Overall distribution of strategies.
\r\n\tThe main idea for any data or information processing system for those aspects of aggregating the data or computing the hierarchy of various process elements is that they should not only be machine-readable but also machine-understandable. Moreover, an adequate knowledge-based system is perceived to be, on the one hand, understandable by people, and on the other hand understandable by the machines.
\r\n\tAs devices become smarter and produce data about themselves, it will become increasingly important for scientists to take advantage of more powerful tools and/or data integration techniques to help provide a common standard for information dissemination across the different platforms. To this end, the content of this book shows that technologies such as the semantic web, machine learning, deep learning, natural language processing, and learning analytics which encompasses the wider spectrum of the Linked Open Data (LOD) are of paramount. Therefore, the work presents two main drivers for the Linked Open Data technologies: (i) encoding knowledge about specific data and process domains, and (ii) advanced reasoning and analysis of the big data at a more conceptual level.
\r\n\tThis book intends to provide the reader with a comprehensive overview of the current state-of-the-art within the Linked Open Data and the benefits of the methods – ranging from the semantics-aware techniques that exploit knowledge kept in (big) data to improve data reasoning (big analysis) beyond the possibilities offered by most traditional data mining techniques.
Creation and development of modern technologies is based on fundamental research. Development of new materials is based on the knowledge of fundamentals of the processes that determine the formation of a material, as well as the correlation of structure and physical properties. Progress in the creation of new materials with certain properties (mechanical, electrical, magnetic) depends on the level of understanding of the processes that underlie the formation of a particular structure. The discovery and development of the materials with new physical properties, in turn, lead to the creation of new instruments and devices. Metallic glass and nanocrystalline metallic materials formed from metallic glasses, of course, apply to such materials.\n
Although many years passed after production of the first metallic glass, interest in them is only growing. In 1960, a group of researchers led by Professor Duwez first obtained metal alloy in a strange non‐crystalline state . X‐ray diffraction patterns had no lines corresponding to whatever crystalline phases, and there was only a broad halo. This work  is considered to be the first publication, which refers to amorphous metal alloys or metallic glasses. However, a year earlier Miroshnichenko and Sally  in Dnepropetrovsk (USSR) have already demonstrated the ability to produce metal alloys in a non‐crystalline state. Obviously, due to not very popular scientific “Factory laboratory” journal, this work went unnoticed. Whatever it was, work  is considered to be the first publication devoted to the study of the amorphous phase in metallic systems (as opposed to, e.g., already investigated oxide systems). After the first publication, an avalanche of the works went; an amorphous phase could be obtained in a growing number of systems, and within few years the number of amorphous alloys was already counted in the hundreds. Interest in the metallic glass was due to their unusual structure, quite untypical of alloys, and a whole set of outstanding physical and chemical properties. Amorphous alloys may be high‐strength, magnetically hard and soft magnetic, corrosion‐resistant, and others. Thus, microhardness HV of metallic glasses based on transition metals (Fe, Co, Ni) may exceed 1000, tensile strength may be greater than 4.0 GN/m2. These values exceed the maximum values of strength and hardness of usual metals and alloys used in the industry. For example, the strength of the wire from iron‐based metallic glasses is higher than the strength of piano wire . Iron‐based alloys have very good magnetic properties of low coercivity (0.5–1 A/m) and high saturation magnetization exceeding 1.4 T. Even higher hysteresis properties were obtained for Co70Fe5Si15B10  and Co‐Fe‐P‐B  alloys that have almost zero magnetostriction. In general, the main characteristics of the soft magnetic amorphous alloys based on iron, cobalt, and nickel are the high values of residual induction and low magnetic reversal losses; high values of magnetic permeability (high iron content) or close to zero values of magnetostriction (high content of cobalt). Magnetic properties can also be increased with an addition of the alloying elements, the values of the magnetic permeability can be as high as 120,000 . With a slight change in the composition, the properties of metallic glasses can vary quite significantly.\n
Most of the physical properties of solids are structurally sensitive. This dependence is typical for metallic glasses. For example, the soft magnetic properties of amorphous alloys can be improved by relaxation annealing, annealing in a magnetic field; mechanical properties naturally depend on the presence of residual stresses, corrosion properties depend on the chemical composition and state of the surface layer. Partially crystallized metallic glasses (peculiar composite consisting of amorphous and crystalline phases) have a number of very good properties that differ from the properties of both amorphous and crystalline materials. Importantly, the amorphous state is unstable; when heating or aging amorphous phase may decompose with a natural degradation of properties. Therefore, from the standpoint of basic science, and from the perspective of the industrial use of new materials, it is extremely important to study both the actual structure of the amorphous phase in metal alloys and its stability, the transition to the partially crystalline or fully crystalline state, as well as the correlation of structure and properties of the material.\n
The purpose of this review is to analyze the current state of research of structure evolution in amorphous and nanocrystalline metallic alloys. Particular attention is given to pre‐crystallization processes and specific features of heterogeneous amorphous phase formation. The decomposition of homogeneous amorphous phase and the formation of regions with different chemical compositions and/or different short‐range order are considered for different types of metallic glasses. Formation of a nanocrystalline structure from homogeneous and heterogeneous amorphous phase is studied. Structure‐property correlations are described.\n
The most common method of producing metallic glass or amorphous alloy is a melt quenching onto a moving substrate. When the melt is cooled, the cooling rate is about 106–109 K/s (depending on the method of quenching). With such a large cooling rate at room temperature, the structure of liquid is frozen and the sample is non‐crystalline.\n
Not all alloys can be obtained in an amorphous state. The most commonly considered three main criteria that determine diffusionless solidification : thermodynamic criterion, morphological criterion and heat criterion. Usually kinetic and structural criteria are also discussed [8–10]. Some alloys may be prepared as amorphous will have less cooling rate [11–24].\n
The most common method for studying the structure of amorphous alloys is a method of large‐angle X‐ray scattering or as it is often simply called X‐ray method [25, 26]. For detailed information about the structure of the amorphous phase, it is necessary to build the partial radial distribution functions [27–31]. At present, methods of construction of total and partial radial distribution functions are not used very often, although it should be noted the study of Mattern et al.  or the study cited in . In analyzing the structure of metallic glasses, as a rule, with the help of Ehrenfest equation, the radius of the first coordination sphere as well as its changes at all types of influences are estimated; and distortion of diffuse maxima (the appearance of an additional shoulder, splitting of the peak, and others.) is determined. In combination with other methods of research, such an approach appears to be more productive.\n
Another commonly used method for analyzing the structure of the amorphous phase is the method of small‐angle X‐ray (SAXS) and neutron scattering . The most important feature of this method is the possibility of studying heterogeneities in the structure of disordered systems as are metallic glass. In an absolutely homogeneous medium, there is no small‐angle scattering, and the scattering pattern varies considerably with the appearance of any heterogeneities of the electron density in the structure.\n
In addition to the X‐ray methods for studying the structure, the most important method is the transmission electron microscopy (TEM). Without dwelling on the specifics of the method, it is important to note that the analysis of the structure of amorphous phase is based on both electron diffraction and analysis of bright‐field and dark‐field TEM images. The high‐resolution electron microscopy and micro‐ or nanobeam diffraction methods are used to study the structural features of the early stages of crystallization of the amorphous phase, and the structure of the nanocrystals. The last method allows determining atomic arrangement in amorphous structure, strain in crystalline materials with a high spatial resolution, etc. The development of the nanobeam electron diffraction with a coherent electron beam lesser than 1 nm in diameter has made it possible to obtain two‐dimensional diffraction patterns from a nanoscale region to detect local atomic structure. Combination of the nanobeam diffraction experimental method with ab initio molecular dynamics simulation allows obtaining and developing new knowledge about amorphous structure [35, 36]. The newly developed Cs‐corrected TEM technique offers a great advantage to probe the local atomic structure of disordered metallic glasses since it allows achieving a coherent electron beam as small as ∼3 Å in diameter, which cannot be obtained before by conventional TEM .\n
In studying the structure of the amorphous phase, indirect methods may be used such as the measurement of certain properties, whose changes reflect changes in the structure. For example, structure change can be fixed by measuring the temperature dependence of the magnetic properties. Thus, during heating of the ferromagnetic Fe27Ni63P14B6 amorphous alloy, there was an increase in the Curie temperature . Since the Curie temperature is determined by the nearest environment of atoms, its change, of course, indicates a change in the structure of amorphous phase. In , it was shown that after the heat treatment, the amorphous Fe‐P‐B alloy is not uniform, and it is characterized by two different Curie temperatures. Numerous studies of amorphous alloys by Mössbauer spectroscopy showed that depending on the conditions of heat treatment, the parameters of the Mössbauer spectra may vary considerably . Application of NMR spectroscopy revealed that the temperature change can lead to changing type of short‐range order in the amorphous phase .\n
A number of researchers have tried to describe the structure of the amorphous phase in metallic glasses by different models. The first model was the model of a chaotic close packing of hard spheres , which allowed successfully describing the distribution function of the atoms in the amorphous structure. Model chaotic close packing of hard spheres was initially designed to one‐component systems, and later was adapted to the binary system . Later this model has been improved by the introduction of interatomic potentials (soft‐sphere model), which allowed to build atomic pair distribution function  with the more realistic values of the position and intensity of the main part and the shoulder of the second maximum of the distribution function. The next step in the modeling of the structure of metallic glasses was attempts to build a structure made up not of individual atoms and of coordination polyhedra [45, 46]. Another group of models of the metallic glass structure is based on the idea that elements of the crystal structure retained in liquid and amorphous alloys . The review  lists all the main issues to date models of the structure of amorphous alloys: model of chaotic packing of hard spheres; model of polyhedra packing; the stereochemical model, model of efficient packing of quasi‐equivalence clusters [47–51] and the model of middle‐range order or fractal packaging .\n
Any approach to the description of the amorphous structure suggests that it is a homogeneous isotropic structure. In fact, it was turned out that the structure of the amorphous phase in alloys cannot always be uniform and isotropic. Figure 1 shows a typical X‐ray scattering curve of amorphous alloy. The figure shows intensive first diffuse peak, determining the shortest distance between atoms and the subsequent weak halo. A feature of the amorphous phase in the metal‐metalloid alloys is significantly weaker scattering from metalloid atoms compared to metallic atoms (e.g., an amorphous phase in alloys of Fe‐B); therefore, the scattering is determined primarily by the metal atom. Other situation occurs in the case when the amorphous phase contains two or more metals with comparable scattering amplitude (e.g., Fe‐Zr). In such systems, the appearance of inhomogeneity areas is much more pronounced, since the formation of regions with different chemical compositions (e.g., enriched in iron or zirconium)  leads to the appearance of at least two types of the shortest distances between atoms, which naturally affect the X‐ray diffraction pattern. Such changes have been found in a number of systems [54–60].\n\n
It should be noted that X‐ray diffraction pattern of the sample shown in Figure 1 does not indicate that the amorphous phase is uniform. The appearance of a shoulder or a second peak occurs when the radii of the coordination spheres in different regions of the sample are different. If the areas, even with different chemical compositions, have the same radius of the first coordination sphere, no features on the X‐ray diffraction patterns will be seen.\n
Heterogeneities in the structure of the amorphous phase were observed not only in as‐prepared state. In some cases, the appearance of heterogeneities in the structure was found after various external influences: heat, irradiation, and others [61–65]. A lot of information about heterogeneities in the amorphous phase was obtained using the method of small‐angle X‐ray scattering [66–70]. It is interesting to note that the occurrence of heterogeneities may be related to the composition of the amorphous phase . The impact of external influences on the structure of the amorphous phase will be discussed in more detail in Section 6.\n
