Hardening behavior after high-temperature solution treatment of Ag-20Pd-12Au-xCu alloys with different Cu contents for dental prosthetic restorations.

Ag-Pd-Au-Cu alloys have been used widely for dental prosthetic applications. Significant enhancement of the mechanical properties of the Ag-20Pd-12Au-14.5Cu alloy as a result of the precipitation of the ß' phase through high-temperature solution treatment (ST), which is different from conventional aging treatment in these alloys, has been reported. The relationship between the unique hardening behavior and precipitation of the ß' phase in Ag-20Pd-12Au-xCu alloys (x=6.5, 13, 14.5, 17, and 20mass%) subjected to the high-temperature ST at 1123K for 3.6ks was investigated in this study. Unique hardening behavior after the high-temperature ST also occurs in Ag-20Pd-12Au-xCu alloys (x=13, 17, and 20) with precipitation of the ß' phase. However, hardening is not observed and the ß' phase does not precipitate in the Ag-20Pd-12Au-6.5Cu alloy after the same ST. The tensile strength and 0.2% proof stress also increase in Ag-20Pd-12Au-xCu alloys (x=13, 14.5, 17, and 20) after the high-temperature ST. In addition, these values after the high-temperature ST increase with increasing Cu content in Ag-20Pd-12Au-xCu alloys (x=14.5, 17, and 20). The formation process of the ß' phase can be explained in terms of diffusion of Ag and Cu atoms and precipitation of the ß' phase. Clarification of the relationship between hardening and precipitation of the ß' phase via high-temperature ST is expected to help the development of more effective heat treatments for hardening in Ag-20Pd-12Au-xCu alloys.

Contribution of ß' and ß precipitates to hardening in as-solutionized Ag-20Pd-12Au-14.5Cu alloys for dental prosthesis applications.

Dental Ag-20Pd-12Au-14.5Cu alloys exhibit a unique hardening behavior, which the mechanical strengths enhance significantly which enhances the mechanical strength significantly after high-temperature (1123K) solution treatment without aging treatment. The mechanism of the unique hardening is not clear. The contribution of two precipitates (ß' and ß phases) to the unique hardening behavior in the as-solutionized Ag-20Pd-12Au-14.5Cu alloys was investigated. In addition, the chemical composition of the ß' phase was investigated. The fine ß' phase densely precipitates in a matrix. The ß' phase (semi-coherent precipitate), which causes lattice strain, contributes greatly to the unique hardening behavior. On the other hand, the coarse ß phase sparsely precipitates in the matrix. The contribution of the ß phase (incoherent precipitate), which does not cause lattice strain, is small. The chemical composition of the ß' phase was determined. This study reveals that the fine ß' phase precipitated by high-temperature solution treatment leads to the unique hardening behavior in dental Ag-20Pd-12Au-14.5Cu alloys in the viewpoints of the lattice strain contrast and interface coherency. It is expected to make the heat treatment process more practical for hardening. The determined chemical composition of ß' phase would be helpful to study an unknown formation process of ß' phase.

Precipitation of ß' phase and hardening in dental-casting Ag-20Pd-12Au-14.5Cu alloys subjected to aging treatments.

The age-hardening behavior of the dental-casting Ag-20Pd-12Au-14.5Cu alloy subjected to aging treatment at around 673K is well known, and this hardening has been widely employed in various applications. To date, the age-hardening of this alloy has been explained to attribute to the precipitation of a ß phase, which is a B2-type ordered CuPd phase or PdCuxZn1-x phase. In this study, results obtained from microstructural observations using a transmission electron microscopy and a scanning transmission electron microscopy revealed that a fine L10-type ordered ß' phase precipitated in the matrix and a coarse-structure region (consisting of Ag- and Cu-rich regions) appeared after aging treatment at 673K and contributed to increase in hardness. The microstructure of the coarse ß phase, which existed before aging treatment, did not change by aging treatment. Thus, it is concluded that the fine ß' phase precipitated by aging treatment contributed more to increase in hardness than the coarse-structure region and coarse ß phase.

