J . Phys. Chem. 1989, 93, 7895-7902 symmetry axis of the latter substantially favors the formation of the solvent-separated pair over the contact ion pair. In contrast, it is this contact pair which is the global minimum for a dielectric continuum model. Conversely, for the asymmetric approach of Na+ to D M P , along the direction of one of the phosphateanionic oxygen bonds, the contact and solvent-separated species are nearly isoenergetic and stabilized by roughly 1 kcal/mol over the solvent-separated species for the symmetric intermolecular geometry. These results demonstrate the orientational dependence of PMF's involving nonspherical molecules. Correspondingly, it is noteworthy that, at least according to the present calculations, the contact ion pair (in an asymmetric configuration) is expected to have a population comparable to that of solvent-separated species. Such proximity can significantly influence counterion spin relaxation,I8 and further, indicates that modeling of the effective interaction via a single hydrated or unhydrated radius for the cation is unlikely to be successful. Comparison of the results obtained from the two distinct simulation types provides the first indication of the degree to which the methods employed in the calculation of PMF's affect the results. It is seen that the relative hydration free energy for the association of the ions is predicted equally well by the results of the two methods employed here only for small interionic separations corresponding to the region around the contact minimum. At larger separations, an unphysical behavior of the P M F results for the smaller system, and this can be explained solely by the choice of potential cutoff. An interesting question that remains to be addressed concerns the site-site decomposability of such free energy surfaces2 The results obtained here reflect the total potentials of average force between Na+ and the molecular anion D M P in a fixed relative geometry. How would the results obtained from the addition of the PMF's for the isolated component atomic pairs compare to
7895
the present results? The results obtained here provide a reference for future investigation of this approximate approach. However, it seems unlikely that the relatively large free energy cost associated with the formation of the contact ion pair for the symmetric approach to the anion could be recovered from such an approximation. As mentioned in the introduction to this paper, previous work from this lab has focused on the interaction of DNA with the counterionic environment.18 In that work, the solvent was modeled as a dielectric continuum. The usefulness of the dielectric continuum studies can be clarified by comparison of certain of those results with future results obtained with more precise modeling of the solvent, via the PMF's presented here. The full exploitation of computer simulation methods in the study of these systems requires that we neither model the solvent at an unnecessarily fundamental level nor neglect the effects of the solvent's molecular nature. Reliable techniques for the elucidation of PMF's are of paramount importance in this regard. Further study is thus required. Specifically, additional testing of the calculation of these quantities from sources such as integral equations is needed, as is more work on the systematics of computer simulation as applied to these problems and on the sensitivity of the results to choice of potential model. Further studies along these lines are planned.
Acknowledgment. Support of this work by grants from the National Institute of General Medical Sciences and the Robert A. Welch Foundation is acknowledged, as is computational support from the University of Texas System Center for High Performance Computing. P.J.R. is the recipient of an NSF Presidential Young Investigator Award and a Camille and Henry Dreyfus Foundation Teacher-Scholar Award. Registry No. NaMe2P0, 32586-82-6.
Chemical Disorder in Non-Oxide Chalcogenide Glasses. Site Speciation in the System Phosphorus-Selenium by Magic Angle Spinning NMR at Very High Spinning Speeds David Lathrop and Hellmut Eckert* Department of Chemistry, University of California at Santa Barbara, Goleta, California 93106 (Received: March 9, 1989)
The local structure of phosphorusselenium glasses with P contents ranging from 5 to 75 atom % P is investigated by magic angle spinning (MAS) 31PNMR. In contrast to most oxidic glass systems, P-Se glasses require very high spinning speeds (12-14 kHz) for obtaining the resolution needed to differentiate between distinct sites present in these glasses. Chemical shift assignments are based on parallel solid-state NMR investigationson the crystalline reference compounds a-P4Se3,/3-P4Se3, P4Se4,and a-P4Se31z. The solid-state NMR spectrum of P4Se4suggests that the molecular structure of this compound is not the one previously proposed on the basis of IR spectroscopy but is rather like the selenium analogue of o-P4S4. The results obtained on P-Se glasses confirm the prominent role of P4Se3molecular constituents in glasses containing P contents 150 atom % but also show these units are absent at lower P contents. Below 35 atom % P, the MAS-NMR spectra are decidedly bimodal, indicating site differentiation between PSeJl2 and Se=PSe3/z units. The compositional dependence of the peak area ratio is explained consistently in terms of a melt-equilibrium reaction between different short-range-order environments according to PSe3,z + [Se,] Se=PSe3/z, with a phenomenological equilibrium constant K = 0.85 f 0.05 (atom fraction)-'. The near-unity value o f K reflects the efficient competition of homoatomic (Se-Se) versus heteroatomic (P=Se) bond formation in P-Se glasses, hence providing a rationale for the pronounced glass-forming tendency in this system.
-
Introduction Non-oxide chalcogenide glass=, are based on the sulfides, selenides, and tellurides of the main group I1I-V elements, show much promise for applications in infrared and semiconductor technology and optical communications devices.i spite of the strong technological potential of these glasses, their physico(1) Taylor, P. C. Muter. Res. SOC.Bull. 1987, 36.
0022-3654/89/2093-7895$01.50/0
chemical properties are not well understood in terms of their structural organization on a molecular level. Preliminary structural concepts suggested for individual systems have been COncePtuallY divergent, invoking valence alternation pairs,2 the existence of molecular cluster units with "broken chemical ~ r d e r " , and ~?~ (2) Dembovskii, S. A.; Chechetkina, E. A. J . Noncryst. Solids 1986,85, 364. ( 3 ) Boolchand, P. Hyperfine Interact. 1986, 27, 3 .
