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Article

The Average Structure of a Fine-Grained Nepheline to 900 °C: Disorder of O1, Al-Si, and K-Vacancy

by
Sytle M. Antao
Department of Earth, Energy, and Environment, University of Calgary, Calgary, AB T2N 1N4, Canada
Minerals 2025, 15(9), 972; https://doi.org/10.3390/min15090972
Submission received: 24 July 2025 / Revised: 30 August 2025 / Accepted: 9 September 2025 / Published: 13 September 2025
(This article belongs to the Section Crystallography and Physical Chemistry of Minerals & Nanominerals)
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Abstract

A fine-grained nepheline sample from Egan Chutes, Ontario, with the chemical composition (K1.32▯0.68)(Na6.05Ca0.22)[Al7.77Si8.21O32], where ▯ represents vacancies, was studied through in situ synchrotron powder X-ray diffraction (XRD) data and Rietveld structure refinement from 26 to 900 °C on heating and cooling. The average structure was refined in the space group P63. The satellite reflections in nepheline give rise to order–disorder transitions. The average <Al,Si-O>{4} distances in nepheline indicate a partially ordered Al-Si distribution, especially in the Al2 and Si2 sites at room T before heating. The nepheline structure shows that except for the positional disorder of the O1 oxygen atom, the other atoms are well defined and contain no unusual features. Vacancies, ▯, occur at the K site. Different satellite (s) reflections arise from (1) positional order of the O1 atoms to 299 °C (s1 disappears), (2) K-▯ order to 486 °C (s2 and s3 disappear), and (3) some Al-Si order 900 °C, where some satellite reflections are present. Complete Al-Si order is obtained at room T on cooling.

1. Introduction

Satellite reflections occur in samples of nepheline, ideally Na3K[Al4Si4O16], from various localities [1,2,3,4,5,6,7]. The satellite reflections show a wide range of characteristics with respect to their intensity, sharpness, and position, and also the temperature at which these disappear. These features indicate an average structure for nepheline with varying degrees of order (or disorder). Although various structural models have been proposed for the superstructure [3,4,5,8,9,10,11], there is no model that explains the satellite reflections and all of the subtle features that have been observed in nepheline samples.
Extra reflections in diffraction data are intriguing and help with our understanding of mineral properties. The satellite reflections in nepheline may indicate the ordering of O1 atoms, K and ▯ (vacancies) [12], or Al-Si [3]. Based on a study of the intensities of the satellite reflections, the superstructure in nepheline is the result of a coordinated displacive transformation, similar to that found in tridymite, instead of a substitutional order [11]. In garnet, extra reflections were observed that arose from the presence of multiple phases and gave rise to strain-induced anomalous birefringence [13,14]. Nepheline samples from Mount Nyiragongo, Africa, contained intergrowths of three nepheline phases with slightly different structural parameters and no satellite reflections [15]. Similar intergrowths in nepheline phases from Mount Nyiragongo were observed [16].
Structural studies have not provided conclusive evidence as to the nature of the domain structure. The presence of Al-Si order alone cannot account for the formation of the superstructure in nepheline, as the Al-Si atoms are consistent with P63 symmetry. The satellite reflections in nepheline have been attributed to the O1 atom order [1,17], whereas displacive modulation of the framework <Al,Si-O>{4} tetrahedra was indicated as the cause [8].
The satellite reflections and average crystal structure of nepheline were studied using single-crystal X-ray diffraction, transmission electron microscopy (TEM), and thermal analyses [1]. Subsequently, it was shown that the nepheline structure obtained using single-crystal and powder diffraction methods resulted in different average <Al2,Si2-O>{4} distances [2] that appeared to be more disordered in the powdered sample compared to those in the single-crystal sample. Possible antiphase domain boundaries (APBs) are the cause of these different <Al2,Si2-O>{4} distances [2]. The Al1 and Si1 sites were assumed to be fully ordered. The excess Si over Al observed in chemical analyses was rationalized using the <Al,Si -O>{4} distances. Foreman and Peacor [12] examined the average single-crystal structure of nepheline at a few temperatures (T) up to 900 °C, but their unit-cell parameters were different from those found by Sahama [7]. Several natural nepheline samples from Africa have been studied at room temperature using synchrotron high-resolution powder X-ray diffraction (HRPXRD) [15]. In addition, several synthetic nepheline samples have also been studied at room temperature using HRPXRD [18]. The average structure of natural nepheline was first investigated by Buerger et al. [19]. The structure of nepheline from various geological environments has been refined [1,2,8,12,20,21,22,23,24,25,26,27,28,29]. A modulated structure of nepheline was examined by Friese et al. [30]. The iron (Fe3+) in nepheline was examined recently [31]. The structure of an AlGe analog of nepheline is also available [32]. The average nepheline structure is displayed in Figure 1.
Based on the <Al,Si-O> distances in nepheline, it appears that the T1 (=Si1) and T2 (=Al1) sites are fully ordered, whereas the T3 (=Si2) and T4 (=Al2) sites are partially ordered before heating. The Si1-Al1 pair is bonded to positionally disordered O1 atoms but not the Si2-Al2 pair. In addition, the Si1 and Al1 tetrahedra are surrounded only by Na atoms, whereas the Si2 and Al2 tetrahedra are surrounded by both K and Na atoms (Figure 1).
Based on a previous study, positional disorder of the O1 atom involves a small rotation of the (Al,Si)O4 tetrahedra, requires the lowest energy, and occurs at the lowest T [1]. In addition, the K-▯ disorder along the 63 channel requires a little more energy and occurs at a higher T. Finally, disorder of the Al and Si atoms involves the largest energy and occurs at the highest T. In this study, these possibilities are investigated by examining the average crystal structure of nepheline from 26 to 900 °C on heating and cooling. The intensities of seven satellite reflections (s) were also monitored.

