Jo Van Hoof
email: jo.vanhoof@kuleuven.be

Lieven Verschaffel
email: lieven.verschaffel@kuleuven.be

Wim De Neys
email: wim.de-neys@parisdescartes.fr

Wim Van

Wim Van Dooren
email: wim.vandooren@kuleuven.be

Intuitive errors in

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Introduction

A good understanding of rational numbers is of crucial importance for learners' later mathematics development (e.g., [START_REF] Obersteiner | Understanding rational numbers-obstacles for learners with and without mathematical learning difficulties[END_REF][START_REF] Siegler | Early predictors of high school mathematics achievement[END_REF][START_REF] Van Hoof | The transition from natural to rational number knowledge[END_REF]). To give one example, in a longitudinal study Siegler and colleagues (2012) found that 5 th graders' rational number understanding predicted their mathematics and algebra scores in high school. This was even found after they had controlled for reading achievement, IQ, working memory, whole number knowledge, family income, and family education. These results are not surprising, given the hierarchically structured development of mathematics on both the cultural (phylogenetic) and individual (ontogenetic) planes [START_REF] De Corte | Learning and teaching mathematics[END_REF].

A good understanding of rational numbers also plays an important role in daily life: reading recipes, calculating prices during sales etc. (see for example [START_REF] Reyna | The importance of mathematics in health and human judgment: Numeracy, risk communication, and medical decision making[END_REF]. Even though the crucial role of a good rational number understanding for school mathematics and for daily life has been documented amply, and a lot of effort is being put in teaching learners rational number, many elementary and secondary school learners, adults, and even (prospective) teachers continue to struggle with many aspects of this kind of numbers (e.g., [START_REF] Christou | Natural number bias in operations with missing numbers[END_REF][START_REF] Depaepe | onderwijs (groep 1) [Content knowledge and pedagogical content knowledge in the domain of rational numbers. A comparative study with pre-service teachers[END_REF][START_REF] Mcmullen | Modeling the developmental trajectories of rational number concept(s)[END_REF][START_REF] Siegler | Early predictors of high school mathematics achievement[END_REF][START_REF] Vamvakoussi | Naturally biased? In search for reaction time evidence for a natural number bias in adults[END_REF][START_REF] Van Hoof | Towards a mathematically more correct understanding of rational numbers: A longitudinal study with upper elementary school learners[END_REF]. This clearly points to the need to further investigate why fractions are so hard to understand and to reveal which cognitive processes underlie this understanding.

While there may be many reasons why fractions are so hard to grasp (for an overview, see, for example, [START_REF] Moss | Pipes, tubes, and beakers: New approaches to teaching the rational-number system[END_REF], a vast amount of previous research showed that a major source of difficulties with rational numbers is the "natural number bias" (for an overview, see [START_REF] Van Hoof | The transition from natural to rational number knowledge[END_REF]. The natural number bias describes the phenomenon of applying natural number knowledge in rational number tasks where this is inappropriate (e.g., [START_REF] Ni | Teaching and learning fraction and rational numbers: The origins and implications of whole number bias[END_REF]. For example, with regard to the numerical size of numbers, learners have been found to erroneously think that the larger the natural numbers that constitute the fraction are, the larger the numerical value of the fraction is. For example: 7/11 is wrongly assumed to be larger than 4/5, given that 7 is larger than 4 and 11 is larger than 5.

In the same line, witch decimal numbers, learners have been found to erroneously think that the more digits a decimal number has, the larger the numerical value of the decimal number is. For example: 0.16 is wrongly assumed to be larger than 0.4, given that 16 is larger than 4.

Indications for the natural number bias are typically found in higher accuracy levels on fraction tasks where one can use natural number knowledge to come to the right answer (named congruent items, e.g., which fraction is the larger one? 7/11 or 3/8; 7 is larger than 3 and 11 is larger than 8; just like 7/11 is larger than 3/8) compared to the lower accuracy levels on fractions tasks in which the use of natural number knowledge leads to the incorrect answer (named incongruent items, e.g., which fraction is the larger one? 6/11 or 3/4, 6 is larger than 3 and 11 is larger than 4, however 6/11 is smaller than 3/4) (e.g., [START_REF] Ni | Teaching and learning fraction and rational numbers: The origins and implications of whole number bias[END_REF][START_REF] Vamvakoussi | Understanding the structure of the set of rational numbers: A conceptual change approach[END_REF][START_REF] Vamvakoussi | Naturally biased? In search for reaction time evidence for a natural number bias in adults[END_REF][START_REF] Van Hoof | Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education[END_REF].

When being introduced into rational numbers, there are several aspects in which the rules for natural numbers are no longer necessarily applicable, leading to systematic mistakes. For example, contrary to what happens in the domain of natural numbers, in the rational number domain multiplication does not longer always lead to a larger outcome (with fractions smaller than 1; for example 3 * 1/2 is 3/2 which is smaller than 3). Moreover, unlike with natural numbers (that are characterized by a discrete structure) one cannot say which number comes next after a given rational number (as rational numbers are characterized by a dense structure), because there are always infinitely many numbers in between two given rational numbers.

While learners struggle with these and other aspects whereon natural and rational numbers differ, previous studies showed that a first step in learners' understanding of rational numbers is a good understanding of their numerical size. For example, Van Hoof et al. ( 2018) longitudinally followed 201 upper elementary school learners in the crucial years of instruction in rational numbers (4 th to 6 th grade). Results showed that learners first needed to have a good understanding of the size of fractions before they were able to reason about operations with fractions. Similar results were found in a Finnish sample [START_REF] Mcmullen | Modeling the developmental trajectories of rational number concept(s)[END_REF]. Next to the results of these longitudinal studies, Siegler et al.'s integrated theory of numerical development (e.g., [START_REF] Siegler | An integrated theory of whole number and fractions development[END_REF] also points to the crucial role of the understanding of the size of rational numbers. The integrated theory of numerical development states that "although whole numbers and fractions differ in many ways that influence their development, an important commonality is the centrality of knowledge of numerical magnitudes in overall understanding." (Siegler, Thompson, & Schneider, 2011, p. 273). Given the crucial role of a good fraction magnitude understanding, the present study focuses on the understanding and processing of the magnitude of fractions.

A lot of research investigating the natural number bias starts from the conceptual change perspective (e.g., [START_REF] Christou | Natural number bias in operations with missing numbers[END_REF][START_REF] Vamvakoussi | Naturally biased? In search for reaction time evidence for a natural number bias in adults[END_REF][START_REF] Van Hoof | Towards a mathematically more correct understanding of rational numbers: A longitudinal study with upper elementary school learners[END_REF][START_REF] Vosniadou | International handbook of research on conceptual change[END_REF]. According to this perspective, the construction of a mathematical concept in a learners' mind is a gradual and time consuming process, starting from a naïve, intuitive idea of a concept (in our case number, including fractions) to the mathematically correct concept. This process is characterized by many intermediate states of understanding, given that new (and sometimes incompatible) information is added to the already existing conceptual structures, often leading to inconsistencies and misconceptions [START_REF] Vosniadou | International handbook of research on conceptual change[END_REF]. The conceptual change theory offers an explanation for learners' large and continued struggle with fractions. Given that in the first years of life and in the first years of (mathematics) instruction the only numbers learners encounter are natural numbers, people tend to create a concept of number that is solely based on natural numbers, with accompanying rules and characteristics (for example, multiplication always makes larger).

Therefore, a drastic change of the conceptualization of number is necessary to be able to understand rational numbers (e.g., [START_REF] Christou | Natural number bias in operations with missing numbers[END_REF][START_REF] Mcmullen | Modeling the developmental trajectories of rational number concept(s)[END_REF][START_REF] Vamvakoussi | Naturally biased? In search for reaction time evidence for a natural number bias in adults[END_REF][START_REF] Vamvakoussi | Understanding the structure of the set of rational numbers: A conceptual change approach[END_REF][START_REF] Vosniadou | International handbook of research on conceptual change[END_REF].

In sum, studies starting from the conceptual change theory provide a good understanding of learners' development of a mathematical concept, starting from a naïve, intuitive idea of a concept (in our case number, including fractions) to the mathematically correct concept. Moreover, when a conceptual change has taken place, this does not imply that the initial intuitive idea is gone. The correct concept can coexist with the intuitive concept [START_REF] Dewolf | The representation of the fraction magnitudes and the whole number bias reconsidered[END_REF]. This idea is closely related to the dual process perspective. The dual process perspective and more specifically the default interventionist theory (e.g., [START_REF] Evans | Dual-processing accounts of reasoning, judgment and social cognition[END_REF]; but see also for example [START_REF] Pennycook | What makes us think? A three-stage dualprocess model of analytic engagement[END_REF][START_REF] De Neys | Bias, conflict, and fast logic: Towards a hybrid dual process future[END_REF]; for critiques on this traditional model) supplements the conceptual change theory by handing the theoretical and methodological tools to investigate and explain how people who have all the required domain-specific knowledge and skills to solve a certain task, can still make mistakes, namely because they are still affected by erroneous intuitive reasoning. More specifically, reaction time studies have been shown useful to shed light on the intuitive character of learners' mistakes in several mathematical tasks (see for example [START_REF] Gillard | Dual processes in psychology of mathematics education and cognitive psychology[END_REF][START_REF] Lem | Experts' misinterpretation of box plots -a dual processing approach[END_REF].

