calcium phosphates ( ca  p ) are of 
 great importance in biomineralization 
 and environmental sciences . hydroxyapatite [ ca10(po4)6(oh)2 ] is the most widely investigated 
 ca  p mineral and is the main constituent of teeth and bones . its many functional properties allow a wide range of applications 
 such as hard tissue analogues , catalysts , liquid - chromatographic columns , chemical sensors , and it has become a promising candidate as a 
 heavy metal sequestration agent in wastewater treatment . biological mechanisms of hydroxyapatite formation have attracted 
 recent attention in fields ranging from biology and chemistry to materials 
 science and bioengineering . elucidation of the 
 mechanism of formation is important not only for design and fabrication 
 of advanced biomaterials but also for a clearer understanding of how 
 hard tissues are created in vivo . in classical 
 nucleation theory , crystal formation occurs from a 
 critical nucleus formed by direct assembly of ions from solution , 
 and it assumes that the composition and structure of the earliest 
 precursors are the same as those of the final crystalline phase . the classical assumptions are challenged by recent studies of biomineral 
 nucleation , in which weak acid anion complexes form and undergo phase 
 transformation via a series of equilibrium reactions . nucleation of hap begins with the formation of amorphous 
 calcium 
 phosphate precursors ( acp ) , and a relatively long induction period 
 precedes the appearance of nuclei . posner s clusters , ca9(po4)6 , have been proposed as the initial acp building blocks . in contrast , recent constant composition ( cc ) nucleation results 
 obtained with high ph resolution ( 0.001 ph unit ) have enabled the 
 detection of small but reproducible increases in ph early in the induction 
 period ( figure s1 of the supporting information ) . much of the previous work on hap 
 mineralization was done with solutions at a high supersaturation and 
 in the presence of atmospheric carbon dioxide . these techniques result 
 in rapid mineralization , with far less control than the cc methods . the presence of co2 affects ph and calcium ion activity , 
 both of which are known to influence ca it is difficult to elucidate the mechanism of nucleation , especially 
 the pathway of crystallization from solvated ions to final apatitic 
 mineral . the investigation has been designed to study the events that 
 occur in early stages of ca a new in situ method has been developed 
 by combining ph measurements , calcium ion activity selective electrodes , 
 and conductivity measurements to obtain much greater sensitivity in 
 monitoring ionic interactions . during nucleation , all ionized species 
 present in the reaction media were monitored rather than simply the 
 hydrogen ions . the formation and transformation of amorphous precursor 
 was observed during the early induction stages , providing a new deeper 
 understanding of early nucleation events . a novel two - step nonclassical 
 nucleation mechanism of hydroxyapatite was proposed involving two 
 amorphous phases . hitherto , homogeneous and heterogeneous nucleation 
 experiments involved the potentiometric monitoring of the hydrogen 
 ion activities ( 0.001 ph resolution ) associated with the nucleation 
 events . the new method adds calcium ion activity selective 
 electrodes and conductivity measurements , encompassing all ionized 
 species in the reaction media . the formation 
 of interacting ion pairs in the solutions results in a reduction of 
 specific conductance as the charge - carrying species interact ; this 
 additional information on the onset of nucleation provides unique 
 kinetic data of formation of the ca calcium chloride dihydrate 
 ( cacl22h2o ) was purchased from omnipur 
 ( purity  99.0% , lot no . solutions used in this study were 
 prepared fresh and filtered twice through 50 nm pore size filters 
 ( sterlitech , lot no . experiments were made in 
 150 ml aliquots , ph 7.400 , at 37.0  0.1 c in magnetically 
 stirred double - walled 250 ml pyrex vessels . the relative supersaturation , 
  , and supersaturation ratio , s , are given 