Nucleation and growth of the crystals are suppressed at rapid cooling of the melt, and below the melting point metastable supercooled liquid is formed. With the temperature decrease the viscosity increases and the diffusion slows down, that is why at room temperature the solidified structure has the same atomic arrangement as it is in the melt prior to cooling. This non‐equilibrium state is usually called the glass and the temperature at which solidification occurs—a glass transition temperature Tg. The Tg is generally defined as the temperature when the viscosity of the supercooled liquid reaches 1012 poises . At the glass transition temperature, a lot of properties change drastically: specific heat, the temperature dependence of the specific volume, enthalpy, and others. Since amorphous alloys are obtained by melt quenching with cooling rates of 106–109 K/s, the structure of the amorphous phase after quenching is non‐equilibrium. When heated, the amorphous phase relaxes to an equilibrium state. There is reversible and irreversible structural relaxation. The volume, viscosity, diffusion mobility, and embrittlement change irreversibly during relaxation; induced magnetic anisotropy may change reversibly, a decrease of internal stress (e.g., during annealing), Young’s modulus, specific heat, coercive force, Curie temperature, the internal friction can vary and reversibly and irreversibly depending on the alloy composition [71, 72]. Relaxation processes were widely studied [73–81].\n
The main features of the deformation of metallic glasses are a great amount of elastic deformation (up to 4% in the bulk amorphous alloys), high strength, and fracture toughness . Elementary carriers of deformation in metallic glasses are groups of atoms . In contrast to crystalline materials in which the acts of deformation can be estimated from the behavior of dislocations by transmission electron microscopy, it is virtually impossible to observe such a process in metallic glasses. It is usually assumed that the reason for plastic flow and fracture is the formation of shear bands that develop over time. Deformation of metallic glasses proceeds differently in the two different modes of loading and temperature. At high stresses and relatively low temperatures, deformation occurs heterogeneously and it is much localized. As a result, narrow shear bands formed, the orientation of the shear bands is close to the orientation of the maximum shear stress [83, 84]. The time of formation of shear band is estimated as τ < 3 ms. Shear bands and slip steps were observed for a number of amorphous alloys. Shear bands are oriented at an angle of 55 ± 5° to the direction of deformation. Upon annealing, the difference in the structure of shear bands and the surrounding matrix can fully or partially disappear. At low stresses, the deformation is carried out by a homogeneous creep mechanism.\n
It is important to note one more feature of the deformation of metallic glasses. When stress is applied initially, in accordance with Hooke’s law, elastic deformation occurs in which the elongation linearly depends on the stress. At higher loads, this dependence deviates from the linear law. If so‐called mechanical hysteresis loop is observed after the load removing, and the sample does not return to its original shape, one talks about the inelastic deformation of the material. The energy corresponding to the area of the loop, connected with the displacement of atoms in a stable position. The quantity of such displacement in the amorphous alloys is generally about an order of magnitude greater than in crystalline alloys. It is believed that the inelasticity of amorphous alloys is related to the free volume in their structure: if the free space is small, the inelastic deformation is also small. A further plastic deformation of amorphous alloys occurs by the formation and propagation of shear bands. It has been found that the velocity of propagation of shear bands does not depend on the strain rate in the range 2 x 10-4–10-2 s-1 . For such different metallic glasses as ductile Pd40Ni40P20 alloy (value of the plastic strain of about 3%) and fragile Mg58Cu31Y6Nd5 (value of plastic deformation of 0%), the average velocity of propagation of shear bands varies slightly and is 317 and 366 μm/s, respectively .\n
Another feature of plastic deformation of amorphous alloys is the increase in the concentration of free volume in the shear bands, that is, increase in the average distance between the atoms. In general, the features of the shear band structure and, in particular, the reasons for the accelerated mass transfer in these areas are being actively discussed recently. A number of studies assumed that the severe plastic deformation leads to temperature increase up to the melting of the material in shear bands [86–87]. According to another view, shear bands are regions with a disordered amorphous structure of reduced density, so that the diffusion mass transfer in these areas can be facilitated. Probably, mass transfer processes depend both on the temperature rise and on the less dense structure, but these issues are still subject to a more detailed study.\n
The mechanical properties of amorphous alloys have aroused great interest from the moment when the metallic glasses were first obtained as a ribbon, and it was possible to carry out systematic research. One of the most complete early reviews devoted to the study of the mechanical properties was K. Pampillo’s review . Metallic glasses are high‐strength materials, some of them can be cut, rolled, and even stamp, and it makes metallic glass attractive for technical applications [88–91]. The properties of metallic glasses are highly dependent on the prehistory of the samples and their chemical composition. Since metallic glasses contain fluctuations, atomic structure may vary slightly from place to place. Structural heterogeneities inevitably lead to irregularities in mechanical properties. Areas with less local viscosity are less stable and can be advantageous in some places of localization of inelastic deformation. These areas are places that facilitated the formation of shear bands [92–94]. Johnson and Samwer  derived a universal dependence of the yield strength on the temperature (T/Tg)2/3. A number of studies suggest that this relationship may be more complicated [96, 97], but the overall trend has been maintained in different systems.\n
When heated, amorphous alloys crystallize, but the crystallization is often preceded by separation of the amorphous phase into regions of different chemical compositions and different short‐range order, that is, the formation of two or more amorphous phases. These phases do not separate with sharp interface, and the transformation may exhibit spinodal decomposition characteristics [54, 61]. Changes in the structure of the amorphous phase during annealing were studied for the alloys of various compositions. Figure 2 presents the X‐ray diffraction pattern of Al87Ni8La5 sample annealed at 150°C . After annealing, the samples were amorphous. The structure of the amorphous phase was found to change during annealing, which is revealed in the change of the diffuse maximum in the X‐ray diffraction patterns. The first diffuse maximum in the X‐ray diffraction pattern of the as‐prepared amorphous ribbon was symmetrical, and after annealing it shows a shoulder on the large‐angle side, the degree of the maximum distortion increasing with annealing time. Figure 2 presents the X‐ray diffraction pattern of the sample annealed for 25 h (first diffuse peak region). It is seen that subsequent to heat treatment the diffuse maximum is a superposition of two maxima. The positions of the scattering maxima are known to determine the radius of the first coordination sphere R1,\n
where (S1)max = 4π(sinθ / λ is the wave vector corresponding to the first (second, third…) maximum of the intensity curve, θ the scattering angle, and λ the radiation wavelength . Thus, the two diffuse maxima point to the presence of amorphous matrix regions with different radii of the first coordination sphere. The difference in the angular positions of the diffuse maxima is indicative of the formation of amorphous regions with different chemical compositions of the two amorphous phases. The maximum located at the smaller angles corresponds to the amorphous phase with a large radius of the first coordination sphere (or the largest interatomic distance in the amorphous phase). Since in the system in question the largest atoms are those of lanthanum (radii RNi = 0.124 nm, RAl = 0.143 nm, RLa = 0.188 nm), the amorphous phase is lanthanum‐enriched. Thus, the isothermal annealing of amorphous Al87Ni8La5 alloy leads to decomposition of the amorphous phase: formation of regions of different chemical compositions and with different types of short‐range order.\n
Similar results were obtained in studies of the effect of prolonged low‐temperature annealing on the structure of amorphous Fe‐Zr alloy . The annealing of Fe90Zr10 sample results in a shoulder on the smaller angle side of the first maximum in the X‐ray diffraction pattern: the isothermal annealing leads to amorphous phase decomposition and formation of at least two new amorphous phases with different component concentrations. Such a structural change was also mentioned by the authors of  in the studies of metallic Fe‐Zr glass by the methods of anomalous X‐ray scattering, nuclear gamma resonance spectroscopy, and magnetic property measurement.\n\n\n
Figure 3a presents the alloy structure after annealing at 100°C for 6850 h, and Figure 3b presents the corresponding electron diffraction pattern. After this annealing, the sample contains 10–30 nm size crystals. The nanocrystals have non‐sharp boundaries in the transmission electron microscopy images. The structure is distinguished by diffuse grain boundaries in the microstructure image and persisting blurred rings in the microdiffraction pattern. Such diffusivity cannot be explained by the small grain size since the diffraction patterns of usual nanostructures with crystal sizes of 5–10 nm exhibit much more pronounced ring reflections . With increasing annealing time, the structure becomes more distinct and the boundaries between nanocrystals become sharper, and rings in the electron diffraction patterns begin to split. Figure 4 shows an electron diffraction pattern exhibiting splitting of ring reflection, its more pronounced areas indicated by arrows. It is important to note that these changes in structure occur without appreciable change in scale—the size of nanocrystals is not appreciably changed. The electron diffraction and X‐ray diffraction patterns enabled to establish that two solid solutions of Zr in Fe form in the sample, their lattices having close but different parameters and, naturally, different component ratios. The above characteristic features of transformation indicate a progressive and continuous transition from single‐phase to two‐phase amorphous structure, then to crystalline structure with diffuse grain boundaries, and, finally, to fully crystalline structure with a constant size the regions of composition changes, point to the spinodal nature of transformation.\n\n
Evolution of the amorphous phase depends on temperature. As it was mentioned above, heating and annealing of the metallic glasses can be carried out in two different temperature ranges: above and below the glass transition temperature. Above the glass transition temperature, the amorphous phase is in a supercooled liquid state, below glass transition temperature it is in fact the amorphous state. It is known that when passing through the glass transition temperature Tg, material properties change sharply (viscosity, enthalpy, heat capacity, specific volume, and others.). This leads to significant differences in the process of diffusive mass transfer in these temperature ranges, and in turn, to changes in the structure. For comparison, let us consider the changes in the structure of the same alloy that occur above and below the glass transition temperature in the two nickel‐based glasses: Ni‐Mo‐P and Ni‐Mo‐B.\n
Amorphous Ni70Mo10P20 alloy. The glass transition temperature (Tg = 430°C for a heating rate of 20K/ min) of the alloy is below the crystallization temperature (Tx = 457°C) . This allows to investigate the changes in the structure both in the supercooled liquid state (above Tg) and in the amorphous state (below Tg). Heating above the glass transition temperature leads to a noticeable change in the structure of the amorphous phase. Figures 5 and 6 show the TEM images of the as‐prepared sample (Figure 5) and annealed above Tg sample (Figure 6) . Under the same conditions of preparation of electron microscopy foils, in the annealed sample, in contrast to the original, there is a pronounced spotted contrast. Figure 7 shows the X‐ray diffraction patterns of as‐prepared and annealed above Tg samples. After annealing, the shape of diffuse maximum distorted. When analyzing the structure of the amorphous alloy by micro‐micro‐diffraction method it has been found that the scattering vector corresponding to the maximum intensity of diffuse halo of an amorphous phase varies from one area to another along the sample. Observed area of spotted contrast and matrix is described by the different scattering vectors, indicating that the difference in short‐range order in the light and dark areas. With further heating, the crystallization begins in places that appear lighter in the images. In these places, crystals of Ni(Mo) FCC solid solution form; the size of the crystals is 20–30 nm, and crystals are in direct contact with each other (Figure 8). If the heat treatment was carried out below the glass transition temperature, changes in the structure of amorphous phase were not observed. The structure of the sample annealed at 400°C for 1 hour (below Tg) contains the amorphous phase and crystalline eutectic colonies. Thus, the processes leading to separation of amorphous phase occur at the temperatures above Tg; above and below the glass transition temperature, amorphous structure varies differently, later leading to the formation of different crystal structures and, of course, different physical properties.
Amorphous Ni70Mo10B20 alloy . In this alloy, the glass transition temperature is also below the crystallization temperature. Upon heating the amorphous alloy above the glass transition temperature, the X‐ray diffraction pattern also changes due to the appearance of areas with different chemical compositions. So before the crystallization the amorphous phase is heterogeneous and contains areas with higher and lower molybdenum concentration (and possibly boron). Crystallization of the alloy above the glass transition temperature leads to the formation of three crystalline phases simultaneously: two face‐centered crystalline phases and an orthorhombic phase Ni3B. FCC phases are Ni and Ni(Mo) solid solution. All three phases form substantially simultaneously. The crystal size is less than 50 nm. Figures 9 and 10 show the images of Ni (Figure 9) and Ni(Mo) solid solution (Figure 10) nanocrystals formed above the glass transition temperature. Each nanocrystal is surrounded by the amorphous matrix. Studies of the structure by transmission and high resolution electron microscopy methods showed that the formation of the phases is independently from each other. The formation of each of the crystalline phases occurs in “their” concentration region, that is, the formation of crystalline phases in each concentration region can occur by the polymorphic mechanism without changing the chemical composition or by primary crystallization mechanism with slight change in concentration. These types of the crystallization (primary or polymorphic instead of eutectic crystallization) are due to changes in the amorphous structure before the crystallization which ensures the formation of amorphous regions to “fit” the compositional ordering. Below the glass transition temperature, phase separation is not observed, the crystallization occurs by the eutectic mechanism.
