legacy and tourism: an application of spatial hedonic pricing analysis to the case

Keywords: pricing, hedonic functions, hotels, Nord-Pas-de-Calais, public goods, tourism JEL classifications: C21, D40, H41, L83

 Hedonic pricing analysis with GIS applied to industrial sites in tourism destinations  The presence of an industrial site (i.e repellent public good), still operating or not, near to a hotel, negatively affects the hotel rates.  This effect can be compensated by the presence of an attractive public good which validate economic policies in order to develop attractions based on industrial legacy.  The spatial model take into account the spatial autocorrelation Industrial legacy and tourism: an application of spatial hedonic pricing analysis to the case of hotel rooms in Nord-Pas de Calais, France

The prices of public goods and public bads for hotel rooms in

For the politic maker, historic heritage can be an underlying resource to attract tourists, giving rise to the so-called heritage tourism [START_REF] Garrod | Managing heritage tourism[END_REF][START_REF] Poria | The core of heritage tourism[END_REF][START_REF] Worden | Heritage Tourism in Southeast Asia[END_REF]. Heritage is usually defined as whatever a given area has inherited from history, 'which can mean anything from historic buildings, to art works, to beautiful scenery' [START_REF] Yale | From tourist attractions to heritage tourism: ELM publications[END_REF]. Physical remains from the industrial past like facilities (e.g. factories, mills, forges, etc.), machinery, architecture, housing and industrial landscapes have sometimes become the key motivators for visitation to a destination. They serve as core resource for a distinctive subset of the field of heritage tourism, namely the industrial heritage-based tourism [START_REF] Conlin | Memento du tourisme[END_REF][START_REF] Jones | Blaenavon and United Nations World Heritage Site status: Is conservation of industrial heritage a road to local economic development?[END_REF][START_REF] Xie | Developing industrial heritage tourism: A case study of the proposed jeep museum in Toledo, Ohio[END_REF].

Industrial legacy can also be a serious impediment to the development of tourism. First, the development of industrial activities, at least until quite recently, has been generally done without any concern for environmental issues and has led to serious environmental degradation and scenery spoiling. The closing down of old industries has resulted in the emergence of numerous industrial wastelands and brownfield sites contaminated with hazardous substances, pollutants or contaminants. Second, former industrial areas are seriously handicapped by a poor image and bad reputation associated with hard work, tough living conditions, workers' misery and social struggles (European Parliament, 2013). The combination of both the environmental hazards and rough social conditions as a strong repellent factor for many kinds of tourism.

All these environmental, aesthetical and psychological burdens may more than offset the historical and nostalgic attractiveness of old industrial remains and eventually deter the tourism development of a region. The effect of industrial legacy on tourism attractiveness is difficult to estimate, but an indirect assessment can be made by using the hedonic price method [START_REF] Rosen | Hedonic prices and implicit markets: product differentiation in pure competition[END_REF]. This is the aim of this article. According to the hedonic hypothesis, some products are viewed as a bundle of characteristics or attributes, each of which brings consumers some degree of satisfaction or dissatisfaction. Tourism products, especially accommodation, belong to this category. They can be considered as bundles of various attributes, both private (star rating, room service, bar, availability of sport facilities…) and public (available amenities, landscapes, quality of the environment, brand image…) [START_REF] Rigall-I-Torrent | Public goods in tourism municipalities: formal analysis, empirical evidence and implications for sustainable development[END_REF].

The observed price of any such product, e.g. hotel rates, is the sum of the unobserved prices of the bundle of attributes associated with it. The hedonic method allows one to estimate the implicit price of each characteristic which can be interpreted as the marginal value that consumers attach to this characteristic. If industrial legacy is a source of antagonistic public attributes, this method enables us to estimate their implicit prices and to know how tourists value each of them. By evaluating their contribution to the hotel rates, we can thus obtain an assessment of the impact of industrial legacy on tourism attractiveness of a region.

The hedonic price method has already been used in tourism for analysing the impact of various private and public attributes on the price of different types of accommodation [START_REF] Andersson | Hotel attributes and hedonic prices: an analysis of internet-based transactions in Singapore's market for hotel rooms[END_REF][START_REF] Chen | An application of hedonic pricing analysis to the case of hotel rooms in Taipei[END_REF][START_REF] Espinet | Effect on prices of the attributes of holiday hotels: a hedonic prices approach[END_REF].

However, the focus has been put so far on private attributes and on beneficial public attributes.

The influence of adverse public attributes, or 'public bads', has not yet been considered, except for crowdedness and congestion [START_REF] Alegre | Tourist areas: Examining the effects of location attributes on tour-operator package holiday prices[END_REF]Rigall-I-Torrent and Fluvià, 2011). This article is the first in the hedonic literature in tourism to explicitly tackle the impact of unambiguous repellent public attributes (e.g. brownfield sites, slag heaps, industrial seaports). Moreover, we provide a strong validation of economic policies which try to compensate this effect by the inclusion of tourism attraction in the same area. Such an analysis should be of high interest to both hotel managers and policymakers, especially in regions belonging to Europe's 'Rustbelt', since tourism is often viewed as one of the conservation and regeneration tools which may help the process of economic restructuring of old industrial regions [START_REF] Hospers | Industrial heritage tourism and regional restructuring in the European Union[END_REF]European Parliament, 2013). As underlined by [START_REF] Xie | Developing industrial heritage tourism: A case study of the proposed jeep museum in Toledo, Ohio[END_REF], developing industrial heritage needs comprehensive tourism planning, and this article's analysis can provide valuable information for the design and implementation of such a planning process.

The study was conducted on hotel rates in Nord-Pas de Calais (NPdC), an old industrial region in north of France. NPdC became the second leading industrial region of France during the 19 th century, specialized in 'smokestack' industries such as coal, steel and textiles. Like other forerunners of the Industrial Revolution, it was severely hit by industrial decline from the 1970s and joined the so-called 'Europe's Rustbelt'. NPdC is an ideal case study as it still has a lot of material vestiges from its industrial past, related to both productive activity (mining plants, factories, port installations) and scenery (mining villages, working-class housing, industrial landscapes), which create a large potential for industry heritage tourism. At the same time however, the region has a great potential for other types of tourism (cultural and historical tourism, leisure and beach tourism, business tourism) which may be hurt by the remains and damage of this industrial past.

On the methodological side, a geographical information system (GIS) has been used in order to obtain the distance of hotels to the amenities. Geolocalized data proved to provide more accurate information than the dummy variables usually used in the literature as threshold and distance effects on hotel prices may differ from one amenity to another. By using GIS data, we are also able to measure and to compare results of the presence of repellent public good and to identify the effects due to the decision to construct an attractive public goods in the same area.

Moreover, given the spatial nature of the framework, we took into consideration the possibility that exogenous spatial factors jointly influence the prices of nearby hotels [START_REF] Balaguer | Relationship between spatial agglomeration and hotel prices. Evidence from business and tourism consumers[END_REF]. Therefore, a specific method has been used to prevent effects caused by heteroskedasticity and spatially autocorrelated disturbance terms.

The article is divided in five sections, in addition to this introduction. Section 2 presents the analytical setting underlying the hedonic method. Section 3 gives a brief description of the region of Nord-Pas-de-Calais and shows the data and the model specifications. Section 4 gives the results and interpretations. The main conclusions are set out in a final section.

Framework analysis

Hedonic price models [START_REF] Rosen | Hedonic prices and implicit markets: product differentiation in pure competition[END_REF] allow to estimate the implicit prices of a product's characteristics and their contribution to the overall price of this product. As a tourism product (a tour-operator package holiday, a stay in a hotel room, a ski lift, etc.) can be considered as a collection of objectively measured attributes, this method has been used to study the determinants of tourism prices [START_REF] Alegre | Tourist areas: Examining the effects of location attributes on tour-operator package holiday prices[END_REF][START_REF] Papatheodorou | Dunkerque: aux accueils de l'office de tourisme, près de 500 000 visites l'an passé[END_REF][START_REF] Thrane | Hedonic price models and sun-and-beach package tours: the Norwegian case[END_REF].

However, until recently, attention has been paid exclusively to private (intrinsic) attributes of the product (star category, swimming pool, parking place, air-conditioning… in the case of a stay in a hotel room) rather than on its public attributes (scenery, available amenities, cultural facilities, brand image…), even if the importance of locational characteristics on tourism prices has been recognized for a long time [START_REF] Bull | Pricing a motel's location[END_REF]. Rigall-I-Torrent andFluvià (2007, 2011) made a substantial contribution to the hedonic pricing literature in tourism by explicitly integrating public attributes into the analysis, both theoretically and empirically. We adopt and complete their approach by adding unambiguous repellent factors (e.g. brownfield sites and slag heaps) into the list of public attributes.

Thus, a one-night stay in a hotel room is regarded in the present study as a vector (i.e. a collection) of both private attributes and public attributes. Public attributes are composed of three subcategories: attractive public attributes (for example, proximity to the beach, scenery, availability of entertainment sites), repellent public attributes (for example, the proximity to brownfield sites, slag heaps, industrial ports or plants) and network externalities (for example, job density, proximity to shopping malls, hotel partnerships). The latter subcategory of public attributes is based on the idea that the satisfaction obtained from a hotel room by tourists also depends on the availability of complementary goods and services provided by nearby businesses, such as restaurants, pubs or shopping centers, or by partnerships concluded by the hotel (Rigall-I-Torrent and Fluvià, 2011).

A one-night stay in a hotel room can therefore be represented by the following vector:

ℎ = (𝑐 1 , 𝑐 2 , … 𝑐 𝑁 , 𝑎 1 𝑗 , 𝑎 2 𝑗 , … 𝑎 𝐵 𝑗 , 𝑟 1 𝑗 , 𝑟 2 𝑗 , … , 𝑟 𝐺 𝑗 , 𝑘 1 𝑗 , 𝑘 2 𝑗 , … , 𝑘 𝑀 𝑗 ) (1)
where h is a one-night stay in a hotel room, 𝑐 𝑛 is the measured value of the hotel's private attribute n (n=1…N); 𝑎 𝑏 𝑗 is the measured value of the attractive public good b in location j (b=1…B); 𝑟 𝑔 𝑗 is the measured value of the repellent public good g in location j (g=1…G); and 𝑘 𝑚 𝑗 is the measured value of the network externality m in location j (m=1…M).

