Maud Dampérat

Ping Lei

Florence Jeannot

IRT Approach for rating scales: applications for normal and non-normal distributions

Keywords: Item Response Theory (IRT), Graded Response Model (GRM), Rating Scale, Classical Test Theory (CCT), Measurement Theory

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In marketing, the choice of measurement and selection of items are of major interest because it largely determines the quality of research and the credibility of the results. However, multiitem scale development methods that are currently used and inherited from classical psychometrics are the subject of much criticism. Multi-item scales are often considered too long and expensive to be administered to non-student samples or in applied studies (Jong, Steenkamp & Veldkamp, 2008). It is also difficult to identify items and rating points scales that are misunderstood by respondents and thus need to be eliminated or reformulated. In addition, the common practice to select items with high loadings for a short version of a scale does not allow the researcher to accurately measure all aspects of a construct. As a result, an investigation of the methods and practices used in modern psychometric to build scales and their interest for marketing is necessary.

Currently, for building multi-item scales, marketing researchers are often inspired by classical test theory (CCT) (Churchill, 1989;[START_REF] Peter | Reliability: a review of psychometrics basics and recent marketing practices[END_REF][START_REF] Rossiter | The C-OAR-SE procedure for scale development in marketing[END_REF] using several methods to select items to measure a construct and to study their reliability and validity. The most commonly used approach in marketing can be summarized in three steps. The first step relies upon an exploratory factor analysis (principal component factor analysis or common factors analysis) and to select items based on a study of how they are correlated with each other. This analysis is also used to obtain a score for each individual (called "factor score") and estimate the value of a construct as a weighted sum of the responses to the items of the scale. The measurement error is assumed to be constant for all values of the construct. In the second step, the reliability of the scale is tested using Cronbach's alpha coefficient (1951) or Joreskog's rho [START_REF] Fornell | Evaluating structural equation models with unobservable variables and measurement error[END_REF]. The reliability analysis is based on the relationships between items, especially the total item-score correlation of the test to evaluate the measurement error. The reliability is computed on all the items if the scale is unidimensional or on the items of each dimension if the scale is multidimensional. The reliability analysis favors the selection of similar items. The alpha coefficient does not distinguish the redundant items from the original ones. Its only purpose is the maximization of the value of the coefficient. For the third step, convergent validity and discriminant validity of the sample items are evaluated using a confirmatory factor analysis (CFA). However, structural equation modeling tends to favor the multiplication of items (at least four items when one construct is studied), especially redundant ones, to get a better validity. Thus, the difficulties of developing scales are mainly related to choosing the right items to measure a given construct and can be summarized as follows: how to reduce the number of items used while ensuring a satisfactory quality of measurement?

To improve the scales construction, modern psychometrics now rely mainly on the item response theory (IRT) approach [START_REF] Nunnally | Psychometric theory, Third Edition[END_REF]. It provides much more detailed information on the quality of the measurement than the methods commonly used in marketing, including measures of discrimination, accuracy and difficulty of items. IRT approach distinguishes items by providing additional information about redundant items, identifies inaccurate and confusing items or rating points obviously considered too complex by respondents. With this additional information to assess the quality of a scale, the researcher is then able to avoid the proliferation of redundant items and remove items misunderstood by respondents. This favors the development of short and relevant scales. IRT assesses the quality of each item more accurately [START_REF] Nunnally | Psychometric theory, Third Edition[END_REF][START_REF] Singh | Tackling measurement problems with item response theory: principles, characteristics and assessment with an illustrative example[END_REF] and justifies the item disposal.

IRT differs from CCT in the sense that measurement error may vary depending on the value of the construct while CCT considers it as a constant. Independently analyzing each item of a scale, IRT makes it easier to understand why the reliability or validity of a construct cannot be established [START_REF] Waller | Using IRT to separate measurement bias to group differences on homogeneous and heterogeneous scales: an illustration with the MMPI[END_REF]. Thus, if with the CCT approach, reliability and validity are calculated for all the items of a scale, with the IRT approach, the items independently contribute to the accuracy of the measurement. This principle called "local independence" means that for people obtaining the same value on a construct, responses to items are stochastically independent. IRT has been of constant interest for many years in journals such as Multivariate Behavioral Research and Psychological Method and is widely used in psychology because of its flexibility according to the type of measurement used (binary, ordinal or rating scales) and its original contribution to the analysis of multi-item scales [START_REF] Thissen | Data analysis using item response theory[END_REF].

Paradoxically, IRT remains rarely used in marketing. In 1985, Bechtel boasted its interest in marketing, backed by the article of [START_REF] Balasubramanian | Measuring consumer attitudes toward the marketplace with tailored interviews[END_REF]. It took a decade to see the emergence of a renewed interest for this method [START_REF] De | Using item response theory to measure extreme response style in marketing research: a global investigation[END_REF][START_REF] De | A model for the construction of country-specific yet internationally comparable short-form marketing scales[END_REF][START_REF] Bacon | Breaking the binary model code: IRT models offer flexible marketing measurement[END_REF], especially thanks to the contribution of [START_REF] Singh | Tackling measurement problems with item response theory: principles, characteristics and assessment with an illustrative example[END_REF]. Yet its interest is obvious considering the issues raised by the selection of items during the development/use of a scale. [START_REF] Singh | Tackling measurement problems with item response theory: principles, characteristics and assessment with an illustrative example[END_REF], the most complete article on IRT, uses rating scales measuring role conflict and role ambiguity concepts. To show the interest of the IRT approach, these two rating scales have been converted into dichotomous scales, which was a prerequisite for using Multilog software. At that time, rating scales could not be analyzed as such because the available software was of great complexity [START_REF] Singh | Tackling measurement problems with item response theory: principles, characteristics and assessment with an illustrative example[END_REF]. At the present time, various software such as Mplus and Parscale allow to easily examine rating scales using an IRT approach.

The purpose of this article is precisely to present the IRT approach as applied to rating scales (Malhotra & Birks, 2006). The specific application of IRT approach for rating scales is called graded response model (GRM). GRM generates simple graphical curves to select the appropriate items and is proposed as a complement to the CCT, but also as an alternative to it, especially when the scales comprise less than four items. The originality of this article is the proposal of a three-step approach including indicators and interpretation rules for the application of IRT to rating scales in marketing. To demonstrate GRM's potential interest in marketing, we used two scales: one is normally distributed (need of cognition) while the other follows a non-normal distribution (customer satisfaction). And we compare the results from GRM analysis to those obtained with CCT.

BASIC ELEMENTS OF THE IRT METHOD

IRT models, also called "latent trait models," follow the same principles but differ in the analysis that can be performed. They connect all item characteristics and an individual characteristic (latent trait θ) to the probability of choosing a response. Then items can be directly compared to the trait being studied based upon parameters selected by the researcher (e.g., the difficulty and discrimination associated with each item parameter).

Value of the latent variable associated with an item (θ)

The latent trait associated to each item of a scale is called θ (or theta). It represents the person's ability to respond to an item. θ has no origin as it is a rating latent variable that allows to compare items or people from their values on θ. It is constructed to have a mean of 0 and a variance of 1. θ is the latent trait used in the computation of all IRT models.

Response probability values of a latent variable (P)

P is the probability to answer an item "right." This probability varies between 0 and 1. The function P(θ) linking the latent variable θ to the probability of response is represented by a cumulative distribution which forms an S-curve (typical of logistic functions) called item characteristic curve (ICC). Response probability tends to 0 for low values of θ and then increases only when the values of θ increase. When θ becomes high, the probability tends to 1.

Evaluation of the difficulty of an item (δ)

δ (or delta) is called a "difficulty" parameter. It is an indicator of the difficulty of understanding an item by respondents. This parameter corresponds to the value of θ at the inflection point of the item characteristic curve. It represents the point on the latent trait scale for which individuals have a 50% probability of choosing the item. Items with negative values of δ are considered easier because people are relatively more likely to choose them, while items with positive values of δ are considered more difficult. The value of δ thus indicates the greater or lesser difficulty of understanding an item by respondents. This parameter allows the comparison of the difficulty between the items. The simplest IRT model is the one-parameter IRT model, which is also called the Rasch model [START_REF] Bechtel | Generalizing the Rasch model for consumer rating scales[END_REF]. It only evaluates the difficulty parameter (δ) using binary data such as Boolean-type measured from answers to yes/no questions. The one parameter IRT model function is as follows:

P(θ)=1-1 / (1+e -(θ-δ) )
δ parameter is also used in more complex IRT models in addition to other indicators of accuracy of the item. For multi-item and multipoint scales, the difficulty is measured for each item and for each point under the name of threshold difficulty.

Assessment of the discrimination of an item (α)

α (alpha) parameter is called "discrimination." This parameter is measured by the slope of the characteristics of an item to its inflection point. The slope value is between 0 and infinity (+∞).

The steeper the slope, the higher it can differentiate respondents who have the ability to respond to an item "right" from those who have not. To evaluate the discrimination of an item, the two-parameter IRT models are needed because two-parameter IRT models compute not only the difficulty of the item (δ) but also item discrimination (α). In this way, items can be differentiated from low to high responses by each respondent. For a model with two parameters (α and δ), the function becomes:

P(θ)=1-1/ (1+e -α(θ-δ) )
These two-parameter models are used for all types of dichotomous scales.

IRT MODEL AND INDICATORS FOR RATING SCALES

Different models of IRT have been adapted to variable types (binary, ordinal or rating), and the number of parameters selected. These models can be estimated using software such as Multilog, Mplus, Rumm, Bilog, Parscale or using different mathematical principles according to the number of parameters to be estimated and the type of measurement scale used. Following the presentation of the GRM with two parameters (α and δ), whose specifications are appropriate for rating scales, we successively study the different indicators available for this type of model and their interpretation rules.

