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Lazurite

A valid IMA mineral species
This page kindly sponsored by Mary Keesling
Hide all sections | Show all sections

About LazuriteHide

Formula:
Na7Ca(Al6Si6O24)(SO4)(S3) · H2O
Often there is minor K substituting for Na.
The IMA used to take the ideal formula with S as the dominant anion and not sulfate, from Hassan et al. (1985), but even that reference indicates that sulfate is dominant, making lazurite either a sulfide rich variety of Hauyne or just a theoretical endmember of a series with hauyne. To deal with this problem the IMA, based on the work of Sapozhnikov et al (2021), now only requires just more than a quarter of the cages to contain the (S3)-1 blue colorant. While the formula was formerly given as Na6Ca2(Al6Si6O24)(SO4,S,S2,S3,Cl,OH)2 has now been redefined to Na7Ca(Al6Si6O24)(SO4)(S3)1- · H2O

Colour:
Ultramarine, midnight blue, bluish green, green
Lustre:
Resinous
Hardness:
5 - 5½
Specific Gravity:
2.38 - 2.45
Crystal System:
Isometric
Name:
From the Persian "Lazhward" for "blue." Also for its dark blue color resemblance to "azurite." Both Lazurite and azurite derive from "Lazhward".

Dana (System of Mineralogy, 1868) considered lapis-lazuli to be the dark blue mineral in the lazulite-calcite rock of the same name, but these were renamed lazurite in 1891 Brögger W C, Bäckström H 1891.
Lazurite is the blue component of the 'gemstone' (or, more usually, decorative rock) Lapis Lazuli, which is a lazurite-calcite-pyrite rock that has been mined as a gem material for some 9,000 years. Dana (System of Mineralogy, 1868) considered lapis-lazuli to be the dark blue crystals in this rock, but these were renamed lazurite in 1891 Brögger W C, Bäckström H 1891.

Before the 2021 redefinition, all* lazurites were only sulfide-rich varieties of Hauyne and not a separate species.Moore & Woodside, 2014 The former definition requires more than half the cages to contain sulfide, but the new definition only requires a quarter of the cages filled with (S3)-1.
* With one exception: Rastsvetaeva et al. (2002) give a formula Na6.34Ca1.66(Al6Si6O24)((SO4)0.88S1.26) for a sample from the Malo-Bystrinskoe deposit.

Lazurite is an ultramarine to midnight-blue, opaque, and non-fluorescent mineral with a bright blue streak. The lower limit of polysulphide (primarily S3−1), which is responsible for the blue colour of lazurite, is ~0.4 at%; however, in some cases, there is no explicit correlation between blue colour and polysulphide content (Tauson et al., 2012).

Some blue-green and green "lazurites" (hauynes) have a small unit-cell edge. Since S is smaller than SO4, these were mistakenly thought to be probably dominant in sulfur. These "lazurites" are translucent and fluorescent under long-wave UV and have a white streak just as hauyne has. The name lazurite should not be applied to these small-cell green hauynes.

Lazurite and hauyne are members of the Sodalite Group, in the feldspathoid family. The two sodalite cages in lazurite are mostly made from either [Na3Ca·SO4]+3. or [Na4(S3)–]+3 clusters. If there's enough (S3)-1 to just more than fill a quarter of the cages, then we have Lazurite with the above formula. With just over three quarters of the cages containing sulfate, we have hauyne. Notice that (S3)-1 quenches fluorescence, so if it fluoresces it is hauyne, but if not, it may not have enough (S3)-1 for lazurite and just be a nonfluorescent hauyne. It would be much simpler to define Lazurite as a nonfluorescent hauyne. The sodalite variety Hackmanite is defined as a reversible photochromic sulfide containing variety of sodalite.


It is difficult to determine the oxidation state of sulfur in a sodalite cage. S, S2, S3, S4, SO3, and SO4 have been suggested.Tauson et al. 2003 ,"Fleet et al., 2005. By XPS and XAS spectroscopy, Tauson et al. (2012) detected sulfate and polysulphides as main constituents in the structural cages of lazurites; additionally, sulfite, thiosulphate, monosulphide, and elemental sulfur were found.

As such, most of the pictures showing "lazurite" do not show true lazurite.

