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Incommensurate density modulation in a Na-rich plagioclasefeldspar: Z-contrast imaging and single-crystal X-raydiffraction study

Huifang Xu, Shiyun Jin and Bruce C. Noll

Acta Cryst. (2016). B72, 904–915

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Acta Cryst. (2016). B72, 904–915 Xu, Jin and Noll · Na-rich plagioclase feldspar

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904 https://doi.org/10.1107/S205252061601578X Acta Cryst. (2016). B72, 904–915

Received 24 June 2016

Accepted 6 October 2016

Edited by M. Dusek, Academy of Sciences of the

Czech Republic, Czech Republic

Keywords: density modulation; Z-contrast

imaging; e-plagioclase; andesine; incommensu-

rate.

CCDC reference: 1508719

B-IncStrDB reference: 12652EIb3rf

Supporting information: this article has

supporting information at journals.iucr.org/b

Incommensurate density modulation in a Na-richplagioclase feldspar: Z-contrast imaging and single-crystal X-ray diffraction study

Huifang Xu,a* Shiyun Jina and Bruce C. Nollb

aDepartment of Geoscience, University of Wisconsin–Madison, 1215 W. Dayton St., Madison, WI 53706, USA, andbBruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA. *Correspondence e-mail: hfxu@geology.wisc.edu

Plagioclase feldspars are the most abundant mineral in the Earth’s crust.Intermediate plagioclase feldspars commonly display incommensurately modu-lated or aperiodic structures. Z-contrast images show both Ca–Na ordering anddensity modulation. The local structure of lamellae domains has I1-likesymmetry. The neighboring lamellae domains are in an inversion twinningrelationship. With a state-of-the-art X-ray diffraction unit, second-order satellitereflections (f-reflections) are observed for the first time in andesine (An45), aNa-rich e-plagioclase. The f-reflections indicate a structure with a densitymodulation which is close to a Ca-rich e-plagioclase. The similarity between thise-andesine structure and previously solved e-labradorite structure is confirmed.Refinement of the structure shows density modulation of ! 7 mol % incompositional variation of the anorthite (An) component. The results from Z-contrast imaging and low-temperature single X-ray diffraction (XRD)provide a structure consistent with density modulation. The discovery of f-reflections in Na-rich e-plagioclase extends the composition range of e1 structurewith density modulation to as low as at least An45, which is the lower end of thecomposition range of Bøggild intergrowth. The new result supports the loop-shaped solvus for Bøggild intergrowth, below which is a homogenous stable areafor e1 structure in the phase diagram. The phase transition between e2 structurewithout density modulation and e1 structure with density modulation shouldhappen at low temperature. There is a change in modulation periodaccompanying the phase transition, as well as higher occupancy of Al in theT1o site. The andesine with density modulation also indicates extremely slowcooling of its host rock.

1. Introduction

Plagioclase feldspars [Na1 " xCax(Si3 " xAl1 + xO8)] thatcommonly occur in igneous and metamorphic rocks are themost abundant minerals in the earth’s crust. Although plagi-oclase feldspars form a complete solid solution at hightemperature, their subsolidus phase relations at lowtemperature (< 1073 K) are complicated and poorly under-stood due to the coupled ordering between CaAl and NaSi(Ribbe, 1983a; Smith, 1984; Smith & Brown, 1988). There arethree miscibility gaps (or solvi for peristerite, Bøggild inter-growth and Huttenlocher intergrowth) in the albite (Ab =NaAlSi3O8)–anorthite (An = CaAl2Si2O8) binary system.However, the exact shape and position of solvus for Bøggildintergrowth remains controversial (Smith, 1974; Smith &Brown, 1988; Carpenter, 1994). Although crystal structures forend members of albite and anorthite are relatively simple, thestructures for intermediate plagioclase feldspars with incom-mensurate modulations are very complicated at lowtemperature, and are not simple mixtures of albite and anor-thite subunits (Smith & Brown, 1988). The crystal structures

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# 2016 International Union of Crystallography

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and formation mechanism of the modulated structure inintermediate plagioclase have been an enigma for decadesbeginning with the first discovery in 1940 (Chao & Taylor,1940; Kirkpatrick et al., 1987; McConnell, 2008). The modu-lated structure and its formation mechanism affect ourunderstanding about mineral associations of plagioclase feld-spars and their subsolidus reactions like ordering and ex-solution (Grove et al., 1983; Smith & Brown, 1988; Carpenter,1994).

Feldspar is a group of tectosilicate minerals, with each Si orAl tetrahedron sharing all four corners with other tetrahedra,forming a three-dimensional framework. The unique topologyof the tetrahedra framework defines the feldspar group(Ribbe, 1983b). The simplest feldspar structure is of the C2/msanidine, which is the potassium member of the feldspargroup. Although all plagioclase feldspars are of triclinicsymmetry, the same unit cell axes are inherited from sanidinestructure, which would result in unconventional space-groupsettings of the triclinic system. Albite (NaAlSi3O8) structure,with ordered and tilted tetrahedra framework, has a symmetryof C1; while anorthite (CaAl2Si2O8), with a different orderingpattern of Al–Si, has lost a translational symmetry along the c-axis, resulting in the doubling of the unit cell and an I1 spacegroup. The reflections from C1 symmetry are called a-reflec-tions, and the extra reflections in I1 symmetry are called b-reflections. Further ordering in anorthite may result in anotherloss of translational symmetry, and give rise to c- and d-reflections that are not relevant to this research.