Graded response model suitable for rating scales

IRT models with two-parameters (α and δ) have been adapted to the measurement scales commonly used in marketing such as attitude scales, personality or involvement. The GRM, as an extension of the two-parameter model, is the IRT model suited to rating scales such as Likert scales (Samejima, 1969). It is also called the Rasch model with multiple responses or rating scale (Sijtsman & Hemker, 1998). In GRM, each scale item is described by one item slope parameter α and j from 1 to m between category threshold parameter δij. For GRM, the characteristic curves of items can be expressed based on Samejima (1969):

𝑃𝑃𝑃𝑃𝑃𝑃(𝜃𝜃) = 𝑒𝑒 [𝛼𝛼𝛼𝛼(𝜃𝜃-δ𝛼𝛼𝑖𝑖)] 1 + 𝑒𝑒 [𝛼𝛼𝛼𝛼(𝜃𝜃-δ𝛼𝛼𝑖𝑖)]
where j = 1,…… m, j being the between category threshold parameter, and i the item scale.

Indicators and interpretation rules for the use of the GRM

GRM provides the opportunity to perform various analyses to represent, compare and evaluate the items and their rating points on the latent trait θ. The steps of the analysis are summarized in Table 1. At each stage, the indicators to analyze and their rules of interpretation are specified. * 5-point scales from 1 "strongly agree" to 5 "strongly disagree"

Steps

Table 2: NFC scale -Items distribution of point scores for each item

This scale has acceptable reliability (Cronbach's alpha = 0.617 and Jöreskog rho = 0.626).

The correlations between each of the five items and the total score varies for items NFC1 and NFC3 (respectively 0.551 and 0.577) to a value greater than 0.6 for items NFC2 (0.662), NFC4 (0.672) and NFC5 (0.667), showing that these items are correlated to the construct [START_REF] Carmines | Reliability and Validity Assessment[END_REF]. A confirmatory factor analysis of the data indicates that the model fit is satisfactory: Chi ²/df = 6.5/5 is not statistically significant with p = 0.257, GFI = 0.986, SRMR = 0.036 and RMSEA = 0.041. The standardized Lambdas of each of the five items are all statistically significant: 0.328 (NFC1), 0.562 (NFC2), 0.416 (NFC3), 0.601 (NFC4), 0.584 (NFC5). The convergent validity index (0.260) is less than the threshold of 0.50, showing a problem within the scale. Generally, it is advised to suppress the items with the lower loading, NFC1 and NFC3.

Step 1 -Item characteristic curve: an indicator of discrimination

The characteristic curve of an item is used to evaluate the discriminating power of an item for a given latent trait. Each curve is a function which relates values of a latent variable (θ) with its observation probability (P(θ)). For a multi-item scale, there are as many curves as the number of items in the scale. These curves show a logistic distribution linking the probability of response as ordinate values to θ the latent variable as abscissa. These characteristic curves are particularly important because they are used not only to study the properties of those items but also those of the latent trait they measure. The juxtaposition of the curves of each item allows the evaluation of the different capacities of the items in the representation of the construct and thus their comparison.

The examination of the curves is used to evaluate the relevance of an item and eliminate those that are not discriminatory [START_REF] Nunnally | Psychometric theory, Third Edition[END_REF]Vrignaud, 2002). Thus an item whose shape characteristics curve deviates too much from the logistics perfect shape (S-curve), especially if the distribution is too flat, is eliminated. Such flattened curves mean that the item is not discriminatory and therefore provides no additional information on the scale [START_REF] Jolibert | Marketing research : méthodes de recherche et d'études en marketing[END_REF]. After the examination of the curves' shape, the study of discrimination parameters can be added. These parameters present the same information as the curves shapes examination. The higher the value of the α parameter, the higher the item will be considered discriminatory. To guide the interpretation of the α parameter, the researcher can use the following table (Table 3). Rule of Interpretation: Following a review of the curves and/or study parameters of discrimination (α), any item whose distribution is too flat or that the estimator has a discrimination qualified low to zero (α ≤ 0.64) must be eliminated as the item is found nondiscriminating. It is advised to select the most discriminating items.

Value of the parameter α

Illustration with need for cognition scale: Mplus software was used to perform the GRM analyses. The characteristic curves of the items show that the items NFC2, NFC4 and NFC5 differ from the other two (NFC1 and NFC3) (see Figure 1). The curves associated with NFC1 and NFC3 show flatter slopes than the curves of NFC2, NFC4, and NFC5 indicating a lower degree of discrimination. For further analysis and for the sake of simplicity, we chose to compare the items NFC1 and NFC3 with the NFC5 item, because items NFC1 and NFC3 have very different characteristics curves from items NFC2, NFC4 and NFC5. The information curve of an item provides a representation of the accuracy of the latent variable θ. This accuracy is measured by the variability of the item around the central value of θ. The accuracy thus depends on the variance of θ, denoted σ2, and is calculated by the formula 1/σ2. The resulting curve has a Gaussian shape. The accuracy of the item is great when its variance is low. Graphically, when the information curve associated with an item is spread around the central value of θ, the accuracy of the item is great. When the measurement accuracy is insufficient for some items, it is best to remove them.

Items

Rule of interpretation: after reviewing the shape of information curves, items are selected on the basis of a highly constricted curve "pointed" at the central value of the latent trait (θ) because these items show a good accuracy of the information provided.

Illustration with need for cognition scale: the information curve associated with NFC5 has a higher peak for the central value of θ than NFC1 and NFC3 (see Figure 2). The NFC5 item is therefore more precise than NFC1 and NFC3 items on the latent trait. The lack of precision of items NFC1 and NFC3 is an additional argument for a possible elimination of the two items from the need for cognition scale. For multi items scales and rating scales, the difficulty parameter (δ) is measured for each item but also for each rating point of the scale. Each graph is associated with a single item and presents as many curves as the number of rating points of an item. It shows the value θ associated with the item on the horizontal axis and its response probability on the vertical axis. For a rating scale, only the two extreme rating points show a monotonic response curve. Typically, the rating point that has the lowest value among all difficulty has a response curve that decreases monotonically from 1 (for θ = -∞) to 0 (for θ = +∞). Conversely, for the rating point with the highest value, δ has a function which increases monotonically from 0 (for θ = -∞) to 1 (for θ = +∞). The other curves are from unimodal distribution correspond to the order of the rating points. Each rating point corresponds to a segment of the latent trait θ for which the response is probable.

The responses curve of each point of an item enables the calculation of the threshold of difficulty associated with the transition from one rating point to another (δij). This threshold is the difficulty associated with the transition between two consecutive rating points. Note that an intersection point is the point where two rating points' response curves intersect. Thus there are m intersection points for a m+1 rating points, e.g., from "not at all" to "a little" we have one intersection point and another for "a little" to "moderately." Thus there are two intersection points for three rating points scale. The difficulty threshold is measured -in units of θ -at the intersection point. To each difficulty threshold corresponds a value of θ which can be interpreted as the value for which the next point response becomes more probable than the actual one. If the intersection points are well separated from each other, it means that the threshold of difficulty for each point increases, which is desirable [START_REF] Masters | A Rasch model for partial credit scoring[END_REF].

Examination of the response curves for each item rating point allows the identification of rating points considered difficult for respondents because of their lower probability to be selectedspotted lower height than the other. Ideally, the response probability associated with each rating point must be substantially the same, which is characterized by graphic response probabilities P (θ) relatively equivalent at the intersection curves between consecutive responses.

Rule of interpretation: after examining the response curves of each rating point of an item, retained items are those whose rating point's difficulty will be similar, showing curves of the same height for each point, having a response probability P(θ) roughly equivalent for all points.

Illustration with need for cognition scale: Figure 3 shows the response curves of the five items. NFC4 presents a rather good response curve showing a satisfying discrimination parameter at each rating point. As NCF 2 et NCF 5 are presenting similar response curves, we discuss NFC5 only. NFC 1 and 3 show very different response curves. Therefore, they are specifically analyzed.

The rating point crossing of NFC 4 curves show a rather regular progressivity on theta (θ). The rating point 3 of the scale shows a slightly higher probability to be selected by the respondents, which is relatively frequent for a neutral point.

The study of the response curves to the 5 rating points of the item NFC5 shows a high and close probability for the rating points 1, 2 and 3. Conversely, going from rating points 3 to 4 has a lower probability than the other intersection points because of its greater response difficulty. To conclude, only rating point 4 of the item NFC5 shows a particular problem in relation to other points that behave normally.

The curves for NFC1 show that rating points 2 and 4 have a lower probability of response due to the greater response difficulty. These rating points have a lower response probability than point 3. Rating point 3 is the central point and has been heavily used by the respondents (more than 40% probability) that did not want or were able to answer the question. Rating point 4 has a low probability of response (about 20 %) due to a greater difficulty. The increase in thresholds of difficulty between consecutive ratings is neither regular nor increasing in θ. Indeed, the intersection points of 2 to 3 and 3 to 4 occurs on more extreme values of θ than the intersection points of 1 to 2 and 4 to 5 indicating that point 3 plays an abnormal role. The item NFC1 needs to be reformulated.

The response curves analysis of item NFC3 rating points show that ratings 2 and 4 have lower responses probabilities (around 20 %) compared to rating 3 (about 30%). Rating 3 also plays an abnormal role. Item 3 appears to be not used as a rating scale. The thresholds of difficulty between levels 2 and 3 and 3 and 4 reached values of θ more extreme than the threshold between levels 1 and 2 or between 4 and 5, indicating that the item NFC3 has a problem of understanding by respondents. However, compared to item NFC1, NFC3 is slightly better in terms of response distribution between the different rating points. The item NFC3 therefore needs to be reformulated.

APPLICATION FOR THE NON-NORMAL SCALE OF SATISFACTION

We used the satisfaction scale because it is characterized by the absence of normality already observed by Babin and Griffin (1998). According to the CCT, we performed an exploratory factor analysis, reliability analysis (alpha, rho) and a confirmatory factor analysis using AMOS 18 of a customer satisfaction scale. Mplus software was used to perform the GRM analyses.

