Comparison of tensile stress–strain curves for 0.016 in. diameter stainless steel, Co-Cr-Ni, nonsuperelastic Nitinol™, and superelastic Japanese NiTi wires (From Ref.  and reproduced with permission from American Association of Orthodontists)
Determination of elastic modulus (E) and yield strength (YS) of a linearly elastic alloy from the tensile stress–strain plot is described in textbooks [3, 4], and reports of tensile properties of orthodontic wires are available [5, 6]. An important clinical property of an orthodontic wire is springback, which is defined as (YS/E) . This relationship for springback is used to indicate the practical tensile elastic strain recovered when the wire is unloaded, rather than (PL/E), where PL is the proportional limit, since orthodontists may activate wires into the permanent deformation range.
Mechanical properties of orthodontic wires are generally measured in the clinically relevant mode of bending, which is much more convenient to perform than the tension test. Figure 1.2 shows cantilever bending plots for stainless steel, Nitinol™, and Chinese NiTi (marketed as Ni-Ti™ by Sybron/Ormco) orthodontic wires, using 5 mm test spans appropriate for interbracket distances . The effect of test span length on springback is pronounced, when comparing the original cantilever bending plots for Nitinol™ with 0.5 in. spans . The Ni-Ti™ wire also exhibits superelastic behavior (and nonlinear elasticity), but the upper and lower superelastic plateaus evident with the tension test are not as sharply defined with the cantilever bending test , because of the variation in stress and strain over the wire cross section . Springback in bending is much greater for superelastic NiTi wires than nonsuperelastic NiTi wires .
Cantilever bending plots for 0.016 in. diameter stainless steel, Nitinol™, and Chinese NiTi orthodontic wires. For 5 mm test spans and bending deflection of 80°, springback is approximately 75° for Chinese NiTi and 50° for Nitinol™ (From Ref.  and reproduced with permission from American Association of Orthodontists)
While the original version of American Dental Association Specification No. 32 had a cantilever bending test to evaluate mechanical properties of orthodontic wires , the current version  has three-point bending and tension tests. The specification testing mode depends on the manner in which the mechanical properties are given by the manufacturer. The wires are classified as type I or II, depending upon whether they exhibit linear or nonlinear elastic behavior, respectively, during unloading from temperatures up to 50°C. The bending test may be performed at room temperature (23 ± 2)°C for type I wires but must be performed at (36 ± 1)°C for type II wires. The test span between knife-edge supports is 10 mm, and the midspan deflection rate is 7.5 ± 2.5 mm/min. Type I wire specimens are bent to a permanent deflection of 0.1 mm, and the bending stiffness (units of N/mm) from the slope of the linear force–deflection plot and the bending force (N) for 0.1 mm permanent offset are determined. If the tension test is performed on a type I wire, the elastic modulus (GPa), 0.2 % offset yield strength (MPa), and percentage elongation are determined for a 20 ± 0.2 mm gauge length, using a crosshead speed between 0.5 and 2.0 mm/min. Type II wire specimens are tested only in three-point bending and are deflected to 3.1 mm. Forces during unloading are measured at deflections of 3.0, 2.0, 1.0, and 0.5 mm, along with the permanent deflection after unloading.
For ceramic brackets, it is essential to have sufficient strength to resist forces imposed during initial manipulation and bonding and the subsequent debonding. Such strength requires suitable resistance to fracture, since the ceramics used for brackets are brittle materials that fail by crack propagation, and ceramic brackets have historically shown a tendency for tie-wing fracture during debonding. The critical fundamental mechanical property is fracture toughness [13, 14], which is related to the force or energy for crack propagation. Fracture occurs with greater facility for single-crystal alumina brackets than polycrystalline alumina brackets where the irregular path of crack propagation is along grain boundaries .
For convenience, the fracture toughness of dental ceramics is generally measured under plane-strain conditions as K Ic, in which the tensile stress is applied perpendicular to the crack face in a crack-opening mode . Several approaches have been used to measure the fracture toughness of bulk dental ceramics, including fractographic analysis, indentation methods, and bending tests with notched beams [16–21]. Figure 1.3 shows the idealized fracture pattern for the Vickers indentation technique, which is the only method that would permit measurement of fracture toughness for the very small ceramic brackets.
