Isomorphic Systems Research Articles

The Cu-Ni-Y (Copper-Nickel-Yttrium) System

The Cu-Ni system [Massalski2] (Fig. 1) is a simple isomorphous system with a continuous liquid solution separated by a narrow two-phase region from a continuous solid solution. The face centered cubic (fcc) solid solution of Cu and Ni (c), however, undergoes a short range order transformation at temperatures less than 300 C. The Cu-Y system [Massalski2] (Fig. 2) has five intermediate phases, Cu6YðgÞ;Cu4YðdÞ;Cu7Y2ðhÞ;Cu2YðiÞ; and CuYðt1Þ; of which the d; i; and t1 phases melt congruently at 975, 935, and 935 C, respectively. The g and h phases form through peritectic reactions L + dM g at 910 C and L + dM h at 920 C. Four eutectic reactions: L $ c þ g; L $ h þ i;L $ i þ t1; and L M c + e occur at 860, 840, 830, and 770 C, respectively. e is the terminal solid solution (aY). A metastable phase of composition Cu5Y was found to form through rapid quenching of a liquid alloy. The h; i; and t1 phases are of invariant compositions. The Ni-Y system [1991Nas] (Fig. 3) has nine intermediate phases: Ni17Y2(f), Ni5Y(x), Ni4Y(j), Ni7Y2(q), Ni3Y(p), Ni2Y(k), NiY(s), Ni2Y3(w), and NiY3(n). The Ni5Y(x) and NiY(s) phases melt congruently at 1430 and 1070 C, respectively. All the other phases form through peritectic reactions: L + x M f at 1350 C, L + x M j at 1340 C, L + j M q at 1298 C, L + q M p at 1237 C, L + p M k at 1106 C, L + s M w at 820 C, and L + e M n at 902 C, where e is the terminal solid solution (Y). All the intermediate phases are of invariant compositions. Three eutectic reactions L M f + c, L M k + s, and L M w + n occur at 1085, 950, and 805 C, respectively.

The Co-Ni-Sn (Cobalt-Nickel-Tin) System

The Co-Ni system [1991Nas] (Fig. 1) is a simple isomorphous system. In the fcc a solid solution, there are indications of formation of short range order near the CoNi3 composition. The Co-Sn system [1983Nis, Massalski2] (Fig. 2) has three intermediate phases, Co3Sn2 in two allotropic forms, Co3Sn2(HT) and Co3Sn2(LT); CoSn; and CoSn2. The Co3Sn2 phase melts congruently at 1170 C and the other two phases form through peritectic reactions L + Co3Sn2(HT)MCoSn at 936 C and L + CoSn M CoSn2 at 525 C. Co3Sn2(HT) fi Co3Sn2(LT) transformation occurs at 500 C. Two eutectic reactions L M (aCo) + Co3Sn2(HT) and L M CoSn2 + (bSn) occur at 1112 and 229 C, respectively. The fcc (aCo) fi hcp (eCo) reaction, possibly a eutectoid type reaction, occurs at 420 C. The Ni-Sn system [1991Nas, Massalski2] (Fig. 3) has three intermediate phases, Ni3Sn and Ni3Sn2, both of which exist in two allotropic forms, and Ni3Sn4. Both Ni3Sn2 and Ni3Sn phases melt congruently at 1264 and 1174 C, respectively, and the Ni3Sn4 phase forms through a peritectic reaction L + Ni3Sn2 M Ni3Sn4 at 795 C. Three eutectic reactions L M (Ni) + Ni3Sn(HT), L M Ni3Sn(HT) + Ni3Sn2(HT), and L M Ni3Sn4 + (bSn) occur respectively at 1130, 1160, and 231 C. The Ni3Sn(LT) phase forms through a congruent transformation at 977 C. The Ni3Sn2(HT) fi Ni3Sn2(LT) transformation occurs at 600 C.

