ResearchArticle [616220]

ResearchArticle
Atomistic Simulation of Intrinsic Defects and Trivalent
and Tetravalent Ion Doping in Hydroxyapatite
Ricardo D. S. Santos1and Marcos V. dos S. Rezende2
1DepartamentodeF ´ısica,UniversidadeFederaldeSergipe,49100-000S ˜aoCrist´ov˜ao,SE,Brazil
2DepartamentodeF ´ısica,UniversidadeFederaldeSergipe,49500-000Itabaiana,SE,Brazil
CorrespondenceshouldbeaddressedtoMarcosV.dosS.Rezende;[anonimizat]
Received26June2014;Revised4September2014;Accepted16September2014;Published12October2014
AcademicEditor:DarioAlfe
Copyright © 2014 R.D.S.SantosandM.V.d.S.Rezende. This is an open access article distributed under the Creative Commons
AttributionLicense,whichpermitsunrestricteduse,distributio n,andreproductioninanymedium,providedtheoriginalworkis
properlycited.
Atomisticsimulationtechniqueshavebeenemployedinordertoinvestigatekeyissuesrelatedtointrinsicdefectsandavarietyof
dopants from trivalent and tetravalent ions. The most favorable intrinsic defect is determined to be a scheme involving calcium
andhydroxylvacancies.ItisfoundthattrivalentionshaveanenergeticpreferencefortheCasite,whiletetravalentionscanenterPsites.Chargecompensationispredictedtooccurbasicallyviathreeschemes.Ingeneral,thechargecompensationviatheformation
ofcalciumvacanciesismorefavorable.Trivalentdopantionsaremorestablethantetravalentdopants.
1. Introduction
Hydroxyapatite (Ca10(PO4)6(OH)2)h a sb e e ni n t e n s i v e l y
investigatedduetothepossibilityofapplyingitinarangeofbiomedical applications. This is attributed to characteristicssuchasitsmechanicalproperties,biocompatibility,osteocon-
ductivity, nontoxic properties, noninflammatory properties,
andthesimilarityofthemineralconstituentstohumanboneand teeth [ 1–6] .Du et oth e sep r o pe rti e s ,i tc a nbea p p l i edi n
the manufacture of artificial bone material, as a coating onsurgical implants, and in tissue engineering, drug and genedelivery, and other biomedical areas [ 7–11]. Hydroxyapatite
has a hexagonal crystal structure, with space group P63/m,where the experimental dimensions of the unit cell are 𝑎=
𝑏 = 9.419 ˚A,𝑐 = 6.881 ˚A,𝛼=𝛽=9 0
∘,a n d𝛾=
120∘[12].Therearetwocrystallographicallydifferentsitesfor
Ca2+, which have different coordination numbers. Ca(I) is
coordinatedwithnineoxygenionsandCa(II)iscoordinatedwith six oxygen ions and one from the hydroxyl group. TheaverageCa–Odistancesarelesserthan3 ˚A.
Manyworkshaveinvestigatedthesubstitutionofextrin-
sic dopant in hydroxyapatite (HAP) in order to improve thematerial properties [ 13–17]. The incorporation of dopant intheHAPstructurecontributestoincreasingarangeofpoten-
tial applications in fields such as water purification, bonepathologies, bioceramics, catalysis, and luminescence [ 18].
For example, it is reported that Sb
3+-doped HAP has useful
applicationsinfluorescentlamps[ 19].Cr3+wasincorporated
as a dopant in the material with the aim of developing abiosensor[ 20].HAPcanalsobedopedbytrivalentlanthanide
ions such as Nd
3+[21,22], Yb3+[23,24], Er3+[25], Gd3+,
andEu3+[26,27].TheincorporationofEuandGdinaHAP
structurecanaffecttheboneremodelingcycle,andtheyhavepotentialforthetreatmentofbonedensitydisorderssuchasosteoporosis[ 26,27].Euionsexhibitfavorablespectroscopic
propertiesandcanalsobeusedforbiologicalimaging[ 28,29]
andinlasers.Ontheotherhand,gadoliniumcanbeusedasacontrastagenttoprovideabrightermagneticresonance(MR)imagingsignal[ 30].
