Ionic Radius Ratio Research Articles

Fabrication and Phase Transition of La2-X Lu x Zr2O7 Transparent Ceramics

Materials with A2B2O7 formula have been drawing the attention of researchers for a diversity of applications, such as fast-ion conductors, photocatalysts, thermal barrier coatings, matrices for immobilization of highly active radionuclides from nuclear wastes and host materials for scintillators. A2B2O7 materials have three crystal phases decided by the ionic radius ratios (r A/r B). According to the rule of Subramanian et al [1], pyrochlore phase was favored when r A/r B lay within the range of 1.46~1.78. Defective fluorite phase is stable for r A/r B < 1.46, whilst the monoclinic phase is stable for r A/r B > 1.78. In this study, a new series of La2-x Lu x Zr2O7 (x = 0~2.0) transparent ceramics [2] with high density and average atomic number, which are hoped to be scintillator matrix, were fabricated by vacuum sintering and an interesting phenomenon was found. As Lu content increased, the crystal phase gradually transformed from pyrochlore to defective fluorite phase with the existence of a two-phase region (x = 0.6 ~ 1.2) (Figure 1). The appearance of a two-phase region illustrated that Subramanian’s theory is not available when there is large difference in ionic radii of the elements that occupy at Ln position (r La 3+ = 1.160 Å, r Lu 3+ = 0.977 Å). In addition, the grain growth of pyrochlore phase was inhibited due to the appearance of defective fluorite phase. Grain sizes of samples dominated by pyrochlore phase were 11~14 μm. Samples with two phases (x = 0.6~1.2) have much smaller grain sizes (< 3 μm), while samples dominated by defective fluorite phase have larger grain sizes (82~60 μm). All the samples (except for x = 0) are transparent and the highest in-line transmittance is reached to 72.4% (1100 nm) at x = 1.2 though two phases coexist. To verify that the two-phase region was not an accident, we fabricated LaLuZr2O7 powder by combustion method instead of solid state reaction and sintered in the same way. From XRD results, two phases are observed in both the synthesized powder and ceramic. Also, With 2 ~ 3 μm average grain size, the LaLuZr2O7 ceramic reaches high transparency with an in-line transmittance of 73.4% at 1100 nm, which is slightly higher than that made by solid state reaction method, showing the advantage of combustion method in synthesizing good powder. Rayleigh-Gans-Debye scattering theory was used to explain the high transmittance of the ceramics with two phases. When the refractive indices of the coexisting two phases are close to each other and the average grain size is smaller than 10 μm, the two phases have little influence on transparency of the ceramics. [1] Subramanian MA, Aravamudan G, Subba Rao GV. Oxide pyrochlores-A review. Prog Solid State Chem 1983, 15: 55-143. [2] Z.J. Wang, G.H. Zhou, X.P. Qin, F. Zhang, J.P. Ai, P. Liu, S.W. Wang. Fabrication and phase transition of La2-xLuxZr2O7 transparent ceramics. J Eur Ceram soc 2014, 34: 3951–3958. Figure 1

Growth of Ag3Sn and Sn Nanoparticles Based on the Variation of Reaction Conditions

Tin and tin-based nanoalloys especially Sn-3.5Ag (wt.%) eutectic alloys have been prepared by numerous methods as the promising alternative solder in electronic packaging application. However, issues of agglomeration and oxidation emerged owing to shrinking size of nanoparticles. In this study, the Sn/Ag3Sn nanoparticles as small as 10[Formula: see text]nm have been synthesized successfully through chemical reduction method. Concentration of precursor and reducing agent have been studied so as to control the reaction rate, thus achieving the optimized conditions avoiding agglomeration. A centralized size distribution has been achieved by separating nucleation and growth periods. It has been revealed that the obtained nanoparticles are composed of [Formula: see text]-Sn and Ag3Sn which represent a successful co-reduction. [Formula: see text]-Sn and Ag3Sn NPs have various average size for their distinct critical nucleation radius and disparate mole ratio of Sn and Ag. The [Formula: see text]-Sn surface has almost 4-nm thick amorphous tin oxide layer but Ag3Sn surface has not, because the lattice distortion caused by the replacement of silver by tin hinders the diffusion of oxygen, improving oxidation resistance and dispersing performance.