0 1989 American Chemical Society
7896 The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 Se
se\p-
/
Se
P
es‘
Se
II PSew Se= P Sew2 Figure 1. Possible nearest-neighbor environments in P-Se glasses.
polymeric models involving highly organized entities constituting “intermediate range ~ r d e r ” . Many ~ of the techniques that have played a major part in the development of such models (including EXAFS, Mhsbauer, FTIR, and Raman spectroscopy) suffer from the drawbacks that the interpretation is not straightforward, that quantitative information is difficult to obtain, and that ordered environments tend to be emphasized. Solid-state NMR techniques avoid such problems while offering new powerful approaches to glass s t r ~ c t u r e . ~Recently, ,~ the increased spectroscopic resolution obtained through the use of fast magic angle spinning has enabled the identification and quantitation of specific short-range-order environments, and thus provided extremely valuable information on the structure of many oxide-based systems, specifically and phosphatelo glasses. Such investigations have confirmed that the distribution function of structural parameters in oxidic glasses is not a featureless continuum but that these glasses contain well-defined shortrange-order environments (“discrete site hypothesis”’l), compatible with Zachariasen’s description of network modification.12 It would be of interest to investigate whether and to which extent such concepts are still applicable to non-oxidic glasses. To date, however, modern solid-state N M R studies of such systems have been hampered by various experimental difficulties, such as poor resolution caused by wide chemical shift distributions,13 long spin-lattice relaxation times,14 and problems in relating spectroscopic parameters to structural information. In the present study we will show that such difficulties can be overcome by high-field magic angle spinning (MAS)-NMR at very high spinning speeds, combined with systematic studies of model compounds with crystallographically well-defined nearest-neighbor environments. Results will be presented for binary phosphorus-selenium glasses, a system that has been subject to considerable study in the past d e ~ a d e . l ~Homogeneous -~~ glasses (4) Phillips, J . C. J . Noncryst. Solids 1981, 43, 37. (5) Tenhover, M.; Hazle, M. A.; Grasselli, R. K. Phys. Reu. Lett. 1983, 51, 404. (6) Muller-Warmuth, W.; Eckert, H. Phys. Rep. 1982, 88, 91. (7) Turner, G. L.; Kirkpatrick, R. J.; Risbud, S. H.; Oldfield, E. Am. Ceram. SOC.Bull. 1987, 66, 656. (8) Kirkpatrick, A. J.; Smith, K. A,; Kinsey, R. A,; Oldfield, E. Am. Mineral. 1985, 70, 106. (9) Schneider, E.; Stebbins, J. F.; Pines, A. J . Noncryst. Solids 1987.89, 371. (IO) Villa, M.; Scagliotti, M.; Chiodelli, G. J . Noncryst. Solids 1987, 94, 101.
( I I ) Taylor, P. C.; Friebele. E. J. J . Noncryst. Solids 1974, 16, 375. (12) Zachariasen, W. W. J . Am. Ceram. SOC.1932, 54, 3841. (13) Lathrop, D.; Eckert, H. J . Noncryst. Solids 1988, 107, 417. (14) Tenhover, M.; Boyer, R. D.; Henderson, R. S.; Hammond, T. E.; Shreve, G.A. Solid State Commun. 1988, 65, 1517. ( I 5) Borisova, 2. U. In Glassy Semiconductors;Plenum Press: New York, 1981: p 70.
Lathrop and Eckert are formed with compositions ranging from 0 to 52 mol % phosphorus; a second, small region of glass formation is found between 62 and 80 mol %. The only well-characterized crystalline compound is P4Se3,*’although crystalline compounds with stoichiometries P4Se4 and P4Se5have also been r e p ~ r t e d . ~Sel~,~~ enium analogues of the well-known sulfide compounds P4S7,P,S9, and P4Sloare not known. Attempts at synthesizing such compounds have resulted in glasses extremely resistant toward recrystallization. The structure of these glasses has been subject of much speculation. Figure 1 summarizes the variety of microenvironments, proposed on the basis of multitechnique spectroscopic investigations. The presence of doubly bonded P=Se units is inferred from vibrational s p e c t r o ~ c o p ybut , ~ the ~ ~ extent ~~~~ to which such units do occur has been subject to debate. Combined EXAFS and neutron diffraction studies have resulted in confidence intervals for the fraction of P atoms involved in either P=Se double bonds or P-P single Previous 31Psolid-state wideline N M R data obtained on these glasses have lacked the specificity required for detailed structural interpretation^.^^^^ In the present contribution, we will examine the previous structural proposals for P-Se glasses in light of our new, modern N M R data and also discuss more general aspects of the principles of glass formation in such non-oxide systems.