Finally redefined (IMA proposal 20 H, 2021) as bearing both the sulfate(VI) and trisulfide as essential anions. There are commensurate and incommensurate modulations in the structure. The cubic sub-cell is equal to 9.087(3) Å. The neotype sample is slightly birefringent.

A possible triclinic dimorph (?) is known: UM1976-26-SiOSO:AlCaClHNa. Compare this with closely related, orthorhombic Vladimirivanovite and the polytype Lazurite-O. Lazurite-C is a monoclinic polytype.




Unique IdentifiersHide

Mindat ID:
2357
Long-form identifier:
mindat:1:1:2357:9
GUID
(UUID V4):
e927d6d5-4642-409a-b046-b9dc7c05ea85

IMA Classification of LazuriteHide

Approved
IMA status notes:
Redefined by the IMA
IMA Formula:
Na7Ca(Al6Si6O24)(SO4)(S3)1- · H2O
Approval history:
Based on Brögger W C, Bäckström H 1891 the name lazurite was grandfathered by the IMA who later gave it Hassan's ideal formula, Na3Ca(Si3Al3)O12S Hassan et al. 1985. The data used by Hassan all came from hauynes with approximately Na6Ca2(Al6Si6O24)(SO4,S,Cl,OH)2 as no sulfide-dominant mineral required by Hassan's formula had been observed.

The situation was similar to sodalite and hackmanite defined as a sulfur dominant sodalite which was never found. In sodalite, Cl is the dominant cage filler and such an ideal hackmanite would have S as the cage filler. Though S readily substitutes for Cl in sodalite, no sulfide-dominant species was ever observed. On that basis hackmanite never was approved, avoiding the approval of a hypothetical mineral. Before the 2021 redefinition, the situation was reversed with lazurite and hauyne. What was commonly called lazurite, all had dominant SO4 and were sulfide-rich hauynes, just as all hackmanites were sulfide-rich sodalites. Now Hackmanite is defined as a reversible photochromic variety of sodalite.

The redefinition of Lazurite as Hauyne with just more than a quarter of its cages containing sulfide is due to acceptance of the proposal 20-H (Newsletter #60). The neotype specimen originates from the Malo-Bystrinskoe azurite deposit, Baikal Lake area, eastern Siberia, Russia, and was published by Sapozhnikov et al (2021).

Classification of LazuriteHide

9.FB.10

9 : SILICATES (Germanates)
F : Tektosilicates without zeolitic H2O
B : Tektosilicates with additional anions
76.2.3.4

76 : TECTOSILICATES Al-Si Framework
2 : Al-Si Framework Feldspathoids and related species
17.9.1

17 : Silicates Containing other Anions
9 : Silicates with sulphide or sulphite

Mineral SymbolsHide

As of 2021 there are now IMA–CNMNC approved mineral symbols (abbreviations) for each mineral species, useful for tables and diagrams.

Please only use the official IMA–CNMNC symbol. Older variants are listed for historical use only.

SymbolSourceReference
LzrIMA–CNMNCWarr, L.N. (2021). IMA–CNMNC approved mineral symbols. Mineralogical Magazine, 85(3), 291-320. doi:10.1180/mgm.2021.43
LzrWhitney & Evans (2010)Whitney, D.L. and Evans, B.W. (2010) Abbreviations for names of rock-forming minerals. American Mineralogist, 95, 185–187 doi:10.2138/am.2010.3371
LzrThe Canadian Mineralogist (2019)The Canadian Mineralogist (2019) The Canadian Mineralogist list of symbols for rock- and ore-forming minerals (December 30, 2019). download

Physical Properties of LazuriteHide

Resinous
Transparency:
Opaque
Colour:
Ultramarine, midnight blue, bluish green, green
Comment:
Ultramarine to midnight blue are the usual gem colours. The chromofore is the trisulfide radical anion (S3#-1#). Modulated translucent blue and green small cell hauynes with a white streak have been wrongly called lazurite and do not have enough S3- to deaden the fluorescence.
Streak:
Bright blue for lazurite, white for the small cell hauynes.
Hardness:
5 - 5½ on Mohs scale
Hardness Data:
Measured
Tenacity:
Brittle
Cleavage:
Imperfect/Fair
Imperfect on {110}
Fracture:
Sub-Conchoidal
Density:
2.38 - 2.45 g/cm3 (Measured)    2.4(1) g/cm3 (Calculated)
Comment:
Variable density results from varible sodalite cage contents

Optical Data of LazuriteHide

Type:
Isotropic
RI values:
n = 1.502 - 1.522
Birefringence:
slight (neotype): α' = 1.523(2), γ' = 1.525(2).
Surface Relief:
Low
Comments:
Anomalously anisotropic.

