Absence Of Voids Research Articles

Surface waves in fiber-reinforced anisotropic general viscoelastic media of higher orders with voids, rotation, and electromagnetic field

ABSTRACTIn this article, we investigated an effect of external magnetic field on the propagation of surface waves in a perfect electrically conducting fiber-reinforced anisotropic general viscoelastic media of rational and higher orders with voids in a rotating medium. The general surface wave speed is derived to investigate effect of electromagnetic field and rotation on surface waves in the presence of voids and viscosity. Boundary conditions are applied to obtain the secular equation for generalized types of waves. Particular cases of Stoneley, Love and Rayleigh waves are derived. The results obtained are more general in the sense that some earlier published results are obtained from our result as special cases. In the absence of voids, the results for viscoelasticity of order zero are in good agreement with the fiber-reinforced materials. Also by neglecting the reinforced elastic parameters, the results reduce to a well-known isotropic medium. It is observed that surface waves cannot propagate in a strong initially applied electromagnetic field and rotation. Numerical results for particular cases have been obtained and displayed graphically. The results indicate that the effects of voids, anisotropic, fiber-reinforcement, rotation and electromagnetic field are very pronounced and applicable for the phenomena.

Coupling effect of waste automotive engine oil in the preparation of wood reinforced LDPE plastic composites for panels

We demonstrated the formulation of wood plastic composite (WPC) materials with flexural strength of 13.69 ± 0.09 MPa for applications in outdoor fencing using municipal waste precursors like low density polyethylene (LDPE) plastics (54.0 wt. %), sawn wood dust with particle size between 64 and 500 μm derived from variable hardwood species (36.0 wt. %) and used automotive engine oil (10 wt. %). The WPC panels were prepared by pre-compounding, extruding at a screw auger torque of 79.8 Nm and pressing through a rectangular mould of dimension 132 mm × 37 mm × 5 mm at temperature 150 °C. The efficacy of black waste oil, as a coupling agent, was demonstrated by the absence of voids and pull-outs on microscopic examination using scanning electron microscopy. No hazardous substances were exhaled during thermo-gravimetric mass spectrometry analysis. The percentage crystallinity of the LDPE in the as-prepared material determined by differential scanning calorimetry was 11.3%.

Effect of different mixing and placement methods on the quality of MTA apical plug in simulated apexification model.

Background It is necessary apical plug material to exhibit proper adaptation with the root canal walls. Presence of voids at the interface between the root canal wall and this material result in micro leakage, which might have a relationship with post treatment disease. The aim of the present study was to evaluate the effect of different mixing (manual and ultrasonic) and placement (manual and manual in association with indirect ultrasonic) method of Mineral Trioxide Aggregate (MTA) on the void count and dimension in the apical plug in natural teeth with simulated open apices.Material and Methods Eighty human maxillary central incisors were selected. After simulation of the open apex model, the teeth were assigned to 4 groups based on the mixing and placement techniques of MTA: group 1, manual mixing and manual placement; group 2, manual mixing and manual placement in association with indirect ultrasonic; group 3, ultrasonic mixing and and manual placement; and group 4, ultrasonic mixing and manual placement in association with indirect ultrasonic. The prepared samples were placed within gypsum sockets in which the periodontal ligament was reconstructed with polyether impression material. In group 1, after mixing, the material was condensed with a hand plugger. In group 2, after mixing, the ultrasonic tip was contacted with the hand plugger for 2 seconds. In groups 3 and 4, mixing was carried out with the ultrasonic tip for 5 seconds and in groups 3 and 4, similar to groups 1 and 2, respectively, the materials were placed as apical plugs, measuring 3 mm in length. A wet cotton pellet was placed at canal orifices and dressed with Cavit. After one week, the cone beam computed tomography (CBCT) technique was used to count the number of voids between the material and root canal walls. The void dimensions were determined using the following scoring system: score 1, absence of voids; score 2, the void size less than half of the dimensions of the evaluated cross-section; score 3, the void size larger than half of the dimensions of the evaluated cross-section. Chi-squared and Fisher’s exact tests were used for statistical analyses. Statistical significance was set at P<0.05.Results The maximum (13) and minimum (3) number of voids were detected in groups 2 and 3, respectively. There were no significant differences between groups 1 and 3 in the number of voids (p >0.05). Evaluation of void dimensions showed no score 3 in any of the study groups and the dimensions of all the voids conformed to score 2.Conclusions Under the limitations of the present study, use of ultrasonic mixing and manual placement techniques resulted in a decrease in the number of voids in the apical plug. Key words:Apical plug, MTA, ultrasonic, void.