A systematic investigation of cation substitution in HAP
may provide a better understanding of their properties,which is still lacking. Some theoretical studies based on firstprinciple calculations for HAP materials have been realizedin order to elucidate some basic physics [ 31–33]. However,
many questions regarding the study of defects remain open.
Dopantionswith3+and4+valencestatessuchasrareearth
Hindawi Publishing Corporation
Advances in Condensed Matter Physics
Volume 2014, Article ID 609024, 8 pages
http://dx.doi.org/10.1155/2014/609024

2 AdvancesinCondensedMatterPhysics
ionsandsometransitionmetalswillbeincorporatedintothe
Ca or P sites. The compensation mechanism for this dopingremainsinconclusive.Forthisreason,thispapermakesuseofcomputermodelingmethodsinordertopredictthepreferreddopant sites and charge compensation mechanisms in thematerial.
For Eu-doped HAP, for example, an investigation of the
structural response is essential due to the intimate relation-ship between its properties and lattice distortions caused bytheEusubstitutionandthechargecompensationinvolvedinthe Eu emission, which are associated with the crystal field
[34]. It is well known that the emission spectrum of Eu
3+
strongly depends on the symmetry of the site which Eu3+
occupies. If it occupies a site with inversion symmetry, only
themagnetic-dipoletransition5D0–7F1canbeobserved;but
if there is no inversion symmetry at the site of the Eu3+ion,
theelectric-dipoletransitions5D0–7F2canbeobserved.Also,
the transition is sensitive to the coordination environment[35].
In the present work, atomistic simulation based on
the lattice energy minimization is used to provide usefulinformation on the energetically favoured intrinsic defectsand a variety of dopants from trivalent and tetravalent ions.Specifically, trivalent rare earth ions and some trivalent andtetravalent transition metals were considered due to theirinfluenceonvariousproperties[ 31–33].Adetailedinvestiga-
tiononthedefectsbehaviorofHAPisveryimportantinorderto understand their importance on the improvement of thematerialproperties.Inthesemethods,detailedestimationoflatticerelaxationandtheCoulombenergiesofalargenumber
oflatticeionsarounddefectspeciesareprovidedwithouthigh
computationaldemanding,onthecontraryoftheDFTbasedmethods.
2. Methodology
The simulation techniques used in this work are basedon energy minimization, with interactions represented byinteratomic potentials. Interactions between ions in thesolid are represented in terms of a long-range Coulombterm plus a short-range term, as described by Buckinghampotential, that accounts for electron cloud overlap Paulirepulsionanddispersion(VanderWaals)interactions.Polar-izability of the oxygen ions is incorporated by means ofthe Dick-Overhauser shell model [ 36]. Most of the inter-
atomic potential models that were obtained empirically for
the simulation of hydroxyapatite materials [ 37–41]s h o w e d
excellent agreement with the experimental structures andproperties.However,inordertoimprovethefitwithrespectto structural and mechanical properties, the interatomicpotential initially derived by Mostafa and Brown [ 42]w a s
refitted empirically using the GULP code [ 43]. In our refit,
the𝐴and𝜌parameters for P–O interaction from Mostafa
and Brown [ 42]w e r em o d i fi e d .I no u rw o r k ,t h et r e eb o d y
potential for P–O interaction used by Mostafa and Brown[42]wasnotconsidered.DefectsaremodeledusingtheMott-
Littleton approximation [ 44], in which a spherical region of
lattice surrounding the defect is treated explicitly, with allTable1:Interatomicpotentialsparametersforhydroxyapatite.