Schematic illustration of Vickers hardness indentation and desired fracture pattern in ceramic material for determination of fracture toughness (From Ref.  and reproduced with permission from Academy of Dental Materials)
The Vickers indentation technique was used to obtain fracture toughness values of 3.60 and 5.22 MPa ≅ m½ for two brands of polycrystalline alumina brackets . However, these results were apparently obtained with radial cracks much shorter than the lengths of the diagonals for the indentations and thus may not be correct. Pham and colleagues [23, 24] found that the Vickers indentation technique did not yield appropriate long straight radial cracks emanating from the corners of Vickers indentations for five brands of polycrystalline alumina brackets, and the radial cracks followed the alumina grain boundaries in each ceramic. In contrast, Tilson and colleagues [25, 26] observed straight radial cracks in zirconia brackets (Hi-Brace™, Toray Ceram) with the Vickers indentation technique and obtained 3.92 ± 0.35 MPa ≅ m½ for fracture toughness. However, SEM observations at high magnification revealed that the apparent straight radial cracks were the result of the very fine zirconia grain size, with crack propagation apparently still occurring along grain boundaries.
From these experimental results, it is recommended that future fracture toughness studies should focus on the bulk ceramic used to fabricate the brackets and that manufacturing efforts should be directed toward producing brackets of the highest purity ceramic with minimal surface cracks and porosity. Another approach for comparison of different ceramic brackets is to evaluate the force required to fracture the tie wings, which requires the use of a very small, well-controlled loading member . A convenient technique for measuring the fracture toughness of bulk ceramic materials is the single edge-notch technique, schematically shown in Fig. 1.4 .
Rectangular specimen geometry for single edge-notch technique used to measure fracture toughness. Appropriate specimen thickness or breadth (B) is necessary to have plane-strain conditions (From Ref.  and reproduced with permission from Quintessence Publishing Company)
1.3 Corrosion Studies of Orthodontic Wire Alloys
Corrosion of orthodontic wires has become an active area of research, because of concern about biocompatibility. The major focus has been on nickel-titanium wires, which have potential to release nickel ions in vivo. A classic study, using potentiodynamic polarization , found that only the nickel-titanium alloy (Nitinol™) exhibited breakdown of passivity. X-ray analyses with the SEM suggested that loss of nickel could have occurred at the pitted regions. These results were consistent with clinical observations of stainless steel and Nitinol™ wires . Long-term immersion of Nitinol™ was observed to have no effect on flexural properties and that occasional fracture was due to surface defects from manufacturing and not corrosion .
Figure 1.5 illustrates cyclic potentiodynamic polarization plots for three superelastic nickel-titanium wires, Nitinol SE™ (3 M/Unitek), Sentinol™, and Ni-Ti™ [1, 32, 33]. The directions of the forward and reverse scans are indicated by arrows. Similar results were found for nonsuperelastic Titanal™ (Lancer), Orthonol™ (RMO), and Nitinol™ wire alloys. The upper curve for each plot is the anodic region, and the lower curve is the cathodic region. These curves asymptotically approach each other at the zero-current potential . The nickel-titanium wire alloys (and the other three orthodontic wire alloy types) have native surface oxide layers that provide corrosion resistance, and breakdown of the oxide layers (accompanied by pitting) can be seen in Fig. 1.5, where the current rapidly increases at sufficiently high anodic potentials. Because the wire surface has changed, the reverse scan does not follow the forward scan, and Fig. 1.5 shows that the zero-current potential has decreased for the reverse scan. The breakdown potential for the passive film depends on the surface roughness and oxide composition.
Corrosion studies have investigated breakdown potentials for oxide layers [35–37], ion release from wires [38–40], and galvanic coupling with brackets [41–44]. The in vitro corrosion of nickel-titanium wire products (including coated wires) has been compared [45–49] along with the potential of nickel-titanium wire for stress corrosion cracking . An area of particularly active research interest has been effects of fluoride solutions (relevant to use of topical fluoride agents) on beta-titanium and nickel-titanium wires [51–59]. The beta-titanium wires, which are inherently the most biocompatible because of the absence of nickel, are susceptible to hydrogen absorption, leading to embrittlement and delayed fracture [51, 52]. The nickel-titanium wires also appear to be susceptible to hydrogen embrittlement . The interested reader should consult the original articles for the diverse experimental procedures in these studies.
In closing this section, it is important to note that standardized in vitro corrosion tests may not adequately simulate the complex oral environment, where diverse chemical species and fluctuating stresses are present. This has been shown in studies of retrieved nickel-titanium archwires, where there was an apparent decrease in the grain size of the nickel-titanium wire  and an absence of significant nickel ion release in vivo . Additional studies of this type are highly recommended for the future. Another very important related area for research is the cytotoxicity of the wire alloys. Studies generally show that the nickel-titanium alloys have low cytotoxicity  and that the surface quality of these alloys and the cobalt-chromium-nickel alloy Elgiloy  is an important factor.