Experimental Section Sample Preparation and Characterization. Glasses containing 5-75 mol % phosphorus were prepared, according to literature methods, within evacuated Vycor ampules, heated at 650 “ C for 2 days, and quenched by turning off the furnace. All sample manipulations were carried out in a drybox. Glass transition temperatures were measured on a Dupont 912 dual sample differential scanning calorimeter, using heating rates of 5-10 “C/min. All glasses exhibit single glass-transition temperatures with numerical values in close agreement with literature values, and none of them show any recrystallization behavior under DSC conditions. Formation of completely amorphous samples was also verified by X-ray powder diffraction, using a Scintag diffractometer. Crystalline a-P4Se3 was obtained by slow cooling of a melt containing the elements in a stoichiometric ratio and subsequent recrystallization of the product from anhydrous carbon disulfide (HPLC grade). Crystalline P-P4Se3was obtained by cooling the melt more rapidly and omitting the recrystallization step. The identity and purity of both phases were verified by differential scanning calorimetry (mp 246 “C, lit. 247 “C), X-ray powder
(16) Borisova, Z. U.; Kasatkin, B. E.; Kim, E. I. Izu. Akad Nauk SSSR Neorg. Mater. 1973, 9, 822. (17) Baidakov, L. A.; Borisova, 2. U. In Amorphous and Liquid Semiconductors, Proceedings of the International Conference on Amorphous and Liquid Semiconductors, 5th, 1973; Stuke, J., Brenig, W., Eds.; Taylor and Francis: London, 1974; p 1035. (18) Kim, E. I.; Chernov, A. P.; Dembovskii, S. A.; Borisova, Z. U. Izu. Akad Nauk SSSR Neorg. Mater. 1976, 12, 1021. (19) Blachnik, R.; Hoppe, A. J . Noncryst. Solids 1979, 34, 191. (20) Monteil, Y.; Vincent, H. J . Inorg. Nucl. Chem. 1975, 37, 2053. (21) Monteil, Y.; Vincent, H. 2. Anorg. Allg. Chem. 1977, 428, 259. (22) Monteil, Y.; Vincent, H. Can. J . Chem. 1974, 52, 2190. (23) Heyder, F.; Linke, D. 2.Chem. 1973, 13, 480. (24) Price, D. L.; Misawa, M.; Susman, S.; Morrison, T. I.; Shenoy, G. K.; Grimsditch, M. J . Noncryst. Solids 1984, 66, 443. (25) Arai, M.; Johnson, R. W.; Price, D. L.; Susman, S.; Gay, M.; Enderby, J. E. J . Noncryst. Solids 1986, 83, 80. (26) Kumar, A,; Malhotra, L. K.; Chopra, K. L. J . Noncryst. Solids 1987, 92, 51. (27) Keulen, E.; Vos, A., Acta Crystallogr. 1959, 12, 323. (28) Monteil, Y.; Vincent, H. 2. Anorg. Allg. Chem. 1975, 416, 181. (29) Penney, G. T.; Sheldrick, G.M. J . Chem. Soc. A 1971, 245. (30) Baidakov, L. A.; Shcherbakov, V. A. Izv. Akad Nauk SSSR, Neorg. Mater. 1969, 5, 1882. (31) Baidakov, L. A.; Borisova, Z. U. Amorphous and Liquid Semiconductors, Proceedings of the International Conference on Amorphous and Liquid Semiconductors, 5th, 1973; Stuke, J., Brenig, W., Eds.; Taylor and Francis: London 1974; p 1035. (32) Baidakov, L. A,; Katruzov, A. N.; El Labani, H. M . Izu. Akad. Nauk SSSR, Neorg. Mater. 1978, 14, 1818. (33) Eckert, H.; Muller-Warmuth, W. J . Noncryst. Solids 1985, 70, 199.
Chemical Disorder in Non-Oxide Chalcogenide Glasses
The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 1897
PPM
PPm
~
long delay (60
s)
C I'
1
M.-V.
:
difference spectrum
short delay 1 (10 ms)
1
n
Ii,
This work
Figure 2. 31P MAS-NMR spectra of crystalline compounds with known P-Se local environments. Central peaks are indicated by asterisks. (a, top left) 12 1.65-MHzspectrum of a-P4Se3,spinning speed 4.7 kHz. The upper curve shows an expansion of the centerband region of the PSe,,* groups. (b, bottom left) 121.46-MHzspectrum of P-P4Se3,spinning speed 7.3 kHz. (c, top right) 121.65-MHz spectrum of P4Se4,spinning speed 4.9 kHz. The spectrum was detected by placing a 180' pulse on the first rotational echo. The figure shows the decomposition into individual components with different spin-lattice relaxation times. Assignments are as follows: resonance a, P4Se4;resonance b, apical P in P4Se3impurity; resonance c, basal P in P$e3 impurity. Shown below are the molecular structure of P4Se4originally proposed by Monteil-Vincent (M-V) and the structure proposed in the present study. (d, bottom right) 121.65 MHz spectrum of a-P4Se312,spinning speed 5.0 kHz.
diffraction, and liquid-state N M R (doublet at -106 ppm, quartet at 37 ppm vs 85% HjPO,), in good agreement with literature data.j4 Crystalline P4Se4 was synthesized from P4Se3 and Se in a flame-sealed evacuated Vycor ampule within the temperature interval 260-290 OC as reported.2B Differential scanning calorimetry shows the a to p transition at 298 OC (lit. 300 "C) and a melting point of 330 OC (lit. 330 0C.35). N o liquid-state N M R spectrum could be obtained due to the apparent low solubility of this compound in CS2or other solvents, even at elevated temperatures. Crystalline a-P4Se312was obtained by refluxing stoichiometric amounts of P4Se3 and I2 in CS2 in variation of a procedure published p r e v i ~ u s l y . As ~ ~ verified by solution-state jlP NMR, this reaction generally yields a mixture of a-and P-P4Se3I2,the a-isomer being favored at longer refluxing times. Upon cooling below 0 OC,large red crystals of the a-modification were grown, which were further purified by recrystallization from CS2. Identity and purity were ascertained by DSC (sharp melting point at 157 O C ; no literature value reported) and solution-state j l P N M R (AA'BB' pattern in agreement with literature data).j7 Several attempts to reproduce the previously reported synthesis29of P4SeS from P,Se3 and Brz were found to result in a small amount of an insoluble red precipitate (no well-defined melting point) that formed immediately after mixing the reagents. The N M R (34) 1135. (35) (36) (37)
Blachnik, R.;Wickel, U.; Schmitt, P. Z . Naturforsch., B 1984, 39, Blachnik, R.; Hoppe, A. Z . Anorg. Allg. Chem. 1979, 457, 91. Mai, J. Chem. Ber. 1927, 60, 2222. Blachnik, R.; Kurz, G.; Wickel, U. Z . Naturforsch., B 1984,39,778.
