### Abstract

We present a study of the orientational order parameter σ for D2 molecules with both rotational angular momentum J=1 (para-D2) and J=0 (ortho-D2) in the orderrd cubic phase. Our study covers the temperature range between 0.4 and 4 K at mole fractions X of (J=1) molecules 0.55≤X≤0.96, The order parameters σ(J=1)(T, X) and σ(J=0)(T,X) are proportional to the respective doublet splitting observed in the NMR spectrum. In the ordered phase, two doublets spaced symmetrically around the central Larmor frequency are recorded. The outer one, with a splitting δν(J=1) up to about 78 kHz, represents the signal from the (J=1) molecules. The inner one, with splitting δν(J=0) an order of magnitude smaller than δν(J=1), is caused by polarization of the (J=0) molecules by the (J=1) field. A description is presented of the line shape as a function of T and X. Using the results from several samples, we obtain the extrapolated (J=1) order parameter for X=1 as a function of T. At the order-disorder transition temperature Tλ, the doublet structure suddenly disappears and is replaced by a sharp central line which is characteristic of the orientationally disordered phase. The first-order nature of the transition is thus clearly shown. The experimental order parameter for (J=1) molecules σ(J=1)(X=1, T) is compared with predictions from a meanfield and a cluster-variation theory, and also with results from Raman spectroscopy. As X decreases, the line structure shows a progressively greater temperature variation and becomes more smeared out as the order-disorder transition is approached. Below a critical mole fraction Xc=0.54, obtained by extrapolation, no doublet structure is observed. The limiting value of both σ(J=1) and σ(J=0) as a function of X at TTλ (X) is in good agreement with predictions by Harris. A fit of the experiment to theory leads to a factor of about 0.02 for the reduction of the order parameter by the zero-point motion, in agreement with theoretical predictions. It is also shown that, within experimental error, the temperature variation of both order parameters σ(J=1) and σ(J=0) for a given X is the same. We briefly discuss the failure to observe the doublet splitting for the NMR pair spectrum of two neighboring (J=1) molecules in an hcp D2 sample with X=0.05, and mention other peculiarities that at this time remain unexplained for dilute mixtures of (J=1) molecules in (J=0) D2. The possible existence of a large crystalline field that might account for these anomalies is suggested.

Original language | English |
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Pages (from-to) | 1112-1121 |

Number of pages | 10 |

Journal | Physical Review B |

Volume | 6 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1972 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*6*(4), 1112-1121. https://doi.org/10.1103/PhysRevB.6.1112

**Orientational order parameter in cubic D2.** / Meyer, H.; Weinhaus, F.; Maraviglia, B.; Mills, R. L.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 6, no. 4, pp. 1112-1121. https://doi.org/10.1103/PhysRevB.6.1112

}

TY - JOUR

T1 - Orientational order parameter in cubic D2

AU - Meyer, H.

AU - Weinhaus, F.

AU - Maraviglia, B.

AU - Mills, R. L.

PY - 1972

Y1 - 1972

N2 - We present a study of the orientational order parameter σ for D2 molecules with both rotational angular momentum J=1 (para-D2) and J=0 (ortho-D2) in the orderrd cubic phase. Our study covers the temperature range between 0.4 and 4 K at mole fractions X of (J=1) molecules 0.55≤X≤0.96, The order parameters σ(J=1)(T, X) and σ(J=0)(T,X) are proportional to the respective doublet splitting observed in the NMR spectrum. In the ordered phase, two doublets spaced symmetrically around the central Larmor frequency are recorded. The outer one, with a splitting δν(J=1) up to about 78 kHz, represents the signal from the (J=1) molecules. The inner one, with splitting δν(J=0) an order of magnitude smaller than δν(J=1), is caused by polarization of the (J=0) molecules by the (J=1) field. A description is presented of the line shape as a function of T and X. Using the results from several samples, we obtain the extrapolated (J=1) order parameter for X=1 as a function of T. At the order-disorder transition temperature Tλ, the doublet structure suddenly disappears and is replaced by a sharp central line which is characteristic of the orientationally disordered phase. The first-order nature of the transition is thus clearly shown. The experimental order parameter for (J=1) molecules σ(J=1)(X=1, T) is compared with predictions from a meanfield and a cluster-variation theory, and also with results from Raman spectroscopy. As X decreases, the line structure shows a progressively greater temperature variation and becomes more smeared out as the order-disorder transition is approached. Below a critical mole fraction Xc=0.54, obtained by extrapolation, no doublet structure is observed. The limiting value of both σ(J=1) and σ(J=0) as a function of X at TTλ (X) is in good agreement with predictions by Harris. A fit of the experiment to theory leads to a factor of about 0.02 for the reduction of the order parameter by the zero-point motion, in agreement with theoretical predictions. It is also shown that, within experimental error, the temperature variation of both order parameters σ(J=1) and σ(J=0) for a given X is the same. We briefly discuss the failure to observe the doublet splitting for the NMR pair spectrum of two neighboring (J=1) molecules in an hcp D2 sample with X=0.05, and mention other peculiarities that at this time remain unexplained for dilute mixtures of (J=1) molecules in (J=0) D2. The possible existence of a large crystalline field that might account for these anomalies is suggested.

AB - We present a study of the orientational order parameter σ for D2 molecules with both rotational angular momentum J=1 (para-D2) and J=0 (ortho-D2) in the orderrd cubic phase. Our study covers the temperature range between 0.4 and 4 K at mole fractions X of (J=1) molecules 0.55≤X≤0.96, The order parameters σ(J=1)(T, X) and σ(J=0)(T,X) are proportional to the respective doublet splitting observed in the NMR spectrum. In the ordered phase, two doublets spaced symmetrically around the central Larmor frequency are recorded. The outer one, with a splitting δν(J=1) up to about 78 kHz, represents the signal from the (J=1) molecules. The inner one, with splitting δν(J=0) an order of magnitude smaller than δν(J=1), is caused by polarization of the (J=0) molecules by the (J=1) field. A description is presented of the line shape as a function of T and X. Using the results from several samples, we obtain the extrapolated (J=1) order parameter for X=1 as a function of T. At the order-disorder transition temperature Tλ, the doublet structure suddenly disappears and is replaced by a sharp central line which is characteristic of the orientationally disordered phase. The first-order nature of the transition is thus clearly shown. The experimental order parameter for (J=1) molecules σ(J=1)(X=1, T) is compared with predictions from a meanfield and a cluster-variation theory, and also with results from Raman spectroscopy. As X decreases, the line structure shows a progressively greater temperature variation and becomes more smeared out as the order-disorder transition is approached. Below a critical mole fraction Xc=0.54, obtained by extrapolation, no doublet structure is observed. The limiting value of both σ(J=1) and σ(J=0) as a function of X at TTλ (X) is in good agreement with predictions by Harris. A fit of the experiment to theory leads to a factor of about 0.02 for the reduction of the order parameter by the zero-point motion, in agreement with theoretical predictions. It is also shown that, within experimental error, the temperature variation of both order parameters σ(J=1) and σ(J=0) for a given X is the same. We briefly discuss the failure to observe the doublet splitting for the NMR pair spectrum of two neighboring (J=1) molecules in an hcp D2 sample with X=0.05, and mention other peculiarities that at this time remain unexplained for dilute mixtures of (J=1) molecules in (J=0) D2. The possible existence of a large crystalline field that might account for these anomalies is suggested.

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U2 - 10.1103/PhysRevB.6.1112

DO - 10.1103/PhysRevB.6.1112

M3 - Article

VL - 6

SP - 1112

EP - 1121

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 4

ER -