonding. Quantitative structural information such as coordination numbers and bond lengths can be obtained from the interpretation of experimental data such as those obtained by diffraction experiments, 1,2 Raman, 3 and nuclear magnetic resonance (NMR) spectroscopies. 4 However, the presence of structural disorder, mainly related to the distribution of bond angles and bond lengths, makes the identification and quantification of various boron species difficult. It has been 2 ACS Paragon Plus Environment

Page 3 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


widely accepted that amorphous borates generally consist of a network formed by three(BO3 ) and four-coordinated (BO4 ) boron-oxygen units due to bonding involving sp2 and sp3 hybrid orbitals. The BO3 groups can contribute to the formation of six-member boroxol rings (BOring 3 ), which are interconnected with the rest of the BO3 network via bridging oxygen atoms. Other BO3 units are found in non-ring structure (BOnonring ) and connect the 3 glass network through trigonal bonds. These borate networks are easily depolymerized by alkali cations incorporated in the glass, which are compensated by the negatively charged BO4 units. 5,6 This depolymerization leads to the transformation of the bridging oxygen (Ob ) atoms into non-bridging oxygen (Onb ) atoms bonded to a single boron atom. The combination of the boron units and oxygen species suggests the presence of superstructural units in glass network formation, which are frequently referred to as tetraborate and diborate units. 7,8 Similar to the various superstructural units of glass networks, the local environment of alkali cations can be classified by the number and type of neighboring oxygen species. NMR spectroscopy plays an important role in the structural analysis of borate glasses. Selective observation of the local structure for each nuclide can obtain spectra with higher resolution than that available using other spectroscopic approaches; this enables the identification of various structural units.

11

B NMR studies started from 11 B wide-line NMR spectra

of borate glasses in the 1950s. 9 Although

11

B is a highly sensitive nuclide for NMR experi-

ments, it possesses a quadrupole moment and exhibits coupling with the local electric field gradient tensor. The coupling between the quadrupole moment and the local electric field gradient yields anisotropic and broadened resonance lines, which can be described in terms of the quadrupole coupling constant, Cq , and an asymmetry parameter, η, in order to characterize the quadrupole interaction strength. Chemical shifts, δiso based on nuclear shielding are important NMR parameters, that provide the structural identification of boron species nonring such as BO4 , BOring . Modern 3 , and BO3

11

B magic-angle spinning (MAS) NMR under

a high magnetic field can reduce the quadrupole interactions, and can obtain well-resolved spectra for BO3 and BO4 . Furthermore, spectral simulation 10 is now routinely applied to



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

11

Page 4 of 31

B MAS NMR spectra in order to deconvolute the resonance lines corresponding to BO4 ,

nonring BOring . The results obtained from this fitting procedure can estimate the 3 , and BO3

NMR parameters and population of each boron species, but the validity of fitting models for these B species remains an open question. In addition to the

11

B NMR studies,

17

O NMR experiments on borate and alkali borate

glasses have been performed, focusing on understanding the

17

O NMR parameters and the

structural correlations. 4,5,11,12 It is well-known that 17 O MAS NMR spectra can also provide information about the network connectivity. The improved resolution obtained by removing the quadrupole interaction allows the identification of the various bridging oxygen sites. A pioneering

17

O NMR investigation of borate glasses was performed by Youngman et al. in

1995 using double-rotation NMR as a double-axis analog of MAS, 12 and three distinct oxygen atoms with different δiso were resolved. The three different detected δiso were assigned to O in boroxol rings, bridging O with two boroxol rings, and bridging O with two non-ring boron neighbors. Alkali cations such

23

Na and 7 Li are active nuclides for NMR measurements in

glasses, which can be useful for structural analysis. 13–15 Usually, uncharacteristically broadened resonance of these nuclides are only obtained for 7 Li and 23 Na MAS NMR experiments for glass materials. Chemical shifts of alkali cations depend on the cation environment in the glass but are thus less useful as a means of structural identification. The combination of complementary experimental NMR data measurements and atomicscale calculations is now a well-established approach for studying the structure of materials, which has been shown to obtain quantitatively accurate structural information. Due to the development of the density functional theory (DFT) gauge including projector augmented wave (GIPAW) method, 16,17 prediction of accurate NMR parameters is possible for a given atomic configuration. This new approach for understanding the NMR spectra not only enables accurate spectral assignment but can also be used to estimate the NMR parameter distribution, as described in a recent review article. 18 For disordered systems, classical molecular dynamics (MD) simulations are generally employed to obtain a sample glass struc-