Comparative evaluation of different obturation techniques in primary molars: An in vivo study

Abstract Aim: The study was undertaken to compare the filling quality of a 30 gauge cannula (NaviTip™, Ultradent Inc., South Jordan, UT, USA) used on a pressure syringe with a lentulospiral in primary molars. Materials and Methods: Thirty mandibular first and second primary molars in 28 healthy children of both sexes in the age group of 4-8 years were included in the study. All pulpectomy procedures were performed by one investigator. Before obturation, the subjects were randomly selected for the two obturation techniques. Effectiveness of the two obturation techniques was assessed by three independent evaluators using postoperative radiographs taken immediately after each obturation. Filling quality was determined by analyzing presence or absence of voids, extent of fill and apical seal. Results: The results of the obturation quality of the tested techniques were collected and statistically analyzed using chi-square test. There was a significant difference for the presence of voids between the two groups. NaviTip group showed the best results for the number of voids (mesial χ2 = 3.567, P = 0.0497) (distal χ2 = 5.058, P = 0.0269). The lentulospiral group showed more number of optimal fillings. When results were compared in terms of apical seal, NaviTip showed better apical seal but statistically no difference (P &gt;.05). Conclusion: Lentulospiral produced the best results in terms of length of obturation, while NaviTip syringe was efficient enough in controlling voids and produced the best results for apical seal.

Fabrication of high strength in-situ Al-Al3Ti nanocomposite by mechanical alloying and hot extrusion: Investigation of fracture toughness

High energy vibratiory mill was used to produce Nanocrystalline Al-20wt% Ti powders by mechanical alloying. The milled powders were then consolidated by hot extrusion at 530°C. Produced bulk nanocomposite samples were studied by XRD analysis, optical microscopy (OM), Field Emission Scanning Electron Microscopy (FESEM), EDS spectroscopy, densitometry and hardness tests. Three point bending on SENB specimens was applied under quasi static condition to determine the fracture toughness and also investigate the fracture surface using SEM. The results indicated that after extrusion a fully dense Al-Al3Ti nanocomposite with the crystallite size of 200−400nm is produced in which the Al3Ti particles with the size of 50−500nm were homogeneously distributed. The mechanical properties of samples such as modulus, flexural strength and hardness were significantly increased to 130GPa, 910MPa and 136HV, respectively. These results are the consequence of refinement of Al matrix grain size, distribution of Al3Ti nano-particles and the absence of voids. The high density of grain boundries and particle-matrix interfaces provide a lot of sites for nucleation of dimples which leads to the delay in crack initiation stage. Accordingly, the fracture toughness of the nanocomposite sample obtained KQ=27.4MPam which is a high value in comparison with the conventional Al composites. On a macroscopic scale, the fracture surface was brittle and flat, while SEM images showed dimpled fracture surfaces confirming microvoid coalescence as the main fracture mechanism.

Comparison of Resin Cement Insertion Techniques for Luting Fiberglass Posts

Objective: To evaluate the effect of two insertion techniques of self-adhesive dual resin cement on the bond strength of fiberglass posts in different portions of the root. The homogeneity of the cement layer along the root canal was also evaluated. Material and Methods: The root canals of 28 bovine teeth were instrumented, filled, and 14mm-space was prepared for luting fiberglass posts (Reforpost #3, Angelus), maintaining 4mm of apical sealing. The roots were randomly allocated into two groups according to the cement insertion technique (n=14): Lentulo Drill (Dentsply/Maillefer) or Centrix syringe (Dentsply). The posts were fixed with self-adhesive resin cement (RelyX U200, 3M ESPE). After 7 days, the roots were cross-sectioned to obtain three 1.0-mm-thick samples of each third of the space prepared for the post. Two samples of each third were subjected to push-out test (0.5 mm/min; 200N) and the third specimen was used for the analysis of cementation layer homogeneity. Images of specimens (40x magnification) were assessed and classified by two calibrated examiners (Kappa = 0.87) according to the presence or absence of voids and misfit. Data were analyzed by two-way ANOVA and Pearson Chi-Square test. Results: There was no statistically significant effect of insertion technique (p=0.278) or post-space thirds (p = 0.521) on bond strength of fiberglass posts. Chi-Square test showed that cement insertion with the Lentulo drill produced more cement voids than Centrix syringe (p = 0.023). Conclusion: The cement insertion technique did not influence bond strength of fiberglass posts in bovine root dentin. The use of Centrix syringe for cement insertion is preferred since it produced more homogenous cement layer.

