Electrodiffusion versus Chemical Diffusion in Alkali Calcium

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Electrodiffusion Versus Chemical Diffusion in Alkali Calcium Phosphate Glasses – Implication of Structural Changes Anneli Hein, Johannes Martin, Martin Schaefer, and Karl-Michael Weitzel J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b11113 • Publication Date (Web): 24 Jan 2017 Downloaded from http://pubs.acs.org on January 26, 2017

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ELECTRO-DIFFUSION

The Journal of Physical Chemistry

ϕ, n

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CHEMICAL DIFFUSION


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Electrodiffusion versus chemical diffusion in alkali calcium phosphate glasses – implication of structural changes Anneli Hein, Johannes Martin, Martin Schäfer, Karl-Michael Weitzel* Fachbereich Chemie, Philipps-Universität Marburg, Marburg, Germany

Abstract A long term transport experiment has been performed on a bioactive calcium phosphate glass of the molar composition 30 CaO *25 NaO *45 P2O5 using the technique of bombardment induced ion transport (BIIT) with potassium as foreign bombarder ion. Ion transport due to gradients of the electrical potential and the concentration lead to incorporation of K+ and depletion of both Na+ and Ca++ by electrodiffusion in forward direction. The resulting concentration profiles have been quantitatively analyzed by the time-of-flight secondary ion mass spectrometry (ToFSIMS). The concentration profiles of the P+ and POx+ signals (x = 1:4) resemble those of the K+, Na+ and Ca++ signals, indicating a characteristic change of the local bonding situation. This is interpreted as an indirect hint of a change of local structure of the glass network. Since the concentration profiles imprinted by the BIIT constitute pronounced concentration gradients, these depletion profiles further evolve on a much longer time scale due to chemical diffusion (absence of electric potential gradients). The former depletion zone is partially refilled by chemical diffusion. At the same time the structural changes of the glass network are demonstrated to be reversible. Numerical simulations on the basis of the coupled Nernst-Planck-Poisson equations allow deriving the diffusion coefficients of sodium, potassium and calcium for both cases, i.e. electrodiffusion and chemical diffusion. The two experiments are sensitive to different

aspects

of

the diffusion

coefficients

and

thus

are

complementary. The analysis is sensitive to the concentration dependence of D(Na+) and D(Ca++) for the electrodiffusion and of D(K+) for the chemical diffusion. For the chemical diffusion of Na+ and Ca++ in backward direction D(Ca++) is larger than D(Na+) indicating that the extra sites occupied by Ca++ in the preceding electrodiffusion are energetically high-lying. ACS Paragon Plus Environment

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submit to : Journal of Physical Chemistry C

Graphical abstract

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1. Introduction Research in the field of ion transport in solid electrolytes currently receives ample attention due to its multitude of application for energy storage or energy conversion 1,2,3,4,5,6,7

but also for medical applications of bioactive glasses

8,9,10,11,12,13

. Often, the

structure-function relation is not easy to comprehend in particular in amorphous materials where structure properties like interatomic distances exhibit distributions rather than having fixed values

14,15,16,17,18,19

to a modification of the local structure

. In fact, the ion transport itself may lead

20,21

such that different ions experience a

different local potential landscape which in turn influences their transport characteristics. Evidently, this is of particular relevance in ion-exchange studies 22. A very interesting class of ion conducting glasses is represented by bioactive glasses which are applied in the context of artificial bone growth

8,9,10,23

. Glass systems of

particular interest in this field include calcium phosphate glasses ceramic hydroxyapatite

9,26,27,28

8,12,24,25

as well as

and combined silicate and phosphate glasses

8,10

.

Thermal electro-poling of such glasses has been employed to increase the bone growth rate

29,30

and to investigate the structure-function relation

31,32

which indicates

that ion transport processes at the glass interface seem to play an important role in this context. In the work presented here, we investigate the transport of alkali and alkaline earth ions and their correlation with local structure. The model glass system chosen is a bioactive calcium phosphate glass of molar composition 30%CaO* 25%NaO* 45%P2O5. Throughout this manuscript we refer to this glass as Ca30Na. The technique employed is the recently developed low energy bombardment induced ion transport (BIIT)

33,34,35,36

which makes use of thermionic generation of ions. In the

case presented here, potassium ions were softly attached to the sample surface


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triggering the buildup of a concentration and potential gradient, which induce ion transport towards a grounded electrode mounted at the backside of the sample. In a recent BIIT investigation of an analogue Ca30K glass we observed that the native alkali ion (K+) as well as the alkaline earth ion (Ca++) became mobile upon foreign ion bombardment with Cs+