Page 5 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ture prior to the GIPAW calculation, and then following the structural optimization of the equilibrium MD structure within the DFT framework, the GIPAW calculation is applied to the electronic wave function. The computed NMR parameters are then compared with the experimental spectra. To reproduce a broadened NMR parameter distribution, a more advanced statistical approach was used for the simulation of NMR spectra including the two-dimensional multiple quantum MAS NMR spectrum by introducing a Gaussian-like distribution function. 19 As reviewed in reference, 18 GIPAW calculations based on MD-derived structures offer a novel approach for estimating the NMR parameter distributions. While the use of this approach has led to the development of new methodology for interpreting NMR parameter distributions, several basic questions still remain unresolved. For example, it is unclear whether a single MD-derived structure is sufficiently representative of the atomic configurations sampled by the system; furthermore, the proper functional form of the NMR parameter distribution function is unknown and the structural configuration used for NMR modeling may be inaccurate due to deficiencies in classical force fields and the use of an unrealistically high quenching rate for obtaining the MD-derived structure. Several new features are introduced into the computational modeling used in this study in order to address the possible deficiencies of the standard GIPAW simulations of the NMR spectra. First, we obtain structural distributions from multiple ab initio MD (AIMD)-derived structures. Second, NMR parameters are directly obtained from GIPAW calculations for atomic configurations. While this approach clearly incurs a higher computational cost, it enables the direct calculation of NMR spectra without the use of the arbitrary distribution functions. In this study, we apply the AIMD-GIPAW method to the study of the 0.3 Li2 O−0.7 B2 O3 glass system. This alkali-borate glass exhibits complex network formation, and the composition of the network in terms of the different structural motifs is a subject of ongoing structural modeling by experimental and theoretical investigations. Therefore, we used the study of this composition for the validation of the AIMD-GIPAW method and to describe the various structural units of the 0.3 Li2 O−0.7 B2 O3 lithium borate glass. While 5 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 31

solid-state NMR spectroscopy has been demonstrated to be a unique structural analysis tool for borate glasses, information provided by NMR alone is insufficiently detailed to serve as the finger-prints for the characterization of the more complex structures. Therefore, in the present study, we aim to use the AIMD-GIPAW method to explore the possibility of identifying the various structural units of a lithium borate glass based on 7 Li,

11

B, and

17

O NMR

parameter data.

Computational details AIMD simulations were performed for an initial 202-atom configuration obtained in our previous AIMD study. 20 We used the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) to the exchange-correlation functional. The Brillouin zone was sampled at the Γ-point. All calculations were performed using our density functional theory code F EM T ECK 21 (finite element method-based total energy calculation kit). The production run in this study was performed using an average cutoff energy of 84 Ry and a time step of 1.2 fs. 764 atomic configurations were saved for use in GIPAW calculations. The nuclei were classically treated, and their equations of motion were integrated using the Verlet algorithm with forces calculated from the electronic structure. The temperature was controlled using a Berendsen thermostat 22 with a target temperature of 1250 K. The simulation system was composed of 202 particles, including Li, B, and O atoms, with the desired composition of 0.3 Li2 O−0.7 B2 O3 . We emphasize that the theoretical studies of glass melts with a flexible structure is worth to survey possible structural sets for NMR parameters of glasses. GIPAW calculations were performed using the Quantum Espresso package; 23 therefore, DFT calculations were again carried out to obtain accurate NMR parameters based on the AIMD-derived atomic configurations. We used a 1×1×1 Monkhorst-Pack grid and a planewave basis up to an energy cutoff (ecutwfc = 80 Ry and ecutrho = 500 Ry) for PBE GGA calculations using the projector augmented-wave potentials taken from PS library 0.3.1. 24


Page 7 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The energy fluctuation of the system during GIPAW calculation steps was shown in Fig. S1 of Supporting Information. We have confirmed that the obtained total energy and NMR parameter values are converged with respect to the energy cutoff and k-point sampling density. The reference isotropic shielding and nuclear quadrupole moment (here for 17

11

B and

O) were adjusted based on the values obtained by GIPAW calculations of the referenced

crystal compounds. Here, the chosen reference crystalline systems were LiBr and LiF for 7

Li; LiBO2 , NaBO2 , and B2 O3 for 11 B; and α-quartz, β-cristobarite, and coesite for 17 O. We

did not apply an additional structural optimization and volume scaling from experimental crystalline structure used previously to quantitatively assess the NMR parameters from DFT calculations. 25,26 Although GIPAW results with scaling volume and structural optimization showed better agreement with experimental values, the use of referenced results allows us to accurately predict the NMR parameters within an acceptable error range (see Table S1 in Supporting Information). Therefore, we implemented all GIPAW calculations based on referenced materials without additional structural optimization. Structural classification must be used to identify the relationships between NMR parameters and structural properties. Structural definitions of B, O, and Li units used in the following discussion were determined based on the atomic configuration. First, the existence of the bond between B and O was defined using a threshold of 2 Å, determined based on the first-coordination sphere of the B–O pair distribution function. By defining B–O bonds, nonring structural assignments of each atom in the configuration, such as BOring , Ob , and 3 , BO3

