*5.1. X-ray Diffraction*

We begin with X-ray diffraction studies of polyacetylene. The initial 1982 work in this field [22] is discussed in a 1984 monograph [23], re-evaluated in a 1992 experimental study with new X-ray data [24], and then discussed in a 2010 computational paper [25]. Beginning with [22], it is noted that there are two possible monoclinic structures with two chains per unit cell P21/a and P21/n corresponding to the case of in-phase bond alternation or out-of-phase, respectively. For the former P21/a in-phase case, the (001) reflection is expected to be strong; for P21/n, it is forbidden. In this experiment [22], the (001) reflection is observed very weakly. The information in [22] as to bond alternation stems from an analysis of the shape of this (001) reflection with a two-parameter least squares fit of the alteration parameter u0 and the monoclinic angle β to data with an intensity of unspecified physical origin, that depends on sample preparation, that clearly consists of more than one reflection and for which the statistics of the fit are not reported. The data presented in [22] are critically analyzed in [23] and in particular, the two parameter fit was repeated. No distinct minimum was observed for the least squared fit. The newer 1992 experimental study with new data of [24] took a global look at the full data set. It was decisively determined that the structure is P21/n with expectation of a forbidden (001) but again, observed weakly. The authors note, "A possible explanation of the (001) intensity might be the coexistence of a small, variable fraction of bulk P21/a second phase. However, in our sample the (00L) intensities imply 20% P21/a while the ratio of I(021)/I(011) gives an upper limit of only 4%. This inconsistency between on-axis and off-axis measures rule out the phase separation argument." They continue, "An alternative explanation is that local defects are responsible for the (001) intensity. For example, since the energy difference between the two structures is small, one might envision defects such as short chain segments which correlate in-phase with the surrounding long chains. Such defects would be a natural consequence of small molecular weight fragments, and could easily be quenched in from the polymerization. They would contribute to the (001) but not to general (HKL) intensities as is observed." Or they could be low molecular weight interstitial oligopolyenes. In the analysis of this data [24], the bond alternation parameter was not adjusted to fit the data. Instead, a value determined by NMR was used. This removes this X-ray study from having an impact on the bond-alternation issue. The validity of this NMR determination is discussed below.