 by eq 1:1 in which  ( = 18 ) is the number of ions 
 in a formula unit of hap , and iap and ksp are the ionic activity and thermodynamic solubility products supersaturated solutions were prepared by 
 the slow mixing of sodium 
 chloride ( nacl ) , potassium dihydrogen phosphate ( kh2po4 ) , potassium hydroxide ( koh ) , and calcium chloride ( cacl2 ) stock solutions ( [ ca ] = 0.045 m ) . the solution 
 composition for different supersaturation experiments was shown in 
 table 1 . to avoid a high local supersaturation 
 as a result of the rapid mixing , a slower addition rate ( 200 l / min ; 
 brinkmann metrohm 775 dosimat ) was used for the addition of ca to the reaction solution . co2 was purged from 
 the reaction vessel by constant bubbling of pure , presaturated , n2 gas ( > 2h ) into both reaction solutions and calcium chloride 
 stock solution prior to mixing . the ph electrode 
 ( orion 91 - 01  0.1 mv ) and calcium ion selective electrode ( orion 
 93 - 20  0.1 mv ) were coupled with a single - junction ag / agcl reference 
 electrode ( orion 90 - 01 ) . the resolution of the conductivity 
 electrode was 0.01 s / cm . the ph electrode was calibrated weekly 
 utilizing ph = 6.841 and ph = 7.385 phosphate buffers ; the ca electrode was calibrated daily . precipitates , separated 
 by filtration ( 50 nm pore size ) were dried 
 and sputter - coated with graphite under vacuum prior to examination 
 by field - emission scanning electron microscopy ( sem , hitachi su-70 ) 
 at 20kev . direct in situ monitoring of the evolution of acp 
 in aqueous solution 
 is a challenge , due to the instability of acp and the lack of a proper 
 technique for characterization in solution . an ex situ approach was 
 adopted ; samples were captured by micropipet from the reaction solution 
 ( hap of 19.5 ) , and a small drop placed on formvar - carbon - coated 
 copper grids . the sample was then dried in an oven ( 70.0 c ) before final characterization by electron microscopy . transmission 
 electron microscopy ( tem ) investigations of nucleated particles removed 
 at various time intervals were carried out using a jeol-2010 tem at 
 an accelerating voltage of 200 kv . the elemental analysis was performed 
 using x - ray photoelectron spectrometry ( xps ssx-100 ) at 10 to 10 torr . the 
 figures in the left column have been expended for detail and are presented 
 in the right column . ( a ) ph changes in hap nucleation experiment with 
 relative supersaturation hap = 20.0 . ( b ) no calcium 
 was added for 1270 min after ph monitoring began to ensure electrode 
 stability . ( c ) ph ( black ) , calcium electrode potential ( blue ) , and 
 electrical conductance ( red ) changes during hap nucleation with time 
 0 corresponding to the moment calcium addition was complete ( hap = 19.5 , i.s . the nucleation experiments were made in an n2 environment 
 and were initiated by the slow addition of calcium stock solution 
 [ 0.045 m ] . prior to the addition of calcium ( figure 1a , 12701290 min ) , ph remained constant ( figure 1a , 01270 min ) and a small but non - negligible 
 ph increase ( ph  0.010 ) was clearly observed after 
 the addition ( figure 1a , 12901480 min ) . since the ph is a function of the molar ratio of hpo4/h2po4 , it 
 is suggested that the observed ph increase is associated with a reaction 
 involving either the release of hpo4 ions to the reaction solution or the association of h2po4 with complexes in solution . p nucleation 
 has never previously been noted ( figure 1a , 
 12701480 ) , and the results confirm its association with ca the combined ph , conductivity , and calcium 
 ion activity results 
 indicate that the induction period can be divided into two stages : 
 an early nucleation period ( stage i , from 0 to 300 min ) and a later 
 nucleation stage ( stage ii , from 300 to 650 min ) ( figure 1 , panels b and c ) . during induction stage i , an 
 increase in solution conductivity was observed ( about 3.5  0.1 
 s / cm ) in conjunction with the observed ph increase . the start 
 of stage ii is identified as the ph maximum , during which change in 