The dual process theory assumes that people have two types of reasoning processes: the first one is named the intuitive reasoning process (T1) and the second one is named the analytic reasoning process (T2). T1 processing is often characterized as fast, automatic, associative, and undemanding of working memory capacity, whereas T2 is often characterized as slow, controlled, deliberate, and highly demanding of working memory capacity. The fast T1-intuitions are presumed to take place spontaneously and also often lead to successful responses to a task. However, fast intuitive reasoning processes can lead to wrong answers to tasks where more extensive, analytical thought processes are necessary. In this case, two outcomes are possible. First, it is possible that an incorrect intuitive reasoning process takes place without intervention by the analytical T2 processing. In this case, the process will lead to a wrong answer. A second possibility is that the analytical T2 processing does intervene, evaluates the intuitively obtained answer, and tries to inhibit it, leading to a different outcome (e.g., De Neys, 2017; 2009).

Gillard, Van Dooren, Schaeken, & Verschaffel,
A central claim within the dual-process framework that can be used as a basis to empirically investigate whether an answer is the outcome of an intuitive or an analytic process, is the different speed of processing, given that T1 reasoning is faster than T2 reasoning. Using this dual process perspective, several studies showed that participants took more time to correctly solve incongruent fraction tasks than congruent ones. These reaction times studies suggest that analytical reasoning takes place when one is solving an incongruent fraction item correctly, and therefore that the natural number bias has an intuitive character (e.g., [START_REF] Obersteiner | The natural number bias and magnitude representation in fraction comparison by expert mathematicians[END_REF][START_REF] Vamvakoussi | Naturally biased? In search for reaction time evidence for a natural number bias in adults[END_REF][START_REF] Van Hoof | Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks[END_REF]. A fundamental limitation of these studies however is that they are exclusively correlational in nature. The causal relation between slower, analytical processing and correctly solving incongruent items has not been investigated yet. Although it has been shown that a correct response to an incongruent item is associated with longer reaction times, this does not allow to conclude that shorter reaction times decrease the chance of solving incongruent items correctly [START_REF] De Neys | Dual processing in reasoning: Two systems but one reasoner[END_REF].

Important to note is that in the research literature many different definitions of intuition and intuitive reasoning exist. There is however a broad agreement that "intuition is some kind of information acquired without conscious, deliberative reasoning" (Epstein, 2010, p. 296). In the present study we define intuitive reasoning as fast, automatic, and undemanding of working memory capacity, which is in line with the dual process theory of reasoning and more specifically the default interventionist theory (e.g., [START_REF] Evans | Dual-processing accounts of reasoning, judgment and social cognition[END_REF]. It should be noted however that some scholars have raised additional characteristics of intuitive reasoning. [START_REF] Fischbein | Intuition in science and mathematics: An educational approach[END_REF], for example, stated that intuitions are characterized by self-evidence, intrinsic certainty, immediacy, etc. Also [START_REF] Epstein | Demystifying Intuition: What it is, what it does, and how it does it[END_REF] cognitive-experiential self-theory gives a prominent role to humans affect in intuitive reasoning (e.g., [START_REF] Epstein | Demystifying Intuition: What it is, what it does, and how it does it[END_REF].

The Present Study

In the present study we examined whether the natural number bias has an intuitive character, starting from the dual process claim that intuitive responses take less time than analytical responses. As we noted, previous studies using chronometric comparisons of different response types already found that answering correctly on congruent items takes less time compared to answering correctly to incongruent items (e.g., [START_REF] Babai | Intuitive rules in science and mathematics: A reaction time study[END_REF][START_REF] Vamvakoussi | Naturally biased? In search for reaction time evidence for a natural number bias in adults[END_REF]. Relying on dual process assumptions that differentiate between intuitive and analytic processes, this suggested that the process in which the natural number bias manifests itself can be characterized as intuitive (e.g., [START_REF] Van Hoof | Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks[END_REF].

The present study aimed to address several shortcomings of previous work. First, by experimentally manipulating the allotted response time, we looked for causal evidence for the intuitive nature of the natural number bias. The advantage of using time restriction is that it does not only allow us to investigate whether longer reaction times are found on correctly solved incongruent compared to congruent trials; it also allows to investigate whether more intuitive responses are given on a fraction comparison task under time restriction compared to when participants have all the time they need to solve the fraction comparisons. Compared to purely chronometric comparisons, this experimental manipulation has the advantage that it may yield stronger evidence for the intuitive character of the natural number bias [START_REF] Gillard | Dual processes in the psychology of mathematics education and beyond[END_REF].

Second, an additional limitation of correlational reaction time studies is that one can reasonably assume that participants, for example in high demanding classroom cultures (classrooms in which students feel the pressure to have the highest possible accuracy level on all tests given), may take much more time than actually needed to solve the items, just to be sure that their answers are correct (e.g., double-checking the answer). This behavior can sometimes lead to very long reaction times, noisy data (as not all learners may show this behavior to the same extent, and time needed for double-checking may vary between learners) and ceiling levels in accuracy on all types of items, masking possible effects such as the natural number bias. To check whether this was the case in the present study, we analyzed the data of the participants who scored ceiling levels (100% accuracy) both on congruent and incongruent items separately to investigate whether a time restriction would lead to similar results as compared to the whole sample.

Third, as far as we know, previous studies used time restriction based on median reaction times calculated on group level to investigate intuitive responses (e.g., [START_REF] Gillard | Dual processes in psychology of mathematics education and cognitive psychology[END_REF]. This might be problematic, given that large individual differences are found in people's cognitive processes and general reaction speed (e.g., [START_REF] Friedman | Individual differences in executive functions are almost entirely genetic in origin[END_REF].

Therefore, in the present study optimal time restriction was calculated for each participant separately based on the median reaction time each individual needed to correctly solve congruent items during the first measurement point.

Research Questions

The present study addressed four research questions. The first research question was whether we could find the natural number bias in participants' accuracy and reaction time data when there is no time restriction (= research question 1). Our hypothesis was that the natural number bias would be found in participants' reaction time (longer reaction times on correctly solved incongruent items compared to correctly solved congruent items), but not in their accuracy: given that our sample comprised adults, high accuracies were expected both on congruent and incongruent items [START_REF] Vamvakoussi | Naturally biased? In search for reaction time evidence for a natural number bias in adults[END_REF][START_REF] Van Hoof | Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks[END_REF][START_REF] Vosniadou | International handbook of research on conceptual change[END_REF]. As a result, the natural number bias could be reasonably expected only in participants' reaction time data. As stated above, we will separately investigate whether a natural number bias can be found in the reaction times of the subgroup of participants who scores 100% on all items at time 1.

The second research question of the present study was whether the natural number bias has an intuitive character (= research question 2). According to the dual-process perspective, when there is limited time to answer to a certain task, the analytical reasoning process will be less likely to intervene, leading to more intuitive responses compared to when there is no time restriction. Therefore, we hypothesized that if the natural number bias has indeed an intuitive character, restricting responding time would lead to an increase in intuitive natural-number based answers and thus in a decrease in correct answers on incongruent items, while correct answers to congruent items would not, or at least significantly less, be affected since intuitive responding leads a learner to the correct answer in such items. As with research question 1, we will also investigate whether evidence for the intuitive character of the natural number bias can be found in the subgroup of participants who scores 100% on all items at time 1.

Conditionally on the confirmation of the second hypothesis, a third research question was whether participants would detect a conflict between their intuitive natural number Results indicate that incorrect responders typically take slightly longer to answer the incongruent versus congruent problems. We applied the same logic in our fraction task to explore participants' fraction error sensitivity. By comparing participants' reaction times on correctly solved congruent items and incorrectly solved incongruent items, we tried to shed light on this research question. If the reaction time on incorrectly solved incongruent items is comparable to congruent items, this would mean that no conflict detection has taken place and the error goes unnoticed. On the contrary, if the reaction times on incorrectly solved incongruent items are higher than on correctly solved congruent items, this points to some minimal conflict sensitivity.

A fourth and final research question concerned the nature of this conflict detection process. If conflict sensitivity is observed, does it result from analytic thinking or not? (= research question 4). Given that we collected data under time restriction, we were able to answer this question. As explained above, the time restriction gave participants enough time to respond, but not enough time for analytical processes to take place. Therefore, if the reaction times on incorrectly solved incongruent items are still higher than on correctly solved congruent items even under time pressure, this would not only indicate that the participants detect conflict, but that this conflict detection has an intuitive nature. If people detect conflict because of an analytic reasoning process, we would not expect to observe it under time restriction.

Method

Participants.

