An analysis was conducted on the possibility of making an assessment of the degree of plastic deformation ε in X2CrNi18-9 steel by measuring three electromagnetic diagnostic signals: the Barkhausen noise features, the impedance components in in-series LCR circuits, and the residual magnetic field components. The impact of ε on a series of different extracted features of diagnostic signals was investigated. The occurrence of two regions of sensitivity was found for all the features of the analysed signals. The two regions were separated by the following critical deformation value: ε ~ 10% for the components of the residual magnetic field and ε ~ 15% for the normalised components of impedance. As for the Barkhausen noise signal, the values were as follows: ε ~ 20% for the mean value, ε ~ 20% for the peak value of the signal envelope, and ε ~ 5% for the total number of the signal events. Metallographic tests were performed, which revealed essential changes in the microstructure of the tested material for the established critical values. The martensite transformation occurring during the plastic deformation process of X2CrNi18-9 austenitic steel process generated a magnetic phase. This magnetic phase was strong enough to relate the strain state to the values of diagnostic signals. The changes in the material electromagnetic properties due to martensitic transformation (γ → α’) began much earlier than indicated by the metallographic testing results. Research is now being conducted in many scientific centres on methods that will enable the determination of the effect of cold plastic strain ,2,3,4, mAustenitic steels are widely used materials, and the strain-induced martensite transformation occurring in them, depending on the chemical composition, the magnitude of the rolling reduction, and the deformation temperature can have both favourable effects causing the material strengthening (a higher yield point or an increase in tensile strength) and unfavourable consequences causing a decrease in corrosion resistance and the appearance of the ferromagnetic phase ,13,14,15Novotný et al.  introducO’Sullivan et al.  characteIn , the autIn , the autr). Magnetic measurements based on austenite instability detection in mechanical and thermal correlations are an alternative to ultrasonic wave attenuation tests. Moreover, they give a more complete picture of the wear degree of the retaining ring .In , the autVincent et al.  investigIn , AISI 31In , the autAugustyniak et al.  tested sThis paper is focused on the analysis of the possibility of characterizing the plastic—strain ratio in specimens made of X2CrNi18-9 steel by measuring the residual magnetic field, the impedance components in in-series LCR circuits, and the Barkhausen noise. The same measurement quantities were used to characterise the active stress state in . AdditioThe authors of this paper have often used magnetic methods of non-destructive testing to solve various problems related to the broadly understood characterisation of the material state. For this reason, the theoretical foundations have already been presented many times. A synthetic description of the theoretical basis related to this article is included in , where aIn chromium-nickel alloy steels, e.g., X5CrNi18-10, X2CrNi18-9, or X18CrNiSi18-9, depending on the concentration of Cr and Ni and other alloying elements , an austenitic structure occurs in the supersaturated state at room temperature. The austenitic structure gets stabilised with an increase in Ni and other austenitic elements. In addition, the structure may also contain some ferromagnetic ferrite δ arising due to the conditions of steel crystallization. Depending on the amount of alloying elements, the ferrite content may increase up to several percent. To evaluate the structure and compactness of the magnetic phase, equivalents of austenite- and ferrite-forming elements can be used. This indicates that the chemical composition of steel itself has a direct impact on the content of the magnetic phase, which can be changed, usually increased, by heat treatment, strain due to cold or hot working, or by welding processes.s, or due to critical plastic deformation at temperatures higher than Ms. Due to the chemical composition, temperature Ms is lower than room temperature, which ensures high durability of austenite. Austenitic steels are commonly used materials, and the strain-induced martensite transformation occurring in them can have both favourable effects strengthening the material and unfavourable consequences resulting in a decrease in their corrosion resistance and the appearance of the ferromagnetic phase [Austenitic Fe-Cr-Ni steels in the post-supersaturation state retain the austenitic structure (γ-phase) with a face-centred cubic (fcc) lattice. Depending on the chemical composition, austenite can be a metastable phase undergoing martensite transformation at cooling below temperature Mic phase ,11,12,13ε and ferromagnetic martensite α’ with a body-centred cubic lattice [Due to cold plastic strain, austenitic chromium-nickel steels undergo significant strengthening depending on their chemical composition, the magnitude of the rolling reduction, and the deformation temperature. Under the influence of cold plastic strain, a change occurs in the dislocation structure. As a result, metastable austenite undergoes a partial transformation into martensite  lattice ,13. A si lattice ,37: one −2 [The factor deciding about the possibility of martensite ε formation is the austenite stacking fault energy (SFE), which depends on the steel chemical composition and the deformation temperature. Martensite ε can be created during cold plastic deformation if the SFE at room temperature is <30 MJm−2 . The SFE−2 , the for−2 , which mThe testing was performed for flat specimens made of X2CrNi18-9 steel . The test conditions were as follows: temperature: 21 ± 2 °C and the traverse speed: 2 mm/min. After the set value of deformation was achieved, the specimens were unloaded and examined beyond the machine on the test stand, keeping the same orientation of the specimen in relation to the Earth’s magnetic field. Relative deformation was defined for an 80 mm long section of the specimen  were measured using the TSC-2M  measuring head. The measuring apparatus was calibrated in the magnetic field of the Earth, with the assumed value of 40 A/m. The measurements on the test stand were always carried out in the same place and with the same position of the specimen. The magnetic field components in the location where the measurements were performed had the following values: HT = 8 A/m, HN = 40 A/m. The magnetic field strength was measured along the measurement line  was used for RMF measurements. For RMF, two components . The system diagram is shown in The Barkhausen noise was measured only in two directions: perpendicular  working  and from working ,41.The absolute values of the Barkhausen noise parameters are calculated using the following Equation (1):The metallographic examination was conducted to verify the changes in the material indicated in the NDT test. To avoid the influence of the directionality of the ferrite bands, the tested material was sampled transversely to the rolling direction. The deformed part was sectioned using a precise cut-off machine , and intensive cooling was applied.3 water solution. Due to the applied preparation method, local etch defects, so-called etch pits, were observed on the surface of the metallographic specimens. XRD was performed in a D8 Advance Diffractometer  using CuKα radiation; the magnetic phase (the content of the strain-induced martensite α’-phase) was measured using the MPD-100A magnetic field detector .The metallographic observations were conducted using light microscopy  and scanning electron microscopy . The specimens were pre-ground using water abrasive paper and then polished and etched electrolytically  to avoid the influence of the effect of abrasive papers on the surface of the specimen. A cross-sectional microscopic examination was carried out after polishing and electrolytic etching in a 10% CrOHardness measurements were performed using the Vickers method with an intender load of 10 kG (98.07 N), with a Zwick/Roell ZHU 187.5 hardness tester .The tested steel was characterised by an austenitic structure, with a small content of ferrite δ arranged in the steel rolling direction. The structure showed only a few twin boundaries —T increased, while the curves of normal component HN in the plastically deformed region made an anticlockwise rotation. In the place of transition from the deformed to the non-deformed region, local extrema occurred of both tangential component HT /ωL0, ωL/ωL0 becomes unequivocally visible only when plastic deformation reaches the level of about 15% and higher. For frequencies in the range from 0.1 kHz to 10 kHz, an increase in the plastic deformation degree was accompanied by a rise in the value of ωL/ωL0, while for the frequency of 100 kHz, ωL/ωL0 first increased until the plastic deformation degree reached the level of about 15% to show a decreasing trend later on. A constant trend in changes in the (R − R0)/ωL0 component occurred only at frequencies f equal to 1 kHz and 10 kHz for plastic deformation degrees higher than 15%.In An analysis was performed of the possibilities of developing a correlation between the plastic deformation degree and the Barkhausen noise signal. The Barkhausen noise was measured for 10 magnetisation cycles. Two halves could be distinguished in a single magnetisation cycle cf. —the firsRMS, the envelope of the BN signal , and the distribution of the total number of events NoETOT. The formula for RMS voltage URMS was described in [TOT was characterised in [The following BN quantitative parameters were analysed: the RMS voltage value Uribed in , and therised in ,17.BNi voltage pulses. A multiple smoothing filtering operation using the Savitzky–Golay filter was used for this purpose. The envelope was characterised by local extrema, which could be described using their coordinates defining the magnetisation current PEAKPOS and the Barkhausen noise voltage PEAKVAL, which are graphically presented in The BN envelope was obtained through the smoothing averaging operation on the absolute values of the URMS) is shown in RMS values from plastic deformation ε of about 20%, both for the parallel and the perpendicular direction  on ε for close-to-zero positive and negative values of voltage Ug. It could be assumed that above ε ~ 5%, two NoETOT values corresponded to a given deformation state, identifying this state unequivocally. This made it possible to develop a solution to an inverse problem—the evaluation of the plastic deformation degree based on the number of total events NoETOT.VAL, the values of which were analysed for the descending and ascending halves of the magnetisation. The relations between ε and PEAKVAL for the descending halves of the magnetisation are shown in VAL values were observed; in the range of ε from 5 to 20%, these changes were slight, after ε = 20% a significant increase in PEAKVAL values was observed. For the perpendicular direction, clear changes could be seen when the plastic deformation degree