High-strength Ceramic Materials Research Articles

Glass-ceramic binder of cordierite composition for low-temperature sintering of high-strength ceramic materials based on oxygen-free silicon compounds

The mechanical properties of composite ceramic materials obtained based on oxygen-free silicon compounds are largely determined by the properties of the glass binder. This paper presents the results of studies aimed at determining the most fusible glass in the pseudo-binary system 2MgO2Al2O35SiO2–2MnO2Al2O35SiO2 with a high tendency to crystallize as a glass-ceramic binder for low-temperature sintering of high-strength ceramic materials based on oxygen-free silicon compounds. The crystallization tendency of the experimental melts decreases with an increase in in the content of manganese cordierite, as confirmed by X-ray and infrared spectroscopic studies. Based on experimental studies, a melting diagram was constructed, which was used to determine the ratio between magnesium cordierite and manganese cordierite (50:50 wt.%), ensuring a minimum melt temperature of 12750C. The melting point of the glass of the specified composition is 14500C. The synthesized glass is characterized by a softening point of 8000C and crystallizes intensively at 10300C. The The thermal coefficient of linear expansion of the crystallized glass samples is 20.810–7 0C–1. X-ray diffraction and electron microscopic studies have shown that the developed glass is almost completely crystallized during heat treatment for 2 hours, forming a cordierite solid solution 2(Mg,Mn)O2Al2O35SiO2. The size of the cordierite phase crystals ranges from 0.5 to 3.0 m. Due to its fusibility and high crystallization tendency, the developed glass, can be proposed as a promising glass-ceramic binder for the production of high-strength ceramic materials (wear and impact resistant) based on SiC and Si3N4 with reduced sintering temperatures.

Overcoming the intrinsic brittleness of high-strength Al2O3–GdAlO3 ceramics through refined eutectic microstructure

High-strength ceramic materials are known for their exceptional mechanical properties; however, they are often plagued by brittleness, limiting their applications. Because of the inherent difficulty of dislocation glide and multiplication in ceramics, efforts to overcome the brittleness of ceramics by activating plastic deformation have faced challenges. This work demonstrates that Al2O3–GdAlO3 (Gadolinium Aluminum Perovskite: GAP) eutectic micropillars with submicron-scale fibrous microstructures exhibit remarkable plastic deformability. They displayed engineering plastic strains of up to 5% even at 25 °C, while the micropillars of Al2O3 or GAP single crystals exhibited brittle fracture similar to conventional high-strength ceramics. The plasticity in Al2O3–GAP eutectic was attributed to the activation of primary prismatic slip and secondary basal slip in the Al2O3 phase, which is typically considered inactive at room temperature. These findings suggest that plastic deformability can be achieved in high-strength ceramic materials by fabricating refined eutectic microstructures.

Preparation of egg-structured ceramsites from molybdenum tailings with improved properties

Conversion of solid waste tailings into building materials is an effective way to turn waste into resources as well as resolve the problems of their accumulation and pollution. Herein, in this paper, light-weight and high strength molybdenum tailings ceramsites (LHMCs) were prepared using molybdenum tailings as the main raw material supplemented with fly ash, sludge, steel slag and other solid wastes by egg-structure (three-layer structure) design and high-temperature sintering. The effects of raw material ratio, amount of carbon powder agent, sintering temperature, and sintering time on the properties of LHMCs were investigated, and the optimal preparation process was proposed to be preheating at 400 °C for 60 min and sintering at 1150 °C for 40 min. The results of the physicochemical properties, morphology, and component analysis of LHMCs show that the LHMCs with egg-structure including porous core, reinforced middle layer, and dense outer layer can significantly increase the strength of the ceramsites under the premise of ensuring the low density of the ceramsites. Meanwhile, the doping of molybdenum tailings improves the physical properties of the ceramsites and achieves the reuse of waste tailings. Importantly, the optimized LHMCs can meet the performance requirements of 900-grade ceramsites. This paper proposes a strategy for the preparation of tailings-doped light-weight and high-strength ceramic building materials, which provides a new idea for the recycling of solid waste.