A finite element simulation of initial movement, orthodontic movement, and the centre of resistance of the maxillary teeth connected with an archwire.

The purpose of this article is to simulate long-term movement of maxillary teeth connected with an archwire and to clarify the difference between the initial tooth movement and the long-term orthodontic movement. Initial tooth movement was calculated based on the elastic deformation of the periodontal ligament. Orthodontic tooth movement was simulated based on the bone remodeling law of the alveolar bone, while consequentially updating the force system. In the initial tooth movement, all teeth tipped individually due to an elastic deflection of the archwire. In the long-term movement, the maxillary teeth moved as one united body, as if the archwire were a rigid material. Difference of both movement patterns was due to the change in force system during tooth movement. The long-term movement could not be predicted from the initial tooth movement. Movement pattern and location of the centre of resistance in the long-term movement were almost the same as those in the initial tooth movement as calculated by assuming the archwire to be a rigid material.

Finite element analysis of the effect of force directions on tooth movement in extraction space closure with miniscrew sliding mechanics.

INTRODUCTION: Miniscrews placed in bone have been used as orthodontic anchorage in extraction space closure with sliding mechanics. The movement patterns of the teeth depend on the force directions. To move the teeth in a desired pattern, the appropriate direction of force must be selected. The purpose of this article is to clarify the relationship between force directions and movement patterns. METHODS: By using the finite element method, orthodontic movements were simulated based on the remodeling law of the alveolar bone. The power arm length and the miniscrew position were varied to change the force directions. RESULTS: When the power arm was lengthened, rotation of the entire maxillary dentition decreased. The posterior teeth were effective for preventing rotation of the anterior teeth through an archwire. In cases of a high position of a miniscrew, bodily tooth movement was almost achieved. The vertical component of the force produced intrusion or extrusion of the entire dentition. CONCLUSIONS: Within the limits of the method, the mechanical simulations demonstrated the effect of force direction on movement patterns.

Numerical simulations of canine retraction with T-loop springs based on the updated moment-to-force ratio.

The purpose of this study was to develop a new finite element method for simulating long-term tooth movements and to compare the movement process occurring in canine retraction using a T-loop spring having large bends and with that having small bends. Orthodontic tooth movement was assumed to occur in the same manner as the initial tooth movement, which was controlled by the moment-to-force (M/F) ratios acting on the tooth. The M/F ratios were calculated as the reaction forces from the spring ends. For these M/F ratios, the teeth were moved based on the initial tooth movements, which were calculated by using the bilinear elastic model of the periodontal ligament. Repeating these calculations, the teeth were moved step by step while updating the M/F ratio. In the spring with large bends, the canine at first moved bodily, followed by root distal tipping. The bodily movement was quickly achieved, but over a short distance. In the spring with small bends, the canine at first rotated and root mesial tipping occurred, subsequently the canine uprighted and the rotation decreased. After a long time elapsed, the canine moved bodily over a long distance. It was found that the long-term tooth movement produced by the T-loop springs could be simulated by the method proposed in this study. The force system acting on the teeth and the movement type remarkably changed during the long-term tooth movement. The spring with large bends could move the canine bodily faster than that with small bends.

Numeric simulations of en-masse space closure with sliding mechanics.