Stabilization of Face-Centered Cubic High-Pressure Phase of REH3 (RE = Y, Gd, Dy) at Ambient Pressure by Alkali or Alkaline-Earth Substitution.

Heavy rare-earth trihydrides such as GdH3, DyH3, and yttrium trihydide (YH3) usually show a hexagonal crystal structure under ambient pressure. This structure is known to transform to a face-centered cubic (FCC) one at higher pressures (at the order of GPa), and the FCC one returns to the hexagonal structure when the applied pressure is released. In this study, we investigated the structure of alkaline or alkaline-earth (A)-substituted REH3 (RE = Y, Gd, Dy; A = Li, K, or Mg) using X-ray diffraction, and measured the phase transition pressure. We found that this FCC high-pressure phase can be stabilized by 10-33 mol % A substitution for RE in the REH3. The mechanism of phase stabilization is simply explained by the ionic radius ratio between the cation and anion ( rcat/ rani), as well as the stabilities of other ionic crystals such as perovskite materials. For all considered REH3 samples, the FCC phase becomes stable when rcat/ rani > 0.856, such as in the case of 10 mol % Li-substituted YH3.

Soot Oxidation Activity of Redox and Non-Redox Metal Oxides Synthesised by EDTA–Citrate Method

In the present study, redox (CeO2, SnO2, Pr6O11 and Mn3O4) and non-redox (Gd2O3, La2O3 ZrO2 and HfO2) metal oxides were successfully synthesised using the EDTA–citrate complexing method and tested for soot oxidation activity. The characterization of the metal oxides is carried out using FTIR, XRD, BET surface area, pore volume analyser, SEM and TEM. The redox nature and metal–oxygen bond information of the metal oxides are obtained from XPS analysis. In redox metal oxides, three critical parameters [lattice oxygen binding energy, reduction temperature and Δr (ionic size difference of the corresponding metal oxide oxidation states)] govern the soot oxidation activity. Among the redox metal oxide samples, Mn3O4 and Pr6O11 samples showed lower binding energy for oxygen (Oβ—529.4, 528.9 eV respectively), lower reduction temperature (Tα—317 and 512 °C respectively) and have smaller Δr value (9 pm and 17 pm respectively). Thus, displayed a better soot oxidation activity (T50 = 484 and 482 °C respectively) than compared to other redox metal oxides. Among the non-redox metal oxides, HfO2 sample displayed higher BET surface area (21.06 m2/g), lattice strain (0.0157), smaller ionic radius (58.2 pm) and higher relative surface oxygen ratio (58%) and thus resulted in a significantly better soot oxidation activity (T50 = 483 °C) than compared to other non-redox metal oxides.

Synthesis and crystal structure of LiNbO3-type Mg3Al2Si3O12: A possible indicator of shock conditions of meteorites