 solution conductivity and ph slows and both begin to decrease ( figure 1c ) . the concentration of the free calcium ion remained 
 constant during the induction time ( figure 1c ) . an increase in the solution conductivity indicates an increase 
 in the total ion concentration . it is suggested that ion pairing of 
 hpo4 and ca occurs rapidly 
 as the ca is added to the reaction solution ; this forms 
 a calcium - deficient complex ( time 1290 min , figure 1a ; time 0 min , figure 1 , panels b and 
 c ) comprised of hydrated calcium ions and protonated phosphate ions . this release is observed 
 when ph and conductivity increase , stage i ( time 0300 min , 
 figure 1 , panels b and c ) . the slow decrease 
 in ph and conductivity during stage ii has been associated with deprotonation . tem micrographs and saed patterns of 
 precipitates at ( a  c ) the early induction period and ( d  f ) 
 the later induction period . ( g  j ) morphology evolution from 
 acp - i to acp - ii phase under continuous electron irradiation for a 
 same sample . scale bar : ( a  d ) 50 , ( e ) 100 , ( f ) 10 , and ( g  j ) 
 20 nm . the precipitates were collected 
 by filtration ( pore size of 50 
 nm ) at different time intervals ; the samples were analyzed by high - resolution 
 transmission electron microscopy ( tem ) , and selected area electron 
 diffraction ( saed ) . separated particles with a porous appearance , 
 and a diameter of 25 nm sample extraction was completed 
 within 20 min of the start calcium addition ( figure 2a ) . aggregation of these particles was observed at 120 min , 
 the aggregates were collected and identified as amorphous ( acp - i ) 
 by saed ( figure 2b ) . at 240 min ( still in nucleation 
 stage i ) , part of the aggregates underwent partial dehydration and 
 a more dense structure was observed ( figure 2c ) . sheet - like aggregates larger than 100 nm ( acp - ii ) containing 
 electron dense regions ( < 10 nm ) were observed after 400 min . saed 
 data indicated that most of the aggregates remained amorphous ( acp - ii ) , 
 but a small amount of crystalline domains developed within the amorphous 
 phase ( figure 2d ) . it is noteworthy that the size of the amorphous aggregate increased 
 to a maximum value prior to the observation of crystalline domains . 
 once these domains were observed , the size of the aggregates decreased 
 as amorphous structures transformed to high - density precritical nuclei 
 ( table s1 of the supporting information ) . the final random pearl - chain structure is detected at 600 min 
 ( figure 2e ) . characteristic diffraction of 
 the ( 131 ) plane of hap precritical nuclei was clearly observed ( figure 2f ) after 600 min ; at this point , the size of crystalline 
 domains are still too small ( < 5 nm ) to induce crystal growth . crystal 
 domains form within the amorphous aggregates ; with time the overall 
 diameter of the aggregate is reduced as the crystal domains increase 
 in size and quantity . after 700 min , crystal growth is observed in 
 conjunction with a large drop in ph , conductivity , and free calcium 
 ion activity . j ) 
 can be observed as the porous loose structure transforms to dense 
 aggregates containing crystalline domains . the amorphous particles 
 retained their porous morphology for 2.5 min . throughout this time , 
 an increase in pore size and a decrease in pore concentration was 
 observed , likely caused by the electron bombardment . these nanoparticles 
 had a porous morphology after drying due to their originally high 
 hydration . after 4.0 min , crystalline domains with sizes less than 
 5 nm emerged ; these had a similar morphology to samples taken from 
 the nucleation reaction solution at 400 min ( figure 2d and figure s2 of the supporting information ) . there was no particle breaking detected , as in dissolution  reprecipitation and solution - mediated transformation mechanisms . the very 
 small precritical nuclei are metastable , and the number particles 
 observed varies with time ( figure s2 of the supporting 
 information ) . tem micrographs indicated that two different 
 amorphous phases ( acp - i 
 and acp - ii ) existed in the early and later induction periods . the 
