Nano-Phase Kna(Si6al2)O16 in Adularia: a New Member in the Alkali Feldspar Series with Ordered K–Na Distribution

Article Nano-Phase KNa(Si6Al2)O16 in Adularia: A New Member in the Alkali Feldspar Series with Ordered K–Na Distribution

Huifang Xu * , Shiyun Jin, Seungyeol Lee and Franklin W. C. Hobbs

Department of Geoscience, University of Wisconsin—Madison, Madison, WI 53706, USA; [email protected] (S.J.); [email protected] (S.L.); [email protected] (F.W.C.H.) * Correspondence: [email protected]; Tel.: +1-608-265-5887

Received: 11 October 2019; Accepted: 22 October 2019; Published: 23 October 2019

Abstract: Alkali feldspars with diffuse reflections that violate C-centering symmetry were reported in Na-bearing adularia, orthoclase and microcline. TEM results indicate elongated nano-precipitates with intermediate composition of KNa(Si6Al2)O16 cause the diffuse reflections. Density functional theory (DFT) calculation indicates ordered distribution of K and Na atoms in the nano-phase with Pa symmetry. K and Na atoms are slightly off special positions for K atoms in the orthoclase structure. Formation of the intermediate nano-phase may lower the interface energy between the nano-phase and the host orthoclase. Previously reported P21/a symmetry was resulted from an artifact of overlapped diffraction spots from the nano-precipitates (Pa) and host orthoclase (C2/m). Adularia, orthoclase and microcline with the Pa nano-precipitates indicate very slow cooling of their host rocks at low temperature.

Keywords: adularia; orthoclase; microcline; primitive alkali feldspar; non-centric symmetry; XRD; TEM; G.P. zone; Na–K ordering

1. Introduction Adularias are hydrothermal K-rich feldspars that display a dominant {110} crystallographic form. Some adularia crystals display diffuse diffractions that violate C-centering symmetry [1–4]. Similar diffuse diffractions were also observed in K-feldspar lamellae in orthoclase and microcline (~Or90) from two granites [5]. The mechanism for the cause of the diffuse diffractions was not well understood. A common explanation is that nano-scale domains with P21/a symmetry are related by APBs (or out-of-phase domain boundaries) [3,6]. Tweed pattern was also observed in the adularia [7,8]. It was suggested domains related by P21/a symmetry causes the diffuse diffractions that violate C-centering [8]. However, Smith [9] proposed that domains violating C-centering are very small (nano-meter scale) within the adularia host. Only the very small phases/precipitates contribute to the diffuse diffractions. A crystal structure with P21/a symmetry was proposed but was not determined [9]. Smith and Brown [10] suggested that “such adularias should be restudied by optics, X-rays, microprobe and TEM as they are quite different from orthoclase.” In this paper, we provide both structural and textural information about the adularia using TEM, X-ray diffraction and density functional theory (DFT) calculation.

2. Sample and Experimental Methods A gem quality adularia single crystal (a collection the Department of Earth and Planetary Sciences, Johns Hopkins University) from St. Gotthard of Switzerland was selected for TEM and XRD studies. Similar samples from the same locality were studied by Laves and Goldsmith [6],

Minerals 2019, 9, 649; doi:10.3390/min9110649 www.mdpi.com/journal/minerals Minerals 2019, 9, 649 2 of 9