The satisfaction scale includes four items. A sample of 151 responses was collected. Each item includes 7 rating points. These range from 1 "not at all satisfied" to 7 "extremely satisfied" for SAT1. SAT2 is measured by a 7-points semantic differential "delighted/terrible." SAT3 and SAT4 are measured using Likert scales from 1 "strongly disagree" to 7 "strongly agree" (see * 7-point from 1 "not satisfied at all" to 7 "extremely satisfied" ** Semantic differential using 7-point from "delighted" to "terrible" *** 7-point from 1 "strongly disagree" to 7 "strongly agree" Table 5: Satisfaction scale -Labels and characteristics of the distribution of items

Normality tests of the satisfaction scale items were performed (see Table 5 for results). The items of this scale are all statistically significant at the 0.05 level for the asymmetry coefficients (tSAT1 = -4.99, tSAT2 = -4.64, tSAT3 = -4.08; tSAT4 = -3.49). The satisfaction scale is therefore asymmetric and asymptotically shifted to the right. For flattening, SAT1 and SAT2 are sharper than those of a normal distribution at the 0.05 level (tSAT1 = 2.37, tSAT2 = 2.87), while SAT3 and SAT4 are normally distributed (tSAT3 = 0.18, tSAT4 = 0.00). The coefficient of multinormality (Mardia coefficient) is 9.27 (t = 8.22), which confirms the absence of multinormality of the satisfaction scale.

Results of the classical measurement analysis

Exploratory factor analysis

The results of the exploratory factor analysis of the satisfaction scale are satisfactory with a percentage of the total explained variance of 84.5 % and a quality of representation 0.85 for SAT1, 0.87 for SAT2, 0.84 for SAT3 and 0.82 for SAT4. The Cattell test presents a very strong inflexion point before the second factor, which is a characteristic of a one-dimensional scale. Saturations (or loadings) of the satisfaction scale items are respectively 0.92 for SAT1, 0.93 for SAT2, 0.92 for SAT3 and 0.91 for SAT4. To conclude, these four items are factorable and seem to form a unidimensional scale of satisfaction.

Reliability analysis

The satisfaction scale has good reliability (Cronbach's alpha = 0.93 and rho = 0.79 Jöreskog).

If one removes each of the four items successively, the coefficient alpha for three items remains high. Thus, the correlation of the three items with the total score is 0.91 without SAT1, 0.91 without SAT2, 0.92 without SAT3 and 0.92 without SAT4. These high correlations show that the four items are well correlated to the construct of satisfaction [START_REF] Carmines | Reliability and Validity Assessment[END_REF].

Confirmatory factor analysis

Confirmatory factor analysis is performed on the four items of satisfaction, despite the absence of normality. The results show that the model fits well to the data: Khi²/df = 0.80/2 is not statistically significant with p = 0.667, GFI = 0.997, SRMR = 0.048, and RMSEA = 0.000. The standardized Lambdas of each of the four items are all statistically significant and very close to the lambdas obtained by bootstrap: 0.902 (SAT1) and 0.913 (SAT2), 0.883 (SAT3), and 0.805 (SAT4). The score of convergent validity (0.79) is well above the threshold of 0.5, indicating that the scale is valid. These four items are based on the criteria commonly used in marketing and are a very good reflection of satisfaction and the satisfaction scale measures as well. A bootstrap analysis to control non-normality shows very stable lambdas since bootstrap coefficients are very close lambdas standardized 0.903 for SAT1, 0.913 for SAT2, 0.885 for SAT3, and 0.806 for SAT4. In conclusion, the confirmatory factor analysis showed that the four items selected are good indicators of satisfaction.

Results of the GRM analysis

Step 1 -Item characteristic curve

The characteristic curves of the items show that items SAT1, SAT2, SAT3 and SAT4 present similar results of discrimination (see Figure 4).

Step 2 -Item information curve

Information curves of the items show that SAT2 and on a lesser extent SAT1 have a neat peak on θ, meanwhile SAT3 and SAT4 information curves have the flattest curves (see figure 5). It means that SAT2, but also SAT1 have a greater precision than SAT3 and SAT4 on the latent trait. recommendations, this shows that rating points have relatively equivalent probabilities to be chosen except for rating 3 of SAT3 and SAT4 which have a lower probability. Rating 3 of SAT3 shows also a very small increase on θ. Ratings 2 to 6 of SAT 3 tends to reach a lower probability than the other items, confirming the low difficulty of the item and therefore its unattractive character to measure satisfaction. To conclude, GRM results show that the SAT3 is the least suitable item for measuring satisfaction. To assess the quality of a scale, GRM parameters are used to distinguish items that are appropriate to measure a given construct in order to avoid item proliferation providing too little additional information. Choosing items that have both similar and high difficulty parameters maximizes the reliability [START_REF] Lord | The relationship of the reliability of multiple choice items to the distribution of items difficulties[END_REF]. However, it is better to maximize the information that increases the spread of difficulty parameters of the items [START_REF] Nunnally | Psychometric theory, Third Edition[END_REF], even if the final reliability is lower.

Compared to structural equation modeling, the GRM analysis provides additional information to judge the relevance of the scale point labeling in assessing its difficulty. Often items are rejected for statistical reason only. However, some items may be relevant but very poorly labeled. GRM analysis pinpoints where to improve the wording of the rating points and where a poor understanding of the respondents occurs.

For scales using few items, the researcher usually relies on choosing items on the correlation coefficient between items or when the number of items is equal to 3 only on the value of the Cronbach coefficient to study the reliability of the scale. IRT allows the analysis of the probability of response to a latent trait. It provides new information on the discriminating power of an item to its latent trait, the accuracy of an item and the difficulty associated with the point crossing within each item. It allows the selection of the most representative items of the latent trait, regardless of the normality of the distribution of items.

The use of GRM analysis for the study of one-dimensional rating scales is advocated by [START_REF] Meade | A comparison of item response theory and confirmatory factor analytic methodologies for establishing equivalence/invariance[END_REF] due to its complementary information and usefulness for decision -making of managers and researchers. However, GRM analysis is more complex to use than the confirmatory factor analysis for testing multidimensional scales. Note that recent work from Sitjsman [START_REF] Paas | Nonparametric item response theory for investigating dimensionality of marketing scales: A SERVQUAL application[END_REF] is promising and should soon lead to the development of a software testing IRT graded response model for multidimensional scales.

The main obstacle to a widespread application of the GRM analysis is the low number of software and especially their lack of ergonomics. Beyond their scientific interest, their implementation can be somewhat complex and no analytical procedure is currently available in traditional marketing integrated software such as IBM-SPSS or Statistica. Software development is therefore a perspective of major improvement that would encourage the use of this method in marketing.

Figure 1 :

 1 Figure 1: Characteristic curve for the 5 NFC items

Figure 2 :

 2 Figure 2: NFC scale -Information curve for each item

Figure 3 :

 3 Figure 3: NFC scale -Rating points response curve for NFC items

Figure 4 :

 4 Figure 4: Satisfaction scale -Item characteristic curve for item scales

Figure 5 :

 5 Figure 5: Satisfaction scale (SAT) -Item information curve for each item

Figure 6 :

 6 Figure 6: Satisfaction scale -Points response curves for each item

Table 1 :

 1 Steps, indicators and interpretation of a rating scale IRTThe steps in the analysis and interpretation of indicators of IRT are emphasized in using a shortened version of the need for cognition (NFC) scale. The NFC was administered to a sample of 184 consumers. The scale consists of five items from the[START_REF] Cacioppo | The need for cognition[END_REF] scale. These items are rated on a five-point Likert scale varying from 1 "strongly agree" to 5 "strongly disagree." The wording of items and the number of occurrences per point per item are provided in Table2.

		Indicators	Analysis	Objectives	Computational norms	Interpretation
	1	Discrimina-tion parameter of an item (α)	Analysis of the shape of an item characteristics curve (S logistic curve)	To test how well does the item differentiate low from high responses	α = slope value for the probability P(θ) equal to 50%	Remove items whose discrimination parameter is less than or equal to 0,64 (Baker, 2001), and selecting preferentially the most discriminating items
	2	Accuracy of an item (σ²)	Analysis of the shape of the information curve of an item (bell curve of a normal distribution)	To test the variability of an item around its value central	1/σ² = variability of an item around its on θ central value	Selecting preferentially items having a positive kurtosis on θ
	3	Difficulty threshold of each rating point	Analysis of the response curves to each rating point of an item (bell	To test how difficult an item can be understood	δij = value of θ at the intersection point between two successive	Selecting preferentially items having successive rating points showing a steady increase on θ

Table 3 :

 3 Criteria of discrimination parameters values. SourceBaker (2001), p. 34.

	Evaluation of the item discrimination

Step 2 -Item information curve: an indicator of accuracy.

	2.1.2.
		Discrimination parameters (α)	SD
	NFC1	0.681	0.242
	NFC2	1.301	0.333
	NFC3	0.868	0.255
	NFC4	1.446	0.359
	NFC5	1.489	0.399
	Table 4: NFC scale -Values of discrimination parameters for each item

  Table 5 for the question labels). SAT2 and SAT3 were reversed, i.e. encoded in reverse order to facilitate the comparison of items.

					Responses distribution
					For each point of the scale
		Items		σ	1 2 3	4	5	6	7	Skewness (test t)	Kurtosis (test t)
	SAT1* -Regarding my relationship with this seller, I am…	5.27 1.28 2 3 13 11 47 55 20	-0.995 (-4.99)	0.943 (2.37)
	SAT2**	(inverted)	-
	Speaking satisfaction with my of relationship with this	5.26 1.18 1 4 8 15 54 52 17	-0.926 (-4.64)	1.143 (2.87)
	seller, I am …
	SAT3*** (inverted) -
	Compared to what I
	expected, I 'm a little disappointed (s) of my	5.17 1.54 4 8 7 28 27 46 31	-0.813 (-4.08)	0.070 (0.18)
	relationship with this
	seller
	SAT4*** -I am satisfied of my relationships with this seller	5.05 1.43 2 9 10 24 41 43 22	-0.695 (-3.49)	0.000 (0.00)
					109

Table 6

 6

	Items	Discrimination parameters (α)	SD
	SAT1	4.08	0.66
	SAT2	5.03	0.92
	SAT3	3.77	0.58
	SAT4	3.80	0.62

) show that SAT2 is the most discriminant item (αSAT2 = 5.03). Meanwhile, SAT3 is the least discriminant (αSAT3 = 3.77). According to

Baker's criterion (2001)

, discriminant parameters of all items are qualified as very strong.