Onb were possible based on the number of interatomic bonds and the connectivity. The association of these structural classifications with GIPAW outputs obtained using Quantum Espresso was performed using an in-house program.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 31

Results and discussion Boron-11 The structures of the identified borate species are shown in Fig. 1 with red and blue circles corresponding to B and O, respectively. Black edged red circles in the figure represent the B atoms referred to by the labels in the figure. Dotted lines on O atoms represent bonding to other B atoms and negative signs indicate Onb . We used B3, P3, and Q4 to denote BOnonring , 3 BOring 3 , and BO4 , respectively, which are the same as those in the previous crystalline borate 11

B MAS NMR study. 27 The fourth letter (n of Tn) in the notation indicates the number of

Ob bonded to the represented B. For the Q4 species, the last character (“r” or “dr”) in the notation indicates the species of borate units joining one (“r”) or two rings (“dr”). δiso distributions for all B species are presented in Fig. 2. The δiso distribution curves are obtained based on 764 snapshots and a histogram with 0.45455 ppm bin width, which is sufficient to characterize the δiso distribution. The distribution line shapes for each B species were symmetric Gaussian. The obtained 11

B chemical shift ranges are in agreement with the experimental values found in previous

borate and borosilicate glass studies. 28 The half-width of each distribution is approximately 10 ppm with essentially the same value for all B species. The averaged δiso values of BO3 species listed in Table 1 display the following general trend:

δiso (P3T2) ≥ δiso (P3T3) > δiso (B3T2) > δiso (B3T3)

(1)

and for BO4 species:

δiso (Q4T3) ≫ δiso (Q4T4dr) > δiso (Q4T4r) > δiso (Q4T4)

(2)

Formation of B3T1 and Q4T3r was not confirmed in our AIMD simulation. Q4T3 structural units have not been experimentally reported for borate systems, and are clearly un8 ACS Paragon Plus Environment

Page 9 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


reasonable in terms of charge balance. Although a small population of Q4T3 was indeed observed in the simulated structures, these Q4T3 units are expected to be in a transient state rather than representing a stable structural unit. Simulations of experimental

11

B MAS NMR spectra by a fitting procedure on the ba-

nonring sis of three borate units, namely, BOring , and BO4 have now become a standard 3 , BO3

technique for determining the populations of these borate structural motifs. Because of the small Cq value, in this fitting procedure, the BO4 line shape is described using either a single Gaussian function or a symmetric line pattern regardless of the strength of the quadrupole interaction. To the best of our knowledge, the direct observation of multiple BO4 species bonding with different number of Ob has not been reported in the past. We find the calculated average δiso of Q4T4, Q4T3, and Q4T4dr are 1.58, 3.23, and 4.12 ppm; these values are sufficiently separated to be resolved by NMR experiments using high-resolution NMR spectra, which can be obtained with better equipment than the NMR apparatus used in the present study. As an example, theoretical lineshapes of

11

B MAS and static NMR spec-

tra were shown in Fig. S2 of Supporting Information. Since structural distribution and residual interactions affect the line broadening of the experimentally obtained

11

B NMR

spectra, advanced solid-state NMR experiments including multidimensional techniques under extremely high-magnetic field can be revealed the presence and the relative contents of these BO4 species. Kreker and Stebbins observed that δiso tends to decrease with increasing polymerization, i.e., with the replacement of Onb by Ob in the structures. 27 An identical trend for BOnonring (B3T3 and B3T2) and BOring (P3T3 and P3T2) is observed in our the3 3 oretical approaches. Chemical shift tensors may also give us useful information to identify atomic configurations. Although these parameters are quite difficult to experimentally observe for glasses at the moment, it would be helpful to show these theoretical distributions for future comparison.

11

B chemical shift anisotropy and asymmetry distributions were pro-

vided in Supporting Information (Fig. S5). A clear difference between B3T3 and B3T2 was confirmed by chemical shift anisotropy. This feature is valuable for experimental NMR setup



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 31

to investigate B species in borate glasses. Figure 3 shows Cq distribution of the B species, obtained from a histogram with 0.045455 MHz bin width. The average and standard deviation of Cq for each B species are also listed in Table 1. Cq values of all BO3 species are larger than those for the BO4 species, which is in agreement with the trend observed in the experimental results obtained by previous 11