Smith and MacKenzie [1], Coville and Ribbe [3] and Phillips and Ribbe [4]. TEM samples were prepared by depositing a suspension of a crushed small grain on a holey carbon grid. TEM imaging, X-ray energy-dispersive spectroscopy (EDS) and selected-area electron diffraction (SAED) analyses were carried out using a Philips CM200-UT microscope equipped with a GE light element and energy-dispersive X-ray spectroscopy (EDS) at the Materials Science Center at the University of Wisconsin-Madison operated at 200 kV. Chemical analyses were obtained using the EDS (spot size 5 with a beam diameter of ~100 nm). Quantitative EDS results were obtained using experimentally determined k-factors from standards of albite, anorthite, orthoclase and labradorite [11]. Powder XRD patterns were collected using a Rigaku Rapid II XRD system (Mo-Kα radiation) in the Geoscience Department at the University of Wisconsin-Madison. Diffraction data were recorded on a 2-D image-plate detector. The original 2-D diffraction rings were then converted to produce conventional 2θ vs. intensity patterns using Rigaku’s 2DP software. The unit cell parameters at room temperature were determined by the Rietveld method using the Jade 9 software. A pseudo-Voigt function was used for fitting the peak profiles. The single-crystal X-ray diffraction data were collected on a Bruker Quazar APEXII diffractometer with MoKα IµS source at 100 K. Four ω runs and 1 ϕ run were programmed with a scan width of 0.5◦ and a 30 s exposure time. The instrument was running at power of 50 kV and 0.6 mA. The detector was set at a distance of 5 cm from the crystal. Data were indexed on a primitive cell and the unit cell parameters constrained to monoclinic symmetry were refined with the APEXII software. DFT calculations were run on the Vienna Ab initio Simulation Package (VASP)using the generalized gradient approximation functional with Perdew, Burke and Ernzerhof (PBE) parameters [12–15]. Pseudopotentials derived by the projector augmented wave method were used with an energy cut off of 450 eV. A 4 2 4 k-point mesh was used along with Gaussian smearing and a 0.2 eV sigma value. × × Initial structures were based on a monoclinic unit cell with space group Pa. Both cell volume and shape were allowed to fully relax. Microcline and albite structures were run using a triclinic structure as a reference for the intermediary phases.

3. Results and Discussions A [001] zone-axis selected-area electron diffraction (SAED) pattern shows streaking of main reflections along a* and b* directions (Figure1, inserted SAED and FFT patterns). Di ffuse diffractions that violate C-centering are not obvious in hk0 reflections. Multi-beam bright-field TEM image shows a tweed pattern (Figure1). A similar texture was observed by McConnell [ 8]. Nano-precipitates are not obvious in the image along the [001] direction. X-ray EDS spectra show the bulk adularia contains small amounts of Na (ranging from ~Ab9 to ~Ab14) and trace amounts of Ba (~Cn0.1) (Supplementary Figure S1). A [100] zone axis SAED pattern and precession image from XRD show some diffuse diffractions along the b* direction (see the areas indicated by arrows in Figure2). A [2 10] zone-axis SAED pattern clearly shows diffuse diffractions that violate the C-centering lattice (Figure3, inserted SAED pattern). Dark-field TEM image using a relatively strong diffuse reflection shows needle-like precipitates in the adularia (Figure3). The needle-like nano-precipitates are about 10 to 30 nm long along the c-axis and about 1–3 nm wide perpendicular to the c-axis. There are about 20 vol.% of precipitates in the host. The dark-field image shows that only needle-like precipitates contribute to the diffuse diffractions, instead of proposed APB-like domains [3] or boundary area in the tweed texture [7,8]. Minerals 2019,, 9,, 649 33 of of 9 Minerals 2019, 9, 649 3 of 9

Figure 1. TEM image showing tweed texture due to domains related by Albite‐twin and Pericline Figuretwins. Average 1.1. TEMTEM image imagestructure showing showing of the tweed tweed crystal texture texture is monoclinic, due due to domains to domains i.e., related orthoclase. related by Albite-twin byThe Albite inserted‐ andtwin PericlineSAED and Pericline pattern twins. Average(uptwins.‐right Average structure corner) structure and of the Fast crystal ofFourier the is crystal monoclinic,transform is monoclinic, (FFT) i.e., orthoclase.pattern i.e., (low orthoclase. The‐left inserted corner) The SAEDdisplayinserted pattern streaking SAED (up-right pattern along corner)the(up ‐aright*‐ and and corner) b Fast*‐directions. Fourier and Fast transformNo Fourier diffuse (FFT)transform reflections pattern (FFT) that (low-left violatepattern corner) C (low‐centering‐left display corner) occur streaking displayin the SAED along streaking thepattern.a *-along and bthe*-directions. a*‐ and b*‐ Nodirections. diﬀuse reﬂectionsNo diffuse that reflections violate thatC-centering violate C occur‐centering in the occur SAED in pattern. the SAED pattern.