Table 6 :

 6 Satisfaction scale -Discriminant parameters of items scale

CONCLUSION

GRM analysis allows a more detailed analysis of the items used to measure a latent variable than the structural equation modeling [START_REF] Reise | Assessing the fit of measurement models at the individual level: a comparison of item responses theory and covariance structure approaches[END_REF] because it focuses on each item of the scale of measurement and each rating point used by respondents [START_REF] Thissen | Data analysis using item response theory[END_REF]. Results of the analysis of the NFC scale based on confirmatory factor analysis are not different from those of GRM analysis. Both studies reject NFC1 and NFC3. GRM analysis understands and justifies the removal of an item that is obviously misunderstood by respondents. The confirmatory factor analysis provides the same deletion but needs new data collection. So there is a complementarity between these two methods, and GRM analysis should precede the confirmatory factor analysis on the timeline.

When non-normal distribution occurs on one or more items of a rating scale, the use of GRM analysis is recommended. Results of the satisfaction scale show that the item distributions are characterized by a strong asymmetry. In this case, the use of GRM analysis, which does not assume a linear relationship between the items and the θ latent trait, allows a more rigorous estimate of the scale and its items. GRM analysis shows that only three of the four original items of the satisfaction scale are selected. The item SAT3 is characterized by decreased precision -an information not available using CCT. The item SAT3 focuses on the disappointment felt by the respondent when considering his/her relationship with the salesperson, with an explicit reference to the customer's expectations ("compared to what I expected"). As this item is not a direct measure of customer satisfaction, it is not surprising that the GRM analysis highlights its weaknesses. The satisfaction scale with three items and without SAT3 is thus preferable to having four items. GRM analysis does not impose any condition on the item distribution and can be performed in the absence of normality. Facing non-normal distribution (skewness or kurtosis), the GRM analysis may complement measurement theory tests to select items [START_REF] Nunnally | Psychometric theory, Third Edition[END_REF]. GRM analysis focuses on each item and its rating points of the measurement scale [START_REF] Thissen | Data analysis using item response theory[END_REF], which allows a more detailed analysis of the items used to measure a latent trait than that obtained by structural equation modeling [START_REF] Reise | Assessing the fit of measurement models at the individual level: a comparison of item responses theory and covariance structure approaches[END_REF]. It analyzes in great detail the quality of items of a measurement scale. It refines and thus completes analysis based on classical measurement tests. GRM analysis can be inserted in the scale construction process. Usually, marketing researchers start from a set of items from which items are selected on the basis of item content (content validity and face validity) and their technical characteristics (construct validity). The GRM analysis provides a set of indicators from which to choose the best items before their use on larger samples. It can be inserted after the analysis of reliability, content validity and face validity and before a confirmatory factor analysis. IRT is used in addition to or as a substitute for the confirmatory factor analysis to ensure that the items and rating points are understood by respondents. It is therefore appropriate to use the GRM analysis to select the items before the confirmatory factor analysis. Overall, GRM analysis promotes a very careful choice of items.

AUTHORS


Pauline Glatz
email: pauline.glatz@upmc.fr

Monique Comte

Laurent Cormier

Lionel Montagne

Bertrand Doumert

Galan G Moore

Different roles of phosphorous in the nucleation of lithium aluminosilicate glasses

Keywords: P 2 O 5, Glass structure, Glass-ceramics, Thermal Analysis, NMR spectroscopy

Glasses in the Li

2 O-Al 2 O 3 -SiO 2 (LAS) system with different Al 2 O 3 Li 2 O ratio with or without addition of P 2 O 5 have been synthesized and characterized by thermal analysis. The glass structure and the phosphorous environments in the glasses and their evolutions with annealing have been studied by 31 P Solid-State Nuclear Magnetic Resonance (SSNMR) and 31P/27Al D-HMQC (Dipolar Hetero-nuclear Multiple-Quantum Coherence) correlation NMR. The crystallization behavior has been studied by XRD, SSNMR and RAMAN spectroscopy. The results showed a different role for P 2 O 5 depending on the Al 2 O 3 Li 2 O ratio. For low alumina content, P 2 O 5 plays a nucleating role while it acts as crystallization inhibitor for high alumina content. These different roles are related to different local environments of the phosphorus in the as-cast glasses. Our study emphasizes the importance of POAl complexes in the crystallization process of aluminosilicate glasses.

Introduction

Glass-ceramics are materials obtained by controlled crystallization of glasses, which is achieved by thermal heat treatment on parent glasses. [START_REF] Höland | Glass-ceramics technology[END_REF] The lithium aluminum silicate (LAS) ternary system is one of the most studied and a large number of materials with this composition are commercialized due to their excellent thermo-physical properties. As typical examples we can mention: the near-zero thermal expansion property for β-quartz solid solution glass-ceramics used for telescope mirror, stove cooktops and firedoor applications [START_REF] Beall | Nanophase glass-ceramics[END_REF][START_REF] Comte | Commercial applications of glass-ceramics[END_REF], or the good mechanical properties for compositions with low amount of Al 2 O 3 used in the field of restorative dentistry [START_REF] Huang | A novel highstrength lithium disilicate glass-ceramic featuring a highly intertwined microstructure[END_REF]. Since the properties of the glass-ceramics are widely dependent of the nature and relative amount of crystalline phases, the control of nucleation is a key step in order to optimize the final properties.

To promote bulk crystallization and obtained an uniform distribution of crystals in the material, nucleating agents such as TiO 2 , ZrO 2 , and P 2 O 5 are typically added in the Li 2 O-Al 2 O 3 -SiO 2 (LAS) glass composition. [START_REF] Holand | Control of nucleation in glass ceramics[END_REF][START_REF] Pinckney | Microstructural evolution in some silicate glass-ceramics: A review[END_REF][START_REF] Zanotto | Recent studies of internal and surface nucleation in silicate glasses[END_REF]. In particular, phosphorous, which is classified as a typical network former in glasses, has a complex structural role that strongly impacts its solution behavior, the melt viscosity [START_REF] Toplis | The variable influence of P 2 O 5 on the viscosity of melts of differing alkali/aluminium ratio: Implications for the structural role of phosphorus in silicate melts[END_REF] or its ability to promote liquid-liquid phase separation and affect the crystallization mechanisms [START_REF] James | Liquid-phase separation in glass-forming systems[END_REF].

In a study on the effect of the

Al 2 O 3 M 2 O
ratio (where M=Li,Na) on the crystallization of LAS system with P 2 O 5 addition [START_REF] Arvind | Evolution of crystalline phases as a function of composition and dwell time in lithium aluminium silicate glass-ceramics[END_REF], different crystalline phases were reported depending on the Al 2 O 3 content and volume crystallization was observed at low Al 2 O 3 amount contrary to surface crystallization observed at high alumina content. Indeed, P 2 O 5 is a well-known nucleating agent for low alumina LAS compositions, yielding to Li 2 Si 2 O 5 crystallization. [START_REF] Holand | Control of nucleation in glass ceramics[END_REF][START_REF] Höland | Studies of crystal phase formations in high-strength lithium disilicate glass-ceramics[END_REF][START_REF] Zheng | Effects of P 2 O 5 and heat treatment on crystallization and microstructure in lithium disilicate glass ceramics[END_REF][START_REF] Wang | Flexural strength and translucent characteristics of lithium disilicate glass-ceramics with different P 2 O 5 content[END_REF][START_REF] Clausbruch | The effect of P 2 O 5 on the crystallization and microstructure of glass-ceramics in the SiO 2 -Li 2 O-K 2 O-ZnO-P 2 O 5 system[END_REF] In terms of nucleation mechanism, Headley and Loehman [START_REF] Headley | Crystallization of a glass-ceramic by epitaxial growth[END_REF] reported that lithium orthophosphate Li 3 PO 4 crystals act as heterogeneous nuclei for silicate crystalline phases (metasilicate Li 2 SiO 3 and disilicate Li 2 Si 2 O 5 phases). Successive studies using solid state 31 P MAS-NMR gave insight on the changes around phosphorous occurring during the crystallization processes [START_REF] Holland | Early stages of crystallisation of lithium disilicate glasses containing P 2 O 5 -An NMR study[END_REF][START_REF] Bischoff | Phase evolution in lithium disilicate glass-ceramics based on non-stoichiometric compositions of a multi-component system: structural studies by 29 Si single and double resonance solid state NMR[END_REF][START_REF] Huang | Crystallization of a highstrength lithium disilicate glass-ceramic: An XRD and solid-state NMR investigation[END_REF]. Indeed, MAS-NMR techniques probe the local environment around phosphorus and reveal modifications occurring in the first crystallization steps which could conceivably be missed by other techniques [START_REF] Ananthanarayanan | A comparative overview of glass-ceramic characterization by MAS-NMR and XRD[END_REF]. On a disilicate (aluminum-free) glass-ceramic composition, Holland et al [START_REF] Holland | Early stages of crystallisation of lithium disilicate glasses containing P 2 O 5 -An NMR study[END_REF] reported that crystalline Li 3 PO 4 was not detected by MAS-NMR before the formation of Li 2 Si 2 O 5 phases. However, recent studies revealed that a highly disordered Li 3 PO 4 phase is formed concomitantly with Li 2 SiO 3 crystallization [START_REF] Bischoff | Phase evolution in lithium disilicate glass-ceramics based on non-stoichiometric compositions of a multi-component system: structural studies by 29 Si single and double resonance solid state NMR[END_REF] [START_REF] Huang | Crystallization of a highstrength lithium disilicate glass-ceramic: An XRD and solid-state NMR investigation[END_REF].