Thermal Conductivity and Interface Thermal Conductance of Titanium Silicide Films on Si

Titanium silicide films were prepared by magnetron sputtering of Ti on B-doped Si (100) and annealing at different temperatures up to 700 °C in argon atmosphere. Films were also prepared by laser physical vapor deposition (LPVD) of Ti at 500 °C and 600 °C on B-doped Si (100) followed by in situ annealing. The films were characterized by X-ray diffraction for phase identification, scanning electron microscopy for interface microstructure and oxygen level, atomic force microscopy for interface roughness, transient thermoreflectance for thermal conductivity and interface thermal conductance of the interface with Si. Annealing at 700 °C for 1 h was responsible for the complete formation of C54 phase. LPVD at 500 °C and 600 °C was responsible for C54 formation with smaller grain size, but unreacted Ti and other silicide phases were also present. The interface in all the films was continuous with the absence of voids. The thermal conductivity of the films increased for higher processing temperature. The interface thermal conductance for films prepared below 700 °C was lower. Film annealed at 700 °C significantly showed higher interface thermal conductance and lower effective thermal resistance. Comparison of thermal properties of the TiSi2 films with that of WSi2 films prepared previously showed that the effective thermal resistance of the C54 phase is lower.

English

In this paper, gravitational effects on propagation of surface waves in a homogeneous fibre-reinforced anisotropic general viscoelastic media of higher order with voids is investigated. The general surface wave speed is derived to study the effects of gravity on surface waves. Particular cases for Stoneley and Rayleigh waves are discussed. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. In the absence of voids our results for viscoelastic of order zero are well agreement to fibre-reinforced materials. Also by neglecting the reinforced elastic parameters, the results reduce to well known isotropic medium. Numerical results for particular materials are given and illustrated graphically. The results indicate that the effect of the gravitational, voids and the reinforced elastic parameters on surface waves are very pronounced. &nbsp; Key words. Fibre-reinforced, viscoelastic, surface waves, gravity, anisotropic, voids.

Thermal Conductivity Changes in Titanium-Graphene Composite upon Annealing

Ti-graphene composite films were prepared on polished Ti substrates by deposition of graphene platelets from suspension followed by deposition of Ti by magnetron sputtering. The films were annealed at different temperatures up to 1073 K (800 °C) and different time periods in argon atmosphere. The annealed films were characterized by X-ray diffraction for phase identification, scanning electron microscopy for microstructure, energy-dispersive spectrometry for chemical analysis, atomic force microscopy for surface roughness, and transient thermoreflectance for thermal conductivity and interface thermal conductance. The results showed that the interface between the composite film and Ti substrate remained continuous with the absence of voids. Oxygen concentration in the composite films has increased for higher temperature and time of annealing. TiO2 and TiC phases are formed only in the film annealed at 1073 K (800 °C). The thermal conductivity of the composite film decreased with increasing oxygen concentration. The effective thermal conductance of the film annealed at 1073 K (800 °C) was significantly lower. The interface thermal conductance between the composite film and the Ti substrate is also reduced for higher oxygen concentration. Formation of microscopic TiO2 phase bound by interface boundaries and oxygen incorporation is considered responsible for the lower thermal conductance of the Ti-graphene composite annealed at 1073 K (800 °C).