(a) (b) (a) (b) Figure 2.2. [100][100] zone-axis zone‐axis SAED SAED pattern pattern (a) and(a) precessionand precession image image from single-crystal from single‐ XRDcrystal (b )XRD showing (b) weakshowingFigure and 2. weak di[100]ﬀuse and zone di diffuseﬀractions‐axis diffractionsSAED violating pattern Cviolating-centering (a) and C‐centering in precession alkali feldspars. in alkaliimage feldspars. from single ‐crystal XRD (b) showing weak and diffuse diffractions violating C‐centering in alkali feldspars.

Minerals 2019, 9, 649 4 of 9 Minerals 2019, 9, 649 4 of 9

FigureFigure 3. AA DF DF TEM TEM image image showing showing needle needle-like‐like elongated elongated nano nano-precipitates‐precipitates along along the c the‐axis.c-axis. The Theinserted inserted [210] [2 1zone0] zone-axis‐axis SAED SAED pattern pattern shows shows weak weak and and diffuse diﬀuse reflections reﬂections violating violating C‐-centeringcentering inin alkalialkali feldspars.feldspars.

TheThe nano-precipitatesnano‐precipitates are are Guinier–Preston Guinier–Preston zones, zones, or G.P.zones, or G.P. that zones, have intermediatethat have intermediate composition betweencomposition the end between members the ofend albite members and orthoclase of albite (microcline), and orthoclase K0.5 Na(microcline),0.5(Si3Al)O 8Kor0.5Na KNa(Si0.5(Si36Al)OAl2)O8 16or. SimilarKNa(Si6Al G.P.2)O zones16. Similar were G.P. observed zones were in very observed slowly in cooled very slowly orthopyroxenes cooled orthopyroxenes [16,17]. The [16,17]. G.P. zone The precipitatesG.P. zone precipitates are an exsolved are an phase exsolved that formed phase atthat low formed temperature. at low temperature. The precipitates The with precipitates stoichiometry with ofstoichiometry KNa(Si6Al2)O of16 KNa(Siwith an6Al ordered2)O16 with Na–K an distribution ordered Na–K will distribution have Pa symmetry will have instead Pa symmetry of P21/a symmetry. instead Naof P2 and1/a Ksymmetry. atoms are Na ordered and K and atoms off arespecial ordered positions and off in specialPa symmetry. positions Both in Pa T1 symmetry.and T2 sites Both in the T1 orthoclaseand T2 sites (C2 in/m the) structure orthoclase will (C2/m split) into structure four sites will (T split1oo,T into1o2,T four1io,T sites1i2 for (T1oo T1, site,T1o2, andT1io, TT2oo1i2 ,Tfor2o2 T,T1 site,2io, Tand2i2 forT2oo T, 2Tsite),2o2, T2io respectively., T2i2 for T2 site), An adulariarespectively. (~Or An99–100 adularia) from a(~Or sub-Cambrian99–100) from a paleosol sub‐Cambrian does not paleosol show precipitatesdoes not show and precipitates diffuse diff ractionsand diffuse violating diffractionsC-centering violating (Supplementary C‐centering (Supplementary Figure S2) [18]. TheFigure tweed S2) pattern[18]. The indicates tweed onlypattern local indicates domains only related local by Albitedomains and related Pericline by twins Albite at theand nano-meter Pericline twins scale, whichat the willnano not‐meter result scale, in di whichffuse di willffractions not result violating in diffuseC-centering. diffractions The violating formation C‐centering. of the nano-precipitates The formation inof Na-bearingthe nano‐precipitates K-feldspar isin the Na key‐bearing for the diK‐fffeldsparuse diffractions is the violatingkey for Cthe-centering. diffuse diffractions The diffuse reflections violating displayC‐centering. streaking The perpendiculardiffuse reflections to the cdisplay-axis, which streaking also indicates perpendicular elongated to nano-precipitatesthe c‐axis, which along also theindicatesc-axis (Figureelongated3). Thenano tunnel-like‐precipitates structure along alongthe c‐axisc-axis (Figure in the feldspar3). The tunnel allows‐like K–Na structure diffusion along and orderingc‐axis in atthe low feldspar temperature, allows whichK–Na causesdiffusion the elongatedand ordering nano-precipitates at low temperature, in the adularia which causes (Figure the3). elongatedCompared nano‐ toprecipitates the unit cell in parametersthe adularia at (Figure the room 3). temperature from powder XRD (a = 8.539(2), b = 12.970(3),Comparedc = to7.202(2) the unit Å, cellβ = parameters116.03(2)◦), at the the unit room cell temperature of adularia from at 100 powder K from XRD single-crystal (a = 8.539(2), XRD b (=a 12.970(3),= 8.5291(1), c =b 7.202(2)= 12.9795(2), Å, β =c =116.03(2)°),7.2032(1) Å,theβ unit= 116.0521(7) cell of adularia◦) shows at the100 extremely K from single anisotropic‐crystal thermal XRD (a contraction,= 8.5291(1), b only = 12.9795(2), with shortening c = 7.2032(1) of the aÅ,-axis. β = 116.0521(7)°) The same trend shows of thermal the extremely contraction anisotropic was observed thermal in orthoclasecontraction, and only sanidine with shortening [19]. of the a‐axis. The same trend of thermal contraction was observed in orthoclaseTo confirm and the sanidine Al in the [19]. tetrahedral sites for the ordered Pa structure, structural models with differentTo confirm Al–Si distribution the Al in the were tetrahedral calculated sites using for thethe DFT ordered method. Pa structure, The most structural stable structure models is with the configurationdifferent Al–Si with distribution Al in T1oo wereand calculated T1io sites, using respectively the DFT (Figure method.4). The The most ordered stable structure structure shows is the oppositeconfiguration shifts with of Na Al and in T K1oo atoms and T o1ioff thesites, special respectively position. (Figure Details 4). aboutThe ordered the structure structure and shows bond distancesopposite shifts are listed of Na in Tablesand K1 atomsand2, respectively.off the special The position. di ffuse Details reflections about are the very structure weak in and the [100]bond zone-axisdistances diareffraction listed in pattern Tables (Figure 1 and2 2,), butrespectively. obvious in The the diffuse [2 10] zone-axis reflections diff areraction very patterns weak in (Figures the [100]3 zone‐axis diffraction pattern (Figure 2), but obvious in the [21 0] zone‐axis diffraction patterns (Figures 3 and 4). The calculated SAED pattern match observed diffraction patterns well (Figure 5 and the inserted SAED pattern in Figure 3).