Red mud in high-strength ceramics production

The work is devoted to the creation of high-strength ceramic materials with technogenic waste fillers.Purpose: Investigation of the ceramic and composite production based on chemical and metallurgical wastes to create new types of high quality constructional ceramics.Methodology/approach: The use of refractory clay with the addition of high-iron bauxite sludge as the main raw material. Bauxite sludge functions in compositions with aluminosilicate raw materials at burning at 1100 to 1200 °С, reduce to sintering due to its melting at 1150 °С.Research findings: Refractory clay compositions with red mud in the amount of 20 to 50 % at the burning temperature of 1050 °С, provide the ceramic formation possessing the compressive strength 1.3 to 1.5 times higher than that of clay samples without additives, i.e., 91 and 122–132 MPa, respectively.Value: The obtained ceramic compositions based on red mud determine a production of high-strength anorthite and anorthite-helenite ceramics using dry pressing.

The Effect of Surface Treatments of Presintered Zirconia on Sintered Surfaces

Zirconia is a high-strength ceramic material that expands the design and application possibilities for all-ceramic restorations and dental implants. To enhance the bonding of zirconia restorations to tooth substrates and the osseointegration of implants with the surrounding bone, the surface should be modified by surface treatment. Unfortunately, the effective treatment of sintered zirconia is difficult. Surface treatment for presintered zirconia may be less difficult; thus, the effectiveness of surface treatments of presintered zirconia was investigated herein. The zirconia specimens were randomly divided into eight groups: (1) control (untreated) and seven treated groups subjected to surface treatment (s.ttt.) in the presintered stage, followed by sintering: (2) s.ttt. 1: hydrofluoric acid (HF) gel left during sintering; (3) s.ttt. 2: HF gel washed before sintering; (4) s.ttt. 3: coated with nanosilica; (5) s.ttt. 4: coated with microsilica; (6) s.ttt. 5: coat followed by airborne-particle abrasion; (7) s.ttt. 6: coat followed by partial etching; and (8) s.ttt. 7: coat followed by total etching. The surface microstructure was examined using scanning electron microscopy (SEM) and the crystalline phase was identified using X-ray diffraction (XRD). Biaxial flexural strength was also tested. The results of SEM for s.ttt. 1 and 2 displayed irregular surfaces. S.ttt. 3 showed deeper penetration of the nanosilica into zirconia (27 µm) compared to the microsilica used in s.ttt. 4. S.ttt. 5 and 6 showed irregular coats. S.ttt. 7 showed intergranular pores. The XRD of s.ttt. 1, 2, and 3 revealed tetragonal zirconia as the control group. S.ttt. 4 and 5 showed cristobalite silica and tetragonal zirconia. S.ttt. 6 and 7 contained amorphous silica and tetragonal zirconia, while s.ttt. 7 also showed monoclinic zirconia. The highest flexural strength was for s.ttt. 4 (982.4 MPa), while the lowest was for s.ttt. 7 (386.6 MPa). There was no significant difference in the flexural strength between the control, s.ttt. 1, and 2 (846.3 MPa, 830.0 MPa, and 835 MPa, respectively). Compared to the control group, s.ttt. 3 had a lower flexural strength (634.1 MPa), while s.ttt. 5 and 6 had higher flexural strengths (863.1 MPa and 872.2 MPa, respectively). It can be concluded that the surface modification of presintered zirconia is a promising method as long as no phase transformation or deep subsurface penetration occurs.

Long-term results of a randomized clinical trial of 2 types of ceramic crowns in participants with extensive tooth wear