B NMR studies. 11,29 Figure 3 shows that each distribution exhibits a short tail toward

higher Cq instead of a symmetric Gaussian shape. Similar to the δiso results, the observed clear difference between the Cq values for B3T3 and B3T2 was confirmed that the number of Onb bonded to B is a critical parameter for quadrupole pole interaction of B nuclei. For the BO4 species, the Cq values show an extremely broad distribution with an extent of up to almost 2 MHz. Due to the neglect of the effect of the atomic dynamics, it is expected that a disordered tetrahedral structure obtained from a single snapshot structure of AIMD simulation at a given time step would lead to estimated Cq values that are higher than those obtained experimentally. Cq values of BO4 listed in Table 1 are constant to within 0.1 MHz, indicating that the boron ring formation is insensitive to Cq . No clear correlation could be found for η in various B units defined in this study. A combined effect of δiso and Cq was also displayed on a contour map (Fig. S8 in Supporting Information). The difference in BO4 , BOnonring , and BOring was more clear on the figure. 3 3

Oxygen-17 17

O NMR parameters are sensitive to changes in the local environment. Therefore, numerous

17

O NMR data of oxide glasses including silicates and borosilicates have been performed to

understand oxygen connectivity. 30–32 A pioneering structural study of borate glasses using 17

O NMR was performed using double rotation (DOR) NMR experiments to remove the

second-order quadrupole interaction, 12 enabling the resolution of the different oxygen sites in B2 O3 . Three distinct oxygen sites in B2 O3 were clearly resolved in the

17

O DOR NMR

spectra assigned to the O atoms contained within the boroxol rings, O atoms bridging two 10 ACS Paragon Plus Environment

Page 11 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


boroxol rings, and O atoms bridging two non-ring B units. In the present study, we defined the structural units on the basis of distinct Ob and Onb sites resulting from the interruption of the network by alkali cations with schematic illustrations of the five different O species shown in Fig. 4. For these structures, red and blue circles correspond to B and O, dotted lines represent bonds to other boron atoms, and negative signs indicate Onb . The notation of T, Tr, and Tdr is used to identify the borate structural units to which the O atoms belong, where T, Tr and Tdr denote bonding with only non-ring B or B in BO4 , with B in one ring boron, and with B in interconnecting double rings, respectively. Figure 5 shows the δiso distribution of each O species plotted based on a histogram with 2.7273 ppm bin width. The distributions of all O species exhibit single peaks at approximately 100 ppm with full width at half maximum of 50 ppm. Figure 5 shows that the δiso distribution for

17

O is extremely broad compared with the experimentally reported

17

O

DOR NMR spectra. 12 The fluctuations of atomic motion in the real sample may cause the narrowing of δiso distribution, which was not taken into consideration in the GIPAW calculations. Interestingly, result is that the line shape for the O2Tdr site is triangular rather than Gaussian, corresponding to a unique distribution of structural parameters such as bond lengths and angles. The O1T δiso distribution exhibits two peaks at approximately 100 and 25 ppm, indicating that we have to consider the use of an additional structural classification for the O1T sites. The relationship between the O1T

17

O chemical shift and the distance to

the nearest Li and B is shown in Figure 6. The O1T-Li distance does not show a correlation with δiso , while the O1T-B distance is weakly correlated with δiso . The electronic state with a shorter distance between Onb and B would exhibit a higher electronic density corresponding to the higher field shift. Sensitive distinction between O species was also observed in chemical shift anisotropy and asymmetry (see Fig. S6 in Supporting Information). As far as we know, an experimental observation has not been reported previously. These distributions may be utilized for oxygen identification in the future. Therefore, theoretical lineshapes of MAS and static NMR spectra were shown in Fig. S3 of Supporting Information as an example.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 31

The Cq distribution for each O species are shown in Fig. 7. The peak position of each species clearly reflects the changes in the O local environment caused by various electric fields. A clear trend is observed for Cq values of O2T, O2Tr, and O2Tdr sites with double bonds showing higher values than the O1T and O1Tr sites with single bonds. The Onb sites experimentally resolved by triple quantum MAS NMR in borosilicate glasses exhibit clearly lower Cq values compared with those for the Ob site 11 as well as the values obtained in our theoretical calculations. The formation of double bonds with B leads a decrease in the three-dimensional symmetry of the electric field of the nuclei. Table 2 shows the fraction, mean values, and standard errors of 17 O NMR parameters for each species. The theoretical results for the O2Tr and O2T species can be compared with experimental values obtained for borate glasses without Li2 O. 12 The theoretical δiso values are in good agreement with the experimental values. However, the Cq values are higher than the experimental values by approximately 1.0 MHz, possibly due to the effect of nuclear motion in the experimental frame and the cation electronic field. However, the combinations of δiso and Cq exhibit unique trends for each of the five O species, showing that it is possible to resolve new oxygen environments by 17 O NMR. In summary, our calculations suggest that 17

O NMR experiments can reveal the differences between the O atoms with respect to both

their bridging number and the type of bonded B species. A contour map of

17

O δiso and

Cq was shown to visualize the correlation effect of NMR parameters (Fig. S9 in Supporting Information). As seen in Figs. 5 and 7, Cq was more sensitive to identify O species. As seen in Figs. 5 and 7, Cq was more sensitive to the status of O species.