Following [START_REF] Rosen | Hedonic prices and implicit markets: product differentiation in pure competition[END_REF], the equilibrium price for a night in a hotel room can be expressed as a combination of the implicit prices for the private and public attributes included in the overnight and thus as a function of all these attributes:

𝑝(ℎ) = 𝑝(𝑐 1 , 𝑐 2 , … 𝑐 𝑁 , 𝑎 1 𝑗 , 𝑎 2 𝑗 , … 𝑎 𝐵 𝑗 , 𝑟 1 𝑗 , 𝑟 2 𝑗 , … , 𝑟 𝐺 𝑗 , 𝑘 1 𝑗 , 𝑘 2 𝑗 , … , 𝑘 𝑀 𝑗 ) (2)
The partial derivative of 𝑝(ℎ) with respect to any attribute (e.g. 𝜕𝑝(ℎ) 𝜕𝑐 2 ⁄ ) gives the implicit price of this attribute.

Presentation of the region and the data

The Nord Pas-de-Calais region

Nord-Pas de Calais (NPdC) has been chosen as the basis for this study because of both its rich industrial past and its great potential for various types of tourism. NPdC is the northernmost region in France, on the border with Belgium, and is located in Northern Europe's former coal belt. As a forerunner of the Industrial Revolution, it has inherited many material vestiges in the form of mining plants, factories, housing and scenery (industrial architecture, slag heaps, etc.), creating a real potential for industry heritage tourism. However, as is usual for regions belonging to 'Europe's Rustbelt', NPdC has also inherited serious environmental issues and scenery degradation. For example, 641 sites are at present officially registered as actually or potentially contaminated because of industrial activity, accounting for 14% of all polluted sites in France and ranking NPdC second among the most polluted regions in the country (BASOL database, 2014). Considering all former industrial sites leads to a total of 16 800 sites that may be contaminated throughout the 12 414 km² of the region. 74 industrial facilities are classified as Seveso (i.e establishments displaying major technological and environmental hazards) representing 6.7% of total Seveso sites in France. Former mining activity has resulted in 874 identified mine shafts and is the source of specific hazards (firedamp, subsidence, landslide, slag heaps combustion and explosion risk, flood-risk areas, etc.) which still need surveillance and preventive action [START_REF] Baudelle | La gestion des risques hérités de l'activité minière dans le Nord-Pas-de-Calais/Managing hazards inherited from mining activity in the region of Nord-Pas-de-Calais[END_REF]. The mining and industrial past is also responsible for a negative image of the region (the 'Black Country') and enduring stereotypes: generalized poverty, permanent economic decline, alcoholism, hard living conditions in foggy and dark mining villages, illiteracy, etc. [START_REF] Cegarra | Le Nord, ombres et lumières[END_REF] All these burdens can seriously handicap the development of tourism, especially since

NPdC has proved to be endowed with many valuable tourism attractors related to its rich historical past, natural resources and special geographical location. Called a "fatal avenue" by General de Gaulle (a Lille native) due to its strategic position in Europe, the region has always been one of the most fought-over regions in Europe and was a special theatre of military operations during the two World Wars. These factors have resulted in numerous historical sites (for example, the battlefields of Bouvines and Azincourt, military cemeteries and memorials, the twelve Vauban citadels, etc.). Moreover, the sandy beaches of the 'Côte d'Opale', the numerous nature reserves, parks, marshlands and forests make the region an attractive leisure destination. All these tourism assets are accentuated by a strategic geographical position as 100 million potential tourists are located within a radius of 300 km.

Therefore, it is not surprising that tourism activity has become a significant activity for Nord-Pas de Calais region. According to the French Ministry for the Economy and Finance (Direction générale des entreprises, 2016), NPdC is ranked 9 th among the 22 French metropolitan administrative regions for tourism employment, and tourism provides as many jobs in this region as the car industry or the insurance and financial industries. The 6.3 million overnight stays in hotels accounted for 2.6% of total overnight stays in France in 2015, i.e. more than Corsica and half the total of Paris and its suburbs. However, despite these results, there is a general agreement that the region's tourism potential is underexploited. One major reason could be the damage caused by its industrial and mining past.

Data collection and selected variables

Several sources were used to build a comprehensive database on the NPdC region hotels for year 2013: the NPdC regional tourism committee (Comité régional du tourisme, CRT thereafter) for information on hotels, a phone survey for hotel prices, Google Maps and NPdC geographic information and spatial analysis system (SIGALE) for location information and the French national institute of statistics and economic studies (INSEE) for socio-economic information. Only officially rated hotels were kept for the study, which gives an initial sample of 414 hotels. Non-rated hotels were discarded from the sample since, according to the NPdC CRT, they have an erratic activity, a rather short life and display too poor quality for being influenced by usual attributes. These are the main reasons why the CRT gathers information on rated hotels only: name and address, star-rating (from one to five stars), participation to a hotel partnership ('club hôtelier'), room equipment (TV, air conditioning, Wi-Fi, etc.), activities (golf, spa…). After discarding rated hotels with missing data (often due to a non-response from the hotels), the final sample reduced to 337 hotels, which accounts for about 81% of the initial sample.

As the information gathered and provided by the CRT was incomplete, a phone survey was conducted to get missing information, especially on hotel rates. The prices of a double room during peak season and off-peak season have been chosen as dependent variables. The choice of the double room rates permits to use a standard rate as it is the more common product. "Peak season" is the maximum price (in a period with a high demand, as holidays) and "off-peak season" is the minimum price (low demand) for the same room. Notice that, as usual in the hedonic pricing literature on hotel rates, the prices used in our empirical study are not transaction prices, but prices displayed in hotel brochures. Effective transaction rates paid by tourists as resulting from yield management, last minute or age-based discounts, cannot materially (and for reason of confidentiality) be collected. However, the use of displayed prices is acceptable, as suggested by (Rigall-I-Torrent and Fluvià, 2011), since it can reasonably be assumed that they correctly reflect "expected" prices paid by tourists. Moreover, the market for hotel rooms in Nord-Pas de Calais is competitive and therefore, it is very unlikely that displayed prices systematically diverge from equilibrium market prices.

One problem with price hedonic method is that it offers few theoretical guidelines for selecting independent variables [START_REF] Andersson | Hypothesis testing in hedonic price estimation-On the selection of independent variables[END_REF]. In the present study, the selection of hotel attributes, both private and public, followed the two-steps procedure indicated by [START_REF] Espinet | Effect on prices of the attributes of holiday hotels: a hedonic prices approach[END_REF]. First, the examination of the NPdC CRT database and interviews with professionals of the sector led to the identification of 40 private (hotel-related) attributes. The two same sources were completed by the NPdC geographic information and spatial analysis system (SIGALE)

and by the INSEE database to define 16 public (attractive, repellent and network-related)

attributes. Obviously, these lists are too large to be used in any manageable statistical model.

Therefore, a second step is needed in order to select the more relevant and significant variables.

This was done on the basis suggested by [START_REF] Espinet | Effect on prices of the attributes of holiday hotels: a hedonic prices approach[END_REF], especially by taking into account the opinions expressed by professionals of the sector and experts of the NPdC CRT, the availability of reliable information for all hotels, statistical significance in exploratory analyses (based on stepwise procedure) and real variation of attributes across hotels 1 . This process left us with the following independent variables. In addition, this step was also conducted to limit and control the possible presence of multicollinearity. To avoid problems resulting from multicollinearity, a variance inflation factor (VIF) was used. The VIF for variable h is given by VIF(j)=1/(1-R²(j)), where R(j) is the coefficient of the multiple correlation between the h variable and the other explanatory or independent variables. A higher value of VIF represents a higher degree of correlation. All the final estimations present VIF values less than 10.

Private attributes

1 Preliminary results are available upon requests  Hotel star rating. In France, there is an official star-rating classification for hotels at the national level. Hotel rating is carried out every five years by accredited inspection bodies using a five-star system defined by Atout France, the France tourism development agency. This system is based on a list of specified requirements (Atout France, 2009) which involve many important hotel's private attributes (room surface, quality of room furniture, presence of flat screen TV, Wi-Fi access, private car parking, disability access, types of breakfast, etc.). Star rating can therefore be reasonably chosen as a synthetic index of the hotel's overall intrinsic quality as based on private characteristics. This is in line with prior research [START_REF] Aguiló | Determinants of the price of German tourist packages on the island of Mallorca[END_REF][START_REF] Papatheodorou | Dunkerque: aux accueils de l'office de tourisme, près de 500 000 visites l'an passé[END_REF] and empirical practice: for example, [START_REF] Balaguer | Relationship between spatial agglomeration and hotel prices. Evidence from business and tourism consumers[END_REF] and [START_REF] Becerra | Being better vs. being different: Differentiation, competition, and pricing strategies in the Spanish hotel industry[END_REF] used star rating classification as a measure of vertical differentiation in the hotel industry in Spain. Moreover, using hotel star rating alone instead of using a list of private attributes including the star rating itself, as often done in the literature, allows to avoid two problems. First, considering simultaneously the effects of both private attributes and hotel star rating on hotel prices in a regression model would lead to a specification error because the hotel star rating variable would become an endogenous explanatory variable [START_REF] Thrane | Hedonic price models and sun-and-beach package tours: the Norwegian case[END_REF]. Second, using hotel star rating alone reduces the possibility of multicollinearity between explanatory variables, which is a common problem arising in hedonic price models. Hotel star rating was included in the regression as dummy variables: Two stars, Three stars, Four of five stars.

These dummy variables were coded 1 when the number of stars of the hotel reported by the NPdC CRT was respectively two, three and four or five. The reference group is made up of one star hotels.

 Bar, golf and air conditioning. These private attributes were added to the list of independent variables as they are not, or only very partially, considered by the official hotel star rating. These dummy variables were coded 1 when the NPdC CRT indicated that a bar is available at the hotel, located near a golf course or when air conditioning is available in the room.

Public attributes

Public attributes are composed of three subcategories: network externalities, attractive public attributes and repellent public attributes.

Network externalities

Recall that the satisfaction obtained from a hotel room by tourists is assumed to depend also on the availability of complementary goods and services provided by nearby businesses. Three variables were selected.

 'Club hôtelier' membership. This variable indicates a hotel partnership which allows to share clients, communication, services like booking, catering, etc. This dummy variable was coded as 1 when the NPdC CRT reported that the hotel is part of such a 'club hôtelier'.

 Distance to a shopping mall. Only shopping malls whose size was at least 10,000 m² were retained.