Thus, structure formed above and below the glass transition temperature varies markedly. It should be noted that the scale of the chemical composition change may be different: it is about (15–20 nanometers) in (Fe‐Zr system)  or more than 50 nm (Ni‐Mo‐B system) . This difference is connected with opportunity of implementing a diffusion mass transport in different temperature conditions. As noted above, the results, showing the development of heterogeneities in an amorphous matrix, were obtained using small‐angle X‐ray scattering method as well [63, 66, 99, 102–104]. Changes in the structure of the amorphous phase do not necessarily have the character of a separation at heat treatment. The type of short‐range order can vary with the temperature [41, 105]. Concentration redistribution of the components in the amorphous phase can occur not only before the onset of crystallization. In some cases, the amorphous alloy separation may accompany the first stage of crystallization [99, 106].\n
The structure of amorphous phase can vary considerably, not only by heating but also by deformation. The question of a possible change in the structure under the influence of the deformation came into sight from the very beginning of amorphous alloy research. As was mentioned problems of homogeneous deformation and inhomogeneous flow, the fracture processes, their dependence on the temperature and composition was discussed in [83, 107]. In the last few years, new works were published that confirm the change in the structure of the amorphous phase at different types of influences which do not lead to crystallization . A group of studies on the structure evolution carried out directly in the process of deformation of Zr‐based amorphous alloys aroused great interest. The samples were deformed by tension, and synchrotron source was used for structure investigation in‐situ. It allowed detecting the structure occurring at the elastic deformation [109–111]. It has been found that in the absence of plastic deformation, the tensile results in a change of the distance between atoms in an amorphous structure, and these changes depend on the orientation of the applied stress. It was shown that the initial symmetric with respect to zero diffuse peak position becomes asymmetric in the process of deformation. The results indicate that the first coordination sphere, characterizing the arrangement of atoms in the amorphous structure, transformed into an ellipsoid in the deformation process. In the study of elastic deformation of Zr62Al8Ni13Cu17 and La62Al14(Cu5/6Ag1/6)14Ce5Ni5 metallic glasses the deformation was shown  to be indeed an anisotropic. The Zr‐based amorphous alloys are brittle, and they practically do not undergo plastic deformation, so only the region of elastic deformation was considered in the above‐mentioned paper. At the same time, it would be interesting to determine whether the observed changes in the structure can be stored when the load is removed and whether they exist at plastic deformation. Such studies have been carried out for the amorphous Pd40Ni40P20 alloy . The deformation by multiple rolling was found to cause formation of anisotropic amorphous structure. The distance between atoms along the rolling direction was found to increase at the deformation, whereas it does not change in the perpendicular direction. Changes in the structure during deformation have been observed using a small‐angle X‐ray scattering method [113, 114].\n
In addition to the occurrence of the anisotropy in the structure, plastic deformation may lead to separation of the amorphous phase. Figure 11 shows the X‐ray diffraction patterns of amorphous Al88Ni2Y10 and Al88Ni10Y2 alloys after deformation by multiple rolling . It is seen that the first diffuse maximum for Al88Ni10Y2 alloy is asymmetric and, as in the case of heat treatment, it is a superposition of at least two maxima. Note that changing the structure under the influence of plastic deformation depends on the alloy composition. It is evident that the first diffuse maximum from the Al88Ni10Y2 sample (curve 1 in the X‐ray diffraction pattern) is asymmetric and, obviously, it is a superposition of at least two maxima. Two amorphous halos indicate the appearance of regions, which differ in composition. So, rolling of the Al88Ni10Y2 alloy leads to separation of the amorphous phase into regions with different chemical compositions. Deformation of Al88Ni2Y10 alloy (curve 2, Figure 11) leads to formation of a small amount of nanocrystals.\n\n
The physical properties of amorphous alloys are very sensitive to structure evolution; they depend on external influences. Amorphous phase is not thermally stable, so the subsequent annealing, not leading to crystallization, causes the structure change:\n
The microhardness change. Changes in the structure during annealing are accompanied by changes in microhardness of amorphous phase. For example, microhardness marked increases at low‐temperature annealing of amorphous Fe80B20 alloy . Since the microhardness of the material characterizes the strength of the bonds between atoms in the structure, change of microhardness shows evident amorphous structure evolution. The increase of the microhardness during annealing is obviously caused by both decreasing free volume and ordering processes.
The Curie temperature change. Study of the amorphous Fe27Ni63P14B6 alloy  showed rising Curie temperature at heating in the temperature range below the crystallization temperature. Later, these changes were observed in a number of other alloys [39, 117]. Heat treatment of amorphous Fe‐B‐P alloy was found to lead to separation of the amorphous phase into region differing in composition and/or short‐range order, which can be characterized by different Curie temperatures. The changes of the properties with heat treatment may be reversible [118, 119].
Changes in plasticity. The ductility of amorphous alloy decreases during heating. This decrease can start at a sufficiently low temperature compared to the temperature of crystallization depending on the chemical composition. The embrittlement of amorphous alloys was first detected in the Fe40Ni40P14B alloy, and it was believed that it is caused by the presence of phosphorus, since it was found that the fracture surface is enriched with phosphorus . However, Masumoto et al.  showed that the Fe‐Si‐B alloys without phosphorus are also fragile.
Since amorphous state is metastable, the amorphous alloys transform into a more stable crystalline state at heating. In most cases, the crystallization of the amorphous phase occurs by the mechanism of nucleation and growth. The most detailed crystallization reactions were studied by U. Koester in Bochum University . The transition of the amorphous phase into crystalline phases depending upon the alloy composition can occur by one of the following reactions.\n
primary (or preferential) crystallization;
When the primary crystallization occurs, concentration gradient arises in front of the growing crystal. The growth rate decreases with time because the reaction involves the atoms diffusing on the long distances. It has been found that the spherical radius R of the growing crystal parabolically depends on the annealing time t in many metallic glasses which crystallize in the primary crystallization reaction [120, 121]. This means that the crystal growth is controlled by bulk diffusion,
where α—dimensionless parameter depending on the composition at the interface particle/matrix, and D—the coefficient of volume diffusion.\n
The crystal nucleation can be homogeneous and heterogeneous, in the last case the formation of crystals will be facilitated on the surfaces or so‐called “frozen” crystallization centers [124, 125]. The ratio of nucleation and growth rates is a very important factor in the formation of structure. At low nucleation rate and high growth rate, small number of crystals forms and they can grow to considerable size. In the case of high nucleation rate and a small growth rate, very large number of crystals forms in the amorphous matrix.\n\n
In addition to the above reaction of nucleation and growth crystallization, the mechanism of spinodal decomposition may occur at the metallic glass crystallization . The possibility of such a separation in metallic glasses was discussed in a number of papers [127, 128–130]. The crystal structure formed during the crystallization of the amorphous phase can vary significantly in phase composition, morphology, crystal size, mutual arrangement of structural components . In the last decades, much attention has been paid to nanocrystalline structure. The nanocrystalline structure in most cases is formed by the primary crystallization reaction. The Fe‐Cu‐Nb‐Si‐B alloy, called Finemet, was the first alloy obtained in the nanocrystalline structure .\n
An important feature of the crystallization of metallic glasses is the fact that in most cases, crystallization begins with the formation of metastable phases. As an example, crystallization of most extensively studied Fe‐B metal glasses may be considered [133–135]. In accordance with the phase diagram of the system , the crystallization of compositions close to the eutectic must occur by α‐Fe and tetragonal Fe2B boride formation. However, the crystallization leads to the formation of α‐Fe is formed of tetragonal Fe3B boride. This boride may form different structures (crystalline lattice of different space group), which undergoes several changes before equilibrium phase turns into Fe2B at heating or annealing. Specific features of metastable Fe3B boride were studied in a lot of work [93, 134, 136, 137]. Figure 12 illustrates a diagram of Fe‐B metallic glass transformation; the regions of existence of different borides are shown.\n
Another example is the crystallization of the amorphous Ni34Zr66 alloy . This alloy belongs to a small group of metallic glasses, which, in principle, can crystallize by polymorphic crystallization mechanism with formation of equilibrium NiZr2 crystalline phase (tetragonal lattice of I4/mcm space group). However, NiZr2 phase was not observed at the crystallization; a metastable phase with an orthorhombic lattice was formed. In contrast to the equilibrium phase, the structure of the metastable phase has a lower symmetry.\n
The formation of metastable phases at the crystallization of the amorphous phase is often observed for multi‐component systems. Crystallization of multi‐component Zr‐based alloys and changes in the structure and properties at treatment were examined for the alloys of different composition [139–145]. The crystalline structure forming at amorphous phase decomposition is strongly dependent on the chemical composition. For example, the amorphous Zr65Cu17.5Ni10Al7.5 alloy crystallizes with simultaneous formation of three phases: NiZr2‐type phase with cubic lattice, NiZr2 tetragonal phase and a metastable hexagonal phase, the crystals of all phases are randomly distributed in the amorphous matrix. When reducing the zirconium concentration, the phase composition varies. At the first stage of crystallization of the amorphous Zr50Ti16Cu15Ni19 alloy, three phases are formed, two of them are crystalline and the third phase is quasicrystalline. Quasicrystalline phase was observed in a number of crystallized metallic glasses of different composition [145–149].\n\n
One more example: decomposition of the amorphous phase in the Al85Ni10Ce5 metallic glass [150, 151]. The alloy crystallization begins with the formation of metastable phase. Figure 13 shows the X‐ray diffraction pattern of the alloy after the first crystallization stage. After finishing the first stage, the sample is predominantly crystalline, but it retains a certain amount of amorphous phase. All the observed diffraction lines correspond to one crystalline phase with a body‐centered cubic lattice. Figure 13 shows only a part of the investigated spectrum; the sum of the squares of the indices ∑ = h2 + k2 + l2 is shown near each line. Usually the pure aluminum crystals form at the first stage of crystallization of Al‐Ni‐RE (RE = Y, Yb, Ce) alloys (nickel and rare earth components do not dissolve in FCC‐Al). Since the ratio of the cell parameters of metastable phase and fcc‐Al aMS/aAl = 6.05, it was assumed that the metastable phase forms in a situation when the concentration redistribution of the components of the “uniform” amorphous phase has no time to occur. As a result, metastable solid solution of the alloy components in Al lattice form, it has a much larger lattice parameter, wherein the concentration of nickel and cerium is noticeably greater than their equilibrium solubility in the All lattice.\n
Changes in the structure during the phase transformation from an amorphous phase to the crystalline equilibrium phase are accompanied by a change in the physical properties [118, 152]. Structure formed at the crystallization of metallic glasses varies also during deformation or pressure increase [153–155], icosahedral quasicrystals have been found at the crystallization of a number of metallic glasses [155–158].\n
Under certain conditions, crystallization leads to the formation of a nanocrystalline structure. Nanocrystalline materials may be single‐phase and multiphase polycrystalline samples with a grain size of up to 100 nm (at least in one direction). Owing to the extremely small size of the grain, the structure of nanocrystalline materials is characterized by a large volume fraction of grain boundaries and interfaces, which can largely determine a variety of physical and chemical properties of the material. Indeed, it has been found that many properties of nanocrystalline material are fundamentally different from those of conventional polycrystalline and amorphous alloys [159, 160]. For instance, nanocrystalline materials may have high strength and hardness, good ductility and toughness, reduced elastic modules, higher diffusion rates, large heat capacity and thermal expansion coefficient, and higher magnetic properties as compared to conventional materials [161–164]. The nanocrystalline materials not only provide an excellent opportunity to study the nature of structure, properties, and structure/properties correlation of solids down to the nanometer range, but they are also very attractive in terms of possible industrial use of new materials . Changes in the structure and properties of amorphous and amorphous-nanocrystalline materials have been studied in a number of papers [166–169]. Small grain size makes a great development and length of the grain boundaries. The grain volume fraction of the grain boundaries in the total amount of the nanocrystalline particles in the material can be estimated in spherical shape approximation as in :\n