INTRODUCTION: En-masse sliding mechanics have been typically used for space closure. Because of friction created at the bracket-wire interface, the force system during tooth movement has not been clarified. METHODS: Long-term tooth movements in en-masse sliding mechanics were simulated with the finite element method. RESULTS: Tipping of the anterior teeth occurred immediately after application of retraction forces. The force system then changed so that the teeth moved almost bodily, and friction occurred at the bracket-wire interface. Net force transferred to the anterior teeth was approximately one fourth of the applied force. The amount of the mesial force acting on the posterior teeth was the same as that acting on the anterior teeth. Irrespective of the amount of friction, the ratio of movement distances between the posterior and anterior teeth was almost the same. By increasing the applied force or decreasing the frictional coefficient, the teeth moved rapidly, but the tipping angle of the anterior teeth increased because of the elastic deflection of the archwire. CONCLUSIONS: Finite element simulation clarified the tooth movement and the force system in en-masse sliding mechanics. Long-term tooth movement could not be predicted from the initial force system. The friction was not detrimental to the anchorage. Increasing the applied force or decreasing the friction for rapid tooth movement might result in tipping of the teeth.

Effects of transpalatal arch on molar movement produced by mesial force: a finite element simulation.

INTRODUCTION: The transpalatal arch (TPA), which splints together 2 maxillary molars, has been believed to preserve anchorage. The purpose of this study was to clarify this effect from a mechanical point of view. METHODS: The finite element method was used to simulate the movement of anchor teeth subjected to mesial forces with and without a TPA. RESULTS: In the initial movement produced by elastic deformation of the periodontal ligament, stress magnitude in the periodontal ligament was not changed by the TPA. In the orthodontic movement produced by bone remodeling, the mesial force tipped the anchor teeth irrespective of the TPA. The tipping angles of anchor teeth with and without the TPA were almost the same. The anchor teeth without the TPA were rotated in the occlusal plane and moved transversely. CONCLUSIONS: The TPA had no effect on the initial movement. In the orthodontic movement, the TPA had almost no effect, preserving anchorage for mesial movement. However, the TPA prevented rotational and transverse movements of the anchor teeth. These results are valid when the assumptions used in this calculation are satisfied.

A numerical simulation of tooth movement produced by molar uprighting spring.

INTRODUCTION: Uprighting a tipped molar by using an uprighting spring is a fundamental orthodontic treatment technique. However, mechanical analyses have not been carried out for molar uprighting, and the mechanism of tooth movement has not been clarified. The purposes of this article were to clarify these mechanisms and to demonstrate the usefulness of mechanical simulations by which the effects of many factors on tooth movement can be estimated quantitatively. METHODS: A 3-dimensional finite element method was used to simulate the uprighting of a second molar with a molar uprighting spring. The effects of a retainer and spring-arm bending on the tooth movements were shown quantitatively. RESULTS: The retainer was useful to reduce the movement of anchor teeth. The same effect could be achieved by bending the spring arm in the lingual direction, but the molar was greatly rotated in the occlusal plane and was tipped in the buccal direction. CONCLUSIONS: The usefulness of a mechanical simulation method to predict orthodontic tooth movement in clinical situations was demonstrated.

A numerical simulation of orthodontic tooth movement produced by a canine retraction spring.

Tooth movements produced by a canine retraction spring were calculated. Although a gable bend and an anti-rotational bend were incorporated into the spring, the canine tipped and rotated initially. Retraction force decreased and moment-to-force ratio increased after the spring legs closed. Then, the initial tipping and rotation began to be corrected. As a result, the canine moved almost bodily after a prolonged period of time. Such tooth movements cannot be estimated from the initial force system. The gable bend decreased tipping movement, but increased rotational movement. On the other hand, the anti-rotational bend decreased rotational movement but increased tipping movement. In other words, one bend decreased the effect of the other, when both bends were incorporated in the spring.

Calculation of natural frequencies of teeth supported with the periodontal ligament.

Natural frequencies and vibration modes of four kinds of teeth were calculated by using a mechanical model. The alveolar bone and the tooth were assumed as rigid bodies, while the periodontal ligament was assumed as an elastic spring. All the natural frequencies were within a range of 1 to 10 kHz. The first natural frequencies of four teeth were about 1.5 kHz, and decreased as the root length decreased. Their vibration modes were tipping movements of the root. The natural frequency of the twisting vibration mode, or rotating movement around the tooth axis, was affected by root configuration. When subjected to a periodic force, the tooth and periodontal ligament would vibrate with the corresponding resonance mode. This phenomenon may be used as a method for the diagnosis and the treatment of a periodontal tissue.