 Job density by town. This variable is defined as the number of jobs divided by the administrative surface of the town (number of jobs per square kilometer). Data come from the NPdC geographic information and spatial analysis system (SIGALE) and from the INSEE database. The job density by town captures the positive impact that economic vitality can have on the attractiveness of hotels through a better availability of public facilities and numerous shopping and entertainment opportunities it creates in the areas where hotels are located. All these goods and services are complementary to a hotel stay and thus can make a substantial difference when tourists choose a hotel [START_REF] Balaguer | Relationship between spatial agglomeration and hotel prices. Evidence from business and tourism consumers[END_REF]Rigall-I-Torrent and Fluvià, 2011). Moreover, economic activity stimulates the demand for hotel accommodation through business tourism.

Three categories of job density were identified in order to capture the intensity of the effect of economic activity: 'low job density', when the jobs density by town is less or equal to 1000 per km 2 ; 'medium job density', when the job density by town is between 1000 and 4000 per km 2 ; 'high job density' when the job density by town is more than or equal to 4000 per km 2 . The reference group is made up of the 'high job density' group. In the estimation, we added the two others categories of job density with the inclusion of two dummies variables.

Attractive public goods

Two variables were selected.

 Distance to the beach. This control variable was included because location near beaches was shown to influence hotels' strategy and pricing policies [START_REF] Espinet | Effect on prices of the attributes of holiday hotels: a hedonic prices approach[END_REF]Rigall-I-Torrent et al., 2011).

 Distance to tourist attractions. The twenty most visited attractions in the NPdC in 2013 were selected as the major region's tourism endowments (Comité régional du tourisme, 2014).

Repellent public goods

Three variables were selected.

 Distance to slag heaps (mountains of mining residuals). There are about 340 slag heaps in NPdC. They are usually viewed, together with mining villages, as one of the most typical symbols of the mining and industrial past of the France's 'Black Country', and are most often associated with the negative image of the region.

 Distance to brownfield sites (closed and contaminated industrial sites, physically still present). As shown in subsection 3.1., brownfield sites are among the most problematic legacies to the region of its industrial past.

 Distance to the port of Dunkerque. The sea port of Dunkerque was chosen as potentially repellent public good for tourism as it is the third biggest industrial and commercial port in France, spreading over 7000 hectares and containing several industries (petrochemical, iron and steel plants), and a lot of terminals and warehouses dedicated to a large variety of products (for example, petrochemicals, grains, steel, coal).

The influence of most public attributes on a hotel's rates depends on their distance to the hotel.

To determine the most significant distance, we first created a geographic information system.

We manually input the physical addresses of hotels and all public attributes concerned by distance (attractive, repellent and presence of shopping malls) in MapInfo Professional software and computed the geographical Euclidean distance based on GPS coordinates between each hotel and all these public attributes. We then tested different levels of distance for each public attribute and selected the most significant one. All the selected distances appear in the estimation. Eventually, we used a dummy variable coded as 1 when the distance to the public attribute was less than or equal to the selected distance. The choice to use dummy variable is motivated by two reasons. First, all the relation have not the same specification (some are quadratic, some are linear, etc.). Second, the threshold changes between the variables (the size and so the visual impacts differs among slag heaps and brownfield for example). The use of dummy variable help to simplify and to compare the results obtained.

Hotels are found all over the region, but they are concentrated on the coast and in the higher population density zone of Nord-Pas de Calais, namely, Lille (see Figure .1). Table A.1 in the appendix reports some descriptive statistics for all the variables considered in the study.

Specification and estimation results

Model specification

The question of the relevant functional form for the regression model has been a matter of preoccupation for a long time in the price hedonic literature since there is no theoretical guidance on the best functional form [START_REF] Andersson | Hypothesis testing in hedonic price estimation-On the selection of independent variables[END_REF][START_REF] Rasmussen | On the choice of functional form for hedonic price functions[END_REF]. We used a Box-Cox transformation to choose the specification, as usually recommended (Spizer, 1984). This test showed that, with our data, the log-linear form is the best specification (see table A.2, in appendix). Accordingly, the dependent variable is the natural logarithm of the price of a double room while the independent variables enter the regression additively.

Two regression models were estimated, one for the peak season and one for the off-peak season:

𝑙𝑜𝑔(𝑃 𝑖 ) = 𝜇 + ∑ 𝛽 𝑛 𝑛 𝑐 𝑖𝑛 + ∑ 𝜁 𝑏 𝑏 𝑎 𝑖𝑏 + ∑ 𝛿 𝑔 𝑔 𝑟 𝑖𝑔 + ∑ 𝛾 𝑚 𝑚 𝑘 𝑖𝑚 + ɛ 𝑖 (4)
where 𝑙𝑜𝑔(𝑃 𝑖 ) is the logarithm of the price of a one-night stay in hotel i's double room (peak season and off-peak season) as explained in section 3.2; 𝑐 𝑖𝑛 is the n th private attribute of hotel i; 𝑎 𝑖𝑏 is the b th attractive public good attribute related to the location of hotel i; 𝑟 𝑖𝑔 is the g th repellent public good attribute related to the location of hotel i; 𝑘 𝑖𝑚 is the m th networking attribute of hotel i; 𝛽, 𝜁, 𝛿 and 𝛾 are the estimated parameter vectors; and ɛ 𝑖 is a random error term, independent and identically distributed with zero expectation and constant variance.

Equation ( 3) can be written in a matrix form:

𝑙𝑜𝑔(𝑃) = 𝜇. e + Cβ + Aζ + Rδ + Kγ + ε (5)
We know from the literature on spatial econometrics [START_REF] Anselin | A test for spatial autocorrelation in seemingly unrelated regressions[END_REF][START_REF] Gelfand | Handbook of spatial statistics[END_REF] that equation (4) cannot be estimated consistently using standard ordinary least squares (OLS) if there is spatial dependence. And spatial dependence is very likely to occur in tourism, especially in the case of hotels, given the importance of the spatial dimension in this activity. Exogenous spatial factors can jointly influence the prices of closely located hotels and their pricing strategies [START_REF] Balaguer | Relationship between spatial agglomeration and hotel prices. Evidence from business and tourism consumers[END_REF]. Higher room prices in a particular area could lead to higher prices in a neighboring area. Hence, spatial autocorrelation phenomenon should be explicitly accounted for in the model. Moreover, spatial autocorrelation can also be caused by a misspecification of the model, omitted variables or when there are unobservable common shocks affecting neighboring hotels (such as shocks on local costs, e.g.

property tax, urban rents…). As such, it can be considered as a useful diagnostic tool helping to detect some misspecification and to improve the quality of the model.

Econometrically, we have to test for the existence of spatial auto-correlation and to use the appropriate specification and estimation procedure. Different types of specification can be used to take into account the spatial effect in the model (SAR or SARMA). We select the spatial error model (SEM) for estimation. It supposes that the error term ε in equation ( 4) can exhibit spatial dependence too, i.e. it can be correlated across hotels. When there is spatial error dependence, the error vector ε follows the relationship:

ε =λWη +u (6)
where W is the weighted matrix based on Euclidean distance decay such as 𝑊 𝑖𝑗 𝑑 𝑖𝑗 ⁄ , and 𝑑 𝑖𝑗 is the distance between hotels i and j. λ represents the intensity of spatial autocorrelation among errors and u is a well-behaved error vector. Spatial error dependence is likely to arise either when the error term 𝜀 includes omitted variables that are also spatially dependent or when neighboring hotels are affected by unobservable common shocks. Note that in the presence of spatial dependence, OLS have to be substituted by other estimation techniques, either the maximum-likelihood (ML) estimation method or the instrumental variables (IV) estimation method. Finally, as we explained at the subsection 3.2, the results are not biased by a presence of multicollinearity.

Estimation results

Our estimation strategy is as follows. First, we estimate the model without taking into account the possibility of spatial dependence using OLS (see. Eq. ( 4)). The results of this estimation are shown in Table 2, columns 1 and 2. Second, we perform five appropriate non-Trobust and robust spatial tests based on the Lagrange Multiplier (LM) (see. Table 1). The SARMA test allows us to test the general hypothesis of the presence of spatial autocorrelation.

Following the Moran index, the comparison of the significance levels of LMlag (for autoregressive or lag endogenous variable), LMerr (for spatial autocorrelation errors) and their robust versions (RLMlag and RLMerr) shows some spatial autocorrelation due to residuals rather than to the lagged endogenous variable. Therefore, we select the spatial error model (SEM) for estimation. As standard OLS cannot be used, we choose a non-linear optimization routine -the maximum likelihood (ML) estimation approach-in order to get unbiased and consistent estimators of the parameters in equations ( 4) and ( 6). This method has been preferred to the IV method as it does not require finding reliable instruments. The estimation results using ML are shown in Table 2, column 3 for peak season and column 4 for off-peak season. Note that, since the spatial autocorrelation term is significant and strong, the SEM model has more explanatory power than the OLS model and provides better estimates. Using these results, we also calculate the linear variations for the selected variables on hotel prices. The results are contained in Table 3.

The results have to be interpreted with reference to the first line of Table 3. According to the SEM model and given the selected reference group, the average price of a double room in a one star hotel located in a high job density area with no other attribute is €61.25 in peak season and €46.29 in off-peak season.

As expected, the private attributes (hotel star rating, bar, golf and air conditioning) have positive and highly significant effects on the hotel rates. In particular, the category of a hotel strongly influences its price. A two-star hotel can set a price €24.12 higher than a one-star hotel in peak season with otherwise identical characteristics, whereas a four or five-star hotel can charge €83.35 more. All effects are more important during the peak season, as the demand is higher and the occupancy rates rise.

Among public attributes, variables related to network externalities are in most cases significant at the standard levels. Being part of a 'Club hôtelier' partnership allows hotels to set higher prices, especially in peak season. This can be viewed as an implicit fee charged to customers for a particular service. According to the NPdC CRT, overbooked hotels redirect customers to hotels belonging to the same 'Club hôtelier', saving them additional searching costs.

The proximity of a large shopping mall, extending over at least 10,000 m², has a negative coefficient, even though statistically significant only in off-peak season. Although shopping tends to be part of any travel experience, big shopping facilities, provided in NPdC mainly in the form of hypermarkets, are clearly not valued by tourists when located in close proximity.

This negative effect is probably aggravated by their usual location in the outskirts of the city.