The Co-Ni-Si (Cobalt-Nickel-Silicon) System

The Co-Ni system [Massalski2] (Fig. 1) is a simple isomorphous system with liquidus and solidus temperatures very close to each other. The face centered cubic (fcc) solid solution of (aCo, Ni), designated here as c phase, possibly has a short range ordering reaction at the CoNi3 composition. At the Co-end, the fcc aCo transforms to close packed hexagonal (cph) eCo phase at T 422 C: The Co-Si system [Massalski2] (Fig. 2) has five intermediate phases, Co3SiðiÞ; aCo2SiðdÞ; bCo2SiðqÞ;CoSiðgÞ; and CoSi2 (f), of which the bCo2Si, CoSi, and CoSi2 phases melt congruently at 1334, 1460, and 1326 C; respectively. The Co3Si and aCo2Si phases form through peritectic reactions, L + d$ i at 1214 C and L + qM d at 1320 C: The cph (eCo) phase is stabilized to higher temperatures with addition of Si to Co and at 1250 C a peritectic reaction, L + (aCo)M (eCo), occurs. The Co3SiðiÞ and bCo2Si (q) phases exist only at higher temperatures and decompose through eutectoid reactions, i $ ðeCoÞ þ d at 1193 C and qM d + g at 1286 C. The four eutectic reactions L $ ðeCoÞ þ i;L $ q þ g;L $ g þ f; and LM f + (Si) occur at 1204, 1286, 1310, and 1259 C; respectively. The CoSi2 phase is of invariant composition. The Ni-Si system [Massalski2] (Fig. 3) has eight intermediate phases, Ni3Si (b1), Ni3Si (b2 and b3), Ni31Si12ðcÞ;Ni2SiðdÞ;Ni2SiðhÞ;Ni3Si2ðe and e0Þ;NiSiðnÞ; and NiSi2ðf and f0Þ; of which several phases, b2 and b3, e and e0 and f and f0; exist in polymorphic forms with polymorphic transformation temperatures of 1115, 830, and 981 C; respectively. The b1, b3, d, e¢, and f0 phases form through peritectic or peritectoid reactions: Lþ c0 $ b3 at 1178 C, L + hM d at 1255 C;Lþ ðSiÞ $ f0 at 993 C; ðNiÞ þ b2 $ b1 at 1035 C; and h + nM e¢ at 845 C: There are eight eutectic or eutectoid reactions in the Ni-Si system: LM (Ni) + b3 at 1145 C;L $ c0 þ d at 1215 C, L $ h þ n at 964 C, L $ n þ f at 966 C; b2 $ b1 þ c0 at 990 C; h $ d þ e0 at 825 C; e0 $ d þ e at 820 C; and e0 $ e þ n at 800 C: The c0; d; n and f phases are single composition phases.

Controlling Cu⋯Cu distances using halides: (8-phenylthionaphth-1-yl)diphenylphosphine copper halide dimers

In the isomorphous binuclear Cu2X2L2 systems (L = (8-phenylthionaphth-1-yl)diphenylphosphine the Cu...Cu separation is reduced as the halide size increases.

Electrochemical Properties of TiN and ZrN Coated Ti-Hf Alloy

The Ti-Hf alloy system forms α-β isomorphous system and does not form any intermetallic compounds, which is also beneficial for good mechanical properties. And in order to avoid the release of materials, surface modifications are generally carried out to form a TiN and ZrN layer on the surface. Electrochemical properties of TiN and ZrN coated Ti-Hf alloy by RFsputtering has been researched using various electrochemical methods. Ti-10wt%, 20wt%, 30wt%, and 40wt% Hf alloys manufactured by non consumable vacuum arc melting furnace. All the specimens were heat treatment at 1000°C for 24hr in Ar atmosphere followed by furnace cooling, respectively. The specimens were coated with TiN and ZrN respectively, by RF-magnetron sputtering method. The microstructures were conducted by using OM, EDX and SEM. The corrosion tests were carried out using potentiodynamic(PARSTAT 2273, EG&G, USA) and potentiostatic test in 0.9% NaCl solution at 36.5 ±1 °C. Microstructure clearly observed that lamellar structure translated to needle-like structure with increased Hf contents. From the analysis of TiN and ZrN coated layer analysis, TiN and ZrN coated surface showed columlar structure with 600nm and 100nm thickness, respectively. The corrosion resistance of TiN and ZrN coated Ti alloys were higher than those of the non-coated Ti-alloy in 0.9%NaCl solution, indicating better protective effect.