2. Experimental Methods

The fine-grained nepheline sample (1–2 mm in size) used in this study is from Egan Chutes on the York River, near Bancroft, Ontario, Canada. The sample is a constituent of a nepheline–scapolite–albite–biotite gneiss, and nepheline crystals from the same hand specimen have been used in several studies [1,2,12]. One pure single crystal of nepheline (with a maximum diameter of about 1 mm) was used in this study. This crystal was hand-picked under a binocular microscope and finely ground in an agate mortar and pestle for the high-T synchrotron powder X-ray diffraction (XRD) experiments that were performed at beamline 1-BM, Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA.
The powdered sample was loaded into a quartz capillary (diameter = 1 mm) and held in place by stuffing quartz wool at both ends of the open capillary, which was oscillated during the experiment over a range of 2°. The high-T XRD data were collected using in situ synchrotron radiation [λ = 0.62266(5) Å] at room pressure and from 26 to 900 °C on heating and cooling. Elevated T was obtained using a heater and a thermocouple element placed inside the capillary and close to the sample. Data were collected at specific steps as the sample was heated at a rate of about 7 °C/min and on cooling at a rate of about 28 °C/min to a maximum 2θ of about 30°. The nepheline sample was heated from 26 to 900 °C in two hours and cooled to room T in 45 min. An image plate (IP) detector (Mar345) mounted perpendicular to the beam path was used to collect full-circle Debye–Scherrer rings with an exposure time of 15 s. An external LaB6 standard was used to determine the sample-to-detector distance, wavelength, and tilt of the IP. The two-dimensional diffraction rings recorded using the IP were integrated using the Fit2d program (v. 12) to produce conventional I-2θ XRD traces [33].
The average crystal structure of nepheline was modeled with the Rietveld method [34], as implemented in the GSAS program [35], and using the EXPGUI interface [36]. The chemical composition used in the refinement is K1.31▯0.69Na6[Al8Si8O32], compared to (K1.32▯0.68)(Na6.05Ca0.22)[Al7.77Si8.21O32] obtained from electron microprobe analyses (EMPA; see Hassan et al. [1]); the latter indicates an unrealistic amount of Ca in the Na site, which can accommodate only six atoms. The initial structural parameters were taken from Antao and Hassan [2]. Structural refinements were carried out by varying the parameters in the following sequence: scale factor, background, unit-cell, profile, atom positions, and isotropic displacement parameters. Finally, all variables were refined simultaneously. The refined structural parameters were then used as the input for the next higher-T structure. The occupancy factor for each site was considered to be invariant with T. The unit-cell parameters and R (F2) values from the Rietveld refinements are given in Table 1. The R (F2) value is larger for the HRPXRD data than the IP data because of the vastly different numbers of reflections and different detectors used. The positional coordinates and isotropic displacement parameters are given in Table S1, and the bond distances and bridging T-O-T angles are given in Table S2. These tables contain data at selected T, but all of the structural data are displayed graphically. Tables S1 and S2 are available online as Supplementary Materials.

3. Results and Discussion

3.1. Variations in the Unit-Cell Parameters

The variations in the unit-cell parameters of the average structure of nepheline with T are displayed (Figure 2). At room T, the unit-cell parameters from various studies using samples from low-T pegmatitic environments are similar. The c unit-cell parameters from Sahama [7] match the data from this study quite well, but their c/a ratio deviates above about 400 °C (Figure 2e). The high-T unit-cell parameters from Foreman and Peacor [12] are quite different from the data in this study (although both samples are from the same hand specimen), but their c/a values are closer to the values obtained in this study.
Table 1. Unit-cell parameters and Rietveld refinement statistics for nepheline from Egan Chutes at selected T.
Table 1. Unit-cell parameters and Rietveld refinement statistics for nepheline from Egan Chutes at selected T.
T/°Ca/Åc/ÅV/Å3* R (F2)
† 25 (HRPXRD)9.99564(1)8.37774(1)724.902(2)0.0714
Heating
269.9949(2)8.3766(2)724.68(3)0.0306
10210.0052(2)8.3825(2)726.70(3)0.0306
19810.0198(2)8.3909(2)729.55(3)0.0299
29910.0365(2)8.3991(2)732.71(3)0.0359
39910.0537(2)8.4074(2)735.94(3)0.0296
49810.0718(2)8.4163(2)739.38(3)0.0320
59810.0920(2)8.4268(2)743.27(3)0.0328
69810.1134(2)8.4370(2)747.32(3)0.0324
80010.1347(2)8.4472(2)751.39(3)0.0304
90010.1562(2)8.4568(2)755.44(2)0.0346
Cooling
82510.1375(2)8.4476(2)751.84(2)0.0327
70110.1087(2)8.4336(2)746.32(2)0.0339
64010.0946(2)8.4266(2)743.64(2)0.0356
51210.0680(2)8.4128(2)738.51(3)0.0324
38710.0451(2)8.4008(2)734.11(3)0.0306
26310.0255(2)8.3909(2)730.38(2)0.0343
14410.0120(2)8.3855(2)727.95(3)0.0352
619.9991(2)8.3780(2)725.42(3)0.0376
309.9952(2)8.3756(2)724.65(3)0.0405
* R (F2) = structure factor based on observed and calculated structure amplitudes = [∑(Fo2 − Fc2)2/∑(Fo2)2]1/2. † HRPXRD data in Table 1, Tables S1 and S2 are from Antao and Hassan [2] and are displayed in graphs.
On heating nepheline to 900 °C, although the unit-cell parameters increase smoothly, two “small breaks” occur at about (1) 227 and (2) 723 °C (Figure 2). The c axis contracts slightly at both breaks, whereas the a axis contracts at about 723 °C. These small changes in the unit-cell parameters occur where significant changes occur in the other structural parameters, as discussed below. On cooling from 900 to 30 °C, the unit-cell parameters revert to a slightly different path than that on heating (Figure 2). The d/d0 ratio shows that the a axis expands much more than the c axis, so the c/a ratio decreases (Figure 2d).
The volume thermal expansivity was obtained by fitting all of the unit-cell volume data on cooling to the equation
V ( T ) = V T r exp ∫ T r T α V ( T ) d T ] ,
where V(T) is the volume at any temperature T, VTr is the volume at the reference T, and αV(T) is a polynomial equation for the volume thermal expansion coefficient: αV(T) = αV0 + αV1T + αV2T−2. The values αV0 = 2.75 (±0.08) × 10−5 °C−1 and αV1 = 4.34 (±0.21) × 10−8 °C−2 were obtained with VTr = 724.68(3) Å3 at 26 °C (Figure 2c).
Similarly, by fitting all of the a unit-cell parameter data on cooling, the following coefficients were obtained: αa0 = 1.07 (±0.03) × 10−5 °C−1 and αa1 = 1.65 (±0.07) × 10−8 °C−2 with aTr = 9.9949(2) Å at 26 °C (Figure 2a). Fitting all of the c unit-cell parameter data on cooling, the following coefficients were obtained: αc0 = 6.13 (±0.33) × 10−6 °C−1 and αc1 = 1.04 (±0.08) × 10−8 °C−2 with cTr = 8.3766(2) Å at 26 °C (Figure 2b).