Lithium-7 While the spin = 3/2 7 Li nucleus is commonly used for solid-state NMR, the 7 Li NMR spectra for lithium oxide glass materials generally show a single broad peak, which does not provide useful information for the investigations of the details of the local Li environment. In lithium silicate glasses, the 7 Li chemical shift was found to change continuously with composition, 12 ACS Paragon Plus Environment

Page 13 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


with Li+ uniformly distributed in the glass network. 33 Because the 7 Li chemical shift range is rather small, the correlations between the local structure and NMR parameters are very limited. Therefore, it is important to theoretically elucidate the 7 Li chemical shift arising from different possible atomic configurations in order to resolve new Li environments. The Li–O radial distribution function can provide the coordination number of the first neighbor shell and indicates that the average number of O coordination for Li is four. 20 Based on this, we assumed that five Li structures are present that are coordinated by a different number of Ob , as shown in Fig. 8. The δiso and Cq distributions for different Li species are displayed in Figs. 9 and 10, respectively, and Table 3 lists the values of the average and standard error for these species. A contour map of 7 Li δiso and Cq was also shown in Fig. S10 of Supporting Information. A trend of δiso values with Ob number was found, with the higher Ob coordination leading to higher field shift for all cases except LiT0. The full width at half maximum of the δiso distribution is approximately 2 ppm; this is expected to lead to difficulties for observing individual peaks for the limited experimental resolution. Previous experiments have shown that the average 7 Li δiso of lithium silicate glasses becomes more positive with increasing Li2 O contents, corresponding to the increasing number of Onb in the glass network. 33 Our results are in good agreement with this experimentally observed behavior, namely higher coordination number of Onb leads to the lower field shift of δiso . Since the NMR spectra predicted by GIPAW calculations can completely resolve the contribution of different Li coordination environments, this represents a robust demonstration of the relationship between the Onb number and δiso . The Cq distribution of different Li sites can also be distinguished despite the overlap of the peaks for the different Li species. Although only a small Cq change for 7 Li was estimated from GIPAW calculations, the trend of increasing Cq with decreasing number of Ob neighbors can be clearly observed from the average values shown in Table 3. We also calculated distributions of 7 Li chemical shift anisotropy and asymmetry (Fig. S7 in



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Supporting Information).

7

Page 14 of 31

Li chemical shift anisotropy was broadened distribution, while

chemical shift asymmetry was more sensitive for Li identification. Although these changes may be difficult to observe in experimental spectra, we show theoretical lineshapes of MAS and static NMR spectra in Fig. S4 of Supporting Information. To the best of our knowledge, such a weak dependence of δiso and Cq has been theoretically obtained for the first time in the present study and will be useful to interpret the slight changes in the experimental 7 Li NMR spectra for different composition and environments such as those obtained under high pressure. 34

Conclusions NMR parameter distributions of

11

B,

17

O, and 7 Li in a lithium borate glass were obtained

by GIPAW calculations with 764 theoretical structural models derived from AIMD for an in-depth interpretation of the experimental solid-state NMR data. The calculated chemical shift ranges for

11

B are in agreement with the experimental

values obtained in the studies of borate and borosilicate glasses.

11

B δiso values are affected

nonring by the number of Ob neighbors and the coordination type (BOring , and BO4 ). The 3 , BO3

general NMR parameter trends were found by defining 10 types of B sites depending on the bonding structure and number of Ob neighbors. An increase in the number of Ob induces the shift toward the lower field by approximately 1 ppm regardless of the B coordination type. Furthermore, the δiso of B incorporating a double-ring structure was shifted to lower fields by 1 ppm compared to that of B in a single ring structure. Similar to δiso , a clear difference in the Cq values of B3T3 and B3T2 confirmed that the number of Onb bonding with B affects the electronic distribution of B nuclei by approximately 0.2 MHz. 17

O spectra obtained from GIPAW calculations could reproduce the trends experimentally

observed for oxide glasses for the Ob and Onb sites. The

17

O NMR parameters and the

local structure were correlated with Ob connecting double boroxol rings displaying δiso at a


Page 15 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


lower field than that found for the Ob connected to a single boroxol ring. This enabled the quantification of the content of these O species from experimental spectra. Slight changes in 7 Li NMR parameters for different types of O neighbors could be detected by the statistical treatment of GIPAW calculations. The determination of 7 Li NMR parameters by GIPAW calculations combined with AIMD opens for the detection of the details of the environment surrounding the 7 Li atom by solid-state NMR.