1.4 X-Ray Diffraction
X-ray diffraction (XRD) is an important analytical tool in materials science for investigating the structure of metals. Orthodontic wires can be readily studied by conventional XRD, using a test specimen consisting of several adjacent segments of the wire and having a width greater than the incident x-ray beam size. Each crystalline phase has a characteristic XRD pattern, which is dependent upon crystal structure, lattice parameter(s), and atomic species in the unit cell. The principles and applications of XRD are discussed in a well-known textbook , and a succinct presentation of relevant information is also available  for people interested in orthodontic materials research.
For conventional XRD used to investigate orthodontic wire alloys, a beam of nearly monochromatic x-rays (typically Cu Kα) is used, and the XRD spectrum or pattern is recorded with a diffractometer. The relationship between the angle of incidence (θ) and wavelength for the x-ray beam and the lattice parameter(s) of the material being analyzed, in order to have a diffracted beam with x-ray waves in phase (yielding a strong peak), is given by Bragg’s law. The diffraction angle recorded by the diffractometer is (2θ).
The crystal planes that yield the XRD peaks for a given material depend upon the structure factor. X-ray diffraction standards for powder specimens of materials, which have randomly oriented crystals, are maintained by the International Centre for Diffraction Data (ICDD). The standard for a material provides the relative intensities of the diffracting crystal planes and the corresponding interplanar spacings. These interplanar spacings are converted to the diffraction angles, using Bragg’s law with the wavelength of the given characteristic x-rays from specific electron transitions in the source. When a material contains more than one phase, the XRD pattern contains the peaks from all of the phases.
X-ray diffraction analysis of several sizes of two stainless steel wire products showed that the 0.016 in. diameter and 0.017 in. × 0.025 in. wires of both products had a duplex austenite and martensite structure, rather than the completely austenitic structure . It was found that heat treatment of one wire product converted this duplex structure to the austenitic structure, but the duplex structure persisted for the other product. The heat treatment responses were attributed to a difference in carbon content for the wire products from the two manufacturers. The XRD pattern for as-received beta-titanium wire (TMA™, Ormco) had peaks for the body-centered cubic beta-titanium structure, which were broad with preferred crystallographic orientation, as expected for the work-hardened wire [1, 66].
Conventional x-ray diffraction has been used extensively to study nickel-titanium wires [1, 32, 66–68]. Figure 1.6 shows the XRD pattern for Neo Sentalloy™ (GAC) , in which the crystal planes in the austenite and martensite structures have been indicated. Although this wire alloy has shape memory in the oral environment, when it is in the fully austenitic condition, the XRD pattern in Fig. 1.6 also shows peaks for martensite because the analysis was performed at room temperature, which is below the austenite finish (A f) temperature for Neo Sentalloy™, as shown in the next section. The much weaker intensity of the USE 220 austenite peak, compared to the 211 peak, referring to the relatively intensities in the ICDD powder standard , is indicative of preferred orientation.
Figure 1.7 shows the XRD pattern for Ni-Ti™ (Ormco) after heat treatment for 2 h at 600°C [1, 32], which causes complete loss of the superelastic behavior for this wire alloy . The wire has the completely austenitic structure, indicating that the martensite start temperature (M s) is below room temperature after the heat treatment, so that minimal austenite transformed to martensite when the wire was cooled to room temperature for the XRD analysis [1, 32]. The sharp XRD peaks are indicative of substantial stress relief after heat treatment and perhaps recrystallization of the wire structure with new, stress-free grains. There is also strong preferred orientation. Referring to the ICDD standard, the peaks in Fig. 1.7 correspond to the 110, 200, 211, 220, and 310 reflections.
An exciting recent development is the use of micro-x-ray diffraction (micro-XRD) to investigate orthodontic wires [69–73]. With the micro-XRD technique, which employs a relatively large tube current, the spot size for the incident x-ray beam can be as small as 100 μm. For example, analyses of tension and compression regions on bent wires, and of soldered and welded joints for orthodontic wires, become possible.
1.5 Differential Scanning Calorimetry (DSC) and Temperature-Modulated DSC
Conventional differential scanning calorimetry (DSC) has become the major analytical tool for study of the transformations of the NiTi microstructural phases with changes in temperature for the nickel-titanium orthodontic wires. Two classic articles [74, 75] describe the first reported use of DSC to investigate these wires, and there were several subsequent studies [76–78]. The current ANSI/ADA specification and ISO standard for orthodontic wires  stipulates the use of DSC to determine the A f temperature for nickel-titanium wires. The advantages of DSC over XRD are its ability to determine the NiTi phases present at a given temperature, to investigate the phase transformation processes with changes in temperature, and to measure the enthalpy changes (ΔH) for these processes. The enthalpy changes provide insight into the transformation processes, which is not possible with x-ray diffraction or with the measurement of electrical resistivity changes. While the latter measurements can be readily performed over a range of temperatures, this is not generally possible with XRD apparatus.