37

. Thus, we may expect that in the current investigation the

native Na+ as well as Ca++ ions may also exhibit measurable mobility. Subsequent to the BIIT experiment the sample is investigated using the time-of-flight secondary-ion-mass spectrometry (ToF-SIMS) method which allows to determine the composition of the sample layer-wise with a depth resolution of about 2 nm. It will be shown that the foreign ion bombardment not only generates electrodiffusion profiles but ultimately changes the local glass structure in the region of the surface down to several 10 nm below the surface. From the material science point of view the question then is whether these concentration depletion profiles are stationary, which is evidently a function of time and temperature. We will demonstrate that on a long time scale the Na+ and Ca++ ions diffuse back toward the sample surface filling up the depletion zone. The former change of network structure is shown to be reversible. An intriguing side aspect of the transport investigation is that the ion-induced forward transport is driven by the gradient of the electrochemical potential while in the second part of the experiment the transport is driven by the gradient of the chemical potential. All experimental concentration profiles will be directly compared to theoretical calculations based on the Nernst-Planck-Poisson (NPP) equations allowing to deduce the diffusion coefficients of all mobile ion species.



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2. Experimental and theoretical approach 2.1

Material synthesis

The preparation of the glass synthesis followed the steps of the standard meltquenching technique. Stoichiometric amounts of CaCO3 (Sigma Aldrich, 99.0%), Na2CO3 (Sigma Aldrich 99.9999%) and (NH4)2HPO4 (Sigma Aldrich 98.0%) were dried overnight at 120 °C and weighed into a porcelain mortar. After thorough grinding the reagents were mixed for twenty minutes in a plastic beaker. For further processing the glass batch was subsequently filled into a platinum crucible. To avoid possible impurities – in particular from alkali salts – the crucible was routinely cleaned by boiling in hydro chloric acid at 120 °C for one hour. The crucible was dried, filled with the glass batch and subsequently put into the oven where it was slowly heated to 950 °C. The slow increase of the temperature led to stepwise evaporation of NH3(g), H2O(g) and CO2(g) according to the respective boiling temperatures following the reactions 2 HPO4(NH4)2(s) P2O5(s) + 4 NH3(g) + 3 H2O(g) and CaCO3(s) CaO(s) + CO2(g), Na2CO3(s) Na2O(s) + CO2(g) The melting of the glass batch finally took place at 1150 °C. The hot melt was immediately poured into a cylindrical form of stainless steel which had been heated to 250 °C and was relaxed at 330 °C for 36 hours. During several attempts, this temperature has been proven to be well below the glass transition temperature of 370 °C and thus best suited for the relaxation of the glass 38. The glass cylinder was cut into slices of 400 µm to 800 µm thickness using a Mecatome T 180 cutting machine (Presi Inc.). The slices were thoroughly cleaned 5 ACS Paragon Plus Environment

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with isopropanol and finally, polished to minimize the surface roughness38. The polishing included grinding to delete sharp edges followed by a five step polishing process from 6 µm, 3 µm, 1 µm, 1/4 µm to 1/10 µm maximum surface roughness. For polishing a Labopol 5 (Struers Inc.) was utilized in combination with polishing tissues which were impregnated with diamond polishing paste (Kemet Inc.) with the respective granulation. Before introducing the sample into the vacuum the slices were cleaned again with isopropanol and glued to a copper electrode using a silver containing heat conducting glue.

2.2

Bombardment induced ion transport

The method of bombardment induced ion transport (BIIT) is a recent technique developed for investigating conduction properties of solid electrolytes

34,35,38

. Sample

specific properties like conductivity or diffusion coefficients giving insight into properties of ion transport are accessible using only one contacted electrode. The underlying principle is based on accelerating ions from a thermionic emitter towards the sample surface by applying a well-defined repeller potential, Urep , which ultimately defines the ion kinetic energy. The ion beam is guided toward the front side of the sample. The bombarded region of the sample is defined by a steel mask with diameter 8 mm which is mechanically pressed onto the sample. The ions reaching the sample charge up its surface until a specific value of the surface potential is reached which cannot exceed the applied repeller voltage. Note, that implantation of ions is carefully excluded in this experiment. Since the backside of the glass is in contact with a grounded electrode, concentration and potential gradients arise. Due to these gradients ions inside the sample start to migrate towards the grounded backside electrode. At the same time ions from the bombarding beam diffuse into the sample and extrude the native ions further into the sample. Ions reaching the 6 ACS Paragon Plus Environment