spectrum of the supernatant solution showed formation of some PBr3 but no peaks assignable to a spin system consistent with the previously proposed molecular structure. NMR Studies. Room temperature NMR spectra were obtained at 121.65 and 121.46 MHz, using General Electric GN-300 and Nicolet NT-300 spectrometers, respectively. Magic-angle spinning N M R experiments were carried out at variable spinning speeds (5.0-14.0 kHz) using a standard 7-mm as well as a 5-mm ultrahigh-speed MAS-NMR probe (both from DOTY Scientific). Single-pulse acquisition was used, with 90" pulse lengths of 7.0 and 4.5 ps, respectively. Spectra were typically recorded by using 45" pulses with recycle delays of 1-10 min. Experiments using longer recycle delays were shown to leave relative peak area ratios unchanged. In certain cases, spin-echo N M R signals were generated by placing a 180' pulse at the first rotational echo. Although this method assists in reducing phase twists, the spectra obtained in this manner are not truly quantitative, owing to the different decay rates of different frequency components during the evolution and refocusing period. All chemical shifts are referenced with respect to 85% H3P04 (downfield shifts positive). Where possible, chemical shift tensor elements were deduced from spinning sideband patterns, using the method of Herzfeld and Berger.j8
Results, Assignments, and Interpretation N M R Studies of Crystalline Model Compounds. To enable a structural discussion of the N M R data of P-Se glasses, important spectroscopic benchmark data were obtained on the limited (38) Herzfeld, J.; Berger, A. E. J . Chem. Phys. 1980, 73, 6021
7898 The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 number of crystalline reference compounds with known P-Se environments. These spectra are presented in Figure 2a-d and will be discussed here briefly in terms of the structural properties of these compounds. a-P4Se3. The crystal structure of a-P4Se3contains four independent molecules with slightly different local environments for the individual P atoms.27 The 31PMAS-NMR spectrum (see Figure 2a) shows three sharp spinning sideband patterns, centered at 90.1, 86.5, and 68.1 ppm, and one broader pattern, centered at -64.4 ppm in the upfield region. The first three peaks display near to axial chemical shift tensors, whose components and orientations (maximum deshielding along the C3axis) are of comparable magnitude to those found for the apical P atoms in P4S3.39 On this basis, we assign this peak pattern to the apical P atoms of the four independent P4Se3molecules in the unit cell. This interpretation is also nicely compatible with the l:l:2 ratio of the integrated intensities, if it is assumed that the resonance positions of two apical P atoms coincide. Previous MAS-NMR studies of phosphorus sulfides have indicated that 31P chemical shielding tensors are quite sensitive to variations in the S-P-S bond angles within the cage units.39 A look at the crystal structure of P4Se3 reveals that the spread of these bond angles is similar for three molecules (labeled Mol. 1-111 in ref 27), whereas molecule IV shows a much more pronounced asymmetry in the Se-P-Se angles. We thus assign tentatively the more isolated resonance at 68.1 ppm to the apical P atoms in molecule IV. The broader upfield pattern is assigned to the basal P atoms. Note that the location of the centerband implies that the sideband pattern extends well into the downfield region of positive 8 values, where it overlaps with the stronger resonances of the apical P atoms. The observation of substantial broadening for the basal P atoms parallels that made for P4S3,where no sharp MAS-NMR signals assignable to this species could be observed at A recent room temperature neutron diffraction study of P4S3indicates that the average vibrational amplitude of the basal P atoms is significantly higher than that of the apical P atoms,40suggesting the Occurrence of reorientational jumps of the P4S3molecules about their C, axes, as this phase approaches the phase transition to the plastic-crystalline @-phaseat 41 “C. These jumps interfere with the ability of magic-angle spinning to refocus the transverse magnetization of individual spin packets after a full rotor cycle, and hence impair the line-narrowing process. Our results suggest that a similar situation obtains for a-P4Se3. However, the partial observation of sideband patterns in this case indicates that at room temperature the reorientational jumps are significantly slower in this compound, possibly due to the fact that the corresponding phase transition occurs at a higher temperature (81 “C). @-P4Se3.Figure 2b shows the 31PMAS-NMR spectrum of plastic crystalline @-P4Se3.In complete analogy to the results obtained on the corresponding sulfide analogue,41well-resolved spectra reminiscent of liquid-state N M R are observed in the solid state. Compared to the spectra of other crystalline sulfides and selenides at comparable speeds and field strengths, the weakness of the spinning sidebands in @-P4Se3indicates effective averaging of the chemical shift anisotropy by the extensive mobility of these molecules. Note, however, the large differences between the isotropic chemical shift data for the a-phase, @-phase, and the solution phase, indicative of the pronounced influence of the solid-state environment, as discussed later. P4Se4. Although no detailed crystallographic information is available for P4Se4, Monteil and Vincent have proposed the molecular structure included in Figure 2 ~ , which ~ * shows the MAS-NMR spectrum. In addition to a dominant line (a) at 127 ppm, a minor peak (b) at 63 ppm and a stronger resonance (c) centered at -85 ppm are visible in the spectrum. Resonance c and its corresponding spinning sidebands have very short spinlattice relaxation times enabling selective observation using very (39) Eckert, H.; Liang, C. S.; Stucky, G. D. J . Phys. Chem. 1989,93,452. (40) Chattopadhyay, T. K.; May, W.; Von Schnering, H. G.; Pawley, G . S. Z . Krisfallogr. 1983, 165, 41. (41) Andrew, E. R.; Hinshaw, W. S.; Jasinski, A. Chem. Phys. Left. 1974, 24, 399.