A numerical simulation of tooth movement by wire bending.

INTRODUCTION: In orthodontic treatment, wires are bent and attached to teeth to move them via elastic recovery. To predict how a tooth will move, the initial force system produced from the wire is calculated. However, the initial force system changes as the tooth moves and may not be used to predict the final tooth position. The purpose of this study was to develop a comprehensive mechanical, 3-dimensional, numerical model for predicting tooth movement. METHODS: Tooth movements produced by wire bending were simulated numerically. The teeth moved as a result of bone remodeling, which occurs in proportion to stress in the periodontal ligament. RESULTS: With an off-center bend, a tooth near the bending position was subjected to a large moment and tipped more noticeably than the other teeth. Also, a tooth far from the bending position moved slightly in the mesial or the distal direction. With the center V-bend, when the second molar was added as an anchor tooth, the tipping angle and the intrusion of the canine increased, and movement of the first molar was prevented. When a wire with an inverse curve of Spee was placed in the mandibular arch, the calculated tendency of vertical tooth movements was the same as the measured result. In these tooth movements, the initial force system changed as the teeth moved. Tooth movement was influenced by the size of the root surface area. CONCLUSIONS: Tooth movements produced by wire bending could be estimated. It was difficult to predict final tooth positions from the initial force system.

The effects of friction and flexural rigidity of the archwire on canine movement in sliding mechanics: a numerical simulation with a 3-dimensional finite element method.

INTRODUCTION: The purposes of this article were to clarify the combined effect of friction and an archwire's flexural rigidity on canine movement in sliding mechanics, and to explain how to select a suitable archwire and force level for efficient bodily movement. METHODS: A numerical simulation was carried out by using a 3-dimensional finite element method. RESULTS: As the frictional force decreased, both the net force acting on and the moving speed of the canine increased. The elastic deformation of the archwire increased, and the moving pattern of the canine changed from bodily movement to tipping, although there was no clearance between the archwire and the bracket slot. When a light wire was used, wire deformation increased, and the canine experienced greater tipping. These effects of friction and wire properties on canine movement (tipping and rotational angles) are combined by using a single parameter, EI/P, where EI is the flexural rigidity of the archwire, and P is the net force acting on the canine. A suitable combination of EI and P will cause canine bodily movement. The EI is determined from the archwire's size and material. CONCLUSIONS: We propose a method for estimating a suitable combination in this article.

Numerical simulation of canine retraction by sliding mechanics.

BACKGROUND: Bone remodeling laws have been used to simulate the movement of a single tooth, but the calculations for simulating the movement of several teeth simultaneously are time-consuming. The purpose of this article is to discuss a method that allows the simulation of more complex tooth movements. METHODS: A 3-dimensional finite element method was used to simulate the orthodontic tooth movement (retraction) of a maxillary canine by sliding mechanics and any associated movement of the anchor teeth. Absorption and apposition of the alveolar bone were produced in proportion to the stress of the periodontal ligament. RESULTS: In a reference case, the canine was retracted by a 2N force with 0.016-in square wire. The frictional coefficient between wire and bracket was 0.2. The movement of both the canine and the anchor teeth could be calculated with the elastic deformation of wire. The canine tipped during the initial unsteady state and then moved bodily during the steady state. It became upright when the orthodontic force was removed. The anchor teeth moved in the steady state and tipped in the mesial direction. The decrease in applied force by friction was about 70%. The tipping of the canine decreased when the wire size was increased or when the applied force was decreased. CONCLUSIONS: Simple assumptions were used in this calculation to simulate orthodontic tooth movements. The calculated results were reasonable in mechanical considerations. This method might enable one to estimate various tooth movements clinically. However, precise comparisons between calculated and clinical results, and the improvement of the calculation model, are left for a future study.