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backside electrode are neutralized resulting in a current, Iback, which is detected throughout the measurement. For measuring the conductivity of a sample the repeller voltage and the sample temperature are varied and the resulting backside current is recorded. The current-voltage curves gained in this way show a linear regime in which Ohm’s law holds and the conductivity can be calculated according to σsp = L/(R A) = (IbackL)/(UrepA), where R is the actual resistance of the sample, L is the sample thickness and A the bombarded area size. During generation of the electrodiffusion profiles the repeller voltage as well as the temperature are kept constant over a chosen period of time ∆t. Under these conditions the backside current Iback is constant such that the incorporated charge can be calculated according to QI = Iback∆t

2.3

Time-of–flight secondary ion mass spectrometry

Concentration depth profiles have been measured by means of the time-of-flight secondary ion mass spectrometry (ToF-SIMS, IONTOF GmbH, Münster, Germany). A bismuth liquid metal ion gun (LMIG) and an oxygen sputter gun are operated in the non-interlaced mode. The ToF-MS shown in this work exhibit a mass resolution m/∆m of approximately 6000. For all ToF-SIMS measurements the following settings were utilized. The LMIG used Bi+ at 1pA target current in the high current bunched mode whereas the DSC sputter gun used oxygen with 240 nA target current and 3 kV acceleration voltage. As the examined sample is electronically insulating a flood gun has been used for charge compensation. The detector was operated in the positive ion mode. The ToF-SIMS craters formed in the profiling were subsequently analyzed by means of a DekTak 7 ACS Paragon Plus Environment

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profilometer, yielding a depth which in turn was used for calibrating the depth axis of the profiles.

2.4

Numerical Simulation

To complement the experimental measurement of concentration profiles the transport of charge carriers inside the glass has also been calculated using a coupled set of the NERNST-PLANCK and the POISSON equations (NPP). As mentioned in the introduction two different transport experiments will be described in the result section, i. an electrodiffusion experiment and ii. a chemical diffusion experiment. We first turn to the electrodiffusion. The concept of theoretically describing electrodiffusion profiles has been described in detail in

35

. The crucial parts required for understanding the

calculations of this work will be outlined below. Since the sample has a very large aspect ratio it is safe to perform the calculation in one dimension. As a consequence, the flux density is given by the one dimensional NERNST-PLANCK equation, where the z-axis defines the direction perpendicular to the sample surface

= − +

(1)

The index ν refers to the ion species (Na+, Ca++, K+). The ion flux density Jν depends on the concentration dependent diffusion coefficients as well as on the gradients of the electric potential φ and the ion densities nν. The elementary charge is e while kBT is the BOLTZMANN’s constant times the temperature.

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Modifying the carrier density distribution implies a redistribution of charge. As a consequence, the POISSON equation needs to be solved side by side with the NERNST-PLANCK equation

² = − ( + + 2 − − 2 )

(2)

where the superscript zero refers to the initial ion distribution prior to the bombardment. Throughout the calculation we assume a dielectrically homogeneous sample material with εr=6.7. The time dependence of the ion transport is described by FICK’s second law

= −

(3)

In order to solve equations (1) - (3) we discretize the sample into space elements ∆z and assign average ion densities and potentials to each of the space elements. Solving equation (2) requires appropriate boundary conditions for the electric potential. These are essentially given by the experiment during which the backside of the sample is grounded such that zero potential may be assumed there. Potential steps that may arise from the neutralization processes of the carriers at the backside electrode are neglected. The potential at the front side of the sample is given by a dynamic equilibrium between the impinging ions and the ions transported from the surface into and through the material. The situation for the simulation of the chemical diffusion part of the experiment can be described as follows. At the end of the BIIT experiment the sample is exposed to air, such that the surface is neutralized and no gradient of the electric potential 9 ACS Paragon Plus Environment

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remains. Consequently, the potential at the front- and backside of the glass is now set to zero and only the gradient given by the particle density remains. Nevertheless, any subsequent transport of one ion species in the glass is still correlated to all other charge carriers by the POISSON boundary condition.