Path-integral simulations beyond the adiabatic approximation

Within the adiabatic approximation, it is trivial to generalize existing imaginary time path-integral techniques to the case of multiple electronic surfaces. However, there are many times where nonadiabatic effects can play an important role. To this end, we reformulate the well-known path-integral expressions to incorporate multiple potential surfaces, without necessitating the adiabatic approximation. We show that the resulting expression, like its adiabatic counterpart, can be interpreted in terms of a simple classical isomorphic system and thus is amenable to simulation through Monte Carlo techniques. We derive simple expressions to compute expectation values of a general operator in both the nuclear coordinate and electronic state, and demonstrate the existence of a simple internal diagnostic that can be used to evaluate the magnitude of equilibrium nonadiabatic effects.

Muon spin rotation and relaxation studies on the solid solution of the two spin-gap systems(CH3)2CHNH3−CuCl3and(CH3)2CHNH3−CuBr3

Muon-spin-rotation and relaxation studies have been performed on (CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$ with $x$=0.85 and 0.95, which are solid solutions of the two isomorphic spin-gap systems (CH$_3$)$_2$CHNH$_3$CuCl$_3$ and (CH$_3$)$_2$CHNH$_3$CuBr$_3$ with different spin gaps. The sample with $x$=0.85 showed a clear muon spin rotation under zero-field below $T_{\rm N}$=11.65K, indicating the existence of a long-range antiferromagnetic order. A critical exponent of the hyperfine field was obtained to be $\beta$=0.33, which agrees with 3D-Ising model. In the other sample with $x$=0.95, an anomalous enhancement of the muon spin relaxation was observed at very low temperatures indicating a critical slowing down due to a magnetic instability of the ground state.

Quasiconformal dimensions of self-similar fractals

The Sierpinski gasket and other self-similar fractal subsets of \mathbb R^d , d\ge 2 , can be mapped by quasiconformal self-maps of \mathbb R^d onto sets of Hausdorff dimension arbitrarily close to one. In \mathbb R^2 we construct explicit mappings. In \mathbb R^d , d\ge 3 , the results follow from general theorems on the equivalence of invariant sets for iterated function systems under quasisymmetric maps and global quasiconformal maps. More specifically, we present geometric conditions ensuring that (i) isomorphic systems have quasisymmetrically equivalent invariant sets, and (ii) one-parameter isotopies of systems have invariant sets which are equivalent under global quasiconformal maps.

Partial phase diagram of the Au–Ag–Zr ternary system

On the basis of Au–Ag, Au–Zr and Ag–Zr binary phase diagrams, the 700 °C isothermal section of the gold–silver-rich field in the Au–Ag–Zr ternary system was established by X-ray diffraction analysis, electron probe microanalyses (EPMA) and optical microscopy. It is found that there is the long single-phase region, Au(Ag) or Ag(Au), along the Au–Ag binary isomorphous system on the gold–silver-rich side of the 700 °C isothermal section. The solid solubility of Zr in Au(Ag) decreases with the silver content of Au(Ag). It is confirmed that the partial 700 °C isothermal section consist of five single-phase regions: solid solution Au(Ag) or Ag(Au), Au 4Zr, Au 3Zr, Au 2Zr and AgZr; seven two-phase regions: Au 4Zr + Au(Ag), Au 3Zr + Au(Ag), Au 2Zr + Au(Ag), Au 4Zr + Au 3Zr, Au 3Zr + Au 2Zr, AgZr + Au(Ag) and AgZr + Au 2Zr; three three-phase regions: Au 4Zr + Au 3Zr + Au(Ag), Au 3Zr + Au 2Zr + Au(Ag) and Au 2Zr + AgZr + Au(Ag). No new ternary compound is formed in the gold–silver-rich field of the Au–Ag–Zr ternary system.

Comparison of the Impurity Effects on Lattice Dynamics in K2SnCl6 between Isomorphic and Nonisomorphic Systems Near the Structural Phase Transition Temperature Revealed by Nuclear Resonance

Nuclear resonance studies of the two different types impurity doped potassium hexachloro-stannates, the isomorphic system such as (K-Rb)2SnCl6 and K2(Sn-Re)Cl6 and the nonisomorphic system K2SnCl6:Al3+ in the high temperature cubic phase revealed contrasting features with one the other characterized by static in the former and dynamic feature in the latter case respectively. The resonance spectra of the nonisomorphic system indicate additionally a sign of the local structural transition above the conventional structural phase transition temperature. This seems to be triggered by the ligand-deficient octahedral defects and can be explained in terms of the enhanced activity of the octahedral defects for the hindered rotation.