In aluminosilicate glasses, MAS-NMR showed that phosphorus has different environments depending on the

Experimental Section

Materials

Glasses were prepared in the Li 2 O-Al 2 O 3 -SiO 2 (LAS) ternary system with addition of P 2 O 5 oxide as a nucleating agent. Analytical grade precursors (Li 2 CO 3 , Al 2 O 3 , SiO 2 and (NH 4 ) 2 HPO 4 ) were ground together, dried and melted in a Pt crucible at 1550 • C for 2 h, then quenched by immersing the bottom of the crucible into water. The glasses were ground and molten once again to ensure a good homogeneity. Table 1 reports the glass compositions.

They are located along the 74 mol% SiO 2 isopleth, with 0 or 1 mol% P 2 O 5 .

These compositions cover a range with a ratio R=

Differential scanning calorimetry

Differential Scanning Calorimetry (DSC) thermograms were recorded on a 404 C Pegasus calorimeter from Netzsch (Selb, Germany). All the measurements were carried out in air and heat treatments were conducted at 10 • C/min with a bulk sample of ∼50 mg in Pt crucible, using an empty Pt crucible as reference.

The crystallization temperature of the first exothermic event was determined at the maximum of the peak. The glass transition temperatures T g , the onset crystallization temperatures T x and the temperatures of the maximum of the first crystallization peak T c are reported in Table 1.

XRD

X-ray diffraction was carried out at room temperature using a diffractometer (PANalytical X'Pert PRO) with Ni-filtered CuKα radiation (λ =1.5418 Å). Data were recorded in the 10 • ≤2θ ≤80 • range with a step increment of 0.016 • and an interval time of 0.82 sec per step.

RAMAN spectroscopy

Raman spectra of the glasses and annealed glasses were obtained using a Horiba LabRam HR Evolution system with Ultra-Low Frequency (ULF) module, 1800 gr/mm grating, and a 532 nm laser operating at 100 mW. A x10 magnification objective was used for this study. Each sample was analyzed with an exposure time of 30 sec (per window) with 10 accumulations and a spectral window from 5 to 2000 cm -1 . No temperature correction nor normalization have been used for these spectra.

Scanning Electron Microscopy

Scanning Electron Microscopy (SEM) was used to observe the microstructure of the samples. Bulk glass pieces were embedded in epoxy resin, then cross sections were polished and etched with 1 mol% HF for 30 seconds. They have been coated with iridium (2 nm thick) and observed using a SEM-FEG (Field Emission Gun) ZEISS LEO 1550 (Jena, Germany), at a 5 kV accelerating voltage. Observations have been done with the In-lens secondary electrons detector.

2.6. Solid-state NMR 31 P and 27 Al MAS-NMR (Magic Angle Spinning Nuclear Magnetic Resonance) spectra were recorded at 9.4 and 18.8 T on Bruker AVANCE I and AVANCE III spectrometers, respectively, with a 4 mm probe at 12.5 kHz spinning speed for 31 P and a 3.2 mm probe at 20 kHz spinning speed for 27 Al. The Larmor frequencies were 161.9 and 208.5 MHz for 31 P and 27 Al, respectively.

For 31 P, the pulse duration was 4.8 µs (π/2), and the recycle delay (rd) was 120 s. For 27 Al, the pulse duration was 1 µs (π/10), and the rd 2 s. The recycle delays have been defined to enable enough relaxation to get quantitative spectra. The 31 P chemical shifts are relative to 85% H 3 PO 4 solution at 0 ppm and those of 27 Al are referred to Al(NO 3 ) 3 solution as 0 ppm. Decomposition of NMR spectra was done by using dmfit software [START_REF] Massiot | Modelling one-and two-dimensional solid-state NMR spectra[END_REF]. The 27 Al/ 31 P 2D maps were edited with the dipolar heteronuclear multiple quantum coherence (D-HMQC) sequence [START_REF] Trebosc | Through-space R 3 -HETCOR experiments between spin-1/2 and half-integer quadrupolar nuclei in solid-state NMR[END_REF] on a 18.8 T spectrometer with a 3.2 mm HPAl probe operating at a spinning frequency of 20 kHz. The 988×23 datas points and 3988×19 for LAS0.2-P1 and LAS0.7-P1 samples, respectively, were acquired with a 27 Al selective 90 • -τ -180 • -τ spin-echo. The 31 P channel was irradiated with 90 • pulses and with a 1.1 ms recoupling time with the SR4 2 1 sequence. Each t1 was recorded with 16384 scans for LAS0.2-P1 (18432 for LAS0.7-P1) with a rd of 0.5 s.

Results

Study of the crystallization

DSC investigations

Figure 1 shows the DSC curves obtained during heating of the glasses with and without P 2 O 5 and for different alumina contents. These curves show an endothermic shift of the baseline, which is characteristic of the glass transition (T g ). The increase in T g when R ratio increases can be attributed to the polymerization of the aluminosilicate glass network. The crystallization of the glasses is revealed by exothermic peaks, which are more or less intense and broad as will be discussed hereafter. We observe two different crystallization behaviors depending on the R ratio: for low alumina content, R<0. [START_REF] Höland | Studies of crystal phase formations in high-strength lithium disilicate glass-ceramics[END_REF]. For R≥0.7, crystallization peaks are observed at higher temperatures for the glasses with P 2 O 5 , compared to those without P 2 O 5 . In addition, large crystallization exotherms (i.e.

-Al 2 O 3 -Li 2 O-K 2 O-ZrO 2 -P 2 O 5 system
large ∆T, where ∆T is the width of the crystallization exotherm) are observed both with and without P 2 O 5 . The complete attribution of the different exother-mic events is beyond the scope of this paper. The parameter ∆T x (=T x -T g ), reflecting the glass stability (GS) [START_REF] Nascimento | Can glass stability parameters infer glass forming ability?[END_REF], can also be considered. The higher the ∆T x , the lower the ability of a glass to crystallize. In our case, the exact interpretation is not easy as two crystallization mechanisms can occur: volume crystallization and surface crystallization. However, a different behavior for the glasses containing P 2 O 5 is clearly observable: when R<0.7, ∆T x is lower (lower GS) for compositions with P 2 O 5 than ∆T x for compositions without P 2 O 5 . For R≥0.7, the opposite effect is observed: the addition of P 2 O 5 increases the glass stability. As the role of P 2 O 5 is different for low or high alumina content, we will focus our investigation on two glass compositions representative of these two different crystallization behaviors: the LAS0.2-P1 composition corresponding to R<0.7 range and the LAS0.7-P1 composition corresponding to R≥0.7 range.

Crystalline phases detected by XRD and RAMAN analysis

The lack of Bragg peaks in the XRD pattern of the LAS0. For the LAS0.7-P1 composition (figure 2b), the as-cast glass also shows an amorphous bump, but the crystallization sequence is different for the annealed samples. The first Bragg peak appears at 750 Raman study was performed on the two selected glass and glass-ceramic compositions. No curve fitting or deconvolution of the spectra have been done, since spectra were recorded only to get the signatures of the different amorphous and crystalline phases. In addition, information can be obtained on the phosphorous environment in the glass and its evolution with temperature by looking at the 950 cm -1 region, which will be detailed in the next section. Main Raman peaks are assigned in figure 3.

For both glasses in figure 3(bottom), two main regions can be observed.

The region between 350-650 cm -1 is attributed mainly to bending vibrations of Si-O and Al-O bonds associated with high-membered rings of the aluminosilicate network [START_REF] Yadav | A review of the structures of oxide glasses by Raman spectroscopy[END_REF]. The region between 1000-1200 cm -1 is attributed to Si-O-Si, Si-O-Al asymmetric stretching vibrations and symmetric Si-O -stretching vibrations [START_REF] Yadav | A review of the structures of oxide glasses by Raman spectroscopy[END_REF].

For the LAS0.2-P1 composition (figure 3a), no sharp bands are observable before treatment at 650 (613 and 977 cm -1 in [START_REF] Richet | Melting and premelting of silicates: Raman spectroscopy and X-ray diffraction of Li 2 SiO 3 and Na 2 SiO 3[END_REF]). In addition, the band at 488 cm -1 , characteristic of petalite crystals [START_REF] Kaminskii | Lithium silicate, LiAlSi 4 O 10 (petalite) -a novel monoclinic SRS-active crystal[END_REF], is also detected at this temperature. At 740 • C for 1 hour, the presence of a sharp band at 462 cm -1 indicates β-quartz crystallization [START_REF] Alekseeva | Raman spectroscopy quantifying the composition of stuffed β-quartz derivative phases in lithium aluminosilicate glass-ceramics[END_REF].

With further annealing, at 815 • C 1 hour, the shift of the band at 462 cm -1 to 479 cm -1 indicates the appearance of β-quartz solid solution [START_REF] Alekseeva | Raman spectroscopy quantifying the composition of stuffed β-quartz derivative phases in lithium aluminosilicate glass-ceramics[END_REF]. At 900

• C 1
hour, the band is shifted to a large band near 488 cm -1 , characteristic of the presence of β-spodumene solid solution (close to pure β-spodumene at 492 cm -1 in [START_REF] Sharma | Raman-study of crystalline polymorphs and glasses of spodumene composition quenched from various pressures[END_REF]). The crystallization of Li 3 PO 4 is evident at high temperature with the sharp peak at 947 cm -1 close to that of pure γ-Li 3 PO 4 at 950 cm -1 according to [START_REF] Popović | Raman spectroscopic study of phase transitions in Li 3 PO 4[END_REF].