3. Results and discussion 3.1

Long-term Bombardment by means of BIIT

The long-term bombardment presented here, was performed by shining a potassium ion beam onto a Ca30Na sample of 404 µm thickness for 120 hours. The sample temperature was set to 80 °C, while the applied repeller voltage was set to 121 V, corresponding to an average field of 300 V / mm inside the sample. During the entire experiment the ion beam was intense enough to guarantee a homogeneously charged sample surface. Subsequent to the bombardment the sample was investigated by means of ToF-SIMS. Inevitably, the need to detect some signals in ToF-SIMS at very low levels implies that other signals may reach close to detector saturation. The latter is the case for e.g. the

39

K+ (the most abundant natural potassium isotope), the

one natural sodium isotope) and the

40

23

Na+ (there is only

Ca+ signals. In this situation the signal of

another chemical species, known to be conformal to the first, needs to be analyzed. Throughout the entire manuscript the

41

K+, the Na2+ and the

40

Ca++ are presented as

indicative of the total potassium, sodium and calcium signals respectively. The conformity has been ensured in reference experiments. The raw data of the concentration depth profiles as well as a reference profile of an unbombarded sample are shown in Figure S1 and S2 in the supplementary material. 10 ACS Paragon Plus Environment


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Figure 1 in the main text depicts the concentration profiles normalized according to the procedure outlined below. As evident from the raw data, part of the calcium ions have been depleted in the front region of the sample. In recent work we have demonstrated that in this case the charge density is conserved, but the particle density is not

37

. Therefore, the concentration profiles were normalized assuming

electro-neutrality inside the glass. This assumption implies that either one foreign K+ ion replaces one Na+ ion, or two K+ ions replace one Ca++ ion. According to the stoichiometry of the original glass, the relative contributions of sodium and calcium to the charge density are 5/11 and 6/11. This relation is maintained in the bulk of the glass which remains unmodified throughout the bombardment. Therefore, the ToFSIMS signals can be transformed into relative charge contributions using

=

6 = #$%%%% 11

=

5 = '$%%%% 11

(4) (5)

where ρCa and ρNa are the relative charge density contributions of calcium and

%%%% sodium while $%%%% and $ are their average ToF-SIMS signal intensities in the bulk. Due to the electro-neutrality of the glass 37, the following relation holds in the diffusion zone

%%%% ) 1 = #$%%%% + '$ + ($ .

(6)

For an optimum match of the coefficient c, we perform a least square analysis to Eq. (6), resulting in (7):


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(=

∑. +,,. /+,,. +01,. /2+,,. +31,. ∑. +²,,.

.

(8)

Finally, all contributions to the charge density are transformed into relative particle densities, which are shown in Figure 1. For a correct interpretation of depth profiles, it is crucial to determine the beginning of the glass matrix, i.e. the position of the original surface. Since it is clear at this point that both the Na+ and the Ca++ exhibit a finite mobility, and further oxygen has been used as sputtering source, we have chosen the phosphorous signal as indicative of the glass matrix. Reference measurements of a fresh, un-bombarded glass sample reveal that the following phosphorous containing signals are observed in the order of decreasing intensity: PO+ >> P+ ≈ PO3+ ≈ PO2+ >> PO4+. These signals all exhibit a step-like increase at the same position where the Ca and Na signals increase, i.e. at the glass surface. In fact, at the beginning of the investigation we assumed that all ToF-SIMS signals containing phosphorous would be stationary. As we demonstrate below, this assumption is not correct. Nevertheless, whatever the first phosphorous signal is marks the beginning of the glass matrix.



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Figure 1. Normalized ToF-SIMS concentration profiles. Signals depicted are particle density of the + mobile ion species normalized considering charge conservation of the glass material. Additionally P + and PO4 signals are shown for illustration of structural changes in the glass. The glass surface is at 0 nm. The blue dotted line marks the depth for which the concentration dependent diffusion coefficients have been marked in Figure 2.

As it turns out the first phosphorous signal observed in depth profiling the bombarded sample is the PO4+. Consequently the edge of the PO4+ profile is taken as zero point for the depth axis. The edge of the K+ signal is observed at the same position. The raw data for the five phosphorous containing species are shown in Figure S1 of the supplementary material. For further discussion in the main text the PO4+ and the P+ signals have been normalized to the sum of the respective raw data and plotted as an upper part of Figure 1. Evidently in the bombarded sample the P+ signal is markedly suppressed by the PO4+ signal in the first 40nm. The signals beyond 60nm resemble the bulk glass and at the same time also the situation in a fresh unbombarded glass. The most prominent result of the ToF-SIMS analysis is that the foreign bombarder ion, K+, has electro-diffused further into the glass down to a depth of about 50nm. At 13 ACS Paragon Plus Environment