The compositions of plagioclase feldspars are normallydescribed by the mol % of anorthite, with An0 for albite andAn100 for anorthite. Exsolution lamellae are often observed inslowly cooled plagioclase with compositions between ! An46

and ! An60 (Ribbe, 1983a), which is called Bøggild inter-growth. These exsolution lamellae are normally at a scale ofhundreds of nanometers, which result in a play of light anddisplay iridescent colors. Plagioclase feldspars with composi-tion within the compositional range of Bøggild intergrowthwere reported several times in metamorphic rocks, which

indicate the solvus for Bøggild intergrowth is not of normalshape where no stable phase should exist within the range atlow temperature (Grove et al., 1983; Wenk, 1979). McConnell(1974, 2008) proposed a loop-shaped miscibility gap forBøggild intergrowth that closed at low temperature, which issupported by the well ordered homogenous modulation in alow-temperature labradorite (Jin & Xu, 2017).

Low-temperature intermediate plagioclase feldspars withcompositions from ! An25 to ! An75 display main a-reflec-tions (i.e hkl with h + k = 2n, l = 2n) and extra satellitereflections that characterize incommensurate modulatedstructures (Bown & Gay, 1959; Ribbe, 1983a; Smith & Brown,1988). The first-order satellites are called e-reflections, and thisparticular plagioclase is named e-plagioclase. The e-reflectionsare pairs of satellite diffraction spots neighboring b-reflections(i.e. hkl with l = 2n + 1, h + k + l = 2n), although the b-reflections do not appear. The second-order satellites, alsoknown as f-reflections, are pairs of very weak satellitediffraction spots neighboring a-reflections (Ribbe, 1983a; Fig.1). The second-order satellite reflections (f-reflections) wereonly reported in Ca-rich e-plagioclase (Smith & Brown, 1988;Smith, 1984). Therefore, the e-plagioclase are categorized intotwo types: e1 (Ca-rich with f-reflections) and e2 (Na-richwithout f-reflections). Both modulation direction and modu-lation period change as the plagioclase composition andordering state changes. The modulation period changes from! 20 A (for ! An25 plagioclase) to ! 80 A (for ! An75

plagioclase; Smith & Brown, 1988).The crystal structure of e-plagioclase had puzzled miner-

alogists for more than 70 years. Several different models for e-plagioclase have been raised over the decades, even verydifferent structure models have been proposed based on theexact same set of experimental data (Horst et al., 1981;Yamamoto et al., 1984). Most proposed models were based ona centrosymmetric space group with anorthite and albite-likesubunits. However, based on the average structure of modu-lated plagioclase feldspars studied to date, Al–Si ordering(like Al occupancy in the T1o site) and electron-density

mapping of Ca–Na atoms indicatethat the incommensurate modu-lated structure is not a mixture oflow albite and anorthite subunits(Kitamura et al., 1984; Ribbe,1983a; Smith & Gay, 1958; Wenk &Nakajima, 1980). Direct observa-tion of the polarity in a Ca-rich e-plagioclase structure was observedwith Z-contrast imaging (Xu, 2015),and the enigma of the e-plagioclasestructure was finally solved withsingle-crystal X-ray diffractionrecently (Jin & Xu, 2017). Thestructure of e-plagioclase can besimplified as periodic I1-likelamellar domains with polarity,connected by I1-like inversion twinboundaries. Chemical variation

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Acta Cryst. (2016). B72, 904–915 Xu, Jin and Noll # Na-rich plagioclase feldspar 905

Figure 1[100] zone-axis electron diffraction patterns. The Miller indices of satellites depend on the choice of q-vector (a). The a-, e- and f-reflections are labeled, with two alternate choices of q-vector marked withsolid and dash arrows, respectively. (b). Miller indices of main and satellite reflections based on (3 + 1)-dimensional superspace and conventional q-vector for the intermediate plagioclase based on Anorthitecell (Bown & Gay, 1959). (c) Miller indices are based on (3 + 1)-dimensional superspace and a ‘primitive’q-vector (with albite cell for main reflections and no extra extinction condition). The centering conditionfor this setting is (1

2,12, 0, 1

2).

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along the modulation direction (commonly known as ‘densitymodulation’ in feldspar mineralogy) only exist in the e1structure (with second-order satellites of f-reflections), andcan only be characterized by f-reflections in a refinement. Theinversion twin boundaries are more Ca-rich than the I1-likedomains.

Even though an individual structure of e-plagioclase issolved, many problems remain in the plagioclase solid solu-tion. The subsolidus phase relation between e1 and e2 is stillunclear. The e1 structure with f-reflections, which was believedto only exist in Ca-rich plagioclase, is reported in Na-richplagioclase for the first time in this paper. This discoverywidens the chemical range of the e1 structure, and is valuablefor correlating the structural variation along with composi-tional change in e-plagioclase. It is also critical for under-standing the thermodynamic stability, formation mechanismsand possible phase relations between plagioclase structures.Therefore, a thorough investigation of this structure isnecessary as a step towards solving the puzzle. Smith & Brown(1988; p. 113) described the problem quite well: ‘It must bestated that quite frankly, although each group of scientists hasproduced an impressive set of data and conclusions, there hasbeen no comprehensive attempt to make comparative tests inthe true spirit of scientific inquiry. All models appear to containconsiderable truth, but it is not clear how much of the ‘elephant’has been described! The hunters must set up a joint safari, andcollect new data at low temperature on specimens which spanthe entire composition range of e-plagioclase.’ Here we applystate-of-the-art Z-contrast imaging and single-crystal X-raydiffraction to this problem as both have been proven to bepowerful tools for characterizing complicated crystal struc-tures.