3.2. Satellite Reflections

Satellite reflections were observed using TEM and HRPXRD for the nepheline sample used in this study [1,2]. These reflections are highly variable, even within the same sample, and show that the nepheline structure is incommensurately modulated. Figure 3 displays examples of XRD traces and seven labeled satellite reflections (s1 to s5, s6-L, and s6-R; L and R indicate the left and right satellite reflections on either side of the main (120) reflection); all peaks (main and satellite reflections) are from nepheline. The well-refined traces at different temperatures show no significant changes on heating or cooling, especially with regard to the main reflections (Figure 3a–d). The weak satellite reflections are labeled at room T (Figure 3e,f), and some main reflections are indexed to indicate the locations of the satellite reflections. The subtle changes with T are illustrated with a stack of traces (Figure 4), where the intensities change for individual satellite reflections and a few disappear (s1, s2, s3). The satellite reflections are quite weak and are not easily observed in Figure 4 because of the scale used. However, with a magnified scale, these are easy to observe (Figure 3e,f).
A crude method was used to extract the intensities of seven satellite reflections that were monitored with T. The satellite peak heights (with the background subtracted), including those from the main reflection (040), were used as the peak intensities. The extracted intensities were normalized to their individual room-T values, and the resulting square-root values of the normalized intensities, I1/2, were plotted as a function of T on heating and cooling (Figure 5a,b). The intensity of the (040) reflection decreases linearly with increasing T, as expected, and gives confidence that the intensities extracted for the satellite reflections are reliable.
The s1 satellite reflection disappears at about 299 °C, whereas the s2 and s3 satellite reflections disappear at about 486 °C (Figure 5a), indicating order–disorder transitions at these temperatures. The nepheline sample was heated rapidly from 26 to 900 °C in two hours and cooled to room T in 45 min.
The s4, s5, s6-L, and s6-R satellite reflections are present, but their intensities decrease near 900 °C; these satellite reflections are related to Al-Si order (Figure 5a). The intensity of s4 decreases near 486 °C and increases thereafter. The intensity of the s6-L reflection increases, after which point it decreases toward 900 °C. With increasing T, the intensities of all reflections should decrease because of thermal motion and possible disorder of the atoms. Conversely, any increase in intensity may indicate a further increase in the order of the atoms. Consequently, the increase in intensity for the s6-L reflection is inferred as increasing Al-Si order. Based on the s4 and s6-L satellite reflections, some disordering of the Al-Si atoms begins at about 800 °C and continues to 900 °C. The Al-Si order increases on cooling to about 825 °C, based on the s5 reflection (Figure 5b).
The (040) reflection recovers 97% of its intensity at about 263 °C and then decreases to 72% at 30 °C on cooling (Figure 5b). In general, the intensities of the satellite reflections were recovered from 900 to 263 °C on cooling, and thereafter, these decreased from 263 to 30 °C. Clearly, the s1, s2, and s3 satellite reflections were not recovered on cooling.
The differential scanning calorimetry (DSC) and differential thermal analysis (DTA) data for the nepheline sample in this study show three peaks at about 292, 401, and 963 °C that correspond to three separate order–disorder transitions (see Figure 4c in reference [1]). In another DSC run to 500 °C, two peaks at 331 °C and 429 °C were observed, and when the sample was re-run to 500 °C, after cooling to room T, no peak was observed [1]. The peak at about 292 or 331 °C from thermal analyses corresponds to the disappearance of the s1 satellite reflection at 299 °C in this study, whereas the peak at about 401 or 429 °C corresponds to the disappearance of the s2 and s3 satellite reflections at 486 °C. The peak at 963 °C corresponds to Al-Si disorder, as melting occurs at a higher T [1]. In these experiments, time also affects the transition temperatures.

4. Structural Variations with T

The average structural parameters of nepheline obtained at 26 °C are similar to those obtained by others [1,2,12]. The K site contains 0.65K + 0.35▯ (vacancies), and the Na site is fully occupied by Na atoms. The charge balance at the K site is maintained by having a slight excess of Si over Al atoms. In the graphs shown below, the structural data from other studies are given for comparison [2,12].