Job density matters a great deal. Being located in a low or medium job density area drives the price of hotels down by a substantial amount relative to a high job density area, by almost 30% in peak season and 13% in off-peak season, ceteris paribus (see Table 2). This can be viewed as the result of differences in tourism demand intensity mainly attributable to two factors. First, as they are often located in cities, high job density areas concentrate public facilities, offer a wide range of entertainment activities and catering services, and provide a retail environment which is better adapted to the kind of shopping experience sought by tourists than hypermarkets (UNWTO, 2014). Second, business tourism, which can be a large contributor to the demand for hotel rooms, is often concentrated in these areas. According to the CRT, in 2015 business tourism was responsible for 57% of overnight stays in Lille, the economic and administrative capital of NPdC. Moreover, combined with higher occupancy rates, the traditional lower own-price elasticity of demand for business tourism [START_REF] Peng | A meta-analysis of international tourism demand elasticities[END_REF] may contribute to explain the ability of hotels located in a high job density area to raise peak season prices much more than hotels located in a low or medium job density area.

Our estimations also indicate that the proximity of attractive public goods generally enables hotels to charge higher prices. This is especially the case for tourist attractions during both peak and off-peak seasons. Having a beach close by example also exerts a positive, significant and important influence on hotel rates, but only during the peak season. For the offpeak season, the coefficient has a negative sign, although not significant. This negative effect may be explained by the bad weather conditions usually prevailing in winter by the English Channel, which may lead travellers to prefer a hotel set back from the seaside.

Lastly and importantly for our purpose, all variables aimed at capturing the adverse effects of the region's industrial legacy on the hotel rates display the expected negative sign and are significant for the peak season. While the close presence of a slag heap or of a brownfield site exerts comparable effects (with an average drop in the price from 5.3% and 6.6% for slag heap and from 7.4% and 8.5% for brownfields), the proximity of the Dunkerque seaport has a much stronger repulsive influence on travellers (from 12.8% and 15.1%). This could be due to the difference of scale of these variables, since the actively operating Dunkerque seaport extends over 7000 hectares and thus acts as a larger source of nuisances. Note that the repulsive influence of the seaport seems to vanish in off-peak season, becoming statistically non-significant. As local people form the bulk of tourists at this time (La Voix du Nord, 2014), hotels are likely to be used mostly by tourists motivated either by some specific aspects of that city or by non-leisure purposes, such as business, hence by tourists with low own-price elasticity of demand. Actually, off-peak season turns out to be less sensitive to 'public bads' as only brownfield sites exert a statistically significant negative effect on hotel rates.

Finally, even though the test on spatial autocorrelation between hotel prices has led us to select a SEM model, note that both specifications give rise to similar results. Moreover, the coefficient of lambda is not significant, ceteris paribus.

Conclusion and discussion

While being a potential tourism attractor for a region through the so-called industrial heritage-based tourism, industrial legacy can also be a serious impediment to the development of other forms of tourism and to the overall tourism attractiveness of the region. The aim of this article is to provide an indirect assessment of the detrimental impact of industrial legacy on tourism attractiveness by studying its effect on an easily measurable factor, i.e. hotel rates. The hedonic method has been used to decompose hotel prices in Nord-Pas de Calais, an old industrial region in north of France, into the implicit prices of a set of attributes, both private and public, including the repellent public attributes inherited from the industrial past of the region. This is the first article in the hedonic literature in tourism to evaluate the effect of these adverse public factors. We also took into account the presence of potential spatial autocorrelation between hotels rates and used geolocalized data to better deal with the variability of threshold and distance effects.

After controlling for the usual hotel private attributes, network externalities and attractive public goods, including tourism attractions, our analysis shows that the inherited adverse public attributes have a significant negative impact on hotel rates, especially during the peak season. In other words, consumers attach negative marginal values to the visible evidence of industrial legacy, suggesting an adverse influence on tourism attractiveness.

However, the implicit price of some of these adverse public attributes is in the same order of magnitude as the implicit price of a tourist attraction. The proximity of a brownfield site or a slag heap decreases the hotel rates during the peak season by respectively 6.7% and 7.7% whereas the presence of a tourism attraction increases them by 6.9% (see. Table 2). For example, In other words, having an attractive public attribute close by could alleviate, or even compensate for, the presence of an adverse public attribute inherited from the industrial past.

The dissatisfaction caused to consumers by any of these inherited 'public bads' could well be offset by the satisfaction provided by a new exploited tourism resource. This result leads to a conclusion of particular interest to hotel managers and public sector policymakers. It suggests that some room is available for public policy to compensate for the damage caused to the region's attractiveness by its industrial legacy. It gives some rationale to local regeneration initiatives of the kind of the opening in Lens, a former coal-mining town, of a satellite branch of the Louvre Museum (the Louvre Lens art museum) in 2012 on an ancient mine yard surrounded by slag heaps and mining villages. On average, in this city of Lens for a hotel close to a slag heap, the hotel rates decrease by 5 € compared to identical hotels in another city, cetirus paribus. According to our estimate, the presence of this museum can be to increase the price of 5 €, which can neutralize the effect of the repulsive public good. This project was explicitly seen by the authorities as a tool for reviving the area and modernizing the region's image, (La Voix du Nord, 2014). Moreover, we support with our analysis that a destination have to create marketing strategies in order to promote this industrial legacy. The originality to use it, in a positive way and not in an undergone way, can develop new tourism market opportunities.

For example, in the slag heap of Noeux-les-Mines, it is possible to practice artificial ski.

However, the current study has some limitations which should be kept in mind. First, it has been conducted for a specific point in time, not for a period. Temporal data could reveal that the negative effects of industrial legacy might have been stronger ten or fifteen years ago, when the local strategy of creation or enhancement of attractive public attributes, especially based on historic and industrial legacy, was at an early stage. Second, the study specifically focused on hotel rates whereas other forms of accommodation, especially camping, are widely used in the NPdC region. However, data on the latter dramatically lack. Third, the effects on prices of yield management and, more importantly, of the online reservation platforms have not been taken into account. And as a matter of fact, effective prices can seriously diverge from declared prices, which were chosen as the dependent variable in our study due to data availability. Nevertheless, our results can be interpreted as averages. Moreover the market power of online reservation platforms has been recently restricted by the legislation to the benefit of the hotels which are now in a better position for negotiating rates.

Nevertheless, we argue that the use of GIS data with a hedonic model has a powerful scientific potential. For example, with this type of method, it is possible to accurately measure the price decline, based on the problems of insecurity / crime in a sector for the tourism industry.

It is also possible to search the optimal distance of a hotel, in terms of price, for its location near a tourist attraction (beach, museum, etc.). The effect of the quality of the environment can also be measured with this form of methodology. However, this search potential requires an improvement in the speed of data collection. The huge improvement in computer programming should help to solve this point.

Tables and Figures:

Figure 1. Geographical repartition of hotels in the Nord-Pas de Calais region.

Source: based on the authors' survey.

  following the example of the Tate in Liverpool, the Guggenheim Museum in Bilbao and the Pompidou-Metz Museum in Metz, the capital city of Lorraine, another region belonging to France's rustbelt. Our results support the relevance of this type of policy, at least for NPdC, and more generally of any policy related to a strategy of counteracting inherited 'public bads' through the creation of new attractive public attributes or the enhancement of existing ones. In that respect, transforming the region's numerous historical and industrial legacies into valuable resources for many forms of tourism (legacy tourism, memorial tourism, historic tourism, warfare tourism, industrial heritage tourism) is confirmed to be an excellent option for the region and should be reinforced (see, for example, the museum La Piscine of Roubaix, the mining site of Wallers-Arenberg, the ski-resort on a slag heap in Noeux-les-Mines, the mining historic center of Lewarde, the Remembrance Trails of the Great War, the V2 rocket launching site at Helfaut, etc.) Site labelling and certification can be a powerful tool for such a strategy as they may provide a cultural attractiveness to scorned inherited sites, helping to erase the usual perception of their supposed or real unpleasant features. The inscription in 2012 of the mines of the Nord-Pas de Calais region to the list of UNESCO World Heritage Sites as 'a living and changing landscape' falls into this category. Site labelling and certification can also give more visibility to existing tourism resources, contributing in another way to counteract inherited 'public bads'. For example, evidence shows that Dunkerque, whose industrial seaport was found to have such a negative effect on hotel rates, benefited in terms of tourist frequentation from having its belfry (Beffroi de Saint-Eloi) included in the 23 belfries from the Nord-Pas-de-Calais and Picardy regions added in 2005 by UNESCO to the list of the World Heritage Sites

Table 1 .

 1 Lagrange multiplier tests. -value in brackets PS stands for peak season, OS stands for off-peak season Source: The authors, based on authors' survey.

		Distance matrix	Neighbour matrix
		PS	OS	PS	OS
	I's Moran	0.0680	0.0108	0.1300	0.0716
		(<.0001)	(0.1888)	(<.0001)	(<.0001)
	LMerr	9.2236	5.123	2.8185	9.6646
		(0.0023)	(0.0236)	(0.0931)	(0.0018)
	LMlag	7.2485	0.443	2.5315	3.1095
		(0.0070)	(0.5057)	(0.1116)	(0.0778)
	RLMerr	2.8165	6.6642	0.7501	6.7663
		(0.0933)	(0.0098)	(0.3864)	(0.0092)
	RLMlag	0.8414	1.9842	0.4632	0.2112
		(0.359)	(0.1589)	(0.4961)	(0.6459)
	SARMA	10.065	7.1072	3.2816	9.8758
		(0.0065)	(0.0286)	(0.1938)	(0.0071)

p

Table 2 .

 2 Estimation results based on the ordinary least squares method (OLS) and on the spatial error model (SEM) Standard errors in brackets. *** p<0.01, ** p<0.05, * p<0.1 PS stands for peak season, OS stands for off-peak season Source: The authors, based on authors' survey.

	OLS	SEM

Table 3 .

 3 Estimation results on the linear variation of prices (in euros) ** p<0.01, ** p<0.05, * p<0.1 PS stands for peak season, OS stands for off-peak season. Source: The authors, based on authors' survey.

	OLS	SEM

*

This work was supported by the Conseil Régional Nord Pas-de-Calais. We want to thank the participant of the IATE 2015 conference (Hong-Kong), the LISA seminar and the CAEPEM seminar for their comments and suggestions.