Since our study required that participants had a good understanding of fractions, we decided to collect data with adults. In total, 55 Flemish adults volunteered to participate in this study (mean age = 26,85 years, SD = 7,62). Thirteen participants were pre-service teacher students in their second year of their three-year bachelors studies. These students had already followed a course on the conceptual knowledge of rational numbers. The other 42 participants were adult volunteers with at least a bachelor's degree and with various study backgrounds and ages. Of course, all participants were taught extensively about rational numbers during their schooling career in elementary and secondary education. As can be seen in Figure 1, at time 1, when there was no time restriction to respond to the fraction comparison items, the accuracy levels were very high (mean accuracy of 98,05% on congruent and 95,58% on incongruent items), indicating a good understanding of the numerical size of fractions. All participants signed informed consent and data were collected according to the ethical guidelines of the University of Leuven.

Materials.

To investigate people's processing of the magnitude of fractions participants solved a fraction comparison task (further abbreviated with FCT), which consisted of 70 fraction comparison items. Every item contained two fractions that were shown simultaneously on a computer screen, using the E-prime software. Participants had to select the fraction with the largest numerical size, by pressing the corresponding key on the keyboard, i.e. 'f' if the largest fraction appeared on the left side of the screen and 'j' if the largest fraction appeared on the right side of the screen. Participants were encouraged to answer as accurately and quickly as possible. To investigate the presence of a natural number bias, a distinction was made between congruent and incongruent items. Congruent items are items in which natural number based responding leads to a correct answer, while incongruent items are items in which natural number based responding leads to an incorrect answer. In total, there were 14 congruent items; i.e. items where the two fractions had the same denominator (e.g., 6/13 vs 9/13; 9/13 is larger than 6/13 just like 9 is larger than 6), 14 incongruent items;

i.e. items where the two fractions had the same numerator (e.g., 8/11 vs 8/17, 8/11 is larger than 8/17 although 11 is smaller than 17) and 42 buffer items where the two fractions had no common components (e.g. 11/23 vs 18/31).

It should be noted that all buffer items can be defined as congruent (e.g., 11/23 vs 18/31) or incongruent (e.g., 14/25 vs 18/31) with natural number reasoning. However, recent studies (see for example Gomez, Silva, & Dartnell, 2017) showed that a subgroup of learners use the strategy of 'gap thinking' when solving fraction comparison tasks, namely comparing the absolute difference between numerator and denominator in both fractions and concluding that the largest fraction is the one with the smallest difference. The gap strategy has a different effect on fraction comparison tasks with and without common components: while the gap strategy always leads to the correct answer in fractions with common components, this is not the case for fractions without common components. More specifically, for fraction comparison tasks without common components, all incongruent tasks can be solved accurately with the gap thinking strategy, while this is not true for congruent fraction comparison tasks without common components. Some of these latter tasks can be solved accurately with the gap thinking strategy, while others can not. For example, for the congruent item "28/43 vs 18/37" gap thinking will lead one to choose the correct alternative, but for another congruent item such as "11/23 vs 18/31" gap thinking will lead one to choose the incorrect alternative. Given this different effect of gap strategy use on distinct tasks without common components, we considered them as buffer items, the goal of which was to minimize possible learning effects during the test.

The FCT item set was further controlled for the distance effect (the mean distance between fractions in each type of comparison tasks was comparable; all between 0,153 and 0,176), benchmarking to 0 (fractions were all above 0,2), benchmarking to 1 (fractions were all below 0,8), benchmarking to 1/2 (in each type of fraction comparison task half of items were characterized by the fact that both fractions were on the same side of 1/2 (both below or above 1/2), while the other half were characterized by the fact that one fraction was below 1/2 and one fraction was above 1/2). Moreover, in half of the items, the largest fraction was on the left side of the screen, while in the other half the largest fraction was on the right side of the screen. At last all fractions were below 1 and no simplifiable fractions were included.

Participants solved the FCT twice. Since the FCT is a quite demanding task and we wanted to control for a possible learning effect, participants were tested on two different days, with at least 1 week in between. During the first testing day, there was no time Participants were informed that, with each trial, a countdown clock on the computer screen would indicate how much time they still have left to answer. If no response was given within the available time or if a response was given only given after the time limit, this trial was not included in the data analysis.

Results

To answer the first research question, a paired samples t-test was conducted comparing participants' accuracy scores on congruent versus incongruent items when there was no time restriction. Although accuracy was generally very high, a significant difference in the expected direction was found in the scores on congruent (M= 98.05%; SD= 3.37) and incongruent items (M=95.58%, SD= 7.59); t(54)= 2.31, p= .03, d= 0.31. If we looked at the individual accuracies, we saw that there were 27 participants (49%) who got perfect accuracy scores (100%) both on congruent and incongruent items and show no natural number bias at all in their accuracy scores when there was no time restriction. As stated above, it might have been that this subgroup of participants took more time than needed to compare the fractions, just to be sure that they answered correctly, which could have led to very long reaction times and noisy data. We analyzed the reaction time data and the effect of time restriction on this subgroup separately (see below).

Next, we looked at participants' reaction times. Participants' median latencies were used, given that these are less affected by outliers. To investigate whether a natural number bias could be found in participants' median reaction times on correctly solved trials, a paired samples t-test was conducted. When there was no time restriction, significantly lower median reaction times were found on correctly solved congruent items (M= 2492 ms; SD= 1204) compared to correctly solved incongruent ones (M= 4090 ms, SD= 4651); t(54)= -2.56, p= .01, d= 0.35. The same result was found in the subgroup of participants who showed no natural number bias (i.e., those who had ceiling accuracy levels both on congruent and incongruent items) in their accuracy levels when there was no time restriction. Also in this group (n=27), a significant difference could be found in the median reaction times between correctly solved congruent items (M= 2063 ms; SD= 579) and correctly solved incongruent ones (M= 2868, SD= 1129); t(26)= -5.69, p < .001, d= 1.09.

To answer the second question, we looked, first, whether time restriction led to an increase in natural-number based answers and thus in a decrease in correct answers on incongruent items, and, second, whether correct answers to congruent items were not, or at least significantly less, affected by the time restriction since intuitive reasoning leads a learner to the correct answer in such items. In the following analysis on participants'

processing times, all trials where no response was given were removed from the data analysis (n= 80, 5,2% of total trials). First, a paired samples t-test was conducted to compare participants' accuracy scores on the incongruent items without and with time restriction. As expected, significant higher accuracy levels on the incongruent items were found when there was no time restriction (M= 95.58%; SD= 7.59), compared to when there was a time restriction to solve the FCT (M= 76.34%, SD= 18.23); t(54)= 7.69, p < .001, d= 1.04. Second, we investigated the effect of the time restriction on congruent items. A paired sample t-test was conducted to compare participants' accuracy scores on the congruent items without and with time restriction. Significant higher accuracy levels on the congruent items were found when there was no time restriction (M= 98.05%; SD= 3.75), compared to when there was a time restriction (M= 89.73%, SD= 9.49); t( 54 Next, we zoomed in on the data of the 27 participants who scored ceiling levels at time 1 both on congruent and incongruent items separately, to investigate whether a time restriction would also in this group lead to a larger performance decrease on incongruent than on congruent items. First, a paired sample t-test showed significant higher accuracy levels on incongruent items when there was no time restriction (M= 100%; SD= 0), compared to when there was a time restriction (M= 76.11%; SD= 18.36); t(26)= 6.76, p < .001, d= 1.30.

Second, a paired sample t-test showed that also on congruent items significant higher accuracy levels could be found when there was no time restriction (M= 100%; SD= 0), compared to when there was a time restriction (M= 90.07%; SD= 8.77); t(26)= 5.89, p < .001, d= 1.13. Results showed that scores decreased significantly more on incongruent (mean difference score = 23.89, SD= 18.36) versus congruent items (mean difference score = 9.93, SD= 8.77) under time restriction; t(26)= -4.05, p < .001, d = .78.

We were unable to answer the third research question, given the ceiling levels when there was no time restriction on both congruent and incongruent items (only six participants made more than one mistake). Since there were lower accuracy levels under time restriction, we were however still able to look whether there was a conflict detection, and moreover, which nature this possible conflict detection had in fraction comparison tasks (research question 4). As previously explained, the time restriction gave participants enough time to respond, but not enough time for analytical processes to take place. Therefore, if the reaction times on incorrectly solved incongruent items would be significantly higher than on correctly solved congruent items, this would not only indicate that the participants detected conflict, but that this conflict detection had an intuitive nature. Logically, only participants who made mistakes on incongruent trials were included in the data analysis. Results showed a significant difference in the reaction times on correctly solved congruent (M= 1364; SD= 526) and incorrectly solved incongruent items (M=1575, SD= 1059); t(49)= -2.28, p = .03, d= 0.32, when there was a time restriction, indicating the intuitive nature of the conflict detection.

Discussion

The main purpose of the present study was to provide causal evidence for the fact that the natural number bias has an intuitive character. Previous studies [START_REF] Obersteiner | The natural number bias and magnitude representation in fraction comparison by expert mathematicians[END_REF][START_REF] Vamvakoussi | Naturally biased? In search for reaction time evidence for a natural number bias in adults[END_REF], Van Hoof et al., 2013) already showed that adults need more time to correctly solve fraction tasks that are not in line with their knowledge of natural numbers compared to fraction tasks in which natural number responding leads to a correct answer. These findings already gave some indication that analytical processes might be needed to correctly solve incongruent items, or, in other words, that the process in which the natural number bias manifests itself can be characterized as intuitive. An important limitation of these previous studies however was their correlational nature. Although it was found that longer reaction times are accompanying correctly solved incongruent compared to correctly solved congruent fraction tasks, this does not necessarily imply that longer processing times are necessary to correctly solve incongruent items. In other words, this does not provide causal evidence for the intuitive character of the natural number bias [START_REF] De Neys | Dual processing in reasoning: Two systems but one reasoner[END_REF]. The present study addressed this limitation using the experimental manipulation of time restriction. Four research questions were raised.