Chemistry of LazuriteHide

Mindat Formula:
Na7Ca(Al6Si6O24)(SO4)(S3) · H2O

Often there is minor K substituting for Na.
The IMA used to take the ideal formula with S as the dominant anion and not sulfate, from Hassan et al. (1985), but even that reference indicates that sulfate is dominant, making lazurite either a sulfide rich variety of Hauyne or just a theoretical endmember of a series with hauyne. To deal with this problem the IMA, based on the work of Sapozhnikov et al (2021), now only requires just more than a quarter of the cages to contain the (S3)-1 blue colorant. While the formula was formerly given as Na6Ca2(Al6Si6O24)(SO4,S,S2,S3,Cl,OH)2 has now been redefined to Na7Ca(Al6Si6O24)(SO4)(S3)1- · H2O

Common Impurities:
Fe,Mg,K,H2O

Crystallography of LazuriteHide

Crystal System:
Isometric
Class (H-M):
4 3m - Hextetrahedral
Space Group:
P4 3n
Cell Parameters:
a = 9.087(3) Å
Unit Cell V:
750.35 ų (Calculated from Unit Cell)
Z:
1
Morphology:
Dodecahedrons, cubes, granular, disseminated, massive.
Twinning:
None observed
Comment:
Has monoclinic (Lazurite-C) and orthorhombic polytypes (Lazurite-O). The latter was originally thought to be triclinic. An orthorhombic variant was a approved as Vladimirivanovite; another is UM1976-26-SiOSO:AlCaClHNa. (In)commensurately modulated green lazurite from Baffin Island (Hassan et al., 1985) and Ladjuar Medan (F. Camara, priv. comm. 2009) both have a cell edge of 9.05 A; see also Sapozhnikov et al. (1992) and Bolotina (2007) and references therein.

X-Ray Powder DiffractionHide

Image Loading

Radiation - Copper Kα
Data Set:
Data courtesy of RRUFF project at University of Arizona, used with permission.
Powder Diffraction Data:
d-spacingIntensity
6.43 Å(40)
3.71 Å(100)
2.622 Å(80)
2.872 Å(45)
2.272 Å(25)
2.141 Å(35)
1.782 Å(30)
Comments:
ICDD 17-749.
Lazurite appears to be defined partly by the powder patterns labeled Lazurite. With more sulfate in the cages they get bigger, so smaller cell edges get called lazurite. However, this is not always definitive, as some will small unit cells are sulphide poor.

Geological EnvironmentHide

Paragenetic Mode(s):
Paragenetic ModeEarliest Age (Ga)
High-𝑇 alteration and/or metamorphism
31 : Thermally altered carbonate, phosphate, and iron formations
Geological Setting:
Contact metamorphic mineral in marble and skarns. Also in some syenites and alkaline volcanics.

Type Occurrence of LazuriteHide

General Appearance of Type Material:
Velvet Lazurite of Sapozhnikov et al (2021)
Place of Conservation of Type Material:
Neotype: In the collection of the Sidorov Mineralogical Museum (INRTU), Lermontova St. 83, Irkutsk 664074, Rus-sia, registration number MMU/MF 27914.
Geological Setting of Type Material:
The Malo-Bystrinskoe lazurite gem deposit, Baikal Lake area, Eastern Siberian region, Russia.

Synonyms of LazuriteHide

Other Language Names for LazuriteHide

German:Lazurit
Norwegian:Lasuritt
Spanish:Lazurita

Relationship of Lazurite to other SpeciesHide

Other Members of this group:
Bolotinaite(Na7◻)(Al6Si6O24)F · 4H2OIso. 4 3m : I4 3m
HaüyneNa3Ca(Si3Al3)O12(SO4)Iso. 4 3m : P4 3n
NoseanNa8(Al6Si6O24)(SO4) · H2OIso. 4 3m : P4 3n
SapozhnikoviteNa8(Al6Si6O24)(HS)2Iso. 4 3m : P4 3n
SodaliteNa4(Si3Al3)O12ClIso. 4 3m : P4 3n
Tsaregorodtsevite(N(CH3)4)(AlSi5O12)Orth. 2 2 2 : I2 2 2
VladimirivanoviteNa6Ca2(Al6Si6O24)(SO4,S3,S2,Cl)2 · H2OOrth. mmm (2/m 2/m 2/m)