exceeded ε ~30% ; after 10% deformation, the magnetic phase increased only up to 1.4 ± 0.1%. An increase in deformation to 20% caused a rise in the magnetic phase content to about 3.0 ± 0.1%, and after 40% deformation to about 14.8 ± 0.1%. The observed increase should be considered to be a value included within the measurement error. The presence of α’, as the effect of deformation, is visible in the XRD analysis. The diffraction lines for the material in the delivery condition (DC) revealed only the γ-phase. Changes could be observed in the diffraction diagrams for the steel post-deformation state in comparison to the DC. An increase in the specimen deformation decreased the intensity of austenite lines, and new martensite lines appeared, whose intensity increased with deformation .The considered issue of the evaluation of plastic deformation based on changes in electromagnetic quantities is one of the so-called inverse problems of non-destructive testing.Three case studies were presented, in which the following diagnostic signals were used: the residual magnetic field components, the impedance components of the in-series LCR circuit, and the Barkhausen noise features. The changes in microstructure and the resulting changes in electromagnetic properties generated diagnostic signals with an averaged and repeatable value that could be captured using relatively wide-range measuring transducers .RMS, PEAKVAL, and NoETOT parameters it was ε ~ 20%, ε ~ 20%, and ε ~ 5%, respectively. The differences in the critical deformation value were due to the specificity of the signal individual features. At the same time, they indicated that the changes in the material physical properties  began much earlier compared to what was suggested by the results of magnetic phase measurements . However, in the case of deformation higher than critical, where the martensite transformation began, it was possible to use them to evaluate the state of the material. The critical deformation degree determined, based on the performed analyses of diagnostic signals, was as follows: for the RMF ε ~ 10%, the LCR ε ~ 15%, and for the Uents cf. . Based oThe NDT results were verified by metallographic examination. In the tested X2CrNi18-9 steel, the ferromagnetic phase—ferrite δ—was present in small amounts already in the non-deformed state. As the deformation increased, and then after a certain critical strain was exceeded, a clear increment in the total share of ferromagnetic phases occurred due to the occurrence of martensite transformation and the formation of martensite α’, as revealed by the XRD and hardness testing.While typical testing methods showed that the content of the magnetic phase was relatively small even at high deformation (40%), the assessment based on the discussed diagnostic signals made it possible to reveal those changes even for the deformation degree as low as 10–15%. Structural changes (LM and SEM) related to the presence of slip bands were observed already at the deformation degree of 10%, with their density causing significant scattering of diagnostic signals. It was only when the strain exceeded the critical deformation degree of 10% that the martensite transformation (γ → α’) occurred and, thereby, a significant amount of the magnetic phase appeared. In 10% deformation, the content of the magnetic phase increased from 0.2% to 1.4%. This value rose up to 14.8% for 40% deformation. The wide range of results provided by the magnetic field detector led to the conclusion that the content of the magnetic phase strongly depends on the strain rate and the material condition , which indicates that varying conditions of the operating environment can result in different content of the magnetic phase and cause differences in the received diagnostic signals. The presence of the phase, related to the occurrence of the phase transformation, involved the occurrence of signals strong enough to be interpreted and used in diagnostic works aiming to evaluate the state of steel.The changes in the ferromagnetic phase during plastic deformation of austenitic steels created an opportunity to assess the state of austenitic steel using electromagnetic non-destructive testing methods. The obtained results were unique to the analysed cases. Depending on the properties of the measuring apparatus and its calibration, the initial state of the material, and many other influencing factors , the obt


R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 2-generator property. In the present paper, we study the arithmetic of stable integral domains, with a focus on arithmetic properties of semigroups of ideals of stable orders in Dedekind domains.A commutative ring  A non-zero ideal R). The domain R is called (finitely) stable if every non-zero (finitely generated) ideal of R is stable. By definition, invertible ideals are stable and this implies that Dedekind domains are stable and Prüfer domains are finitely stable. On the other hand, stable domains need neither be noetherian, nor one-dimensional, nor integrally closed. For background on stable rings, their applications, and for results till 2000 we refer to the survey [Motivated by a paper of Bass , Lipman,e survey  by Olbere survey , 44–47.R is a BF-domain  if a = bc with set of atoms of H and we say that H is atomic if every non-unit is a finite product of atoms. Two elements associated if a = bc for some k is a factorization length and the set a is called the set of lengths of a. For convenience, we set system of sets of lengths of H,Let elasticity is accepted if H ishalf-factorial if it is atomic and monoid if it is atomic and each element of H is divisible by only finitely many non-associated atoms, andan FF-monoid if it is atomic and all sets of lengths are finite.a BF-We say that the H is atomic but not half-factorial, then we have By definition, an atomic monoid is half-factorial if and only if H is cancellative, H. We denote byseminormal closure of H, and bycomplete integral closure of H.Suppose that H is seminormal  if A is a divisorial ideal  if A is an s-ideal if A = AH. If s-ideal of H, then prime s-ideal of H if for all s-ideal I of H let radical of I. The monoid H is said to beMori if it satisfies the ascending chain condition on divisorial ideals,Krull if it is a completely integrally closed Mori monoid,monoid if the intersection of all non-empty prime s-ideals is non-empty,a G-primary if strongly primary if finitely primary (of rank s and exponent α) if H is a submonoid of a factorial monoid Then H be a primary Mori monoid, H is strongly primary.) Mori monoids and strongly primary monoids are BF-monoids.Finitely primary monoids and primary Mori monoids are strongly primary.  primary, seminormal, completely integrally closed) if its monoid R is primary if and only if R is one-dimensional and local. The domain Rfinite character if every non-zero element is contained in only finitely many maximal ideals.has divisorial if every non-zero ideal is divisorial.is h-local if R has finite character and every non-zero prime ideal of R is contained in a unique maximal ideal of R.is By a One-dimensional Mori domains have finite character by [S be an integral domain such that R is an order in S if S is a finitely generated R-module. Moreover, the following statements are equivalent if R is not a field [R is an order in a Dedekind domain.R is one-dimensional noetherian and the integral closure R is a finitely generated R-module.Let quadratic if R-module between R and S is a ring. If R. Thus every quadratic extension is an integral extension.The extension 3.In this section, we first gather main properties of stable domains –3.5. TheR be a domain. A non-zero ideal stable if it is invertible as an ideal of the overring R. The domain is called finitelystable if every non-zero (finitely generated) ideal of R is stable. Since invertible ideals are obviously stable, Dedekind domains are stable and Prüfer domains are finitely stable. Conversely, if R is completely integrally closed and stable, then R and R is a Dedekind domain. Recall that R is an almost Dedekind domain if R is a Dedekind domain if and only if R is a stable almost Dedekind domain. In particular, every almost Dedekind domain that is not a Dedekind domain is not stable. For an example of an almost Dedekind domain that is not a Dedekind domain we refer to [Let Proposition 3.1.Let R be a domain that is not a field. Then the following statements are equivalent.R is a one-dimensional stable domain.R is a finitely stable Mori domain.R is a stable Mori domain.Proof.This is due to Gabelli and Roitman. More precisely, the equivalence of (a) and (b) is proved in [R is a Prüfer domain. Next we consider the local case.Examples given by Olberding in , 46 showCorollary 3.2.Let R be a local domain that is not a field.The following statements are equivalent.R is a one-dimensional stable domain.R is a primary stable domain.R is a stable Mori domain.R is a strongly primary stable domain.If these conditions hold and (b) (c) age 2 of ).(d) R be a domain. By Let R is a local domain whose ideals are 2-generated, then R is finitely stable with stable maximal ideal (e.g. see R is noetherian). Nevertheless, such a domain is  neither half-factorial nor an FF-domain. In what follows, we present suitable counterexamples.Note that if e.g. see  and the K be a quadratic number field with maximal order p be a prime number such that p is split (i.e. p = 2.) Let K with conductor S is a local domain whose ideals are 2-generated and there are precisely two maximal ideals of S. It follows from [S is not half-factorial.  R is noetherian, and thus R is one-dimensional by R is not integrally closed. Since R is not integrally closed, we have that (b) R-module by R is finitely stable.Consequently, R is a one-dimensional stable domain by R is 2-generated by (c) R is said to be weakly Krull ifA domain afrullah , 3, and Theorem 3.7.Let R be a domain with, and suppose that R is either weakly Krull or Mori. Then R is stable if and only if every ideal of R is 2-generated. If this holds, then R is an order in a Dedekind domain.Proof.R is 2-generated, then R is stable by R be stable.If every ideal of R is weakly Krull. Then, for every R is weakly Krull, this implies that R is Mori by [Let us first suppose that R is Mori in both cases. Using R is one-dimensional. Therefore, R is 2-generated. □Thus Corollary 3.8.Let R be a seminormal G-domain and suppose that R is either Mori or one-dimensional. Then R is stable if and only if every ideal of R is 2-generated. If this holds, then R is an order in a Dedekind domain.Proof.R is a seminormal G-domain, Since Example 3.9.K be a field, Y an indeterminate over K, and X an indeterminate over K(Y). Then R is not a valuation domain. By There exist integrally closed one-dimensional local Mori domains which are neither valuation domains nor finitely stable. Let R is a local two-dimensional domain with maximal ideal R is stable as well by [R is not Mori by There exists a seminormal two-dimensional local stable domain. Let R is seminormal. Indeed, we know D is seminormal. Now clearly R is seminormal in D. Therefore, R is seminormal.R which is a BF-domain, whence R is a finitely stable BF-domain that is not Mori . In SecH be a cancellative monoid and K a quotient group of H. An ideal system on H is a map Let r be an ideal system on H. A subset r-ideal if rI = I. Furthermore, a subset r-ideal of H if there is some cJ is an r-ideal of H. We denote by r-ideals, and we define r-multiplication by setting r-multiplication is a reduced semigroup with identity element H. Let r-ideals, r-invertible fractional r-ideals, and r-invertible r-ideals of H with r-multiplication. We denote by s-ideals of H, by r-r-ideals of H, and by r-r-ideals of H. We say that r is finitary if We refer to , 32 for s-system, the v-system, and the t-system. For every ideal system r, we have r is finitary, then H has finite r-character if each r-ideals of H.We will use the R be a domain with quotient field K and r an ideal system on R  for all  (b) for all  (c) The following statements are equivalent.2. is half-factorial.  (a) for all  (b) for all  (c) Ifandfor every, then  (d) H is half-factorial and for every nonprincipalit follows that  (e) Proof.H is finitely primary of rank one, there is some Since 1.(a) mq is a product of a atoms of H and b atoms of H. We infer that 1.(b) 1.(c) H is strongly primary and r-H is r-local, we have that I is a non-empty s-ideal of H, then 2. Note that r-ideal of H, there is some 2.(a) mHq is an r-product of a atoms of r-product of b atoms of 2.(b) 2.(c) 2.(c) H is half-factorial. Let 2.(d) 2.(e) A is principal. Then A = uH for some Case 1. A is not principal. Then Case 2. Observe that some of the semigroups . Thencatenary degree and the monotone catenary degree of H. By definition, we have H is factorial if and only if H is cancellative but not factorial, then, by [H is half-factorial and that Let transfer homomorphism if the following two properties are satisfied.A monoid homomorphism (T 1) u = vw, (T 2) If H is said to be a transfer Krull monoid if it allows a transfer homomorphism θ to a Krull monoid B. Since the identity map is a transfer homomorphism, Krull monoids are transfer Krull, but transfer Krull monoids need neither be commutative (though here we restrict to the commutative setting), nor Mori, nor completely integrally closed. The arithmetic of Krull monoids is best understood (compared with various other classes of monoids and domains), and a transfer homomorphism allows to pull back arithmetical properties of the Krull monoid B to the original monoid H. We refer to the surveys [A monoid  surveys , 28 for H is half-factorial, then All Dedekind domains are transfer Krull and stable. However, there are orders in Dedekind domains that are transfer Krull but not stable  and therWe start with a result on the finiteness of the catenary degree of weakly Krull Mori domains.Theorem 5.1.Let R be a weakly Krull Mori domain.For every, andif and only ifandis local.andIf, thenis a Mori monoid and it is half-factorial if and only if it is transfer Krull.Proof.R is a weakly Krull Mori domain, we have t-Let Since the catenary degree of a coproduct equals the supremum of the individual catenary degrees [Since See [Since H with There are primary Mori monoids H be a finitely primary monoid of rank H and some system H is said to bestrongly ring-like if Let The concept of strongly ring-like monoids was introduced by Hassler , and thenumerical monoid is a submonoid of value monoidA Proposition 5.2.Let R be a local stable Mori domain with. Thenis finitely primary of rankand it is strongly ring-like. If s = 2, thenand if s = 1 and, then the elasticityis accepted withProof.R is one-dimensional. By [R is 2-generated by Proposition 3.5.4, whence R is noetherian. If R, then s = 2, then s = 1. Since By R be a one-dimensional local Mori domain with R is stable, then, by Let Lemma 5.3.Let R be a Mori domain and a G-domain and let I be a divisorial stable ideal of R. Thenfor someProof.I is divisorial and R is a Mori domain, we have that Since every overring of a G-domain is a G-domain, Example 5.4(Stable orders in number fields). 1. Let R is 2-generated, R is a stable order in the Dedekind domain Let K be an algebraic number field, R is stable by a result of Greither [R and 2. Let s and exponent α, with all notation as in s = 1 and by R in a quadratic number field whose localization n but the catenary degree Next we discuss the catenary degree of finitely primary monoids, which has received a lot of attention in the literature. Let ure  holds. By (a) R is a one-dimensional Mori domain, we have that (b) R is a one-dimensional Mori domain, we have that R is of finite character. Furthermore, if R. Let R is a Mori domain and t-finitely generated and locally principal and R.(c) (d) R is a Mori domain, we have that (d) (e) (f) 2. If Thus the claim follows from R be as in Let R is a semilocal domain, then R is not semilocal, then the statements for R. If R is any order in an algebraic number field, then R can be transfer Krull without being half-factorial [By Theorem 5.10.Let R be a stable order in a Dedekind domain.The following statements are equivalent.is transfer Krull.is transfer Krull.is half-factorial.is half-factorial.cmon(I*(R))<∞.has finite elasticity if and only ifis bijective. If this holds, then the elasticity is accepted.Proof.1. This is an immediate consequence of R is an order in a Dedekind domain, R is a weakly Krull Mori domain with non-zero conductor. By 2. Since 3. By [Thus the assertion follows from In Remark 5.11(Structure of sets of lengths and of their unions).R is an order in a Dedekind domain, then sets of lengths of (Structure of sets of lengths) If H be an atomic monoid. For every (Structure of unions of sets of lengths) Let is the union of sets of lengths containing k. The structure theorem for unions of sets of lengths states that there is a bound M such that almost all sets Remark 5.12(On catenary degrees).Remark 5.13. We compare the arithmetic of stable orders with the arithmetic of seminormal orders in Dedekind domains. Note that stable orders need not be seminormal  and semR be a seminormal order in a Dedekind domain and let π is bijective, then π is not bijective, then π is bijective. For stable orders, only one implication is true .R in a Dedekind domain such that The Statements 1.(c) and 1.(d) of L be the field with 16 elements, let X be an indeterminate over L and let R is a local divisorial half-factorial Cohen-Kaplansky domain such that Let Proof.R is a half-factorial local Cohen-Kaplansky domain, K-basis of L and R. Note that R is divisorial by [E of R let S(E) is a K-subspace of V and T(E) is a K-subspace of L.By [A and B are proper ideals of R, then Claim: If A and B be proper ideals of R. First let Let Now let A and B of R such that I = AB. It follows by the claim that K-subspace W of S(A). We infer that Assume that a = 1. Then Case 1: a = y. Then Case 2: Case 3: Case 4: Case 5: Case 6: Case 7: Remark 5.15(Transfer Krull does not imply stability). If R is an order in a Dedekind domain with R such that R has ideals which are not 2-generated. Thus, R is not stable.We construct a seminormal one-dimensional local noetherian domain X be an indeterminate over L, and K-basis of L. Then R-module. Since R is noetherian, and hence Let R itself is local and one-dimensional. Moreover, R is transfer Krull by [Since x0 is the constant term of x), and thus if R is seminormal.Now if y0 is the constant term of y). If Note that x1, y1 be the linear coefficients of x respectively y. Then Assume to the contrary, that


The Ig fold has had a remarkable success in vertebrate evolution, with a presence in over 2% of human genes. The Ig fold is not just the elementary structural domain of antibodies and TCRs, it is also at the heart of a staggering 30% of immunologic cell surface receptors, making it a major orchestrator of cell–cell interactions. While BCRs, TCRs, and numerous Ig-based cell surface receptors form homo- or heterodimers on the same cell surface (in cis), many of them interface as ligand-receptors (checkpoints) on interacting cells (in trans) through their Ig domains. New Ig-Ig interfaces are still being discovered between Ig-based cell surface receptors, even in well-known families such as B7. What is largely ignored, however, is that the Ig fold itself is pseudosymmetric, a property that makes the Ig domain a versatile self-associative 3D structure and may, in part, explain its success in evolution, especially through its ability to bind in cis or in trans in the context of cell surface receptor–ligand interactions. In this paper, we review the Ig domains’ tertiary and quaternary pseudosymmetries, with particular attention to the newly identified double Ig fold in the solved CD19 molecular structure to highlight the underlying fundamental folding elements of Ig domains, i.e., Ig protodomains. This pseudosymmetric property of Ig domains gives us a decoding frame of reference to understand the fold, relate all Ig domain forms, single or double, and suggest new protein engineering avenues. We previously established that ca. 20% of known protein folds/domains are pseudosymmetric , and thahttps://www.rcsb.org/search/browse/symmetry, accessed on 27 August 2021). The symmetric assembly of (chained) protodomains is a general property found in biopolymers beyond proteins, as in RNA riboswitches for example [A pseudosymmetric domain is formed of two or more protodomains, according to an accepted duplication–fusion mechanism , and mul example ,20, demoRemarkably, thinking of an ancient peptide/protein world, a very early investigation of immunoglobulins in sequence space  suggesteAnother early study suggested some “evidence for an ancestral immunoglobulin gene coding for half a domain”  based onFor many Ig domains, and even more so when also considering structurally similar (Ig-like) domains, such as FN3 or Cadherins, the sempiternal question comes back: are these domains evolutionarily related? Do these domains have a common ancestor? For many highly diversified superfold domains ,3,4,31, https://www.ncbi.nlm.nih.gov/Structure/icn3d/full.html?&mmdbid=7fab&bu=1&showanno=1&source=full-feature, accessed on 27 August 2021) [https://structure.ncbi.nlm.nih.gov/icn3d/share.html?JcP3sd1gGfqXEBEM8, accessed on 27 August 2021) [https://www.ncbi.nlm.nih.gov/Structure/icn3d/full.html?