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the same time, sodium and calcium have been depleted on the same length scale. More specifically, the sodium signal has completely decreased to zero intensity over a depth of about 40nm, while calcium exhibits a step-like variation. A first step is observed around 10 nm and a second around 40 nm. The plateau in the calcium signal is most likely connected to the widening of the glass network and thus to a structural modification of the glass material in the electrodiffusion as further discussed below. Evidently, in the first nanometers of the profile, the sum over the particle densities of all mobile species is larger than one due to the conservation of charge density discussed above. This increase in the local particle density is difficult to comprehend without a change in the local glass structure. The Ca30Na glass is based on a calcium phosphate network. Information on this network may therefore be extracted from an analysis of the phosphorous signal and its oxides POx. Here, three qualitatively different trends can be distinguished in the POx signals, c.f. figure S1 of the supplementary material. The P+ and PO+ signals exhibit a minimum at the front side of the bombarded sample. These signals rise sharply with increasing distance from the surface. The PO4+ signal on the other hand exhibits the opposite trend. I.e. the PO4+ signals has a maximum close to the surface and ultimately decreases to basically zero with increased distance from the surface, cf. figure 1 of the main text. The intermediate PO2+ and PO3+ signals exhibit a trend intermediate between the other two limiting cases. I.e. both the PO2+ and the PO3+ exhibit a small peak close to the sample surface but reach their maximum value in the bulk, cf. Figure S1 of the supplementary material. These trends give i.) an indirect hint at a structural change of the glass network connected to the electrodiffusion process and ii.) a hint that this structural change is correlated to the bonding situation of the phosphorous to the oxygen. Here, the term structural change refers to a likely 14 ACS Paragon Plus Environment


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modification of interatomic distances in the glass network. Similar indication of structural changes becomes evident from µ-RAMAN studies of ion exchanged glasses as well as solid state NMR studies

39,40

. A classical structure determination

would require additional techniques, e.g. x-ray analysis. It is further interesting to note that the characteristics of the PO4+ signal resembles that of the foreign ion K+ signal while the P+ and the PO+ characteristics resemble that of the Ca++ signal. In the analysis of the mass spectra we discovered a close proximity of species PO4+ and K2OH+ with masses at 94.99 and 94.75 amu. The signals of these two species are small and - more important – rather broad – leading to an accidental overlap of the two. Due to the high mass resolution of around 6000 and a Gauss fitting of the two peaks it was possible to identify the PO4+ species beyond doubt. The evolution of a diffusion zone with the incorporation of a foreign ion and an increase in the local particle density is likely to be accompanied by modification of the local glass structure. Based on previous work from our group the relevant conductivities and ion diffusion coefficients are expected to be different in this diffusion zone compared to the bulk. The diffusion coefficient of Ca++ is in general difficult to derive from impedance spectroscopy in the presence of mobile alkali ions. This information is, however, accessible from a comparison of experimental depth profiles and theoretical profiles calculated in the framework of the NPP model. The calculated profiles leading to the best agreement with the experimental data are shown as straight lines in figure 1 (the calculation parameters can be retrieved from the supplementary material). The agreement between experimental and calculated concentrations is considered good in the range of depth from approximately 10 nm into the bulk of the sample. We are reluctant to interpret the signals in the first 10 nm of depth profiling because of known difficulties of the ToF-SIMS technique. 15 ACS Paragon Plus Environment

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The current level of agreement is only reached by assuming that two of the diffusion coefficients are concentration dependent. As a result of the analysis, the concentration dependent diffusion coefficients for all mobile species are shown in Figure 2. More specifically the diffusion coefficient of the native Na+ ions decreases by approximately a factor of 4 in going to smaller local fractional abundance. The diffusion coefficient of Ca even drops by approximately a factor of 10 in going to smaller local abundance. For these two species the x-axis of Figure 2 is normalized to the bulk density. For the foreign ion K+ there is no bulk abundance. Here, the local particle density has been normalized to the sum of the depleted Na and Ca charge densities. It deserves to be emphasized that the variation of D(K+) with the local composition of the glass appears to be smaller than the sensitivity of our analysis. Note, that lines parallel to the y-axis do not belong to the same position in the glass. Points belonging together must obey the charge density conservation. As one example, diffusion coefficients belonging to the crossing point of concentration profiles at a depth of ca. 42nm (marked by a blue dotted line in Figure 1) are marked by black symbols in Figure 2. At this diffusion front the diffusion coefficient of Na is the largest, that of the Ca is the smallest. As an alternative representation the relevant diffusion coefficients are also plotted as a function of the depth in the sample as figure S6 of the supplementary material.