where δ is the average thickness of the interface and d is an average grain diameter . Thus, one can estimate the volume of the grain boundary. For example, when the thickness of the interface δ is 3–4 atomic monolayers (0.5–1.5 nm) and the average grain size is 10–20 nm, the fraction of surface layer is about 50%.\n\n
Crystallization of amorphous alloys usually takes place under conditions of existence of the large driving forces and low diffusion mobility. These conditions are favorable rather for nucleation and not for crystal growth. Formation and specific features of nanocrystalline structure were studied for different materials [171–175]. Specific nanocrystalline/amorphous composite structure has excellent magnetic or mechanical properties in a number of alloys [176–178].\n
To establish the mechanism of nanocrystallization, one can use a method of analysis of crystal size distributions. For example, controlled crystallization of the amorphous Al86Ni11Yb3 alloy  was found to lead to the formation of nanocrystalline structure with nanocrystal size of 5–12 nm. The nanocrystals are formed according to the mechanism of the non‐stationary heterogeneous nucleation and from frozen‐in crystal nuclei. For the conclusion of the nucleation mechanism, the distributions of nanocrystals by size were plotted for different durations of isothermal annealing; the distributions were analyzed. The size distributions obtained upon treatment for 5 and 15 min are depicted in Figure 14a and b, respectively. It is apparent that the heterogeneous nucleation with a latent period proceeds in our case. This is confirmed by the following facts. (1) Small‐sized crystals are absent in the distribution obtained upon treatment for 15 min. (2) A sharply descending portion in the small‐size range is observed in the distribution at a treatment time of 5 min, which is impossible in the case of homogeneous nucleation. (3) The fraction of large‐sized particles (the right‐hand branch of the distribution) decreases gradually, which is characteristic of the non‐stationary rate of nanocrystal nucleation (with the latent period). Therefore, at the very early stage of metallic glass annealing, there exists a certain time interval during which the stationary size distribution of subcritical nuclei (corresponding to the classical theory) is reached.\n\n
Computer simulations were carried out for heterogeneous nucleation and diffusion controlled growth. The calculated crystal distributions by size for annealed Al86Ni11Yb3 alloy (473 K for 5 and 15 min) are shown by lines in Figure 14; the experimental size distributions are represented by columns. Good agreement with the experimental data was obtained for the following crystallization parameters: QN = 90 × 103 J/mol and τ = 150 s. The effective diffusion coefficient of Ni and Yb in amorphous Al86Ni11Yb3 alloy is 1.4×10-19 m2s-1 for 5 min annealing and 6 × 10-20 m2s-1 for 15 min annealing. Since the diffusion coefficient of nickel, as a rule, is considerably larger than that of ytterbium, it is assumed that the nanocrystal growth is limited by the diffusion rate of ytterbium. As seen in Figure 14, the calculated and experimental data are very similar. However, the difference between the calculated and experimental distributions is in the presence of a tail of large‐sized particles in the experimental histograms. Most likely, the occurrence of large‐sized particles can be explained in terms of the presence of a small number of so‐called “frozen‐in crystal nuclei” in the initial alloy. The formation of crystals from these nuclei is facilitated. As a result, particles begin to grow earlier (prior to the completion of the latent period of attaining the stationary size distribution of subcritical nuclei) and reach larger sizes. Figure 15 shows the dependence of the average crystal size in the Al86Ni11Yb3 alloy on the annealing time. The similar results were obtained for the crystallization of amorphous Al‐Ni‐Y alloys . It has been found that the nanocrystals are nucleated by heterogeneous mechanism in the aluminum‐based alloys; and the nucleation begins in the regions depleted in the rare earth component [99, 174]. Specific features of the nanocrystal formation are studied in detail in [180–183].\n
Since metallic glasses are often used as the starting material for producing nanostructures, and problem of deformation of the composite amorphous‐nanocrystalline material is very important. Naturally, an important question is what component (nanocrystal or amorphous phase) determines the mechanical properties of the material and, in particular, if the nanocrystals can be deformed. Questions of the deformation of nanostructures are discussed in detail in . Usually single unloaded volume unit contains a small amount of induced defects or does not contain them at all. The smaller the size of the nano volume, the smaller the number of induced defects it contains. A critical particle size with a free surface dc was assumed to can be estimated if believe that below the probability of the existence of the defect sharply decreases [171, 172]. It was suggested that dc is about 10–100 nm. Such estimates have been made for free nanoparticles. It was assumed that I also believe that the mechanisms of plastic deformation and fracture of nanocrystalline materials are determined by the size effect.\n
In this way, the solution to this problem largely rests on the question whether the nanocrystals contain dislocations, which are carriers of plastic deformation. In the early stages of research, it has been suggested that there is a critical size below which all the crystals are perfect; and the crystals contain stacking faults, twins, etc. when exceeding this size. In fact, at the initial moment when the crystals nucleate and grow in an isotropic amorphous phase, they really are perfect. When the crystal growing, when the volume per one atom in the crystal is differ then the volume per atom in the amorphous phase, there are tension stresses around the crystals. The value of these stresses increases as the crystals grow and conditions for the formation of linear defects arise. Is there, indeed, a certain critical size of crystal separating perfect and imperfect crystals? The answer is quite important in particular for determining the strength and ductility of the material. For example, it was supposed in  that such a critical crystallite size determines the boundaries of the regions where mechanisms of dislocation strengthening and plasticity cease to operate.\n
Specific features of the nanocrystalline structure were studied in detail in [174–178] for Al‐ and Ni‐based alloys. The results showed that the Al nanocrystals and Ni nanocrystals formed in eutectic Ni‐Mo‐B systems were defect‐free. These nanocrystals have equiaxial shape, small size, and they do not contain linear defects. The nanocrystals of Ni (Mo) solid solution in all studied alloys were defect‐free at the beginning of crystallization, while the size of the nanocrystals is not more than about 5 nm. However, in the fully formed nanostructure the average size is much larger (20–50 nm), and the nanocrystals contain a significant number of defects. In analyzing the reasons of defect formation in the nanocrystals, two factors: the size factor and the energy of stacking fault formation, were considered. This size factor is associated with the inability to generate dislocations in nanocrystals smaller than 100 Burgers vector (operation conditions of dislocation sources, such as the Frank‐Read ). It is also obvious that the probability of appearance of defects (e.g., stacking faults) depends on the energy of their formation, and of course, this factor must be taken into account when comparing the degree of perfection of different nanocrystals. In terms of the magnitude of the Burgers vector b, the average size of the nanocrystals is:\n
Ni in the alloy with 20 at.% B 8–20 b,\n
Al ∼40–45 b\n
As was mentioned, when analyzing the degree of nanocrystals perfection in the Al‐ and Ni‐based systems, the influence of the energy of stacking fault formation was considered . The value of the energy of stacking fault formation is 135 erg/cm2 for Al and 240 erg/cm2 for Ni. However, it is known that the energy of stacking fault formation decreases with increasing electron concentration when doping . For example, stacking fault energy in Cu‐Ag alloys decreases ∼10 times with increasing electron concentration to 20% [186, 187]. Unlike aluminum nanocrystals that are one‐component, nickel nanocrystals contain about 17 at.% Mo, which leads to an increase in the electron concentration to about 20%. It is therefore natural to expect a significant reduction (several times) the stacking fault energy. This reduction of the energy of stacking fault formation can explain more perfect structure of Al nanocrystals as compared to Ni(Mo) nanocrystals.\n
However, what is a predominant reason of defect formation in the nanocrystals (the size factor or the energy of formation of stacking faults) is not clear.\n
What can cause the formation of defects in the nanocrystals? As shown above, a significant number of defects were observed in nanocrystals of Ni (Mo) solid solution. Since the nucleation and nanocrystal growth occur by the primary mechanism of crystallization, it is natural to expect that the concentration of molybdenum in nickel lattice varies from the center to the periphery of the nanocrystal. It is known that [187, 188] peculiar ordered structure can be formed in the crystals of two‐component systems. It can be assumed that the formation of twins in the nanocrystals of Ni(Mo) solid solution can occur in this way, that is, the formation be facilitated due to the uneven distribution of molybdenum atoms in solid solution. Naturally, formation of stacking faults by this mechanism is not possible in the case of single‐component nanocrystals.\n
It should be noted that the shape of Ni(Mo) nanocrystals with size of 30–50 nm differs from the equilibrium shape, and their growth leads to accumulation of the stresses associated with a crystallographic anisotropy and a difference in the density of the amorphous and crystalline phases. When increasing the size of the nanocrystals, the concentration of molybdenum in Ni (Mo) solid solution reduces, which, as previously noted, leads to increasing energy of stacking fault formation and, hence, decreasing the probability of twin formation by fluctuations of composition. On the other hand, molybdenum concentration in solid solution decreases during the growth of the nanocrystals; and its concentration increases at the reaction front (in the amorphous matrix in front of the crystal growing boundary). Details of the experimental observation of the distribution in front of the growing particle are given in .\n
In the processes of the primary crystallization the amorphous phase of Ni‐based alloys is enriching in molybdenum. Naturally, the Mo concentration is increased near the growing nanocrystal and this increased concentration diminishes with the distance from the nanocrystal. Heterogeneities in the composition of the surrounded regions may be important for the origin of the twins or stacking faults near the nanocrystal boundary and its intergrowth into the nanocrystal. It should also be noted that by increasing the Mo concentration in the nickel lattice, stacking fault energy decreases, that is, formation of defects is facilitated. If these reasons, indeed, define the appearance of defects in the nanocrystals, you should expect the formation of twins and stacking faults in the near‐boundary areas. The studies have shown that nanocrystals with defects in the near‐boundary areas, in fact, present in the nanocrystalline structure. Figure 16 shows a nanocrystal Ni(Mo) solid solution with defect‐free central part and twins and stacking faults in the near‐boundary regions.\n
Obviously, chemical heterogeneity is not only reason enough for the defects formation; small nanocrystals (up to ∼ 5 nm) are always defect‐free. Formation of the crystals in the amorphous matrix occurs in the field of stresses caused by the difference in specific volume per atom in the amorphous phase and in crystalline structure. Naturally, these stresses increase with the crystal sizes increasing. At the initial stages of crystal growth in isotropic amorphous phase these stresses are too small to induce the formation of defects in the nanocrystals. In the process of growth the nanocrystals reach the size when there is a growing stresses may cause the formation of defects.\n
It should be noted that the formation of microtwins and stacking faults cannot be determined by only size factor. One way of determining the degree of structure perfection of the nanocrystals formed in the amorphous phase was based on the following analysis of the diffraction line broadening:\n
broadening of the diffraction line caused by the small grain size is proportional to 1/cos θ or sec θ (θ is the angle of the reflection);
broadening of the diffraction line caused by randomly distributed dislocation is proportional to tg θ. If the nanocrystals do not contain defects, the half‐widths of the diffraction reflections depend linearly on the secant of the diffraction angle. Figure 17 shows such dependencies for Al‐based alloy (Al82Ni11Ce3Si4) and Ni‐based alloy ((Ni70Mo30)90B10). These alloys contain the nanocrystals with practically the same size: 12 nm nanocrystals in Al82Ni11Ce3Si4 and 13 nm in (Ni70Mo30)90B10. Therefore, curves 1 (for Al82Ni11Ce3Si4 alloy) and 2 (for (Ni70Mo30)90B10 alloy) correspond to two nanocrystalline alloys containing nanocrystals with approximately the same size (∼13 nm). (It should be noted that the lattice parameter of the aluminum and nickel varies markedly, which determines the different quantities of points in the curves.) It is evident that a linear relationship is indeed characteristic of nanocrystals in an aluminum alloy, while linear dependence was not observed for nickel‐based alloy. This means that the nanocrystals of the same size may be defect‐free or contain linear defects in the different systems.