Buckingham𝐴𝑖𝑗(eV)𝜌𝑖𝑗(˚A)𝐶𝑖𝑗(eV˚A6)
H2c o r e–O1s h e l l 311.97 0.2500 0.00
Cacore–O2c o r e 850.00 0.3316 0.00
Cacore–O1s h e l l 1288.00 0.3334 0.00
Pcore–O2c o r e 518.47 0.3510 0.00
Pcore–O1s h e l l 914.00 0.3380 0.00
O2c o r e–O2c o r e 22764.0 0.1490 0.00
O1s h e l l–O2c o r e 22764.0 0.1490 13.94
O1s h e l l–O1s h e l l 22764.0 0.1490 32.58
Morse𝐷(eV)𝛽(˚A−1)𝑟0(˚A)
O2c o r e–H2c o r e 7.0525 3.1749 0.9485
Spring𝑘(eV˚A−2)
O1c o r e–O1c o r e 98.67
Cargas(|𝑒|)
O1c o r e 0.86 Cacore 2.0
O1s h e l l−2.86 Pcore 5.0
O2c o r e−1.426 Hcore 0.426
interactions being considered, and more distant parts of the
latticearetreatedusingacontinuumapproach.
3. Results
Suitable potential parameters are highly necessary in orderto give a good description of the material by atomisticsimulation. The refitted potential parameters used in thiswork are listed in Table 1. The obtained structural parame-
ters are compared with the experimental values and othertheoretical calculations in Table 2. It can be seen that the
lattice parameters obtained in this work are more accuratethan those obtained previously using atomistic simulationwith the refit procedure [ 42] or using other force fields
with the partial charge model [ 45–47]o rt h o s eo b t a i n e d
using density function (DFT) calculation [ 48]. Our set of
potentials reproduces lattice parameter to within 0.1%, thatis, lesser than the other theoretical works. Available elasticpropertiesofHAPmaterialsareusedtovalidateandrefinethepotential parameters. Table 3shows the agreement between
thecalculatedandexperimentalvaluesoftheelasticconstantsfortheHAPstructure.Itcanbeseenthatourobtainedvaluesareclosertothoseofexperimentalworksandotherprevious
theoretical works. The variability in the experimental elastic
constantsreportedintheliteratureisshownin Table 3.
TodetermineFrenkelandSchottkytypedefectformation
energies,isolatedpointdefect(vacancyandinterstitial)ener-giesandrelevantlatticeenergieswerefirstcalculated.Severalpossiblepositionsweretestedtoconfirmtheoptimalpositiono fthein tersti tialsi tef o rdef ectoccu pa ncy ,a ndtheposi tio nswhich have the lowest energy were taken for interstitialcations and oxygen, respectively. We also calculated antisitepair defects, which involve the exchange of a cation withanother cation of different species. In addition, two otherintrinsic defect schemes are considered. Scheme (i) involvesonecalciumvacancyandtwohydroxylvacancies,andscheme

AdvancesinCondensedMatterPhysics 3
Table 2: Lattice parameters (𝑎,𝑏,𝑐,𝛼,𝛽 ,and𝛾)calculatedinthepresentworkcomparedtoexperimentalandothertheoricalworks.
Latticeparameters
𝑎𝑏𝑐𝛼𝛽𝛾
Presentwork 9.419 9.419 6.874 90.0 90.0 120.0Tanaka et al. (Exp.) [ 12] 9.419 9.419 6.881 90.0 90.0 120.0
MostafaandBrown(Theo.)[ 42] 9.412 9.412 6.853 90.0 90.0 120.0
deLeeuw(Theo.)[ 48] 9.563 9.563 6.832 90.0 90.0 120.0
Leeetal.(Theo.)[ 45] 9.528 9.528 6.607 90.0 90.0 120.0
RaboneanddeLeeuw(Theo.)[ 46] 9.350 9.350 6.860 90.0 90.0 120.0
Hauptmannetal.(Theo.)[ 47] 9.455 9.455 6.901 90.0 90.0 120.0
T able3:Calculatedandexperimentalelasticconstantsofh ydroxyapatite.