Lathrop and Eckert short recycle delays (see Figure 2c). The short T I suggests that this signal belongs to a component with high molecular mobility. The isotropic chemical shifts strongly suggest that the signals b and c belong to P4Se3molecules. Liquid-state 31PN M R studies of CS2 extracts of P4Se4samples show the corresponding resonances of P4Se3,thus confirming the above interpretation. The slight chemical shift difference between P4Se3in the bulk and P4Se3 impurities in P4Se4 can be attributed to the influence of the solid-state environment. The same explanation accounts for the substantial differences in the spinning sideband intensities between resonance c of Figure 2c and the spectrum of bulk @-P4Se3.The comparison suggests that the P4Se3molecules reorient much more rapidly in the bulk @-phase,resulting in a more complete averaging of the chemical shift anisotropy compared to the P4Se3molecular impurities in P4Se4. The remaining unassigned N M R signal (which accounts for roughly 80%of the total area) has only a single MAS-NMR center peak. Clearly, this is not compatible with the preliminary structure proposal by Monteil and Vincent, which would not only predict three peak patterns in a 2:l:l ratio but also line splittings due to homonuclear spin-spin coupling. (Such splittings have been observed previously in solid P4S7,P4S9,and P4S5.39)The N M R result strongly suggests to us that the molecular structure of P4Se4 is not the one previously proposed, but rather the one included in Figure 2c. It has the same geometry as a-P4S4,whose crystal structure has been determined by X-ray c r y s t a l l ~ g r a p h y . ~ ~ ~ ~ ~ a-P4Se3Z2.The unit cell of a-P4Se312consists of only one-half molecule, indicating that the two respective P atoms with identical chemical environments, Le., P(1) and P(l’) as well as P(2) and P(2’) are also crystallographically identical. This result is in excellent agreement with the MAS-NMR spectrum, Figure 2d, which shows only two resolved spinning sideband patterns centered at 130 and 110.5 ppm. On the basis of the liquid-state N M R spectrum we assign these peaks to P(2,2’) and P(l,l’), respectively, using the notation of ref 37. This assignment is also consistent with the fact that the more downfield peaks are substantially broader. As discussed in detail elsewhere,44 such broadening effects are well-known to occur for N M R signals of atoms in the vicinity of quadrupolar nuclei such as 1271,whose magnetic moments are not quantized along the magnetic field direction. Given the magnitude of the nuclear electric quadrupole moment of I2’I, observability of a solid-state N M R peak for a directly bonded spin nucleus (also seen in @-P&1245) is somewhat surprising, especially in view of the strong effect the quadrupolar bromine isotopes exert in comparable situation^.^^ Our result suggests that the dipole coupling is efficiently attenuated by fast relaxation of the iodine atoms, possibly due to some slow molecular reorientation process. N M R Studies of P-Se Glasses. Figure 3a,b shows the 31PMAS N M R spectra of glasses with high phosphorus contents. In the glass-forming region extending from 62 to 80 mol % P the spectra show the resonances centered at 63 and -75 to -85 ppm, previously assigned to molecular P4Se3embedded in a solid-state environment. The assignment is further confirmed by extracting the glasses with CS2,leading to a decrease of the relative intensity of these peaks in the remaining solid, as well as to the appearance of the liquid-state N M R spectrum of P4Se3in the CS2 solution. The peak at 148.5 ppm, whose intensity remains largely unaltered upon washing, cannot be assigned at this time. These sharp resonances are superimposed on a broad background not narrowed by MAS, which is assigned to a more phosphorus-rich environment. The width of this resonance reflects a very wide chemical shift distribution. Figure 3b shows the comparison of glassy and crystalline P4Se4 (50 atom % P). Very close resemblance between both phases can (42) Minshall, P. C.; Sheldrick, G. M. Acta Crystallogr. 1978, B34, 1326. (43) Griffin, A. M.; Minshall, P. C.; Sheldrick, G. M. J . Chem. Soc., Chem. Commun. 1976, 809. (44) Menger, E. M.; Veeman, W. S. J . Magn. Reson. 1982, 46, 257. (45) Tullius, M.; Lathrop, D. A,; Eckert, H. J . Phys. Chem., in press. (46) Eckert, H.; Yesinowski, J. P.; Sandman, D. J.; Velazquez, C. S. J . Am. Chem. SOC.1987, 109, 761.