Cork–polymer biocomposites: Mechanical, structural and thermal properties

This work addresses to the preparation of biocomposites resulting from the combination of different biodegradable aliphatic polyesters with cork (30wt.%). The lignocellulosic biomass with closed cellular structure was compounded with poly(L-lactic acid) (PLLA), polyhydroxybutyrate-co-hydroxyvalerate (PHBV), poly-ε-caprolactone (PCL) and starch-poly-ε-caprolactone (SPCL) blend using a twin-screw extruder prior to injection moulding into tensile samples. The physico-mechanical and thermal properties of the matrices and the bio-based cork composites were investigated. This study shows that the addition of cork contributes to produce lightweight materials using PLLA and PHBV matrices and promotes an increase on the stiffness of PCL. The fracture morphology observations showed good physical cork–matrix bonding with absence of voids or cavities between cork and the bio-based polyesters. Cork increases the crystallinity degree of the biocomposites. These findings suggest that the cork–polymer biocomposites are a viable alternative to develop more sustainable composite materials, such as automotive interior parts and bio-based caps for wine bottles as it has been shown as proof-of-concept.

Comparative Evaluation of Obturating Techniques in Primary Teeth: An in vivo Study.

ABSTRACTAim: The present study was undertaken to compare two methods of obturation in primary teeth by using lentulospirals and pressure syringe, radiographically.Materials and methods: Sixty teeth in subjects with mean age of 5.88 ± 1.58 years were obturated randomly using two different obturating techniques, i.e. group I: Thirty teeth obturated with pressure syringe, and group II: Thirty teeth obturated with lentulospiral. Quality of obturation and presence or absence of voids were assessed by taking radiographs after obturation was done using both the techniques. Results of quality of obturation were statistically analyzed using Chi-square test and Mann-Whitney’s test, whereas voids were analyzed using Chi-square test.Results: No statistically significant difference between the quality of obturation using pressure syringe or lentulospiral (p > 0.05) was observed. However, significantly higher number of voids were found for lentulospiral technique as compared to pressure syringe (p < 0.01).Conclusion: Both the techniques were found to be equally efficient statistically, though lentulospiral produced more voids.How to cite this article: Vashista K, Sandhu M, Sachdev V. Comparative Evaluation of Obturating Techniques in Primary Teeth: An in vivo Study. Int J Clin Pediatr Dent 2015;8(3): 176-180.

Calcium hydroxide fillings in curved canals: influence of apical enlargement using the rotary systems ProTaper, K3, and two hand instrumentation techniques

Objective: This study aimed to analyze the influence of the instrumentation technique (hand or rotary), and apical enlargement on calcium hydroxide (CH) fillings in curved canals. Materials and method: One hundred and ten simulated root canals were divided into eleven experimental groups (G). Canals were prepared with K-Flexofile hand instruments, using either crown-down (GCD 25, GCD 30 and GCD 35) or step-back (GSB 25, GSB 30 and GSB 35) techniques; and with rotary instruments, using either ProTaper (GPT F1 and GPT F2) or K3 (GK3 25, GK3 30 and GK3 35) systems. The apical diameter correspon- ded to 0.20 mm (GPT F1), 0.25 mm (GCD 25, GSB 25, GPT F2 and GK3 25), 0.30 mm (GCD 30, GSB 30, GK3 30), and 0.35 mm (GCD 35, GSB 35, GK3 35). A CH paste, previously colored with blue Indian ink, was injected into the canals using a special syringe. The four sides of the blocks with simulated canals were scanned and the images were transferred to the AutoCAD-2008 software, for assessing the amount (%) of filling in the apical 5 mm (ANOVA; Tukey’s Test; α=0.05). Qualitative analysis was also performed regarding the presence or absence of voids (Chisquare Test; α=0.05). Results: In GSB, there was significant difference between diameters 25 and 30. GSB showed lower amount of filling (P<0.05) than GK3, when the apical diameter corresponded to 0.30 mm. GCD showed lower amount of filling (P<0.05) than the other groups (SB, PT, and K3), when the apical diameter corresponded to 0.25 mm. No significant difference was detected when comparing the four sides of the blocks. Conclusion: Preparation technique and apical diameter had slight or no relevant influence on CH paste filling in simulated curved root canals. Statistical differences found in this study may be clinically irrelevant, since the amount of filling, regardless of preparation technique and apical diameter, was very close or equal to 100%. Keywords: Endodontics. Root canal preparation. Calcium hydroxide.