4.1. Variations in <K-O>{9}, <Na-O>{9}, and O1-O1 Distances with T

The variations in the average <K-O>{9} and <Na-O>{9} distances with T are shown (Figure 6a). On cooling, these distances follow a smooth path, as shown by the fitted polynomials. Foreman and Peacor [12] showed a smooth variation for <K-O>{9} but not for <Na-O>{9}. These distances increase with T, but there are deviations from the general trend that occur at about (1) 227, (2) 299, (3) 527, and (4) 723 °C (Figure 6a). Between these temperatures, the distances vary smoothly and suggest that the average structure of nepheline is “locked in”. Breaks at about 227 and 723 °C also occur in some of the unit-cell parameters (Figure 2). The heating and cooling paths are slightly different (Figure 6a).
In general, on cooling, the bond distances vary smoothly. The three independent K-O distances change from 900 to 299 °C, but a different trend is observed from 299 to 30 °C (Figure 6b); the K-O5 and K-O6 distances cross over near 340 °C. On heating, the K-O5 and K-O6 distances change considerably from 213 to 299 °C and cross over near 299 °C. The K-O2 distance shows the least variation. Changes occur at about (1) 227, (2) 299, (3) 527, and (4) 723 °C. The K-O distances also vary in the modulated nepheline structure at room T [30].
Initially, the K-O6 distance is the largest, but on cooling to room T, the K-O5 distance is the largest. A transition occurs at about 299 °C, as indicated by the loss of the s1 satellite reflection, and the K-O5 and K-O6 distances do not recover their original values. Therefore, the average nepheline structure on cooling to room T is a little different because the s1, s2, and s3 satellite reflections are not recovered.
The individual Na-O distances vary smoothly on cooling (Figure 7a). The Na-O1 distances do not show any unusual behavior. The Na-O4a and Na-O4b distances cross over at about 450 °C (Figure 7a). On heating, the Na-O4a and Na-O4b distances cross over at about 569 °C (Figure 7b). The Na-O3a and Na-O3b distances cross over at about 227 °C, and the Na-O5 and Na-O6 distances cross over at about 299 °C. Changes are observed at about the following T: (1) 227, (2) 299, (3) 486, (4) 527, and (5) 569 °C. These changes are not pronounced in the average <Na-O>{9} distances, which show smooth variation with T on heating and cooling (Figure 7a,b). Different scales are used in Figure 6a and Figure 7 to illustrate the average <Na-O>{9} distances.
The O1 atom is positionally disordered about the three-fold axis and gives rise to short O1-O1 distances that are less than about 1.02 Å. These are the O1-O1 distances that are considered in this study. A large change in the O1-O1 distance occurs at about 227 °C on heating and is related to O1 positional disorder (Figure 8). The s1 satellite reflection disappears at about 299 °C, which is close to 227 °C and probably reflects O1 positional disorder. The O1-O1 distances on cooling follow two main trends that meet at about 640 °C (Figure 8).

4.2. Variations in <Al,Si-O>{4} Distances and <Al-O-Si>{6} Angles with T

In framework minerals, (Al,Si)O4 tetrahedra generally behave as rigid bodies, and significant changes are not expected. On cooling, the <Al2-O>{4} and <Si2-O>{4} distances change uniformly (Figure 9a). The recovered <Al2-O>{4} distance of 1.778(7) Å is larger than the initial value of 1.705(6) Å, and the recovered <Si2-O>{4} of 1.590(7) Å is shorter than the initial distance of 1.653(6) Å. These recovered distances on cooling indicate complete Al-Si order in the Al2 and Si2 sites. Some features (O1 positional order, K-▯ order, or Al-Si order) cause the average <Al2,Si2-O>{4} distances to indicate partial order in the Al2 and Si2 sites at room T [2]. In the present study, the average <Al,Si-O>{4} distances change on cooling to room T and indicate complete Al-Si order.
On heating, the <Al2,Si2-O>{4} distances can be characterized by three T ranges: (1) 26 to 286, (2) 299 to 554, and (3) 569 to 900 °C (Figure 9a). In these ranges, the <Al2-O>{4} and <Si2-O>{4} distances are nearly constant, vary uniformly, and are nearly parallel to each other. In range (2), the <Al2-O>{4} distances are large, and the <Si2-O>{4} distances are small (Figure 9a). There are changes at about 299 and 554 °C (Figure 9a). At 900 °C, the <Al2-O>{4} and <Si2-O>{4} distances are slightly different from each other, but those in Foreman and Peacor [12] are nearly identical.
On cooling, the <Al1-O>{4} and <Si1-O>{4} distances vary smoothly to 30 °C, and these cross over at about 600 °C (Figure 9b). On cooling, <Al1-O>{4} is 1.739(13) Å and <Si1-O>{4} is 1.594(14) Å, compared to the initial distances of 1.788(11) and 1.558(9) Å, respectively. These distances indicate complete Al-Si order in the Al1 and Si1 sites at room T (Figure 9b). On heating, the <Al1-O>{4} and <Si1-O>{4} distances cross over at about 580 °C, and these vary smoothly to 900 °C. A cross over was also observed by Foreman and Peacor [12] at about 600 °C, which is close to the T observed in this study.
According to Foreman and Peacor [12], the Al and Si atoms are ordered to 900 °C. The DSC results from Hassan et al. [1] indicate that Al and Si disorder occurs at 963 °C. The presence of satellite reflections (s4, s5, s6-L, and s6-R) indicates small amounts of Al-Si disorder near 900 °C (Figure 5a). Around 900 °C, the average <Al2-O>{4} distances are nearly equal, as similarly observed for the average <Si2-O>{4} distances (Figure 9a). Around 900 °C, the average <Al1-O>{4} distances are also nearly equal, as similarly observed for the average <Si1-O>{4} distances (Figure 9b). Because the <Al1-O>{4} and <Si1-O>{4} distances are not the same at 900 °C and nor are the <Al2-O>{4} and <Si2-O>{4} distances, the data indicate incomplete Al-Si disorder. The cooling data indicate complete Al-Si order.
In general, the average of the <Al-O-Si>{6} bridging angles shows an increase with T, but changes occur at about (1) 227, (2) 299, and (3) 527 °C (Figure 10). On cooling, the <Al-O-Si>{6} angle follows a smooth path.

4.3. Variations in Isotropic Displacement Parameters, U, and z Atom Coordinates with T

The U values vary smoothly and are similar to each other on heating and cooling, except for that for the K atom, which remains large on cooling (Figure 11). Because the K atom is initially involved in the K-▯ order, its initial U value is small and increases rapidly after complete disorder occurs at about 486 °C. As the K-▯ disorder is maintained on cooling, the U values for the K atoms are large. Changes in the U value occur at about (1) 227 and (2) 527 °C.
The z coordinates for Na, K, O1, and Al,Si sites show changes at about 227, 299, 486, and 527 °C on heating but not on cooling (Figure 12). A significantly large change in the z coordinates for several atoms occurs at about 227 °C on heating. The atom coordinates and bond distances are related, so these reflect similar features.