Chemical Disorder in Non-Oxide Chalcogenide Glasses
The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 7899 TABLE I: 31P NMR Chemical Shifts (3=0.5 ppm vs 85%H3P04) of P-Se Environments in Crystalline Reference Compounds
unit PSe3/2
comDound a-P4Se3(solid)
P-P4Se3(solid) P4Se3(liquid) PAs3Se3(liquid) P-P4Se+ (Ilpuld) P3Se41(liquid) Se212P-PSe212 P4Se4(solid) a-P4Se312(liquid) a-P4Se312(solid)
6.,i
reference
68.1 86.5 90.1 63.5 36 87 171.3 122 127.0 105.4 110.5'
this work this work
this work this work 34 34 37 48
this work 37 this work
'The I-P(P)l13(Sel,2)group resonates at 130 ppm in the solid state. TABLE I 1 31P NMR Chemical Shifts and Site Quantitation in P-Se Glasses and Crystalline Phases
atom % P
6(3IP)'
5.0 133110 10.0 135110 15.0 13619 25.0 136110 28.6 135110 35.0 129110 45.0 126 50.0 125/60'/-77' 50.0 (cryst (P4Se4)) 1 27.0/59.7c/-84.7c~d 57.4 (cryst (a-P4Se3)) 90.1/86.5e/68.1f/
area ratio.b % 57:43 63:37 69:3 1 78:22 84: 16 89:ll
-64.4 (basal P atoms) (apical P atoms) 57.4 (cryst (P-P,Se,)) 63.5/(apical P atoms) -76.8 (basal P atoms)
66.6 75.0
148.51631-778 148.5/63/-77g
u f l ppm except for crystalline phases, where error is f0.5 ppm. Chemical shift reference is 85% H3P04. b f 2 % . CPeaksassigned to molecular P4Se3,total area fraction ca. 20% of total phosphorus. db33, 6z2, all = 61, -53, -265 ppm. 622ra,, = 222, 19, 19 ppm. f b 3 , , 622, d , , = 216, 6, -18 ppm. *Peaks at 63 and -77 ppm are assigned to molecular P,Se,. In addition, a broad background, assigned to a P-rich phase, is present. The large width of this line precludes an accurate determination of the amount of molecular P4Se3in this case.
Figure 3. MAS-NMR spectra of P-Se glasses with high phosphorus contents. Central peaks are indicated by asterisks. (a, top) 121.65-MHz spectrum of a glass containing 66.6 atom % P prior to and after Soxhlet extraction with CS2. Spinning speed 5.2 kHz. To facilitate detection of the broad component, the spectrum was detected by placing a 180' pulse on the first rotational echo. Note the diminished signal intensity for the sharp peaks after extraction. (b, bottom) 121.46-MHz spectrum of a glass containing 50 atom % P (top trace) and of crystalline P4Se4(bottom trace). Spinning speeds 14.0 and 12.9 kHz, respectively. Note the close resemblance of the spectra in the glassy and the crystalline state, including the presence of molecular P4Se3.
be noted, including the appearance of impurity P4Se3molecules. In contrast, P$e3 molecules are absent in all glasses with lower P contents. Figure 4 shows representative MAS-NMR spectra as a function of spinning speed for two glasses containing 50 and 35 atom % P, respectively. The spectra obtained at 5 kHz bear no more information than the static spectrum, since, due to excessive line broadening by a wide chemical shift distribution, no distinction between centerband and spinning sidebands can be made.13 At spinning speeds in excess of 8 kHz some sideband structure becomes visible, but only at speeds > 12 kHz can it be safely assumed that the dominant feature in the spectra is not significantly affected by overlapping spinning sideband intensity. Thus, these results illustrate the need for ultrahigh spinning speeds in order to resolve and quantitate the spectral features belonging to different short-range-order environments.
Figure 5 shows the compositional dependence of the MASN M R spectra at low P contents. Between 35 and 50 atom % P the spectra are dominated by a broad resonance line in the region of 120-140 ppm. Since spin-echo experiments reveal unambiguously that units with P-P bonds contribute to the glass structure in this compositional region,47 and, on the other hand, infrared measurements indicate that the fraction of M e units is 10w,'9*2124 we assign this peak to a superposition of resonances from PSe,,, and Se2 2P PSe2,2 microstructures. This assignment agrees with the solid-state NMR chemical shift data on the binary phosphorus selenides investigated in this study as well as with liquid-state In N M R data on other model compounds (see Table particular, those data reveal that the chemical shift ranges for PSe3/2and Sezj2P-PSe2j2units overlap strongly. This justifies our interpretation that the chemical shift difference between these microstructures is smaller than the shift dispersion caused by the disorder in the glass. Detailed inspection of the compositional dependence reveals that the center of gravity, defined by the first moment, moves gradually downfield with decreasing phosphorus content. Since our spin-echo N M R data indicate that the fraction of P-P bonded units decreases with decreasing phosphorus contents, we deduce from the chemical shift trend that the chemical shift distribution centers near 135 ppm for PSe3,, groups, and near 125 ppm for the Se2/2P-PSe2 units. The most striking feature o6served in glasses with 35 atom % P and less is the appearance of an additional peak in the vicinity of 10 ppm, whose quantitative contribution increases steadily with decreasing P/Se ratio. We assign this resonance to tetrahedral I).36948
(47) Lathrop, D. A,; Eckert, H. J . Am. Chem. SOC.1989, 111, 3536. (48) Blachnik, R.; Buchmeier, W.; Schneider, C.; Wickel, U. 2.Nururforsch., B. 1987, 42, 41.
7900 The Journal of Physical Chemistry, Vol. 93, No. 23, 1989
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Se=PSe3/2 groups, since its intensity parallels both the statistical probability of these units and the intensity of the IR band assigned to the P=Se stretching mode by other In the absence of a crystallographically well-defined model compound containing this unit, our assignment of this new upfield resonance relies heavily on the analogy to homologous phosphorus oxygen and phosphorus sulfur compounds. Systematic inspection of the large body of shift data for P compounds indicates that O=P(OR)3 compounds resonate ca. 140-160 ppm upfield from P(OR)3 compounds with the same ligand^.^^,^^ A similar, albeit smaller systematic chemical shift difference (25-40 ppm), can be noted for the analogous sulfide compounds. Finally, as described further below, our ability to explain the compositional dependence of the peak area fraction of the upfield resonance in terms of a simple thermodynamic model lends further credence to our assignment.