However, it is more correct to compare the nanocrystals with the same size, expressed in the Burgers vector units (i.e., with the same number of interatomic distances); these values are 42b and 52b for curves 1 and 2, respectively. Therefore, for comparison, the figure also shows curve 3 corresponding to Al88Ni10Y2 alloy with the nanocrystal size of ∼50b. As seen from the figure, in this case, the dependence (curve 3) is also linear, indicating that the broadening of the diffraction lines is caused by size factor only, that is, nanocrystals are defect‐free. Thus, the size factor is not the only reason that determines the occurrence of defects in the nanocrystals; heterogeneities in composition play an important role as well.\n
In connection with the above, one point should be noted. As already mentioned, some researchers have suggested that there is a certain critical size of the nanocrystal, below which it is defect‐free. For each such material critical size of the nanovolume can be estimated when a probability of the existence of induced defect sharply decreases . Since the yield strength and elastic modulus for nickel are much larger (about three times) than that for aluminum, one would expect that the critical size of dislocation‐free Al nanocrystals will be lower than that for N nanocrystals, but the experimental results do not match. The results show that the size of the nanocrystal, whereby there occur defects, actually, is different for different systems. It depends both on the chemical composition and concentration of the components and on the conditions of nanocrystal formation; one would expect that the formation of the nanocrystal, for example, in thin sections the size of defect‐free crystal should be reduced significantly because the proximity surface will contribute to the resulting stress.\n
Obviously, to estimate perfection of the nanocrystalline structure, one should consider both the size of the crystals and the possible chemical heterogeneity, facilitating the formation of defects. The second factor is rather significant for nanocrystals comprising two or more components, the first one is important for any type of nanocrystals.\n
As noted above, the changes occurring in the amorphous phase structure before the onset of crystallization may significantly affect the morphology and parameters of the crystalline structure forming on subsequent heating [116, 190, 191]. The amorphous phase is the parent phase for nanocrystals, which are formed by thermal and/or deformation effects. By varying the type and effect parameters, one can create amorphous‐nanocrystalline materials with different size and volume fraction of nanocrystals. Nanocrystal formation usually occurs by the primary crystallization mechanism. This reaction leads to change of the amorphous phase composition and to enrich the amorphous phase in refractory components and metalloids. This process can result in an increased stability of the amorphous phase. The crystallization process thus can stop, and the resulting amorphous‐nanocrystalline composites have high thermal stability. Heterogeneities in the amorphous phase may lead to the formation of different crystal phases. The noted structural changes do not exhaust all the possibilities for transformation of the system toward the equilibrium state. This wide variety of structures defines a set of good physical and chemical properties. For example,  annealing of amorphous Fe‐B alloy at temperatures below the crystallization temperature was found to alter microhardness and stability of the amorphous phase and ten‐fold increase of the crystal size after subsequent crystallization. It has been found that heat treatment at different temperature ranges leads not only to a change of the phase composition but also to the formation of the structure with substantially smaller crystals upon subsequent heating. Formation of smaller crystals was also observed is the case of crystallization of heterogeneous amorphous structure. This last point is particularly important because it indicates the possibility of structure design, based on the decomposition and separation inside amorphous phase. The separation of amorphous phase makes it possible to produce amorphous samples with crystalline surfaces (Figure 18) and crystalline samples with amorphous surface (Figure 19) in Fe‐B‐P alloys .\n\n
As most properties are structure‐sensitive, the knowledge of the ways for structure design leads to the possibility of forming materials with the desired properties. Creating new materials with good properties, as already mentioned, is one of the major challenges of modern science.\n
Cameroon French has been the focus of many studies, and the research carried out so far has mainly explored phonetical, phonological, morphological, syntactic, lexical, and semantic features. In recent years, the scope of research on Cameroon French has been expanded considerably, with scholars also giving more attention to pragmatic and discursive aspects of this postcolonial variety of French. The topics examined so far include address terms , speech acts (e.g., compliments and compliment responses , greetings , invitations and expressions of sympathy ), politeness strategies , discourse markers , etc.
The present study focuses on the analysis of pragmatic and linguistic choices made by Cameroon French speakers when expressing gratitude in three different situations. The speech act of giving thanks has been studied in many different languages and mostly within the framework of speech act and politeness theories. While there is an abundant literature on thanks in languages such as English, French, German, Spanish, Arabic, etc., there is a need to look at the impact of region on the realization of thanks in different regional varieties of the same language. With respect to French, the studies currently available mainly focus on the variety spoken in France. This paper is an attempt to extend the scope of research on thanks in French by examining the ways in which Cameroon French speakers express their gratitude in different situations. The study is based on data collected by means of a discourse completion task questionnaire that was administered to two groups of university students1. This paper is structured as follows. After this introduction, the next section presents the theoretical framework of the study. Section 3 reports on the methodology employed. The findings of the study are presented and discussed in Section 4. Section 5 summarizes the main outcomes of the study and evokes some avenues for future research.
Thanking is generally described as an expressive speech act, i.e., its illocutionary force is the expression of a psychological state about the speaker or the world. This speech act is produced in face-to-face situations or in written form when the speaker feels indebted to the addressee for a favor or help done in the past. The communicative act of thanking can also be performed as a reaction to compliments, offers, invitations, greetings, good wishes, etc. Thanks can also function as a closing signal in conversations or transactions in service encounters.
In research on the speech act of thanking in and across languages and cultures, it has been shown that giving thanks may occur in a single speech act (e.g., thanks, thank you, that is kind of you in English; merci, je vous remercie, c’est très gentil, in French; danke, vielen Dank, ich danke Ihnen in German; etc.). Gratitude expressions may also appear in combinations of several acts or speech act sets. In such cases, speakers may combine/repeat two or more expressions of gratitude or combine expressions of gratitude with other speech acts. For instance, in the data used for the present study, the communicative act of thanking is realized in some cases by combining greetings with thanks (Bonjour monsieur, je vous remercie pour votre aide “Good morning sir. I thank you for your help”) or thanks with familiarization acts (Oh! Merci beaucoup de ton aide! Moi c’est Sonia et toi? “Oh, thanks very much for your help. I am Sonia and you?”). Given the complexity of many examples provided by the participants, it would be more appropriate to consider thanking as a speech act set or a communicative act made up of several acts (cf. ). It is also interesting to note that the choice of single or complex realization patterns depends on a number of factors, including social distance (degree of familiarity between the interlocutors), power distance (social or institutional status of the interlocutors), the magnitude of the benevolent act carried out, and politeness considerations in the social context where the interaction is taking place. As Siebold (, p. 158) put it: “the greater the imposition there is on the giver, the more polite gratitude forms will be used”.2
The present study is based on Brown and Levinson’s  theory of politeness, which uses the central concept of face of Goffman. Within this framework, there are two opposing views on thanks. The first view describes thanks as a face-flattering act, whereby giving thanks is considered as a communicative act that recognizes the effort of the interlocutor and enhances his/her negative face. A gratitude expression is viewed as a means employed to establish and maintain a harmonious social atmosphere between the speaker and the hearer. In other words, the speech act of thanking has a “convivial function” (, p. 83). Overall, a gratitude expression can be defined as a
“recognition of something which has already happened in [the speaker’s] favor. In this situation, the thanks acts as a kind of reward for the action carried out by the hearer […]. The speaker doing the thanking appreciates the efforts of the hearer, who has previously to some extent forfeited his own freedom of action through this act. In this way, the expression of thanks serves to recognize the personal restriction experienced by the hearer for the benefit of the speaker, thus safeguarding and protecting his negative face” (, p. 157).
On the other hand, giving thanks is viewed as a face-threatening act. Brown and Levinson , for instance, describe thanks as a threat to the speaker’s negative face, as the latter “accepts a debt [and] humbles his own face.” The self-humiliation is due to the fact that s/he who expresses his or her gratitude is “to some degree subordinated to the hearer as a result of accepting the benevolent act in [his/her] favor and is at times in conflict with [his/her] positive face.” Eisenstein and Bodman  also classify thanking as a face-threatening act: they are of the opinion that the speaker threatens his/her own negative face by acknowledging a debt to the hearer (p. 65).
Overall, it is safe to view thanks as a multidirectional communicative activity, with respect to face concerns. Thanks can flatter the positive image of the hearer, since the gratitude expression presents the hearer (the thankee) as someone who has done something beneficial to the speaker (the thanker). In this case, the thanks is an attempt to satisfy the hearer’s need to be approved of. Thanks can also be considered as an enhancing strategy directed toward the negative face of the hearer as it is employed to recognize the efforts of the hearer . Thanks can also enhance the positive face of the speaker by presenting him/her as someone who recognizes the efforts of others and acknowledges benevolent actions. By expressing his/her gratitude, the speaker emerges as someone who knows how to satisfy the desire of the hearer. At the same time, thanks can threaten the positive face of the speaker because s/he subordinates himself/herself to the hearer. Finally, thanks can threaten the negative face of the speaker, since s/he admits having an obligation to the hearer.
The speech act of thanking has been extensively examined in many languages and from many different perspectives. Many studies have dealt with gratitude expressions and responses to thanks in languages such as Akan , German , English [11, 14], and Cameroon English (, p. 548).3 Studies from a cross-cultural or contrastive pragmatics perspective compare French and Italian , German and Spanish , German and Iraqi Arabic , French and Romanian , etc., gratitude expressions with Jordan and England . Comparative studies focusing on regional varieties of English include Jautz’s  analysis of gratitude expressions in British and New Zealand English radio programs and Elwood’s  examination of gratitude expressions in Irish English and New Zealand English.
As far as French is concerned, the studies currently available mostly analyze the speech act of thanking alongside other speech acts. For instance, Kerbrat-Orecchioni  examines apologies, thanks, and responses to both acts in the same chapter of her book on speech acts in discourse. She classifies thanks expressions in many subcategories. She distinguishes between direct thanks, i.e., those using either the performative utterance “je te/vous remercie” or the elliptical “merci” (, p. 129) and indirect thanks, i.e., those occurring in the form of different speech acts. She identifies the following types of indirect thanks:
expressions that focus on the thanker (the beneficiary of the benevolent act): expressions of a specific feeling (gratitude, pleasure, joy) such as “Je vous suis reconnaissant” and “je suis ravi/touché.”
expressions that focus on the thankee (the author of the benevolent act): appreciations of the addressee such as “c’est très gentil à vous” and “vous êtes bien amiable.”
expressions indicating that there is/was no need to grant the favor: “Il ne fallait” and “tu n’aurais pas dû.”
expressions that focus on the benevolent act: appreciations of the act such as “C’est superbe” and “c’est trop beau.” (, p. 129–130).
A number of studies have been carried out in the past on gratitude expressions and responses to thanks in Cameroonian contexts. Investigations on the speech act of thanking include Dnzoutchep Nguewo’s  comparative study of gratitude expressions in German and some languages spoken in the western region of Cameroon. The author illustrates the complex structure of the speech act of thanking, which he describes as a communicative act made up of several other speech acts, and supported by compliments, good wishes, address terms, etc. The complexity of gratitude expressions in the Cameroonian languages examined is viewed by the author as a reflection of sociocultural norms of many ethnic groups in the western region of Cameroon. Another investigation of the author yielded similar results (cf. ). Another analysis of thanking in Cameroonian context is Anchimbe’s  study of thanking in written political discourse called “motions of support.” These are letters read on the radio or TV or published in newspapers, addressed to the president thanking him for a political favor or action deemed beneficial to the group writing the motion. The study shows that thanking in “motions of support” appears as a communicative act made up of several other speech acts (cf. , p. 240). Also interesting is the conclusion that “the sociocultural interactional norms of indigenous Cameroonian cultures could be said to have influenced the structure and content of [Motions of Support] through their decorum and the extensive use of linguistic oratory in traditional hereditary systems” (, p. 240–241).
The goal of the present study is to contribute to a better understanding of Cameroon French speakers’ patterns in giving thanks. The approach used here operates on the premises of postcolonial pragmatics (cf. ), which takes into account the complex, multilingual, multiethnic, and multicultural postcolonial nature of the Cameroonian society, and thus considers giving thanks in Cameroon French (an ex-colonial language in a postcolonial space) as a postcolonial pragmatic behavior. Using this framework, the analysis reveals traces of indigenous cultural and communication patterns in the communicative act of giving thanks in Cameroon French. This impact could be noted in the use of nominal address terms by Cameroon French speakers as markers of group culture and in-group identity, on the one hand, and as expressions of deference and respect in formal situations, on the other hand. Also interesting here is the complexity of thanks utterances, which seems to be a reflection of indigenous sociocultural norms (see Section 5).
The data for the study were collected in Yaoundé and Douala, Cameroon, by means of a discourse completion task questionnaire (see ) consisting of several situations in which the participants had to realize a number of different speech acts in short dialogs. Each scenario comprised a brief description of the setting, i.e., “the general circumstances […] and the relevant situational parameters concerning social dominance, social distance, and degree of imposition” (, p. 43).