Statement of problemEvidence is sparse regarding the long-term outcomes of restorative treatment of patients with extensive tooth wear. PurposeThe purpose of this long-term prospective randomized clinical trial was to evaluate the performance and success rate of pressed lithium disilicate (LD) and translucent zirconia (TZ) crowns in participants with extensive tooth wear. Material and methodsA total of 62 participants with extensive tooth wear (17 women, 45 men; mean age 44.8 years; range 25-63 years) received a total of 713 crowns, LD=362 and TZ=351. Both types of crowns had chamfer preparations and were adhesively luted with dual-polymerizing composite resin cement (PANAVIA F 2.0; Kuraray Noritake Dental Inc). The restorations were clinically reevaluated on average 14, 31, 39, 54, and 65 months after insertion of the crowns according to the modified United States Public Health Service (USPHS) criteria. ResultsAfter an observation period of up to 6 years, the survival rate for both types of crowns was 99.7%, with 1 lost LD crown after 1 year as a result of loss of retention and 1 lost TZ crown after 3 years because of tooth fracture at the cemento-enamel junction. The success rates were similar for both types of crowns: 98.6% for LD and 99.1% for TZ. Reasons for failures were that 3 participants in each group developed apical lesions, minimal ceramic fractures, or their crowns were rebonded after loss of adhesion. Assessment of color at baseline was significantly different with a better match for LD (84.8% Alfa, 15.2% Bravo) than for TZ crowns (36.5% Alfa, 63.5% Bravo), including TZ crowns with veneered porcelain (P<.001). Secondary caries and cracks did not occur. A post hoc analysis of clinical performance did not indicate any significant differences between extensive tooth wear with primarily mechanical or chemical factors. ConclusionsNo differences were found between the 2 types of ceramic materials concerning the long-term success and clinical performance, except that TZ crowns were rated by a blinded clinician as less esthetic than LD crowns. The use of high-strength ceramic materials, as well as reliable adhesive bonding, are probably the key factors in the long-term success of ceramic crowns in participants with extensive tooth wear independent of the specific etiology.

Comparing the Repair of Veneered Zirconia Crowns with Ceramic or Composite Resin: An in Vitro Study.

Statement of problem: Current techniques for repairing porcelain-chipped restorations have several limitations. With advances in CAD/CAM technology, the combination of resin cements and high-strength ceramic materials might offer new options for repairing the chipping of veneering ceramic. Purpose: The purpose of this study is to compare the load-to-failure of veneered zirconia crowns repaired by different materials. Material and Methods: Veneered zirconia crowns were made on aluminum dies (n = 10/group). Feldspathic porcelain (Vita VM9, Vident) was applied to the zirconia coping (Vita In-Ceram YZ, Vident) in a cylindrical shape (Ø 10.5 mm, height 7.5 mm). A bevel cut on the porcelain veneer (45 degree, 3 mm width) was made at one side of each crown to simulate porcelain chipping. The crowns were then divided into four different groups according to the repair materials: 1. Conventional resin composite (A; Tetric EvoCeram, Ivoclar Vivadent); 2. Flowable resin composite (B; G-aenial Universal Flo, GC america); 3. CAD/CAM milled feldspathic ceramic (C; Vita Trilux Forte, Vident); 4. CAD/CAM milled lithium disilicate glass-ceramic (D; IPS e.max CAD, Ivoclar Vivadent). Resin cement (Multilink Automix, Ivoclar Vivadent) was used to cement the CAD/CAM ceramic materials to the beveled crowns. Each crown underwent 5000 cycles of thermocycling. The strength test was performed on an Instron universal testing machine by loading force on the center of repaired part to record load-to-failure. Data were analyzed by ANOVA and Tukey HSD post-hoc tests (α = 0.05). Results: Mean loads-to-failure (in Newton +/− SD) of repaired veneered zirconia crowns were: Gr. A: 660.0 ± 200.5; Gr. B: 681.7 ± 175.9; Gr. C: 1236.0 ± 188.8; Gr. D: 1536.3 ± 286.1. Catastrophic failure was the most dominant failure mode in every group. Few specimens exhibited cohesive failure. Only one specimen in group D had adhesive failure. Conclusions: Within the limitation of the study, veneered zirconia crowns repaired with CAD/CAM ceramic materials have significantly higher load-to-failure than veneered crowns repaired with resin composite (p ≤ 0.05). Clinical Implications: Traditionally, porcelain-chipped restorations are often repaired with resin composite and bonding technique. Repairing chipped porcelain with CAD/CAM ceramics fitting the fractured parts can be alternative option with potential advantages. More well-designed studies are necessary to justify this novel repair technique.

Phase stability, elastic, anisotropic properties, lattice dynamical and thermodynamic properties of B12M (M=Th, U, Np, Pu) dodecaborides

Dodecaborides are promising high strength ceramic and refractory materials, due to the excellent physical properties. However, the scarce systematic investigations of physical properties of B12M (M=Th, U, Np, Pu) dodecaborides hinder the better applications of these dodecaborides. By means of the first-principles approach, we systemically investigated the phase stability, elastic, anisotropic properties, dynamical stability and thermodynamic properties of B12M (M=Th, U, Np, Pu) dodecaborides. The optimized structure constants are consistent with available experimental data. The values of formation enthalpies and V/V0 under pressure indicate B12M have good phase stability. The elastic parameters and modulus indicate that B12M dodecaborides are all brittle and superhard materials. The results of anisotropic factors, 3D surface contours and 2D projections of B12M indicate that they are all anisotropic, but the extent of anisotropy is relatively small. Anisotropy of acoustic velocities and the 2D planar projections of the minimum thermal conductivity are also calculated and discussed. The lattice dynamic properties indicate that four dodecaborides are all satisfied with the dynamic stability conditions. The relationship between thermodynamic quantity and temperature was calculated and discussed for four dodecaborides.

