0.25°/min for 20 from one background position to the other; attenuators: 00.25 mm thick layers of Nb, 2 layers for first attenuator, 4 for second, 6 for third; scan range correction: table look-up method to obtain values recommended in reference [7]; intensity data on paper tape, processed by program written by B. Dickens for Univac 1108 computer; this program contains adaptations of subroutines written for similar program by F. A. Mauer (NBS), standard reflection plotting routine and extinct reflection editing routine from programs by J. M. Stewart, University of Maryland, and uses an intense standard reflection (at low 20 angle) measured every 50 reflections to correct for any change in intensity of the primary x-ray beam. Counts in peak = 1 = P (T/2TB) (BL + Вμ), σ (I) = [P + (Bɩ I − +BH) (T/ (2TB) )2]/2, F= [(AF) (LP) (I)]12,

=

=

B

σ (F) = (σ(1)/2) (LPI), LP=2 sin 20/(cos2 20m+ cos2 20), B 1.58883 × 106 [X2 (cos2 20m + cos 20c) dA/dp]/[AV2 sin2 Oc(cos2 20m + cos2 20c)] (for extinction corrections, calculated at same time as absorption correction). P= counts at the peak position, B1 and BH = background counts at lower and higher 20 respectively, T-time spend counting peak, T= time spent counting each background, AF attenuator factor, LP = Lorentz-polarization correction, 0,= Bragg angle for reflection under consideration, 0m= Bragg angle for monochomator (= 6.005° here), A= transmission factor in the absorption correction, μ is the linear absorption coefficient, dA/du is in mm, V is the volume of the unit cell in A3. Data merging program for equivalent reflections, written by B. Dickens for Univac 1108 computer; in this program each set of equivalent reflections is treated as follows: Reflections which were all unobserved were averaged and given the largest individual standard deviation in the set. Unobserved reflections in the presence of at least one observed reflection were discarded. Observed reflections which occurred only once in the reflection list subsequent to this step were copied unchanged but their standard deviations were increased by a factor of three. Observed reflections with magnitudes which agreed within the counting statistics and reflections with magnitudes whose ratios fell within the range 0.95 to 1.06 were averaged and given as standard deviation the maximum of the standard deviation from counting statistics and the standard deviation from the range estimate [8, 9]. Under these circumstances, reflections whose magnitudes did not pass the criteria were discarded. If no members of a set of equivalent reflections passed the criteria, the highest magnitude was taken. and the associated standard deviation multiplied by five. The justification for these arbitrary increases of standard deviation is that, without some corroboration, every reflection is suspect because of the possibilities of multiple reflection, including the "tail" of nearby intense reflections in its measurement, change in intensity of x-ray beam during reflection measurement, misalignment of crystal, etc. Since we usually measure three sets of equivalent reflections with care the number of standard deviations increased in this way is very small. Scattering factors: those for the neutral atoms in reference [10]; least-squares refinements:

full-matrix, with Zw(F-Fel)2 minimized; refine ments include unobserved reflections which calculate higher than 20 above background; least-squares weights: 1/2(F); Rw= [Σw(|F|-|Fe\)2/Σw |F ̧] =]' -, | R=ΣF-F/EF; thermal parameters have the form exp [- 1/4(a*2B1h2 + b*2B22k2 + c*2B + 2a*b*B12hk + 2a*c*B13hl + 2b*c*B23kl)]. Most least squares and electron density synthesis calculations were carried out with the X-ray 67 system [11] c computing programs.

=

Final Refinement: Rw 0.024; R= 0.040, average shift/error for last cycle =0.0017; standard deviation of an observation of unit weight

= [Σw(F.-F.)/(765-28)] 1/2 = 0.775.

The structure was refined isotropically from the positions given by Bragg to Ru= 0.031, R= 0.047, an then anisotropically to R = 0.024, R=0.040. The low value of Ru supports the earlier indications that the crystal used in the data collection is not twinned. The highest peak in an electron density difference synthess calculated after anisotropic refinement to R=0.02 corresponded to about 1/3 of an electron and was abou 0.95 A from C towards O(1). The largest correlatio coefficients are 0.34-0.44 between the scale factor an: the B1, B22 and B33 temperature factors of Ca.

Two cycles of least squares refinement in whic I the isotropic secondary extinction parameter r F2 = Fine/(1+ Br Fune) was varied [12] together with all other unconstrained parameters resulted in 5 change in R or R and gave a value of -0.3(9) × 16-* for the extinction parameter. There was no significan change in the structural details or their standard devia tions. Thus, we believe secondary extinction to be negligible in our crystal of aragonite. Only the observe: reflections were used in these refinements. Thre cycles of least squares refinement in which alloware was made for the anomalous scattering of Ca (values taken from reference 10) gave an increase from 0.0 to 0.025 for Rw. R was unchanged. There were significant changes in the atomic positions.

The atomic parameters from the refinements withe. corrections for anomalous dispersion are given table 1. The observed and calculated structure factors are given in table 2. The thermal parameters from : refinements which included corrections for 1 anomalous scattering of Ca are Ca: 0.71(1), 0.65 0.65(1), 0.00, 0.00, -0.01(1); C: 0.67(5), 0.80(6), 0.43 0.00, 0.00, 0.08(5): 0(1): 1.45(5), 0.51(4). 1.01(5), 0 0.00, 0.04(5): 0(2): 0.67(3), 0.98(3), 1.00(3), -0.32 -0.02(3), — 0.09(3). Only those for Ca are significar different from the values in table 1. Distances 4 angles referred to in the paper were calculated us ́the values in table 1.