Highlights

Appendix


Y Yang

P Castany

E Bertrand

M Cornen

J X Lin

T Gloriant
email: thierry.gloriant@insa-rennes.fr

Stress release-induced interfacial twin boundary ω phase formation in a β type Ti-based single crystal displaying stress-induced α" martensitic transformation

Keywords: ITB-ω phase, deformation twinning, {1 1 2}<1 1 1> β, {1 1 0}<1 1 phase, stress-induced martensitic transformation

The ω phase transformation in numerous group IV transition metals plays a key role to change the phase stability and modify mechanical properties, although its formation mechanisms and effect to accommodate strains are still unclear. A <1 1 0> β single crystal of β-type Ti-24Nb-4Zr-8Sn alloy (wt. %) is used to investigate the aforementioned problems. This alloy displays a β to α" stress-induced martensitic transformation, which is reversible and leads to superelasticity. Profiles obtained from in situ synchrotron X-ray diffraction during cyclic tensile tests reveal definitely the appearance of ω phase due to applied stress releasing after unloading while these identified ω peaks shall vanish totally on subsequent loading. TEM microstructural observations show its morphology as thin layer locating on the boundary of {1 1 2}<1 1 1> β twins coinciding well with the feature of interfacial twin boundary (ITB) ω phase, which is proved to be formed passively during the reversion of {1 1 0}<1 1 0> α" twins. The martensitic twinning components of {1 1 0}<1 1 0> α" are indeed confirmed from crystallographic reconstructions based on the orientation relationship between the β and α" phases. A geometrical model is hence schematically used to analyze in details the orientation relationships between both deformation {1 1 2}<1 1 1> β twins and ITB-ω phase, as well as with the original {1 1 0}<1 1 0> α" twinning.

Introduction

Metastable β-type titanium based alloys are currently developed for applications in medicine and aerospace. Phase transformations from the body-centered cubic β phase (Im-3m, N o 229) to base-centered orthorhombic α" phase (Cmcm, N o 63) and hexagonal ω phase (P6/mmm, N o 191) are observed to be formed leading to several particular properties, such as superelasticity and shape memory effect. Although the stress-induced α" phase transformation from β phase has been widely studied with the classic theory of martensitic crystallography (PTMC) [START_REF] Klostermann | The concept of the habit plane and the phenomenological theories of the martensite transformation[END_REF][START_REF] Lieberman | Cubic to Orthorhombic Diffusionless Phase Change-Experimental and Theoretical Studies of AuCd[END_REF][START_REF] Sinkler | An electron diffraction investigation of the diffuse ω structure in quenched Ti-3d transition metal alloys[END_REF], the role of ω phase was not clearly established. Especially, the importance of ω phase to accommodate internal strains in alloys, its effect on martensitic α" phase transformation and the role as precursor for stable α phase are still in debates.

As brittle particles known to be deleterious on mechanical properties, the isothermal ω phase was firstly identified in aged Ti-Cr alloy [START_REF] Frost | Isothermal transformation of titanium-chromium alloys[END_REF]. Various external stimulation including rapid cooling from single β phase field in high temperature range, mechanical deformation, extremely high pressure and exposure to radiation were then claimed to enable the inducement of the ω phase in numerous group IV transition metals (Ti, Ta, Hf and Zr) based alloys [START_REF] Yamamoto | Local atomic structure near an Nb atom in aged β -Ti alloys[END_REF][START_REF] Shin | Phase stability dependence of deformation mode correlated mechanical properties and elastic properties in Ti-Nb gum metal[END_REF][START_REF] Hsiung | Shock-induced deformation twinning and omega transformation in tantalum and tantalum-tungsten alloys[END_REF][START_REF] Dey | Formation of a shock deformation induced ω phase in Zr 20 Nb alloy[END_REF][START_REF] Hsiung | Shock-induced displacive transformations in Tantalum and Tantalum-Tungsten alloys[END_REF]. Depending on different historical processes, the particle morphologies of ω phase can be ellipsoidal or cuboidal after ageing [START_REF] Devaraj | Experimental evidence of concurrent compositional and structural instabilities leading to ω precipitation in titaniummolybdenum alloys[END_REF][START_REF] Choudhuri | Coupled experimental and computational investigation of omega phase evolution in a high misfit titanium-vanadium alloy[END_REF][START_REF] Mantri | Change in the deformation mode resulting from beta-omega compositional partitioning in a TiMo alloy: Room versus elevated temperature[END_REF] and plate-like in strained titanium alloys [START_REF] Liu | Athermal and deformation-induced ω-phase transformations in biomedical beta-type alloy Ti-9Cr-0.2O[END_REF][START_REF] Liu | Deformation-induced ω-phase transformation in a β-type titanium alloy during tensile deformation[END_REF][START_REF] Tane | ω Transformation in cold-worked Ti-Nb-Ta-Zr-O alloys with low body-centered cubic phase stability and its correlation with their elastic properties[END_REF]. These morphological differences for ω phase can be attributed to both compositional partition and stressing condition [START_REF] Devaraj | Experimental evidence of concurrent compositional and structural instabilities leading to ω precipitation in titaniummolybdenum alloys[END_REF][START_REF] Choudhuri | Coupled experimental and computational investigation of omega phase evolution in a high misfit titanium-vanadium alloy[END_REF][START_REF] Mantri | Change in the deformation mode resulting from beta-omega compositional partitioning in a TiMo alloy: Room versus elevated temperature[END_REF][START_REF] Zhang | Complexion-mediated martensitic phase transformation in Titanium[END_REF][START_REF] Niinomi | Influence of oxygen on omega phase stability in the Ti-29Nb-13Ta-4.6Zr alloy[END_REF][START_REF] Castany | Martensitic Twinning System at the Origin of {332}<113>beta Twins Observed in Metastable beta Titanium Alloys[END_REF].

However, the model of collapsing one pair of {1 1 1} β planes to an intermediate position leaving the adjacent {1 1 1} β planes unaltered were proved and widely accepted as the formation mechanism of ω phase for nearly all cases [START_REF] Sinkler | An electron diffraction investigation of the diffuse ω structure in quenched Ti-3d transition metal alloys[END_REF][START_REF] Lai | Origin of shear induced β to ω transition in Ti-Nb-based alloys[END_REF][START_REF] Horovitz | Stacking solitons in ω-phase systems and quasielastic scattering[END_REF]. Amongst them, thin layer ω phase located along the twin boundary, which was called ITB-ω [START_REF] Castany | Martensitic Twinning System at the Origin of {332}<113>beta Twins Observed in Metastable beta Titanium Alloys[END_REF], deserves more investigation. The two twinning systems observed in β-type Ti alloys are {1 1 2} <1 1 1> β [START_REF] Castany | Martensitic Twinning System at the Origin of {332}<113>beta Twins Observed in Metastable beta Titanium Alloys[END_REF][START_REF] Lai | Origin of shear induced β to ω transition in Ti-Nb-based alloys[END_REF][START_REF] Xing | Mechanical twinning and omega transition by <111> {112} shear in a metastable β titanium alloy[END_REF][START_REF] Yang | Formation of zigzag-shaped {112}<111> b mechanical twins in Ti-24.5 Nb-0.7 Ta-2 Zr-1.4 O alloy[END_REF][START_REF] Li | Zigzag configuration of mechanical twin and stress-induced omega phase in metastable β Ti-34Nb (at.%) alloy[END_REF][START_REF] Wu | {112}<111> Twinning during ω to body-centered cubic transition[END_REF][START_REF] Hao | Microstructure and mechanical behavior of a Ti-24Nb-4Zr-8Sn alloy processed by warm swaging and warm rolling[END_REF] and {3 3 2} <1 1 3> β [START_REF] Zhan | The dynamic response of a metastable β Ti-Nb alloy to high strain rates at room and elevated temperatures[END_REF][START_REF] Wang | Role of oxygen in stress-induced ω phase transformation and {332}<113> mechanical twinning in βTi-20V alloy[END_REF][START_REF] Yang | Investigation of mechanical twinning ijn the Ti-24Nb-4Zr-8Sn b titanium alloy[END_REF][START_REF] Izumi | Transmission electron microscopic observations of mechanical twinning in metastable beta titanium alloys[END_REF][START_REF] Bertrand | Twinning system selection in a metastable β-titanium alloy by Schmid factor analysis[END_REF][START_REF] Ramarolahy | Microstructure and mechanical behavior of superelastic Ti-24Nb-0.5O and Ti-24Nb-0.5N biomedical alloys[END_REF]. In a recent work carried out in a Ti-Nb alloy [START_REF] Castany | Martensitic Twinning System at the Origin of {332}<113>beta Twins Observed in Metastable beta Titanium Alloys[END_REF], the formation of ITB-ω was observed due to a collapsing process of the {3 3 2} β twin planes. The formation of such ITB-ω phase along {3 3 2} <1 1 3> β twins was also shown to be intrinsically due to the reverse α" to β transformation and the subsequent stress relaxation along twin boundaries.

Such kind of ITB-ω phase was also observed in the vicinity of the {1 1 2 }<1 1 1> β twin boundaries in a deformed Ti-15Mo-5Zr (at. %) alloy [START_REF] Sukedai | Nucleation Behaviour of beta to omega Phase Transformations in beta-Type Ti-Mo Alloys[END_REF]. Further, ω-phase with a zigzag morphology was observed in a Ti-34Nb (at. %) alloy and its formation was proposed to be featured

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3 by three-layer lattice shears arising from the dissociation and cross-slip of screw dislocations on consecutive {1 1 2} β planes [START_REF] Li | Zigzag configuration of mechanical twin and stress-induced omega phase in metastable β Ti-34Nb (at.%) alloy[END_REF]. A detailed dislocation mechanism using the dissociation of the core of 1/2 <1 1 1> β dislocations into three 1/6 <1 1 1> β twinning dislocations and 1/12 <1 1 1> β , 1/3 <1 1 1> β and 1/12 <1 1 1> β transition dislocations was described for interpretation of the mentioned boundary complexions [START_REF] Xing | Mechanical twinning and omega transition by <111> {112} shear in a metastable β titanium alloy[END_REF]. Another mechanism was proposed from first principle calculations coupling with microstructural observations in the Ti-30Nb-3Pd (at. %) alloy: The nucleation and growth of {1 1 2}<1 1 1> β twins can be described on the basis of the reverse transformation of ω phase into β phase [START_REF] Wu | {112}<111> Twinning during ω to body-centered cubic transition[END_REF][START_REF] Ping | Review on ω Phase in Body-Centered Cubic Metals and Alloys[END_REF]. With such a mechanism, {1 1 2}<1 1 1> β twins are formed inside ω particles and the ITB-ω phase observed along twin boundaries are the untransformed part of ω particles involved in the twinning process. The formation of ITB-ω phase along {1 1 2}<1 1 1> β twin boundaries is thus mainly describe from mechanisms which do not consider the β-α" transformation. But the comprehensive participation of martensitic α" transformation and {1 1 2} <1 1 1> β deformation twins on the formation mechanism for the ITB-ω phase is of great interest and a deeper understanding on the formation sequence or mediation details have never been reported.