&mmdbid=1rei&bu=1&showanno=1&source=full-feature, accessed on 27 August 2021) [Let us briefly review the pseudosymmetric assembly of Ig domains. Twofold (C2) quaternary symmetry has been demonstrated in the very first structural studies on Ig domain dimers, especially of IgV domains ,34,35. Tst 2021)  and can st 2021) , and wasst 2021) .https://structure.ncbi.nlm.nih.gov/icn3d/share.html?ScHMZf2B5i1xQ3JZA, accessed on 27 August 2021) [Multiple different dimeric interfaces have been characterized between IgV domains at the N terminus of cell surface receptors and ligands, where a majority of them interact through their GFCC’ sheets, but in a wide variety of orientations. Other pseudosymmetric parallel dimer interfaces for CTLA-4 or CD28 homodimers on T-cell surfaces, for example, use instead their A’G strands and their hinges beyond their G strand to dimerize, and in doing so free the GFCC’ sheet of both IgV domains to interact with other IgV domains in either cis or trans; in particular, in trans using the GFCC’ sheet of their ligands CD80 or CD86, that themselves homodimerize in cis using their strands C”D see , and/or st 2021)  on the sst 2021) ,41,42. Ist 2021) .To help with the understanding of Ig-Ig interfaces, for some canonical homodimers, such as CD8aa or VL-VL Bence Jones proteins, the tertiary C2 axis of symmetry combines with the quaternary C2 to lead to a quasi D2 symmetry group. This holds true even for VHVL or CD8ab heterodimers. Interestingly, some inverted homodimer interfaces are observed, where IgV domains are flipped (180 degrees) with regard to each other, resulting in a quaternary axis of symmetry rotated by 90 degrees, still orthogonal, however, to the tertiary C2 symmetry axis and an overall quasi D2 symmetry in considering the quaternary structure see . These sIn the following, we focus on the tertiary symmetries across all topological variants of Ig domains and dissect the formation of a new tertiary fold—the double Ig domain observed in CD19, which confirms the protodomain hypothesis.As mentioned in the introduction, nature may have used a protodomain duplication–fusion mechanism in a distant evolutionary past to build current day pseudosymmetric domains, and we can gain insight in domain creation from an analysis of tertiary pseudosymmetry of structurally characterized domains to look at domain creation and evolution in terms of their constituting parts. The immunoglobulin fold is at the heart of a very large number of cell surface proteins of the immune system, beyond immunoglobulins themselves, and we have seen that the Ig fold exhibits tertiary symmetry as well as quaternary symmetry, as in CD8 or VL-VL homodimers or the very well-known antibody variable domain association—VH-VL.In One can reconcile all Ig forms  by considering an Ig domain formation through a pseudosymmetrical combination of protodomains with a variety of linking sequences that can form or remove strands on one sheet or the other see . This opRecently the structure of CD19 has been solved . Prior tThe double Ig fold adopted by CD19  can be uhttps://structure.ncbi.nlm.nih.gov/icn3d/share.html?AdsvRptE9BHqWnN56, accessed on 27 August 2021) and it is not the same as a CD19 fold  as formed by two Ig domains of “parallel topology”, where sequential protodomains AB-CC’ (p1/p3) and DE-FG (p2/p4) are linked by short linkers (p1-p2 and p3-p4), the two parallel domains assemble pseudosymmetrically with an inverted topology (using a membrane protein denomination)  see . Amazingion) see . This ision) see D. The A’ion) see . This ishttps://www.ncbi.nlm.nih.gov/Structure/cdd/cddsrv.cgi?uid=cl11960, accessed on 27 August 2021) [The accepted nomenclature on beta strands  has progst 2021) . Some aust 2021) , but theIn this paper, we take a step back and look at the common symmetric architecture of all Ig domains: a protodomain decomposition allows us to reconcile all Ig domain topologies in light of that common pseudosymmetric domain architecture, which could imply either a variable fusion mechanism linking these protodomains together to produce various domain topologies  or a divergent evolution from symmetrically fused protodomains. CD19 escapes the current classification and exemplifies a new topological double Ig domain innovation that can be explained by how Ig protodomains fold and combine. At the same time, the protodomain decomposition validates the single Ig pseudosymmetric domain organization.All Ig domains can be related, however protodomains within Ig domains of different topologies exhibit symmetry breaking when considering AB-CC’ and DE-FG protodomains, as some of the lateral strands A/A’, C’ or D are not present. Let us first go over these topological variations:In IgVs, the A strand splits in A/A’ , with A extending the A|BED sheet in antiparallel while A’ snaps to extend the A’|GFCC’|C” sheet in parallel and straddles one lateral side on the sandwich. In some other IgVs, such as in CD4, the A strand is reduced to A’ to participate in that sheet only. The IgV is the only Ig domain with a C” strand that extends the A’|GFCC’|C” sheet and forms in doing so a CDR2 loop (C’-C”). However, the C” strand can also participate, instead, to the ABED|C”. This is the case of CTLA-4 , which hIn IgC1s, the A strand lies entirely on the A|BED sheet, there is no split A/A’ with A’ snapping to the other sheet, which is reduced to GFC (no C’).In IgC2s, the A strand lies entirely on the A|BE sheet (no D). There is no split A/A’ and a GFCC’ sheet.In the I-set, as in many IgVs, A and A’ are split and A participates in the A|BED sheet in antiparallel, while A’ swaps to the opposing sheet in parallel to strand G: A’|GFCC’. The C’ strand is very short (2–3 residues), followed by a very straight C’D linker to the D strand on the opposite sheet.In VNAR domains, the heavy chain-only variable domain of sharks ,52, the In cadherins, the A strand lies entirely on the A’|GFC sheet (no C’) facing a BED sheet.In FN3, similarly does not split, the A strand but lies entirely on the A|BE sheet (no D strand) vs. the GFC|C’ sheet.In CD19, for each of the two fused structural Ig domains, the A’ strand lies entirely on A’|GFCC’ sheets and BED sheets are formed opposite to them. Both Ig domains extend each other’s sheets in a unique way, as two fused long sheets: (A’|GFCC’)1(C’CFG|A)2 vs. (BED)1(DEB)2, which is only possible through an inversion of one domain through a unique folding/swapping mechanism D.There are many papers reviewing differences between topological variants of the Ig domain ,54 and aMultiple cell surface receptors have an IgV-like domain at the N-terminus for ligand-binding, and many of their ligands also have an IgV-like domain at their N terminus. Ig-C1 or Ig-C2 domains often follow N-termini IgV-like domains in tandem. This is the case of CD4 , which shttps://structure.ncbi.nlm.nih.gov/icn3d/share.html?tBzknU8spazpwCup7, accessed on 27 August 2021) where the C’ strand that would match the G strand by symmetry in an IgV  strands, partially breaking the symmetry and leading to topological variants. For example, comparing the two protodomains in an I-set domain through self-alignment  signature in Ig domains . In the The immutable architectural element, the common core of Ig and Ig-like domains, is the BC-EF intertwined symmetric straddle , which iIn Ig domains, the A strand is quite interesting and distinguishes various Ig domains. The A strand in an IgC1 will form a regular hairpin and strands AB of protodomain 1 will pair with DE of protodomain 2, but in the context of an IgV, the A strand will split in two, A and A’, usually through a proline or glycines, and the A’ will participate in the opposite sheet in parallel. In some cases, the A strand lies only on the opposing sheet as A’, and the protodomains will remain pseudosymmetric only on three strands, BED vs. CFG. In summary, when considering Ig domains and comparing the various topologies, independently of the CDRs in antibodies, BCRs, and TCRs, the most variable regions, structurally and topologically, are on the edges of the domain (barrel sandwich), based on how the protodomains are linked, leading to multiple topologies between C and E strands, with, in particular, the C’-CDR2-C”-C”D structured linker in IgVs, as well as the A strand topology variants at the N terminus, with strands A (ABED sheet), or A’ or split A-A’(A’GFCC’ sheet), participating in both sheets see . Our appWe performed a sequence search for a hypothetical inverse Ig domain based on a composite permuted sequence of protodomains p2–p3, but did not identify any inverse sequence, except in CD19 orthologs. If we search structurally , we get https://structure.ncbi.nlm.nih.gov/icn3d/share.html?TgULdqAYtGCK52NS8, accessed on 27 August 2021), while tandem Tudors fold sequentially as p1 + p2 and p3 + p4 (PDBid: 1XNI)  [https://structure.ncbi.nlm.nih.gov/icn3d/share.html?kyrVG3gcjmLytS2f8, accessed on 27 August 2021) or a double Tudor domain , but in that case long links are not a geometric requirement to invert protodomains and interdigitation of protodomains may be driven more by their sequence affinity.While unique among Ig domain topologies, the interdigitated folding of Ig protodomains in CD19 double Ig domain rather in tandem see  is reminst 2021) ,69 (see st 2021) ,70, as tIn the case of CD19, however, we have proposed the hypothesis of protodomains as folding units and inter-protodomain linker length as a distinctive element allowing Ig domains to fold in parallel (short linker) vs. in antiparallel (long linker); in the latter case, enabling structural tandem domain formation, while in the former, enabling interdigitation. If protodomains form stable supersecondary structures, then the linker length will enable either structural tandem or interdigitated domain formation. Pseudosymmetric assembly of protodomains as a domain requires a linker whose length depends on their folded topology. In the case of Igs with two-hairpin protodomains, a long enough linker is needed to invert the second protodomain vs. the first one as a single Ig, but a very short linker will prohibit two consecutive protodomains from folding as a closed Ig domain and lead to an open parallel Ig domain that can interdigitate with a copy of itself, as in CD19. Linker length is known to control intrachain domain pairing of VH and VL domains as either scFv (single chain Fv) fragments vs. interchain dimeric assembly as diabodies ,72. The https://www.ncbi.nlm.nih.gov/Structure/icn3d/full.html?showalignseq=1&align=7bz5,1cd8&atype=0, accessed on 27 August 2021). Interfaces can also exhibit a slightly rotated, even inverted, interdomain orientation (see earlier). X-ray structures used for our analyses represent static averages on dynamic proteins. We have been performing molecular dynamics simulations on some of these IgV-IgV interfaces at the heart of cell surface receptor–ligands interactions, as well as VL-VH and VL-VL pairs, to understand their dynamic behavior and stability. This is especially important when constructing chained VL-VH antibody fragments in scFv and diabody forms, as mentioned in the previous paragraph, where not just pairing of VH and VL domains, but also their dynamics, can be modified by VL-VH linkers vs. native antibody dimeric forms (unpublished work), likely to impact antibody–antigen interactions. Recently published work in the context of VH-VL interdomain dynamics in antibody fragments using molecular dynamics and NMR showed that these interfaces fluctuate in relative orientation by a few degrees, coupled with conformational rearrangements of CDR loops [Many quaternary (dimeric) interfaces of IgV domains involving the GFCC’ sheet interaction adopt a canonical interface, as in antibody variable domains VH-VL or in CD8 homo- or heterodimers   vs. a VL-VL homodimer (Bence Jones protein 1REI), their quaternary structures align within 1.53A for 202 residues with 57% sequence identity (021) see . InteracAs for IgV heterodimeric canonical interfaces, we can analyze the Ig domain tertiary fold geometry conservation under the prism of a coevolution of residues at protodomain–protodomain interfaces. In Ig domains, the interface involves the central strands B-C and