Biomimetic in situ nucleation of calcium phosphates by protein immobilization on high strength ceramic materials

Zirconia has been commonly used in the dental industry because of its excellent biological, mechanical and aesthetic properties. This material, however, is classified as nearly inert. To bioactivate the ceramic surface, biomimetic depositions of calcium phosphate coatings have been developed. We demonstrate an accelerated biomimetic coating method on zirconia using a specific pre-treatment with biological agents. We have chosen bovine serum albumin as a standard protein. Through the pre-treatment of the zirconia using a hydroxylation or additionally immobilizing the bovine serum albumin on the surface, we could influence the CaP deposition rate. Immunohistochemical analyses verified the presence of BSA on the zirconia surfaces. After immersion in simulated body fluid at 40°C, the samples were analyzed by scanning electron microscopy and X-ray diffraction to visualize the CaP formation. Here we could show as proof-of-principle that it is possible to accelerate biomimetic coating processes on zirconia implants containing BSA on their surface.

Development of High-Strength Glass–Ceramic Materials by Utilization of Slag Discharged from Steel-Making Industry in Korea

Development of High-Strength Glass–Ceramic Materials by Utilization of Slag Discharged from Steel-Making Industry in Korea

All-ceramic materials in dentistry

In dentistry, ceramics are often referred to as nonmetallic, inorganic structures primarily containing compounds of oxygen with one or more metallic or semimetallic elements. They are composed of sodium, potassium, calcium, magnesium, aluminum, silicon, phosphorus, zirconium, and titanium. Structurally, dental ceramics contain a crystal phase and a glass phase based on the silica structure, characterized by silica tetrahedra, containing central Si4+ ion with four O− ions. Biocompatibility, esthetics, durability, and easier customization properties have led to the increased usage of ceramics. The specialty of ceramic teeth is its ability to mimic the natural tooth in color and translucency along with its strength. Ceramics have excellent intraoral stability and wear resistance adding to their durability. Basically, the inorganic composition of teeth and bones are ceramics which is hydroxyapatite. Over the past few years, the technological evolution of ceramics for dental applications has been incredible, as new materials and processing techniques are being introduced. The improvement in strength, as well as toughness, has made it possible to expand the range of indications to long-span fixed partial prostheses, implant abutments, and implants. While porcelain-based materials are still a major component in dental science, there have been moves to replace metal ceramics systems with all-ceramic systems. Numerous all-ceramics are being developed which is highly esthetic, biocompatible to tissue, and long-lasting in nature. Advances in computer-aided design/computer-aided manufacturing technologies have led to immense popularity of high-strength ceramic materials. These materials are highly esthetic, biocompatible to tissue, and long-lasting in nature. In this review, we will discuss all-ceramic materials which are used in dentistry.

The Effect of Physicochemical Surface Treatment Methods on Bond Strength of Zirconia to Resin Cement: A Review of the Literature

Objective: Zirconium oxide has gained the spotlight during the recent years as a high strength ceramic material. However, despite its mechanical superiorities, it forms a weak bond with different synthetic substrates and tissues due to its neutral nature and resistance against chemical agents. Therefore, it is important to improve the bonding technique in order to prevent microleakage and increase retention and fracture resistance of the restoration. Literature Review: Since the discovery of zirconium oxide, several surface treatment methods have been evaluated to increase its bond strength to resin cement such as surface grinding with micro- abrasion, burs or abrasive papers, tribochemical silica coating, silicoating, glass micropearls, glaze- on technique, selective infiltration etching, hot etching and use of phosphate ester monomers. The mentioned techniques and related articles are reviewed and discussed in the present study. Conclusion: Despite extensive studies, no consensus has been reached about a specific treatment as the standard protocol for improving the bond strength of zirconia restorations.