In the present work, a β-type titanium based alloy with the chemical composition of Ti-24Nb-4Zr-7.9Sn (wt. %, short for Ti2448 thereafter) was investigated. This Ti2448 alloy was firstly designed for biomedical implants and prostheses because it exhibits a Young's modulus as low as 42 GPa and a superelastic behavior characterized by a maximum recoverable strain of 3.3% [START_REF] Hao | Microstructure and mechanical behavior of a Ti-24Nb-4Zr-8Sn alloy processed by warm swaging and warm rolling[END_REF][START_REF] Zhang | Manufacture by selective laser melting and mechanical behavior of a biomedical Ti-24Nb-4Zr-8Sn alloy[END_REF][START_REF] Yang | Texture investigation of the superelastic Ti-24Nb-4Zr-8Sn alloy[END_REF][START_REF] Liu | Processing and properties of topologically optimised biomedical Ti-24Nb-4Zr-8Sn scaffolds manufactured by selective laser melting[END_REF][START_REF] Yang | Characterization of the martensitic transformation in the superelastic Ti-24Nb-4Zr-8Sn alloy by in situ synchrotron X-ray diffraction and dynamic mechanical analysis[END_REF][START_REF] Wang | Tracing the coupled atomic shear and shuffle for a cubic to a hexagonal crystal transition[END_REF][START_REF] Wang | Elastically confined martensitic transformation at the nano-scale in a multifunctional titanium alloy[END_REF]. As the origin of superelasticity, the stress-induced α" martensitic transformation was evidenced in polycrystalline deformed specimens [START_REF] Yang | Characterization of the martensitic transformation in the superelastic Ti-24Nb-4Zr-8Sn alloy by in situ synchrotron X-ray diffraction and dynamic mechanical analysis[END_REF]. In the present case, a <1 1 0> β single crystal of this Ti2448 alloy was elaborated to simplify the microstructure. In situ synchrotron X-ray diffraction (SXRD) under cyclic tensile test were used to detect the stress-induced martensitic α" phase transformation and ITB-ω phase formation. Further TEM and orientation analysis were performed to reveal the transformation details. A new deformation sequence for deformation β twinning and ITB-ω formation, as well as the relevant geometrical model indicating the change of the crystallographic lattice were finally obtained.

Materials and methods

Ingot of Ti-24Nb-4Zr-8Sn (wt. %) alloy with diameter of 55 mm was made by arc melting under argon and hot forged at 1273 K into 25 mm diameter bar. A cylinder of 8.6 mm in diameter was cut from the as-forged bar and used to grow seed-crystal rods in an optical floating-zone furnace (FZ-T-12000-X-VP-S, Crystal System Inc.) under the protection of flowing argon. The growth was

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carried out at a rate of 5 mm.h -1 and a rotation rate of 25 rpm. The seed crystal was cut along the <1 1 0> β direction after the orientation was determined by both X-ray diffraction (XRD) and Laue X-ray back reflection analyses within 1° of the desired orientation and then used to grow single-crystal rods. The orientation of the grown single crystal was also confirmed by Laue X-ray back reflection analysis. XRD and transmission electron microscopy (TEM) were used to examine the single β phase and confirm the absence of formation of both ω phase and α" martensitic phase.

Chemical analyses showed that the grown crystals has a similar composition compared to the forged bar.

Cyclic tensile test at room temperature consisting of strain increments of 0.5 % followed by stress release up to an elongation of 5.5 % was conducted with an INSTRON 3369 tensile machine (strain rate: 10 -4 s -1 ). An extensometer was used to ensure the accurate control of the strain. The tensile direction was chosen parallel to the single crystal growth direction, i.e. the <1 1 0> β direction. In order to observe the deformed microstructure, single crystal specimens were cut after tensile tests and prepared by mechanically grinding with increasing grades of SiC abrasive paper, then polished with colloidal silica suspension and finally etched in a solution composed of 8 % HF, 15 % HNO 3 and 77 % H 2 O (vol. %). Further observations were conducted using a JEOL 2100 transmission electron microscope (TEM) operating at 200 kV. Thin foils for TEM observations were cut as disks of 3 mm in diameter, further polished to a thickness of 150 µm and prepared by a twin-jet electro-polishing technique with a 6 % perchloric acid and 94 % methanol (vol. %) solution at -25 ºC. Twin-jet electro-polishing was stopped before perforation and the samples were finally thinned by ion milling with a Fischione 1010 Model.

In situ synchrotron X-ray diffraction (SXRD) under cyclic tensile test was conducted on beam line ID31 at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) with a 5 kN micro-tensile dispositive. The high-resolution ID31 beamline offers a high-energy incident X-ray beam (λ= 0.040002106 nm) coupled with a nine-channel multi-analyzer installed as detectors. The transmitted diffracted beams were collected over the θ angular range 2-14 ° with a scanning step of 0.005 °. The in situ cyclic tensile tests under synchrotron radiation were realized on the same single crystal tensile specimen (gauge width of 3 mm and a thickness of 0.5 mm) with increments of 0.5 % until 5.5 %. SXRD scans were therefore obtained after each strain increment for both loading and unloading conditions. More details about the setup configuration can be found in reference [START_REF] Castany | In situ synchrotron X-ray diffraction study of the martensitic transformation in superelastic Ti-24Nb-0.5N and Ti-24Nb-0.5O alloys[END_REF].

Tensile test

Fig. 1 displays the cyclic tensile curve from 0 to 5.5 % strain for the <1 1 0> β single crystal. On this curve, large hysteresis loops can be clearly observed due to the stress-induced martensitic transformation (SIM) occurring. Indeed, after the linear elasticity of the β phase, a stress plateau can be noticed in the strain range of 0.75 ~ 3 % which corresponds to the main stage of SIM α" transformation. Thus, the critical stress for the SIM α" transformation can be evaluated to be 250 MPa with the method of intersection point between two tangent lines. After 3 % of strain, the martensitic α" phase begins to deform elastically followed by its plastic deformation. The recoverable strains used to evaluate the superelasticity at different applied strains are measured with the method illustrated in reference [START_REF] Grosdidier | Deformation induced martensite and superelasticity in a b-metastable titanium alloy[END_REF] and displayed with black open circles according to the right vertical axis. It can be noticed that the recoverable strain increases linearly with the applied strain up to 4 % of strain. Up to this value, the applied strain can be totally recovered due to the reversibility of the SIM α" transformation. On the other hand, the incipient Young's modulus and the ultimate tensile strength are measured to be 51 GPa and 623 MPa, respectively.

In situ SXRD characterization

Fig. 2a presents the whole SXRD profiles of the single crystal during the cyclic tensile test on loading (upper in red) and after unloading (lower in black) between 0 and 5.5 % of applied strain.

On the first initial profile, only (1 1 0) β and (2 2 0) β peaks are detected, which is in accordance with the <1 1 0> β single crystalline state. When the applied strain increases, SIM α" transformation occurs. However, the diffracted peaks belonging to α″ phase are very close to the {1 1 0} β and {2 2 0} β peaks that is why three enlarged angle ranges from Fig. 2a are presented in Fig. 2b, 2c and2d for a better identification of the phase evolution.

In the Fig. 2b that shows profiles on loading, it can be noticed that the (1 1 0) β peak slightly shifts to the low angles due to the elastic expansion of the β lattice until the detection of the (0 2 0) α" diffraction peak when the applied strain reaches 1 %. Then, the other typical diffraction peaks of (0 0 2) α" and (1 1 1) α" appear at higher applied strain. Once the strain exceeds 3 %, the β phase seems to disappear totally that will be confirmed hereafter from the calculation of transformation strains. This assumption is highlighted by the vanishing of (1 1 0) β peak replaced by the superimposition of the three (0 2 0) α" , (0 0 2) α" and (1 1 1) α" diffraction peaks. Under the

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corresponding unloading conditions in Fig. 2c, nearly all the diffraction peaks of the α" phase disappear while the peak of the β phase appears back, showing the α" phase reverses back to its parent β phase before the strain reaches 3.5 %. Positions of peaks of α" phase are also indicated, but the quantity of residual martensite is negligible for the 3.5% condition, while its presence is more obvious at higher strain, even if the β phase is the main phase remaining after unloading. Moreover, the reversed (1 1 0) β peak and remaining peaks of α" (when there are) keep in the same position, implying that the shift of all peaks observed on loading is due to the elasticity of the two phases.

For profiles under the unloading condition released from a higher applied strains at 4.5 ~ 5.5 % in Fig. 2c, diffraction peaks of (0 0 2) α" and (1 1 1) α" with tiny intensity are left around the main (1 1 0) β peak. This is because the SIM α" transformation cannot be totally reversed due to the onset of plastic deformation which inhibits the reverse martensitic transformation.

Another interesting phenomenon can be noticed in Fig. 2d. Indeed, two small but well-identified peaks at 5.6° and 7.6° are clearly visible. However, they cannot be indexed from any α" or β phases. In fact, these two peaks can be indexed as the (0 1 -1 0) ω and (0 0 0 1) ω planes of the ω phase, which is also a common observed phase in both deformed and quenched metastable Ti-based alloys. Such a formation of ω phase when the stress is released from the plastic deformation domain was never reported and the reason of its appearance will be explicated further from the microstructural analysis.

The deformation sequence of the present <1 1 0> β single crystal can be therefore extracted on the basis of both the SXRD profiles and analysis of cyclic tensile curves in the Fig. 1. The deformation begins from pure elastic deformation of β phase. At the 0.5 % strain, the SIM α" starts to occur and continues to coexist with the elastic deformation of the β phase until the fulfillment of the phase transformation at 3 % strain. At the strain range of 3 ~ 4.5 %, the SIM α" phase deforms elasticity then stepped into a complete plastic deformation range of 4.5 ~5.5 % characterized by the stabilization of permanent deformation. During this last step, an unexpected formation of ω phase after releasing the stress is also evidenced.