Minerals 2019, 9, 649 5 of 9 and4). The calculated SAED pattern match observed di ffraction patterns well (Figure5 and the inserted SAED pattern in Figure3). We also carried out single-crystal XRD refinement for two phases of the host orthoclase (C2/m) and the nano-precipitates (Pa) with same orientation and unit cell parameters using JANA2006 software (Supplementary Tables S1–S4, Supplementary Figures S3 and S4). The refinement results show that Na and K atoms are off special position slightly. The deviation (y coordinate) is slightly larger for Na atom than that for K atom, which is similar to the results from DFT calculation.

Table 1. Fractional coordinates for the nano-phase alkali feldspar with Pa symmetry (0 K).

Label Atom x y z

Mo Na 0.76710 0.73584 0.14141 M2 K 0.72382 0.24384 0.86156 T1oo Al 0.99905 0.43201 0.20296 T1o2 Si 0.98176 0.42819 0.75421 T1io Al 0.50176 0.93246 0.79588 T1i2 Si 0.51655 0.92662 0.24160 T2oo Si 0.29038 0.36899 0.63497 T2o2 Si 0.68963 0.36265 0.32198 T2io Si 0.20559 0.86970 0.35674 T2i2 Si 0.80675 0.86349 0.67794 Oa1_1 O 0.99984 0.38887 0.97310 Oa1_2 O 0.51152 0.88700 0.02930 Oa2o O 0.11072 0.75651 0.28148 Oa22 O 0.37894 0.25641 0.71607 Oboo O 0.16227 0.39553 0.74253 Obo2 O 0.80957 0.38101 0.20447 Obio O 0.33133 0.89222 0.24267 Obi2 O 0.69325 0.88182 0.80208 Ocoo O 0.45947 0.44707 0.72688 Oco2 O 0.51662 0.43469 0.24071 Ocio O 0.03766 0.94857 0.26821 Oci2 O 0.98068 0.93439 0.75671 Odoo O 0.18882 0.37127 0.38839 Odo2 O 0.80901 0.37269 0.57356 Odio O 0.31467 0.87414 0.60170 Odi2 O 0.68582 0.87183 0.42717

Note: Unit cell parameters are a = 8.49384 Å, b = 13.02193 Å, c = 7.27200 Å, β = 116.380◦.