3. Description of the Structure

The structure of aragonite, the main points of wh.. are well known, is shown in figure 1. The Ca ions in pseudohexagonal layers parallel to (001) and layer sequence is ABAB. The Ca layers are separat by CO3 groups which lie in two layers parallel to 00 and form columns parallel to [001].

1

3.1. The Ca lon Environments

The Ca ion lies on the mirror plane at x= 1/4. Its nvironment is shown in figure 2 and summarized in able 3. The coordination of nine oxygens to Ca consists f three CO, edges, O(1, 2), O(1, 2) and O(2, 2) nd three apexes, O(1", 2", 2"). The apparent thermal notion of Ca is almost isotropic (table 1, fig. 2).

Corrections as given by Busing and Levy [13] to btain the mean separation between atoms from the bserved atomic positional and thermal parameters ere calculated using a program written by Finger [12]. hese corrections are included in tables 3 and 4.

3.2. The CO Group

The details of the CO3 group and its environment re given in table 4 and shown in figure 3. The positions eported by Bragg [3] give C-O distances of 1.26 Å and .30 A, and O-C-O angles of 117°, 117° and 127°, hich, under the circumstances, are all close to those eported here. The C-O distances and O-C-O ngles reported here for the CO3 group do not differ rom each other significantly at the 95 percent confience level; the same is true for the O-C-O angles. In iew of the possibility of unknown systematic error, necssarily excluded from the calculations, our results

therefore do not preclude trigonality of the CO3 group. Because the oxygens in the CO3 group have very similar environments, little deviation from trigonality is expected. The CO3 group is nonplanar however. The carbon atom is 0.026(4) Å out of the plane of the oxygen atoms in the CO; group in aragonite. This displacement is approximately seven times the standard deviation and is clearly significant. The displacement is towards. the nearest Ca layer and is presumably a result of polarization of each oxygen atom by the three bonded Ca ions. If the displacement were caused by Ca . . . C interactions, the C atom would not move towards the Ca layer.

The difference in the O-C-O angles, 119.6° and 120.13°, if real, is consistent with the O(2, 2) edge of the CO3 group being coordinated slightly more strongly to Ca as judged from the Ca . . . O distances. However, this stronger coordination of O(2) to Ca would also suggest that C-O(2) should be longer than C-O(1). This is not the case. The average value of the C-O distances is 1.286 A. This agrees well with the C-O distances of 1.283(2) A reported [14] for calcite in which 32 symmetry is forced on the CO3 group by spacegroup R3c. If the apparent thermal motions of the atoms in the CO3 group are attributed to thermal motion rather than to slight positional disorder, there

may also be obtained from experiments of suddenly applied steady shear. Thus, in principle, we should be able to obtain W(y, t) from a series of experiments, and then proceed to check the BKZ theory by comparing measured and predicted stress for simple shearing histories.

Of course, one can never realize experimentally these shearing histories exactly as assumed. From some of the experiments which approximated suddenly applied constant rate of shear history, discussed in section 6, we were able to get a rough approximation of the relaxation function. Applying corrections which will be discussed later using an iterative scheme, we recalculated a function W which is consistent with all our experiments which include measurements of viscosity as a function of the rate of shear, stress relaxation after shear (for different rates of shear), measurement of stress as a function of time for suddenly applied steady shear, and single step stress relaxation experiments. These results, we felt, justified the use of an expression for W(y, t) which can describe all our experiments and which is a special form of a more detailed expression consistent with the behavior of other materials and other deformations, viz:

3. Experimental

The data reported in this paper were obtained on: 10-percent solution of polyisobutylene (vistanex L-100. Enjay Chemical Co.) in cetane. A Weissenber Rheogoniometer was used to shear the sample between a flat plate (7.5 cm diameter) and a cone such tha the angle of the gap was 0.0268 radians. The cone was at the bottom and was connected to the driving shar. The plate was at the top and was connected to a torsion bar which was used to measure the torque. For mos of the experiments a torsion bar of 1/8-in diameter was used. The stress-time measurements and the dynam response were recorded on an oscillograph.

The chamber enclosing the cone-plate assemb was kept at a temperature of 25.0 °C ±0.1 °C. Ambient temperature was controlled at 25.0 °C ±0.5 °C. Aambient temperature 3 degrees below the chamber temperature caused a noticeable change in the curve of viscosity versus rate of shear at high rates of shear The zero shear viscosity at this temperature varies about 5 percent per degree.

Periodically, degradation checks were made or samples of 10-percent PIB by taking viscosity versus rate of shear data. No changes were observed over a 2 year period.

x

-S H(T) (

T2 +72

d ln 7,

using an approximation technique similar to the fam: iar derivative schemes [6] for the relaxation spectrum H(T). Even though we must depend on extrapolation for values of H ( 7) at small 7, the effect on G(t) is sligh

Figure 1 shows the dynamic data and figure 2 the derived values of G(t). The dotted portion of figure: represents values extrapolated to times smaller tha

*Certain commercial equipment, instruments, or materials are identified in this ja in order to adequately specify the experimental procedure. In no case does such identi tion imply recommendation or endorsement by the National Bureau of Standards, nes it imply that the material or equipment identified is necessarily the best available te purpose.