Recordings of spontaneous or naturally occurring conversations could have been the ideal data for a study like this. Getting such data is, however, difficult: apart from the time-consuming nature of such recordings, a large quantity of the data obtained may contain a very small number of gratitude expressions. It may also be difficult to examine the impact of factors such as social status, social distance, types of gratitude expressions, etc., because these variables are difficult and even impossible to control in spontaneous conversations (cf. [29, 30], p. 35–37). The discourse completion task (DCT) questionnaire is one of the most widely used data collection instruments in pragmatic research. Established in the CCSARP , this instrument has the greatest advantage of producing a large number of data in a short time and it helps to account for variation in speech act realization influenced by social and contextual variables. While such data may not always be natural, they at least help to “inform about speakers’ pragmalinguistic knowledge of the strategies and linguistic forms by which communicative acts can be implemented and about their sociopragmatic knowledge of the context factors under which strategic and linguistic choices are appropriate” (, p. 329). The three scenarios used to elicit thanks, the focus of the present study, were described as follows:
Situation 1 (friend): Vous déjeunez avec votre ami(e) dans un restaurant du coin. Au moment de payer l’addition, vous constatez que vous n’avez pas votre porte-monnaie sur vous. Vous l’avez certainement oublié à la maison. Votre ami(e) paie pour vous. Qu’est-ce que vous lui dites? “You are having lunch with a friend in a restaurant. When you are about to settle the bill you realize that you left your wallet at home. Your friend pays for your lunch. What do you say to him/her?”
Situation 2 (stranger): En allant en classe, vous laissez tomber accidentellement vos documents et notes de cours, lesquels s’éparpillent dans le couloir encombré. Un(e) étudiant(e) inconnu(e) vous aide à ramasser vos documents. Qu’est-ce que vous lui dites? “On your way to class, you accidentally drop your notes and a student you do not know helps you pick them. What do you say to him/her?”
Situation 3 (professor): Votre professeur(e) vous accorde quelques jours supplémentaires pour la remise de votre travail de recherche. Lorsque vous lui remettez le travail en question que lui dites-vous? “Your professor grants you an extension to submit a term paper. When you turn in the paper, what do you say to him/her?”
In situation 1 (friend), the speaker, i.e., the person thanking for the favor (the thanker), and the addressee, the person being thanked for the favor (the thankee), are close friends and equal in social status. In situation 2 (stranger), the speaker and the addressee do not know each other. The relationship here is one of total social distance. Situation 3 (professor) illustrates an asymmetrical interaction: the addressee has a higher power position (professor) than the speaker (student) and they know each other as acquaintances. The respondents were asked to write down what they would say in order to express their gratitude in the three situations.
A group of 148 French-speaking Cameroonian students participated in the study: 104 students at the University of Douala and 44 students at the University of Yaoundé I. Of the 148 respondents, 100 (67.6%) were females and 48 (32.4%) were males. They ranged in age from 18 to 30; however, 105 (70.9%) of the respondents were between 20 and 25 years old. The respondents were speakers of French in a multilingual context where two official languages (French and English) are permanently in contact with more than 250 native languages. All the participants indicated that they acquired French through school education and that they have been speaking French for more than 15 years. With regard to the questions of the main language used at home, 118 (79.7%) use indigenous languages and 41 (27.7%) use French. Concerning the main language used with friends: 144 (97.3%) use French, 11 (7.4%) use Camfranglais, 8 (5.4%) use English, 3 (2%), and 3 (2%) use German. The complex sociolinguistic and cultural background and language choices of the participants certainly also play an important role in the choice of strategies when expressing gratitude in French4.
The participants provided 411 answers for the three questionnaire tasks, namely 139 examples in situation 1, 137 examples in situation 2, and 135 examples in situation 35. The analysis of the examples collected involved both quantitative and qualitative aspects. Some of the utterances provided consist of only one move/act as in merci, c’est gentil, je suis recnnaissant. Each of such utterances is a communicative unit that realizes thanks independently of any other unit of a conversational turn: they are “head acts.”
Other examples in the corpus consist of two moves as in (1) or more than two moves as in (2) and (3). In (1), the speaker combines a direct gratitude expression, namely merci beaucoup, with an indirect gratitude expression, namely an appreciation of the addressee (c’est gentil de ta part). Each of these strategies could be used alone to express gratitude. The example (2) consists of three moves: two direct thanks, namely merci and je ne sais comment vous remercier, and an invitation act (“Ça vous dirait de prendre un verre ensemble?”), which serves here as a supportive move. In (3), the speaker employs a more complex structure and does three things: (a) he uses a familiarization act to introduce himself (the speaker says who he is and why he has come to see the professor), (b) he produces an utterance presenting the paper to the professor, and (c) he expresses his gratitude for the favor. Of these three acts, only the last one could be employed alone to realize the speech act of thanking.
1. Merci beaucoup! C’est gentil de ta part! (friend6)
“Thanks very much. That’s kind of you.”
2. Merci, je ne sais comment vous remercier. Ça vous dirait de prendre un verre ensemble? (stranger)
“Thanks, I don’t know how to thank you. Do you mind having a drink with me?”
3. Monsieur je suis l’étudiant à qui vous avez accordé un autre délai pour la remise du travail, voici le rapport et je vous remercie pour votre compréhension (professor)
“Sir, I am the student whom you granted an extension to submit the paper. Here is the paper and I thank you for your understanding.”
Due to the complexity of some thanks utterances in the data, the first step of the analysis was to segment each of the examples collected in individual acts and to classify each of them as a head act (i.e., a gratitude expression proper) or as a supportive act. The next step was to examine types of gratitude expressions attested in the data, namely direct gratitude expressions and indirect gratitude expressions, with emphasis on their pragmatic functions and distributions. The last step focused on the analysis of types, pragmatic functions, and situational distributions of supportive acts in the corpus. The next section presents the results of the analysis.
Table 1 shows the distribution of the three main strategies used to construct thanks utterances in the data. Overall, the participants produce 754 occurrences in the corpus. Direct expressions of gratitude are by far the most frequently employed in the examples, and they represent 407 occurrences and account for 54% of the data. There are 267 instances of indirect expressions of gratitude, which represent 35.4% of all examples and 80 tokens of supportive acts (10.6%). Table 1 also indicates that while direct gratitude expressions are most preferred in the professor situation, indirect gratitude expressions mostly appear in the friend situation. We also see that the respondents mostly prefer supportive acts in the friend situation.
|Direct expressions of gratitude||123 (43%)||138 (59%)||146 (62%)||407 (54%)|
|Indirect expressions of gratitude||128 (45%)||73 (31.2%)||66 (28%)||267 (35.4%)|
|Supportive acts||34 (12%)||23 (9.8%)||23 (10%)||80 (10.6%)|
|Total||285 (100%)||234 (100%)||235 (100%)||754 (100%)|
The analysis of the complexity of the thanks utterances in the corpus reveals that the participants employ simple thanks as well as complex thanks. Simple expressions of gratitude consist of one act/move as in merci beaucoup “thank you very much” or c’est très gentil (de ta part) “that’s very kind of you.” As can be seen in Table 2, the respondents most frequently use complex gratitude expressions, i.e., those made up of several acts/moves as in (1), (2), and (3). In (1), the second gratitude expression (C’est gentil de ta part) is intended to intensify the illocutionary force of the first one (Merci beaucoup). Example (2) consists of three moves. The first two acts “Merci” and “je ne sais comment vous remercier” are used to express the speaker’s gratitude, while the third move “Ça vous dirait de prendre un verre ensemble?” serves to intensify the two preceding gratitude expressions. In (3), the speaker expresses his gratitude using a combination of three moves: a familiarization act (Monsieur je suis l’étudiant à qui vous avez accordé un autre délai pour la remise du travail), a presentation of the work (voici le rapport), and an expression of gratitude (je vous remercie pour votre compréhension). (, p. 131) argues that combinations of several moves in the expression of gratitude appear to be more polite than simple thanks.
|Simple expressions of gratitude||17 (12.2%)||47 (34.3%)||47 (34.8%)||111 (27%)|
|Complex expressions of gratitude||122 (87.8%)||90 (65.7%)||88 (65.2%)||300 (73%)|
|Total||139 (100%)||137 (100%)||135 (100%)||411 (100%)|
The analysis also reveals that the distribution of simple and complex gratitude expressions varies across the three situations. Of the 111 simple expressions identified in the data, there are 47 tokens in the professor situation, 47 in the stranger situation, and only 17 in the friend situation. Complex gratitude expressions are more commonly employed in the friend situation. However, it is worth mentioning that complex utterances are generally much longer in the professor situation than in the other two situations: they are employed in order to emphasize the speaker’s sincerity in expressing gratitude to a superior.
The next section focuses on the realization patterns and distribution of the direct thanks, indirect thanks, and supportive acts found in the data.
Direct expressions of gratitude occur in the data in many different ways. In most cases, the respondents use the word merci “Thanks,” which in some cases is accompanied by modifiers such as adverbs (merci beaucoup “thanks a lot”), address terms (merci mon frère “thanks my brother”), adjectives (grand merci “big thank you”), interjections (oh merci “oh thanks”), or combinations of many intensifiers (merci beaucoup professeur “thank you very much professor”).
Another direct strategy consists in expressing gratitude and stating the beneficial action at the same time. This type appears in the form of merci de/pour + NP (Merci beaucoup pour/de votre aide “thanks very much for your help,” Une fois de plus merci pour votre indulgence “once again thank you for your indulgence”), and merci de VP (Merci mon ami d’avoir payé la note “thanks my friend for having paid my bill”).
A third direct strategy found in the data is the performative utterance je te/vous remercie “I thank you,” which may be modified in many different ways. Some respondents use adverbs and address terms to upgrade the illocutionary force of the performative utterance, as in professeur je vous remercie sincèrement “Professor I sincerely thank you”; je te remercie beaucoup mon ami “I thank you very much my friend.” In other examples, the performative utterance is followed by a statement of the favor/beneficial action as in je vous remercie infiniment pour la faveur que vous m’avez accordée “I thank you very much for the favor you have given me” and je te remercie beaucoup d’avoir payé “I thank you very much for having settled the bill”.
Also attested are examples in which the participants indicate their inability to express their gratitude as in monsieur je ne sais pas comment vous remercier pour votre générosité “Sir, I do not know how to thank you for your generosity.” Some participants indicate lack of words to articulate their gratitude as in Les mots me manquent pour exprimer ma gratitude pour cette faveur “I lack word to express my gratitude for this favor” and Je ne saurais vous remercier autant “I can’t thank you enough.” Also attested are expressions of long term/permanent gratitude/indebtedness as in je ne cesserai de vous dire merci “I won’t stop thanking you.”
The data also consist of examples in which the participants state their desire to express their gratitude as in Professeur, je tiens/tenais à vous remercier de m’avoir accordé un autre délai “Professor, I want(ed) to thank you for giving me another deadline”; Monsieur, je voudrais bien vous remercier pour ce vous m’avez fait. The following examples were also found in the data: Je n’ai qu’une chose à vous dire merci et mille fois merci “I have only one thing to tell you thanks and thousand thanks”; je te dis merci “I say thanks.”
Overall, the performative utterances and their variants are intended to maximize the expression of sincerity in the gratitude expressed and to maximize its acceptance by the interlocutor, and these direct strategies mostly appear in the professor situation (see Table 2). It is worth mentioning that direct thanks appear in the data either alone or in combination with indirect thanks and/or supportive acts, as in (4–6).
4. Merci mon ami d’avoir payé. Prochainement c’est moi qui paye (friend)
“Thanks my friend for paying. Next time I will foot the bill.”
5. Je vous remercie beaucoup pour votre aide. Je ne sais pas ce que j’aurais fait sans vous. Encore merci! (stranger)
“I thank you so much for your help. I do not know what I could have done without you. Thanks again.”
6. Professeur, je tiens à vous remercier de m’avoir accordé un autre délai. Grâce à cela, j’ai pu réaliser mon rapport de recherche. Une fois de plus merci monsieur (professor)
“Professor, I would like to thank you for giving me an extension. Thanks to this, I was able to complete my research report. Once again thank you sir.”
The frequencies and situation distribution of direct thanks strategies are summarized in Table 3.
|Merci + adverbs/address terms/adjectives, interjections, etc.||72||75||76||223 (54.8%)|
|Merci de/pour + NP/VP||10||20||19||49 (12%)|
|Je te/vous remercie and variants||8||15||49||72 (17.7%)|
Table 3 shows that the participants most frequently use the word merci accompanied by various types of modification devices (adverbs, address terms, interjections, etc.) to realize direct thanks. This strategy appears in 223 (54.8%) instances of the 407 tokens of direct thanks, and it is mostly employed by the respondents in both the professor and the stranger situations with fairly equal distribution (76 tokens, i.e., 34%) in the professor situation and 75 examples, i.e., 33.6% in the stranger situation. The frequency of this strategy is a bit lower in the friend situation (72 tokens, i.e., 32.4%).