LiNbO 3 -type Mg 2.98(2) Al 1.99(2) Si 3.02(2) O 12 (py-LN) was synthesized by recovering a run product from 2000 K and 45 GPa to ambient conditions using a large volume press. Rietveld structural refinements were carried out using the one-dimensional synchrotron XRD pattern collected at ambient conditions. The unit-cell lattice parameters were determined to be a = 4.8194(3) A, c = 12.6885(8) A, V = 255.23(3) A 3 , with Z = 6 (hexagonal, R 3 c ). The average A -O and B -O distances of the A O 6 and B O 6 octahedra have values similar to those that can be obtained from the sum of the ionic radii of the averaged A - and B -site cations and oxygen (2.073 and 1.833 A, respectively). The present compound has the B -site cations at the octahedral site largely shifted along the c axis compared with other LiNbO 3 -type phases formed by back-transition from perovskite (Pv)-structure, and as a result, the coordination number of this site is better described as 3+3. It appears therefore that the B -site cation in the octahedral position cannot be completely preserved during the back-transition because of the small size of Si and Al, which occupy usually a tetrahedral site at ambient conditions. The formation of py-LN can be explained by the tilting of B O 6 octahedra of the perovskite structure having the pyrope composition and formed at high P-T conditions. The tilting is driven by the decrease in ionic radius ratio between the A -site cation and oxygen during decompression. This also explains why there is no back-transition from the Pv-structure to the ilmenite-structure during decompression, since this is a reconstructive phase transition whose activation energy cannot be overcome at room temperature. Py-LN may be formed in shocked meteorites by the back-transformation after the garnet-bridgmanite transition, and will indicate shock conditions around 45 GPa and 2000 K.

Correlation Selection Of Perovskites With Optimal Parameters

A descriptor is constructed to predict the composition of ABO3 perovskites that do not contain transition metals and have a high level of ionic conductivity (). The descriptor consists of two parts: the ratio of ionic radii, RA/RB and the ratio of ionization potentials, VB/VA for A- and B- cations. Parameters for 100 perovskite compounds were considered to find the correlation dependences between the descriptor and the magnitude of. Correlation selection approach is proposed to reveal a suitable correlation series. This approach allows determining the composition of perovskites that has a desirable ionic conductivity. Copyright © 2016 VBRI Press.

Investigation of polyaniline films doped with Fe3+ as the electrode material for electrochemical supercapacitors

H+ and Fe3+ ions co–doped polyaniline were synthesized by cyclic voltammetry onto the stainless steel mesh with various concentration of ferric chloride (FeCl3·6H2O) in electrolyte. The structure and morphology of PANI and PANI/Fe3+ films were characterized by Fourier transform infrared (FT–IR), X-ray diffraction (XRD), Scanning electron microscopy (SEM), Energy dispersive X-ray spectroscopy (EDS) and X-ray photoelectron spectroscopy (XPS) techniques. The electrochemical properties of PANI and PANI/Fe3+ films were investigated by cyclic voltammetry, galvanostatic charge–discharge test and electrochemical impedance spectroscopy (EIS) in 0.5molL−1 H2SO4 electrolyte in three–electrode system. The PANI/0.2M Fe3+ film shows a larger specific capacitance of 602F g−1 at a current density of 3mA/cm2 and lower resistance compared with the pure PANI film. The relationship between electrochemical properties of a serious of transition metal ions doped PANI/Mn+ (Mn+=Mn2+, Co2+, Ni2+, Cu2+, Zn2+ and Fe3+) films and the ratio of electronic affinity and ionic radius (Ea/r) has also been researched.

Synchrotron x-ray diffraction analysis of gadolinium and lanthanum titanate oxides irradiated by xenon and tantalum swift heavy ions

ABSTRACTA synthetic cubic pyrochlore, Gd2Ti2O7 (Fd3̅m) irradiated with swift heavy ions is compared with a compositionally-related composition La2Ti2O7 (P21), which has a monoclinic, layered, perovskite-type structure. Irradiation experiments were performed at the GSI Helmholtz Center with 181Ta ions and 129Xe ions at specific energies of 11MeV/amu. At these energies the ions pass entirely through the sample thickness of ∼ 40 μm. Angle-dispersive synchrotron powder x-ray diffraction (XRD) measurements were completed and an increasing ion-induced amorphization with increasing ion fluence was for both phases. The ion track cross-sections for the radiation-induced crystalline-to-amorphous transformation, as determined from the evolution of the integrated peak intensities as a function of fluence, reveal that La2Ti2O7 (track diameter, d ∼ 7.2 nm with 181Ta and 5.1 nm with 129Xe) is more susceptible to amorphization than Gd2Ti2O7 (d ∼ 6.2 nm with 181Ta and 4.6 nm with 129Xe). The radiation response of the two titanate compounds can be understood in the context of their different structures and cation ionic radius ratios rA/rB, where the susceptibility of radiation of titanate pyrochlores is proportionate with this radius ratio. The higher electronic linear energy loss of the 181Ta ions as compared with 129Xe ions leads to a consistent increase of volume amorphized per ion in both materials, which manifests as a larger track diameter.