The Cu-Ni-Pd (copper-nickel-palladium) system

The Cu-Ni system [1991Nas] (Fig. 1) is a simple isomorphous system with a possible phase separation below ∼300 °C. The Cu-Pd system [Massalski2] (Fig. 2) is a simple isomorphous system at high temperatures. The fcc (Cu, Pd) phase, however, undergoes transformation below 600 °C to give two phases and with congruent transformation temperatures of 598 and 508 °C, respectively. Between the two phases and two long period superlattice phases with one dimensional (1D) and two dimensional (2D) antiphase domain structures exist. A eutectoid type reaction ↔ (2D) + has been suggested to exist at ∼400 °C. The Ni-Pd system [1991Nas] (Fig. 3) is an isomorphous system with a solidus/liquidus minimum of 1237 °C at 45.4 at.% Pd. At 700 °C the experimental results suggest the possible existence of short range order/clustering in the fcc (Ni, Pd) phase.

Influence of Quantum Zero Point Energy on the Ferroelectric Behavior of Isomorphous Systems

The influence of the relative amount of zero point energy in the double potential wells associated with reorientable dipoles in ferroelectric systems has been investigated. The quantitative dependence of the dielectric constant ε, the saturation polarization PS0 and the critical temperature TC as a function of zero point energy =łΩ0/2 = kBTS was determined from the appropriate quantum effective field expressions and available data from TSCC (ferroelectric at T < TC ≅131 K) and TSCB (quantum paraelectric at T ≈ 0 K) were analyzed.

Liquid–solid phase equilibrium study of tetradecane and hexadecane binary mixtures as phase change materials (PCMs) for comfort cooling storage

Phase diagrams (equilibrium diagrams) are a convenient way of depicting the concentration–temperature–pressure relationships of a chemical system at equilibrium. They are invaluable to PCMs thermal storage researches and developers. In the present paper, the liquid–solid phase equilibrium of binary mixture system of tetradedcane and hexadecane has been studied. For theoretical evaluation of the thermodynamic equilibrium between the liquid phase and solid phase of tetradecane and hexadecane, several methods were compared: the UNIFAC group-contribution method, the model of Won, and Pedersen’s model. The temperature–composition phase diagram of the binary system has been obtained by the calculation. The diagram illustrates a binary, isomorphous system with a temperature minimum. Differential scanning calorimetry (DSC) was used to study the phase transformation of the binary system. DSC was run at different ramp rates and results indicate that these mixtures melt and freeze over a temperature range and the temperature range depends on the DSC ramp rate, and in a short mixture concentration interval appears low temperature solid–solid peaks. From the DSC results presented, it is concluded that the behaviour of binary mixtures of n-alkanes is far more complicated than considered in earlier studies. The phase diagram and all information from DSC are very important for designing PCM storage system.