The second most common direct strategy is the use of performative utterances. This strategy represents 72 (17.7%) tokens of all direct thanks. With respect to situational distribution, Table 3 indicates that this strategy mostly occurs in the professor situation (49 tokens of 72 attested occurrences, i.e., 68%). The high number of such expressions in this situation may be due to the level of formality and the weight of the favor granted by the superior.
The third strategy is the use of the word merci alone. It represents 63 (15.5%) instances of all direct thanks. It appears mostly in the friend (33 tokens) and the stranger (28 tokens) situations. The very low number of merci in the professor situation (only two examples) is probably due to the fact that this simple form would appear to be very impolite in an asymmetrical situation, where the student has received a huge (unmerited) favor from their professor. In other words, a simple thanks would not be sufficient to express the debt of gratitude of the speaker. As can be seen in Table 3, the low number of merci is compensated by a very high frequency of merci with intensifiers and a very high frequency of performative utterances.
The fourth strategy is the use of the word merci followed by statements of the favor. It appears in 49 (12%) instances of all direct thanks and is mostly employed in the stranger (20 tokens) and the professor (19 instances) situations. After discussing types of direct thanks, let us now turn to the strategies employed to express gratitude indirectly.
The participants produced 267 tokens of indirect gratitude expressions. As can be seen in Table 4, six types of speech acts were used in the data to realize indirect thanks: (a) praising the addressee, (b) promising to compensate, (c) praising the act, (d) expressing indebtedness, (e) expressing wishes, and (f) expressing lack of obligation or necessity for the act. The three most frequent types in the data, namely “praising the addressee,” “promising to compensate,” and “praising the act,” represent more than 70% of all tokens of indirect gratitude expressions.
|Types of indirect gratitude expressions||Friend||Stranger||Professor||Total|
|Praising the addressee||23||54||8||85 (31.8%)|
|Promising to compensate||64||0||0||64 (24%)|
|Praising the act||28||7||25||58 (22.4%)|
|Expressing indebtedness||11||4||25||40 (15%)|
|Expressing wishes||2||5||8||15 (5.6%)|
|Expressing lack of obligation or necessity||0||3||0||3 (1.2%)|
The results also show that the speech acts employed as indirect gratitude expressions are distributed differently across the three situations. As seen in Table 4, the participants used more praises of the addressee in the stranger situation (54 tokens: 63.5%) than in the other two situations (friend (23 tokens: 27%), professor (8 tokens: 9.5%)). The “promising to compensate” strategy only occurs in the friend situation. The third most frequent indirect gratitude expression, “praising the act,” is mostly used in the friend (28 instances: 48.3%) and professor situations (24 tokens: 41.4%). In contrast, the fourth type, “expressing indebtedness,” is most frequent in the professor situation (25 tokens: 62.5%).
Let us now examine the individual speech acts employed as indirect thanks and describe their pragmatic functions and realization patterns.
This strategy serves to return the favor to the addressee by indicating that s/he has done something good. By employing this strategy, the speaker does two things simultaneously: s/he expresses his/her gratitude for the favor and highlights attributes such as kindness, generosity, indulgence, etc., as the driving force of the addressee’s action. In this sense, this type of indirect thanks is a positive politeness strategy and it is employed to notice and approve the addressee’s remarkable character (cf. , p. 103).
The examples attested show that the respondents mostly employ constructions like: c’est (vraiment) gentil (de ta/votre part/à vous) “that’s (very) kind of you,” tu es vraiment gentile “you are really nice,” (C’est) très amiable de votre part “that is very kind of you,” c’est vraiment sympa “that’s really nice,” vous êtres vraiment serviable “you are really helpful,” quelle gentillesse “how nice,” etc. Generally, praises of the addressee are associated with other indirect gratitude expressions as in (7) and/or with direct gratitude expressions as in (8) and (9). Some of the praises focus on the physical appearance of the addressee as in (10).
7. Ce fut gentil de votre part et j’en suis vraiment reconnaissant (professor)
“That was kind of you and I’m really grateful.”
8. Merci de votre geste. Ce fut très gentil de votre part (stranger)
“Thanks for your gesture. That was very kind of you.”
9. Merci beaucoup, les gens comme toi on les compte du bout des doigts (stranger)
“Thanks very much, people like you are very rare.”
10. Merci de m’avoir aidé à ramasser mes documents. Je ne savais pas qu’une jolie fille comme vous pouvait m’aider jusqu’à ramasser mes feuilles pour me remettre (stranger)
“Thanks for helping to pick up the documents. I did not know that a pretty lady like you could help me pick my papers.”
The speaker promises to reimburse what the addressee has spent for them. This type occurs only in the friend situation. This result is due to the nature of the situation. The addressee had spent some money to pay for a friend’s lunch. Despite the friendship, the addressee was not obliged/did not expect to spend his/her money in that manner and the friend did not have the right to oblige him/her to do so. Consequently, the speaker deems it appropriate to thank the friend for the kind gesture and to return the favor by reimbursing the money spent for him/her. This type of indirect thanks could be interpreted as a politeness strategy with two functions: it helps to save the face of the person who benefited from the favor granted and to restore balance/cohesion/harmony in the relationship.
This strategy appears in two realization patterns. The first pattern consists in promising to refund the money spent by the friend. In this case, the respondents mostly use constructions like: je te rembourserai “I will reimburse you,” je te rembourse très prochainement “I will reimburse very soon,” je te rendrai la somme que tu as payée pour moi “I will refund you the amount you spent for me,” Une fois à la maison je te restituerai l’argent “Once we get home I will pay you back the money,” etc. The second pattern consists in promising to settle the bill next time. In this case, the participants employ constructions like: C’est moi qui vais payer prochainement “I am the one to settle the bill next time,” la prochaine fois tu mangeras à mes frais “the next time you will eat at my expense/next time I will settle the bill,” etc. Another construction employed to promise repayment is je te revaudrai ça un jour “I will repay you someday.” It is less used than the other structures. Also attested are the constructions ça va gérer and on va gérér that are also employed as promises to reimburse the money spent. In most of the examples attested, this strategy is associated with direct gratitude expressions as in (11) and/or comments as in (12).
11. Merci mon ami d’avoir payé. Prochainement c’est moi qui paye (friend)
“Thanks my friend for having paid the bill. Next time it’s on me.”
12. Ah, c’est tellement gênant j’ai honte. Je te promets samedi on déjeune et je paie la note OK? (friend)
“Oh, it’s really embarrassing I am ashamed. I promise you that we will have lunch on Saturday and I will settle the bill, right.”
Contrary to praises of the addressee, the praises in question in this section are made to express gratitude while highlighting the value of the beneficial action. While praises of the addressee are explicit face-flattering strategies, positive comments on the beneficial action could be considered as implicit face-enhancing strategies. Praises of the favor appear in two different patterns. The first pattern consists in simply describing the act as good helpful, kind, great, immense, etc., as in (13) (Vous m’avez rendu un grand service). The second pattern consists in explicitly stressing the outcome of the act. More specifically, the speaker indicates that the addressee’s intervention/action/favor really saved the speaker from an embarrassing or humiliating situation as in (14). In (15), the speaker says that the extra time granted by the professor saved them from a disaster. Also attested are examples in which the speaker indicates that s/he really appreciates the action of the addressee, using constructions like ce geste m’a vraiment marqué me va droit au coeur/me touche as in (16).
13. Je vous remercie sincèrement de votre compréhension, vous m’aviez rendu un énorme service (professor)
“I sincerely thank you. You did me a great favor.”
14. Merci gars! Si tu n’avais pas été là cela aura été honteux et humiliant pour moi (friend)
“Thanks man. If you were not there it would have been embarrassing for me.”
15. Je vous remercie grandement monsieur, sans votre faveur je n’imagine pas le désastre de mon travail (professor)
“I sincerely thank you sir, without your favor I can’t imagine the disaster I would have been in with my work.”
16. Merci beaucoup! C’est gentil de ta part. Ce geste me va droit au cœur. Que Dieu contribue à la réalisation de tes rêves (stranger)
“Thanks very much. That’s very kind of you. I really appreciate this gesture. May God make your dreams come true.”
This type is employed to express the speaker’s indebtedness toward the addressee. The respondents mostly use the construction je vous suis reconnaissant “I am grateful,” with variations regarding the intensity/sincerity and time frame of the indebtedness. While adverbs such as vraiment, très, etc., are used by the participants to express sincerity as in j’en suis vraiment reconnaissant/je vous suis très reconnaissant “I am really grateful,” adverbs such as infiniment, toujours, éternellement, etc., seem to emphasize long-term indebtedness as in je vous/te serai toujours reconnaissant “I will always be grateful.” Apart from these utterances, the respondents also employ constructions like: Je te revaudrai ça “I owe you,” je te dois une fière chandelle “I owe you,” je te suis redevable “I owe you,” c’est une dette que j’ai envers vous “It’s a debt I owe you.” The analysis also reveals that this strategy is highly recurrent in the professor situation. This could be explained by the nature of the situation and the type of favor granted to the speaker. The professor granted the student’s request for extra time to submit an assignment. By choosing the expression of indebtedness, the student intends not only to stress the level of sincerity in gratitude expression but also to reinforce the student-professor relationship. This strategy seems to be vital in such situation as the student does not exclude the possibility of future requests of this nature. Therefore, using such a strategy not only convinces the addressee to accept the thanks. It also builds a solid platform for a harmonious student-professor collaboration.
This strategy consists mostly in invoking blessings upon the addressee. The speaker is saying indirectly: “since you have been so kind to me, I wish you well and I invoke God’s blessings upon you.” The most frequent construction used to pray to God to bless the addressee is Que Dieu te/vous bénisse! “May God bless you.” This construction is, in some cases, modified by replacing the verb bénir “to bless” with récompneser “to recompense,” protéger/garder “to protect,” etc., as in C’est Dieu qui vous récompensera “God will reward you”; Dieu vous bénira “God will bless you”; Que Dieu vous garde et vous bénisse. “May God protect and bless you”; Que Dieu vous protège “May God protect you.” Some informants use more complex structure to wish their interlocutors well as in Que Dieu contribue à la réalisation de tes rêves “May contribute to the realization of your dreams.” This type of thanks is always associated with other types, as can be seen in (17).
17. Je vous remercie infiniment que Dieu vous garde et vous bénisse (stranger)
This type of indirect thanks occurs with a very low frequency. It appears three times in the stranger situation where it serves to thank the addressee while reminding him/her that he/she did not have to bother himself/herself as in (18).
18. C’est très gentil de votre part, mais il ne fallait pas vous gêner (stranger)
“That’s very kind of you, but you shouldn’t have bothered.”
As already indicated above, direct and indirect expressions of gratitude are modified by means of supportive acts. The next section presents the types, functions, and distributions of these supportive acts.
Supportive acts are different kinds of speech acts, which may come before or after direct and indirect expressions of gratitude. They play various pragmatic roles and serve mostly as external modification devices (softeners). As can be seen in Table 5, the participants used many different types of speech acts as supportive acts. Their frequencies and distribution vary across the three situations. There are 81 tokens of supportive acts in the data, 34 occurrences in the friend situation, 24 tokens in the stranger, and 23 instances in the professor situation. The most preferred supportive acts are, in decreasing order, comments (30 tokens), familiarization acts (20), apologies/regrets (12 examples), and promises to change (12 instances).
|Promise to change||5||0||7||12|
Comments are used to reinforce direct and indirect thanks. The contents of the comments identified vary from one situation to another. In the friend situation, the speaker attempts to save his/her own face by expressing his/her surprise that s/he could forget his/her wallet as in (19).7 Some comments serve to reiterate the fact that what happened was accidental and not planned, as in (20).
19. Merci mon ami, je vous rendrai ce geste salutaire, je ne comprends pas comment j’ai pu oublier mon porte-monnaie (friend)
“Thanks my friend, I will repay this kind gesture, I can’t understand how I could forget my wallet.”
20. Je te suis profondément reconnaissante. Je ne sais pas où j’avais la tête pour oublier de la sorte mon porte-monnaie. On pourrait se faire une sortie dans le restaurant de ton choix. Qu’en dis-tu? Et je pourrai payer en guise de remerciement (friend)
“I am deeply grateful to you. I don’t where my head was to forget my wallet. We could go to a restaurant of your choice. What do you say? And I will pay as thank you.”