For the LAS0.7-P1 composition (figure 3b), no sharp bands are observable after annealing at 750 • C 1 minute. The spectrum of heated sample at 800 • C for 1 minute shows the crystallization of β-quartz solid solution with the band at 480 cm -1 [START_REF] Alekseeva | Raman spectroscopy quantifying the composition of stuffed β-quartz derivative phases in lithium aluminosilicate glass-ceramics[END_REF] and the shoulder at 453 cm -1 [START_REF] Sharma | Raman-study of crystalline polymorphs and glasses of spodumene composition quenched from various pressures[END_REF]. The apparition of β-spodumene solid solution at the expense of β-quartz solid solution is evident at 850 • C by the shift of the band from 480 to 490 cm -1 and by the 192 cm -1 band [START_REF] Sharma | Raman-study of crystalline polymorphs and glasses of spodumene composition quenched from various pressures[END_REF].

Li 3 PO 4 and Li 2 SiO 3 crystallization are observed after a treatment at 800 • C for 1 hour with the sharp bands at 944 cm -1 for Li 3 PO 4 [START_REF] Popović | Raman spectroscopic study of phase transitions in Li 3 PO 4[END_REF] and 975 and 603 cm -1

for Li 2 SiO 3 [START_REF] Richet | Melting and premelting of silicates: Raman spectroscopy and X-ray diffraction of Li 2 SiO 3 and Na 2 SiO 3[END_REF]. The spectrum of LAS0.2-P1 shows a resonance at 9.2 ppm assigned to orthophosphate units (PO 3 - 4 ) [START_REF] Dupree | The role of small amounts of P 2 O 5 in the structure of alkali disilicate glasses[END_REF]. In addition, a second resonance around 0 ppm can be attributed to pyrophosphates units (P 2 O4 - 7 ) [START_REF] Holland | Early stages of crystallisation of lithium disilicate glasses containing P 2 O 5 -An NMR study[END_REF] and possibly PO 3 - lase evidenced a change of about 8 to 9 ppm for each additional Al [START_REF] Dollase | Structure of Na 3-3x Al x PO 4 , x=0 to 0.5[END_REF]. For the LAS0.7-P1 composition, with a higher alumina content, a single broad resonance is present at -3.5 ppm, shifted to more negative chemical shifts compared to LAS0.2-P1, which is attributed to the presence of more Al 3+ cations compensating the PO 3 - 4 species [START_REF] Toplis | 31 P MAS NMR study of glasses in the system xNa 2 O-(1-x)Al 2 O 3 -2SiO 2 -yP 2 O 5[END_REF]. These species containing P-O-Al bonds are called POAl complexes in this study.

The 27 Al MAS-NMR spectra of the two glasses are shown in figure 5b.

They show a single peak in the region 55-60 ppm, ascribed to aluminum in tetrahedral coordination (Al IV ). Owing to the presence of an excess of Li + for the charge compensation, Al 3+ adopts a tetrahedral conformation, as reported in per-alkaline aluminosilicate glasses [START_REF] Stebbins | Quantification of five-and six-coordinated aluminum ions in aluminosilicate and fluoride-containing glasses by high-field, highresolution 27 Al NMR[END_REF]. In addition, a small peak around 25 ppm for the LAS0.2-P1 is detected and could be due to Al V as it has been detected earlier in per-alkaline-earth aluminosilicate glasses. [START_REF] Neuville | Local Al site distribution in aluminosilicate glasses by 27 Al MQMAS NMR[END_REF] In order to confirm the presence of POAl complexes mentioned above in these glasses, 31 P- 27 Al heteronuclear correlation 2D-NMR spectra have been recorded to probe the spatial proximity of these nuclei [START_REF] Tricot | Structural characterisation of phosphate materials: new insights into the spatial proximities between phosphorus and quadrupolar nuclei using the D-HMQC MAS NMR technique[END_REF]. For that purpose, 27 Al{ 31 P} D-HMQC spectra (figure 6) have been recorded. The two spectra exhibit correlation signals between phosphate and aluminate species indicating that Al(IV)-PO 4 entities are present in the glass, even at low alumina content.

The projections of the 2D spectra are sketched as dashed lines in figure 6. They show that the maximum intensity of the correlation is centered at 3.5 ppm in the 31 P dimension for the LAS0.2-P1. However, this contribution does not take into account all the information under the curve: POAl complex is not the only entity as shown in figure 5. Two other species: PO This indicates that all the P atoms are affected by the correlation and that they see Al 3+ atoms in their environment. This implies that all the P units are connected to Al.

Previous studies on sodium aluminosilicate glasses evidenced the presence of POAl complexes [START_REF] Toplis | 31 P MAS NMR study of glasses in the system xNa 2 O-(1-x)Al 2 O 3 -2SiO 2 -yP 2 O 5[END_REF][START_REF] Schaller | TRAPDOR NMR investigations of phosphorus-bearing aluminosilicate glasses[END_REF][START_REF] Tricot | Structural characterisation of phosphate materials: new insights into the spatial proximities between phosphorus and quadrupolar nuclei using the D-HMQC MAS NMR technique[END_REF]. In their study of peralkaline compositions, Toplis and Schaller [START_REF] Toplis | 31 P MAS NMR study of glasses in the system xNa 2 O-(1-x)Al 2 O 3 -2SiO 2 -yP 2 O 5[END_REF] concluded on the presence of individual PO

Evolution of the local environment around P with temperature

The 31 P MAS-NMR spectra of the glass LAS0.2-P1 and glass-ceramics show differences with thermal treatments (figure 7a). Treatment at 550 Theses changes are also consistent with the thermal evolution associated with P environment observed by RAMAN spectroscopy (figure 3a). The intense band near 950 cm -1 is assigned to the symmetrical stretching vibration of the P-O bond [START_REF] Harbach | Raman Spectra and Optical Absorption Edge of Li 3 PO 4 Single Crystals[END_REF]. For the as-cast glass, this band is broad and located at 957 cm -1 .

This corresponds to P in the silicate network, mainly in orthophosphate species.

With increasing annealing temperatures, the band increases in intensity and becomes sharper and its position is shifted down to 947 cm The RAMAN spectra for the LAS0.7-P1 composition (figure 3b) are also in agreement with the evolution observed by NMR. Unlike the LAS0.2-P1 composition, no PO 3 - 4 band is discernible at 957 cm -1 in the as-cast glass. The band associated with Li 3 PO 4 (944 cm -1 ) first appears after the 800 • C 1 minute treatment like in the NMR spectrum.

Discussion

Chemical dependence of the crystallization process

The DSC study provided evidence for two contrasting crystallization behaviors of the glasses, depending on their alumina contents. At low alumina content, addition of P 2 O 5 results in DSC peaks that become sharper and located at lower temperatures compared to the glasses without P 2 O 5 . It is known that for a given heating rate (10 • C/min in all our DSC experiments), a sharp peak (small ∆T) denotes bulk crystallization while a broad peak (large ∆T) is an indication of surface crystallization [START_REF] Ray | Determining the Nucleation Rate Curve for Lithium Disilicate Glass by Differential Thermal Analysis[END_REF]. SEM analysis (figure 4b) confirms mainly internal crystallization for the LAS0.2-P1 glass (figure 4a). Moreover, the addition of efficient nucleating agents such as TiO 2 and ZrO 2 in some aluminosilicate glasses leads to crystallization peaks at low temperatures [START_REF] Khater | Role of TiO 2 and ZrO 2 on crystallizing phases and microstructure in Li, Ba aluminosilicate glass[END_REF][START_REF] Cormier | Zr environment and nucleation role in aluminosilicate glasses[END_REF].

This effect was also observed for P 2 O 5 in lithium disilicate-based glass [START_REF] Fernandes | The role of P 2 O 5 , TiO 2 and ZrO 2 as nucleating agents on microstructure and crystallization behaviour of lithium disilicate-based glass[END_REF][START_REF] Gaddam | The roles of P 2 O 5 and SiO 2 /Li 2 O ratio on the network structure and crystallization kinetics of non-stoichiometric lithium disilicate based glasses[END_REF],

which was explained by more nucleation sites created with the addition of P 2 O 5 .

For high alumina content R≥0.7, crystallization peaks are broad with or without P 2 O 5 , suggesting surface crystallization in both cases, which is confirmed by SEM analysis (figure 4b). In addition, T c is higher with P 2 O 5 , revealing a delay in crystallization in this glass composition. This suggests an opposite effect of the P 2 O 5 compared to the glass with low alumina content.

This difference of nucleation efficiency with P 2 O 5 has been also evidenced in a previous study [START_REF] Arvind | Evolution of crystalline phases as a function of composition and dwell time in lithium aluminium silicate glass-ceramics[END_REF]. They have observed for a compositionally complex LAS glass with 2.5 wt% P 2 O 5 that surface crystallization is favored at high alumina content while volume crystallization is obtained at low alumina content. However, the origin of this difference has not been investigated. To understand this contrasting behavior, we have considered the structural evolution of the local P environment during different annealing treatments. As shown earlier [START_REF] Höland | Studies of crystal phase formations in high-strength lithium disilicate glass-ceramics[END_REF] [43], crystalline phases containing phosphate are observed by XRD only for high temperature treatments, whereas NMR and Raman spectroscopies are able to detect subtle variations at much lower temperature, even in the T g range. This is because XRD necessitates the organization of large crystallization domains, whereas NMR and RAMAN investigate disordered and ordered local arrangements.

P 2 O 5 as nucleating agent

Upon annealing, important changes of the P environments can be observed with two distinct behaviors for the low and high alumina glass compositions (figure 7). For the LAS0.2-P1 glass, modifications of the P environment is observed for the glass heat treated at 550 • C for 1 hour (figure 7a), i.e. prior to the detection of any crystallization with XRD (figure 2a). This suggests that some structural relaxation takes place, which corresponds to a structural reorganization around phosphorous atoms. Raman analysis (figure 3a) confirms this initial reorganization around P.

In the sample heat treated at 650 units are essentially present in the as-cast glass, surrounded by Li + ions to ensure charge compensation of the tetrahedral units.