The grinding efficiency by diamond points developed for yttria partially stabilized zirconia

Recently, the use of all-ceramic restorations has increased and been applied for many types of clinical treatment such as bridges which can be made with high strength ceramic material: yttria partially stabilized zirconia (Y-PSZ) employing the CAD/CAM system. Consequently, points that can grind high strength ceramic material effectively are necessary for modifying the shape of restorations or removing them. So in our research, we fabricated new diamond points used to grind Y-PSZ. These points were made by electrodeposition of diamond grains. The diameter of the diamond grains are larger (200 µm) than that of traditional points (100 µm). High strength ceramic material was ground to assess the grinding weight and grinding depth various types of points. As a result, Y-PSZ could be ground efficiently with the diamond point which has a larger diameter and employs lager grains (200 µm).

Laser micro structuring of high-stressed embossing dies

This paper describes the laser micro structuring of forming tools for hot embossing. The laser micro structuring allows the manufacturing of the required structural sizes and structure forms as well as the machining of the applied tool materials which can not be manufactured with conventional processes like milling. Through the systematic investigation of the influences of single laser parameters it is possible to influence the processing of 2-D and 212-D micro fluid geometries. For initial experimental investigations the high strength ceramic material silicon carbide is used.

In vitro shear bond strength of dual-curing resin cements to two different high-strength ceramic materials with different surface texture

Objective. The purpose of this study was to evaluate the shear bond strength (SBS) of two dual-curing resin cements to two high-strength ceramics with different surface texture. Material and methods. Composite cylinders were bonded to aluminum oxide (A) and zirconium oxide (Z) ceramic disks with six different surfaces. Investigated surfaces were for both ceramics: dry-pressed Procera Crown (A1, Z1), machined Procera Bridge (A2, Z2), airborne particle abraded Procera bridge (A3, Z3). Additional surfaces were, for alumina, dry-pressed Procera Laminate (A4) and, for zirconia, two modified surfaces (Z4, Z5). Two adhesive resin cements were used (Clearfil Esthetic and RelyX ARC). SBS was tested in a universal testing machine before and after artificial aging by thermal cycling. Results. Mean SBS ranged from 6.1 to 38.4 MPa before and from 0.0 to 41.4 MPa after aging. Clearfil Esthetic in A3, A4, and Z3 performed better than RelyX ARC. Aging decreased SBS, except for Z1, Z4, and Z5. For alumina, A4 was higher in SBS than A2, but similar to A1 and A3. For zirconia, Z5 showed the highest SBS. Z4 was higher than Z2 and Z3, but similar to Z1. Conclusions. Shear bond strength to alumina and zirconia increases with surface roughness. The modified zirconia surface Z5 provides stable long-term shear bond strength and can be bonded to either of the two used cements.

Studies on mechanical strength, thermal expansion of layering porcelains to alumina and zirconia ceramic core materials

The aim of this study was to evaluate and clarify the various mechanical properties and behavior of layering porcelains (Tokuyama Dental Ceramic, IPS Empress 2, Cerabien, Vitadura, Creation) used for veneering high-strength ceramic core materials. The layering porcelains studied exhibited the following range of mechanical properties: compressive strength at 586-1091 MPa, bending strength at 30-97 MPa, diametral tensile strength at 16-28 MPa, Vickers hardness at 481-647 Hv, and fracture toughness at 1.36-2.05 MPa x m1/2. Results of this study indicated that the mechanical shortcomings of conventional porcelain, such as brittleness and hardness, have been overcome by the enhanced mechanical properties of layering porcelain, resulting in improved fracture toughness.

Influence of preparation of ceramic SEVNB specimens on fracture toughness testing results

Objectives Fracture toughness K Ic is an important mechanical property of dental ceramics. One of the most reliable methods to determine the fracture toughness of a ceramic material is the single-edge V-notched-beam (SEVNB) method. The objective of the study is to reveal and quantify the influence of the notch root radius on the fracture toughness value proved on the high strength ceramic material zirconia. Methods Bar specimens ( n = 16) made of high strength zirconia ceramics (3Y-TZP) were notched by a diamond charged cutting wheel. The notch roots were sharpened using the razor blade method with systematically varying notch root radii. The critical stress intensities as a function of the respective notch root radii of all specimens were determined in flexural strength test. Results The notch root radii showed a pronounced effect on the determined fracture toughness values. Notch root radii between 18 and 167 μm were produced. The respective determined fracture toughness values varied between 5.9 and 13.6 MPam 0.5. Significance It is of decisive importance to sharpen the notch root radius of a SEVNB specimen to determine the true fracture toughness value. If the notch root radius is above a critical value, the measured fracture toughness value will be overestimated.