2. Sample and experiment

The studied andesine plagioclase was collected from a noritepegmatite in Damiao iron ore deposit of the Black Hill nearbyChengde City, Hebei Province, North China. Thin sectionswere made from a plagioclase crystal (! 2 $ 2 $ 3 cm). Albitetwins were dominant in the thin section and few Periclinetwins were present. The widest twin lamellae were about0.2 mm, and most twin lamellae were thinner than 0.1 mm, andmany only appear as a fine line under an optical microscope. ACameca SX51 electron microprobe was used to collectchemical composition data. Elements of Si, Al, Ca, Na, K, Mgand Fe were analyzed at 15 kV and 20 nA beam current with a20 micron beam size using mineral standards. The plagioclasemega-crystals have a composition range from An48.3 (in corearea) to An43 (in rim area). The K-feldspar (KAlSi3O8 = Or)component in the plagioclase ranges from Or2.5 to Or5.2. TheNa-feldspar (NaAlSi3O8 = Ab) component in the plagioclaseranges from Ab49 to Ab52. The plagioclase contains needle-like micro-precipitates of ilmenite, magnetite and augite. Thenorite cooled down extremely slowly, and even nano-precipi-tates of Guinier–Preston zones developed in coexisting Fe-bearing orthopyroxene crystals (Xu et al., 2014). A small singlecrystal close to the rim area with an ! An45 composition was

carefully selected under a petrographic microscope for single-crystal XRD work from a [100]-cut thin section to avoid Albiteand Pericline twins and the precipitates. A TEM specimenperpendicular to the [100] a-axis cut was selected from the thinsection and ion milled. Samples for Z-contrast imaging wereprepared by crushing the selected andesine grain from the thinsection between two glass slides with ethanol. A drop of thesuspension was placed on a lacey-carbon Cu grid and air dried.The crushing crystal method can avoid amorphous layersintroduced by ion milling (Xu, 2015). Amorphous-like layerson a TEM specimen will affect the quality of Z-contrastimages. The specimen was lightly plasma cleaned beforeinsertion into the STEM column on a double-tilt specimenholder.

Our preliminary TEM experiment of a [100] zone-axisspecimen was carried out with a Philips 420ST electronmicroscope equipped with an EDAX energy-dispersive X-rayspectrometer and a Princeton Gamma-Tech System-4000analyzer as described by Livi & Veblen (1987). Scanningtransmission electron microscopy (STEM) analyses werecarried out using a FEI Titan 80–200 aberration-correctedSTEM operated at 200 kV. The microscope is equipped with aCEOS probe aberration corrector, an EDAX high-resolutionX-ray energy-dispersive (EDS) detector, and a Gatan imagefiltering system. All Z-contrast images were acquired using acamera length of 160 mm in order to maximize differencesamong different atoms (Xu et al., 2014). The high-angleannular dark-field (HAADF) STEM imaging (or Z-contrastimaging) is capable of a spatial resolution < 0.1 nm using anaberration-corrected STEM. Signal intensity is proportionalto atomic number (! Z2) and a number of atoms along thebeam direction for the imaging acquisition condition (Kirk-land, 1998; Pennycook, 2002; Xu et al., 2014). Interesting areasand crystal grains with desired zone-axis orientations werelocated using the TEM mode. The probe aberration correctionwas carried out first using a standard sample of nano-goldparticles on a single-tilt specimen holder. The double-tiltspecimen holder containing the andesine specimen was againinserted into the STEM column for Z-contrast imaging underSTEM mode. Switching from STEM mode to TEM mode willlose aberration-corrected conditions.

Single-crystal diffraction data was collected on a Bruker D8VENTURE X-ray diffractometer, equipped with an air-cooled PHOTON II detector using CMOS technology. The X-ray source was an Incoatec Mo I!S 3.0 microfocus tubecoupled to a multilayer mirror optic. Data was collected at100 K using an Oxford Cryosystems Cryostream 800 low-temperature apparatus to intensify high-angle satellites. Thecrystal was first screened with a ’ scan with 1% width at 1 sexposure time to check twinning. Once the crystal was ensuredto be free of twins, two ’ runs and 18 ! runs were programmedwith a scan width of 0.5% and 5 s exposure time at a distance of37.24 mm.

Unit-cell parameters were calculated and refined usingAPEX3 software, as well as peak integration and multiscanabsorption correction. The structure was solved with a charge-flipping algorithm (Oszlanyi & Suto!!, 2004, 2005) using

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SUPERFLIP (Palatinus & Chapuis, 2007). The refinement ofthe average structure and modulated structure was done withJANA2006 (Petrıcek et al., 2014). The three-dimensionalcrystal structure was visualized by VESTA (Momma & Izumi,2011).

3. Results

3.1. TEM results

The selected area electron diffraction (SAED) pattern fromthe andesine (! An45) investigated here, displays strong a-reflections, weak e-reflections, and very weak f-reflections (Fig.2). No exsolution lamellae (Bøggild intergrowth) wereobserved in the studied sample, although a trace amount of K-feldspar precipitates were observed locally. [100] zone-axisand [010] zone-axis SAED patterns show a- and e-reflections,because their zone-axes are not perpendicular to the q-vector(see stereonet in Fig. S1). A [311] zone-axis SAED patternshows both e-reflections (first-order satellite reflections) and f-reflections (second-order satellite reflections), because thezone-axis is about perpendicular to the q-vector (see stereonetin Fig. S1). The obtained Z-contrast image along the [311]zone-axis clearly demonstrated structural modulation basedon its fast Fourier transform (FFT) pattern (Fig. 2d). Signalintensity in Z-contrast images is directly related to atomicnumber (Z) and occupancy of the atoms (Pennycook, 2002).Z-contrast imaging that uses non-coherent electrons scatteredat high angle can minimize or even avoid multiple diffraction

that occurs in high-resolution TEM imaging (Pennycook,2002; Kirkland, 1998; Xu et al., 2014). Intensity variation of thewhole unit cell indicates compositional or density modulationin the Z-contrast image (Fig. 3d).

The image clearly shows the modulation along the ! c-axisthrough orientations of Si/Al dumbbells (outlines with yellowovals; Fig. 3). The neighboring dumbbells are no more relatedby inversion than in I1 or C1 plagioclase. Possible symmetryfor the subcells in the lamellar domains is I1, instead of I1 orC1 based on the orientations for the neighboring Si/Al

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Figure 2SAED patterns (a, b, c) and an FFT pattern from an annular bright-fieldimage (d). (a) [100] zone-axis; (b) [311] zone-axis; (c) [010] zone-axis; (d)[311] zone-axis. See stereonet in Fig. S1 for the q-vector and zone-axisdirection.