An ascertained role of P is to promote phase separation in glasses [START_REF] James | Liquid-phase separation in glass-forming systems[END_REF]. However, it is difficult to conclude if the PO The formation of P-O-Fe 3+ complexes in silicate melts was also proposed to hinder the crystallization of magnetite [START_REF] Toplis | The role of phosphorus in crystallization processes of basalt -an experimental study[END_REF].

In addition, T c peaks (Figure 1) appears at lower temperatures in LAS0.

Conclusions

Compositions from the LAS system with different R =

Al 2 O 3
Li 2 O ratio and with P 2 O 5 have been investigated. Thermal analysis showed a distinct crystallization behavior for low and high alumina content. 2 compositions were selected with low and high alumina content, and phase evolution and environment around phosphorus have been explored, as well as their modification after thermal treatments at different temperatures. This work reveals two distinct roles of P 2 O 5 depending on the presence of POAl complexes: easier bulk crystallization is obtained for the R=0.2 composition, indicating a nucleating role for P 2 O 5 , while higher crystallization temperatures are observed for the R=0.7 composition, suggesting that P 2 O 5 enhances glass stability. The POAl complexes could be detected even with low alumina content thanks to the enhanced sensitivity of the D-HMQC NMR pulse sequence. The nucleating role of P 2 O 5 is not related to the crystallization of lithium orthophosphate phases, as these crystals appears after the crystallization of lithium silicate phases. The presence, and development upon annealing, of structurally disordered heterogeneities associated with P is responsible for changes in structure and properties of the remaining glass, which promotes crystallization at low alumina content. With increasing Al 2 O 3 content, the POAl complexes become the dominant species. These complexes result in the dispersion of phosphate species within the glass matrix and prevent the formation of the heterogeneities associated with P. As a consequence, P 2 O 5 can be considered as a crystallization inhibitor in LAS glasses with high alumina content.

Figures

Al 2 O 3 M 2 O

 32 ratio[START_REF] Toplis | 31 P MAS NMR study of glasses in the system xNa 2 O-(1-x)Al 2 O 3 -2SiO 2 -yP 2 O 5[END_REF][START_REF] Schaller | TRAPDOR NMR investigations of phosphorus-bearing aluminosilicate glasses[END_REF]. At low P 2 O 5 content, a majority of PO 3 - 4 orthophosphate and P 2 O 4 - 7 pyrophosphate groups are observed in the glass matrix, while for increasing Al 2 O 3 contents, aluminophosphate groups are formed. Recent developments in NMR provide information on the connectivity of PO 4 tetrahedra with the aluminosilicate network. Spatial proximities between P and Al were reported in systems with low amount of P 2 O 5 and Al 2 O 3 [22][23] and aluminophosphate groups could be detected in such glasses. Nevertheless, such methods were not used up to now for the detailed study of the nucleation process by P 2 O 5 in LAS glass-ceramics. The aim of the present work is to provide new insights to elucidate the role of phosphorous in crystallization mechanisms of LAS compositions with different Al 2 O 3 Li 2 O ratio. We report a combination of characterization and spectroscopic methods to investigate the crystallization sequences and the nucleating role of phosphorous. NMR and Raman spectroscopies enable us to discuss the changes in the phosphorus environments in relation with the crystallization processes, showing a different behavior between the glasses containing low and high Al 2 O 3 contents.

Al 2 O 3 Li 2 OO 3 Li 2 O

 3232 from 0 (Al-free) to 1.3 (peraluminous composition). The glasses are labeled as follow: LASR-Pn, where R is the ratio Al 2 and n the mol% of P 2 O 5 . Transparent, bubble free, glasses were obtained excepted for the LAS0-P1, which is opalescent. For all samples, powder XRD patterns show the characteristic broad peak of amorphous materials and no Bragg peak. The glass compositions were checked by Electron probe micro-analyser (CAMPARIS, Paris, France) with a CAMECA SX-Five apparatus (15 kV, 10 nA) for SiO 2 , Al 2 O 3 , P 2 O 5 and by a Flame-Atomic Absorption Spectrometer in emission mode (Agilent, AA280FS) for Li 2 O content.

2 - 5 sheets (like Li 2

 252 P1 sample (figure 2a) confirms that the initial glass is amorphous. For the annealed samples, the first Bragg peaks are observed for a treatment at 650 • C for 1 minute and are assigned to lithium metasilicate (Li 2 SiO 3 , JCPDS No. 29-0829) and lithium disilicate (Li 2 Si 2 O 5 , JCPDS No. 70-4856) phases. Then, with further treatment at 650 • C for 1 hour, petalite (LiAlSi 4 O 10 , JCPDS No. 83-1470) phase appears, which has a layered structure of Si 2 O 2 - Si 2 O 5 ) linked by Li and Al tetrahedra. A β-quartz phase (JCPDS No. 89-8949) is also observed at this thermal treatment. At 815 • C for 1 hour, a small peak due to Li 3 PO 4 (JCPDS No. 15-0760) is detected and β-quartz solid solution (a lithium aluminosilicate phase, β-quartz ss) appears, as evidenced by the shift of the main peak of the β-quartz phase to lower 2θ value. Petalite and Li 2 SiO 3 are no more observable. With higher treatment temperature (900 • C, 1 hour), β-spodumene solid solution (β-spodumene ss, JCPDS No. 35-0794) phase appears.

3. 1

 1 Figure4ashows SEM image of the LAS0.2-P1 glass treated at 650 • C for 1 minute. Small holes distributed uniformly can be observed. They are attributed to Li 2 SiO 3 crystals observed on the XRD pattern, which are easily dissolved in the HF acid solution used for sample preparation, due to their low polymerization degree (chain-like structure). Figure4bshows SEM image of the LAS0.7-P1 glass treated at 800 • C for 1 minute. Surface crystallization is visible for this sample (constituted of β-quartz ss and β-spodumene ss according to XRD pattern), while no crystal formation is detected in the bulk.

3 - 4 only surrounded by Li + at 9 . 2 7 around 0

 349270 ppm and pyrophosphate species P 2 O 4 - ppm are observable and are not affected by the correlation. For the LAS0.7-P1 composition, the maximum is shifted to -3.5 ppm in the 31 P dimension. The projection of the correlation (in dashed line on the left figure6b) and the 1D spectrum are superimposed.

  • C for 1 hour already induces some modifications of the environment around31 P though this temperature is below the glass transition temperature. The intensity of the contribution near 9.2 ppm increases in intensity and its position is shifted to 9.5 ppm. On the spectrum of the sample treated at 650 • C for 1 minute, the resonance is shifted again to higher chemical shift near 10 ppm and its intensity becomes sharper, indicating the onset of orthophosphate crystallization. Indeed, the chemical shift is close to the chemical shift of pure crystalline Li 3 PO 4 (10 ppm)[START_REF] Dupree | The role of small amounts of P 2 O 5 in the structure of alkali disilicate glasses[END_REF]. However, the linewidth of the resonance is still large (∼3 ppm) indicating a chemical shift distribution due to some residual disorder. The persistence of disorder suggests the presence of a poorly crystallized intermediate species. With further thermal treatments at 650 • C, 740 • C, 815 • C and 900 • C for 1 hour, this contribution becomes even sharper and its linewidth decreases to ∼0.8 ppm at 900 • C, the same order of magnitude for the linewidth has been observed in the study of Bischoff et al.[START_REF] Bischoff | Phase evolution in lithium disilicate glass-ceramics based on non-stoichiometric compositions of a multi-component system: structural studies by 29 Si single and double resonance solid state NMR[END_REF] at high temperature treatment. These modifications reveals the increasing crystallinity of this orthophosphate species (Li 3 PO 4 ). In parallel, the resonances at 3.5 ppm and around 0 ppm decrease in intensity and almost disappear at 815 • C. The only resonance remaining at 900 • C is the one at 10.3 ppm, corresponding to crystalline Li 3 PO 4 (figure7a).

  -1 , very close to the band characteristic of γ-Li 3 PO 4 located at 950 cm -1[START_REF] Popović | Raman spectroscopic study of phase transitions in Li 3 PO 4[END_REF]. The shift in position starts at 550 • C for 1 hour treatment, in agreement with the evolution of the local P environment determined by NMR (figure7a).For the composition LAS0.7-P1, the31 P MAS-NMR spectra of the glass and the glass-ceramics heat-treated at 700 • C and 750 • C for 1 minute are nearly identical. A peak at 10 ppm attributed to nanocrystalline Li 3 PO 4 (linewidth ∼1.8 ppm) appears after a treatment at 800 • C for 1 minute, while the contribution around -3.5 ppm is still present. With annealing at 800 • C, 850 • C and 900 • C for 1 hour, this peak becomes sharper and its position is shifted to 10.6 ppm (linewidth of ∼1.1 ppm). It is the only observable contribution at the end of annealing treatments.

  7-P0 compared to LAS0.7-P1 indicating that P 2 O 5 mitigates the surface crystallization of β-quartz ss. P 2 O 5 plays no role in bulk crystallization but affects in another way the crystallization of this glass by stabilizing the glass structure. Others studies concluded on this dual role of P 2 O 5 depending the composition in SrO-TiO 2 -Al 2 O 3 -SiO 2 -B 2 O 3 system [50]. In addition, in a Na 2 O-2CaO-3SiO 2 glass, addition of 2 wt% of P 2 O 5 enhances glass-forming tendency by diminishing nucleation rate[51].