Acknowledgments The calculations were performed using computer facilities of the Research Institute for Information Technology, Kyushu University.

Associated Content Supporting Information The Supporting Information is available free of charge on the ACS Publications website. NMR parameters for the reference crystalline samples; fluctuation of energy during GIPAW calculations; theoretical line shapes of static and MAS spectra of

11

B,

the statistical distribution of chemical shift anisotropy and asymmetry for 7

17 11

O, and 7 Li;

B,

17

O, and

Li; Two-dimensional correlation NMR spectra of chemical shift and quadrupole coupling

constant for

11

B,

17

O, and 7 Li

This information can be found on the internet at http://pubs.acs.org.

References (1) Krogh-Moe, J. The Structure of Vitreous and liquid Boron Oxide. J. Non-Cryst. Solids 1969, 1, 269–284.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 31

(2) Johnson, P. A.; Wright, A. C.; Sinclair, R. N. A Neutron Diffraction Investigation of the Structure of Vitreous Boron Trioxide. J. Non-Cryst. Solids 1982, 50, 281–311. (3) Ferlat, G.; Charpentier, T.; Seitsonen, A. P.; Takada, A.; Lazzeri, M.; Cormier, L.; Calas, G.; Mauri, F. Boroxol Rings in Liquid and Vitreous B2 O3 from First Principles. Phys. Rev. Lett. 2008, 101, 65504. (4) Jellison Jr, G.; Panek, L.; Bray, P.; Rouse Jr, G. Determinations of Structure and Bonding in Vitreous B2 O3 by means of

B,

10

11

B, and

O NMR. J. Chem. Phys. 1977,

17

66, 802–812. (5) Youngman, R. E.; Zwanziger, J. W. Network Modification in Potassium Borate Glasses: structural Studies with NMR and Raman Spectroscopies. J. Phys. Chem. 1996, 100, 16720–16728. (6) Feller, S.; Dell, W.; Bray, P. 10B NMR Studies of Lithium Borate Glasses. J. Non-Cryst. Solids 1982, 51, 21–30. (7) Dwivedi, B.; Rahman, M.; Kumar, Y.; Khanna, B. Raman Scattering Study of Lithium Borate Glasses. J. Phys. Chem. Solids 1993, 54, 621–628. (8) Bray, P.; Feller, S.; Jellison, G.; Yun, Y.

B NMR Studies of the Structure of Borate

10

Glasses. J. Non-Cryst. Solids 1980, 38, 93–98. (9) Silver, A.; Bray, P. Nuclear Magnetic Resonance Absorption in Glass. I. Nuclear Quadrupole Effects in Boron Oxide, Soda-Boric Oxide, and Borosilicate Glasses. J. Chem. Phys. 1958, 29, 984–990. (10) Massiot, D.; Fayon, F.; Capron, M.; King, I.; Le Calvé, S.; Alonso, B.; Durand, J.-O.; Bujoli, B.; Gan, Z.; Hoatson, G. Modelling One-and Two-dimensional Solid-state NMR Spectra. Magn. Reson. Chem. 2002, 40, 70–76.


Page 17 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(11) Wang, S.; Stebbins, J. F. Multiple-Quantum Magic-Angle Spinning

O NMR Studies

17

of Borate, Borosilicate, and Boroaluminate Glasses. J. Am. Ceram. Soc. 1999, 82, 1519–1528. (12) Youngman, R.; Haubrich, S.; Zwanziger, J.; Janicke, M.; Chmelka, B. Short-and Intermediate-range Structural Ordering in Glassy Boron Oxide. Science 1995, 269, 1416–1420. (13) Krämer, F.; Müller-Warmuth, W.; Scheerer, J. Natrium-23 und Lithium-7 NMRUntersuchungen an Silicat-und Boratgläsern/ 23Na and 7Li NMR Studies of Silicate and Borate Glasses. Zeitschrift für Naturforschung A 1973, 28, 1338–1350. (14) Ratai, E.; Janssen, M.; Eckert, H. Spatial Distributions and Chemical Environments of Cations in Single and Mixed Alkali Borate Glasses: Evidence from Solid State NMR. Solid State Ionics 1998, 105, 25–37. (15) George, A.; Sen, S.; Stebbins, J.