Higher-order asymptotic result for the wrinkling of an everted Varga spherical shell

This paper applies the WKB method to the buckling analysis of an everted spherical shell composed of Varga material. The same problem has been studied by Haughton and Chen in 2003, but they only obtained the leading-order value for the critical radius ratio B/A because they did not seem to realize that the second-order ODE with variable coefficients satisfied by the eigenfunctions could be solved explicitly, where A and B are the inner and outer radii of the undeformed sphere. In the current paper, we managed to find the leading-order and next-order eigenfunctions explicitly in the WKB expansion, and hence obtained two more terms in the asymptotic expansion of B/A. We believe that the same idea can be employed to find the eigenfunctions at higher orders.

Transformation from pyrochlore to fluorite by diffraction and X-ray spectroscopy

We have studied the long-range average and local structures in a number of zirconium containing materials of the type A2B2O7 ( A = Ln or Y; B = Zr, Hf or Sn) using synchrotron X-ray and neutron powder diffraction and X-ray absorption spectroscopy. Studies of the system Gd2-xTbxZr2O7 include neutron diffraction data, obtained at λ ≍ 0.497 Å to minimise absorption, not only provide evidence for independent ordering of the anion and cation sublattices, but also suggest that the disorder transition across the pyrochlore-defect fluorite boundary of Ln2Zr2O7 is rather gradual. In general we observe that while the diffraction data indicate a clear phase transition from ordered pyrochlore to disordered defect-fluorite at specific compositions corresponding to a critical ionic radius ratio of the A and B cations (rA/rB) x ~ 1.0-1.2, X-ray absorption near-edge structure (XANES) results reveal a gradual structural evolution across the compositional range. These findings provide experimental evidence that the local disorder occurs long before the pyrochlore to defect-fluorite phase boundary as determined by X-ray diffraction, and the extent of disorder continues to develop throughout the defect-fluorite region. Where possible the experimental results were supplemented by ab initio atomic scale simulations, which provide a mechanism for disorder to initiate in the pyrochlore structure. Further, the coordination numbers of the cations in both the defect-fluorite and pyrochlore structures were predicted, and the trends agree well with the experimental XANES results. X-ray absorption measurements at the Zr L3-edge, which showed a gradual increase in the effective coordination number of the Zr from near 6-coordinate in the pyrochlore rich samples to near 7-coordinate in the defect fluorites.

Twin primary rainbows scattering by a liquid-filled capillary

The twin primary rainbows scattered by a liquid-filled capillary are investigated with Debye theory and geometric optics. From the numerical simulations, a critical radius ratio of the core to the coating of the coated cylinder is proposed to judge the existence of the α and β supernumerary bows. When the ratio is less than or around the critical value, the α and β supernumerary bows disappear. On the premise that the α and β supernumerary bows exist, the β rainbow can always be detected. However, the α supernumerary bows sometimes submerge in the other scattering structure so that the α rainbow cannot be detected under this condition. Four frequency peaks in the angular frequency spectrum of the twin primary rainbows are investigated numerically. Furthermore the relationship between F3 (the third frequency peak which is similar to the ripple frequency of the scattering by a homogeneous cylinder) and the external radius of the capillary is obtained. Experiments are carried out to verify the numerical works with capillary filled with deionized water.