With conventional DSC, a small test sample of the experimental material (a few wire segments) is placed in one pan and an empty pan (typically aluminum) serves as the inert reference material . Some investigators prefer to use indium as the reference material. Both pans are heated or cooled at a constant rate (typically 10°C/min), and the difference in heat flow (in units of cal/s/g or W/g) to the two pans to maintain the same temperature change for both pans is recorded as a function of temperature.
The conventional DSC plot for the shape memory wire Neo Sentalloy™ is shown in Fig. 1.8 . The single peak (H) on the lower curve for the heating cycle suggests the direct transformation from martensite to austenite. The A f temperature, at which the transformation to austenite has finished, is approximately 36°C. The upper curve for the cooling cycle has two peaks (C1 and C2), which correspond to transformations from austenite to R-phase and R-phase to martensite, respectively. (C3 was placed where low-temperature martensite peaks were previously found from measurements of electrical resistivity changes [79,80]).
Conventional DSC  shows that in vivo shape memory NiTi wire products have A f temperatures lower than body temperature (37°C), whereas superelastic wire products have A f temperatures that exceed body temperature (approximately 60°C for Nitinol SE™ and 40°C for Ni-Ti™). The nonsuperelastic Nitinol™ has A f temperature of approximately 55°C and weak peaks (low ΔH values) [75, 76] corresponding to substantial quantities of stable work-hardened martensite in this wire.
The recently introduced technique of temperature-modulated differential scanning calorimetry (TMDSC) [81, 82] provides insight into phase transformation processes that is not possible with conventional DSC. (The generic term is TMDSC; use of the term modulated differential scanning calorimetry is specific to apparatus from TA Instruments.) With TMDSC, the linear heating or cooling rate is much slower (such as 2°C/min) to maintain a uniform temperature in the bulk specimen, and a small sinusoidal thermal oscillation (such as an amplitude of 0.318°C/min with a period of 60 s) is superimposed on the linear ramp. When selecting the thermal oscillation conditions, it is highly important to maintain a heating-only condition during the heating cycle and a cooling-only condition during the cooling cycle. Thin test specimens are needed, and helium is the preferred purge gas because of its high thermal conductivity, rather than nitrogen which is typically used with conventional DSC. Utilization of the small sinusoidal oscillation superimposed on the linear heating or cooling ramp allows mathematical subdivision of the total heat flow measured by conventional DSC into its reversing and nonreversing components with respect to temperature changes.
The advantages of TMDSC are evident in Fig. 1.9, which shows the heating cycle for Neo Sentalloy™ , compared to the heating cycle on the conventional DSC plot in Fig. 1.8. The dashed nonreversing heat flow curve in Fig. 1.9 shows that a two-step transformation from martensite to austenite occurs, which involves the intermediate R-phase. There is also a strong exothermic peak on the nonreversing heat flow curve arising from low-temperature transformation within martensite (designated as M′ → M for heating).
TMDSC plots of reversing and nonreversing heat flow for heating cycle of Neo Sentalloy™, with phase transformation processes for peaks labeled (From Ref.  and reproduced with permission from American Association of Orthodontists)
The corresponding TMDSC plots for the cooling cycle of Neo Sentalloy™ are shown in Fig. 1.10 . The reversing heat flow curve has a large exothermic peak for the transformation from austenite to R-phase, which can be seen to have a small amount of nonreversing character. Possible transformations from R-phase to martensite are labeled on both the reversing and nonreversing heat flow curves. There is a large exothermic peak on the nonreversing heat flow curve (designated as M → M′ for cooling), which again corresponds to transformation within the martensite structure. As noted previously, low-temperature martensite transformations in NiTi orthodontic wires were originally reported from measurements of electrical resistivity changes . Recent low-temperature transmission electron microscopy examination of 35°C Copper Ni-Ti™ wire has shown that twinning within martensite is the origin of this peak on the TMDSC nonreversing heat flow curves . During both the heating and cooling cycles, the martensite structure undergoes twinning to relieve internal stresses in the microstructure. This low-temperature peak has been observed in all orthodontic wires examined by TMDSC in two studies [83, 85].