4.4. Thermodynamic Model for K-▯ Disorder

Complete K-▯ disorder at 486 °C coincides with the disappearance of the s2 and s3 satellite reflections. The s3 satellite reflection follows a smooth curve (Figure 5a), and a thermodynamic model is given below.
A long-range order parameter, s, is defined for K-▯ disorder that is complete at 759 K (=Tc) at ambient pressure. The order parameter, s = 2xK − 1, where xK is the mole fraction of K atoms, varies between xK = 1 (complete order) and 0 (complete disorder, where xK = 0.5).
The disorder of K-▯ is analogous to cation disorder in dolomite and anion rotational disorder in nitratine and calcite. This disorder is modeled using the mean-field Bragg–Williams (BW) approximation [37,38,39].
T ( s ) T c = s ( 1 − a s 2 ) tan h − 1 s ,
which simplifies to the classical BW model for a binary alloy if a = 0. Tc is the critical temperature at which the transition occurs. Both Tc and a are functions of pressure, P. Equation (1) marks a second-order transition if a ≥ −⅓. For a < −⅓, a first-order transition occurs.
A characteristic feature of a second-order transition is the occurrence of a discontinuous drop in the molar heat capacity (Cp) at Tc. The magnitude of the discontinuity is given by
Δ  Cp (Tc) = 3R/(1 + 3a).
The normalized intensities for the s3 satellite reflection are used to fit a K-▯ disorder model in nepheline because s ∝ I [39,40]. Figure 13 contains the normalized intensities ( I ) for the s3 satellite reflection. Plotting T vs. I , a curve is drawn using Equation (1) with a = 0 and Tc = 759 K, and a good fit is obtained (Figure 13), which corresponds to a continuous second-order transition. The value of a = 0 implies a maximum enthalpy of disorder Hd(0) = RTc(1 − ½ a) ≈ 6.31 kJ/mol and Δ  Cp (Tc) ≈ 24.94 J/K mol.

4.5. Thermal Expansion and Rotations of the (Al,Si)O4 Tetrahedra

The expansion of framework aluminosilicate minerals is usually caused by expansion of the bonds between interstitial cations and framework oxygen atoms, which forces the rigid (Al,Si)O4 tetrahedra to rotate in a cooperative way. In nepheline, the (K,Na)-O bonds expand and cause the (Al,Si)O4 tetrahedra to rotate (Figure 1b,c). The expansion mechanism can be characterized by examining the channels. Figure 1a shows a symmetrical hexagonal-shaped channel, and its expansion is indicated by the O5-O6 distance in Figure 14a. The expansion of the oval-shaped channel (Figure 1a) is characterized by the ratio of the short to long distances, [short(O3-O4)/long(O3-O4)], and the variations are shown in Figure 14b.
If the nepheline structure is viewed along [110], two additional six-membered channels can be observed (Figure 1b). These channels are characterized by the ratio of the short to long distances, [(O5-O6)/(O2-O2)] (top channel in Figure 1b) and [(O1-O2)/(O4-O5)] (bottom channel in Figure 1b), and their variations are shown in Figure 14b. The channel involving the O1-O2 distance expands more than the others.

5. Concluding Remarks

In the nepheline sample from Egan Chutes, except for the O1 oxygen atom, all of the other atoms in nepheline are well defined and contain no unusual features. Based on the <T-O>{4} distances, the Al2 and Si2 sites are partially ordered before heating and fully ordered after heating to 900 °C and cooling back to room T. Vacancies occur in the K site. Different satellite reflections arise from (1) positional disorder of the O1 atom (associated with the s1 satellite reflection), (2) K-▯ order (associated with the s2 and s3 satellite reflections), and (3) Al-Si order (associated with satellite reflections that remain to 900 °C). The s1 satellite reflection is lost at 299 °C and represents disorder of the O1 atom. Complete K-▯ disorder occurs at 486 °C, where the s2 and s3 satellite reflections are lost. The other satellite reflections remain to 900 °C and are related to Al-Si order. Complete Al-Si order can be deduced from the average <(Al,Si)-O>{4} distances that are quenched on cooling.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/min15090972/s1. Table S1: Nepheline from Egan Chutes: atom positions and isotropic displacement parameters (Å2) at selected T. Table S2: Nepheline from Egan Chutes: interatomic distances (Å) and angles (°) at selected T. S3: Selected CIF files.

Funding

This research was funded by an NSERC Discovery Grant to S.M.A., grant number 10013896.

Data Availability Statement

Data are contained within the article and Supplementary Materials.

Acknowledgments

The Editor and the two reviewers are thanked for their comments, which helped to improve this manuscript. D. R. Peacor is thanked for providing the nepheline sample. The XRD data were collected at beamline 1-BM, Advanced Photon Source (APS), Argonne National Laboratory (ANL). The use of the APS was supported by the U.S. Dept. of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.

Conflicts of Interest

The author declares no conflicts of interest.