E-F , with a stringent core interface conservation despite sequence divergence. The central strands are involved in lateral strand–strand interactions (B|E and C|F), leading to beta sheet formation and cross-sheet B-F/C-E core contacts. We can observe a conserved pattern of residue interactions across IgV domains see .CD19 is formed out of four protodomains, as described earlier . Their rhttps://structure.ncbi.nlm.nih.gov/icn3d/share.html?eCkGRhx16cmbmjQUA, accessed on 27 August 2021) acting as a PD-1 checkpoint inhibitor [Nanobodies, i.e., single IgV domains such as VHH domains from camelids, or VNAR domains from sharks, can bind to protein targets using not only their CDRs . Leveraging quaternary pseudosymmetric binding can be a route to designing nanobodies by engineering their outward-facing residues. It should also be possible to symmetrize their GF|CC’ sheet . Although the interest in a pseudosymmetric nanobody may be limited, another way of using symmetry as a design principle would be to, instead, invert the binding direction of nanobodies to interact with IgV targets in either cis or trans when integrated to a cell surface receptor. We plan to test ideas along these lines in the future.In stand-alone nanobodies, further symmetrization could be envisioned (apart from the asymmetry of CDR2 in VHH or HV2 in VNAR) to lead to bivalence in terms of CDR1/3, since the EF loop is equivalent to CDR1 (BC), and the CC’ loop is equivalent to CDR3 (FG) through symmetry. By interpreting EF and CC’ loops that way, and if CDRs are effectively the determining regions in binding specific targets, a nanobody could also be seen as bispecific. These ideas are speculative at this stage and are only mentioned as conceptual pseudosymmetric designs. Another lesson from the CD19 pseudosymmetric fold is highlighting the folding of an inverse Ig domain that could be engineered by circularly permuting Ig protodomains.https://www.ncbi.nlm.nih.gov/Structure/cdd/cddsrv.cgi?hslf=1&uid=409355, accessed on 27 August 2021), IgC1-set CDD , and many instances of IgC2 CDD  and IgI CDD  with detailed Ig sequence–structure features, down to each and every strand of these domains, were used. We used the original PDB numbering for the selected Ig domains in this study. Other commonly used reference numbering for IgV domains, Kabat [Methods to identify pseudosymmetry in protein domains have been published previously . Softwars, Kabat ,87 and Is, Kabat , are indColoring is a very important method to display and highlight properties, and for most figures, as in associated iCn3D links, we used the coloring scheme: blue–green–yellow–orange for protodomain strands ABCC’ or DEFG and red for C”, with grey for loops. For structural alignments, conserved residues are in red and mapped non-conserved residues are in blue. Interactions are colored grey for Van der Walls contacts, green for H-bonds, cyan for salt bridges, red for aromatic pi-stacking, and blue for pi-cation.The analysis of pseudosymmetric domains, while not demonstrating a folding pathway, demonstrates stable folded elements that we call protodomains. The Ig domain can be considered to be formed of two protodomains and the recent identification of a double Ig domain present in CD19 gives a confirmation of the protodomain hypothesis and shows the ability of Ig protodomains to fold independently and assemble in either parallel or antiparallel, similarly to membrane proteins of parallel vs inverted topologies. We have also seen the propensity of Ig domains to pair symmetrically in either parallel or inverted “quaternary topologies” as a result of the tertiary pseudosymmetry of Ig domains themselves.The evolutionary origin of the Ig domains of varying topologies is not entirely solved by this decomposition, yet the decomposition in protodomains involving a symmetric combination, as well as symmetry-breaking elements, offers a number of possible scenarios throughout evolution to explain these topological Ig domain variants. This also tends to suggest that the IgV may be the ancestral topological form of single Ig domains, but the double Ig domain would have had to have its own path.Importantly, the pseudosymmetric deconstruction of Ig domains provides a frame of reference for innovative molecular design. We have seen the formation of interdigitated protodomains in double domains through the largely unexplored possibilities of linkers to control folding. We have observed an inverse Ig domain within the double Ig domain, and one can extrapolate to possibly engineer (circularly) permuted Ig domains for targeted application. As nanobody applications expand, harnessing the pseudosymmetry of single Ig domains can offer multivalent binding surfaces for cell surface ligand designs and efficient targeting of Ig-based cell surface receptors, to lead to next generation checkpoint inhibitors and chimeric antigen receptors for CAR T-cell therapies in the burgeoning field of immunoengineering.


The rapid growth of the frozen c domains leads to the ferroelectric degradation. This finding gives insights into the nature of ferroelectric degradation in nanodevices, and reveals the role of the injected charges in polarization reversal.Failure of polarization reversal, i.e., ferroelectric degradation, induced by cyclic electric loadings in ferroelectric materials, has been a long-standing challenge that negatively impacts the application of ferroelectrics in devices where reliability is critical. It is generally believed that space charges or injected charges dominate the ferroelectric degradation. However, the physics behind the phenomenon remains unclear. Here, using in-situ biasing transmission electron microscopy, we discover change of charge distribution in thin ferroelectrics during cyclic electric loadings. Charge accumulation at domain walls is the main reason of the formation of  Space charges or injected charges dominate the ferroelectric degradation, however, its physics insight remains unclear. Here, the authors reveal the nature of ferroelectric degradation in nanodevices and the role of the injected charges in polarization reversal. However, the application of repeated electric fields has been shown to reduce the ferroelectric performance, leading to polarization reversal failure, i.e., ferroelectric degradation5. Ferroelectric degradation results in short life cycles, which impacts the reliability and endurance of electronic nanodevices6. Ferroelectric degradation changes the physical properties of ferroelectrics, including coercive field7, remnant polarization9, and resistivity10 under cyclic electric loadings. With the increasing usage of nanoscale electronic devices, a comprehensive understanding of the mechanisms and evolution of ferroelectric degradation is essential.Ferroelectric materials have been extensively used in electronic nanodevices because of their polarization reversal behavior under an applied electric field11. The domain wall pinning mechanism claims that the charge carriers and/or defect dipoles accumulate at the domain walls during electric cycling, leading to domain locking14. Some studies proposed a competitive process between domain wall pinning and unpinning, where the detrapping of charge carriers also occurred during ferroelectric degradation to unpin the domain walls. Ferroelectric degradation occurs once the pinning rate dominates16. The domain nucleation suppression mechanism suggests that charge carriers injected from the electrode prohibit the nucleation and growth of domains near the sample surface, degrading the ferroelectric performance17. The microcrack mechanism states that long-term electric cycling could cause the formation of microcracks initiated from the grain boundaries or domain walls19.Ferroelectric degradation is often linked to numerous mechanisms, including domain wall pinning, domain nucleation suppression, and microcracks21, which is generally accumulated at the domain wall under cyclic electric field and accounts for the degraded polarization22. However, it is not clear how these charges lead to the ferroelectric degradation. Direct observation of charge accumulation and real-time evolution of domain structure with cyclic electric field is critical to understand the impact of charge activities on ferroelectric degradation17. Owing to the advancements of in-situ transmission electron microscopy (TEM), real-time nanoscale observation of ferroelectric domain switching behavior under electric fields has become possible25. In addition, the recently developed microelectromechanical system (MEMS)-based nano-chip technique for TEM26 have improved the stability and reliability of the experiment under repeated electric fields, and therefore experiments revealing the mechanism of ferroelectric degradation have become technically feasible.Ferroelectric degradation is usually attributed to the activity of excess charges from the space or injection1/3Nb2/3)O3–0.38PbTiO3 (PMN-0.38PT) single crystals was investigated using in-situ biasing TEM with MEMS-based nano-chips, where an in-plane electric field was repeatedly applied to the sample. Scanning transmission electron microscopy-differential phase contrast (STEM-DPC) imaging was used to explore the charge distribution at domain walls during cyclic electric loading. With the increase of the electric loading cycles, domains with out-of-plane polarization (c domains) were initiated from the original domain walls, during which the charge accumulation was responsible for the nucleation and growth of the c domains. Of particular interest is that the c domains were less responsive to the applied electric field, showing a frozen state under electric field, which is a critical factor in ferroelectric degradation. The discovery of this ferroelectric degradation mechanism not only strengthens the understanding of ferroelectric degradation at nanoscale, but also provides guidance on the design of ferroelectric nanodevices.In this study, the domain switching behavior of Pb, a2 (a2+/a2−), and c (c+/c−) domains, respectively, as indicated in Fig. a1 and a2 domains with 90° ferroelastic domain walls28. To minimize the system energy, the 90° stripe domains follow the head-to-tail configuration, in which the polarizations of the domains in Fig. a1+/a2+ (→/↑) or a1−/a2− (←/↓)  and purple (a2 domains) lattices, respectively. Figure a1 domains will align with the direction of the electric field29. Based on this switching behavior of a1 domains under positive and negative electric fields, the pair of the domains was determined to be a1+/a2+.Figure /↓) Fig. . Figure T along ±00, ± direction in the a1 domains and the [100] direction in the a2 domains. Electron diffraction was used to determine the polarization direction of these domains. Figure * direction . The c domains were immobile during the electric loading, representing a frozen state. After one electric cycle, the entire domain configuration recovered to its original state.Thermodynamic calculations revealed that42. Ferroelectric hysteresis loops at different cycles  were produced using mechanical grinding followed by focused ion-beam processing. The PMN-0.38PT lamellae were fixed at a gap length of 4 µm between the inner two electric contacts of MEMS-based nano-chips by platinum deposition. The lamellae were thinned down by focused ion-beam to a thickness of about 100 nm. In-situ biasing TEM experiments were conducted with a Lightning holder produced by DENSsolutions in a JEM-2100 electron microscope operated at 200 kV. A bipolar bias in a triangular waveform (peak voltage of 4.7 V and frequency of 1/30 Hz) was applied along the ±[100] crystallographic direction of the specimen.The PMN-0.38PT single crystal was grown by a modified Bridgman method46. For a TEM sample, the phase shift of the transfer function of the sample is approximately proportional to its projected electrostatic potential. Accordingly, the differential of the phase shift is proportional to the projected electrostatic field of the sample47. The STEM-DPC technique relates the differential of the phase shift and the electrostatic potential field of the sample34. In this work, STEM-DPC was performed in an aberration-corrected FEI-Themis Z STEM operated at 300 kV. The configuration of the detector segments is illustrated in Supplementary Fig. When a focused electron beam passes through a ferroelectric sample, the local electrostatic potential field causes a phase shift of the electron beam, which changes the intensity distribution of the corresponding convergent beam electron diffraction (CBED) pattern. The differential of this phase shift is linearly related to the position of the center of mass of the CBED patternSupplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Movie 1