 loose acp - i nanoparticles formed when the initial solutions were mixed , 
 and they coagulated into large aggregates in the early induction period 
 accompanied by a small ph increase . during the later induction period , 
 the denser acp - ii formed by dehydration and aggregation . the tiny 
 crystalline domains formed within the acp - ii rather than only at the 
 interparticle boundaries or the acp  solution 
 interface . in the early induction 
 period , the edx and xps results showed distinct 
 calcium and phosphate peaks . the ca / p molar ratio of aggregates removed 
 after 90 min was 0.62 ( edx ) . this ratio would increase with time throughout 
 the induction period ( figure 3 , and figure 
 s3 of the supporting information ) : 0.86 
 at 180 min , 1.01 at 400 min , and 1.20 at 600 min ( xps ) , indicating 
 a calcium - deficient aggregate initially formed after the addition 
 of calcium , at the start of stage - i . as the ph increases , the ca / p 
 molar ratio remains less than 1.0 , acp - i . as the change in ph slows , 
 it begins to decrease and the ratio exceeds 1.0 , corresponding to 
 the formation of acp - ii ( figure 1b ) . a calcium - deficient complex ( acp - i ) with the empirical formula 
 [ ca-(hpo4)1+x ] is formed as ca ions added to solution dehydrate 
 and interact with phosphate ions ( figure 1a ) . 
 for 200 min after the addition of calcium , the release of hpo4 ( 12901480 min , figure 1a ) by acp-1 can be detected , as stoichiometric acp-2 
 ( [ ca - hpo4 ] ) gradually forms . a ph maximum is detected as 
 this process occurs ( 1480 min , figure 1a ) ; 
 after this point crystal domains ( < 10 nm ) can be observed forming 
 inside the sheetlike aggregates of acp-2 ( figure 2d ) . after the ph maximum is reached ( 14801700 min , 
 figure 1a ) , ph and conductivity began to decrease 
 as deprotonation of acp-2 occurs . a large drop in ph and free calcium 
 concentration associated with crystal growth is observed after 1700 
 min ( figure 1a ) , after which point hap crystals 
 could be observed by microscopy ( table s2 of the supporting information ) . ca / p ratio of precipitates at different 
 induction stages in hap 
 nucleation experiment ( hap = 19.5 ) . the ca / p ratio 
 based on the edx and xps results as shown in figure s3 of the supporting information . due to thermodynamic equilibrium among solvent and individual 
 hydrated 
 ions , the ion cluster will spontaneously form by ion association even 
 in undersaturated solutions , and the dehydration process ( release 
 of water molecules from the hydration shell of ions ) provides a substantial 
 entropy gain favoring cluster formation . the reaction kinetics are strongly influenced by the ion dehydration 
 rate , which is known to vary with ionic radius and electronic charge . the relative dehydration rate of hydrogen phosphate ions is much greater 
 than that of calcium ions , accounting for the formation of calcium - deficient 
 clusters . in supersaturated solutions , the nonequilibrium clusters 
 aggregate to form relatively stable calcium - deficient complexes ( acp - i ) . this process is driven by a decrease in surface energy , and the kinetics 
 of aggregation are dependent on the supersaturation of the starting 
 solution . the rate of transformation from loose acp - i to dense acp - ii 
 is dictated by the dehydration and aggregation processes . after acp - ii 
 is formed , the tiny precritical nuclei form within the acp - ii . the 
 phase transformation from precritical nuclei to nuclei is a solid - to - solid 
 transition , independent of the solution supersaturation . when 
 the nucleation experiment were done at supersaturation hap = 18.5 , the total induction time increased from 650 to 
 950 min . the length of stage i increased from 300 to 580 min ; stage - ii 
 was 350 min under both conditions ( figure 4 ) . stage i is defined as the length of time for ca addition 
 until the reaction solution reaches a ph maximum ; stage ii is from 
 this point until crystal growth is observed . the results indicated 
 that the initial supersaturation affects the energy barrier of phase 