Evolutions of the cell parameters of β and SIM α" phases are also determined from the diffraction profiles and are plotted in Fig. 3 as a function of the applied percentage strain under loading conditions. The lattice parameter of β phase is continuously increasing when the strain increases until 3 % strain on loading while keeps constant after unloading. For the SIM α" phase, the b α" and c α" parameters continuously increases when the strain increases while the a α" parameter is roughly constant. It is also worth noting that lattice parameters of the α" phase cannot be properly determined for applied strain smaller than 3 % due to a limited number of diffraction peaks

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although SIM α" transformation already occurs. The cell parameters of β phase, SIM α" phase and ω phase, which are determined within the plastic deformation range after unloading, are presented in Table 1. These values are used to calculate the phase transformation strains for each possible variants of α" martensite (Table 2). As generally assumed, this is the variant leading to the maximum of transformation strain that would be formed, i.e. the CV3 here with a value of about 4.3%. This means the recoverable strain would be measured as 4.3% if all the β phase transforms into α" martensite with a full reversibility after unloading. As the maximum recoverable strain was indeed measured as 4.3% (Fig. 1), one can conclude that all the β phase is transformed during deformation as assumed from the description of SXRD results (Fig. 2).

Microstructural observations

An example of the plastically deformed microstructure observed by optical microscopy for a sample deformed at 4.5 % is presented in Fig. 4. Two groups of deformation bands crossed with each others can be clearly observed on this micrograph. In order to determine the nature of these bands, TEM observations were carried out. Fig. 5 shows the TEM observations of the single crystal deformed at 4.5 % strain. The bright field image (BFI) in Fig. 5a presents dislocation pile-ups indicating the involvement of dislocation slip. The selected area electron diffraction (SAED) of Fig. 5b corresponding to the circled area of the matrix in Fig. 5a was indexed as the β phase with the [1 1 3] β zone axis. A careful analysis of the slip trace on the Fig. 5a according to the crystallographic orientation of the single crystal shows the dislocations slip in a {1 1 0} β plane (more details about the method can be found in reference [START_REF] Castany | Deformation Mechanisms and Biocompatibility of the Superelastic Ti-23Nb-0.7Ta-2Zr-0.5N Alloy[END_REF]). This result is consistent with the most common slip planes observed in the β phase of titanium alloys but also in other bcc alloys [START_REF] Taylor | Thermally-activated deformation of BCC metals and alloys[END_REF][START_REF] Castany | In situ TEM study of dislocation slip in a metastable β titanium alloy[END_REF][START_REF] Castany | Dislocation mobility in gum metalβ-titanium alloy studied viain situtransmission electron microscopy[END_REF]. A BFI from another typical area is presented in Fig. 5c and its corresponding SAED in Fig. 5d. It can be seen the superimposition of three sets of diffraction patterns marked by different colors on the SAED. After indexation, the deformation bands observed in Fig. 5c correspond clearly to the {1 1 2}<1 1 1> β twinning system but additional ω phase diffracted spots are also observed sharing the common zone axis for [

1 1 0] β-matrix // [1 1 0] β-twin // [-1 -1 2 0] ω .
The TEM observations of another area in Fig. 6a and 6b also confirms the formation of plastic {1 1 2}<1 1 1> β twins and the formation of ω phase but with a different diffracting condition corresponding to [-1 -3 1] β-matrix // [-1 -1 -3] β-twin // [1 -2 1 -3] ω zone axis. It can be noticed that, for this specific orientation, the common {1 1 2} plane between the twin and the matrix, which can be seen on the SAED pattern, is not the twinning plane. The twinning plane will be further indicated in

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the Fig. 7a and7b. Diffracted spots related to the twin and ω phase are selected and relevant dark-field images are shown in Fig. 6c and6d. It is worth noting that the ω phase shows a strong contrast, which allows to observe its localization at the twin boundary. This indicates its nature of interfacial twin boundary phase (ITB-ω). The ω phase layer appears here rather thick because the twin interface is inclined according to the electron beam. Due to the crystallographic orientation of this twin, it was not possible to get the twin interface edge-on (see Fig. 7a and7b). It can also be noticed that such an ITB ω phase exhibiting a thin layer morphology was already reported in other β-metastable titanium alloys [START_REF] Zhang | Complexion-mediated martensitic phase transformation in Titanium[END_REF][START_REF] Castany | Martensitic Twinning System at the Origin of {332}<113>beta Twins Observed in Metastable beta Titanium Alloys[END_REF][START_REF] Lai | Origin of shear induced β to ω transition in Ti-Nb-based alloys[END_REF].

This ITB ω phase is thus the ω phase that is detected during the SXRD experiments, as no nano-sized athermal ω phase can be detected from SAED patterns. Indeed, no diffuse streaks are visible on the [113] β zone axis SAED pattern (Fig. 5b) as commonly observed when precipitation of athermal ω phase occurs during the quench [START_REF] Sinkler | An electron diffraction investigation of the diffuse ω structure in quenched Ti-3d transition metal alloys[END_REF][START_REF] Devaraj | Experimental evidence of concurrent compositional and structural instabilities leading to ω precipitation in titaniummolybdenum alloys[END_REF][START_REF] Liu | Athermal and deformation-induced ω-phase transformations in biomedical beta-type alloy Ti-9Cr-0.2O[END_REF]. Therefore, the ω phase detected by SXRD is not athermal ω phase initially present in the microstructure but is truly the ITB ω phase observed by TEM along the twin boundaries.

Discussion

We showed by SXRD analysis that the microstructure of samples after stress released from the plastic deformation range consists mainly of β phase with a small amount of residual SIM α" phase and ITB-ω phase. However, the TEM observations on sample released from 4.5 % do not exhibit any detection of SIM α" phase. The reason is due to internal stress relaxation occurring during the thin foil preparation, which is reasonably accepted. The point to elucidate now concerns the mechanism of the ITB-ω phase formation. Indeed, this phase is never observed when the sample is under stress but only when the sample is released after being deformed in the plastic domain according to our SXRD analyses. The problem is that many transformations occurred in this metastable alloy such as the stress-induced martensitic transformation, twinning and ω-phase formation, which can be reversible and depend on each other.

The SIM α" transformation was confirmed by SXRD experiments with a phase-transformed fraction of 100 % when a strain of 4.5 % is reached. That means that the plastic deformation mechanisms, such as twining and dislocation slip, occur in this SIM α" phase and not in the β phase. Indeed, the plastic deformation starts between 4 and 4.5% of applied strain, as some residual strain starts to be measured after unloading from 4.5% (Fig. 1). In addition, as the formation of ω phase is observed only after unloading from 4.5% of applied strain, that means the ω phase is formed after plastic deformation has occurred, and thus after twinning of martensite has occurred. It is also worth

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noting that the ω phase is not detected after further loading (5%) but appears again when the stress is removed again: The formation of ω phase is thus reversible, meaning that the observed twins in the β phase with the ITB ω phase can transform again into twins in the α" martensite without any ω phase during subsequent loading. Plastic deformation mechanisms of α" martensite are not exhaustively known but twinning was already reported in the literature as the {1 3 0}<3 1 0> α" or the {1 1 0}<1 1 0> α" twinning systems [START_REF] Tobe | Origin of {332} twinning in metastable β-Ti alloys[END_REF][START_REF] Bertrand | Deformation twinning in the full-α″ martensitic Ti-25Ta-20Nb shape memory alloy[END_REF][START_REF] Ping | Stress-induced α″ martensitic (110) twinning in β-Ti alloys[END_REF]. Therefore, the observed {1 1 2}<1 1 1> β twins combined with the stress release-induced ITB-ω phase formation is believed to be linked directly with the α" martensitic twinning under stress condition. In order to prove this hypothesis, the α" martensitic twinning components has to be detailed on the basis of the well-known orientation relationship (OR) between the body-centered cubic β phase and the orthorhombic α" phase given in Table 2 [START_REF] Chai | Self-accommodation in Ti-Nb shape memory alloys[END_REF]. These data are used to make the crystallographic reconstruction of α" twins on loading from the crystallographic orientations of the β phase observed after the stress is removed.

By way of illustration, the crystallographic orientations of the β-matrix and β-twin observed in the Fig. 6 are presented on stereographic projections in Fig. 7a and7b. The common (-1 -2 -1) β twinning plane is indicated as well as the common < 1 1 1> β twinning direction. The corresponding crystallographic orientations of matrix and twin after transformation into α" phase were then determined by applying the OR. Actually, six possible orientations of α", named variants (V1 to V6) were deduced from a certain orientation of β-matrix or β-twin. All the combinations between both orientations of matrix and twin were tested in order to identify a potential twinning relationship in the α" phase under stress condition. For that, a rotation of 180° around the potential common twinning direction or reflection through the common twinning plane were made to confirm the twinning relationship. The tested potential common twinning planes and directions were referenced in several articles related to α" martensite or similar structure in α-uranium [START_REF] Bertrand | Deformation twinning in the full-α″ martensitic Ti-25Ta-20Nb shape memory alloy[END_REF][START_REF] Cahn | Plastic deformation of alpha-uranium twinning and slip[END_REF][START_REF] Crocker | The crystallography of deformation twinning in alpha-uranium[END_REF][START_REF] Field | Deformation twinning and twinning related fracture in coarse-grained α-uranium[END_REF]. Finally, only one convincing possibility was found between the α"-matrix-V3, and α"-twin-V3, both represented in Fig. 7c and Fig. 7d, respectively. The twining relationship found here corresponds thus to a compound {1 1 0}<1 1 0> α" twin.

It is demonstrated clearly that the α"-matrix-V3 and α"-twin-V3 keep a {1 1 0}<1 1 0> α" twinning relationship, because (i) the two projections share a common (-1 -1 0) α" pole and a common [-1 1 0] α" direction indicated in Fig. 7c and7d and (ii) the operation of a reflection through the (-1 -1 0) α" plane or a rotation of 180 o around the [-1 1 0] α" direction for the α"-matrix-V3 leads to the orientation of the α"-twin-V3. Therefore, the α"-matrix-V3 and α"-twin-V3 are in the compound {1 1 0}<1 1 0> α" twinning relationship. Further, the loading direction of the single crystal was ascertained as [1 0 1] β-matrix . Along this loading direction, the phase transformation strain

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10 can be thus calculated according to theory of PTMC [START_REF] Inamura | Composition dependent crystallography of α″-martensite in Ti-Nb-based β-titanium alloy[END_REF] and results were presented in Table 2. The maximum value is calculated as 4.29 % for V3. As it is generally assumed that the variant that is formed during a tensile test is the one giving the maximum of transformation strain, the occurrence of V3 is then in good agreement with the orientation of the single crystal of β phase. It can also be noticed that, according to the Fig. 1, the residual strain of approx. 0.2 % is measured at the applied strain of 4.5 % which is exactly the sum of phase transformation strain (4.29 %) and residual strain (0.2 %). Thus, the results of crystallographic reconstruction to determine the twinning system in α" martensite are in perfect accordance to the variant selection of α" due to the external stress.