Table 2. Bond distances for the T sites in the density functional theory (DFT)-calculated structure.

Oa Ob Oc Od Average

T1oo 1.7662 1.7456 1.7533 1.7637 1.7572 T1o2 1.6131 1.6293 1.6372 1.6396 1.6298 T1io 1.7645 1.7370 1.7534 1.7612 1.7540 T1i2 1.6103 1.6391 1.6371 1.6349 1.6304 T2oo 1.6336 1.6345 1.6403 1.6080 1.6291 T2o2 1.6638 1.6121 1.6178 1.6564 1.6375 T2io 1.6522 1.6438 1.6394 1.6026 1.6345 T2i2 1.6550 1.6046 1.6158 1.6517 1.6318 Minerals 2019, 9, 649 6 of 9 Minerals 2019, 9, 649 6 of 9 Minerals 2019, 9, 649 6 of 9

Figure 4. DFT calculated structure of the intermediate nano‐phase “orthobite” at 0 K showing the Figure 4. DFT calculated structure of the intermediate nano‐phase “orthobite” at 0 K showing the oppositeFigure shifts 4. DFT of calculatedNa (yellow) structure and K of(purple) the intermediate atoms off the nano-phase special position. “orthobite” Al atoms at 0 K (turquoise showing the opposite shifts of Na (yellow) and K (purple) atoms off the special position. Al atoms (turquoise color)opposite are in shifts T1oo of and Na T1io (yellow) sites, and respectively. K (purple) atoms oﬀ the special position. Al atoms (turquoise color) color) are in T1oo and T1io sites, respectively. are in T1oo and T1io sites, respectively.