In the first question we looked for traces of the natural number bias in learners' accuracy and reaction time data when there was no time restriction. A clear indication for the natural number bias was found both in participants' accuracy levels and in their reaction time data at time 1. In general, participants had significantly higher accuracy levels on congruent compared to incongruent fraction comparison tasks. However, about half of them had perfect accuracy on both task types. Further, participants took significantly more time to correctly solve incongruent compared to congruent fraction comparison tasks, and this was also the case for participants with perfect accuracy, showing traces of the natural number bias.

The second research question was about the intuitive nature of the natural number bias. Results showed that time restriction at time 2, or in other words, excluding the involvement of analytical reasoning processes, led to a general decrease of accuracy levels, both on congruent and incongruent items. However, importantly, it was found that participants' accuracy levels decreased significantly more on incongruent items than on congruent items under time restriction, showing the intuitive character of the natural number bias. A strength of the current study was that, by including the time restriction, we provide experimental evidence for the former correlational result. Time restriction also allowed to control for the fact that some effects (like the natural number bias) might be masked in participants who take much more time than actually needed to compare fractions, just to be sure that their answers are solved correctly. We checked whether this was the case by separately analyzing the data of the participants who scored perfectly both on congruent and incongruent items at time 1. Results show that also in this subgroup a time restriction led to a larger performance decrease on incongruent items compared to congruent items. So, while in previous correlational studies, and also in our data without time restriction, no effect of the natural number bias could be found in these participants' accuracy scores (only in their reaction time data), a clear natural number bias could be found in their accuracy scores under time restriction.

High accuracy levels in the condition without time restriction made the data from this condition useless for answering the question whether participants detect a conflict between their intuitive natural number based answer and the correct answer when they incorrectly solve an incongruent fraction comparison item (question 3). However, the data of the condition with time restriction still allowed us to answer this question, as well as the fourth research question about the nature of this conflict detection process. Results showed that participants not only experienced a conflict detection, but moreover that this conflict detection was possible when analytic reasoning was experimentally "knocked out". That is, even under time restriction we observed significant faster reaction times on correctly solved congruent compared to incorrectly solved incongruent items. So, even when experimentally preventing people from reflecting by using analytical reasoning processing (through the use of time restriction), the present study showed that they still experience a conflict and notice that something is wrong (they are still slower on wrongly answered incongruent trials compared to correctly answered congruent trials). This indicates that the conflict detection process is intuitive and not analytic in nature. Interestingly, this fits with conflict detection studies in the reasoning field that also observed that even after experimentally eliminating analytical T2 reasoning (e.g. by time restriction) conflict detection is still preserved (e.g., De

Neys, 2017; [START_REF] Johnson | The doubling system 1: Evidence for automatic substitution sensitivity[END_REF]. In other words, although somewhat speculative, our data suggest that two competing intuitions are cued when adults are solving fraction comparison tasks. First, there is an intuition of number that shares the properties of natural numbers, while second there is an intuition of number that shares the properties of rational numbers and is therefore closer related to the mathematically correct idea of number.

This result is in line with the 'hybrid model' within the dual process literature, which is a recent revision of the traditional default interventionist model [START_REF] De Neys | Bias, conflict, and fast logic: Towards a hybrid dual process future[END_REF]. While the default interventionist model assumes that conflict detection takes place through analytical system 2 intervention, the hybrid model postulates that conflict detection can also occur intuitively as resulting from two competing intuitions (e.g., [START_REF] Bago | Fast logic? Examining the time course assumption of dual process theory[END_REF][START_REF] Pennycook | What makes us think? A three-stage dualprocess model of analytic engagement[END_REF] . For example, Pennycook et al. (2015, p. 34) state that "multiple Type 1 processes may be cued by a stimulus (Stage 1), leading to the potential for conflict detection (Stage 2). If successful, conflict detection leads to Type 2 processing (Stage 3), which may take the form of rationalization (i.e., the Type 1 output is verified post hoc) or decoupling (i.e., the Type 1 output is falsified)". The finding of two kinds of intuitions is moreover in line with [START_REF] Fischbein | Intuition in science and mathematics: An educational approach[END_REF] work on primary and secondary intuitions. Primary intuitions are developed independently of instruction, but through personal experience.

However, when getting instruction on the same concept, other intuitions -called secondary intuitions -may be created. In the present study the intuitive idea of number that shares the properties of natural numbers is a primary intuition, while the intuitive idea of number that shares the properties of rational numbers is a secondary intuition.

We now turn to some implications that emerge from the study. The present study

shows that after years of education (on fractions) people still sometimes make (natural number based) mistakes on fractions, but, at the same time, also intuitively activate the correct fraction knowledge. However, the natural number based intuition might be stronger and people might not always be able to inhibit the intuitive natural number based answer.

This implies that inhibitory processes might play an important role in the understanding of fractions. In recent years, there is a promising and rapidly growing research field on the role of inhibition, i. (specific components of) mathematics, such as fraction understanding, uninvestigated [START_REF] Gilmore | The role of cognitive inhibition in different components of arithmetic[END_REF][START_REF] Van Dooren | Inhibitory control in mathematical thinking, problem solving and learning [Special issue[END_REF]. Future research is needed to investigate the possible crucial role of inhibitory control in learners' fraction understanding.

Further, since rational number understanding is skill-based and a clear difference can be found in the understanding of fractions of novices and educated adults, future research should investigate whether the same pattern of results can also be found in elementary school children who are starting their instruction in the rational number domain.

As stated by [START_REF] Gillard | Dual processes in the psychology of mathematics education and beyond[END_REF], the dual-process framework was not developed with the aim to have large implications for (mathematics) education. However, this theoretical framework and its methodologies may reveal important insights for (mathematics) education. There is a crucial difference between mistakes coming from a learners' misconception on the subject and a mistake coming from an intuitive response (e.g., [START_REF] Gillard | Dual processes in the psychology of mathematics education and beyond[END_REF][START_REF] Leron | Intuitive vs analytical thinking: Four perspectives[END_REF]. Learners' tendency to over-use natural number based strategies to solve fraction tasks calls for a different instructional approach when this tendency is caused by the misconception that rational numbers follow the same rules as natural numbers or when the origin of the tendency is that learners do have a good understanding of fractions but are unable to inhibit their intuitive natural number reasoning.

In the former case, much more consideration should go to address learners' misconceptions of rational numbers, with clear attention given to both the similarities, but also the differences between natural and rational numbers. In the latter case, learners should be made aware of their natural number based intuitions and more attention should go for example to taking time to double-check the answer.

  based answer and the correct answer when they fail to compare an incongruent fraction comparison item correctly (= research question 3). Dual process studies on logical reasoning have indicated that reasoners whose logical inferencing is "biased" by erroneous intuitions often show some minimal error or conflict sensitivity (e.g., De[START_REF] De Neys | Conflict monitoring in dual process theories of reasoning[END_REF][START_REF] Frey | Individual differences in conflict detection during reasoning[END_REF]; see De Neys, 2014, for a review). For example, these studies typically contrast processing latencies on incorrectly solved incongruent items and correctly solved congruent items. If reasoners do not detect that their incorrect responses to incongruent tasks conflicts with the logically appropriate response, their processing time should not differ from the congruent problems on which there is, by definition, no conflict.

  restriction. During the second testing day, a time restriction was applied. Optimal time restriction was calculated for each individual separately, based on the median reaction time (s)he needed to correctly solve congruent items (where intuitive reasoning leads to the correct answer) during the first measurement point. Large individual differences were found in participants' median reaction time needed to correctly solve congruent items at time 1 (Mean = 2492.85, SD = 1204.38, range: 6319.50; measured in milliseconds).

  )= 6.40, p < .001, d= 0.86. Third, we investigated whether the effect of the time restriction was different for congruent compared to incongruent items. A paired samples t-test was conducted comparing participants' accuracy decrease between the condition without time restriction (T1) and the condition with time restriction (T2) on congruent (accuracy congruent items T1 -accuracy congruent items T2) versus incongruent items (accuracy incongruent items T1 -accuracy incongruent items T2). Results showed that the accuracy decrease under time restriction was significantly larger on incongruent (mean difference score = 19.25, SD= 18.57) than on congruent items (mean difference score = 8.32, SD= 9.64); t(54)= -4.33, p < .001, d = .58 (see Figure1).