Common AssociatesHide

Associated Minerals Based on Photo Data:
129 photos of Lazurite associated with CalciteCaCO3
115 photos of Lazurite associated with PyriteFeS2
78 photos of Lazurite associated with PhlogopiteKMg3(AlSi3O10)(OH)2
45 photos of Lazurite associated with Afghanite(Na,K)22Ca10(Si24Al24O96)(SO4)6Cl6
25 photos of Lazurite associated with Marble
15 photos of Lazurite associated with ForsteriteMg2SiO4
15 photos of Lazurite associated with NephelineNa3K(Al4Si4O16)
11 photos of Lazurite associated with DiopsideCaMgSi2O6
9 photos of Lazurite associated with Bystrite(Na,K)7Ca(Al6Si6O24)(S5)Cl
6 photos of Lazurite associated with Lapis lazuli

Related Minerals - Strunz-mindat GroupingHide

9.FB.SteudeliteNa3(K17Ca7)Ca4(Al24Si24O96)(SO3)6F6 · 4H2OHex. 6 m2 : P62c
9.FB.SapozhnikoviteNa8(Al6Si6O24)(HS)2Iso. 4 3m : P4 3n
9.FB.BetziteNa6Ca2(Al6Si6O24)Cl4Hex. 6 : P63
9.FB.SlyudyankaiteNa28Ca4(Si24Al24O96)(SO4)6(S6)1/3(CO2) · 2H2OTric. 1 : P1
9.FB.Bolotinaite(Na7◻)(Al6Si6O24)F · 4H2OIso. 4 3m : I4 3m
9.FB.Wenlanzhangite-(Y)Y2V3+2V4+2(SiO4)2O4(OH)4Tric. 1 : P1
9.FB.05Afghanite(Na,K)22Ca10(Si24Al24O96)(SO4)6Cl6Trig. 3m : P3 1c
9.FB.05Bystrite(Na,K)7Ca(Al6Si6O24)(S5)ClTrig. 3m : P3 1c
9.FB.05Cancrinite(Na,Ca,◻)8(Al6Si6O24)(CO3,SO4)2 · 2H2OHex. 6 : P63
9.FB.05CancrisiliteNa7(Al5Si7O24)(CO3) · 3H2OHex. 6mm : P63mc
9.FB.05Davyne(Na,K)6Ca2(Al6Si6O24)(Cl2,SO4)2Hex. 6/m : P63/m
9.FB.05Franzinite(Na,K)6Ca2(Al6Si6O24)(SO4)2 · 0.5H2OHex.
9.FB.05Giuseppettite(Na,K,Ca)7-8(Al6Si6O24)(SO4,Cl)1-2Trig. 3m : P3 1c
9.FB.05HydroxycancriniteNa8(Al6Si6O24)(OH)2 · 2H2OHex. 6 : P63
9.FB.05Liottite(Na,K)16Ca8(Al6Si6O24)3(SO4)5Cl4Hex. 6 : P6
9.FB.05MicrosommiteNa4K2Ca2(Al6Si6O24)(SO4)Cl2Hex. 6 2 2 : P63 2 2
9.FB.05PitiglianoiteNa6K2(Al6Si6O24)(SO4) · 2H2OHex. 6 : P63
9.FB.05Quadridavyne(Na,K)6Ca2(Al6Si6O24)Cl4Hex. 6/m : P63/m
9.FB.05Sacrofanite(Na61K19Ca32)(Si84Al84O336)(SO4)26Cl2F6 · 2H2OHex.
9.FB.05Tounkite(Na,Ca,K)8(Si6Al6)O24(SO4)2Cl · 0.5H2OHex. 6 2 2 : P62 2 2
9.FB.05Vishnevite(Na,K)8(Al6Si6O24)(SO4,CO3) · 2H2OHex. 6 : P63
9.FB.05Marinellite(Na,K)42Ca6(Al6Si6O24)6(SO4)8Cl2 · 3H2OTrig. 3m : P3 1c
9.FB.05Farneseite(Na,Ca,K)56(Al6Si6O24)7(SO4)12 · 6H2OHex. 6/m : P63/m
9.FB.05Alloriite(Na,Ca,K)26Ca4(Al6Si6O24)4(SO4)6Cl6Trig. 3m : P3 1c
9.FB.05Biachellaite(Na,Ca,K)8(Al6Si6O24)(SO4)2(OH)0.5 · H2OTrig. 3 : P3
9.FB.05Fantappièite[Na82.5Ca33K16.5](Si99Al99O396)(SO4)33 · 4H2OTrig. 3 : R3
9.FB.05KyanoxaliteNa7(Al6-xSi6+xO24)(C2O4)0.5+x · 5H2O (0 < x < 0.5)Hex. 6 : P63
9.FB.05Balliranoite(Na,K)6Ca2(Si6Al6O24)Cl2(CO3)Hex. 6 : P63
9.FB.05CarbobystriteNa8(Al6Si6O24)(CO3) · 3.5H2OTrig. 3m : P3 1c