(a) (b) (a) (b) FigureFigure 5. 5.[21[20]10] zone zone-axis‐axis precession precession image fromfrom single-crystal single‐crystal XRD XRD (a )( anda) and the calculatedthe calculated SAED SAED pattern Figure 5. [210] zone‐axis precession image from single‐crystal XRD (a) and the calculated SAED pattern(b) showing (b) showing consistent consistent intensities intensities for the for di ﬀtheraction diffraction spots violatingspots violatingC-centering, C‐centering, which which also matches also pattern (b) showing consistent intensities for the diffraction spots violating C‐centering, which also matchesthe inserted the inserted SAED SAED pattern pattern in Figure in Figure3. 3. matches the inserted SAED pattern in Figure 3. Na–KNa–K ordering ordering causes causes polarity polarity of ofthe the structure structure (and (and piezoelectric piezoelectric property). property). A Aweak weak second second Na–K ordering causes polarity of the structure (and piezoelectric property). A weak second harmonicharmonic generation generation (SHG) (SHG) signal signal (~1/50 (~1/ 50of ofthat that from from quartz) quartz) was was observed observed only only in inan an adularia adularia from from harmonic generation (SHG) signal (~1/50 of that from quartz) was observed only in an adularia from SwitzerlandSwitzerland [20], [20 which], which indicates indicates the the part part of ofthe the adularia adularia is non is non-centric.‐centric. The The determined determined structure structure of of Switzerland [20], which indicates the part of the adularia is non‐centric. The determined structure of thethe nano nano-precipitates‐precipitates of ofNa(Si Na(Si6Al62Al)O216)O with16 with ordered ordered Na–K Na–K is a is reason a reason for forthe the observed observed SHG SHG signal. signal. the nano‐precipitates of Na(Si6Al2)O16 with ordered Na–K is a reason for the observed SHG signal. BasedBased on on strain strain-free‐free solvus solvus in the in the alkali alkali feldspars feldspars (Figure (Figure 6), 6the), the adularia adularia (~An (~An11) crystallized11) crystallized at Based on strain‐free solvus in the alkali feldspars (Figure 6), the adularia (~An11) crystallized at ~400at ~400°C or◦ Chigher or higher from from a hydrothermal a hydrothermal system. system. When When the thecrystal crystal reached reached ~300 ~300 °C ◦orC orlower, lower, ~400 °C or higher from a hydrothermal system. When the crystal reached ~300 °C or lower, exsolutionexsolution of ofalbite albite lamellae lamellae within within the the K‐ K-sparspar host host is isa low a low energy energy state. state. Exsolution Exsolution between between albite albite exsolution of albite lamellae within the K‐spar host is a low energy state. Exsolution between albite andand microcline microcline will resultresult in in a large a large lattice lattice mismatch. mismatch. Nano-precipitates Nano‐precipitates with intermediate with intermediate composition and microcline will result in a large lattice mismatch. Nano‐precipitates with intermediate compositionof KNa(Si6 ofAl KNa(Si2)O16 and6Al2 K)O end-member16 and K end‐member phase may phase lower may the lower interface the interface energy althoughenergy although it is not it the composition of KNa(Si6Al2)O16 and K end‐member phase may lower the interface energy although it is notlowest the energylowest energy state. Figure state. 7Figure schematically 7 schematically illustrates illustrates free energies free energies for alkali for feldspar alkali feldspar solid solution solid is not the lowest energy state. Figure 7 schematically illustrates free energies for alkali feldspar solid solutionand the and intermediate the intermediate phase at phase low temperature. at low temperature. Formation Formation of the needle-like of the needle precipitates‐like precipitates and ordering solution and the intermediate phase at low temperature. Formation of the needle‐like precipitates andbetween ordering Na between and K at low-temperatureNa and K at low can‐temperature be achieved can through be achieved diﬀusion through in the tunnel-like diffusion positionsin the and ordering between Na and K at low‐temperature can be achieved through diffusion in the tunnelalong‐like the positionsc-axis. The along K-rich the alkali c‐axis. feldspar The K with‐rich thealkali nano-precipitates feldspar with the may nano indicate‐precipitates slow cooling may of tunnel‐like positions along the c‐axis. The K‐rich alkali feldspar with the nano‐precipitates may indicatealkali feldsparsslow cooling and their of alkali host rockfeldspars at low and temperature. their host The rock formation at low processtemperature. for the The nano-precipitates formation indicate slow cooling of alkali feldspars and their host rock at low temperature. The formation processis very for similar the tonano that‐precipitates for the G.P. zonesis very in slowlysimilar cooled to that orthopyroxenes for the G.P. [ 16zones,17]. Thein nano-precipitatesslowly cooled process for the nano‐precipitates is very similar to that for the G.P. zones in slowly cooled orthopyroxenesin an adularia [16,17]. with similar The nano microstructure‐precipitates may in bean aadularia reason for with the similar reported microstructure unusual mixing may behavior be a orthopyroxenes [16,17]. The nano‐precipitates in an adularia with similar microstructure may be a reasonbetween for the Na- reported and K-end unusual members mixing [21 ].behavior between Na‐ and K‐end members [21]. reason for the reported unusual mixing behavior between Na‐ and K‐end members [21].

Minerals 2019, 9, 649 7 of 9

Minerals 2019,, 9,, 649 7 of 9

FigureFigure 6.6. AA phasephase diagramdiagram forforfor alkalialkali feldsparfeldsparfeldspar showingshowing strain-freestrain‐‐freefree solvussolvus vs.vs. coherent solvus,solvus, withwith meta-stablemeta‐‐stable solvus solvus between between the thethe intermediate intermediateintermediate phased phased and theand microcline. thethe microcline. A blue A arrow blue shows arrow a shows possible a pathpossible for thepath adularia forfor thethe withadularia the tweedwith thethe pattern. tweedtweed The pattern. intermediate The intermediateintermediate phase of nano-precipitatesphase of nano‐‐precipitates (“Ob” or “orthobite”(“Ob”(“Ob” or “orthobite” that is between thatthat isis orthoclase between orthoclase and albite) and forms albite) at low formsforms temperature. at lowlow temperature.temperature. The diagram The is diagram modiﬁed isis frommodified Yund fromfrom [22] Yund based [22] on[22] the based recent on mixing thethe recent energy mixing for the energy solid forfor solution thethe solid from solution Hovis [fromfrom21]. The Hovis crest [21].[21]. of

theThe solvus crest of is thethe at ~Or solvus40. isis at ~Or4040..