English

The paper presents the study of the particle size distribution, surface area and their effect on sintering of alumina ( Al 2 O 3 ) using additives such as magnesium oxide ( MgO) and silica ( SiO 2 ), so that the samples could be sintered to high relative density (~ 97.43 %) with controlled grain growth. However, the use of MgO along with SiO 2 on Al 2 O 3 produced the powder compacts having high Green density, sintered density with minimum porosity to achieve high dielectric strength ceramic material, so that material can be used for high-voltage insulator applications.

Fracture resistance of single-tooth implant-supported all-ceramic restorations: An in vitro study

High-strength ceramic materials can be used to fabricate esthetic and stable implant-supported single-tooth restorations. No study was identified that compared the fracture resistance of individual components of single-tooth implant-supported all-ceramic restorative systems after artificial aging. The purpose of this in vitro study was to evaluate the fracture resistance of single-tooth implant-supported all-ceramic restorations consisting of alumina all-ceramic restorations on different implant abutments and to identify the weakest component of the restorative system. Forty-eight standardized maxillary central incisor alumina crowns (Procera) were fabricated for each of the 3 test groups (n = 16) (Control group Ti, titanium abutments; Group Al, alumina abutments; Group Zr, zirconia abutments) for the Replace implant system. The crowns were adhesively luted using a resin luting agent (Panavia 21) and artificially aged through dynamic loading and thermal cycling. Afterwards, all specimens were tested for fracture resistance using compressive load on the palatal surfaces of the crowns. Kruskal-Wallis analysis of variance and post hoc Wilcoxon rank sum tests were performed to test for differences in fracture resistance values (alpha = .05). All test specimens survived the artificial aging process using simulated oral conditions. No screw loosening was recorded. The median fracture resistance was 1454 N, 422.5 N, and 443.6 N for groups Ti, Al, and Zr, respectively. Significant differences were found for the fracture resistance comparisons of group Ti with groups Al and Zr (Kruskal-Wallis test, P < .001). The test results for the comparison of groups Al and Zr were not significant. All 3 implant-supported restorations have the potential to withstand physiologic occlusal forces applied in the anterior region.

Mechanical properties of commercial high strength ceramic core materials

Objective. The objective of the present study is to evaluate and compare the flexural strength, dynamic elastic moduli and true hardness ( H o) values of commercial Vita In-Ceram ® alumina core and Vita In-Ceram ® matrix glass with the standard aluminous porcelain (Hi-Ceram ® and Vitadur ®), Vitadur N ® and Dicor ® glass and glass-ceramic. Methods. The flexural strength was evaluated ( n=5) using 3-point loading and a servo hydraulic Instron testing machine at a cross head speed of 0.5 mm/min. The density of the specimens ( n=3) was measured by means of the water displacement technique. Dynamic Young's shear and bulk moduli and Poisson's ratio ( n=3) were measured using a non-destructive ultrasonic technique using 10 MHz lithium niobate crystals. The true hardness ( n=3) was measured using a Knoop indenter and the fracture toughness ( n=3) was determined using a Vickers indenter and a Tukon hardness tester. Statistical analysis of the data was conducted using ANOVA and a Student–Newman–Keuls (SNK) rank order multiple comparative test. Results. The SNK rank order test analysis of the mean flexural strength was able to separate five commercial core materials into three significant groups at p=0.05. Vita In-Ceram ® alumina and IPS Empress ® 2 exhibited significantly higher flexural strength than aluminous porcelains and IPS Empress ® at p=0.05. The dynamic elastic moduli and true hardness of Vita In-Ceram ® alumina core were significantly higher than the rest of the commercial ceramic core materials at p=0.05. Significance. The ultrasonic test method is a valuable mechanical characterization tool and was able to statistically discriminate between the chemical and structural differences within dental ceramic materials. Significant correlation was obtained between the dynamic Young's modulus and true hardness, p=0.05.