Elasticconstants(GPa)
𝐶11𝐶12𝐶13𝐶33𝐶44 Bulkmodulus
Presentwork 158.58 57.10 58.90 142.11 43.70 89.72Hughesetal.(Exp.)[ 49] 166.7 13.96 66.3 139.6 — 84.6
KatzandUkraincik(Exp.)[ 50] 137.0 42.50 54.90 172.0 39.60 82.60
Pedoneetal. (Theo.)[ 41] 157.5 — 59.7 147.3 43.9 90.66
deLeeuwetal. (Theo.)[ 31] 134.4 48.9 68.5 184.7 51.4 90.0
Snydersetal.(Theo.)[ 32] 117.1 26.2 55.6 231.8 56.4 76.0
(ii)involvesfivecalciumvacanciesandtwophosphorusinter-
stitials. These defects are expressed by Kr ̈oger-Vink notation
a n da r es h o w ni n Table 4. The calculated defect formation
energies, also listed in Table 4,w e r eo b t a i n e db yc o m b i n i n g
the energies of these point defects. The results indicate thatthe formation of defects involving phosphorus is generallyunfavorableduetothehighenergyrequiredtocreatethistypeofdefect.ThedefectsinvolvingPionsarehighlyunfavorableduetostrongP–OCoulombicinteraction;thatis,theywouldhardly occur compared to the other types of defects. Theresult also reveals a low energy ( −0.71eV) for scheme (i).
Th i si sc o n s i s t e n tw i t ht h et h e o r e t i c a lo b s e r v a t i o nr e p o r t e dbydeLeeuwetal.[ 31]usingDFTcalculation.Theworkofde
Leeuwetal.[ 31]revealsthatcalciumvacanciescompensated
byhydroxylarepreferredtothosecompensatedbyphosphatevacancies. They also show that the calcium vacancies com-pensatedbysubstitutionaldefects,suchascarbonategroups,are more favorable for compensation by hydroxyl and that ifthe carbonate defect is accompanied by the substitution ofam o n o v a l e n tN a
+or K+ion for the calcium ion, the defect
formationenergiesarelower.Inthemorefavorableschemes,calcium vacancies are involved, that is, one defect relatedto the calcium deficiency in the hydroxyapatite materials.Experimentalworksrevealthatapatitesareoftenfoundtobedeficientincalciumcomparedtothestoichiometricmaterial
[51–53]. Other mechanisms of defects, not considered by de
Leeuwetal.[ 31],couldbeinvolvedinthecalciumdeficiency
in the hydroxyapatite. From our results, it can be seen thatcalcium pseudo-Schottky and calcium Frenkel defects arethe next most favorable defects. In both schemes, calciumvacanciesareinvolved.Thus,thesedefectsalsocontributetothe higher concentration of calcium vacancy in HAP. Thissuggeststhatahigherconcentrationofcalciumandhydroxylvacanciescouldbepresent,whichmaycontributetocalcium
deficiencyinthehydroxyapatitematerials.
In the doping process, a description of the favorable
substitution site and the charge compensation mechanismis very important information. From atomistic simulationit is possible to obtain quantitative estimates of the relativeenergies of different modes of dopant substitution. For this,
trivalent (M
3+)a n dt e t r a v a l e n t( M4+) dopants ions substi-
tuted at both Ca and P sites were investigated in order tohelp explain experimental results. The charge compensating
mechanisms involved in the incorporation of M
3+and M4+
ionshavenotbeenclearlyestablished,soallpossibleschemes
areconsideredinthiswork.
M3+and M4+dopant ions can, in principle, be incorpo-
ratedintothelatticeateitherCa2+orP5+sites.Inbothcases,
there is more than one possible mode of charge compen-sation. All possible charge compensation mechanisms wereconsideredandareshownasfollows.
Reaction Schemes for Solution of Divalent, Trivalent, Tetrava-
lent, and Pentavalent Dopants. Consider the following mech-
anism.
Trivalent dopants
M
2O3+2CaCa󳨀→2M∙
Ca+O󸀠󸀠
𝑖+2CaO (1)
M2O3+3CaCa󳨀→2M∙
Ca+V󸀠󸀠
Ca+3CaO (2)
2,5M2O3+5CaCa+PP
󳨀→5M∙
Ca+V󸀠󸀠󸀠󸀠󸀠
P+5CaO+0,5P2O5(3)
M2O3+2CaCa+H2O󳨀→2M∙
Ca+2OH󸀠+2CaO(4)

4 AdvancesinCondensedMatterPhysics
Table4:Solutionenergyofintrinsicdisorderinhydroxyapatite(eV/defect).