Technical Quality of Root Fillings Performed by Dental Students in Babol Dental School

Introduction: There is substantial evidence that the technical quality of root canal filling has a significant effect on the outcome of root canal treatment. The aim of this study was to evaluate the technical quality of root canal fillings performed by dental students. Methods: The records of 325 teeth radiographs, treated by dental students in 2008-2009 in Babol Dental School, were selected and evaluated. For each tooth, three periapical radiographs (before treatment, during operation and at the end of treatment) were examined. Filling length, density and taper, and presence or absence of void was evaluated. Obturations that have proper length, density and taper, without any void are classified as acceptable root canal fillings. The SPSS statistical software and Chi-Square test were used for analysis. Results: Of the 325 radiographs, 72% had good length and 75% had acceptable taper. There were 14.2% low densities, whereas, only 3.32% of teeth have no void. At least 17.8% of teeth had underfilling and 10.2% overfilling. Finally, only 17.5% of teeth showed acceptable filling length, taper and density without any void. There was no significant difference between the 4 th and 5 th year students and oral hygienist (who studied oral hygiene and now continuing it to dentistry) in root canal filling quality (P> 0.05). Conclusion: Technical quality of root fillings performed by dental students was found to be less than 20%. .It should be revised in the endodontic curriculum requirement to improve their performance.

Studying light propagation in a locally homogeneous universe through an extended Dyer-Roeder approach

Light is affected by local inhomogeneities in its propagation, which may alter distances and so cosmological parameter estimation. In the era of precision cosmology, the presence of inhomogeneities may induce systematic errors if not properly accounted. In this vein, a new interpretation of the conventional Dyer-Roeder (DR) approach by allowing light received from distant sources to travel in regions denser than average is proposed. It is argued that the existence of a distribution of small and moderate cosmic voids (or "black regions") implies that its matter content was redistributed to the homogeneous and clustered matter components with the former becoming denser than the cosmic average in the absence of voids. Phenomenologically, this means that the DR smoothness parameter (denoted here by $\alpha_E$) can be greater than unity, and, therefore, all previous analyses constraining it should be rediscussed with a free upper limit. Accordingly, by performing a statistical analysis involving 557 type Ia supernovae (SNe Ia) from Union2 compilation data in a flat $\Lambda$CDM model we obtain for the extended parameter, $\alpha_E=1.26^{+0.68}_{-0.54}$ ($1\sigma$). The effects of $\alpha_E$ are also analyzed for generic $\Lambda$CDM models and flat XCDM cosmologies. For both models, we find that a value of $\alpha_E$ greater than unity is able to harmonize SNe Ia and cosmic microwave background observations thereby alleviating the well-known tension between low and high redshift data. Finally, a simple toy model based on the existence of cosmic voids is proposed in order to justify why $\alpha_E$ can be greater than unity as required by supernovae data.

Cautionary note on use of focused ion beam sectioning as technique for characterising oxidation damage in Ni based superalloys

Previous observations on Ni based superalloys, obtained through the use of focused ion beam (FIB) sample preparation and imaging, have reported the presence of subsurface voids after oxidation. In this present study, oxidised specimens of the Ni based superalloy, RR1000, were subjected to conventional sample preparation as well as both dual and single beam FIB preparation, with the aim of re-examining the previous observations of subsurface void formation. It is clear from FIB preparations that features previously interpreted as networks of voids have been demonstrated to be internal oxides by varying the sample tilt angles and imaging signal using either secondary electrons (SEs) or secondary ions (SIs). Conventional preparation methods illustrate the presence of subsurface alumina intrusions and the absence of voids, supporting previous evidence. The positive identification of voids and oxides by FIB can be complex and prone to misinterpretation and thus, the use of several imaging conditions and tilt angles must be used, along with conventional preparation methods, to confirm or refute the presence of ‘voids’ underneath oxides.

Two-dimensional wave propagation in a rotating elastic solid with voids

Two-dimensional wave propagation is studied in an isothermal linear isotropic elastic material with voids rotating with constant angular velocity based on a theory of elastic material with voids developed by Iesan (1986) in the thermoelastic context. It is found that there exist three coupled plane waves propagating with distinct phase speeds. The presence of voids and the rotation of the medium are responsible for this coupling. In the absence of voids, the classical longitudinal and transverse waves are found to be coupled through the rotation of the medium. At very large frequency or when the angular rotation is very small relative to the wave frequency the waves are decoupled and propagate with distinct phase speeds. These are (i) a longitudinal wave, (ii) a transverse wave and (iii) a longitudinal wave corresponding to the change in void volume fraction. The first two correspond to the waves of classical elasticity, while the third is new and arises from the presence of the voids. The results are illustrated graphically.