Various processing techniques significantly affect physicochemical and functional properties of rice flour and the quality of the final products. This study aims to modify rice flour with different treatments and to select the best one to develop rice and wheat-based leavened food products.3 factorial design considering three variables at two levels, namely, pretreatment of rice grain , grinding method (dry or wet grinding), and flour particle size (75−180 and <75 µm). Eight dough samples were prepared by mixing 50 g rice flour from each treatment with 50 g wheat flour. Then, the dough samples were subjected to fermentation and gelatinization under pressure  in a pressure adjustable chamber.Eight treatment combinations were applied on rice flour according to 22, we obtained highly porous and better textured rice and wheat-based leavened food products.Rice flour sample with particle size of 75-180 µm that underwent heat-moisture treatment followed by wet grinding improved the gas retention capacity of the leavened dough. With the externally applied initial air pressure of 1.0 kg/cmRice flour can be modified using the described method to improve its functional properties, and the textural and structural properties of rice and wheat-based leavened food products. Also, conducting fermentation and gelatinization under pressure is a novel food processing technique, which contributes to restricting the escape of gas from leavened rice/wheat composite dough mass. Oryza sativa L.) is the staple food for about 50% of the world population, covering the majority in Asian countries . However, previous studies have not disclosed how the rice grains subjected to heat-moisture treatment or dual modification treatment combined with grinding method and particle size would affect the fuctional flour properties and the formation of porous crumb structure of rice and wheat-based leavened food products.A combination of both physical and chemical starch modifications  can also be applied to improve the physicochemical and functional properties of flour. Peries 2 initial air pressure in a hermetically sealed container contribute to the increase of gas retention capacity of rice and wheat-based leavened dough samples (rice/wheat 50:50). Besides, the obtained product showed a stable and less brittle crumb structure with a uniform crumb cell distribution.According to our previous study  initial air pressure.The objective of this study is to modify rice flour using different treatments such as pretreatments of rice grains , size reduction by adapting two grinding methods (wet and dry grinding), and using two sizes of rice flour particles (75-180 and <75 µm). Furthermore, we evaluated flour gel hydration properties and improved porous structure properties of rice and wheat-based leavened food products prepared under 1.0 kg/cm3 (E500(ii); AB Mauri, Balakong, Malaysia).Certified paddy (BG 300) was obtained from the Rice Research and Development Institute, Bathalagoda, Sri Lanka. Refined wheat flour was purchased from a local supermarket in Colombo, Sri Lanka  11.10%, particle size <180 µm). The refined wheat flour used in the current study was obtained from the same batch. Therefore, the effect of wheat flour on the properties of the crumb samples was assumed as constant. Other major ingredients used in this study include baker’s yeast , table salt , sugar, shortening  and NaHCOPolyethylene terephthalate/linear low density polyethylene (PET/LLDPE) polymer bags  were purchased from Acme Printing and Packaging PLC, Piliyandala, Sri Lanka.3 factorial design considering three variables at two levels, namely pretreatment of rice grains (heat-moisture treatment (HMT) and dual modification treatment), grinding technique (dry and wet grinding) and flour particle size (75−180 µm and <75 µm) as shown in Paddy was dehusked and polished thoroughly. Then, eight batches of rice flour were prepared according to 2Rice grains were subjected to heat-moisture treatment according to the method described by Navaratne (w(moisture)e is equilibrium moisture content that needs to be obtained, w(moisture)i is initial moisture content of rice grains and w(water) is the amount of water (g) that needs to be added to 100 g of rice.where The rice and water were mixed well to make the moisture content of rice around 16.5-17.0%. Subsequently, rice was packed in an airtight, clean, double-laminated PET/LLDPE bag and kept under ambient conditions ((29±2) °C, 68% relative humidity (RH)) for 18-24 h to get the rice at equilibrium moisture content. Then, it was treated at (85±2) °C for 4-5 min in a laboratory-scale rotary dryer .et al.  at (84±2) °C for 1 h.Rice grains were subjected to chemical and physical modification according to the method described by Peries A portion of the treated rice grains was ground  and sieved through 180 and 75 µm sieves using a sieve shaker  to obtain rice flour with particle sizes between 75-180 µm or smaller than 75 µm.A portion of the treated rice grains was soaked in clean water ((25±2) °C) for 4 h, the excess water was drained and the grains were ground . Rice flour was dried  at (55±1) °C for 8 h, and passed through 180 and 75 µm sieves.et al.  g of each flour type was dispersed in 10 mL distilled water and agitated in a shaking water bath  at (80±2) °C for 30 min. Then, the cooked paste was cooled in an ice bath for 10 min and centrifuged  at 3000 rpm for 10 min. The dry solid mass was obtained by evaporating the supernatant overnight at (105±2) °C . Water absorption index (WAI), water solubility index (WSI) and swelling power (SP) were calculated using the respective equations below (φ(glycerol)=0.5). A drop of each sample suspension was mounted on a slide and air-dried. The dried samples were stained with iodine and examined with a light microscope  at 400× magnification. The microscopic images were acquired using a 20-megapixel camera.For light microscopy examinations, the flour samples from each treatment were suspended in aqueous glycerol  and bulk density (in g/cm3) of the crumb samples were calculated.The gelatinized crumb samples were cooled at room temperature ((30±1) °C), 68% RH) for (25±3) min and weighed. Volume of the gelatinized crumb samples was determined following the seed displacement method according to Aplevicz et al. (Crumb samples were cooled at room temperature ((30±1) °C, 68% RH) for (90±3) min and texture profile analysis was conducted using CT3 texture analyser  along with TexturePro CT software (2), average cell area (cm2), cell circularity, and solidity of the scanned images  were evaluated using ImageJ v. 1.51j8 software (Crumb ((3±0.5) mm thickness) cellular structure, namely crumb porosity (%), cell density  of the 8-bit threshold images was analysed following the box-counting method using ImageJ v. 1.51j8 software . In addition, pretreatment and grinding showed a significant influence (p<0.05) on WAI values of the eight rice flour treatments , water solubility index (WSI) and swelling power (SP)) in the eight treatments are given in eatments . Howevereatments , rice flet al. (post hoc tests with Tukey’s comparisons showed that dry-ground flour samples with particle size <75 µm had significantly higher (p<0.05) WSI values than wet-ground flour samples with particle size 75−180 µm. Generally, during dry grinding, a comparatively considerable amount of starch granules are damaged due to high mechanical stress and heat energy  from eight rice flour treatments were compared in order to determine the best treatment parameters based on the gas retention capacity, and textural and structural properties of the crumb samples.i.e. pretreatment, grinding method and particle size) have a statistically significant interaction (p<0.05). According to post hoc tests with Tukey’s comparisons, crumb sample prepared from rice flour with particle size 75−180 µm subjected to heat-moisture treatment and then wet ground had the highest crumb volume, specific volume and the lowest bulk density compared to the other crumb samples . These characteristics demonstrate that the combination of heat-moisture treatment with wet grinding, and particle size 75−180 µm result in the best gas retention capacity of leavened dough.The values of the volume, specific volume and bulk density of eight crumb samples in et al.  in crumb hardness, gumminess and chewiness. Therein, the crumb sample prepared with the flour of particle size 75−180 µm subjected to heat-moisture treatment and then wet ground showed the lowest values compared to the other crumb samples.Texture profile of a leavened food product mainly depends on the development of crumb cellular structure. These attributes play a vital role in determining the consumer perception of the product quality. Food texture is divided into three categories, namely visual texture, auditory texture and tactile texture. Among them, the tactile texture is the most commonly considered textural property of a food product and is defined as the sensation of direct contact between the food and human skin either by hand or by oral surface , particularly using 2 externally applied initial air pressure.Different treatments that include pretreatment of rice grain, grinding method and rice flour particle size remarkably affect rice flour functional properties as well as the development of the porous crumb structure of rice and wheat-based leavened food products (rice/wheat 50:50). Heat-moisture treatment of rice grains followed by wet grinding imparts better crumb volume and better texture properties of rice and wheat-based leavened food products along with a highly porous crumb structure with larger, circular and solid gas cells than the dual modification treatment and dry grinding. Moreover, size reduction by wet grinding in order to get particle size 75−180 µm also positively contributed to higher crumb volume and lower bulk density than dry grinding, which gave particle sizes <75 µm in rice and wheat-based dough samples. Altogether, this study suggests that the combination of the heat-moisture treatment with wet grinding, and particle size 75−180 µm provides an appropriate rice flour which with 50% refined wheat flour results in highly porous and better textured rice and wheat-based leavened food products with higher gas retention capacity. However, to obtain these results, fermentation and gelatinization must be performed under 1.0 kg/cm