Figure 3(a) Noise-filtered Z-contrast image showing structural modulationthrough orientation changes of neighboring Si/Al dumbbells (outlinedwith yellow ovals) and framework. A section of the structure fromstructural refinement is also illustrated at the left side of the image. (b)Intensity profile from an outlined ‘b’ cross section of part of the subcellshowing the modulation wave. (c) Intensity profile from an outlined ‘c’cross section that is next to ‘b’, also showing the modulation wave. (d)Average intensity profile of the whole unit cell showing the total intensityvariation due to density modulation.

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dumbbells (Fig. 4). This is very similar to the phenomenon in aCa-rich e-plagioclase (Xu, 2015). Intensity profiles from partof the unit cell (outlined cross-sections of b and c in Fig. 3a)clearly show structural modulations and Ca/Na ordering in Msites (Figs. 3b and c). Modulation waves and their phase shiftare evident in the intensity profiles. The density modulation iscaused by Ca–Na migration outside the subcells. Each subcellhas a different composition (Ca, Na). The line profile (Fig. 3d)is from the whole unit cell width to show the composition

variations of the whole subcell along the modulation direction.Weak and strong peaks indicate more Na (less Ca) or less Na(more Ca) in the subcells. XRD refinement also shows ! 7%variation in mol % of anorthite component (see the discussionin x3.2.1 for details).

A [010] zone-axis Z-contrast image (Figs. 5a and b) alsorecorded the modulation. FFT patterns clearly show e- andeven very weak f-reflections (Figs. 5c and d). Because theordering between Na and Ca is small, it is not obvious in theimage. However, the line profile across M sites along the a-axisclearly shows ordering between neighboring M sites andmodulation wave (Fig. 5e). The boundary positions are indi-cated by red arrows. The long modulation wave along the a-axis is due to its small component of the q-vector on the a-axis.The Na–Ca ordering in the subcells indicates the acentricity ofthe subcells.

3.2. Single-crystal X-ray diffraction analysis

3.2.1. (3+1)-dimensional modulated structure. With anexposure time of only 5 s, 3753 first-order satellite reflections(e-reflections) were observed in the data collection, as well as2063 independent second-order satellites (f-reflections) with aresolution of 0.72 A. This number of reflections is almost asgood as the result of synchrotron radiation (Boysen & Kek,2015), and is definitely better than any previous lab-basedsingle-crystal X-ray diffraction work on plagioclase feldspars(Horst et al., 1981; Yamamoto et al., 1984; Steurer & Jagod-

zinski, 1988; Jin & Xu, 2017).Fredrickson & Fredrickson (2016)refined the structure of the samesample, but the existence of f-reflections was not carefully exam-ined in their data and only first-order satellite reflections (e-reflec-tions) were reported in the paper.The second-order satellite reflec-tions (f-reflections) are consideredcritical in characterizing the e-plagioclase structure (Jin & Xu,2017), the data they acquired isclearly inadequate for the structurerefinement.

The unit-cell setting in feldsparminerals are usually unconven-tional. The tetrahedral frameworksof all feldspar minerals have thesame topology with a C2/m mono-clinic symmetry, given the orderingof Al–Si and distortion of theframework are ignored. Therefore,even though all the plagioclasefeldspars are of the triclinic crystalsystem, the same choice for crystalaxes are preserved, which wouldresult in an additional centeringcondition for the space group of

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Figure 5Z-contrast image (a) and noise-filtered Z-contrast image (b) along the [010] zone axis show Si/Al sitesand weak Ca/Na sites due to numbers of atoms along the [010] direction. FFT patterns from the annularbright-field image (c) and Z-contrast image (d) show e-reflections and very weak f-reflections. Intensityprofile across the image (b) along the outlined area showing intensity difference between neighboring Msites due to Ca/Na ordering in the I1-like subcells (c ’ 14 A) (e). Red arrows indicate boundaries (orpositions for inversion boundaries). An insert in (b) is a structure model of an ordered subcell (2a $ 2c).

Figure 4Projections of plagioclase structures with C1 (a), of I1 (b) and I1 (c)symmetries along the [311] zone-axis based on an anorthite cell. Differentorientations between neighboring Si/Al dumbbells indicate I1 for thelocal subcells (c). Structures of anorthite and albite are from Angel (1988)and Harlow & Brown (1980), respectively. The I1 structure is based onfully ordered Ca/Na plagioclase (An50) with Al in T1o and T1m sites.

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plagioclase, namely C1 for albite (Na end-member with c ’7 A) and I1 for anorthite (Ca end-member with doubled c-axis). As for the modulated structure, the b-reflections char-acterizing the I1 cell are absent, but the first-order satellitereflections are very close to the absent b-reflection. Therefore,the anorthite cell with doubled c-axis is chosen as a subcell forthe modulated structure, and the modulated structure issolved and refined in the X1("#$)0 superspace group setting,with c’ 14 A subcell and a centering condition of (1

212

12 0), (0 0

12

12), (1

212 0 1

2) (Jin & Xu, 2017; Boysen & Kek, 2015). Fredrickson& Fredrickson (2016) claimed the structure to be of noncen-trosymmetric superspace group X1("#$)0. This statement isseriously questionable, as the model they used for the M sitewas too simple to represent this complicated structure, and theresulting R value for satellite reflections (! 10%) was too high

to draw a conclusion of such nature. Since the structurerefinement was not improved at all in this research by relaxingthe superspace group to the noncentrosymmetric X1("#$)0,we have to keep the centrosymmetry of the structure. Detailedinformation about the crystal can be found in Table 1. Atomicoccupancies and positions are listed in Table 2. Completeinformation on the structure is provided in the supportinginformation.