Selective behaviour of dilute Fe3 + ions in silicate glasses: an Fe K-edge EXAFS and XANES study

Iron K-edge EXAFS and XANES have been used to study the local structural environment of dilute quantities (0.2mol% Fe2O3) of Fe3+ in seven representative SiO2–R2O–R’O glasses where R=(Li, Na, K), R’=(Mg, Ca, Sr, Ba). Sample preparation was carried out by adding excess CeO2 as an oxidising agent and it was confirmed by optical absorption spectroscopy that iron was fully oxidised to Fe3+. This methodology has made possible, for the first time, an unambiguous EXAFS study of the coordination and local structural environment of dilute levels of Fe3+ in alkali–alkaline earth–silica glasses without the complications presented by the presence of Fe in multiple oxidation states. Coordination of Fe3+ in these glasses is strongly affected by the nature of the alkali and alkaline earth cations, with Fe3+–O CN increasing from 4.0±0.4 to 6.2±0.9 with decreasing alkali/alkaline earth ionic radius ratio (IRR). Respective FeO bond lengths of 1.87±0.01Å to 1.92±0.01Å were also obtained. Dilute Fe3+ in the studied glasses displays selective behaviour, as demonstrated by the opposing effects of alkali and alkaline earth ions on measured Fe3+ CN and Fe3+O bond length.

Numerical study of heat loss from a non-evacuated receiver of a solar collector

Heat loss from receivers of solar collectors is a major reason for drop in their efficiency. Receiver pipes enclosed in glass tubes with evacuated annulus show considerable reduction in heat losses. However, manufacturing and maintenance costs for such receivers are high. An inexpensive alternative is a similar receiver with non-evacuated annulus. This paper presents a numerical study of heat loss from a non-evacuated receiver typically used in parabolic trough collectors, generating moderate temperatures and designed particularly for process heat applications. In order to come closer to the realistic situation, rather than assuming uniform temperature distribution on it, receiver pipe temperature has been assumed to be varying along the surface. Sinusoidal and square wave functions are employed in modeling, since actual temperature distributions on solar receiver pipes are combinations of these two functions. Main goal of the paper is to optimize the design of the non-evacuated solar receiver for minimum heat loss, by using CFD technique. Also effects on heat loss from receivers due to different parameters like average temperature (Ta) of the pipe, non-uniformity in the temperature (α) along its surface, hour angle (γ), denoting position of the sun in the sky and radius ratio (RR) of radius of receiver pipe to that of outer glass tube have been studied. It is seen that as non-uniformity in temperature distribution increases in both types of temperature distribution, heat losses from receiver pipes decrease up to 10%. Also as hour angle increases from 0° to 90°, heat loss decreases by 20% in case of sinusoidal temperature distribution and 24% in case of square wave temperature distribution. The effect of radius ratio (RR) on heat loss has been studied. In present study, we found out that 1.375 is critical radius ratio for which heat losses from receiver are minimum

Natural Convection in a Spherical Porous Annulus: The Brinkman Extended Darcy Flow Model

The present study reports results of a numerical investigation of natural convection in a spherical porous annulus. The inner and outer surfaces are subjected to constant temperatures. The Brinkman extended Darcy flow model is considered in this study. The problem has been solved numerically employing successive accelerated replacement scheme. The effect of parameters like Rayleigh number, Darcy number and radius ratio on the fluid flow and heat transfer has been examined. There exists a critical radius ratio $$(\mathrm{rr} = 3)$$ at which the average Nusselt number attains a peak value. The average Nusselt number decreases as the Darcy number increases.