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Figure 2. Density dependence of the diffusion coefficients for the electrodiffusion profile for Ca, Na and K. The points marked by the black symbols all refer to a depth of 42 nm below the surface of the sample. The inset has been included for illustration of small values.

3.2

Chemical Diffusion

As discussed in the introduction this kind of glass is of potential interest as a material for artificial bones. In particular, the concentration profiles imprinted onto the material are of potential interest. This immediately raises the question whether such profiles are stationary. It is a common believe that if the activation energy for ion transport is high enough and the profile is generated at elevated temperature this profile might be stationary at room temperature. Since Ca is in general assumed to be almost immobile one would perhaps expect the profiles shown in Figure 1 to be stationary at room temperature. In the following we describe an investigation which proofs this assumption to be wrong. To this end the glass sample was exposed to air and stored at room temperature for two years. After that time the sample was reinvestigated by means of ToF-SIMS. For comparability of the results the measurements were 17 ACS Paragon Plus Environment

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performed utilizing the same settings of the ToF-SIMS apparatus as in the former measurement. Since the amount of potassium contained in the sample must be conserved during chemical diffusion the total amount of K+ introduced into the sample in part 1 of the experiment can be used to calibrate the x-axis of Figure 3 taking into account the condition of local electro-neutrality. Figure 3 shows the concentration profiles for potassium, sodium and calcium after chemical diffusion. The corresponding raw data are again available in the supplementary material as Figure S2. Compared to the original electrodiffusion profile shown in Figure 1 we note that the K+ profile has now smeared out in the forward direction, while the Na+ and the Ca++ profile have smeared out in the backward direction. The latter has led to a partial refilling of the depletion zone observed in Figure 1. These concentration profiles are the result of a correlated movement of the three mobile cations discussed. For every Na+ diffusing into the backward direction one K+ ion must diffuse in the forward direction. For every Ca++ moving in the backward direction two K+ ions diffuse in the forward direction. As a result of this diffusion K+ ions are now detected at finite intensities down to about 150nm below the glass surface. One of the most striking results of this investigation becomes evident from looking at the phosphorous signals P+ and PO4+ shown as an upper part in Figure 3. Clearly, the P+ signal now dominates everywhere in the glass, the PO4+ signal is depressed to the detection limit. This, however, is the characteristics of the original glass, which implies that the structural changes imprinted onto the glass by the electrodiffusion has now been completely reversed in the chemical diffusion. The same cannot be true for the K+, Na+ and Ca++ signals since the K+ ions cannot leave the sample, but they can only diffuse in the forward direction. Eventually, in the long time limit, the K+ 18 ACS Paragon Plus Environment


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signal would spread out over the entire glass sample. This, however, would probably take several decades.

Figure 3. Normalized ToF-SIMS concentration profiles. Signals depicted are particle density of the mobile ion species normalized considering charge conservation in the glass material. Additionally shown are P+ and PO4+ signals for orientation. The glass surface is at 0 nm. The dotted line marks the depth for which the concentration dependent diffusion coefficients were marked in Figure 4.

The raw signals of all phosphorous signals of the type POx+, x=0 - 4 are also shown in the supplementary material as Figure S2. These phosphorous signals all exhibit the same characteristics, i.e. the relative fractional abundance is position independent. During the chemical diffusion experiment, the sample has been stored at ambient conditions in a sealed box to reduce contact with air humidity. A thorough analysis of concentration profiles reveals no significant indication of incorporation of water and/or H+ (for further details see the supplementary material).


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It seems worth emphasizing the very smooth profiles observed after the extended chemical diffusion. Apparently, this chemical diffusion enables approaching a chemical equilibrium at least for the glass-forming network. As mentioned earlier reaching the true equilibrium for the K+, Na+ and Ca++ would require a much longer time since these displacements are correlated by the Poisson equation. Again, for a quantitative description of the experimental concentration profiles shown in Figure 3 extensive numerical calculations have been performed. Here, the concentration profiles generated by the electrodiffusion have been used as an input, i.e. starting point, of the calculations. Since the experimental profiles are subject to detector noise the numerical concentration profiles have been employed. As demonstrated above these were in good agreement with the experiment. The results of the numerical calculations are depicted in Figure 3 as solid lines. The relevant parameters employed in the numerical calculations are given in the supplementary material as table T2. Evidently again a good agreement between experiment and calculation is observed. This good agreement is only reached by assuming that one of the three diffusion coefficients is concentration dependent. This concentration dependence of the diffusion coefficients is illustrated in Figure 4. The diffusion coefficient of K+ decreases by a factor of 10 with decreasing local fractional abundance. For the highest K+ concentration D(K+) is larger than D(Na+) and D(Ca++). For the smallest K+ concentration D(K+) is smaller than the other two diffusion coefficients. Note, that these diffusion coefficients refer to room temperature while the diffusion coefficients shown in Figure 2 refer to 80 °C. The black symbols included in Figure 4 mark the diffusion coefficients for a depth of ca. 60 nm below the sample surface. This depth is also marked in Figure 3 as a blue dotted line. As an alternative representation the 20 ACS Paragon Plus Environment