In the professor situation, the comments relate to the quality of the work submitted. In order to reinforce his/her gratitude, the student assures the professor that the extra time granted was wisely used and that s/he believes or hopes the professor will not be disappointed as in (21) and (22).
21. Monsieur, je vous remercie infiniment et je crois qu’après la lecture du travail vous ne serez pas déçu (professor)
“Sir I thank you so much and I think that you will not be disappointed after reading the work.”
22. Monsieur je vous remercie une fois de plus pour votre compréhension. J’espère que mon travail sera à la hauteur de vos attentes (professor)
“Sir I thank you once more for your understanding. I hope my work will meet your expectations.”
The only comment found in the stranger situation serves to emphasize the importance of the help rendered and to reinforce the gratitude expressed. As can be seen in (23), the speaker explicitly says that the document the addressee helped to pick is a very important one. In making this comment, the speaker is indirectly appreciating the addressee and the act.
23. Merci énormément. Ce document que vous veniez de me remettre est très important pour moi (stranger)
“Thanks a lot. This document you just handed to me is very important to me.”
The second most common supportive act is familiarization. It appears in 20 instances in the data, and it mostly occurs in the stranger situation. Familiarization appears in the form of self-introductions as in (24).8 These acts entail telling the name of the speaker and/or asking the name of the addressee. Familiarization acts also occur in the form of questions whether the interlocutors can meet subsequently as in (25) and farewells as in (26). Overall, familiarization acts are intended to help the interlocutors know each other better and to prepare the ground for future interactions.
24. Je vous remercie grandement mademoiselle. Puis-je connaitre votre nom? (stranger)
“Thank you very much, miss. Can I know your name?”
25. Merci bien! Que vous êtes gentils! Puis je vous rencontrer après? Ok à toute à l’heure après le cours de 15 heures (stranger)
“Thank you very much. How nice you are. Can I meet you later? Ok see you soon after the class a 3 pm.”
26. Merci, merci pour votre aide. Je m’appelle “X,” et vous? Ravi de vous connaitre et à la prochaine (stranger)
“Thanks, thanks for your help. My name is “X” and you? Nice to meet you and see you next time.”
The third supportive act found in the data, the apology/regret act, generally appears with direct and indirect gratitude expressions. This supportive move serves to indicate that the speaker is aware of the potential disruption of the favor to the addressee’s plan and apologizes for any inconveniences as in (27) and (28)9.
27. Monsieur, je vous remercie pour votre compréhension et je suis une fois de plus désolé pour le retard (professor)
“Sir I thank you for your understanding and once again I am sorry for the delay.”
28. Merci de m’avoir sauvé de cette situation, je suis vraiment désolé, j’ai complètement oublié le porte-monnaie à la maison. Je te rembourserai (friend)
“Thanks for having saved me from this situation. I am very sorry, I completely forgot my wallet at home. I will refund your money.”
The fourth supportive act in the data is the promise to change. It appears in the friend and the professor situations. It serves to mitigate the potential negative impact of the help rendered on the speaker’s face. More precisely, the promise to change is employed to protect the positive face of the speaker. In the friend situation, the favor was granted because the speaker forgot his/her wallet and was unable to pay for his/her food. In the professor situation, the student was not able to submit his/her assignment on time. In both situations, the speaker is grateful to the request granted but feels guilty of any potential negative impact the favor could have on the addressee’s face wants. In order to protect his/her own face, the speaker promises that this will not happen again as can be seen in (29) and (30).
29. Je vous remercie de m’avoir accordé quelques jours supplémentaires. Je m’efforcerai la prochaine fois pour qu’il n’y ait pas de situations embarrassantes pareilles (professor)
“I thank you for having granted me a few more days. I will try next time to avoid such embarrassing situations.”
30. Merci bien, la prochaine fois je m’assurerai que mon porte-monnaie est bel et bien sur moi (friend)
“Thank you very much, next time I will make sure that I have my wallet.”
Another supportive act used with thanks is the act of offering or inviting. Of the four tokens found in the data, there are two examples in the stranger situation and two instances in the professor situation. In the professor situation, the speaker invites the professor to a drink as in (31). In the other example, the speaker offers a gift to the addressee as in (30).
31. Merci infiniment vous êtes vraiment gentil, vous êtes compréhensible. En fait ça (ne) va pas finir ainsi, on va quand même couper une gorge! (professor)
“Thank you very much you are really nice, you are understandable. Actually it is not going to end this way, let’s have a drink together.”
32. Merci monsieur. Acceptez ce présent en signe de reconnaissance (professor)
“Thank you sir. Accept this gift a token of appreciation.”
In the stranger situation, the speaker invites the addressee for lunch as in (33) or for a drink as in (34).
33. Merci de ton aide. Est-ce que je peux t’inviter à déjeuner ce soir afin de te remercier pour ton aimable service? (stranger)
“Thank you for your help. Can I invite you to lunch tonight to thank you for kind service.”
34. Merci, je ne sais comment vous remercier. Ça vous dirait de prendre un verre ensemble? (stranger)
“Thank you, I don’t know how to thank you. How about having a drink together?”
The last supportive act is the act of encouragement or advising. The speaker exhorts the addressee to keep up being helpful to people. This act is preceded by a direct gratitude expression, as can be seen in (32).
35. Merci beaucoup pour votre geste. Il faut toujours continuer comme ça car vous ne serez bloqué en aucun jour quelle que soit la situation et cela vous aider aussi dans la société (stranger)
“Thank you very much for your gesture. Always continue in the same manner and you will face any difficulty for whatever the situation may be and this will also help you in society.”
The respondents use many different strategies to intensify their gratitude expressions. The analysis reveals that direct thanks are the most frequently intensified in the corpus. Our analysis focused on three types of intensification. The first type consists in the use of lexical intensifiers such as adverbs and nominal address terms in direct gratitude expressions. Table 6 summarizes the distribution of the lexical intensifiers across the three situations.
|Merci/je te/vous remercie beaucoup||28||45||12||85|
|Merci/je te/vous remercie infiniment||7||2||8||17|
|Mille fois merci||2||2||1||5|
|Vraiment merci/je vous remercie vraiment||2||2||5||9|
|Merci/je/te vous remercie franchement/énormément/grandement/(très) sincèrement||4||4||5||13|
|Une fois de plus||0||0||6||6|
|Du fond du cœur||0||0||1||1|
|Merci/je te/vous remercie + address term/address term + merci||18||8||43||69|
The second type of intensification consists in mentioning the object of gratitude. Table 7 presents the distribution of this type in the data.
|Merci de/pour + NP/VP||10||20||19||49|
|Je te/vous remercie de/pour + NP/VP||1||4||37||42|
The third type of intensification consists in the combination of different types of gratitude expressions. The most common patterns found in the data involve the combinations of direct gratitude expressions and indirect gratitude expressions. The most preferred combinations in the friend situation are, in decreasing order, merci + promise to reimburse (41 examples), merci/je te remercie + praising the act (27 tokens), and merci + praising the addressee (9 instances). The most frequent combinations in the stranger situation are merci/je vous remercie + praising the addressee (46 tokens) and merci/je vous remercie + praising the act (7 examples). The predominant combination in the professor situation is merci/je vous remercie + appreciation of the act (19 examples). The other combinations are very diverse.
The analysis also reveals that a number of nominal address terms were employed in the thanks utterances. The pragmatic functions of such terms are to signal and draw attention to existing as well as intended relationships between the speaker and the hearer and to upgrade the illocutionary value of the thanks utterances. As can be seen in Table 8, the participants employed 130 instances of nominal forms of address and the vast majority of these terms appear in the professor situation. The nominal forms of address attested in the friend and the stranger situations consist mainly of kinship and solidarity terms: their pragmatic role is to express closeness and solidarity to the interlocutors (friends and strangers). The terms used in the professor situation express respect and deference. In the three situations, the nominal address terms contribute, as already indicated, in enhancing the relational value of the gratitude expressions in which they occur.
|Nominal address terms||Friend (n = 20)||Stranger (n = 11)||Professor (n = 99)||Total|
|Cher ami/chère amie||1||1||0||2|
|(Cher) First name||3||0||0||3|
The aim of this study was to examine some pragmatic aspects of Cameroon French, focusing on expressions of gratitude. Using data provided by a group of University students, the analysis reveals the use of a wide range of strategies to express gratitude in situations involving close friends, strangers, and professors.
Overall, factors such as the weight of the favor granted/received, level of familiarity between the speaker and the hearer, and power distance between the interaction partners played an important role in the choices and combinations of thanks strategies. As far as the complexity of the utterances is concerned, the informants mostly used complex gratitude expressions. The complexity of the utterances is due to the fact that the proper gratitude expressions are either repeated or combined with a number of other speech acts with various pragmatic functions (familiarization, comments, apologies, encouragements, etc.). Such complexity helps the speakers to give thanks while performing other face-saving and/or face-enhancing activities. The results show, for instance, that the familiarization act is mostly employed with strangers. This choice is due to the fact that familiarization is “important in multilingual and multiethnic postcolonial communities because of multiple identities people construct around their languages, cultures, religions, and social groups. Through familiarization, interlocutors quickly know the identity to adopt that fits the context of interaction and the status of their addressees” (, p. 58).
With respect to level of directness, the study has shown that the participants employed direct gratitude expressions as well as indirect gratitude expressions. Far more direct gratitude expressions were registered than indirect gratitude expressions. As far as the realizations of direct thanks are concerned, the results show that the simple form merci “thanks” is rather rare in the professor situation. A possible reason for this choice is that this simple pattern is not suitable to reflect the weight/value of the favor granted and the power asymmetry (student-professor) in this formal situation. When merci is employed in the professor situation, it is mostly accompanied and reinforced by nominal address terms. Also interesting is the fact that explicit performative patterns such as je vous remercie are most frequently employed in the professor situation. It could be said that the formality of the situation plays an important role in the choice of types of direct gratitude expressions.
With respect to indirect gratitude expressions, the results show that Cameroon French speakers use the “praising the addressee” realization pattern much more toward strangers (54 tokens: 63.5%) than with friends (23 tokens: 27%) and professors (8 tokens: 9.5%). The “promising to compensate” strategy only occurs in the friend situation. The “praising the act” pattern is mostly used in the friend situation (28 instances: 48.3%) and the professor situation (24 tokens: 41.4%). In contrast, the “expressing indebtedness” pattern is most frequent in the professor situation (25 tokens: 62.5%).
The analysis also reveals the use of a number of supportive acts and different types of nominal forms of address that seem to be indicative of some sociocultural norms of interaction in postcolonial contexts. For instance, the collectivist nature of the Cameroonian society that is reflected in the abundant use of nominal address terms in gratitude expressions. Looking at the findings summarized in Table 8, we see that most of the terms used in the friend and stranger situations hint at the group-based conceptualization of relationship. Such terms index closeness, affection, in-group belonging, and the pragmatic intent behind their use is to intensify the gratitude expressions. Also noteworthy is the abundant use of honorific terms to index the power imbalance between the speaker (student) and the interlocutor (professor). In a postcolonial context such as Cameroon, such honorifics “mark respect and deference along a continuum of age and social hierarchy” (, p. 100). It could be said that in giving thanks to a professor, Cameroon French speakers use honorifics “as a sign of respect for his/her social, professional status, and possibly age” (, p. 100). Overall, address terms, a major postcolonial pragmatic component, play a vital role in the intensification of gratitude expressions [33, 34, 35, 36].
The study has some limitations. Since it was based on written questionnaire data, it is not sure that the examples provided by the participants would be the same as their choices in naturally occurring situations. Nevertheless, the results obtained here still reflect potential trends of Cameroon French speakers’ thanking behavior. Since the research considered only three situations, we cannot make any claim that the results obtained would be generalized to all situations. There is also a need to consider factors such as age, socioeconomic groups, gender, and ethnic group in the analysis of thanks strategies. It is likely that such factors may lead to the use of strategies that differ from those found in the present study. Future studies can expand the scope of the current study by overcoming these limitations.
This project was supported by a research grant from the Office of Research and Graduate Studies of Cape Breton University (Canada). The author is indebted to all the contacts and participants in the study.