References

  1. Hassan, I.; Antao, S.M.; Hersi, A.A. Single-crystal XRD, TEM, and thermal studies of the satellite reflections in nepheline. Can. Mineral. 2003, 41, 759–783. [Google Scholar] [CrossRef]
  2. Antao, S.M.; Hassan, I. Nepheline: Structure of three samples from the Bancroft area, Ontario, obtained using synchrotron high-resolution powder X-ray diffraction. Can. Mineral. 2010, 48, 69–80. [Google Scholar] [CrossRef]
  3. McConnell, J.D.C. Electron-diffraction study of subsidiary maxima of scattered intensity in nepheline. Mineral. Mag. 1962, 33, 114–125. [Google Scholar] [CrossRef][Green Version]
  4. McConnell, J.D.C. Time-temperature study of the intensity of satellite reflections in nepheline. Am. Mineral. 1981, 66, 990–996. [Google Scholar][Green Version]
  5. McConnell, J.D.C. Incommensurate structures. Philos. Trans. R. Soc. Lond. 1991, A334, 425–437. [Google Scholar][Green Version]
  6. Sahama, T.G. A complex form of natural nepheline form Iivaara, Finland. Am. Mineral. 1958, 43, 165–166. [Google Scholar][Green Version]
  7. Sahama, T.G. Order-disorder in natural nepheline solid solutions. J. Petrol. 1962, 3, 65–81. [Google Scholar] [CrossRef]
  8. Angel, R.J.; Gatta, G.D.; Boffa Ballaran, T.; Carpenter, M.A. The mechanism of coupling in the modulated structure of nepheline. Can. Mineral. 2008, 46, 1465–1476. [Google Scholar] [CrossRef]
  9. Hayward, S.A.; Pryde, A.K.A.; De Dombal, R.F.; Carpenter, M.A.; Dove, M.T. Rigid unit modes in disordered nepheline: A study of a displacive incommensurate phase transition. Phys. Chem. Miner. 2000, 27, 285–290. [Google Scholar] [CrossRef]
  10. Parker, J.M. The domain structure of nepheline. Z. Für Krist. 1972, 136, 255–272. [Google Scholar] [CrossRef]
  11. Parker, J.M.; McConnell, J.D.C. Transformation behaviour in the mineral nepheline. Nature 1971, 234, 178–179. [Google Scholar] [CrossRef]
  12. Foreman, N.; Peacor, D.R. Refinement of the nepheline structure at several temperatures. Z. Für Krist. 1970, 132, 45–70. [Google Scholar] [CrossRef]
  13. Antao, S.M.; Mohib, S.; Zaman, M.; Marr, R.A. Ti-rich andradites: Chemistry, structure, multi-phases, optical anisotropy, and oscillatory zoning. Can. Mineral. 2015, 53, 133–158. [Google Scholar] [CrossRef]
  14. Antao, S.M.; Klincker, A.M. Crystal structure of a birefringent andradite-grossular from Crowsnest Pass, Alberta, Canada. Powder Diffr. 2014, 29, 20–27. [Google Scholar] [CrossRef]
  15. Antao, S.M.; Nicholls, J.W. Crystal chemistry of three volcanic K-rich nepheline samples from Oldoinyo Lengai, Tanzania and Mount Nyiragongo, Eastern Congo, Africa. Front. Earth Sci. 2018, 6, 155. [Google Scholar] [CrossRef]
  16. Sahama, T.G. Kalsilite in the lavas of Mt. Nyiragongo (Belgian Congo). J. Petrol. 1960, 1, 146–171. [Google Scholar] [CrossRef]
  17. Gatta, G.D.; Angel, R.J. Elastic behavior and pressure-induced structural evolution of nepheline: Implications for the nature of the modulated superstructure. Am. Mineral. 2007, 92, 1446–1455. [Google Scholar] [CrossRef]
  18. Antao, S.M.; Hovis, G.L. Structural variations across the nepheline (NaAlSiO4)-kalsilite (KAlSiO4) series. Am. Mineral. 2021, 106, 801–811. [Google Scholar] [CrossRef]
  19. Buerger, M.J.; Klein, G.E.; Donnay, G. Determination of the crystal structure of nepheline. Am. Mineral. 1954, 39, 805–818. [Google Scholar]
  20. Dollase, W.A. Least-squares refinement of the structure of a plutonic nepheline. Z. Für Krist. 1970, 132, 27–44. [Google Scholar] [CrossRef]
  21. Dollase, W.A.; Peacor, D.R. Si-Al Ordering in Nephelines. Contrib. Mineral. Petrol. 1971, 30, 129–134. [Google Scholar] [CrossRef]
  22. Dollase, W.A.; Thomas, W.M. The crystal chemistry of silica-rich, alkali-deficient nepheline. Contrib. Mineral. Petrol. 1978, 66, 311–318. [Google Scholar] [CrossRef]
  23. Gregorkiewitz, M. Crystal structure and Al/Si-ordering of a synthetic nepheline. Bull. De Minéralogie 1984, 107, 499–509. [Google Scholar] [CrossRef]
  24. Simmons, W.B.; Peacor, D.R. Refinement of the crystal structure of a volcanic nepheline. Am. Mineral. 1972, 57, 1711–1719. [Google Scholar]
  25. Hahn, T.; Buerger, M.J. The detailed structure of nepheline, KNa3Al4Si4O16. Z. Für Krist. 1955, 106, 308–338. [Google Scholar] [CrossRef]
  26. Rastsvetaeva, R.K.; Aksenov, S.M.; Chukanov, N.V. Disordering of Al and Si in nepheline from Graulai (Germany). Dokl. Chem. 2010, 435, 339–342. [Google Scholar] [CrossRef]
  27. Tait, K.T.; Sokolova, E.; Hawthorne, F.C.; Khomyakov, A.P. The crystal chemistry of nepheline. Can. Mineral. 2003, 41, 61–70. [Google Scholar] [CrossRef]
  28. Vulić, R.; Balić-Žunić, T.; Belmonte, L.J.; Kahlenberg, V. Crystal chemistry of nephelines from ijolites and nepheline-rich pegmatites: Influence of composition and genesis on the crystal structure investigated by X-ray diffraction. Mineral. Petrol. 2011, 101, 185–194. [Google Scholar] [CrossRef]
  29. Balassone, G.; Kahlenberg, V.; Altomare, A.; Mormone, A.; Rizzi, R.; Saviano, M.; Mondillo, N. Nephelines from the Somma-Vesuvius volcanic complex (Southern Italy): Crystal-chemical, structural and genetic investigations. Mineral. Petrol. 2014, 108, 71–90. [Google Scholar] [CrossRef]
  30. Friese, K.; Grzechnik, A.; Petříćek, V.; Schönleber, A.; van Smaalen, S.; Morgenroth, W. Modulated structure of nepheline. Acta Crystallogr. 2011, B67, 18–29. [Google Scholar] [CrossRef]
  31. Mikhailova, J.A.; Aksenov, S.M.; Pakhomovsky, Y.A.; Moine, B.N.; Dusséaux, C.; Vaitieva, Y.A.; Voronin, M. Iron in Nepheline: Crystal Chemical Features and Petrological Applications. Minerals 2022, 12, 1257. [Google Scholar] [CrossRef]
  32. Hammond, R.P.; Barbier, J. Monoclinic and hexagonal nepheline structures of (Na¾K¼)AlGeO4. Acta Crystallogr. 1998, B54, 211–220. [Google Scholar] [CrossRef]
  33. Hammersley, A.P.; Svensson, S.O.; Hanfland, M.; Fitch, A.N.; Hausermann, D. Two-dimensional detector software: From real detector to idealised image to two-theta scan. High Press. Res. 1996, 14, 235–248. [Google Scholar] [CrossRef]