Type Site Defectequation Solutionenergy
FrenkelCa CaCa→V󸀠󸀠
Ca+Ca∙∙
𝑖 3.75
PPP→V󸀠󸀠󸀠󸀠󸀠
P+P∙∙∙∙∙
𝑖 16.38
OOO→V∙∙
O+O󸀠󸀠
𝑖 4.46
OH OHOH→V∙
OH+OH󸀠
𝑖 6.99
SchottkyTotal5CaCa+3PP+12OO+OH→5V󸀠󸀠
Ca+3V󸀠󸀠󸀠󸀠󸀠
P+12V∙∙
O+V∙
OH+Ca5P3O12OH 4.77
Ca CaCa+OO→V󸀠󸀠
Ca+V∙∙
O+CaO 3.14
P2PP+5OO→2V󸀠󸀠󸀠󸀠󸀠
P+5V∙∙
O+P2O5 8.01
Anti-Schottky Total Ca5P3O12OH→5Ca𝑖+3P𝑖+12O𝑖+OH𝑖 7.65
Schemes(i) Ca CaCa+2(OH)OH→V󸀠󸀠
Ca+2V∙
OH+CaO+H2O −0.71
Schemes(ii) Ca 5CaCa+2PP+5OO→5V󸀠󸀠
Ca+2P∙∙∙∙∙
𝑖+5CaO 38.62
0,5M2O3+PP+CaO󳨀→M󸀠󸀠
P+Ca∙∙
𝑖+0,5P2O5(5)
0,5M2O3+PP+OO󳨀→M󸀠󸀠
P+V∙∙
O+0,5P2O5(6)
1,5M2O3+2CaCa+3PP
󳨀→3M󸀠󸀠
P+2P∙∙∙
Ca+0,5P2O5+2CaO(7)
Tetravalent dopants
0,5M2O4+CaCa󳨀→M∙∙
Ca+O󸀠󸀠
𝑖+CaO (8)
0,5M2O4+3CaCa󳨀→M∙∙
Ca+V󸀠󸀠
Ca+2CaO (9)
2,5M2O4+5CaCa+2PP
󳨀→5M∙∙
Ca+2V󸀠󸀠󸀠󸀠󸀠
P+5CaO+P2O5(10)
0,5M2O4+CaCa+H2O󳨀→M∙∙
Ca+2OH󸀠+CaO(11)
M2O4+2PP+OO󳨀→2M󸀠
P+V∙∙
O+P2O5(12)
M2O4+2PP+CaO󳨀→2M󸀠
P+Ca∙∙
𝑖+P2O5(13)
1,5M2O4+3PP+CaCa󳨀→3M󸀠
P+P∙∙∙
Ca+P2O5+CaO(14)
In the crystal structure of HAP [ 12], there are two types
of Ca2+host site. Therefore, the incorporation in each site
is considered. Seven reaction schemes have been consideredfor the incorporation of the trivalent ions and seven for thetetravalentions.
In (1)t o(4) the trivalent cation metals are considered at
theCa
2+site,andin( 5)t o(7)thetrivalentcationmetalsare
consideredattheP5+site.Ontheotherhand,in( 8)to(11)the
tetravalentcationmetalsareconsideredattheCa2+site,and
in (12)t o(14) the tetravalent cation metals are considered at
theP5+site.Intheallcase,chargecompensationisneeded.