Preparation, characterization and thermophysical properties of (Sm1−xGdx)2Ce2O7 solid solutions

Sm2Ce2O7 has low thermal conductivity and relatively high thermal expansion coefficient which make it suitable for application as high-temperature thermal barrier coatings. (Sm1−xGdx)2Ce2O7 solid solutions were synthesized by solid state reaction in this paper. The influence of Gd2O3-doping on the phase structure and thermophysical properties were investigated. The synthesized (Sm1−xGdx)2Ce2O7 ceramics exhibit a defect-fluorite structure, which is mainly determined by ionic radius ratio r(Aav3+)/r(B4+). The linear thermal expansion coefficients and thermal conductivities of different (Sm1−xGdx)2Ce2O7 decrease with the increasing value of x in the measuring temperature. Their thermal expansion coefficients are higher than that of 8YSZ, the thermal conductivities of (Sm1−xGdx)2Ce2O7 ceramics at 1000°C are located within the range of 1.07–1.69W/mK. The composition dependence of thermal conductivity was discussed by taking into account the phonon scattering by mass and strain fluctuations at the A site.

Non-axisymmetric annular curtain stability

A stability analysis of non-axisymmetric annular curtain is carried out for an axially moving viscous jet subject in surrounding viscous gas media. The effect of inertia, surface tension, gas-to-liquid density ratio, inner-to-outer radius ratio, and gas-to-liquid viscosity ratio on the stability of the jet is studied. In general, the axisymmetric disturbance is found to be the dominant mode. However, for small wavenumber, the non-axisymmetric mode is the most unstable mode and the one likely observed in reality. Inertia and the viscosity ratio for non-axisymmetric disturbances show a similar stability influence as observed for axisymmetric disturbances. The maximum growth rate in non-axisymmetric flow, interestingly, appears at very small wavenumber for all inertia levels. The dominant wavenumber increases (decreases) with inertia for non-axisymmetric (axisymmetric) flow. Gas-to-liquid density ratio, curvature effect, and surface tension, however, exhibit an opposite influence on growth rate compared to axisymmetric disturbances. Surface tension tends to stabilize the flow with reductions of the unstable wavenumber range and the maximum growth rate as well as the dominant wavenumber. The dominant wavenumber remains independent of viscosity ratio indicating the viscosity ratio increases the breakup length of the sheet with very little influence on the size of the drops. The range of unstable wavenumbers is affected only by curvature in axisymmetric flow, whereas all the stability parameters control the range of unstable wavenumbers in non-axisymmetric flow. Inertia and gas density increase the unstable wavenumber range, whereas the radius ratio, surface tension, and the viscosity ratio decrease the unstable wavenumber range. Neutral curves are plotted to separate the stable and unstable domains. Critical radius ratio decreases linearly and nonlinearly with the wavenumber for axisymmetric and non-axisymmetric disturbances, respectively. At smaller Weber numbers, a wider unstable domain is predicted for non-axisymmetric modes. For both axisymmetric and non-axisymmetric modes, the disturbance frequency is found to be the same and equal to the negative of axial wavenumber. Finally, comparison between theory and existing experiment leads to good qualitative agreement. A more accurate comparison is not possible given the difference in flow conditions.

Dynamical separation of spherical bodies in supersonic flow

AbstractAn experimental and computational investigation of the unsteady separation behaviour of two spheres in Mach-4 flow is carried out. The spherical bodies, initially contiguous, are released with negligible relative velocity and thereafter fly freely according to the aerodynamic forces experienced. In experiments performed in a supersonic Ludwieg tube, nylon spheres are initially suspended in the test section by weak threads which are detached by the arrival of the flow. The subsequent sphere motions and unsteady flow structures are recorded using high-speed (13 kHz) focused shadowgraphy. The qualitative separation behaviour and the final lateral velocity of the smaller sphere are found to vary strongly with both the radius ratio and the initial alignment angle of the two spheres. More disparate radii and initial configurations in which the smaller sphere centre lies downstream of the larger sphere centre each increases the tendency for the smaller sphere to be entrained within the flow region bounded by the bow shock of the larger body, rather than expelled from this region. At a critical angle for a given radius ratio (or a critical radius ratio for a given angle), transition from entrainment to expulsion occurs; at this critical value, the final lateral velocity is close to maximum due to the same ‘surfing’ effect noted by Laurence &amp; Deiterding (J. Fluid Mech., vol. 676, 2011, pp. 396–431) at hypersonic Mach numbers. A visualization-based tracking algorithm is used to provide quantitative comparisons between the experiments and high-resolution inviscid numerical simulations, with generally favourable agreement.