The nomenclature of the atom sites in this paper follows theconvention in feldspar mineralogy. There are two topologi-cally different tetrahedral sites (T sites), namely T1 and T2.With the ordering of Al–Si and the distortion of the frame-work, the mirror/twofold rotational symmetry is lost and thetetrahedral sites are separated into T1o, T1m and T2o, T2m,respectively (Ribbe, 1983b). The oxygen sites are named in asimilar manner, except for OA1 and OA2 on the symmetryelements in the C2/m space group which remain the same inthe triclinic system (Ribbe, 1983b; Smith & Brown, 1988). Thenomenclature for the cation site (Na/Ca) is a little morecomplicated. It is generally called the M site. However, the Msite is always split in plagioclase feldspar minerals, indicating apositional disorder in the M site (Smith & Brown, 1988; FitzGerald et al., 1986). It is worth noting that the split nature ofthe M site is independent from the model chosen in therefinement, and even if only one atom site is used in therefinement, the electron density map would still show twomaxima. Thus, two atom positions are used in the model forrefinement, the one with a negative y coordinate is named M1and the one with a positive y coordinate is named M2 (Jin &Xu, 2017).

The structure was first solved by a charge-flipping method.The correct atom types were assigned to each electron densitypeak. Only Si and Ca were put in the structure to start with. Aland Na are added later to the structure based on the bonddistances and partial occupancies. The final structure seemsindependent from the refinement procedure, exactly the samestructure can be arrived by putting Al and Na in the initialstructure. The positions of all the atoms are described andrefined with harmonic displacive modulation functions up tosecond order along a, b and c axes. The occupancies of M sitesand all T sites are also described by harmonic modulationfunctions up to second order, with the M-site occupanciesdirectly refined from the data and T-site occupancies indir-ectly constrained by bond distances. All atoms are refined withharmonic ADPs with up to second order. The modulatedharmonic ADPs is considered necessary in describing thestructure of e-plagioclase as discussed by Jin & Xu (2017). Thecoordination environment of the M site is extremely compli-cated in plagioclase structure, which means the temperatureparameter also changes while the positions of atoms aremodulated. The R value dropped significantly by introducingADP modulation.

Most models for the M site used in previous refinements ofe-plagioclase structures were not well described and weredeemed unimportant. Some models only use one Na atom andone Ca atom with partial occupancies and independent posi-tions for the M site (Boysen & Kek, 2015). Ideally both M1

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Table 1Selected crystallographic data.

AndesineCrystal dataChemical formula Ca0.49Na0.51Si2.56Al1.44O8

Mr 270.1Crystal system, space group Triclinic, X1("#$)0†Temperature (K) 100Wavevectors %h = 0.09163 (9); %k = 0.02581 (9); %l =

"0.28458 (8)a, b, c (A) 8.1661 (3), 12.8545 (2), 14.2350 (4)", #, $ (%) 93.5777 (8), 116.3090 (7), 89.593 (3)V (A3) 1336.52 (7)Z 8F(000) 1071Dx (Mg m"3) 2.685Radiation type Mo K"! (mm"1) 1.24Crystal shape BlockColor ColorlessCrystal size (mm) 0.08 $ 0.06 $ 0.05

Data collectionDiffractometer Bruker CCDRadiation source X-ray microfocus tubeTotal reflections measured 146 201Independent reflections 9366 (1839a + 3753e + 3774f)‡Observed reflections 7205 (1825a + 3317e + 2063f)Rint 0.081& values (%) &max = 29.6, &min = 2.1(sin &/')max (A"1) 0.695Range of h, k, l h = "11! 11, k = "17! 17, l = "20

! 20

RefinementRefinement on F2

R[F2 > 2((F2)] 0.029 (0.027/0.024/0.070)§R(all) 0.037 (0.027/0.029/0.138)GOF(obs) 2.05GOF(all) 1.84No. of reflections 9366No. of parameters 642No. of restraints 0No. of constraints 250Weighting scheme Weighting scheme based on measured

s.u.s w = 1/[(2(I) + 0.0016I2]("/()max 0.049")max, ")min (e A"3) 0.75, "0.78

† Centering condition X: (12,

12,

12,0), (1

2,12,0,12), (0,0,12,

12), corresponding to C0c in Table 3.9 of van

Smaalen (2007). ‡ Letters a, e and f refer to main reflections, first-order satellites andsecond-order satellites, respectively. § Values in parentheses refer to a, e and f-reflections, respectively.

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and M2 sites should be occupied with Ca and Na, but thatwould result in too many parameters and unrealistic occu-pancies (< 0 or > 1). Since the Na occupancy in the M2 site isgenerally low even in quenched volcanic plagioclase (FitzGerald et al., 1986), only Ca is assigned to the M2 site (Fig. 6).This model was first used in the refinement of e-labradorite(Jin & Xu, 2017), and works perfectly for the studied crystal.The potassium component is not considered in the refinement.Vacancies in M sites are possible but very rare in plagioclasefeldspars, and the M sites in this sample seem to be fullyoccupied based on the microprobe analysis. Therefore, thetotal occupancy of the atoms in M1 and M2 sites wasconstrained to 1. The composition from the structure refine-ment is close to the results of microprobe analysis(Ca0.45Na0.51K0.04Si2.55Al1.45O8 or An45An51Or4). The slightlyhigher Ca component (An49) should be attributed to thepotassium component, since K and Ca have similar atomicnumbers and therefore are close in their scattering factors.The occupancies of atoms are within the reasonable range

without needing any other restraints or constraints (Fig. 6).However, the Na occupancy, which depends on total electrondensity, should be more reliable than the detailed Ca distri-bution between the split sites (Jin & Xu, 201 ).