Structural and compositional characterization of MOVPE GaN thin films transferred from sapphire to glass substrates using chemical lift-off and room temperature direct wafer bonding and GaN wafer scale MOVPE growth on ZnO-buffered sapphire

GaN thin films were grown on ZnO/c-Al2O3 with excellent uniformity over 2in. diameter wafers using a low temperature/pressure MOVPE process with N2 as a carrier and dimethylhydrazine as an N source. 5mm×5mm sections of similar GaN layers were direct-fusion-bonded onto soda lime glass substrates after chemical lift-off from the sapphire substrates. X-Ray Diffraction, Scanning Electron Microscopy and Transmission Electron Microscopy confirmed the bonding of crack-free wurtzite GaN films onto a glass substrate with a very good quality of interface, i.e. continuous/uniform adherence and absence of voids or particle inclusions. Using this approach, (In) GaN based devices can be lifted-off expensive single crystal substrates and bonded onto supports with a better cost-performance profile. Moreover, the approach offers the possibility of reclaiming the expensive sapphire substrate so it can be utilized again for growth.

Role of grain boundary and dislocation loop in H blistering in W: A density functional theory assessment

We report a first-principles density functional theory study on the role of grain boundary and dislocation loop in H blistering in W. At low temperature, the Σ3(111) tilt grain boundary can trap up to six H atoms per (1×1) unit in (111) plane before significant sliding occurs. This amount of H weakens greatly the cohesion across the boundary. At room temperature, when only three H can be trapped, this effect can be still significant. A dislocation loop in (100) plane can trap four H per (1×1) unit even at room temperature, whose detrimental effect is strong enough to break the crystal. Our numerical results demonstrate unambiguously the grain boundaries and dislocation loops can serve as precursors of H blistering. In addition, we find no H2 molecules can be formed in either environment before fracture of W bonds starts, well explaining the H blistering in the absence of voids during non-damaging irradiation.

On theory of generalized thermoelastic solids with voids and diffusion

Governing equations of thermoelastic diffusion material with voids are modified with the help of Lord and Shulman theory of generalized thermoelasticity. These governing equations are then solved in two-dimension to show the existence of four coupled longitudinal waves and a shear wave. The complex absolute values of the speeds of the coupled longitudinal waves are computed numerically against the frequency for Magnesium material. The reflection of these plane waves from a stress free thermally insulated boundary is also studied, where the dependence of the reflection coefficients on angle of incidence is shown graphically for the incidence of coupled longitudinal wave only. The speeds and reflection coefficients of plane waves are also computed numerically in the absence of voids and diffusion parameters, which are shown graphically to observe the effects of voids and diffusion.

Analysis of four gutta‐percha techniques used to fill mesial root canals of mandibular molars

To compare the percentage of gutta-percha, sealer and voids and the influence of isthmuses in mesial root canals of mandibular molars filled with different techniques. Canals in 60 mesial roots of mandibular first molars were prepared with ProTaper instruments to size F2 (size 25, 0.08 taper) and filled using a single-cone, lateral compaction, System B or Thermafil techniques. An epoxy resin sealer was labelled with Rhodamine-B dye to allow analysis under a confocal microscope. The percentage of gutta-percha, sealer and area of voids was calculated at 2, 4 and 6 mm from the apex, using Image Tool 3.0 software. Statistical analysis was performed using nonparametric Kruskal-Wallis and Dunn tests (P < 0.05). The influence of isthmuses on the presence or absence of voids was evaluated using the Fisher test. At the 2 mm level, the percentage of gutta-percha, sealer and voids was similar amongst the System B, lateral compaction and single-cone techniques. The single-cone technique revealed significantly less gutta-percha, more sealer and voids in comparison with the Thermafil technique at the 2 and 4 mm level (P < 0.05). The analysis of all sections (2, 4 and 6 mm) revealed that more gutta-percha and less sealer and voids were found in root canals filled with Thermafil and System B techniques (P < 0.05). The Fisher test revealed that the presence of isthmuses increased the occurrence of voids in the lateral compaction group only (P < 0.05). Gutta-percha, sealer filled area and voids were dependent on the canal-filling technique. The presence of isthmuses may influence the quality of root filling.