The results showed that the Tru-COFs were porous (645 m2/g) and chemically stable. Benzyl methylene in conjugated Tru-COFs more effectively produced photoinduced radicals than the model truxene compound. Due to the radical photoresponsiveness, Tru-COFs were efficient catalysts for photocatalytic oxidation of sulfides. We expect that this will provide a new synthetic methodology to obtain C–C bonded functional 2D COFs.The synthesis of new C–C bonded two-dimensional (2D) covalent organic frameworks (COFs) is highly desirable. Here, a simple but effective synthetic strategy has been developed using an irreversible Brønsted acid-catalyzed aldol cyclotrimerization reaction by virtue of truxene as a linkage. Nonolefin C–C bonded 2D truxene-based covalent organic frameworks (Tru-COFs) were constructed by polymerization of 1,3,5-triindanonebenzene (TDB). The structure formation was confirmed by wide-angle X-ray scattering, Fourier-transform infrared spectroscopy, and solid-state  Since the first COFs were reported in 2005, many COFs with different linkages have been obtained using a variety of synthetic strategies, and the resulting materials have shown applications in gas storage/separation, energy storage, semiconductor devices, and photocatalysis –8. Howevoworkers .COFs synthesized through reversible reactions contain self-healing crystal defects, making it very difficult to prepare crystalline COFs via irreversible reactions. To our knowledge, there are relatively few cases for directly connecting two aromatic blocks by C–C bonds to form crystalline COFs, including the Ullmann reaction , Glaser Brønsted acid-catalyzed aldol cyclotrimerization (BAAC) is a simple self-condensation reaction with only one substrate .BAAC reactions were an efficient reaction to synthesize truxene and its derivatives –24; howeo-dichlorobenzene or toluene as the solvent. Most importantly, when toluene was used as the solvent, moderate crystalline polymers can also be obtained. In addition, when 1.0 equiv. PTSA was used, the isolated yield of Tru-COFs was 74.8%, and the BET surface area was 645 m2/g .The crystallinity of Tru-COFs was confirmed by WAXS and featured a main peak at 7.7° (100). Materials Studio 8.0 was used to build the 2D Tru-COF structure models . The AA 2 adsorption at 77 K. As shown in Table 2/g in 38.7% isolated yield  was obviously smaller. We speculate that some irregular pores were irreversibly formed during the reaction, and there are some unreacted defects inside, which might have resulted in a relatively smaller surface area. Furthermore, nonlocal density functional theory calculations reveal that Tru-COFs show a narrow pore size distribution, with a peak maximum at 1.5 nm  after immersion in 9 M NaOH and showed almost no change after immersion in 9 M HCl (680 m2/g)  Figure .π-conjugated system in the material  at 1.0 atm air. The conversion of thioanisole reached 100% in 4 h, with selectivity of methyl phenyl sulfoxide up to 90%. The catalyst was centrifuged and washed, and the recycled catalyst showed no obvious deterioration of conversion and selectivity after the 3rd cycle , PTSA , and 10 mL dry toluene. The mixture was sonicated for 1 minute. Then, the mixture was degassed through three freeze-pump-thaw cycles; the tube was sealed under vacuum and heated at 105°C for 3 days. The mixture was cooled to room temperature and collected by filtration and washed with water, ethanol, and DCM several times. The tea bag was Soxhlet extracted in DCM for 2 days and dried under vacuum at 180°C for 4 h to afford the powder (140 mg) in 74.8% isolated yield. Anal. Calcd. for C


Two-component signal transduction systems (TCSs) are widely conserved in bacteria to respond to and adapt to the changing environment. Since TCSs are also involved in controlling the expression of virulence, biofilm formation, quorum sensing, and antimicrobial resistance in pathogens, they serve as candidates for novel drug targets. TCSs consist of a sensor histidine kinase (HK) and its cognate response regulator (RR). Upon perception of a signal, HKs autophosphorylate their conserved histidine residues, followed by phosphotransfer to their partner RRs. The phosphorylated RRs mostly function as transcriptional regulators and control the expression of genes necessary for stress response. HKs sense their specific signals not only in their extracytoplasmic sensor domain but also in their cytoplasmic and transmembrane domains. The signals are sensed either directly or indirectly via cofactors and accessory proteins. Accumulating evidence shows that a single HK can sense and respond to multiple signals in different domains. The underlying molecular mechanisms of how HK activity is controlled by these signals have been extensively studied both biochemically and structurally. In this article, we introduce the wide diversity of signal perception in different domains of HKs, together with their recently clarified structures and molecular mechanisms. Th. Th24]. E. coli and DctB HK (RR: DctD) of Rhizobium are members of the same PDC family and can sense C4 dicarboxylates  in the PDC. DcuS has a single PDC, while DctB has two PDCs in tandem: a membrane-distal PDC and a membrane-proximal PDC . A. AP. putn2+ ions .2 through the heme cofactor  and EvgS HK of E. coli have cytoplasmic domain structures that are similar to ArcB, a cytoplasmic PAS domain between the TM helix and the atypical catalytic domain consisting of DHp, CA, REC, and Hpt domains. Although ArcB has only a short periplasmic sequence, both BvgS and EvgS have large periplasmic domains, which are composed of two tandem bacterial periplasmic solute-binding protein (PBPb) domains. These periplasmic domains are necessary for perceiving the stimuli for modulating HK activity: nicotinate and sulfate ions for negative regulation against BvgS and acidic pH for positive regulation against EvgS [BvgS HK of nst EvgS ,153,154.nst EvgS .However, in contrast with ArcB, which is positively regulated under anaerobic growth conditions, EvgS can only be activated by acidic pH under aerobic growth conditions. Growth under anaerobic conditions inhibited EvgS activity. A mutant strain with a defect in ubiquinone biosynthesis was not able to activate EvgS at acidic pH, possibly through the involvement of Cys671 within the PAS domain . This reB. bronchiseptica strains with mutations in the PAS domain [The function of the BvgS PAS domain has been extensively examined, but its function remains unknown. Dupré et al. concluded that the major function of the PAS domain is to maintain the conformational tension imposed by the periplasmic moiety of BvgS . A recenS domain .HK activity is also modulated in the catalytic domain. It has been reported that accessory proteins binding to the DHp domain and phosphatases against phosphotransfer proteins control HK activity. Recent reports suggest the involvement of second messengers and even direct sensing of changes in the cytoplasmic environment. We introduce examples of modulation of HK activity in the catalytic domain.B. subtilis KinA and KinB HKs play essential roles in the initiation of sporulation. Two proteins, Sda (46 aa) and KipI (240 aa), are known to inhibit the kinase activity of KinA: KipI against KinA and Sda against both KinA and KinB. Low-resolution structural models of the KinA-Sda and KinA-KipI complexes were determined using data from small-angle X-ray scattering and small-angle neutron contrast variation. Both Sda and KipI have been proposed to bind between the conserved autophosphorylated histidine residue and the hairpin bend of the four-helix bundle [Geobacillus stearothermophilus KinB with Sda has confirmed Sda binding to the base of the DHp domain, with axes of Sda helices roughly perpendicular to the KinB DHp helices [The x bundle ,138. The helices . Based o helices ,139.E. coli [+ homeostasis by controlling the expression of the kdpFABC operon, which encodes a high-affinity K+ transporter [Ntr), changes its phosphorylation state by nitrogen and carbohydrate availability. Only non-phosphorylated PtsN can efficiently bind KdpD for activation, suggesting that PTSNtr coordinates K+ uptake with the metabolic state of the cell [2/KdpE ternary complex. The proposed model is that when a non-phosphorylated PtsN binds to a protomer of a KdpD dimer, it stimulates autophosphorylation of the other protomer [Another protein that binds the DHp domain is PtsN, which stimulates the activity of KdpD HK in E. coli . The Kdpnsporter . PtsN, athe cell . Throughprotomer . High amprotomer . Non-phoprotomer .Cyclic dinucleotides (CDNs), which are newly recognized second messengers, are enzymatically synthesized from two nucleotides within the cell and serve as signaling molecules that control various physiological processes. In bacteria, CDNs are involved in the control of cellular processes such as motility, virulence, biofilm formation, and cell cycle progression . Among CCaulobacter crescentus, a bacterium with an asymmetric division cycle, employs the CckA/ChpT/CtrA system  to control its cell cycle. C-di-GMP directly binds to CckA HK to inhibit kinase activity and stimulate phosphatase activity. This allows replication initiation and cell cycle progression, which drives the cell cycle [2+ was determined by Dubey et al. [ll cycle . The cryy et al. . A monomy et al. . Using Cy et al. ,146.C. crescentus cell cycle progression [ShkA, a cytosolic hybrid HK, is another kinase that is involved in the regulation of gression . In contgression   containing His243.In some HKs, the cytoplasmic domain can directly sense stimuli from changes in the cytoplasmic environment. This is exemplified in detail by the osmosensing and pH sensing of EnvZ HK in iewed in ). The Eniewed in . EnvZ coiewed in . The staSalmonella PhoQ HK [Thermotoga maritima HK853 HK. This study confirmed that the same pH-sensing mechanism is also present in Salmonella EnvZ [243 in Salmonella EnvZ [244 and imidazole rotamerization of His243.The change in intracellular pH is also sensed by the cytoplasmic region of EnvZ ,144. Sen PhoQ HK . Anotherlla EnvZ . Ghosh ella EnvZ . This reHowever, Mideros-Mora et al. are opposed to the pH-gated conformational switch. They have found that the rotamer disposition of the catalytic His is not influenced by the environmental pH from structural studies of HK853-RR468 and analyses of HK structures extracted from the PDB. Instead, they propose that the acidic pH (below pH6) changes the catalytic His into a protonated form, thereby reducing its nucleophilic capacity to catalyze the autophosphorylation and phosphatase reaction . The cat+ concentration extracellularly and intracellularly [In the present article, we introduce some examples of how HKs can perceive multiple signals in various domains. Although we are aware that we have ignored many other cases, such as oligomerization and heterooligomerization of HKs and cross talk between noncognate RRs , we hopellularly  and is a