Since the scattering factors of Al and Si are too close to beaccurately distinguishable from X-ray diffraction, the Aloccupancies of tetrahedral sites are constrained according tothe hT—Oi bond distances, following the equation (Kroll &Ribbe, 1983)

Occ Alð Þ ¼ 0:25 1 þ nAnð Þ þ ðhTi"Oi" hhT"OiiÞ=k:

In the equation above, nAn is the mole percentage of anorthitein the composition, and 1 + nAn would be the total Al occu-pancies in all four T sites, which is fixed by the stoichiometryof the chemical formula of plagioclase; hTi—Oi means theaverage distance of four bonds within each tetrahedron, andhhT—Oii is the average distance of all the T—O bonds in thestructure. The letter k is a constant which is estimated to be0.135 A, and is conventionally used for albite and plagioclasefeldspars (Angel et al., 1990; Jin & Xu, 2017). The resultingoccupancies of all tetrahedral sites lie in a reasonable range

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Figure 6Ca/Na occupancy modulation wave of M1 (Na + Ca) and M2 (Ca) sites.

Figure 7hT—Oi bond distance modulation for four T sites.

Table 2Atomic positions and occupancies in the modulated structure.

Note that all the fractional coordinates are based on the c’ 14 A unit cell, even though the number of independent atoms is the same as in the albite cell (c’ 7 A).

Label Atom Av. Occ. Max. Occ. Min. Occ. x y z Ueq

M1 Na 0.510 (4) 0.629 0.370 0.26775 (13) "0.01365 (17) 0.07936 (18) 0.0202 (4)Ca 0.154 (6) 0.304 0.019

M2 Ca 0.336 (7) 0.614 0.095 0.26963 (19) 0.02545 (17) 0.05004 (14) 0.0233 (5)T1o Si 0.3575 0.828 0.044 0.49368 (3) 0.335066 (19) "0.106559 (19) 0.00664 (9)

Al 0.6425 0.956 0.172T1m Si 0.7438 0.998 0.290 0.50306 (3) 0.318113 (18) 0.116245 (18) 0.00665 (9)

Al 0.2562 0.710 0.002T2o Si 0.7467 0.945 0.430 0.68597 (3) 0.109332 (18) 0.158003 (19) 0.00649 (10)

Al 0.2533 0.570 0.055T2m Si 0.712 0.956 0.261 0.18102 (3) 0.379800 (18) 0.178557 (18) 0.00642 (10)

Al 0.288 0.739 0.044OA1 O 1 – – 0.49699 (10) 0.37113 (5) 0.01169 (5) 0.0142 (2)OA2 O 1 – – 0.58167 (9) "0.00654 (5) 0.13895 (5) 0.0095 (2)OBo O 1 – – 0.81207 (9) 0.10585 (5) 0.09456 (6) 0.0130 (2)OBm O 1 – – 0.31727 (10) 0.35300 (6) 0.12377 (6) 0.0176 (3)OCo O 1 – – 0.48737 (10) 0.20658 (5) "0.13874 (5) 0.0129 (2)OCm O 1 – – 0.51582 (9) 0.18991 (5) 0.10842 (5) 0.0136 (2)ODo O 1 – – 0.29948 (9) 0.39226 (5) 0.30739 (5) 0.0120 (2)ODm O 1 – – 0.68923 (10) 0.36738 (5) 0.21617 (5) 0.0141 (2)

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(between 0 and 1). The modulation of hT—Oi bond distancesis plotted in Fig. 7.

The displacement modulation of the M site shows a patternwith the M2 site (Ca) almost stationary and the M1 site(Ca + Na) moving back and forth, which is very similar to thelow-temperature labradorite structure (Jin & Xu, 2016). Thedisplacement along the a-axis is very minor compared with thedisplacements along the b and c axes (Fig. 8). Electron densitymodulation around two M sites (four sites if we consider the

splitting of each M site) is projected along the a-axis in Fig. 9.Note that the two sites are actually of different x coordinates.The atom positions match the electron density maps very well.Two distinct peaks are shown for most of the modulationperiod, except when the two split sites are moving too closetogether.

The occupancy modulation of an individual M site does notnecessarily mean a variation in composition along the struc-ture, which is commonly referred to as a ‘density modulation’

in feldspar mineralogy (Smith &Brown, 1988; Kitamura et al., 1984).Only by averaging the occupancy ofall symmetrically equivalent M sitesin one unit cell (c ’ 14 A) can thedensity modulation be revealed.Fig. 10 shows the occupancymodulation of each individual Naand the average occupancy. Adensity modulation with a variationof ! 7 mol % is displayed, which ismuch smaller than the labradoritefrom a metamorphic rock (Jin &Xu, 2017). However, the overalltrend is very similar, with the Nacomposition reaching a trough att = 0 and t = 0.5.

The average hT—Oi bonddistances are also plotted in Fig. 11,which shows a consistent trend ofmodulation. The average bonddistance is longer (richer in Al) att = 0 and t = 0.5, even though thecomposition derived from the bonddistances may not fit exactly withthe M site occupancies. Theaverage T—O bond distances for

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Figure 9Electron density maps around two adjacent M sites projected along the a-axis. The two sites havedifferent x coordinates.

Figure 8The displacement modulation of the M site along a, b, c axes and electrondensity contour variation; the red line represents M2(Ca) and the greenline represents M1(Na + Ca), xi (i = 1, 2, 3, 4) are unit cell edges in(3 + 1)-dimensional space.

Figure 10Occupancy modulation of eight symmetrically equivalent Na atomswithin one subcell (c ’ 14 A) and their average. The average occupancy(thick black line) indicates a density modulation of ! 7 mol % variation.The individual M site is labelled with the corresponding symmetryelements from which it is generated based on an I1 space group. Letter ‘o’means original, ‘i’ = inversion, ‘c’ = C centring (1

2a + 12b translation), ‘z’

means 12c translation (e.g. Mooz and Mioz are related by an inversion

centre ‘i’).