  34. Rietveld, H.M. A profile refinement method for nuclear and magnetic structures. J. Appl. Crystallogr. 1969, 2, 65–71. [Google Scholar] [CrossRef]
  35. Larson, A.C.; Von Dreele, R.B. Generalized Structure Analysis System; Report No. LAUR 86-748; Los Alamos National Laboratory: Los Alamos, NM, USA, 2000. [Google Scholar]
  36. Toby, B.H. EXPGUI, a graphical user interface for GSAS. J. Appl. Crystallogr. 2001, 34, 210–213. [Google Scholar] [CrossRef]
  37. Antao, S.M.; Mulder, W.H.; Hassan, I.; Crichton, W.; Parise, J.B. Cation disorder in dolomite, CaMg(CO3)2, and its influence on the aragonite + magnesite ↔ dolomite reaction boundary. Am. Mineral. 2004, 89, 1142–1147. [Google Scholar] [CrossRef]
  38. Antao, S.M.; Hassan, I.; Mulder, W.H.; Lee, P.L.; Toby, B.H. In situ study of the R-3c→R-3m orientational disorder in calcite. Phys. Chem. Miner. 2009, 36, 159–169. [Google Scholar] [CrossRef]
  39. Antao, S.M.; Hassan, I.; Mulder, W.H.; Lee, P.L. The R-3c→R-3m transition in nitratine, NaNO3, and implications for calcite, CaCO3. Phys. Chem. Miner. 2008, 35, 545–557. [Google Scholar] [CrossRef]
  40. Dove, M.T.; Swainson, I.P.; Powell, B.M.; Tennant, D.C. Neutron powder diffraction study of the orientational order-disorder phase transition in calcite, CaCO3. Phys. Chem. Miner. 2005, 32, 493–503. [Google Scholar] [CrossRef]
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Figure 1. (a) The average crystal structure of nepheline projected down the c axis. The A site in the hexagonal-shaped channel contains K atoms and vacancies, and the B site in the oval-shaped channel contains mainly Na atoms. The apices for the T2 (=Al1) and T3 (=Si2) tetrahedra point downwards, and T1 (=Si1) and T4 (=Al2) point upwards. (b) Projection of the structure down [110] showing two additional types of six-membered rings and (c) coordination of K and Na sites for a projection close to that in (b).
Figure 1. (a) The average crystal structure of nepheline projected down the c axis. The A site in the hexagonal-shaped channel contains K atoms and vacancies, and the B site in the oval-shaped channel contains mainly Na atoms. The apices for the T2 (=Al1) and T3 (=Si2) tetrahedra point downwards, and T1 (=Si1) and T4 (=Al2) point upwards. (b) Projection of the structure down [110] showing two additional types of six-membered rings and (c) coordination of K and Na sites for a projection close to that in (b).
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Figure 2. Variations in the unit-cell parameters with T. (a) a, (b) c, (c) volume, V, (d) the d/d0 ratio of the axes and the volume of the unit-cell parameters, and (e) the c/a ratio. The error bars are smaller than the symbols. Data on cooling (blue symbols) are fitted using second-order polynomials (blue curves). Data from the literature are also displayed [2,7,12]. Small changes in the unit-cell parameters occur at about 227 and 723 °C (arrowheads). On heating, the c/a ratio decreases.
Figure 2. Variations in the unit-cell parameters with T. (a) a, (b) c, (c) volume, V, (d) the d/d0 ratio of the axes and the volume of the unit-cell parameters, and (e) the c/a ratio. The error bars are smaller than the symbols. Data on cooling (blue symbols) are fitted using second-order polynomials (blue curves). Data from the literature are also displayed [2,7,12]. Small changes in the unit-cell parameters occur at about 227 and 723 °C (arrowheads). On heating, the c/a ratio decreases.
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Figure 3. Comparison of the XRD traces for nepheline at (a) 26, (b) 498, and (c) 900 °C on heating and (d) 30 °C on cooling, together with the calculated (continuous-line) and observed (crosses) profiles. The difference curve (Iobs − Icalc) is shown at the bottom of each trace. The short vertical lines indicate the allowed reflection positions. The locations of satellite reflections at 26 °C are shown on an expanded scale in (e,f). Seven satellite reflections are labeled, and a few main reflections are indexed.
Figure 3. Comparison of the XRD traces for nepheline at (a) 26, (b) 498, and (c) 900 °C on heating and (d) 30 °C on cooling, together with the calculated (continuous-line) and observed (crosses) profiles. The difference curve (Iobs − Icalc) is shown at the bottom of each trace. The short vertical lines indicate the allowed reflection positions. The locations of satellite reflections at 26 °C are shown on an expanded scale in (e,f). Seven satellite reflections are labeled, and a few main reflections are indexed.
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Figure 4. Stack of traces at different T: (a) cooling from 900 to 30 °C, (b) heating from 26 to 900 °C, and (c) a trace at 26 °C to aid in the location of the satellite reflections. Arrows indicate satellite reflections.
Figure 4. Stack of traces at different T: (a) cooling from 900 to 30 °C, (b) heating from 26 to 900 °C, and (c) a trace at 26 °C to aid in the location of the satellite reflections. Arrows indicate satellite reflections.
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Figure 5. Variations in the normalized intensities of seven satellite reflections with T on (a) heating and (b) cooling. The s1 satellite reflection disappears at 299 °C, whereas the s2 and s3 satellite reflections disappear at 486 °C. These satellite reflections are not recovered on cooling. The intensity of the (040) reflection decreases linearly on heating.
Figure 5. Variations in the normalized intensities of seven satellite reflections with T on (a) heating and (b) cooling. The s1 satellite reflection disappears at 299 °C, whereas the s2 and s3 satellite reflections disappear at 486 °C. These satellite reflections are not recovered on cooling. The intensity of the (040) reflection decreases linearly on heating.