Figure 1 : 5 29

 15 Figure 1: Differential scanning calorimetry curves of the glasses without (orange) P 2 O 5 and with (purple) 1 mol% P 2 O 5

Figure 2 :

 2 Figure 2: XRD patterns of the compositions LAS0.2-P1 (a) and LAS0.7-P1 (b) annealing at different temperatures and times

Figure 3 :

 3 Figure 3: RAMAN spectra of LAS0.2-P1 (a) and LAS0.7-P1 (b) annealed at different temperatures and times

Figure 4 :

 4 Figure 4: SEM image of samples polished then etched with 1 % HF for 30 seconds of (a) LAS0.2-P1 annealed at 650 • C for 1 minute, (b) LAS0.7-P1 annealed at 800 • C for 1 minute

Figure 5 :

 5 Figure 5: (a) 31 P MAS-NMR spectra recorded at 9.4 T, (b) 27 Al MAS-NMR spectra recorded at 18.8 T of as-cast glasses LAS0.2-P1 and LAS0.7-P1

Figure 6 :

 6 Figure 6: 27 Al{ 31 P} D-HMQC spectra recorded at 18.8 T of as-cast glasses LAS0.2P1 (a) and LAS0.7-P1 (b). The dashed lines are the 31 P projections of the 2D spectra.

  JCPDS No. 31-0707). With further annealing at 800 • C for 1 minute, peaks characteristic of β-spodumene solid solution (JCPDS No. 35-0794) appears. Li 2 SiO 3 (JCPDS No. 29-0829) and Li 3 PO 4 (JCPDS No. 15-0760) crystals are observed after 1 hour treatment at 800 • C.

• C for 1 minute and is attributed to a β-quartz solid solution (

  Al atoms. They denoted these species Na 2 (NaAl)PO 4 and Na(NaAl) 2 PO 4 where (NaAl) represents one of the four bonds of a Al(IV) charge balanced by sodium (0.25NaAl 4+ ). Na 2 (NaAl)PO 4 is at 7 ppm while Na(NaAl) 2 PO 4 at -5 ppm. Similarly, in our peralkaline Li-aluminosilicate glasses, we can attribute the resonances at 3.5 ppm and at -3.5 ppm to Li 2 (LiAl)PO 4 and Li(LiAl) 2 PO 4 , respectively. The latter species is the main contribution for the LAS0.7-P1 composition.

	4	3 -	tetra-
	hedra linked to the aluminosilicate framework with the replacement of one or
	two Na atoms by

  • C for 1 minute, the orthophosphate contribution is shifted towards high chemical shift values and its intensity becomes sharper, indicating that P atoms evolves towards an environment consistent with the formation of crystalline Li 3 PO 4 but not well crystallized, as the linewidth is large compared to pure Li 3 PO 4 . This species appears concomitantly with the crystallization of the first phases detected by XRD (Li 2 SiO 3 and Li 2 Si 2 O 5 in our study). This disordered Li 3 PO 4 has been suggested as an intermediate nucle-SiO 3 crystallization while well-ordered crystalline Li 3 PO 4 appears at higher temperature together with the formation of Li 2 Si 2 O 5 [17][18]. Similarly, annealing of the LAS0.2-P1 glass at higher temperatures (650 • C 1h, 740 • C 1h and 815 • C 1h) lead to an increase of the ordering around P as indicated by the sharpening of the NMR resonance at 10 ppm. This is accompanied by the disappearance of the pyrophosphate Li 4 P 2 O 7 and Li 2 (LiAl)PO 4 species. After annealing at 900 • C for 1 hour, the only contribution is at 10.3 ppm, attributed to well-crystallized Li 3 PO 4 and Bragg peaks characteristics of this phase are observed by XRD.

	31 P MAS-NMR spectrum for the LAS0.2-P1 glass show that the monomeric
	PO 3 -4	and dimeric P 2 O 4 -7

ation step in previous crystallization investigations for non stoichiometric disilicate glasses

[START_REF] Bischoff | Phase evolution in lithium disilicate glass-ceramics based on non-stoichiometric compositions of a multi-component system: structural studies by 29 Si single and double resonance solid state NMR[END_REF]

[START_REF] Huang | Crystallization of a highstrength lithium disilicate glass-ceramic: An XRD and solid-state NMR investigation[END_REF]

. In these studies, a strongly disordered P-containing phase appears first with Li 2

  Although the glass studied is transparent and no phase separation is observable by SEM, nano-heterogeneities in terms of P-enriched nano-domains could still be present. Indeed, Dargaud et al.[START_REF] Dargaud | Multi-scale structuration of glasses: Observations of phase separation and nanoscale heterogeneities in glasses by Z-contrast scanning electron transmission microscopy[END_REF] evidenced nano heterogeneities by electron microscopy of 1-5 nm for a MgO-Al 2 O 3 -SiO 2 glass with ZrO 2 addition though the glass is transparent and appears as amorphous by XRD. Interestingly, during the first annealing treatments, the P environment evolves towards the formation of disordered Li 3 PO 4 domains. Locally, these clusters correspond to Li + ions scavenged by the phosphorous atom and a remaining silicate network depleted in Li + ions and, thereby, more polymerized. This is confirmed by Bischoff et al.[START_REF] Bischoff | Phase evolution in lithium disilicate glass-ceramics based on non-stoichiometric compositions of a multi-component system: structural studies by 29 Si single and double resonance solid state NMR[END_REF], who evidenced by a29 Si/ 7 Li NMR correlation technique a lithium clusterization before crystallization of Li 2 SiO 3 . These disordered orthophosphate clusters embedded in the silicate network have two possible effects on the crystallization mechanism. First, the crystallization of silicate phases is possible due to lowering interfacial energy resulting from a high concentration of Li atoms and a low polymerization of the silicate network close to Li-orthophosphate clusters. These compositional and structural fluctuations should promote the formation of Li 2 SiO 3 . This scenario explains the proximity of the silicate phases and Li 3 PO 4 and corresponds to the epitaxial growth observed in In the case of the LAS0.7-P1 composition, the 31 P MAS-NMR spectra of glasses annealed at 700 • C and 750 • C for 1 minute show very little variation compared to the as-cast glass (figure 7b). The first important modification in the NMR spectra appears after annealing at 800 • C for 1 minute, that is after the first crystallization observable by XRD at 750 • C for 1 minute. At 800 • C, a peak at 10 ppm appears due to nanocrystalline Li 3 PO 4 while the contribution Li(LiAl) 2 PO 4 is still present. In the RAMAN spectra in figure 3b, the two first modifications appear simultaneously at 800 • C: the main band characteristic of β-quartz ss and the one due to Li 3 PO 4 . Both NMR and RAMAN agree that no rearrangement around P is observed before crystallization of the LAS0.7-P1 glass, contrary to LAS0.2-P1. When crystallization of Li 3 PO 4 occurs, POAl complexes are no more detected in the NMR spectra.

	3 -4 separation could favor homogeneous nucleation of silicate phases. In both cases, tetrahedra are isolated from each other or bondings are expected and Al atoms are dispersed within the polymeric network
	if they tend to segregate within the silicate network. Using an advanced NMR internal crystallization is achieved. of alkali aluminosilicate glasses [46][47]. Consequently, phosphorus atoms are
	technique ( 31 P spin-counting), Fayon et al. [44] have shown that nanometric-likely well-separated within the aluminosilicate network due to their bonding
	sized heterogeneities can be evidenced in a lime phosphosilicate bioactive glass 4.3. P 2 O 5 as inhibitor of crystallization with Al. Such network organization prevents the formation of phosphate clus-
	with phosphate clusters containing 5-6 PO 3 -4 ters and the formation of Li-rich zones, contrary to LAS0.2-P1. Furthermore, entities. A similar approach ap-
	pears unsuccessful in our glass since we have measured that the relaxation time PO + 4 sites are stabilized as charge balance is ensured by AlO -4 tetrahedra [48].
	is too low (<7 ms) compared to the one (around 20 ms) required to probe P-P
	connectivities with this technique.
	In the LAS0.7-P1 composition, the nanocrystalline Li 3 PO 4 appears after
	crystallization of the aluminosilicate network and this is not preceded by a reor-
	ganization of the P environment. This indicate that for the Al-rich compositions,
	P does not play an active role in the crystallization process, which explains that
	surface crystallization mainly occurs. A nucleating role for P is likely inhibited
	by the formation of POAl complexes. Though spatial proximities between P and
	Al is revealed by the 27 Al{ 31 P} D-HMQC correlation technique for the two com-
	positions with low and high alumina content, the POAl complexes are present in
	a minor amount in LAS0.2-P1 NMR spectra at 3.5 ppm. The POAl complexes
	present for low alumina content strongly suggests a preferential association of
	a early study by Headley and Loehman [15]. Alternatively, the orthophosphate these two cations. For the LAS0.7-P1 glass (figure 6b), the component at-
	heterogeneities are embedded in a silicate network whose composition is shifted tributed to POAl complexes is clearly predominant (at -3.5 ppm) and no PO -43
	towards the center of the Li 2 O-SiO 2 immiscibility dome. This could promote tetrahedra surrounded only by Li + or P 2 O 4 -7 can be detected. This indicates
	phase separation between Li-rich regions and Si-rich regions, not necessarily that addition of P 2 O 5 results in the incorporation of PO + 4 tetrahedral units
	associated with the orthophosphate domains. Again, such liquid-liquid phase within the aluminosilicate network. Due to the Al avoidance rule, few Al-O-Al

species charge compensated by Al 3+ . Indeed, replacing Li + by Al 3+ , which is more strongly bonded, produces an upfield change in the chemical shift, that means more negative values[START_REF] Dollase | Structure of Na 3-3x Al x PO 4 , x=0 to 0.5[END_REF]. In solid solution of crystallized Na 3-3x Al x PO 4 , Dol-

Acknowledgments

We would like to acknowledge Anne Crochet (CETC Corning) for SEM images, Peggy Georges and Sandrine Bercy (CETC Corning) for chemical analysis. We thank also Laurent Delevoye for fruitful discussions. The ANRT is acknowledged for PhD funding (P.G.) under the CIFRE Contract 2015/0529. The authors thank the Chevreul Institute (FR 2638) for its help in the development of this work. Chevreul Institute is supported by the « Ministère de l'Enseignement Supérieur et de la Recherche », the « Région Nord-Pas de calais » and the « Fonds Européen de Développement des Régions ».