Effect of Ca substitution on phase compositions and dielectric properties of Bi2O3–ZnO–Nb2O5 pyrochlore ceramics

Abstract The phase evolution, microstructure and dielectric properties in the Ca 2+ substituted Bi 2 O 3 –ZnO–Nb 2 O 5 system were studied. The crystalline phases of the [Bi 1.8 (Ca x Zn 1− x ) 0.2 ](Zn 0.6 Nb 1.4 )O 7 pyrochlores (0.0≤ x ≤1.0) depend greatly on the ratio of ionic radius A/B. With the Ca 2+ substitution for Zn 2+ in the A site, the crystalline phase transformed from cubic to monoclinic and pure monoclinic phase was obtained for x ≥0.5. As the x value increased from 0.5 to 1.0, the permittivity in the microwave range decreased from 76.4 to 75.0, the quality factor Qf value increased from 1800 to 4700 GHz, and the TCF value shifted from −99 to −147 ppm/°C.

Effect of Uncertainties in Physical Properties on Entropy Generation Between Two Rotating Cylinders With Nanofluids

In this paper, the effects of uncertainties in physical properties on predicting entropy generation for a steady laminar flow of Al2O3–ethylene glycol nanofluid (0≤φ≤6 %) between two concentric rotating cylinders are investigated. For this purpose, six different models by combining of three relations for thermal conductivity (Bruggeman, Hamilton–Crosser, and Yu–Choi) and two relations for dynamic viscosity (Brinkman and Maiga et al.) are applied. The governing equations with reasonable assumptions in cylindrical coordinates are simplified and solved to obtain analytical expressions for average entropy generation (NS)ave and average Bejan number (Be)ave. The results show that, when the contribution of heat transfer to entropy generation for the base fluid is dominant, a critical radius ratio (ΠC) can be determined at which all six models predict the reduction in entropy generation with increases of volume fraction of nanoparticles. It is also found that, when the contribution of viscous effects to entropy generation is adequately high for the base fluid (φ=0), all models predict the increase of entropy generation with increases of particle loading.

Analysis on autofrettage of cylinders

Autofrettage is an effective technique to improve load-bearing capacity and safety for pressure vessels. For autofrettaged cylinder, the depth of plastic zone, or overstrain is a key factor which affects load-bearing capacity and safety. The previous research on overstrain was not done in terms of the point of view of raising load-bearing capacity as far as possible and simultaneously avoiding compressive yield for cylinders experiencing autofrettage handling, and there were no analytic solutions of autofrettage in the above view point presented, the 3rd and 4th strength theories were not applied synthetically in the research to compare the results from these two theories. In this paper, with the aid of the analytic method, based on summing up the authors’ previous research, results from autofrettage of a cylinder based on the 3rd and 4th strength theories are studied and compared, and the laws contained in the results are looked into. Then, the essential cause and reason for the obtained laws are analyzed and the inherent and meaning relations between various parameters in autofrettage theory are revealed. It is shown that the maximum radius ratio for equivalent residual stress at inside surface never exceeds the yield strength even for a cylinder experiencing wholly yielded autofrettage, or the critical radius ratio is k c=2.218 457 489 916 7…, irrespective of the 3rd or 4th strength theories. The equation relating the depth of plastic zone with the thickness of a cylinder is identical for the 3rd and 4th strength theories. In form, the optimum load-bearing capacity of an autofrettaged cylinder is two times the initial yield pressure of the unautofrettaged cylinder irrespective of the 3rd or 4th strength theory. The revealed inherent relations between various parameters and varying laws of the parameters as well as the forms of the relations under the 3rd and 4th strength theories not only have theoretical meanings but also have prospects in engineering application.