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Figure 6. (a) Variations in the average <Na-O>{9} and <K-O>{9} distances with T. (b) Variations in individual and average <K-O>{9} distances with T. Polynomials fitted to the average <Na-O>{9} and <K-O>{9} distances on cooling are shown. Data from the literature are included for comparison [1,2,12]. From Figure 6 onwards, only a few error bars are displayed for clarity. Arrowheads point to temperatures at about 227, 299, 527, 569, and 723 °C.
Figure 6. (a) Variations in the average <Na-O>{9} and <K-O>{9} distances with T. (b) Variations in individual and average <K-O>{9} distances with T. Polynomials fitted to the average <Na-O>{9} and <K-O>{9} distances on cooling are shown. Data from the literature are included for comparison [1,2,12]. From Figure 6 onwards, only a few error bars are displayed for clarity. Arrowheads point to temperatures at about 227, 299, 527, 569, and 723 °C.
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Figure 7. Variations in individual and average <Na-O>{9} distances with T in this study on (a) cooling and (b) heating. The average <Na-O>{9} distances show a smooth variation on both heating and cooling (fitted polynomials). Arrowheads point to temperatures at about 227, 299, 486, 527, and 569 °C.
Figure 7. Variations in individual and average <Na-O>{9} distances with T in this study on (a) cooling and (b) heating. The average <Na-O>{9} distances show a smooth variation on both heating and cooling (fitted polynomials). Arrowheads point to temperatures at about 227, 299, 486, 527, and 569 °C.
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Figure 8. Variations in the O1-O1 distances with T. At about 227 and 527 °C, large changes occur (arrowheads). Data from reference [2] is included for comparison.
Figure 8. Variations in the O1-O1 distances with T. At about 227 and 527 °C, large changes occur (arrowheads). Data from reference [2] is included for comparison.
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Figure 9. Variations in average tetrahedral distances with T: (a) <Al2,Si2-O>{4} and (b) <Al1,Si1-O>{4} distances. Data from the literature are included for comparison [1,2,12]. Arrowheads point to temperatures at about 299 and 554 °C in (a) and 227 and 527 °C in (b).
Figure 9. Variations in average tetrahedral distances with T: (a) <Al2,Si2-O>{4} and (b) <Al1,Si1-O>{4} distances. Data from the literature are included for comparison [1,2,12]. Arrowheads point to temperatures at about 299 and 554 °C in (a) and 227 and 527 °C in (b).
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Figure 10. Variations in the average bridging angles, <Al-O-Si>{6}, with T. Arrowheads point to temperatures at about 227, 299, and 527 °C. Data from reference [2] is included for comparison.
Figure 10. Variations in the average bridging angles, <Al-O-Si>{6}, with T. Arrowheads point to temperatures at about 227, 299, and 527 °C. Data from reference [2] is included for comparison.
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Figure 11. Variations in isotropic displacement parameters, U, with T. The variations on cooling are smooth, whereas those on heating show changes at about 227 and 527 °C (arrowheads).
Figure 11. Variations in isotropic displacement parameters, U, with T. The variations on cooling are smooth, whereas those on heating show changes at about 227 and 527 °C (arrowheads).
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Figure 12. Variations in the z coordinate with T for (a) Na and K, (b) O1, (c) Al1, (d) Al2, (e) Si1, and (f) Si2 sites. Data from Antao and Hassan (green) at room T are also displayed [2]. The blue symbols represent cooling data, and red symbols are for heating data. There are sharp changes in the z coordinates for some atoms at about 227 and 527 °C (arrowheads).
Figure 12. Variations in the z coordinate with T for (a) Na and K, (b) O1, (c) Al1, (d) Al2, (e) Si1, and (f) Si2 sites. Data from Antao and Hassan (green) at room T are also displayed [2]. The blue symbols represent cooling data, and red symbols are for heating data. There are sharp changes in the z coordinates for some atoms at about 227 and 527 °C (arrowheads).
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Figure 13. Variations in the normalized intensity, I1/2, of the s3 satellite reflection on heating (red symbols). The black line is a fit using the modified Bragg–Williams thermodynamic model with a = 0 and Tc = 759 K. The s3 satellite reflection is not recovered on cooling.
Figure 13. Variations in the normalized intensity, I1/2, of the s3 satellite reflection on heating (red symbols). The black line is a fit using the modified Bragg–Williams thermodynamic model with a = 0 and Tc = 759 K. The s3 satellite reflection is not recovered on cooling.
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Figure 14. Variations in the channel widths with T. (a) The O5-O6 diameter of the hexagonal-shaped channel, and (b) ratios of the short and long diameters of the three channels (see text).
Figure 14. Variations in the channel widths with T. (a) The O5-O6 diameter of the hexagonal-shaped channel, and (b) ratios of the short and long diameters of the three channels (see text).
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Antao, S.M. The Average Structure of a Fine-Grained Nepheline to 900 °C: Disorder of O1, Al-Si, and K-Vacancy. Minerals 2025, 15, 972. https://doi.org/10.3390/min15090972

AMA Style

Antao SM. The Average Structure of a Fine-Grained Nepheline to 900 °C: Disorder of O1, Al-Si, and K-Vacancy. Minerals. 2025; 15(9):972. https://doi.org/10.3390/min15090972

Chicago/Turabian Style

Antao, Sytle M. 2025. "The Average Structure of a Fine-Grained Nepheline to 900 °C: Disorder of O1, Al-Si, and K-Vacancy" Minerals 15, no. 9: 972. https://doi.org/10.3390/min15090972

APA Style

Antao, S. M. (2025). The Average Structure of a Fine-Grained Nepheline to 900 °C: Disorder of O1, Al-Si, and K-Vacancy. Minerals, 15(9), 972. https://doi.org/10.3390/min15090972

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