The solution energies for the trivalent defect were cal-
culated by combining the appropriate defect and latticeenergy terms and are listed in Tables 5–7.I ti ss e e nt h a tt h e
solutionenergyisdifferentfortheincorporationoftheearthrare/metal transition with different ionic radius. The latterobservationisexplainedbythelatticeexpansion/contraction,resultinginmore/lessspacetoaccommodateearthrare/metaltransition ions together with any charge compensating
defects. From the tables it can be seen that substitution attheCasiteismorefavorableforalltrivalentdopants.TheCa
sitepreferencehasbeenconfirmedexperimentallybyMartin
et al. [54]a n dW a k a m u r ae ta l .[ 55]. This behavior can be
explainedintermsofthedifferenceinionicradiibetweenthetrivalentdopantionsandthehostsiteions.Theionicradiioftransition metal and rare earth ions vary around 0.55–0.75
and0.86–1.03 ˚A,respectively ,andtheionicradiiofCa
2+and
P5+are1.00and0.38 ˚A,respectively[ 56].Thesmalldifference
betweenthetrivalentdopantionsandCa2+ions contributes
toasmalldeformationinthelatticeandconsequentlyasmallsolutionenergy.Thus,theresultsshowadegreeofcorrelationbetween the dopant size and the solution energy. Dopantswith a large difference in ion size from the host tend to be
moreenergeticallyunfavorable.BetweenthetwodifferentCa
sites,itseemsthat,exceptforLu,Er,Gd,Eu,Sm,andNdshowapreferencefortheCa1sitesubstitution.
I nt h eE u – d o p e dH A P ,t h e
5D0–7F0transition of Eu
emission is particularly informative. This is because the5D0
state is unsplit, and the7F0g r o u n ds t a t ei sa l s ou n s p l i t ,s o
that transitions to it give straightforward information abouttheexcitedstate.Ifmorethanonecomponentisseenforthistransition,itshowsthatthereismorethanoneeuropiumsite[34]. The two peaks attributed to
5D0–7F0transition were
observed in the Eu emission spectra by Jagannathan andKottaisamy[ 57]andMartinetal.[ 54],indicatingthattheEu
ion can be substituted at two sites. From our results, it canbenotedthatthesolutionenergyformorefavorableschemesforEusubstitutionattheCa1site(1.79eV)isclosetothatforthesubstitutionattheCa2site(1.50eV).Thissmalldifferencejustifies the possibility of Eu substitution at both host sites.The results of Martin et al. [ 54] support our hypothesis that
Eu dopant ions prefer to be substituted at the Ca2 site due
to the lower solution energy. They also report that the site
occupancyratiobetweentheCa2andCa1sitesisabout80%,
withthemajorityoftheEu
3+ionsbeingintheCa2sites.
The charge compensation tends to occur basically via
three schemes. In general, charge compensation via theformation of calcium vacancies is more favorable for chargecompensationinthetrivalentdopants,exceptforEr,Gd,andEu,wherethechargecompensationismorefavorablethrough

AdvancesinCondensedMatterPhysics 5
Table5:Solutionenergies(eV)forsubstitutionofthetransitionmetals(M3+=Fe,Mn,Cr,andSc)andrareearth(M3+=LuandYb)ionsin
HAP.
Mechanisms Dopant
Fe3+Mn3+Cr3+Sc3+Lu3+Yb3+
Equation( 1)2M∙
Ca1+O󸀠󸀠
𝑖 4.04 4.06 4.07 3.28 3.01 2.95
2M∙
Ca2+O󸀠󸀠
𝑖 7.63 7.11 5.20 3.68 1.49 3.65
Equation( 2)2M∙
Ca1+V󸀠󸀠
Ca 3.16 3.18 3.19 2.39 2.12 2.06
2M∙
Ca2+V󸀠󸀠
Ca 6.75 6.23 4.32 2.79 1.47 3.65
Equation( 3)5M∙
Ca1+V󸀠󸀠󸀠󸀠󸀠
P 6.01 6.04 6.05 5.47 4.71 4.64
5M∙
Ca2+V󸀠󸀠󸀠󸀠󸀠
P 10.50 9.84 7.46 5.96 2.79 5.52
Equation( 4)M∙
Ca1+OH󸀠8.20 8.22 8.23 7.63 2.62 2.57
M∙
Ca2+OH󸀠10.90 10.50 9.07 7.93 1.46 3.10
Equation( 5)M󸀠󸀠
P+Ca∙∙
𝑖 7.46 7.01 6.40 6.60 7.71 8.77
Equation( 6)M󸀠󸀠
P+V∙∙
O 6.85 6.39 5.79 5.98 7.09 8.15
Equation( 7)3M󸀠󸀠
P+2P∙∙∙
Ca1 16.29 15.74 15.02 15.55 16.58 17.86
3M󸀠󸀠
P+2P∙∙∙
Ca2 21.34 20.79 20.07 20.60 10.10 11.37
Table6:Solutionenergies(eV)forsubstitutionoftherareearth(M3+=Tm,Er,Ho,Dy,Tb,andGd)ionsinHAP.