Figure 1 :

 1 Figure 1: Participants' accuracy scores on congruent (CO) and incongruent (IC) items without time restriction (T1) and with time restriction (T2). Vertical stripes indicate the mean score.

  e. the capability to suppress unnecessary distracting information and undesirable answers, as a critical aspect of learners' cognition and development. Research on the role of inhibition is moreover especially important in the research field of cognitive psychology and mathematics (see the special issue 'Inhibitory control in mathematical thinking, problem solving and learning'[START_REF] Van Dooren | Inhibitory control in mathematical thinking, problem solving and learning [Special issue[END_REF]). However, until now, the notion of inhibition was mostly investigated in relation to mathematics achievement in general using correlational studies, leaving the causal relation between inhibition and

Acknowledgements

Jo Van Hoof holds a post-doctoral fellowship of the Research Foundation-Flanders (FWO).

Notes

The data of the experiment is available from the corresponding author. The experiment was not preregistered.


Romnick B Unabia
email: romnickunabia@gmail.com

Simon Bonebeau

Rolando T Candidato

Jenny Jouin

Olivier Noguera

Lech Pawłowski

Investigation on the structural and microstructural properties of copper-doped hydroxyapatite coatings deposited using solution precursor plasma spraying

Keywords: copper-doped hydroxyapatite, solution precursor plasma spray, microstructure investigation, interstitial insertion

Structural and microstructural investigation on solution precursor plasma sprayed copperdoped hydroxyapatite (Cu-HA) coatings with0, 3, 5 and 10 weight percent (wt.%) of Cu dopant concentration is presented. Scanning electron micrographs show no significant morphological changes at the surface and cross-section of the coatings as copper content increases. X-ray diffraction results show decreases in the HA phase content from 93% to 14% and degree of crystallinity form 94% to 85% along with the increase of impurity phases upon increasing the copper concentration. RAMAN and IR spectra depicted broadening and red-shifting of the phosphate bands due to the distortion of the HA structure induced by the insertion of the copper ions into the HA lattice. X-ray photoelectron spectroscopy results identified that the copper species incorporated in HA structure was Cu + and Cu 2+ ions. Incorporation of copper ions into HA was associated to an interstitial insertion along hexagonal channel of the HA structure which leads to the increase in the lattice a parameter and expansion of the unit cell volume observed in Rietveld refinement measurements. The insertion was induced by the dehydroxylation process of HA due to the high temperatures of the plasma jet. Furthermore, the dopant concentration limitation in order to maintain the dominance of HA phase in the coating is 5 wt.% of Cu.

INTRODUCTION

The occurrence of implant associated infection has been one of the major problems in biomedical application [START_REF] Campoccia | The significance of infection related to orthopedic devices and issues of antibiotic resistance[END_REF][START_REF] Radovanovic | Antimicrobial activity and biocompatibility of Ag + -and Cu 2+ -doped biphasic hydroxyapatite/α-tricalcium phosphate obtained from hydrothermally synthesized Ag +and Cu 2+ -doped hydroxyapatite[END_REF][START_REF] Shanmugan | Copper-substituted hydroxyapatite and fluoroapatite: synthesis, characterization and anti-microbial properties[END_REF]. Hence, development of novel implants with inherent antibacterial capability is highly needed. This capability may be developed by the addition of metal ions to hydroxyapatite, Ca10(PO4)6(OH)2, (HA). The latter has been one important biomaterial for implants due to its biocompatibility and bioactivity [4-Erreur ! Source du renvoi introuvable.]. HA has an advantage of having a flexible structure that provides good absorption matrix for other ions in its lattice to add some biofunctionality such as antibacterial capability [START_REF] Shanmugan | Copper-substituted hydroxyapatite and fluoroapatite: synthesis, characterization and anti-microbial properties[END_REF][START_REF] Shi | Introduction to Biomaterials[END_REF][START_REF] Gomes | Cu-doping of calcium phosphate bioceramics: From mechanism to the control of cytotoxicity[END_REF][START_REF] Stanic | Synthesis, characterization and antimicrobial activity of copper and zinc-doped hydroxyapatite nanopowders[END_REF].

This present study focuses on the incorporation of copper ions to HA as it exhibits antibacterial characteristics, and has been found out to have pro-angiogenic potential, i.e. the ability to stimulate the formation of new blood vessels which increases the viability of boneforming cells into implants [START_REF] Gomes | Cu-doping of calcium phosphate bioceramics: From mechanism to the control of cytotoxicity[END_REF][START_REF] Stanic | Synthesis, characterization and antimicrobial activity of copper and zinc-doped hydroxyapatite nanopowders[END_REF][START_REF] Sen | Copperinduced vascular endothelial growth factor expression and wound healing[END_REF][START_REF] Imrie | Preparation of Copper-doped Hydroxyapatite with varying x in the composition Ca10(PO4)6CuxOyHz, Bioceram[END_REF][START_REF] Kim | Antimicrobial effects of metal ions (Ag + , Cu 2+ , Zn 2+ ) in hydroxyapatite[END_REF][START_REF] Lyasnikova | Comprehensive characterization of plasma-sprayed Coatings based silver-and copper-substituted Hydroxyapatite[END_REF][START_REF] Mariappan | Structural, Optical and Antimicrobial Activity of Copper and Zinc Doped Hydroxyapatite Nanoparticles using Sol-Gel Method[END_REF]. However, the utilization of Cu is potentially toxic to humans if exceeds certain amounts [START_REF] Li | Antibacterial efficacy and cytotoxicity studies of copper (II) and titanium (IV) substituted hydroxyapatite nanoparticles[END_REF][START_REF] Stern | Essentiality and toxicity in copper health risk assessment: overview, update and regulatory considerations[END_REF]. Aside from that, incorporation of other ions in the HA structure bring about structural change which then could influence its physico-chemical properties [START_REF] Shanmugan | Copper-substituted hydroxyapatite and fluoroapatite: synthesis, characterization and anti-microbial properties[END_REF][START_REF] Stanic | Synthesis, characterization and antimicrobial activity of copper and zinc-doped hydroxyapatite nanopowders[END_REF][START_REF] Candidato | Advanced microstructural study of solution precursor plasma sprayed Zn doped hydroxyapatite coatings[END_REF].

In our previous paper [START_REF] Unabia | Preliminary Study on copperdoped hydroxyapatite coatings obtained using solution precursor plasma spray process[END_REF], we presented the optimization of spray parameters to obtain Cu-HA coatings using SPPS process. The present contribution focuses on the structural and microstructural influence of various copper ion concentration in the HA matrix. Moreover, the possible mechanism on the incorporation of Cu ion into the HA structure will also be discussed in this study.

Experimental details

Solution preparation

For the preparation of Cu-doped calcium phosphate solution, copper nitrate trihydrate (Cu(NO3)2・3H2O,Scharlau Lab., Barcelona, Spain, 99.5% purity) was used as copper ion source, calcium nitrate tetrahydrate (Ca(NO3)2.4H2O, Scharlau Lab., Barcelona, Spain, 99% purity) as calcium ion source and triethylphosphite (P(OEt)3, Sigma Aldrich, Saint-Louis, Missouri, USA, 97.5 % purity) as phosphorous ion source. Deionized water was used as solvent in all preparations. After dissolving the Ca and Cu ions precursors, the solution was thoroughly mixed first using magnetic stirring before adding the hydrolyzed tri-ethyl phosphite solution as P ions precursor. The possible synthesis mechanism of all chemical precursors was discussed elsewhere [START_REF] Unabia | Preliminary Study on copperdoped hydroxyapatite coatings obtained using solution precursor plasma spray process[END_REF]. The stoichiometry of final solution precursor was maintained to have atomic ratio [(Ca + Cu)/P] = 1.67. Finally, the mixed solution were continually stirred for 24 hours and left at ambient temperature for 5 days before plasma spraying. The samples' codes according to Cu concentration are pure HA for 0 wt.% Cu, 3% Cu-HA for 3 wt.% Cu, 5% Cu-HA for 5 wt.% Cu and 10% Cu-HA for 10 wt.% Cu.

Plasma spray parameters

SG-100 torch (Praxair S.T., Indianapolis, IN, USA) mounted on a 6-axis ABB IRB 140 industrial robot (Zürich, Switzerland) was used for plasma spraying of Cu-HA coatings. Argon gas with flow rate of 45 slpm (standard liter per minute) and hydrogen gas with flow rate of 5 slpm were used as primary and secondary gases, and were kept constant throughout all spraying experiment. The flow rate of solution was equal to 53 mL/min. The solution was injected into the plasma jet using mechanical injection system using an external injector (nozzle) with diameter of 0.3 mm. The injector was set under the angle of 30 o backwards with respect to the torch axis. The substrate used were stainless steel cylinders (ϕ = 25 mm, thickness = 3.0 mm). They were sandblasted using F36 alumina sand. The spraying distance was 50 mm. A rectangular spray pattern with 3.0 mm off-set distance after each spray scan at a speed of 500mm/s was used to spray. The temperature at the surface of the sprayed coating was monitored using Impac IN 5 pyrometer (LumaSense Technologies, Santa Clara, California, USA).

Coatingscharacterization

The morphological features of the as-deposited Cu-HA at the surface and cross-section were observed using JEOL JSM-IT300LV (Massachusetts, USA) scanning electron microscope (SEM).