23

Na Chemical Shifts and Local Structure in Crys-

talline, Glassy, and Molten Sodium Borates and Germanates. Solid State Nucl. Magn. Reson. 1997, 10, 9–17. (16) Profeta, M.; Mauri, F.; Pickard, C. J. Accurate First Principles Prediction of

17

O NMR

Parameters in SiO2 : Assignment of the Zeolite Ferrierite Spectrum. J. Am. Chem. Soc. 2003, 125, 541–548. (17) Pickard, C. J.; Mauri, F. All-electron Magnetic Response with Pseudopotentials: NMR Chemical Shifts. Phys. Rev. B 2001, 63, 245101–245115. (18) Charpentier, T.; Menziani, M. C.; Pedone, A. Computational Simulations of Solid State NMR Spectra: A New Era in Structure Determination of Oxide Glasses. RSC Adv. 2013, 3, 10550–10578.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 31

(19) Pedone, A.; Charpentier, T.; Menziani, M. C. Multinuclear NMR of CaSiO3 Glass: Simulation from First-principles. Phys. Chem. Chem. Phys. 2010, 12, 6054–6066. (20) Ohkubo, T.; Tsuchida, E.; Gobet, M.; Sarou-Kanian, V.; Bessada, C.; Iwadate, Y. First-Principles Molecular Dynamics Simulation and Conductivity Measurements of a Molten xLi2 O−(1−x)B2 O3 System. J. Phys. Chem. B 2013, 117, 5668–5674. (21) Tsuchida, E.; Tsukada, M. Adaptive Finite-element Method for Electronic-structure Calculations. Phys. Rev. B 1996, 54, 7602–7605. (22) Berendsen, H.; Postma, J.; Van Gunsteren, W.; DiNola, A.; Haak, J. Molecular Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684–3690. (23) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. et al. QUANTUM ESPRESSO: A Modular and Open-source Software Project for Quantum Simulations of Materials. J. Phys.: Cond. Matter 2009, 21, 395502–395521. (24) Dal Corso, A. Pseudopotentials Periodic Table: From H to Pu. Comput. Mater. Sci. 2014, 95, 337–350. (25) Charpentier, T.; Kroll, P.; Mauri, F. First-principles Nuclear Magnetic Resonance Structural Analysis of Vitreous Silica. J. Phys. Chem. C 2009, 113, 7917–7929. (26) Ispas, S.; Charpentier, T.; Mauri, F.; Neuville, D. Structural Properties of Lithium and Sodium Tetrasilicate Glasses: Molecular Dynamics Simulations Versus NMR Experimental and First-principles Data. Solid State Sci. 2010, 12, 183–192. (27) Kroeker, S.; Stebbins, J. F. Three-coordinated Boron-11 Chemical Shifts in Borates. Inorg. Chem. 2001, 40, 6239–6246. (28) Sen, S.; Xu, Z.; Stebbins, J. Temperature Dependent Structural Changes in Borate,


Page 19 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Borosilicate and Boroaluminate Liquids: High-resolution

11

B,

29

Si and

Al NMR Stud-

27

ies. J. Non-cryst. Solids 1998, 226, 29–40. (29) Youngman, R.; Zwanziger, J. Multiple Boron Sites in Borate Glass Detected with Dynamic Angle Spinning Nuclear Magnetic Resonance. J. Non-cryst. Solids 1994, 168, 293–297. (30) Nasikas, N.; Edwards, T.; Sen, S.; Papatheodorou, G. Structural Characteristics of Novel Ca-Mg Orthosilicate and Suborthosilicate Glasses: Results from

29

Si and

17

O

NMR Spectroscopy. J. Phys. Chem. B 2012, 116, 2696–2702. (31) Pedone, A.; Gambuzzi, E.; Menziani, M. C. Unambiguous Description of the Oxygen Environment in Multicomponent Aluminosilicate Glasses from

17

O Solid State NMR

Computational Spectroscopy. J. Phys. Chem. C 2012, 116, 14599–14609. (32) Stebbins, J. F.; Sen, S. Oxide Ion Speciation in Potassium Silicate Glasses: New Limits from

O NMR. J. Non-Cryst. Solids 2013, 368, 17–22.

17

(33) Gee, B.; Janssen, M.; Eckert, H. Local Cation Environments in Mixed Alkali Silicate Glasses Studied by Multinuclear Single and Double Resonance Magic-angle Spinning NMR. J. Non-cryst. Solids 1997, 215, 41–50. (34) Edwards, T.; Endo, T.; Walton, J. H.; Sen, S. Observation of the Transition State for Pressure-induced BO3 −−→ BO4 Conversion in Glass. Science 2014, 345, 1027–1029.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 1: Unit B3T3 B3T2 B3T1 P3T3 P3T2 Q4T4 Q4T3 Q4T4r Q4T3r Q4T4dr

n 6318 7651 n/a 20789 814 1482 28 9425 n/a 1624

Pop. (%) 13.13 15.90 n/a 43.19 1.69 3.08 0.06 19.58 n/a 3.37

Table 2: Unit O1T O2T O1Tr O2Tr O2Tdr

n 9207 10075 814 19813 44009

11

Pop. (%) 10.97 12.01 0.97 23.61 52.44

B NMR parameters δiso (ppm) 16.66 ± 3.99 17.49 ± 3.18 n/a 19.53 ± 3.22 20.05 ± 3.30 1.58 ± 4.07 10.52 ± 3.10 3.23 ± 3.22 n/a 4.11 ± 3.35