Moreover, the twining plane (-1 -1 0) α" and the twining direction [-1 1 0] α" indicated in Fig. 7c coincide exactly with the twining plane (-1 -2 -1) β and the twining direction [1 -1 1] β in Fig. 7a, respectively, indicating a clear lattice correspondence between the deduced {1 1 0}<1 1 0> α" twinning system in the α" phase and the observed {1 1 2}<1 1 1> β twinning system in the relaxed β phase. The crystallographic orientation of the ITB-ω phase obtained from the DP in Fig. 6b is also shown with a stereographic projection in Fig. 7e. Some interfacial features can be found obviously: the twinning planes of (-1 -2 -1) β and (-1 -1 0) α" are indeed parallel to the (0 -1 1 0) ω , while the twinning directions of [1 -1 1] β and [-1 1 0] α" are parallel to the [0 0 0 -1] ω of the ITB-ω phase. The present orientation relationship between β and ω phase is specific for ITB-ω phase with a strong correlation between the twinning elements and the ω phase. Indeed, the twinning plane is parallel to (0 -1 1 0) ω and the twinning direction is parallel to the [0 0 0 1] ω direction. This specific orientation relationship was already pointed out in a gum metal alloy for the same twinning system [START_REF] Zhang | Complexion-mediated martensitic phase transformation in Titanium[END_REF] and also in a Ti-Nb binary alloy for the {3 3 2}<1 1 3> β twinning system [START_REF] Castany | Martensitic Twinning System at the Origin of {332}<113>beta Twins Observed in Metastable beta Titanium Alloys[END_REF], both exhibiting such ITB-ω phase. An explicit illustration of these orientation relationships is exhibited in Fig. 7f based on eighteen unit cells of β phase highlighted with red color. The unit cell of α" phase and ITB-ω phase are then highlighted with blue and green colors, respectively. Moreover, the path for atoms displacements which are necessary to realize the phase transformation are marked by hollows atoms and corresponding arrows.

The release of applied strain from the plastically deformed single crystal causes the reverse martensitic transformation, thus the microstructure is observed as the resultant {1 1 2}<1 1 1> β type with ITB-ω phase that is formed in order to minimize the surface energy of complex boundaries. As reported in a recent work [START_REF] Castany | Martensitic Twinning System at the Origin of {332}<113>beta Twins Observed in Metastable beta Titanium Alloys[END_REF], the ITB-ω phase is assumed to accommodate strains that are originated from the reverse martensitic transformation of the {1 3 0}<3 1 0> α" twin boundary into The geometrical models for the deformation twinning and ITB-ω phase are presented in Fig. 8 according to the lattice correspondence in Fig. 7f. The projection of the lattice is chosen to be along the planes of (0 0 -1) α"-matrix // (0 0 1) α"-twin // (-1 0 1) β-matrix // (1 0 1) β-twin // ( 2 -1 -1 0) ITB-ω . All solid circles indicate the atoms in the plane of figure, while the open circles the atoms below the plane of figure. The red, blue and green atoms refer to the initial lattice, the twinned lattice and the resultant ITB-ω lattice, respectively. The Fig. 8a firstly illustrates {1 1 0}<1 1 0> α" twinning formed via plastic deformation on the basis of fully transformed α" matrix. The twinning plane (-1 -1 0) α"-matrix and twinning direction [-1 1 0] α"-matrix are marked. It is worth noting, that the atomic layers A, B, C are not at equal distance to each other. The distance between these planes is dependent on the value of y, which is a parameter related to the positions of atoms in the orthorhombic cell of the α" phase.

Its value lies between 1/6 and 1/4, while the value y=1/6 describes an hcp structure (α phase) and the value y=1/4 describes a bcc structure (β phase).

The observed {1 1 2}<1 1 1> β twin and ITB-ω phase which are passively formed after releasing the stress are also presented in Fig. 8b. It can be noticed that the reverse transformation from α" to β leads to an equal distance between A, B and C atomic layers. Moreover, these atomic layers are also equally distanced in the ω phase. So, the reverse transformation is helpful to form an ITB-ω phase during the phase rerversion. Some atoms have thus to be slightly moved to form the ω phase (arrows on the fig. 8b). The final configuration of the twin interface after removing the stress is then illustrated in the Fig. 8c with the orientation relationship between the ITB-ω phase and both the twin and matrix of the β phase which are in a {1 1 2}<1 1 1> β twinning remationship.

Conclusions

The present investigation employed a single crystal with a nominal chemical composition of Ti-24Nb-4Zr-8Sn (wt. %) to investigate the ω phase on the twin boundaries. Techniques including cyclic tensile test, in situ synchrotron X-ray diffraction, TEM observations and crystallographic orientation reconstruction are used to comprehensively analyze the deformation features. Results as following are obtained:

(1) The <1 1 0> β Ti2448 single crystal exhibits a maximum recoverable strain of 4.2 % at the applied strain of 4.5 %. Incipient young's modulus and ultimate tensile strength were measured to be 51 GPa and 623 MPa. SXRD profiles confirmed the superelasticity is due to phase transformation and cell parameters were thus obtained.

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(2) Surprisingly, apparition of diffracted peaks related to the ω phase is found on SXRD profiles when the stress is removed, only from the plastic deformation range. These peaks disappear after further loading and appear back after subsequent unloading. The {1 1 2}<1 1 1> β deformation twinning is identified with diffraction patterns and TEM dark field images.

(3) Taking the sample deformed up to 4.5 % as an example, the applied strain is accommodated by martensitic α" phase transformation strain (4.29 %) and plastic deformation leading to residual strain after unloading (0.2 %). The TEM analysis also shown the presence of ITB-ω phase located along twin boundaries. Accordingly to SXRD results, this ITB-ω phase is formed when the stress is released.

(4) From crystallographic reconstruction based on the orientation relationship, results illustrate that the observed {1 1 2}<1 1 1> β and ITB-ω phase are the resultant lattice complexion due to the reversion of {1 1 0} <1 1 0> α" twins. The ITB-ω phase formed is due to the compression strains during the reversed martensitic transformation on the twinning boundaries.

(5) The sequence of deformation can thus be described as follow: during loading, the β phase firstly transforms into α" martensite; when this transformation is fully accomplished, {1 1 0} <1 1 0> α" twins are formed in the α" martensite during subsequent plastic deformation, as well as dislocation slip occurs; when the stress is removed from the plastic deformation range, the reverse transformation from α" to β phase occurs; the twins formed into α" martensite reverse thus into a deformation band exhibiting a {1 1 2}<1 1 1> β twinning relationship; a thin layer of ω phase lying along the twin boundary (ITB ω phase) is also formed in order to relax the stress accompanying this reverse transformation.

{3 3

 3 2}<1 1 3> β twin interfaces in a metastable β-type Ti-Nb alloy. The ITB-ω phase formed in the present case during the transformation from {1 1 0}<1 10 > α" twin boundary into {1 1 2}<1 1 1> β M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT twin actually follows the similar mechanisms but is activated along different crystallographic planes and directions.

1 Fig. 1 . 2 Fig. 2 . 3 Fig. 3 .

 112233 Fig. 1. Cyclic tensile curve of the single crystal Ti-24Nb-4Zr-8Sn alloy with the corresponding measured recoverable strains (open circles).

Fig. 4 . 4 Fig. 5 .Fig. 6 . 6 Fig. 7 7 Fig. 8

 44566778 Fig. 4. Optical microstructure of the single crystal Ti-24Nb-4Zr-8Sn alloy after deformation up to 4.5 % strain.

Table 1 .

 1 Cell parameters of different phases after releasing stress at higher applied strain in the plastic deformation range.

		loading			Unloading
	Cell parameters (Å)	SIM α″ phase	β phase	ω phase
		4.5 %	5.5 %	4.5 %	5.5 %	4.5 %	5.5%
	a	3.261	3.260			4.732	4.732
	b	4.864	4.865	3.298	3.298	4.732	4.732
	c	4.848	4.851			2.991	2.991

Table 2 .

 2 The six lattice correspondence of variants for martensitic α" phase derived from the parent β phase and the calculated strain of phase transformation at the external loading direction of [1 0 1] β .

					Transformation strain along the
	Variants correspondence	ሾሿ હ "	ሾሿ હ "	ሾሿ હ "	loading direction of [101] Applied strain Applied strain of
					of 4.5%	5.5%
	CV1	ሾ100ሿ ఉ	ሾ011ሿ ఉ	ሾ01 ത 1ሿ ఉ	1.50	1.50
	CV2	ሾ100ሿ ఉ	ሾ01 ത 1ሿ ఉ	ሾ01 ത 1 ത ሿ ఉ	1.50	1.50
	CV3	ሾሿ ࢼ	ሾሿ ࢼ	ሾ ഥ ሿ ࢼ	4.29	4.31
	CV4	ሾ010ሿ ఉ	ሾ101 ത ሿ ఉ	ሾ1 ത 01 ത ሿ ఉ	3.94	4.01
	CV5	ሾ001ሿ ఉ	ሾ110ሿ ఉ	ሾ1 ത 10ሿ ఉ	1.50	1.50
	CV6	ሾ001ሿ ఉ	ሾ1 ത 10ሿ ఉ	ሾ1 ത 1 ത 0ሿ ఉ	1.50	1.50

Acknowledgments

The authors acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities and would like to thank Yves Watier for assistance in using the beamline ID31. The authors also acknowledge Prof. Yulin Hao and Dr. Haoliang Wang in Institute of Metal Research Chinese Academy of Sciences for providing single crystal, and Dr. Guanglong Xu for the helpful discussion on the theory of phase transformation. This work was supported by Shenzhen Fundamental Research (JCYJ 20160427170611414).

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