Mechanisms Dopant
Tm3+Er3+Ho3+Dy3+Tb3+Gd3+
Equation( 1)2M∙
Ca1+O󸀠󸀠
𝑖 3.06 2.91 2.85 2.81 2.60 2.72
2M∙
Ca2+O󸀠󸀠
𝑖 3.31 3.31 3.05 2.99 2.74 1.56
Equation( 2)2M∙
Ca1+V󸀠󸀠
Ca 2.17 2.17 1.97 1.93 1.71 1.80
2M∙
Ca2+V󸀠󸀠
Ca 3.31 3.31 3.05 2.99 2.74 1.56
Equation( 3)5M∙
Ca1+V󸀠󸀠󸀠󸀠󸀠
P 4.78 4.59 4.52 4.47 4.20 4.35
5M∙
Ca2+V󸀠󸀠󸀠󸀠󸀠
P 5.09 2.99 4.77 4.70 4.38 2.90
Equation( 4)M∙
Ca1+OH󸀠2.65 2.54 2.50 2.47 2.31 2.40
M∙
Ca2+OH󸀠2.84 1.58 2.65 2.61 2.42 1.52
Equation( 5)M󸀠󸀠
P+Ca∙∙
𝑖 8.90 8.69 8.98 8.78 8.55 8.90
Equation( 6)M󸀠󸀠
P+V∙∙
O 8.30 8.07 8.36 8.17 7.93 8.29
Equation( 7)3M󸀠󸀠
P+2P∙∙∙
Ca1 18.03 17.76 18.11 17.87 17.60 18.02
3M󸀠󸀠
P+2P∙∙∙
Ca2 11.55 11.30 11.62 11.39 11.11 11.54
Table7:Solutionenergies(eV)forsubstitutionoftherareearth(M3+=Eu,Sm,Nd,Pr,Ce,andLa)ionsinHAP.
Mechanisms Dopant
Eu3+Sm3+Nd3+Pr3+Ce3+La3+
Equation( 1)2M∙
Ca1+O󸀠󸀠
𝑖 2.67 2.64 2.59 2.55 2.80 2.08
2M∙
Ca2+O󸀠󸀠
𝑖 1.52 1.42 1.29 2.32 2.62 2.52
Equation( 2)2M∙
Ca1+V󸀠󸀠
Ca 1.79 1.75 1.70 1.67 1.49 1.20
2M∙
Ca2+V󸀠󸀠
Ca 1.52 1.42 1.29 2.32 2.62 2.52
Equation( 3)5M∙
Ca1+V󸀠󸀠󸀠󸀠󸀠
P 4.29 4.25 4.19 4.15 3.93 3.56
5M∙
Ca2+V󸀠󸀠󸀠󸀠󸀠
P 2.85 2.73 2.56 3.86 4.23 4.10
Equation( 4)M∙
Ca1+OH󸀠2.36 2.34 2.30 2.28 2.14 1.92
M∙
Ca2+OH󸀠1.50 1.43 1.33 2.10 2.32 2.25
Equation( 5)M󸀠󸀠
P+Ca∙∙
𝑖 9.12 9.04 8.93 8.66 3.88 9.34
Equation( 6)M󸀠󸀠
P+V∙∙
O 8.51 8.42 8.32 8.05 3.27 8.72
Equation( 7)3M󸀠󸀠
P+2P∙∙∙
Ca1 18.29 18.18 18.05 17.73 12.00 18.54
3M󸀠󸀠
P+2P∙∙∙
Ca2 11.80 11.70 11.57 11.25 5.51 12.06

6 AdvancesinCondensedMatterPhysics
Table8:Solutionenergies(eV)fordifferentdopantsinHAP.