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Page 22 of 32

relevant diffusion coefficients are also plotted as a function of the depth in the sample as figure S6 of the supplementary material.

Figure 4. Density dependent diffusion coefficients for the chemical diffusion profile. The black symbols mark diffusion coefficients belonging to the same position in the glass, i.e. ca. 60 nm below the surface of the sample.

The observation that now D(K+) is the only diffusion coefficient which appears to be concentration dependent is opposite to the observation in the electrodiffusion profiles. There the diffusion coefficients D(Na+) and D(Ca++) appeared to be concentration

dependent.

This

behavior

is

explained

as

follows:

In

the

electrodiffusion profile, potassium is incorporated depleting calcium and sodium such that the concentration of the latter two continuously decreases. In this case, the sodium and the calcium effectively blocks the potassium at the diffusion front. Therefore, we are not sensitive to any hypothetically higher diffusion coefficient once an almost pure potassium region has been formed. The potassium ions simply cannot pass by the sodium and calcium ions without violating the Poisson equation. 21 ACS Paragon Plus Environment

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For the chemical diffusion the backward diffusion of sodium and calcium is effectively blocked by the potassium ions, since the latter occupies the relevant sites. Therefore, in this case we are not sensitive to hypothetically lower diffusion coefficients of sodium and calcium at lower local abundance. A pivotal result of the analysis presented above pertains to the relative magnitude of diffusion coefficients D(Ca++) versus D(Na+). For the electrodiffusion of sodium and calcium (in forward direction) D(Ca++) is always smaller than D(Na+) as expected. A similar observation has been reported by Mager et al.

37

. For the (backward)

chemical diffusion D(Ca++) is larger than D(Na+) for the region analyzed. We are not aware of any other report of D(Ca++) being larger than D(Na+). We rationalize this finding as follows. In the electrodiffusion part of the first experiment, calcium is forced to migrate into energetically rather unfavorable sites. Once the first part of the experiment is stopped and the electric field is turned off, the Ca++ ions remain subject to the chemical gradient in backward direction. Apparently, the activation energy for backward diffusion into the original sites is significantly smaller than the activation energy for migration in forward direction. For the sodium the sites occupied in the forward migration are less unfavorable than for the calcium. Consequently, the difference in forward and backward activation energy is much smaller for sodium. Ultimately, the chemical diffusion coefficient for the calcium sitting in the unfavorable sites exceeds those of the sodium. Evidently, this conclusion refers only to that part of the sample where Ca++ ions have been accumulated in the electrodiffusion part of the experiment. The results presented in Figures 3 and 4 are fully compatible with D(Ca++) being smaller than D(Na+) in the bulk of the sample not affected by the electrodiffusion.



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Sodium containing phosphate glasses have been investigated by means of solid state NMR in order to gain insight into the local structure as manifested by interatomic distances

39,41,42

. Prabakar et al.

41

provide strong evidence of a

correlation between sodium concentration and relative concentration of Qn species, where Q represents a phosphorous atom in the center of an oxygen tetrahedron and n denotes the number of bridging oxygen atoms (0 to 3). While the conventional view is that the alkali ions are only associated with non-bridging oxygen atoms (NBOs), Prabakar et al. demonstrate that the Na+ is indeed also correlated with the Q3 sites. Changing the fractional alkali ion concentration, e.g. by BIIT, is therefore also expected to change the local structure. A changing fraction of Q3 to Q2, Q1 and Q0 tetrahedrons is commonly referred to as depolymerization. The change in POx signals in our ToF-SIMS analysis may in fact be correlated to such a change in the local binding situation. A similar indirect hint at a change of Qn fractions has also been discussed by Alam et al. 39 and Stavrou et al. 40. The question of structural changes induced by ion transport processes and the question of reversibility of such changes are of considerable importance from a fundamental point of view but also for technical applications. In artificial bone replacement calcium phosphate based materials are widely used. From a fundamental point of view the respective transport coefficients for e.g. the Ca++, will decide on the durability or the resorbability of parts of the implant