 transformation from loose acp - i to dense acp - ii . it is suggested acp - ii 
 has an empirical formula of ca - hpo4nh2o , thus the free energy of formation is constant . the 
 composition of acp - i changes with time by the release of extra hpo4 ions in the dehydration process . the 
 gibbs free energy of acp - i is not constant and is affected by the 
 solution supersaturation . throughout stage i , the free energy of acp - i 
 increases with the increase in the ca / p ratio . during stage ii , the 
 phase free energy decreases as the precritical nuclei concentration 
 increases over time ; this indicates the formation of the acp - ii phase 
 is an inflection point of the free energy profile , as shown in figure 6a . ph ( black line ) and electrical conductance ( red line ) changes 
 during hap nucleation under a relatively low supersaturation ( hap = 18.5 ) prepared by the slow addition of calcium solution 
 ( i.s . if calcium is added rapidly , 
 the high local supersaturation will affect the dehydration process 
 and influence ion association and the nucleation behavior . replicate 
 experiments were designed to investigate the effect of the rate of 
 calcium solution addition ; the rate of addition was varied from 9 
 to 90 mol / min ( figure 5 , panels a a rapid ph increase once calcium ions are added to the reaction solution 
 is observed ; the ph increase is 30 min less ( 210 min , figure 1b to 180 min , figure 5a ) 
 when the calcium solution is added more quickly . the faster addition 
 resulted in the change in ph increase ( ph  0.050 ) and 
 decrease in the free calcium ion activity ( figure 5a , b ) . this result indicates that the more calcium - deficient 
 clusters form during the faster addition due to the relatively slow 
 dehydration rate of calcium ions . these clusters were not stable , 
 and the rapid release of extra hpo4 resulted in a sharp increase in ph following the addition of calcium 
 ions . the released hpo4 rapidly associates 
 with free calcium ions in solution , resulting in a decrease in calcium 
 activity and solution conductivity . ( a ) ph , ( b ) calcium electrode potential , and ( c ) electrical conductance 
 ( hap = 19.5 , i.s . = 0.006 m , ph = 7.40 , 37.0 c , 
 and calcium solution addition rate = 2.0 ml / min ) . on the basis of these findings , the hydrated phosphate and calcium ions are mixed 
 forming ion clusters by dehydration . strong interactions between calcium 
 ions and water molecules results in the dehydration rate of calcium 
 ions being much less than that of hydrogen phosphate ions . this causes 
 the initial formation of calcium - deficient clusters [ ca-(hpo4)1+xnh2o ] 30 nm in size ( figure 1a ) . the clusters 
 aggregate to form a nanosized amorphous phase ( acp - i ) in the early 
 induction period , releasing the excess hydrogen phosphate ( figure 2b ) . the composition and free energy of acp - i are 
 affected by the starting driving force ( g ) ( figure 4 ) and the addition rate 
 of calcium ions to the reaction solution ( figure 5 ) . a small increase in ph and conductivity is observed , as 
 hydrolysis of the clusters [ ca-(hpo4)1+xnh2o ] results in the formation 
 of stoichiometric acp - ii complexes [ ca - hpo4mh2o ] ( figure 1b , 0300 
 min ) . precritical nuclei ( ca3(po4)2h2o ) ( > 10 nm ) formed within the acp - ii ( 300 nm ) 
 prior to crystal growth via the deprotonation process accompanied 
 by a ph decrease ( figure 2d ) . as the amount 
 of precritical nuclei phase increases further , large stable nuclei 
 ( 50 nm , figure 2f ) form and induce the crystal 
 growth ( figure 6b).figure 6schematic illustration 
 of the ca ( a ) the relationship of free energy g versus the extent of reaction 
 . an amorphous ca  p complex ( acp - i ) 
 directly forms without thermodynamic barrier as the solutions are 
 mixed . the composition and free energy of acp - i are affected by the 
 initial driving force ( g ) and the rate of addition . the acp - i 
 transforms to dense acp - ii phase by dehydration and aggregation in 
 stage - i , followed by precritical nuclei formation within the acp - ii 
 phase in stage - ii . the nucleus formation rate is influenced by the 