Mechanisms Dopant
Mn4+Cr4+
Equation( 7)M∙∙
Ca1+O󸀠󸀠
𝑖 6.71 6.96
M∙∙
Ca2+O󸀠󸀠
𝑖 7.97 9.35
Equation( 8)M∙∙
Ca1+V󸀠󸀠
Ca 5.39 5.64
M∙∙
Ca2+V󸀠󸀠
Ca 6.65 8.02
Equation( 9)5M∙∙
Ca1+2V󸀠󸀠󸀠󸀠󸀠
P 11.22 11.58
5M∙∙
Ca2+2V󸀠󸀠󸀠󸀠󸀠
P 13.02 14.99
Equation( 10)M∙∙
Ca1+2OH󸀠4.95 5.34
M∙∙
Ca2+2OH󸀠5.51 6.71
Equation( 11)2M󸀠
P+Ca∙∙
𝑖 4.28 5.75
Equation( 12)2M󸀠
P+V∙∙
O 3.87 5.12
Equation( 13)3M󸀠
P+2P∙∙∙
Ca1 9.41 11.06
3M󸀠
P+2P∙∙∙
Ca2 5.35 7.03
interstitial hydroxyl than by calcium vacancies, and for Sm
a n dN d ,w h e r ec h a r g ec o m p e n s a t i o nb yi n t e r s t i t i a lo x y g e nis more favorable. The charge compensation for Eu ions isin agreement with that proposed by Martin et al. [ 54]a n d
Ternane et al. [ 14].
The production of stoichiometric HAP is obtained with
a Ca/P ratio of 1.67. Experimental work realized by Mayeret al. [58] reports that this value is below 1.67 in most cases
and shows a decrease with increases in the La content in thesamples; that is, it indicates the formation of nonstoichio-metricHAP.ThisreductionoftheCa/Pratioisattributedtothe formation of the calcium vacancy generated as a chargecompensationdefectneededinthesubstitutionoftheLaionin the Ca site. The occurrence of this scheme (see ( 2)) is the
mostfavorable,ascanbeseenin Table 7.Similarbehaviorcan
beexpectedforallthetrivalentdopantsthatarecompensatedbycalciumvacancies.
InTable 8,thesolutionenergiesforthetetravalentdefect
calculated by combining the appropriate defect and latticeenergy terms are listed. It can be seen that substitutionat the P
5+site by a compensated oxygen vacancy is more
favorable for Mn4+and Cr4+dopants. This behavior also
can be explained in terms of similar ionic radii between thet e t r a v a l e n td o p a n ti o n sa n dt h eh o s ts i t ei o n s .M na n dC rdopantscanexistaseitherM
3+orM4+.Itisnecessarytoknow
their precise oxidation state. According to our results, thefavorabledopingprocessforthesepolyvalentdopantsshould
beanM
3+formviatheformationofcalciumvacancies.
4. Conclusion
The basic defect chemistry including intrinsic defects and
trivalent and tetravalent extrinsic dopants has been investi-gatedusingatomisticsimulation.Themostfavorableintrinsicdefect schemes are formed by one calcium vacancy andtwohydroxylvacancies.TrivalentandtetravalentdopantionsubstitutionsarefoundtotakeplacepreferentiallyontheCaandPsites,respectively.Inbothcases,calciumvacancydefectformationisthemorelikelychargecompensationmechanismf o rm o s to ft h et r i v a l e n ta n dt e t r a v a l e n td o p a n t s .I ns o m e
trivalent ions, charge compensation by interstitial hydroxyland interstitial oxygen is more favorable. The favorabledoping process for these polyvalent dopants should be an
M
3+formviatheformationofcalciumvacancies.
Conflict of Interests
The authors declare that there is no conflict of interests
regardingthepublicationofthispaper.
Acknowledgments
TheauthorswouldliketoacknowledgethefinancialsupportbyFINEP,CAPES,andCNPq.
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