17

Page 20 of 31

Cq (MHz) η 2.62 ± 0.27 0.44 ± 0.23 2.46 ± 0.21 0.71 ± 0.20 n/a n/a 2.54 ± 0.19 0.46 ± 0.24 2.49 ± 0.14 0.76 ± 0.17 1.25 ± 0.52 0.63 ± 0.24 2.33 ± 0.31 0.59 ± 0.23 1.08 ± 0.44 0.61 ± 0.24 n/a n/a 1.11 ± 0.37 0.58 ± 0.25

O NMR parameters

δiso (ppm) 99.14 ± 36.27 107.94 ± 21.51 120.50 ± 24.02 99.26 ± 21.32 102.03 ± 20.94

Cq (MHz) 3.96 ± 1.02 5.95 ± 0.87 4.21 ± 0.75 5.97 ± 0.96 5.39 ± 0.98

η 0.54 0.58 0.61 0.61 0.59

± ± ± ± ±

0.25 0.24 0.22 0.24 0.25

Table 3: 7 Li NMR parameters Unit LiT4 LiT3 LiT2 LiT1 LiT0

n 4218 12761 3651 749 13

Pop. (%) 19.72 59.65 17.07 3.50 0.06

δiso (ppm) -1.53 ± 1.37 -1.27 ± 1.26 -0.70 ± 1.31 -0.83 ± 1.22 -1.19 ± 0.60

Cq (MHz) 0.16 ± 0.06 0.17 ± 0.06 0.20 ± 0.07 0.25 ± 0.10 0.34 ± 0.05


η 0.60 0.61 0.64 0.58 0.26

± ± ± ± ±

0.25 0.24 0.24 0.26 0.03

Page 21 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


%7

37

47

47U

%7

%7

37

47

47U

47GU

Figure 1: Schematic depiction of borate species. Red and blue circles correspond to boron and oxygen, respectively. Dotted lines represent bonding to other boron atoms; negative signs indicate Onb . Borate species are classified by BOnonring (B3), BOring 3 3 (P3), and BO4 (Q4). n in Tn notation indicates the number of Ob bonding with boron.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 31

Figure 2: 11 B NMR chemical shift distributions of borate species in lithium borate glass. Distributions are drawn based on a histogram with 0.45455 bin width.


Page 23 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3: 11 B quadrupole coupling constant distributions for borate species in lithium borate glass. Distributions are based on a histogram with 0.045455 bin width.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

27

27

Page 24 of 31

27U

27

27U

27GU

Figure 4: Schematic depiction of oxygen species. Red and blue circles correspond to boron and oxygen, respectively. Dotted lines represent bonding to other boron atoms; negative signs indicate Onb . n in On means bonding number of boron, that is, O1 and O2 correspond to Onb and Ob , respectively. T, Tr, and Tdr indicate the structural units to which the O atoms belongs; T, Tr, and Tdr bonding with only non-ring boron atoms, with one-ring boron atom, and with two-ring boron atoms, respectively.


Page 25 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5: 17 O NMR chemical shift distributions for oxygen species in lithium borate glass. The distributions are based on a histogram with 2.7273 bin width.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6: Calculated B distance.

17

Page 26 of 31

O NMR chemical shifts for O1T plotted against the nearest Li and 26 ACS Paragon Plus Environment

Page 27 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7: 17 O quadrupole coupling constant distributions for oxygen species in lithium borate glass. The distributions are drawn based on a histogram with 0.10606 bin width.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

/L7

/L7

/L7

/L7

Page 28 of 31

/L7

Figure 8: Schematic depiction of lithium species for lithium borate glass. Red, blue, and yellow circles correspond to boron, oxygen, and lithium, respectively. n in LiTn indicates the number of Ob in first coordination sphere.


Page 29 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9: 7 Li NMR chemical shift distributions for lithium species in lithium borate glass. The distributions are based on a histogram with 0.1111 bin width.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 31

Figure 10: 7 Li quadrupole coupling constant distributions for oxygen species in lithium borate glass. Distributions are based on a histogram with 0.008080 bin width.


Page 31 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A Graphic for Table of Contents

27

27

27U

27

27U

27GU


Ab Initio Molecular Dynamics Simulations and GIPAW NMR

Recommend Documents