Discussion Site Differentiation in Chalcogenide Glasses by Solid-state 3 i PN M R . The results of the present study underscore the ability of solid-state N M R chemical shifts to provide important site differentiation in phosphorus chalcogenide glasses. They generally confirm the prominent role of molecular P4Se3entities in P-Se glasses, previously inferred from Raman s p e c t r o ~ c o p y ,and ~~ neutron diffraction studies?l and can provide quantitative estimates for such units. The N M R data show also unambiguously that (49) Maier, L; Van Wazer, J. R. J . Am. Chem. SOC.1962, 84, 3054. Van (50) Mark, V.; Dungan, C. H.; Crutchfield, M. M.; Letcher, J. H.; Wazer, J. R. " P Nuclear Magnetic Resonance. In Topics in Phosphorus Chemisrry: Grayson, M., Griffith, E. J., Eds.; Interscience: New York, 1967; Vol. 5. (51) Verall, D. J.; Gladden, L. F.; Elliott, S. R. J . Noncryst. Solids 1988, 106, 47.
appreciable amounts of such molecules only occur at compositions with P contents 250 atom %. The bimodal chemical shift distribution observed in glasses with low P contents also indicates the general applicability of the discrete site hypothesis to P-Se glasses. Compared to oxide glasses, the chemical shift distribution is substantially wider, necessitating the use of extremely high spinning speeds to achieve the required chemical shift resolution. This does not necessarily imply that the distribution of structural parameters is wider in P-Se glasses compared to analogous oxidic glasses. The wide range of 31PN M R chemical shifts observed for PSe3/, groups in different crystalline compounds and in the liquid state reflects extreme sensitivity of 3'P chemical shifts to the detailed local symmetry and weak inter- and intramolecular interactions. Specifically the chemical shifts of the PX312 units in P4S3and P4Se3have to be considered anomalous, arising from the strong magnetic anisotropy of the neighboring basal P3 rings. Fraction of Tetrahedral P Atoms and Stability of the P==Se Bond in P-Se Glasses. The site differentiation provided by the N M R data now enables us to test the previous structural hypotheses for P-Se glasses and to consider alternative models. Figure 6a,b shows the experimental compositional dependence of the fraction of Se=PSe312 units, as extracted from the relative peak area ratios in Figure 5. If we assume formation of such units by a simple reaction of the type PSe3/, + [Sen],,,, Se=PSe3,,; K = [Se=PSe,/,] / [PSe,,,] [Se]
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the N M R data in the region of low P concentrations allow us to obtain a phenomenological equilibrium constant K (assuming a negligible influence of activity coefficients) characterizing the stability of such a tetrahedral phosphorus species. Here [Sen]is the concentration of selenium atoms in excess of a PSe3/2stoi-
Chemical Disorder in Non-Oxide Chalcogenide Glasses
The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 7901 1 .o
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chiometry, assumed to engage in S e s e bonding. The equilibrium formulated above also neglects phosphorus-phosphorus bonded units, whose concentration below 35 atom % P is low according to the previously reported spin-echo N M R results. The solid curve in Figure 6b has been calculated for K = 0.85 (atom fraction)-'. From the experimentally observed scatter at the different P contents, a maximum error of f0.05 (atom fraction)-' can be estimated. Note the good agreement with the experimental data at all different compositions. Since the glasses of the present study were quenched very slowly, the temperature for this equilibrium corresponds to the respective glass-transition temperatures. The speciations of several glasses quenched rapidly from ca. 1000 OC were found not to differ from those in Table I within experimental error. Thus, K appears to be nearly temperature independent, indicating that the enthalpy of the above reaction is near zero. Figure 6a also contrasts the experimental data with the prediction based on a chemically ordered model, assuming exclusive formation of tetrahedral units up to the limiting stoichiometry P4SeIo (28.6 atom % P) and subsequent conversion of such units to 3-fold phosphorus groups at higher P contents. Such a model is clearly shown to be unrealistic. Rather, the N M R data show that, at the "stoichiometric" composition "P4Se10"(which corresponds to
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the known compounds P4O10 and P4Sl0,both of which have terminal chalcogen atoms on all P atoms), only a minority of such tetrahedral phosphorus atoms is present. This conclusion is at variance with previous structural suggestion^.'^*'^^^^ Figure 7 shows the comparison with estimates made for tetrahedral P=Se bonded species using both EXAFS and neutron diffraction data. While the general trend of that study, indicating a decrease of such units with increasing P concentration, agrees with our N M R results, substantial differences arise in the quantitative numbers. Specifically, the N M R data show little if any indication for tetrahedrally bonded P atoms at phosphorus contents between 35 and 50 atom %, whereas EXAFS and neutron diffraction data suggest that a substantial, roughly constant, contribution of these units (ca. 30% of all of the P atoms) remains within this entire compositional region. It needs to be borne in mind, however, that the EXAFS/ND data do not make a distinction with respect to the other three ligands bonded to the tetrahedral P atoms. On the basis of the compositional invariance
7902
J . Phys. Chem. 1989, 93, 7902-7906 P-Se system compared to the P-S system is due to a more efficient thermodynamic competition of such 3-fold units with tetrahedral Se=PSe,/, groups, as expressed by the K value near unity. This is entirely expected since the size difference of the atoms involved should lead to substantial weakening of the P-Se double bond. The N M R results presented in this contribution substantiate this prediction and provide a quantitative assessment of this effect. The excess selenium atoms not involved in P=Se double bonds then engage in chalcogen-chalcogen bonds. The trend for more effective competition of homoatomic versus heteroatomic bond formation apparent from our present study also parallels the results obtained in our previous N M R investigations of boron chalcogenide systems.52
apparent from Figure 7, Price et al. postulate a cluster model for these glasses involving P4SeSand P4Se4units surrounded by Se-rich regions.24 These clusters are assumed to contain P atoms of the type Se=P(Se2j2)(P),13, Le., tetrahedral units containing a P-P bond. We cannot rule out the possibility that such groups might have NMR chemical shifts substantially different from S-PSe3/2 units, and might therefore contribute to the downfield resonance assigned to 3-fold P atoms. This caveat needs to be borne in mind especially in view of the highly variable chemical shifts of threeand four-coordinated P atoms observed in phosphorus-chalcogen bonded environments.