9.FB.05DepmeieriteNa8(Al6Si6O24)(PO4,CO3)1-x · 3H2O (xHex. 6 : P63
9.FB.05KircheriteNa5Ca2K(Al6Si6O24)(SO4)2 · 0.33H2OTrig. 3 2 : R3 2
9.FB.05SulfhydrylbystriteNa5K2Ca[Al6Si6O24](S5)2(SH)Trig. 3m : P3 1c
9.FB.10BicchuliteCa2(Al2SiO6)(OH)2Iso. 4 3m : I4 3m
9.FB.10DanaliteBe3Fe2+4(SiO4)3SIso. 4 3m : P4 3n
9.FB.10GenthelviteBe3Zn4(SiO4)3SIso. 4 3m : P4 3n
9.FB.10 vaHackmaniteNa8Al6Si6O24(Cl2,S)
9.FB.10HaüyneNa3Ca(Si3Al3)O12(SO4)Iso. 4 3m : P4 3n
9.FB.10HelvineBe3Mn2+4(SiO4)3SIso. 4 3m : P4 3n
9.FB.10KamaishiliteCa2(Al2SiO6)(OH)2Tet.
9.FB.10NoseanNa8(Al6Si6O24)(SO4) · H2OIso. 4 3m : P4 3n
9.FB.10SodaliteNa4(Si3Al3)O12ClIso. 4 3m : P4 3n
9.FB.10Tsaregorodtsevite(N(CH3)4)(AlSi5O12)Orth. 2 2 2 : I2 2 2
9.FB.10TugtupiteNa4BeAlSi4O12ClTet. 4 : I4
9.FB.10VladimirivanoviteNa6Ca2(Al6Si6O24)(SO4,S3,S2,Cl)2 · H2OOrth. mmm (2/m 2/m 2/m)
9.FB.15MarialiteNa4Al3Si9O24ClTet. 4/m : I4/m
9.FB.15MeioniteCa4Al6Si6O24CO3Tet. 4/m : I4/m
9.FB.15Silvialite(Ca,Na)4(Al6Si6O24)(SO4,CO3)Tet. 4/m : I4/m

Fluorescence of LazuriteHide

The opaque ultramarine and midnight blue Lazurites are not fluorescent. The translucent green and blue hauynes have an orange brown fluorescence under Long Wave UV.

Other InformationHide

Health Risks:
No information on health risks for this material has been entered into the database. You should always treat mineral specimens with care.
Industrial Uses:
The blue mineral in Lapis Lazuli, an ornamental stone

Lazurite in petrologyHide

An essential component of rock names highlighted in red, an accessory component in rock names highlighted in green.

Internet Links for LazuriteHide

References for LazuriteHide

Reference List:

Localities for LazuriteHide

This map shows a selection of localities that have latitude and longitude coordinates recorded. Click on the symbol to view information about a locality. The symbol next to localities in the list can be used to jump to that position on the map.

Locality ListHide

- This locality has map coordinates listed. - This locality has estimated coordinates. ⓘ - Click for references and further information on this occurrence. ? - Indicates mineral may be doubtful at this locality. - Good crystals or important locality for species. - World class for species or very significant. (TL) - Type Locality for a valid mineral species. (FRL) - First Recorded Locality for everything else (eg varieties). Struck out - Mineral was erroneously reported from this locality. Faded * - Never found at this locality but inferred to have existed at some point in the past (e.g. from pseudomorphs).