X-ray diffraction measurements were performed using a Bragg Brentano D8 Advance (Brucker, Massachusetts, USA) diffractometer with CuKα radiation. The scans were performed in the range of 20° to 70° (2θ), with a step increment of 0.014°. The measured diffractograms were analyzed using Diffrac+EVA software with the JCPDS-ICDD database for the crystalline phase identification. TOPAS v.4.2 [START_REF] Bruker | TOPAS V4.2: General Profile and Structure Analysis Software for Powder Diffraction Data[END_REF] software was used to estimate the relative amount (wt.%) of the crystalline phases present in the coating. The degree of crystallinity of the coating were determined using the following equation 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝑐𝑟𝑦𝑠𝑡𝑎𝑙𝑙𝑖𝑛𝑖𝑡𝑦, % = 𝐼 (300) -𝑉 ( 112 300 ⁄ ) 𝐼 (300) × 100% (Eq. 1)

where𝐼 (300) is the intensity at (300) peak and 𝑉 ( 112 300

⁄

) is the intensity of a valley between (112) peak and (300) peak [START_REF] Landi | Densification behaviour and mechanisms of synthetic hydroxyapatites[END_REF][START_REF] Unabia | Synthesis and characterization of nanocrystalline hydroxyapatite and biphasic calcium phosphate using Ca(OH)2 and (NH4)H2PO4[END_REF].

The average crystallite sizes of the coatings are calculated using Williamson-Hall plot method given in equation 2:

𝛽 cos 𝜃 𝜆 = 𝜀 ( 2sin 𝜃 𝜆 ) + 1 𝜏 (Eq. 2)
Where β is the integral broadening of the peaks in radians, θ is the Bragg angle, λ is the wavelength of the radiation, τ is the effective crystallite size and ε is the effective strain [START_REF] Unabia | Synthesis and characterization of nanocrystalline hydroxyapatite and biphasic calcium phosphate using Ca(OH)2 and (NH4)H2PO4[END_REF][START_REF] Williamson | X-ray line broadening from filed aluminum and wolfram[END_REF]. The planes used for the calculations are (002), (211), (112), (300), (202), (310), ( 222) and

(213).

Due to the abundant presence of peaks, the unit cell refinement of the HA phase was performed using a full pattern matching with the Rietveld method [START_REF] Unabia | Synthesis and characterization of nanocrystalline hydroxyapatite and biphasic calcium phosphate using Ca(OH)2 and (NH4)H2PO4[END_REF] using JANA 2006 software [START_REF] Petricek | Crystallographic computing system JANA2006: general features[END_REF]. In all cases, the refinements were performed using the phases observed including the impurities present in the samples. The structural models used for the refinement of the coatings' phases are listed in Table 1. In every case, the continuous background was modeled with a 10 terms Legendre polynomial function and the vertical position of the sample was refined. The peak profiles were represented by pseudo-Voigt functions. The cell parameters and profile parameters of the main phases were refined, while the cell parameters of the impurities were kept to their original values and their profile parameters were set to reasonable values and not refined.

Table 1. Structural models used for Rietveld refinements.

Phases Powder

Diffraction File

No.

Name and notation in paper

Chemical

Formula

Hydroxyapatite,(HA) Ca10(PO4)6(OH)2 09-0432 [START_REF] Wolff | The Netherlands, ICDD Grant-in-Aid[END_REF] Alpha-tricalcium phosphate,(α-TCP)

Ca3(PO4)2 09-0348 [START_REF] Wolff | The Netherlands, ICDD Grant-in-Aid[END_REF] Tetracalcium phosphate (TTCP) Ca4P2O9 25-1137 [START_REF][END_REF] Calcium copper phosphate (CCP) Ca19Cu2(PO4)14 46-0403 [START_REF] Lazoryak | Moscos State University[END_REF] Calcium oxide (Lime) CaO 37-1497 [START_REF] Mcmurdie | [END_REF] Copper oxide (Tenorite) CuO 48-1548 [START_REF] Langford | High-resolution powder diffraction studies of copper (II) oxideJ[END_REF] The infrared characteristicsof the Cu-HA coatings were determined by Attenuated Total Reflectance -Fourier Transform Infrared (ATR-FTIR) spectroscopy using Nicolet 6700 (Thermofisher, Massachusetts, USA) spectrometer with a scan range at 4,000-400 cm -1 infrared spectral region having 2 cm -1 resolution over 32 scans. All experimental runs were conducted at room temperature and the reflection data were converted into absorption mode.

The experimental Raman spectra of the coatings were recorded at room temperature using an Invia Reflex Renishaw (Wotton-under-Edge, United Kingdom) Raman spectrometer equipped with a laser diode (λ=785 nm, 30 mW) in a backscattering geometry using a 100x objective lens. Prior to measurement, the spectrometer was calibrated with a standard silicon sample. The scattered photons from the sample were dispersed in a 1200 lines/mm grating and collected at the same time on a charge coupled device camera detector. The spectra were obtained in the 75-1200 cm -1 spectral range using a microprobe spot size of 2.0 µm and spectral resolution of 2.0 cm -1 with 10 seconds exposure time. Raman maps (400x400 µm -2 ) were collected using the SteamLine mode (each line is 40 µm long and 1 µm large) with 5 seconds exposure time and a 20x objective lens. For each map a total of 1349 spectra was collected.

The amount of Ca, P and Cu in the coatings were quantitatively measured using Optima 8300 DV Inductive coupled plasmaatomic emission spectroscopy (ICP-AES) (Perkin Elmer, Wellesley, Massachusettes, USA). The coatings are first processed into a solution by dissolving the dried scraped-off coatings with nitric acid and submitted to microwave oven. The solution is then nebulized inside the chamber and is ionized by ICP torch. The photons emitted were then measured as concentration of analyzed atoms (Ca, P and Cu) in mg/L.

X-ray photoelectron spectroscopy (XPS) characterization was carried out to determine the surface chemical composition using Surface Science Instruments X-Probe and S-probe spectrometers. XPS irradiates the sample with a penetration depth of 8-10 nm using a monochromatic Al Kα X-ray sources (hν = 1486.6 eV) causing the emission of photoelectrons and Auger electrons which are identified by hemispherical analyzers and multichannel detectors. The information gathered through XPS was used in the determination of the number and kinds of atoms according to its energies in the spectral peaks.

Results

Microstructural properties of Cu-HA coatings

The surface morphology of the coatings with different Cu concentrations display the characteristic deposits of solution precursor plasma spray (SPPS) process (see Figure 1) which shows agglomerated and melted particles with fine spherical particles (less than 1 µm sizes).

The surface of the coatings revealed a cauliflower-like morphology. Relatively dense microstructure with cone-tip defect and micropores were observed at the cross-section of Cu-HA coatings. There are no particular changes of the coatings' microstructures with the copper concentration.

Pure HA 3% Cu-HA

Phase identification of the coatings

The XRD diagrams of the coatings were analyzed using TOPAS software to identify the crystalline phase formation during the process. The phase identification of all samples is shown in Figure . The coatings sprayed without copper dopant were mainly composed of 93 wt.% HA.

However, presence of TTCP (6 wt.%) and CaO (1wt.%) as minor impurities were observed as decomposition product of HA at high temperatures. The coatings doped with 3 wt.% Cu shows HA as the dominant phase having 88 wt.%, but with some α-TCP (9 wt.%), tenorite CuO (2 wt.%), and very small traces of CaO (<1 wt.%) were also identified. The presence of CuO in the coatings may be attributed either to the decomposition of copper nitrate precursor or the reaction of copper ions with oxygen in HA structure at high temperatures. The coating having composition of 5 wt.% Cu in the HA matrix shows the quantity of HA phase of 81 wt.%. The phases of β-TCP (9 wt.%), α-TCP (8 wt.%) and traces of tenorite (2wt.%) were also observed.

For 10% Cu-HA coating, α-TCP becomes the dominant phase with 71 wt.% while HA phase was only 14 wt.%. The phases ofβ-TCP (11 wt.%) and CaO (2 wt.%), and CuO (1 wt.%) were observed. The traces of calcium copper phosphate CCP phases were observed at high dopant concentration. The latter will not be considered in further discussion. The calculation of the degree of crystallinity shows values in decreasing order from 94% for pure HA, 90% for 3%Cu-HA and 85% for 5%Cu-HA which correlates to the increasing

Pure HA

presence of impurities that could distort the HA structure. The obtained crystallinity of coatings was still suitable for biomedical applications as ISO standard requires at least 45% crystallinity for HA coatings [START_REF]International Organization for Standards, Implants for Surgery -Hydroxyapatite. Part 2: Coatings of Hydroxyapatite[END_REF]. The average crystallite sizes obtained using Williamson-Hall method were equal to 100 nm for pure HA, 118 nm for 3% Cu-HA and 83 nm for 5% Cu-HA which lies in the size range considered as nanomaterials which mimics the biological apatite, i.e., essential for bioactivity during implantation [START_REF] Ducheyne | [END_REF][START_REF] Ferraz | Hydroxyapatite nanoparticles: A review of preparation methodologies[END_REF].