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T1o, T1m, T2o and T2m are 1.7002, 1.6482, 1.6477 and1.6523 A, respectively. The corresponding average Al occu-pancies are 0.64, 0.26, 0.25 and 0.29, respectively.

3.2.2. Three-dimensional structure. A fragment of theaperiodic structure extending 3 subcells (c ’ 14 A) along b-axis and 7 subcells along c-axis is presented in Fig. 12. Themodulation period is too short to separate an individualsubcell representing the inversion twin boundary or thedomain with polarity. The structure basically shows the samepattern as the low temperature e-labradorite structure (Jin &Xu, 2017), except for the change in orientation and period ofthe modulation. A close-up view of two subcells in this frag-ment is shown in Fig. 13. The red cell lies right on the inversiontwin boundary, yet the M sites on the edge already start toshow a strong polarity. The T-site ordering display an anor-thite-like pattern locally at the inversion boundaries.However, there are obviously more Si in this subcell than theinversion twin boundary of the e-labradorite, given that theAn composition at the inversion boundaries is ! 10 mol %lower in the An component (! An48 in e-andesine versus! An60 in e-labradorite). The domain structure with peak Nacomposition, on the other hand, shows almost exactly thesame structure, with very similar composition (! An40 in e-andesine versus ! An43 in e-labradorite). Again, no part of themodulated structure shows an albite-like pattern, except thatAl is generally more concentrated in T1o sites.

Projection of the refined modulated structure along the[311] direction is given in Fig. 14. The orientations of Si/Aldumbbells show the same pattern as in Fig. 3(a). The dumb-bells alternate the orientation within the I1-like domains butremain the same across the inversion twin boundaries. Themodulation direction is almost perpendicular to the [311] zoneaxis. Both Z-contrast image and the refined structure areconsistent in revealing the structural modulation.

The split M site lies in the plane defined by T2 sites, which isparallel to the (100) plane (Fig. 15a). The displacementmodulation of the M site also happens in this plane. In Fig.15(b), the local environment of the M site is shown in aprojection along the a* direction. The split direction of the Msite is very similar to the line connecting diagonal T2 sites.

Therefore, the M1—M2 distances (splitting distance of the Msite) are plotted against the distances between the diagonalT2o and T2m in Fig. 16. The relation between this pair ofdistances is quite interesting. The correlation is quite strongwhere the T2o—T2m distance is smaller than 8.16 A. Yet forthe part with T2o—T2m distance larger than 8.16 A, thecorrelation seems to be lost. Also these two parts are almostexactly separated by t = 0 and t = 0.5, which corresponds to theinversion twin boundaries in the structure. And for each pairof M sites as in Fig. 9 and Fig. 15, if they are not related by aninversion center, one M site should be close together and theother more split. Based on the relationship shown in Fig. 16,the site that is close together seems to be constrained by the T2

tetrahedra surrounding it, whereas the split site is lessdependent on the T2 tetrahedra and may be affected by someother part of the framework.

The tilting of the tetrahedral framework of the structurealso shows a pattern similar to the labradorite sample (Jin &Xu, 2017). The T1o—OA1—T1m angle modulation is plotted inFig. 17. The split M site configuration correlates with thetetrahedral framework distortion in the same way as the e-labradorite structure (Jin & Xu, 2017). For a comprehensive

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Figure 12A fragment of the modulated structure consists of 3 $ 7 anorthite cellsalong the b- and c-axes. The modulation frontier is marked with redplanes in the figure, indicating the mathematical inversion twin boundarypositions. O atoms are omitted in the figure. Ca and Na atoms are shownas large spheres, with blue for Ca and yellow for Na partial occupancies.Al/Si atoms are shown as small spheres; occupancies for Si and Al atomsare shown with dark blue and light blue colors, respectively.

Figure 11Average bond distances of eight symmetrically equivalent T sites and atotal average of all 32 sites within one unit cell (c ’ 14 A).

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idea of the modulated structure, a movie is provided in thesupporting information, in which the phase parameter t isconveyed as the time lapse of the movie.

4. Discussions

This is the first time observation ofthe second-order satellites by X-raydiffraction in an Na-rich e-plagio-clase. It is commonly believed thatf-reflections can only be found incrystals with An contents greaterthan ! An50 (Carpenter, 1994;Smith & Brown, 1988). Although itis quite easy to observe f-reflectionsin transmission electron micro-scopy due to the strong dynamicdiffraction of electrons (McLaren& Marshall, 1974; Carpenter, 1986),no f-reflections have been reportedin X-ray studies of e-plagioclase onNa-rich plagioclase. Even stronglyoverexposed X-ray diffractionphotographs (Steurer & Jagod-zinski, 1988) did not show any f-

reflections in an andesine sample with a composition of! An38.

The similarity between this andesine structure and the e-labradorite structure clearly indicates they belong to the samephase, which means the compositional range of the e1 struc-ture can extend to the Na-rich side. Bøggild intergrowth wasconsidered as a miscibility gap separating the e1 and e2 areas(Carpenter, 1994). The composition of this sample is towardsthe lower end of the Bøggild intergrowth composition range,and no exsolution lamellae are observed in TEM. This isadditional strong evidence proving the loop-shaped solvus forBøggild intergrowth as proposed by McConnell (2008), wherethe e1 phase would appear as a continuous area under theBøggild immiscible loop in the binary phase diagram of theplagioclase solid solution. Although there is no thermo-dynamic law ruling against a discontinuous area for a single

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Figure 14A section of the modulated structure projected along the [311] zone-axis,which is the same as the Z-contrast image (Fig. 3). The Si/Al dumbbellsshow the same configuration as observed in Fig. 3(a). The dumbbellsacross the inversion twin boundaries are related by an inversion center,and show the same angle relative to the guideline. The dumbbells in theI1-like domains, however, shows alternating high/low angles, indicatingstrong polarity in the tetrahedral framework.