All localities listed without proper references should be considered as questionable.
Afghanistan
 
  • Badakhshan
    • Kuran Wa Munjan District
Mountain Minerals specimen
Dudley Blauwet priv. comm. (2008)
Chukanov +6 other references
Hogarth (1979) +2 other references
RWMW Collection
John Attard PXRD
Canada
 
  • Nova Scotia
    • Cumberland Co.
Goodman (1957)
  • Nunavut
    • Qikiqtaaluk Region
      • Baffin Island
181. +3 other references
  • Ontario
    • Hastings County
      • Wollaston Township
Identified by Mineral Associates Inc. ...
    • Ottawa
      • Gloucester Township
Analysis by Canadian Museum of Nature
Chile
 
  • Coquimbo
    • Limarí Province
      • Monte Patria
        • El Polvo
Maskaev et al. (2007)
      • Ovalle
Anthony et al. (2016)
British Natural History Museum online ...
India
 
Italy
 
  • Basilicata
    • Potenza Province
      • Rionero in Vulture
Stoppa et al. (1995) +1 other reference
  • Campania
    • Naples
      • Somma-Vesuvius Complex
vom Rath et al. (1869)
          • Ercolano
Russo et al. (2004)
            • San Vito
Russo et al. (2004)
        • Mount Vesuvius
          • Terzigno
Luigi Chiappino data
  • Lazio
    • Metropolitan City of Rome Capital
Federico et al. (2002)
      • Ariccia
Christof Schäfer
Myanmar
 
  • Mandalay Region
    • Pyin-Oo-Lwin District
      • Mogok Township
        • Kyauk-Pyat-That
          • Gwe-kyi (Gwe-gyi?)
Uwe Kolitsch et al. (to be published)
        • Mogok Valley
Anthony et al. (2016)
        • Pein-Pyit (Painpyit; Pyan Pyit)
Pavel.M. Kartashov (n.d.)
North Macedonia
 
  • Probistip Municipality
    • Kratovo-Zletovo ore district
Serafimovski et al. (2017)
Russia
 
  • Irkutsk Oblast
    • Lake Baikal area
Anthony et al. (2016)
        • Malaya Bystraya River Valley
Chukanov +7 other references
Chukanov +6 other references
Pavel.M. Kartashov (n.d.) +1 other reference
Slovakia
 
  • Žilina Region
    • Turčianske Teplice District
Koděra (1986)
Soviet Union (1922-1991)
 
Sweden
 
  • Jönköping County
    • Vetlanda
      • Alseda
The Swedish Museum of Natural History
Tajikistan
 
  • Gorno-Badakhshan
    • Shughnon
      • Shakhdara range
        • Badom-Dara
Pavel.M. Kartashov (n.d.) +1 other reference
USA
 
  • Alabama
    • Tallapoosa County
Cook et al. (1982)
  • Arkansas
    • Pulaski County
      • Little Rock
Rocks and Minerals (1989)
Henry Barwood - unpublished (2010)
  • California
    • Los Angeles County
      • San Antonio Canyon
        • San Antonio Creek
Van Nostrand Reinholt Press: 367-368. +4 other references
    • San Bernardino County
Anthony et al. (2016)
Anthony et al. (2016)
      • Stoddard Peak
Anthony et al. (2016)
Van Nostrand Reinholt Press: 367-368. +6 other references
  • Colorado
    • Gunnison County
      • Dorchester Mining District
        • Taylor Park
Eckel et al. (1997)
Eckel et al. (1997)
Eckel et al. (1997)
Tank (1972)
  • Nevada
    • Clark County
Castor et al. (2004)
  • New York
    • St. Lawrence County
      • Balmat-Edwards Zinc Mining District
        • Balmat
Rocks & Minerals 82:472-483
Robinson et al. (2007)
Robinson et al. (2007)
        • Edwards
Hogarth (1979)
  • North Carolina
Genth
  • Wyoming
    • Sweetwater County
Am Min 49:778-781
Zimbabwe
 
  • Manicaland
    • Buhera District
      • Shawa complex
Meck et al. (2011)
 
Mineral and/or Locality  
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