Rietveld refinement

Unit cell refinement was performed by a full pattern matching method to clarify the incorporation of copper into the HA structure using JANA 2006 software. Due to the large number of crystalline phases in the sample, the refinement was focused on the main crystalline phase. The impurities were taken into account in the calculation but their characteristics were not refined due to the small intensity of their respective peaks. The obtained results are summarized in Table , along with the parameters from bulk HA. When comparing the standard values from bulk, i.e., prepared via conventional synthesis method, the volume of the unit cell of the pure HA coating synthesized by plasma spraying was significantly lower which could be due to compressive stress induced by the substrate or the result of residual constraints from the very high temperature used during the spraying.

However, when comparing the results of the refinements for the different coatings, we can notice a clear increase of the volume of the unit cell with the addition of Cu. The expectation that Cu substitutes to Ca sites in HA structure was not probable because, if there were substitutions, the volume would tend to decrease due significant difference in the ionic radii of the two species (r(Ca 2+ )=1.00 Å and r(Cu 2+ )=0.73 Å) [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. Moreover, the lattice parameters a and c of the HA increased of very similar quantities with the addition of 3% Cu, while for 5%

Cu, the lattice parameter a seems to be the most affected. Considering these observations, copper ion is probably inserted in the HA structure in interstitial positions along the hexagonal channel. In connection to this claim, related studies on Cu-doping into HA had also described that the insertion mechanism copper ions is at the interstitial 2b Wyckoff site which leads to the formation of the linear oxocuprate O-Cu-O entities along the hexagonal channel [START_REF] Gomes | Cu-doping of calcium phosphate bioceramics: From mechanism to the control of cytotoxicity[END_REF][START_REF] Renaudin | First-row transition metal doping in calcium phosphate bioceramics: a detailed crystallographic study[END_REF][START_REF] Karpov | Synthesis, crystal structure and properties of calcium and barium hydroxyapatites containing copper ions in hexagonal channels[END_REF][START_REF] Zykin | Solid state solubility of copper oxides in hydroxyapatite[END_REF].

Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) Spectroscopy

Figure 3 shows the FTIR spectra of coatings with different copper concentrations. The bending vibration of the phosphate P-O modes at 500-600 cm -1 and the symmetric and asymmetric vibration of the phosphate at 900-1200 cm -1 were observed in all coatings. In addition, the OH of HA lattice can be observed as a shoulder peak at ~630cm -1 and the stretching vibration of OH of HA centered at 3571 cm -1 indicating the formation of the hydroxyapatite material is depicted on all coatings. Broadening and red-shifting of peaks were observed with increasing copper concentration in the coatings, signifying the presence of distortions induced by the incorporation of copper ions into the HA structure. Moreover, this could also be attributed to the increasing impurity phases in relation to the XRD results.

Figure 3: FTIR absorption spectra of SPPS HA with different copper concentration; the OH peaks (left side) were zoomed in for better observation.

Raman spectroscopy

The Raman analysis of the pure HA, 3% Cu-HA and 5% Cu-HA coatings is presented in Figure 4. In the pure HA coating spectra, the observed bands wherein the 428 cm -1 and 447 cm - 1 associated to the ν2 PO4 3-degenerate bending modes, 580 cm -1 , 590 cm -1 and 607 cm -1 attributed to the ν3 PO4 3-asymmetric bending modes, and 1029 cm -1 , 1047 cm -1 and 1076 cm -1 assigned to the ν4 PO4 3-asymmetric stretching modes indicate that HA was the main phase in the coatings. In addition, the strong band observed at 962 cm -1 corresponds to the fully symmetric stretching mode of ν1 PO4 3-.The sharpness of this band confirms the good crystallinity of HA coating [START_REF] Li | Raman spectroscopy determination of phases within thermal sprayed hydroxyapatite splats and subsequent in vitro dissolution examination[END_REF].

Raman mapping was also carried out on the coatings to find out the homogeneity of the phases present in the coating (see supplementary figures). It can be observed that the HA phase is homogeneously distributed in the coatings with minor TCP components localized in specific area in the coatings. Raman spectra of 3% Cu-HA and 5% Cu-HA coatings present the same features as pure HA. However, the main band position was slightly red-shifted and clearly broadened (see Figure 5) which implies that the modification on the HA structure takes place on the phosphate groups (PO4 3-). The measured full width at half maximum (FWHM) of the intense peak around 940-980 cm -1 associated to the ν1 PO4 3-vibrations shows significant increase having values of 7.089 cm -1 , 12.773 cm -1 and 17.027 cm -1 with increasing copper content. This broadening can be associated to the decrease of crystallinity due to the presence of other phases such as αand β-TCP. In addition, a broadening in the 622-636 cm -1 region can be attributed to the presence of Bg vibrations of tenorite CuO in the coatings [START_REF] Rashad | CuO and Co3O4 nanoparticles: synthesis, characterizations, and Raman spectroscopy[END_REF]. With increasing content of Cu, the wavenumber of the symmetric stretching of PO4 3-band decreases from 962 cm -1 down to 955 cm -1 which indicates a change in the PO4 3-surrounding implying an increase of P-O bond distances. This increase signifies expansion in the unit cell of the HA structure which correlates to the unit cell volume increase in our Rietveld refinement results. This behavior can probably be linked to the insertion of Cu atoms interstitially in the HA structure which occurs on a site in the hexagonal channel that can affect the PO4 3-groups leading to an isotropic increase in the HA unit cell volume. Previous studies described that copper ions was in the HA structure leading to the formation of linear O-Cu-O oxocuprate entities which resulted to the expansion of the unit cell volume [START_REF] Gomes | Cu-doping of calcium phosphate bioceramics: From mechanism to the control of cytotoxicity[END_REF].

Figure 5: 900-1000 cm -1 region of Raman spectra of Cu-HA

Chemical analysis by inductively coupled plasma -atomic emission spectroscopy (ICP-AES)and X-ray photoelectron spectroscopy (XPS)

ICP-AES and XPS were carried out in order to quantify the concentration of copper element and determine the electronic state of the copper species in the coatings. One can observe from Figure 6 that the copper content in the coatings was increasing with increasing copper dopant concentration which confirms a successful incorporation of copper ions into the HA structure. It should be noted that the coating was scraped off from the substrate and then subjected to ICP-AES characterization for quantitative elemental analysis. Calculation of calcium to phosphate ratio gives a value of 2.2, 2.1 and 1.9 and a calcium-copper to phosphate ratio of 2.2, 2.4 and 2.2 for pure HA, 3% and 5% Cu-HA coatings, respectively.The values obtained were non-stoichiometric, i.e., higher that 1.67, indicating the deposition of calciumrich coating. This further confirms that no copper substitution has taken place. This nonstoichiometric ratio was also attributed to the phosphorous deficiency in the coatings which was probably due to the dissociation/volatilization of P2O5 at high temperatures [START_REF] Candidato | Advanced microstructural study of solution precursor plasma sprayed Zn doped hydroxyapatite coatings[END_REF].

On the other hand, XPS (see supplementary figures) results revealed the presence of Cu 2+ cations and its corresponding satellite peaks observed at the range of 934-943 eV. Moreover, a strong peak at 932.63 eV is associated to the electronic state of Cu + attributed to the reduction of Cu 2+ at high temperatures above 1100 o C. This result confirmed that copper species inserted in the HA structure were Cu + , and Cu 2+ entities [START_REF] Gomes | Cu-doping of calcium phosphate bioceramics: From mechanism to the control of cytotoxicity[END_REF]. The SEM micrographs of the coatings show no particular changes on their morphology at the surface and cross-section upon doping of copper ions into the HA matrix. This observation was expected due to minute concentration of copper added in the solution precursor feedstock used for spraying. The morphological characteristics of Cu-HA coatings in this present work are in good agreement with the study of Candidato et al. [START_REF] Candidato | Advanced microstructural study of solution precursor plasma sprayed Zn doped hydroxyapatite coatings[END_REF] on SPPS Zn-doped HA. Similarly, insertion of the copper ions into the HA lattice distorts the crystal structure of HA which hinder its crystallization as observed with the decreasing degree of crystallinity as the copper concentration increases. Consequently, the average crystallite sizes of all coating at various copper concentration remains in the range of nanometer scale, i.e. 83 nm to 118 nm which is favorable for bone regeneration application as it mimics the dimensions of the natural bones [START_REF] Ducheyne | [END_REF][START_REF] Ferraz | Hydroxyapatite nanoparticles: A review of preparation methodologies[END_REF]. The production of nanoscale crystallite sizes can be attributed to the breaking up of the solution droplets into fine ones using SPPS process which resulted to full pyrolysis of the droplets as it penetrates into the plasma jet [START_REF] Unabia | Current Progress in Solution Precursor Plasma Spraying of Cermets: A Review[END_REF]. However, the maximum copper concentration to be incorporated in the HA lattice which preserves the dominance of HA phase in the coatings was 5 wt.% Cu due to the fact that the HA structure can only accommodate certain amounts of other ions in its lattice [START_REF] Candidato | Advanced microstructural study of solution precursor plasma sprayed Zn doped hydroxyapatite coatings[END_REF].