 activation energy for nucleation gn and gn . the blue dashed line reflects 
 the results for fast addition of calcium , and the red dashed line 
 for the experiment at higher supersaturation . ( b ) the relationship 
 of the nucleation barrier gn to the radius ( r ) 
 of precritical nuclei formed in the acp - ii phase . ( a ) the relationship of free energy g versus the extent of reaction 
 . an amorphous ca  p complex ( acp - i ) 
 directly forms without thermodynamic barrier as the solutions are 
 mixed . the composition and free energy of acp - i are affected by the 
 initial driving force ( g ) and the rate of addition . the acp - i 
 transforms to dense acp - ii phase by dehydration and aggregation in 
 stage - i , followed by precritical nuclei formation within the acp - ii 
 phase in stage - ii . the nucleus formation rate is influenced by the 
 activation energy for nucleation gn and gn . the blue dashed line reflects 
 the results for fast addition of calcium , and the red dashed line 
 for the experiment at higher supersaturation . ( b ) the relationship 
 of the nucleation barrier gn to the radius ( r ) 
 of precritical nuclei formed in the acp - ii phase . in summary , the combined uses of electrical 
 conductance , hydrogen 
 ion selective electrode , and calcium ion selective electrodes provide 
 a more accurate assessment of the induction period and the kinetics 
 of amorphous precursor formation and transformation . using the new 
 conductance and potentiometric method , for the first time , the nucleation stages 
 of hap have been monitored in situ from solvated ions to the final 
 apatite mineral phase using a combination of electrochemical techniques . 
 a calcium - deficient acp - i [ ca-(hpo4)1+xnh2o ] has been 
 identified as precursor to ca p nucleation , formed due to differences 
 in the dehydration rate of hydrated calcium and phosphate ions . a 
 transformation from acp - i to a stoichiometric acp - ii phase [ ca-(hpo4)mh2o ] occurs as free calcium 
 from solution associate with the clusters . the formation of precritical 
 nuclei within acp - ii occurs by deprotonation in the later induction 
 period . this study is a major step forward in understanding 
 the earliest nucleation events in vitro and in vivo and provides details as to how additives may influence 
 precursor formation in the early induction periods of ca this study has revealed how precursors form 
 and transform during 
 the induction stages of hap nucleation . the results challenge previous 
 views on posner s clusters , as the initial precursor 
 in tooth and bone biomineralization , and suggest that the interaction 
 between amorphous precursor and organic additives plays a critical 
 role in the regulation of biomineral formation in vivo . these results 
 may also have general implications in a basic mechanism for biomineralization 
 from biology and chemistry to materials science and bioengineerging 
 and should contribute to improving methods for controlling carries 
 formation and other dental diseases .
hydroxyapatite 
 ( hap ) participates in vertebral bone and tooth formation by a nonclassical 
 hitherto unknown nucleation mechanism , in which amorphous precursors 
 form and transform during long induction periods . 
 elucidation of the 
 mechanism by which amorphous precursors assemble and transform is 
 essential to understanding how hard tissues form in vivo and will 
 advance the design and fabrication of new biomaterials . the combination 
 of conductance and potentiometric techniques to monitor ca 
 p 
 mineral formation has given new insight into the mechanism of nucleation . 
 differences detected in the dehydration rates of calcium and phosphate 
 ions indicate the formation of nonequilibrium calcium - deficient clusters . 
 the aggregation of these clusters forms a calcium - deficient amorphous 
 phase i [ ca-(hpo4)1+xnh2o]2x ) 
 early in the induction period , which slowly transforms to amorphous 
 phase ii [ ca-(hpo4)mh2o ] by dehydration . 
 precritical nuclei form within amorphous phase 
 ii later in the induction period , leading to mineral formation .