Figure 15M sites and the surrounding tetrahedra projected along the b* (a) and a*(b) direction. The split M site lies within the plane of T2 sites, and the splitdirection (green arrow) of the M site is close to the line connecting twodiagonal T2m–T2o sites (red arrow).

Figure 13A close-up view of the highlighted subcells (c ’ 14 A) in Fig. 12. (a) The centrosymmetric subcell in thecenter of the fragment in Fig. 12; (b) the subcell in between two adjacent inversion twin boundaries withstrong polarity.

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phase in the phase diagram, it would require an exsolvingmechanism to explain the Bøggild exsolution if the e1 phase isindeed separated in the phase diagram. As for the loop-shapedmiscibility gap, it can be considered as a strong first-orderphase boundary between C1 and e1 structures.

The variation of density modulation is much smaller thanthat in low-temperature e-labradorite. Density modulationmight be a parameter depending on phase transitiontemperature and cooling rate, just like any other order para-meter in a order–disorder phase transition. The densitymodulation could also be limited by the compositionalgradient within the structure, which means as the modulationwavelength decreases, the maximum possible amplitude ofdensity modulation may also decrease.

The relationship between e1 and e2 phases is still unclear,because the structure solution and refinement of the e2structure is very limited. The only published e2 structurerefinement was made by Steurer & Jagodzinski (1988) on anandesine sample. Also, because almost all the previousrefinements were based on only a- and e-reflections, they couldnot tell the difference between their andesine An38 and An52

structures (Horst et al., 1981; Yamamoto et al., 1984), which led

to a simple conclusion of similar modulation principles butlower amplitude for An38. Despite the many similaritiesbetween the e1 and e2 structures, there should be some defi-nitive characteristics that separate them. The existence of f-reflections is certainly one of them. More detailed differencesshould be uncovered after high quality refinement of the e2structure is available.

The modulation period of the An38 sample is 26.7 A(Steurer & Jagodzinski, 1988), which is longer than the periodof the sample in this study, 24.8 A. The modulation periodgenerally increases as the anorthite component increases. Thewavelength, however, dropped with an 8 mol % rise in Ancomponent in this case. This is consistent with the previouslyreported discontinuity in the modulation period at ! An50

(Slimming, 1976). It was also illustrated that plagioclasefeldspars with the same or very similar composition could havedifferent modulation periods (Smith & Brown, 1988; their Fig.5.12). There were no data points in Slimming’s paper withinthe range of An45–An50, which made it unclear where and howthe discontinuity happened. It was proposed that thecomplexity might be introduced by Bøggild intergrowth(Carpenter, 1994). With the results in this paper, it seems morelikely that the e1 and e2 modulation periods follow twodifferent trends.

The Al occupancy of the T1o site is higher than the occu-pancy of 0.5 in the anorthite structure, and also higher than theT1o in the e-labradorite structure (Jin & Xu, 2017). Yet it isstill dramatically lower than the mechanical mixture of albiteand anorthite structure, which is 0.77 for this composition. It isworth noting that the Al occupancy of the T1o site is obviouslyhigher than that in the An38 e-plagioclase (e2), even though itstotal Al content is lower. This might indicate that, during thephase transition from e2 to e1 in Na-rich plagioclase, Al tendsto become more concentrated in T1o site, which could be animportant driving force for the phase transition from e2 to e1incommensurately modulated structure.

5. Conclusions

The combination of Z-contrast imaging and single-crystaldiffraction provide an approach for solving an incommensu-rately modulated structure in an Na-rich plagioclase. Z-contrast imaging can provide relatively direct information ofthe crystal structure, yet for the aperiodic crystals the imagingzone axis is limited by the orientation of the modulation or thesatellite diffractions. The structure refinement from X-raydata, on the other hand, can provide three-dimensionalstructure with great detail, but reliability of the result dependsstrongly on the quality of data collected and the model chosenfor the refinement. Careful preparation of single crystals andstate-of-the-art equipment, as well as a prudently chosenmodel are necessary. The Z-contrast imaging and single-crystal refinement results matches well in this study, whichproves the modulated structure of e-plagioclase to be I1-likedomains with an alternating polarity related by inversion twinoperation, instead of anti-phase domain boundaries (or

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Figure 17The modulation of T1o–OA1–T1m angle.

Figure 16The distance between M1 and M2 (splitting distance) plotted against thedistance between the corresponding diagonal T2m–T2o sites. Thecorrelation is lower on the lower left part, where the splitting distanceof the M site is small, but is much less obvious where T2oz–T2mo distanceis larger than 8.16 A.

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APBs). The twin boundaries are of I1 symmetry instead of C1symmetry in all early APB-based models.

Second-order satellite reflections (f-reflections) are firstobserved in the X-ray diffraction pattern in Na-rich e-plagi-oclase, which characterize density modulation with 7 mol % ofcomposition variation in an anorthite component. The simi-larities between this andesine sample and the previouslypublished e-labradorite structure suggests they belong to thesame phase. This result extends the compositional range of e1structure to at least An45. This result supports the loop-shapedsolvus for Bøggild intergrowth, below which is a homogenousstable area for the e1 structure (with both first- and second-order satellite reflections) in the phase diagram. This resultalso suggests the existence of a phase transition between e2(with first-order satellite reflections only) and e1 at lowtemperature, characterized by a shortening in modulationperiod as well as a higher Al occupancy in the T1o site.However, further study on e2 structure is necessary to revealthe detailed differences between the two phases. The rela-tionships between the two different types (e1 versus e2) ofincommensurately modulated structures are still not clear andrequire further study. High quality refinement of e2 structure(without second-order satellite reflections) may reveal somevaluable information about the relationships.

Acknowledgements

This study was supported by NSF (EAR-1530614) and theNASA Astrobiology Institute (N07-5489). Authors thank DrHiromi Konishi for assisting STEM imaging, Dr Ross Angelfor insightful discussions, and two anonymous reviewers forcomments and suggestions.

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