Corresponding TMDSC plots of reversing and nonreversing heat flow for cooling cycle of Neo Sentalloy™ (From Ref.  and reproduced with permission from American Association of Orthodontists)
1.6 Metallographic Preparation
Metallographic preparation is extensively used in order to reveal the true bulk structure of solid materials. The distribution of pores, presence of cracks or other internal defects, quality of joints, and grain size and shape are only a few of the features that can be qualitatively and quantitatively determined by the analytical techniques (i.e., optical and electron microscopy). Sectioning, mounting, grinding, polishing, and etching are the main steps of metallographic preparation although the latter is applied only when the grain structure and microstructural phases are the subject of research. As a standard operating procedure, metallographic preparation must be characterized by reproducibility and reliability. Reproducibility is associated with the ability of a method to provide the same results for the same material, every time it is carried out, while reliability represents the ability of the method to provide the true structure of the material free of possible structural alterations (e.g., deformation and smearing) and other artifacts.
The main goal of sectioning is the removal of a conventionally sized, representative specimen from a larger sample. Although sectioning is routinely used in metallographic preparation of specimens from various applications, this is not the case in orthodontics where the specimens are of very small dimensions. Orthodontic wires can be easily cut by pliers, avoiding the use of sophisticated sectioning machines. Complete details on sectioning are not included in this chapter, but the reader can find extensive information elsewhere .
In general, mounting is considered optional, and it may not be necessary for some bulk specimens. However, a small or oddly shaped specimen (e.g., an orthodontic bracket) should be mounted in order to facilitate handling during metallographic preparation Fig. 1.11. Standard molds usually have diameters of 25, 32, or 38 mm. Caution should be exercised about the final thickness of mounted specimens, as very thin mounted specimens are difficult to handle, and the flatness of very thick ones is difficult to preserve during metallographic preparation.
The first criterion for the selection of the proper mounting material and technique is the protection and preservation of the sample. Delicate and fragile samples may be subjected to physical damage or microstructural alterations due to the heat and pressure required by some mounting materials. Ideally the mounting material should have similar grinding and polishing characteristics as those of the sample. Additionally, the mounting material should effectively resist physical distortion caused by the heat developed during grinding and polishing and withstand exposure to suspensions, lubricants, and etching solutions. The mounting material should have low viscosity so that it can easily penetrate crevices, pores, or other irregularities in the sample. In addition, the mounting material should be easily manipulated and stored and should present no health hazards to the operator. It should not be susceptible to the formation of any defects (e.g., cracks and pores) and should be available for purchase at a reasonable cost. Sometimes an electrically conductive mount is desirable, such as for electrolytic polishing and scanning electron microscopy analysis. Currently, there is no mounting material that fulfills all of the aforementioned requirements, and a variety of materials and methods are available. Proper selection is considered the one that meets the most critical requirements for each combination of material and subsequent analytical technique.
Three pieces of orthodontic wire embedded in acrylic resin (yellow cylinder) reinforced by mineral fillers to provide good ability for achieving planar surface and good edge retention. Cylinder diameter is 25 mm
The available mounting materials can be classified into two groups: (1) materials that require the application of heat and pressure and (2) materials that can be poured into a room temperature mold . The technique used with the first group of materials is termed hot mounting, and the technique used with the second group is termed cold mounting. In the hot mounting technique, the specimen is placed in the mounting press, and after the pouring of resin, the mounted specimen is processed under high pressure and heat. The mounting materials used for this technique are (a) thermosetting resins which cure at elevated temperatures and (b) thermoplastic resins which soften or melt at high temperatures and harden during cooling to room temperature. Epoxy, acrylic, and polyester materials are used in cold mounting. Epoxies are characterized by low shrinkage and excellent adhesion to most materials but have relatively long curing times. Acrylics and polyesters are catalyzed systems and have short curing times.
1.6.4 Grinding and Polishing
The next steps of metallographic preparation after mounting are the grinding and polishing of the sample surface. The purpose of grinding is primarily to remove damaged or deformed material at the sample surface and to produce a plane surface that will be easily removed during the polishing step. Successive steps with finer abrasive particles are employed during this step to remove material from the sample surface until the required result is reached. Grinding and polishing are commonly carried out in special designed metallographic machines in which the abrasive papers are placed on a rotating wheel and the sample surface is firmly placed sequentially against each abrasive paper. Significant heating of the surface during the initial coarse grinding step is avoided by using a copious amount of water or another liquid as a coolant. The aim of polishing is to remove the surface damage introduced during grinding, which is accomplished with several steps of successively finer abrasive particles.