43

. The local

calcium concentration is apparently crucial for the biocompatibility of apatites in artificial bone and tooth material

44

. The long-term evolution of material properties as

alluded to in this work is not only relevant for artificial materials. It is of course of inherent relevance for natural materials, e.g. geopolymers

45

. The correlation of

structural changes and catalytic activity in Cu/ZnO catalyst has been discussed by 23 ACS Paragon Plus Environment

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Grunwaldt et al.

46

. The intercalation of lithium at the electrolyte/electrode interface

clearly involves changes of the local structure means of in-situ XRD studies

49

47,48

, which can e.g. be manifested by

. The energy required for intercalation has been

demonstrated to increase monotonically with the ion radius both for alkali and alkaline earth ion intercalation into iron hexacyanoferrate remains, how reversible these changes are

51

50

.The question often

. Helpful techniques for elucidating the

role of dynamical changes of structures include solid state NMR

52,53,42

but also FIB-

TEM 20 and atom probe tomography 54,55.

4. Summary and outlook A long-term bombardment of a sodium containing calcium phosphate glass with a potassium ion beam has been carried for a time span of 120 hours. The electrodiffusion induced by this bombardment has been quantitatively analyzed by means of ToF-SIMS. Both sodium and calcium ions have been depleted over a zone of approximately 50nm and replaced by the foreign potassium ion. This transport of mobile ions has been shown to be accompanied by a structural change as indicated by the binding situation of phosphorous to oxygen observed through POx+, x = 0 – 4, signals. With increasing potassium incorporation the intensity is shifted from the P+ signal to the PO4+ signal. At the same time the local particle density is enhanced since two K+ ions replace one Ca++ ion conserving charge density. Extensive numerical calculations on the basis of the coupled Nernst-Planck and Poisson equations allow to derive the complete concentration dependence of the diffusion coefficients for sodium and calcium. For the potassium this analysis is not sensitive to the concentration dependence of the diffusion coefficient due to a blocking of the K+ by Na+ and Ca++ at the diffusion front. 24 ACS Paragon Plus Environment


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Subsequently to this electrodiffusion experiment the sample was stored at room temperature for two years allowing for chemical diffusion in the absence of electrical potential gradients. Thereafter the sample has again been profiled by ToF-SIMS. Quantitative analysis of these concentration profiles revealed that the potassium has chemically diffused further into the forward direction, while sodium and calcium diffused backwards partially filling the former depletion by approximately 50%. This chemical transport is accompanied by a reversion of the structural changes in the phosphorous oxide network. After two years of chemical diffusion at room temperature the glass structure appears to agree with the original structure of a fresh sample. Numerical calculations by means of NPP again allow deriving the respective diffusion coefficients. Now the analysis is sensitive to the concentration dependence of K+, while it is insensitive to the concentration dependence of Na+ and Ca++. The reason is that in this case the Na+ and Ca++ are blocked by the K+ at the diffusion front. The extra sites into which the Ca++ ions are forced to hop in the electrodiffusion part of the experiment appear to be energetically high-lying. Consequently, the activation energy for backward transport is significantly lower than for forward transport. Therefore, the D(Ca++) out of these sites is surprisingly high, even higher than that for the Na+ ions in their regular sites. This work has demonstrated that a dedicated ion transport experiment within the frame of BIIT combined with ToF-SIMS measurements and the proper theoretical analysis is capable of revealing very detailed information on transport properties in relation to local structural information. This may be considered a proof of principle experiment. This experiment does not replace a classical structure analysis, but provides a complementary approach where x-ray analysis is not accessible e.g. because of small sample volume. For the future manifold extensions of this work can 25 ACS Paragon Plus Environment

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be envisaged. The focus of part of the current work was on aging of a diffusion sample at room temperature on long time scales. As a result we have derived effective diffusion coefficients. One aim for future work will be to perform electrodiffusion and chemical diffusion at the same temperature and compare the derived diffusion coefficients for electrodiffusion and chemical diffusion in order to address e.g. the Haven ratio.

5. Acknowledgements Financial support of this work from the German Science Foundation (DFG) is gratefully acknowledged.

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Electrodiffusion versus Chemical Diffusion in Alkali Calcium

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