Conclusions The NMR data presented here provide important insights into glass formation in non-oxide chalcogenide systems. In this regard, a comparison of the two systems P-S and P-Se is highly instructive. In contrast to the exceptionally high glass-forming tendency found in the system P-Se, glasses in the system phosphorussulfur form only over a limited range of compositions (0-25 atom % P) and are easily crystallized upon annealing. In contrast to the results discussed here, the N M R spectra of P-S glasses are completely dominated by S=PS3/2 groups and indicate the absence of trigonal PS3/2 units and of any units containing P-P bonds.45 Thus, we conclude that the strong glass-forming tendency in the
Acknowledgment. Financial support of this research by the UCSB Academic Senate and the donors of the Petroleum Research Fund, administered by the American Chemical Society, is gratefully acknowledged. H.E. also thanks the University of California for a Regent’s Junior Fellowship. Registry No. P, 7723-14-0; Se, 7782-49-2; P4Se4, 56863-52-6; P4Se3, 1314-86-9. (52) Hurter, H. U.; Krebs, B.; Eckert, H.; Muller-Warmuth, W. Znorg. Chem. 1985, 24, 1288.
Rotational Relaxation and Interaction-Induced Effects in Liquid Dichloromethane T. W. Zerda Physics Department, Texas Christian University, P.O. Box 32915, Fort Worth, Texas 76129 (Received: March 21, 1989)
Raman spectra of three AI vibrational modes of CH2CI2are studied at pressures varying from 1 to 2000 bar. The rotational second moments and total intensity measurements indicate that induced effects are important for the v4 band while they may be neglected for the vI and vj bands. Rotational correlation functions are obtained from VV and VH polarized components of the v I and v3 bands. In order to find elementary correlation times T ~ T, ~ and , T,, the experimental correlation functions are compared with the theoretical functions obtained from the Fokker-Planck-Langevin model. The elementary times are used to characterize rotational relaxation.
Fixman and Riders proposed the Fokker-Planck-Langevin (FPL) model for molecular rotation in liquids. This is a frictional model in which the molecule is approximated by a solid object immersed in a viscous fluid. Angular velocity of the molecule is constantly modulated by intermolecular torques. A fluctuation in intermolecular interaction generates a torque that only slightly changes the angular momentum of the molecule. For a significant change of angular momentum a large number of fluctuations are necessary. The angular velocity correlation function is assumed to be described by the Langevin equation, and the conditional probability of the molecular reorientation and angular velocity is assumed to be governed by the reorientational Fokker-Planck equation. The FPL model calculations are quite complicated, and only approximated solutions are available. The most accurate results have been obtained by McClung? His numerical technique based on a series expansion of the angular velocity and orientational probability distribution functions allows to compute reorientational correlation functions, memory functions, correlation times, and spectral densities. Recently the FPL model has been extended to asymmetric top molecule^,'^ and general expressions for reorientational correlation functions and correlation times have been derived. This makes possible a comparison of experimental Raman band shapes with
Introduction CH2C1, is an asymmetric molecule with moments of inertia I, = 252.46 X I,, = 273.46 X and I, = 26.96 X 1040 g cm2 [ref 11. Two moments of inertia are almost equal, and most authors regard the molecule as a symmetric t ~ p ,but ~ ,this ~ assumption limits the conclusions of experimental investigations. Different models have been used to discuss reorientational motion of asymmetric molecules. Commonly used are the extended diffusion (ED) model proposed by Gordon4 and later modified by McClungS and expanded to asymmetric molecules by Bull6 and Leickman and c o - ~ o r k e r s . ~The (ED) model assumes free orientation of the molecule between collisions which are instantaneous and random. Two versions of the model have been proposed: (1) each collision changes the orientation and the magnitude of the angular momentum vector ( J diffusion); (2) only the orientation is randomized ( M diffusion). (1) Evans, M.; Evans, G. J.; Coffey, W.; Grigolini, P. Molecular Dynamics; Wiley: New York, 1982. (2) Brier, P. N.; Perry, A. Adu. Mol. Relax. Interact. Processes 1976, 13, I
(3) Rodriguez, A. A.; Schwartz, M. Spectrosc. Lett. 1987, 20, 785; J . Mol. Liq. 1988, 37, 117. (4) Gordon, R. G. J . Chem. Phys. 1966, 44, 1830. (5) McClung, R. E. D. J. Chem. Phys. 1969, 51, 3842; 1972, 57, 5478. (6) Bull, T. E.; Egan, W. J . Chem. Phys. 1984, 81, 3181. (7) Leickman, J. C.; Guissani, Y.; Bratos, S . J. Chem. Phys. 1978, 68,
(8) Fixman, M.; Rider, K. J . Chem. Phys. 1969, 51, 2425. (9) McClung, R. E. D. J . Chem. Phys. 1980, 73, 2435.
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