FigureFigure 7. AA diagram diagram schematically schematically showing showing thethe the energy energy curves curves forfor foralkali alkali feldsparfeldspar feldspar solid solid solution solution and andthethe theintermediateintermediate intermediate phase phase at atlowlow low temperature.temperature. temperature. Formation Formation of of nano nano-precipitates‐‐precipitates “orthobite” “orthobite” with with a KNa(SiKNa(Si666Al22)O)O1616 compositioncomposition insteadinstead instead of of albite albite exsolution exsolution lamellaelamellae was was due toto the the low low interface interface energy betweenbetween thethe intermediateintermediateintermediate phasephase andand thethethe hosthost phase.phase.

4.4. Conclusion Conclusions TEMTEM resultsresults indicateindicateindicate thatthatthat elongatedelongated nano-precipitatesnano‐precipitates withwith anan intermediateintermediateintermediate compositioncomposition ofof KNa(Si Al )O cause the diffuse reflections in the adularia. The ordered distribution of K and Na KNa(Si66Al22)O161616 cause thethe diffuse reflections inin thethe adularia. The ordered distribution of K and Na atomsatoms ininin the thethe nano-phase nano‐phase resulted resulted in Painin symmetry.Pa symmetry. K and K Naand atoms Na atoms are slightly are slightly off the special off thethe position. special Formationposition. Formation of the intermediate of thethe intermediateintermediate nano-phase nano may‐phase lower may the interface lowerlower thethe energy interfaceinterface between energy the between nano-phase thethe andnano the‐phase host and orthoclase, thethe host and orthoclase, the structure and energythethe structure penalty energy is smaller penalty than isis the smaller interfacial thanthan energy thethe interfacialinterfacial benefit. K-richenergy alkali benefit. feldspars K‐rich alkali with the feldsparsPa nano-precipitates with thethe Pa nano indicate‐precipitates very slow indicateindicate cooling very of theirslow hostcooling rocks of attheirtheir low host temperature. rocks at lowlow The temperature.temperature. combined TEM, The combined XRD and TEM, DFT methods XRD and can DFT be methods applied forcan solving be applied crystal for structuressolving crystal of nano-phases structures withinof nano their‐phases host crystalswithin theirtheir in natural host andcrystals synthetic inin natural materials. and Structuresynthetic refinementmaterials. Structure using a single-phase refinement model using fora single the intergrowth‐phase model of nano-precipitatesfor thethe intergrowthintergrowth and of the nano host‐precipitates phase will resultand thethe in host incorrect phase structure. will result inin incorrectincorrect structure.

Supplementary Materials: The followingfollowing are available online at www.mdpi.com/xxx/s1, Figure S1: A representative X‐‐ray EDS spectrum fromfrom thethe adularia; Figure S2: TEM imageimage with SAED and EDS of adularia fromfrom North American sub‐‐Cambrian paleosols. Figure S3: Structure model fromfrom XRD refinement; Figure S4:

Minerals 2019, 9, 649 8 of 9

Supplementary Materials: The following are available online at http://www.mdpi.com/2075-163X/9/11/649/s1, Figure S1: A representative X-ray EDS spectrum from the adularia; Figure S2: TEM image with SAED and EDS of adularia from North American sub-Cambrian paleosols; Figure S3: Structure model from XRD refinement; Figure S4: Precession image from XRD and calculated SAED pattern from the refined structure; Table S1: Experimental and crystallographic information of the adularia sample (100K); Table S2: Fractional coordinates for the adularia average structure with C2/m symmetry (100K); Table S3: Fractional coordinates for the nano-phase alkali feldspar with Pa symmetry (100K); Table S4: Bond distances for the T sites. Author Contributions: H.X. conceived the idea, carried out TEM works, and drafted the manuscript; S.J. carried out single-crystal XRD works; S.L. carried out powder XRD and part of the TEM works; F.W.C.H. carried out DFT calculation; all the co-authors contributed to manuscript writing. Funding: This study was supported by the NSF (EAR-1530614) and the NASA Astrobiology Institute (N07-5489). Acknowledgments: We thank Izabela Szlufarska for helping us on the DFT calculation. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Smith, J.V.; MacKenzie, W. The alkali feldspars V. The nature of orthoclase and microcline perthites and observations concerning the polymorphism of potassium feldspar. Am. Mineral. 1959, 44, 1169–1186. 2. Goldsmith, J.R.; Laves, F. The sodium content of microclines and the microcline-albite series. Inst. Lucas Mallada C.S.I.C. 1961, 8, 81–96. 3. Colville, A.A.; Ribbe, P.H. The crystal structure of an adularia and a refinement of the structure of orthoclase. Am. Mineral. 1968, 53, 25–37. 4. Phillips, M.W.; Ribbe, P.H. The structures of monoclinic potassium-rich feldspars. Am. Mineral. 1973, 58, 263–270. 5. Blasi, A.; Blasi, C.D.P. Aspects of alkali feldspar characterization: Prospects and relevance to problems outstanding. In Feldspars and Their Reactions; Parsons, I., Ed.; Springer: Boston, MA, USA, 1994; pp. 51–101. 6. Laves, F.; Goldsmith, J. Comments on the anorthite papers by Megaw and co-workers presented at this symposium. Estudos Geologicos C.S.I.C. 1961, 8, 155–157. 7. McConnell, J. Electron optical study of effects associated with partial inversion in a silicate phase. Philos. Mag. 1965, 11, 1289–1301. [CrossRef] 8. McConnell, J. Hallimond Lecture 1970 Electron-Optical study of phase transformations. Mineral. Mag. 1971, 38, 1–20. [CrossRef] 9. Smith, J.V. Chemical and textural properties. In Feldspar Minerals; Springer: Berlin, Germany, 1974; Volume 2, pp. 152–195. 10. Smith, J.V.; Brown, W.L. Diffusion, growth, twins and intergrowths. In Feldspar Minerals; Springer: Berlin, Germany, 1988; Volume 1, pp. 398–647. 11. Hill, T.R. High-Resolution Transmission Electron Microscopy Investigation of Nano-Crystals of Pyroxene and Copper in Oregon Sunstones. Ph.D. Thesis, University of Wisconsin-Madison, Madison, WI, USA, 2009. 12. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169. [CrossRef][PubMed] 13. Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758. [CrossRef] 14. Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953. [CrossRef][PubMed] 15. Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. [CrossRef][PubMed] 16. Xu, H.; Shen, Z.; Konishi, H.; Luo, G. Crystal structure of Guinier-Preston zones in orthopyroxene: Z-contrast imaging and ab inito study. Am. Mineral. 2014, 99, 2043–2048. [CrossRef] 17. Champness, P.; Lorimer, G. Precipitation (exsolution) in an orthopyroxene. J. Mater. Sci. 1973, 8, 467–474. [CrossRef] 18. Medaris, L.G., Jr.; Driese, S.G.; Stinchcomb, G.E.; Fournelle, J.H.; Lee, S.; Xu, H.; DiPietro, L.; Gopon, P.; Stewart, E.K. Anatomy of a Sub-Cambrian Paleosol in Wisconsin: Mass fluxes of chemical weathering and climatic conditions in North America during formation of the Cambrian Great Unconformity. J. Geol. 2018, 126, 261–283. Minerals 2019, 9, 649 9 of 9

19. Kimata, M.; Saito, S.; Shimizu, M.; Iida, I.; Matsui, T. Low-temperature crystal structures of orthoclase and sanidine. Neues Jahrb. Mineral. Abh. 1996, 171, 199–213. 20. Zilczer, J.; Loiacono, G. Non-centrosymmetry tests for potassium feldspars: An application of the second-harmonic generator technique. J. Appl. Cryst. 1982, 15, 540–541. [CrossRef] 21. Hovis, G.L. A reﬁned view of the thermodynamic mixing quantities for alkali feldspars and the quandary of excess conﬁgurational entropy. Am. J. Sci. 2017, 317, 597–640. [CrossRef] 22. Yund, R.; Hofmann, A.; Giletti, B.; Yoder, H. Coherent exsolution in the alkali feldspars. In Geochemical Transport and Kinetics; Hofmann, A.W., Giletti, B.J., Yoder, H.S., Jr., Yund, R.A., Eds.; Carnegie Institution of Washington Publication: Washington, DC, USA, 1974; pp. 173–183.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).