The Co-Mo-Ta (Cobalt-Molybdenum-Tantalum) system

The Co-Mo system [Massalski2] (Fig. 1) shows the presence of four intermediate phases: Co9Mo2, Co3Mo, Co7Mo6 ( ), and . The and phases form through peritectic reactions L + ↔ at 1620 °C and L + ↔ at 1510 °C. is the bcc terminal solid solution of Co in Mo. A eutectic reaction L ↔ + occurs at 1335 °C, being the fcc terminal solid solution of Mo in Co. Three peritectoid reactions + ↔ Co9Mo2, Co9Mo2 + ↔ , and possibly + ↔ , where is near Co3Mo and is the cph terminal solid solution of Co, occur at 1200, 1025, and 700 °C, respectively. The Co9Mo2 and phases undergo eutectoid decomposition Co9Mo2 ↔ + Co3Mo at 1018 °C and ↔ + at 1000 °C. The Co–Ta phase diagram is given by [1967Ram] and [1986Bar], and adopted by [Massalski2] (Fig. 2) and [1996Gar]. While [1996Gar] (Fig. 3) gives only a partial diagram at the Co end, the phase diagram given by [Massalski2] shows the presence of six intermediate phases: (Co7Ta2, three Laves phases ( 1, 2, and 3), Co6Ta7, and CoTa2. [1967Ram] also showed the presence of the same six phases given by [1986Bar], but also indicated the presence of two more high temperature (T > 1300 °C) phases near 60 at.% Ta. According to the Co-Ta diagram given by [Massalski2], the CoTa2 and the 3 phases form through peritectic reactions L + ↔ CoTa2 at 1800 °C, where is the bcc terminal solid solution of Co in Ta, and L + 2 ↔ 3 at 1450 °C. The 2 and 2 phases melt congruently at 1620 and 1700 °C, respectively. The 1 and Co7Ta2 phases form through peritectoid reactions 2 + 2 ↔ 1 at 1540 °C and 3 + ↔ Co7Ta2 at 950 °C. Three eutectic reactions L ↔ 2 + CoTa2, L ↔ 2 + 2 and L ↔ + 3 occur at 1670, 1570, and 1280 °C, respectively. The 1 phase undergoes eutectoid transformation 1 ↔ 2 + 2 at 1130 °C. Neither [Massalski2] nor [1996Gar] give any reaction through which the fcc phase changes to the cph phase. [1967Ram] suggested a peritectoid reaction + Co7Ta2 ( ) ↔ at 1000 °C. But according to [Massalski2], the Ta7Co2 phase is stable only below 950 °C, suggesting that the phase formation temperature possibly is below 950 °C. The Mo-Ta system is a simple isomorphous system [Massalski2] (Fig. 4) giving rise to a bcc solid solution phase extending from Mo to Ta.

On Dynamics Related to a Class of Numeration Systems

In this paper, we investigate the class of numeration systems 1, 1+q, 1+q + q2, ...(q⩾2) and we study the associated dynamical systems, called odometers. It is shown that these odometers are measure-theoretically isomorphic to rank one transformations on the unit interval, constructed by a cutting-stacking method. Furthermore, a symbolic coding leads to isomorphic shift systems arising from substitutions. Some skew products of the odometers by cocycles related to the sum of digits are shown to be ergodic.

Structural Analyses and Magnetic Properties of Multiple-Structure Multilayered Co/Au Films

AbstractIn the interfaces of multilayered Co/Au and Co/Pd films, there were some interesting changes with annealing. For profile fittings, which is a comparison between measured peaks of X-ray diffraction and calculated peaks of the extended 3-step model profile fittings, the mixed layers between Co layers and noble metal layers were decreased in Co/Au films while increased in Co/Pd films. These results are based on the difference that Co-Au is a eutectic system while Co-Pd is an isomorphous system. This time, as new research, we fabricated multiple-structure multilayered Co/Au films (MSM Co/Au films). Magnetic properties and structural analyses were carried out with a vibrating sample magnetometer (VSM), X-ray diffraction (XRD), and extended 3-step model profile fittings. MSM Co/Au films have two periodic thicknesses. MSM Co/Au films showed the same perpendicular magnetization as Co/Au and Co/Pd films, which is dependent on the Co layer thickness. Perpendicular magnetization showed the maximum value after 1 h-annealing at 473 K. It was well confirmed that the mixed layers decreased at this annealing condition with the extended 3-step model profile fittings.

On Implementation of Logical Time in Distributed Systems Operating over Wireless Data Networks

We address the problem of maintaining logical time in a distributed system operating over a wireless data network. In such a network a group of mobile nodes currently located in a specific area use services of a mobility service agent to communicate with each other and with the rest of the world. The graph model of the network is represented by fully-connected mesh of star-topology subgraphs. We discuss the complementary logical clocks for the wireline and wireless segment of the network and their integration into an isomorphic logical time system.

Path integral molecular dynamics method based on a pair density matrix approximation: An algorithm for distinguishable and identical particle systems

In this paper, the path integral molecular dynamics (PIMD) method has been extended to employ an efficient approximation of the path action referred to as the pair density matrix approximation. Configurations of the isomorphic classical systems were dynamically sampled by introducing fictitious momenta as in the PIMD based on the standard primitive approximation. The indistinguishability of the particles was handled by a pseudopotential of particle permutation that is an extension of our previous one [J. Chem. Phys. 112, 10 116 (2000)]. As a test of our methodology for Boltzmann statistics, calculations have been performed for liquid helium-4 at 4 K. We found that the PIMD with the pair density matrix approximation dramatically reduced the computational cost to obtain the structural as well as dynamical (using the centroid molecular dynamics approximation) properties at the same level of accuracy as that with the primitive approximation. With respect to the identical particles, we performed the calculation of a bosonic triatomic cluster. Unlike the primitive approximation, the pseudopotential scheme based on the pair density matrix approximation described well the bosonic correlation among the interacting atoms. Convergence with a small number of discretization of the path achieved by this approximation enables us to construct a method of avoiding the problem of the vanishing pseudopotential encountered in the calculations by the primitive approximation.