Copper incorporation mechanism

XPS result shows the electronic states of Cu + and Cu 2+ cations in the Cu-HA coatings confirming the successful incorporation of copper ions into the HA structure. The mechanism of copper incorporation in HA was presumed to be a substitution of copper ions on the Ca(II) sites which is characterized by a decrease in the lattice parameters and cell volume contraction of HA due to the smaller ionic radius of Cu 2+ compared to the Ca 2+ [START_REF] Imrie | Preparation of Copper-doped Hydroxyapatite with varying x in the composition Ca10(PO4)6CuxOyHz, Bioceram[END_REF][START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF][START_REF] Othmani | Synthesis, characterization and catalytic properties of copper-substituted hydroxyapatite nanocrystals[END_REF]. Contrary to the expected substitution mechanism, Rietveld refinement obtained from this present work shows a slight increase in the basal a lattice parameter along with the increase of the unit cell volume with increasing copper dopant concentration into HA. Moreover, ICP-AES results further solidifies our claim that no calcium site substitution has taken place due to the non-stoichiometric Ca/P ratio, i.e., greater than 1.67 for all the coatings indicating that calcium-rich coating was being deposited.

In addition, Raman and IR spectra shows red-shifting and broadening of the peaks associated to the phosphate vibrations of HA with increasing copper concentration. Based on the results, copper ions could possibly be inserted in interstitial position inside the HA matrix along the hexagonal channel. This claim was in agreement with the crystallographic studies on Cu-doping into HA which reported interstitial insertion of Cu atoms at 2b Wyckoff site along the hexagonal channel leading to the formation of linear oxocuprate O-Cu-O entities in the HA structure [START_REF] Gomes | Cu-doping of calcium phosphate bioceramics: From mechanism to the control of cytotoxicity[END_REF][START_REF] Renaudin | First-row transition metal doping in calcium phosphate bioceramics: a detailed crystallographic study[END_REF][START_REF] Karpov | Synthesis, crystal structure and properties of calcium and barium hydroxyapatites containing copper ions in hexagonal channels[END_REF]. This possible copper ion insertion mechanism was favored due to high sintering temperature above 1100 o C of the plasma jet.

It has been reported that the formation of Cu-HA was a result of the transformation of α-TCP polymorph and copper-phosphate phases at temperatures above 1100 o C from the cooling process [START_REF] Gomes | Cu-doping of calcium phosphate bioceramics: From mechanism to the control of cytotoxicity[END_REF]. In here, in-flight particles traveling along the high temperature plasma jet may lead to the dehydroxylation of HA given by the equation: inducing an increase in the lattice c parameters with no significant influence on the unit cell volume [START_REF] Candidato | Advanced microstructural study of solution precursor plasma sprayed Zn doped hydroxyapatite coatings[END_REF]. However, in this present study, the incorporation of the copper ions into the interstitial site along hexagonal channel shows increase in the lattice a parameters only and bring about an isotropic increase in the volume of HA unit cell (see Table 1 Furthermore, the transformation of HA into TCP's due to dehydroxylation also indicates that copper ion insertion might be localized in an interstitial site affecting the hydroxyl column as well. Related studies suggested that existence of ordered isolated [OCuO] units might be present along the channel [START_REF] Zykin | Solid state solubility of copper oxides in hydroxyapatite[END_REF][START_REF] Li | Raman spectroscopy determination of phases within thermal sprayed hydroxyapatite splats and subsequent in vitro dissolution examination[END_REF].

Conclusion

Structural and microstructural investigation on the newly developed solution precursor plasma sprayed copper-doped HA with varied dopant concentration has been presented. No significant changes on the microstructural features on the surface and cross-section of the coatings were evident as copper content increases. A decrease in HA phase content from 93% to 14% and degree of crystallinity form 94% to 85% along with the increase of impurity phases were observed upon increasing the copper dopant concentration. RAMAN and IR spectra shows broadening and red-shifting of the phosphate bands with increasing copper dopant concentration due to the distortion in the HA structure brought about by the insertion of copper ions. XPS results identified that the copper species incorporated in HA structure were Cu + and Cu 2+ ions. Rietveld refinements confirmed the increase of the lattice a parameter and expansion of the unit cell volume due to the incorporation of copper ions into the HA lattice.

These results evidenced that the incorporation mechanism of copper ions is probably an interstitial insertion along hexagonal channel of the HA structure. The insertion was induced by the dehydroxylation process of HA due to the high temperatures of the plasma jet. No calcium substitution has taken place contrary to the claims of some previous reports since SPPS process had deposited calcium-rich coatings as confirmed by the ICP-AES results.

In this study, 5 w.t% Cu is the maximum Cu quantity to be incorporated into the HA matrix keeping the HA phase the dominant phase in the coating. In-vitro characterization of the coatings under simulated body fluids, cytotoxicity and antibacterial testing will be conducted for the investigation of the feasibility of the SPPS Cu-HA coatings for biomedical application with added biofunctionality.

Figure 1

 1 Figure 1 SEM images at the surface and cross-section of SPPS pure HA, 3%Cu-HA, 5%Cu-HA and 10% Cu-HA coatings; inset: low magnification at the surface.

5%

Figure 2 :

 2 Figure 2: X-ray diffraction diagrams of the coatings with 0 wt.%, 3 wt.%, 5wt.% and 10 wt.% Cu showing HA and impurities depending on the Cu concentration.

Figure 4 :

 4 Figure 4: Raman spectra of SPPS Cu-HA coatings with different copper concentration

Figure 6 (. Discussion 4 . 1 .

 641 Figure 6 (left) Copper concentration in the deposited coating and (right) stoichiometric ratio of the coatings

𝐶𝑎 10 (

 10 𝑃𝑂 4 ) 6 (𝑂𝐻) 2 → 𝐶𝑎 10 (𝑃𝑂 4 ) 6 (𝑂𝐻) 2-2𝑥 𝑂 𝑥 ⬚ 𝑥 + 𝑥𝐻 2 𝑂 ↑ (Eq.[START_REF] Shanmugan | Copper-substituted hydroxyapatite and fluoroapatite: synthesis, characterization and anti-microbial properties[END_REF] where ⬚ is the vacancy and x<1. The results in the phase transformation of HA into TCP and the formation of calcium copper phosphate phases that leads to the insertion of copper on the vacancies induce by the dehydroxylation process. The presence of TCP and CCP phases in XRD results which supports the transformation of HA together with the presence of Cu + and Cu 2+ cations in XPS confirms the incorporation of copper ions in the HA matrix producing coatings with chemical formula Ca10Cux(PO4)6(OH)2-2xO2x. However, the limitation on which copper ions are incorporated on the HA matrix was 5 wt.% of Cu in order to maintain HA as the dominant phase in the coatings.On the other hand, comparing our calculated lattice parameters with SPPS Zn-doped HA coating using similar doping concentration shows values of a = 9.4113(6) Å and c = 6.8892(5) Å for Zn-doped HA compared with a =9.4280(3) Å and c = 6.8877(2) Å for Cu-HA suggesting a different insertion mechanism. Previous studies on SPPS Zn-doped HA coating reported interstitial insertion of linear O-Zn-O entity in the OH crystallographic site of HA

Figure 1

 1 Figure 1 Raman mapping of pure HA and 5% Cu-HA showing (red) HA phase, (blue) TTCP phase, and (green) TCP phase.

Figure 2

 2 Figure 2 XPS result showing the binding energy of the Cu 2p spectrum for 5% Cu-HA

Table 2 :

 2 Refined unit cell parameters and volume, goodness of fit, reliability factors and evolution of unit cell parameters for the HA phase.

	HA standard	Pure HA	3%Cu-HA	5%Cu-HA	10%Cu-HA
	Lattice parameters
	a (Å)	9.432	9.4163(2)	9.4229(2)	9.4280(3)	NR
	c (Å)	6.881	6.8829(2)	6.8893(2)	6.8877(2)	NR
	V (Å 3 )	530.72	528.53(2)	529.75(2)	530.21(3)	NR
	Refinement factors
	GOF	-	1.38	1.56	1.25	-
	Rp (%)	-	4.62	4.28	2.86	-
	Rwp(%)	-	6.59	6.78	3.99	-
	Percent difference with respect to pure HA
	a	-	-	0.07	0.12	-
	c	-	-	0.09	0.07	-
	Volume	-	-	0.23	0.32	-

Note: numbers in parenthesis represent the standard deviations. NR-not refined

  ). Furthermore, previous studies have reported that insertion of the linear O-Zn-O in the HA lattice attracts the adjacent phosphate groups but not with case of O-Cu-O oxocuprate[START_REF] Gomes | Cu-doping of calcium phosphate bioceramics: From mechanism to the control of cytotoxicity[END_REF]. Hence, the presence of O-Zn-O attracts the PO bands while O-Cu-O possibly repels the PO band leading to the expansion of the unit cell volume.

Acknowledgement

Romnick Unabia would like to acknowledge the Department of Science and Technology-Accelerated Science and Technology Human Resource Development Program (DOST-ASTHRDP) for the scholarship grant, and Department of Science and Technology -Philippine Council for Industry, Energy and Emerging Technology Research and Development (DOST-PCIEERD) for the financial grant. The authors acknowledges CarMaLim (IRCER, University of Limoges) platform for the equipment used in the characterization. Yann Launay, Richard Mayet, Julie Cornette, Sandra Blanchet and Etienne Laborde are also acknowledged for their help in the characterization of the coatings.