This process is fully reversible; an applied magnetic or electric field controls the transformation. Aside from expanding the concept of multiferroic order, such interconversion can be key to addressing antiferromagnetic domain structures and topological singularities.Systems with long-range order like ferromagnetism or ferroelectricity exhibit uniform, yet differently oriented three-dimensional regions called domains that are separated by two-dimensional topological defects termed domain walls. A change of the ordered state across a domain wall can lead to local non-bulk physical properties such as enhanced conductance or the promotion of unusual phases. Although highly desirable, controlled transfer of these properties between the bulk and the spatially confined walls is usually not possible. Here, we demonstrate this crossover by confining multiferroic Dy Domains and domain walls can have distinctively different physical properties. Here, the authors show how to transfer domains into domain walls and vice versa while maintaining their physical properties. Thereby the authors tune a multiferroic state between three and two dimensions. Examples are the occurrence of magnetization, polarization, magnetoelectric coupling, (super-)conductivity, memory effects, or a change of melting temperature15. Hence, domain walls may be regarded as additional state of a material, virtually a world in its own self and often discussed without reference to the surrounding bulk phase.Recently, the interests in ferroic materials with magnetic or electric order evolved from the spatially expanded bulk domains towards the spatially confined domain walls. As inherent inhomogeneity, domain walls are a source of specific phenomena that are forbidden in the uniform interior of the corresponding domains16. Reversely, the domain walls may seed the recovery of the original bulk state, acting as its memory17.It would be very desirable if the dimensional limitation of these phenomena could be overcome. For example, one could consider the confinement of a multifunctional bulk state into domain walls where they could establish a form of rewritable electromagnetic circuits20, and systems showing a behavior consistent with this concept were reported22. Conclusive observation of a smooth, deterministic transfer of a domain wall into a domain, however, and, in particular, the reversible interconversion between domains and domain walls have not been presented. Notably, the practical consequences of such interconversion for the physical properties and functionalities of materials were never debated.A class of materials in which the transition from bulk domains to domain walls could be virtually continuous are compounds with phase transitions, in which the symmetry of the domains and domain walls coincide crosswise on either sides of the phase boundary. In such materials, domain walls can in principle gradually transform into domains, and vice versa, across a first-order phase transition. This concept was discussed in theoretical physicsWe demonstrate this interconvertibility and apply it to tune a multiferroic state between three and two dimensions in a controlled way. Specifically, we confine a multiferroic bulk state into a multiferroic domain wall at an identified location within a non-multiferroic environment. We act on this spatially confined magnetoelectric object with magnetic or electric fields and evidence the presence of a switchable magnetization and polarization in the wall. We furthermore employ the fields to transfer the multiferroic domain wall back into a multiferroic bulk state. We then discuss the general occurrence and benefits of an ordered state with controllable transfer in between spatial expansion and spatial confinement.0.7Tb0.3FeO3 (see elsewhere23 about sample preparation) as our model system. Multiferroicity occurs at 2.65 K, caused by simultaneous antiferromagnetic ordering of the rare-earth and iron spin systems, coupled by exchange striction23. An electric polarization Ps = 0.12 μC cm−2 coexists with a Dzyaloshinskii–Moriya-type weak magnetization Ms = 0.15 μB per formula unit, both oriented along the c-axis. Subsequently, at TC ≃ 2.3 K a first-order spin reorientation of the iron sublattice from the multiferroic to an antiferromagnetic phase with Ms, Ps = 0 occurs. The simplest possible form to describe such a transition in between two magnetic phases M1 and M2 is the phenomenological effective Hamiltonian20θ distinguishes the domain states on the two sides of the M1 ↔ M2 phase transition. K1 and K2 are magnetocrystalline anisotropy parameters. K1 = 0 and K1 = −2K2 set the limits of the phase-coexistence region of M1 and M2. The gradient term with A as exchange constant further determines the order-parameter rotation across the domain walls.For the reasons given below, we choose the rare-earth orthoferrite Dy0.7Tb0.3FeO3, M1 and M2 are associated with the multiferroic (weakly ferromagnetic) and non-multiferroic (purely antiferromagnetic) phases, respectively, with θM1± = +π/2, −π/2 and θM2± = 0, π. Figure 18. By entering the M1/M2 coexistence region, the domain wall widens and transforms into a domain of the other phase. Conversely, the initial domain shrinks and eventually transforms into a domain wall separating the domains on the opposite side of the coexistence region. Hence, the first-order phase transition between the multiferroic M1 and the non-multiferroic M2 phase in Dy0.7Tb0.3FeO3 should in principle allow us to reversibly convert a multiferroic domain into a multiferroic domain wall in a non-multiferroic environment.In Dy18 experimentally. In Dy0.7Tb0.3FeO3, we can exploit the magnetization of the multiferroic phase to distinguish the M1 and M2 domain states by spatially resolved real-time imaging experiments, using the magneto-optical Faraday effect as magnetization probe. Furthermore, Dy0.7Tb0.3FeO3 exhibits a relatively broad region of phase coexistence. This gives us ample time to image the phase coexistence while tuning the balance between the competing multiferroic and non-multiferroic phases.We first verify the theoretically predicted transformation of a domain wall into a domainc-oriented Dy0.7Tb0.3FeO3 sample cooled across the M1 ↔ M2 transition. We refrain from quantifying K1 and K2 since their absolute values are not relevant for our discussion. In Fig. M1 domain pair at T > TC. Because of the opposite direction of magnetization and, hence, Faraday rotation, the domains appear as bright and dark regions. Figure T ≲ TC. A gray stripe centers at the domain-wall position of Fig. TC, this is the dominating phase and, starting from the original +M1/−M1 domain wall, we perceive the homogeneous expansion of this wall into an M2 domain engulfing the sample as time progresses. Note that this expansion of the non-multiferroic phase occurs in a deterministic way, starting uniformly from the center of the domain wall of the multiferroic phase. This deterministic behavior is in contrast to the needle-like growth of domains of the emergent phase at domain walls of the original phase21 or to the nucleation on random defects as in most first-order phase transitions24. Defects do not play a role in our case as we experimentally verify in Supplementary Note 25 are not covered by Eq.  but rather by the history of the sample, as comparison of Fig. To describe the wall as multiferroic, we furthermore have to show that we can act on it and affect its magnetization and electric polarization by an applied magnetic or electric field. This is also important for its technological utility. This is done in Fig. To conclude, we have experimentally demonstrated the conversion of a multiferroic bulk phase into a multiferroic domain wall at an identified location inside a non-multiferroic environment. The initial multiferroic hallmark properties, namely a magnetization and a polarization that are coupled and switched by an applied field, are retained by the wall. Magnetic or electric fields act on the wall and convert it back into a bulk multiferroic domain with a predetermined direction of magnetization or polarization.2O4 as a very recent example to catch scientific attention28. Note that even if the region of phase coexistence may be narrower than in our case, possibly even too narrow for convenient experimental probing during the transition, a system will still be subject to the same dynamics as found in Dy0.7Tb0.3FeO3. Even non-magnetic types of order can display the spatial interconversion. For example, a (static) expansion of domain walls into domains with phase coexistence based on a chemical gradient rather than the first-order nature of a phase transition was observed in the ferroelectric-to-nonferroelectric transition in InMnO329. Even organic materials may show a transition between bulk phases with neutral and ionic building blocks emerging out of an expanding singularity by progressive charge transfer31.The concept of interconversion can be expanded beyond multiferroics. First, there are plenty of first-order magnetic phase transitions fulfilling the rather basic conditions of Eq.  with CaF15, the magnetoelectric properties are not confined to the domain walls but can be expanded into the bulk when needed. The magnetoelectric properties of the walls may be employed to visualize or even tailor domain patterns in materials whose order is normally difficult to access, such as 180° antiferromagnets. Finally, our work provides a rare opportunity of deterministic nucleation in a first-order phase transition since the nucleating phase is seeded by the order and symmetry in domain walls rather than occurring on random defects.Second, our work expands the possibilities for functionalizing domain walls. Unlike in previous examples0.7Tb0.3FeO3 were grown by the floating-zone method under O2 atmosphere. Using back-reflection X-ray Laue diffractometry, thin c-oriented plates of 2.5 × 2.5 mm2 were cut, lapped, and polished with a silica slurry down to ~60–80 μm with optically flat surfaces on both sides. Temperature and magnetic field treatment was done in a liquid-helium-cooled magnetic-field cryostat (Oxford Spectromag 4000-10T). For Faraday imaging, a light-emitting diode with a central wavelength of 660 nm (Thorlabs M660L4) was used along with a monochromatic digital camera (The Imaging Source DMK 22BUC03) for image acquisition. Image processing is limited to adjustments of brightness, contrast and levels and homogeneously applied to the entire image, unless noted. The images of each figure were adjusted equally. For electric field measurements, 3-nm platinum electrodes were deposited on both surfaces of the specimen.Single-crystals of DyFurther information on research design is available in the Supplementary InformationLasing Reporting Summary