The Co-Cr-Ti system (cobalt-chromium-titanium)

Co3Cr, Co2Cr, and Co3Cr2, have been suggested to form from Introduction the e phase, as shown in Fig. 1b. The Co-Ti system (Fig. 2), taken from [Mass2] and origiThe Co-Cr-Ti system has been studied mostly near the nally assessed by [1987Mur], shows the presence of five Co corner where a ternary intermediate phase x, with a-Mn intermediate phases, Co3Ti, Co2Ti (h), Co2Ti (c), CoTi, and type crystal structure, has been found to exist. Two partial CoTi2, of which the Co2Ti (c) is a cubic Cu2Mg-type Laves isothermal sections, a few partial isopleths, and a liquidus phase and the Co2Ti (h) is a hexagonal MgNi2-type Laves projection have been reported for the Co corner. Only one phase. The CoTi phase melts congruently at 1325 8C, and isothermal section has been reported for the Cr corner of all the other phases form from the liquid through peritectic the Co-Cr-Ti system. Further investigation is required to reactions: L 1 CoTi } CoTi2 at 1058 8C, L 1 CoTi } Co2Ti establish proper phase equilibria for the complete Co-Cr(c) at 1235 8C, L 1 Co2Ti (c) } Co2 Ti (h) at 1210 8C, and Ti system. L 1 g } Co3Ti at 1190 8C. Two eutectic and one eutectoid reactions occur, L } Co2Ti (h) 1 Co3Ti at 1170 8C, L } a 1 CoTi2 at 1020 8C, and a } v 1 CoTi2 at 685 8C, where a and v are the bcc and hcp terminal solid solutions of (bBinary Systems Ti) and (a-Ti), respectively. The Cr-Ti system (Fig. 3), taken from [Mass2] and origiThe Co-Cr phase diagram in Fig. 1a is from the review nally reviewed by [1987Mur], shows an isomorphous system of [1990Gup] based on [1978All]. It shows a eutectic reaction with a minimum of 1408 8C at ,60 at.% Ti. Two Laves L } a 1 g at 1397 8C, where a and g are the terminal phases, cubic Cr2Ti (c) and hexagonal Cr2Ti (h) form from solid solutions of bcc (Cr) and fcc (Co), respectively. An the solid solution a phase at slightly different compositions. intermediate s phase forms from the bcc a solid solution The Cr2Ti (h) phase exists in two allotropic forms Cr2Ti (hh) congruently at 1283 8C. The fcc g phase transforms to hcp and Cr2Ti (hl), where hl and hl refer to the high-temperature e phase, terminal solid solution of hcp (Co), through a peritecMgZn2-type structure and low-temperature MgNi2-type toid reaction g 1 s } e at 967 8C. A eutectoid reaction a } g 1 s occurs at 1266 8C. Three more intermediate phases, structure which differ only in atomic layering. The Cr2Ti (hh)

14N NQR Studies of Impurity Effects on the Local Structure of NaNO2 -based Mixed Systems

The influence of impurities on the 14N NQR lineshape of Na1-xAgxNO2 and [NaNO2]1-x-[BNO3]x (B = Na, K) at room temperature has been investigated. Carrying out spectral analysis in conjunction with classification of the local field inhomogeneities according to the structurally isomorphic, Na1-xAgxNO2 , and anisomorphic [NaNO2]1-x[BNO3]x systems, enabled an under-standing of the microscopic nature of impurity-induced local disorder. The iso-and anisomorphic systems reveal their own unique features of the impurity induced local disorder. They are charac-terized by a static, random distribution of impurities in the isomorphic system and a fast motion of the impurity-induced mobile point defects in the anisomorphic system. However, for both systems, neither a change of the 14N NQR frequency nor a multisplitting of the lines is observed because of the relatively low symmetry.