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All sources NASA NTRS DOE OSTI

DOE OSTI2017

Thermal and magnetic hysteresis associated with martensitic and magnetic phase transformations in Ni 52 Mn 25 In 16 Co 7 Heusler alloy

Ni-Mn-In-Co Heusler alloys demonstrate promising magnetocaloric performance for use as refrigerants in magnetic cooling systems with the goal of replacing the lower efficiency, eco-adverse fluid-compression technology. The largest change in entropy occurs when the applied magnetic field causes a merged structural and magnetic transformation and the associated entropy changes of the two transformations works constructively. In this study, magnetic and crystalline phase transformations were each treated separately and the effects of the application of magnetic field on thermal hystereses associated with both structural and magnetic transformations of the Ni 52 Mn 25 In 16 Co 7 were studied. From the analysis of synchrotron diffraction data and thermomagnetic measurements, it was revealed that the alloy undergoes both structural (from cubic austenite to a mixture of 7M & 5M modulated martensite) and magnetic (ferromagnetic to a low-magnetization phase) phase transformations. Here, thermal hysteresis is associated with both transformations, and the variation of the thermal hystereses of the magnetic and structural transformations with applied magnetic field is significantly different. Because of the differences between the hystereses loops of the two transformations, they merge only upon heating under a certain magnetic field.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Determination of the stretch tensor for structural transformations

Structural transformations in crystalline solids are increasingly the basis of the functional behavior of materials. Both low hysteresis and reversibility of phase transformations have been linked to the satisfaction of the nongeneric conditions of compatibility between phases in diverse alloy systems. According to the Cauchy–Born rule, these conditions are expressed as properties of transformation stretch tensor. The transformation stretch tensor is difficult to measure directly due to the lack of knowledge about the exact transforming pathway during the structural change, and the complicating effects of microstructure. In this paper we give a rigorous algorithmic approach for determining the transformation stretch tensor from X-ray measurements of structure and lattice parameters. For some traditional and emerging phase transformations, the results given by the algorithm suggest unexpected transformation mechanisms.

42 ENGINEERING↗

DOE OSTI2018

Use of in-situ TEM to characterize the deformation-induced martensitic transformation in 304 stainless steel at cryogenic temperature

Highlights: • Unique experimental visualization of DIM transformation in 304SS in-situ in a TEM at cryogenic temperatures. • Three cases of DIM were captured in situ showing how stress and temperature are both effective on the transformation. • (i) formation of ε- martensite through overlapping/bundling of SFs (γ →SFs →ε), • (ii) direct (γ→ α’) transformation with interface migration upon pulling the sample at constant temperature, • (iii) direct γ→ α’ transformation upon cooling, without further pulling the sample. - Abstract: Tensile tests are conducted in-situ in a TEM at cryogenic temperatures (from − 100 °C to 0 °C) using a cooling TEM straining-stage with the goal of capturing the growth of the martensitic phase as it develops under stress in the material. The in-situ technique is used to explore the mechanism of deformation induced martensitic transformation in 304 and 304L austenitic stainless steels. The formation of stacking faults is captured, as well as the subsequent formation of ε-martensite, confirming the role played by Stacking faults (SFs) as intermediate step during the transformation from γ-austenite to ε-martensite. In addition, direct transformation from γ-austenite to α′-martensite is captured (i) upon straining at a fixed temperature and (ii) upon cooling after pulling on the sample, indicating how straining and temperature are both effective on the transformation.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Characterising the polymorphic phase transformation at a localised point on a Cu6Sn5 grain

Highlights: • A single-targeted Cu{sub 6}Sn{sub 5} grain adjacent to Sn-rich sites and Cu{sub 3}Sn was investigated using HVTEM. • Phase transformation from hexagonal to monoclinic in a single-targeted Cu{sub 6}Sn{sub 5} grains. • A time-temperature transformation (TTT) diagram was constructed using the HVTEM results. - Abstract: Cu{sub 6}Sn{sub 5} is an important intermetallic for electric interconnects and anode material of Li-ion batteries, with a polymorphic transformation from hexagonal eta-Cu{sub 6}Sn{sub 5} at temperatures higher than 186 °C to monoclinic eta′-Cu{sub 6}Sn{sub 5} at lower temperatures. The polymorphic transformation of Cu{sub 6}Sn{sub 5} has the potential to generate internal stresses in soldered joints during both the soldering process and subsequent device operation involving thermal cycling. Here we developed a systematic method to characterise the polymorphic transformations at localised points in a single grain of Cu{sub 6}Sn{sub 5} that is in intimate contact with adjacent Sn rich and Cu{sub 3}Sn phases to establish a time–temperature transformation (TTT) diagram of the eta to eta′-Cu{sub 6}Sn{sub 5} transformation. The method involves in situ temperature-controlled high-voltage transmission electron microscopy (HVTEM) of a single-targeted Cu{sub 6}Sn{sub 5} grain with observation of diffraction patterns during multiple heating and cooling experiments on a 0.5 μm thick sample made by focused ion beam milling (FIB). The results are compared to previously reported powder X-ray diffraction data. It is concluded that there is good agreement between both techniques and the transformations observed in the powder are representative of those in individual grains present in polycrystalline structures. Based on the newly developed TTT, it was established that the high-temperature eta-Cu{sub 6}Sn{sub 5} could be stablised down to room temperature if the cooling rate exceeded 20 °C min{sup −1}.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Deformation mode and strain path dependence of martensite phase transformation in a medium manganese TRIP steel

The martensite phase transformation dependence upon deformation modes and strain paths in a medium manganese (10 wt%) TRIP steel stamped into a T-shape panel was quantified through combination of 3D digital image correlation and synchrotron X-ray diffraction. The T-shape emulates a portion of a common anti-intrusion component. The stamping speed was kept intentionally slow (1 mm/s) so as to avoid excessive heat generation. The steel, which belongs to the third generation advanced high strength steel (3GAHSS) family, was chosen for two reasons: (1) it is two-phase, i.e. austenite and ferrite, with martensite resulting from deformation-induced phase transformation; (2) the 66 vol.% initial retained austenite volume fraction (RAVF) enabled a thorough examination of the martensite phase transformation at large deformation levels without exhaustion. Strain fields were coupled with measured RAVF values of small specimens extracted from specific locations on a formed T-shape panel. This enabled an exploration of the effects of linear, bilinear, and non-linear strain paths as well as deformation modes such as tension, plane strain, biaxial tension, and equibiaxial tension. Results suggest a significant martensite phase transformation dependence on deformation mode and strain path in the absence of fracture and when martensite phase transformation is unaffected by heat generated during forming. In general, the uniaxial and biaxial tension deformation modes facilitate the martensite phase transformation, while the smallest amount of martensite phase transformation occurs under plane strain. In conclusion, some discussion as to further application of the experimental methods detailed in this study to other 3GAHSS and the effects of fracture on martensite phase transformation is provided.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Expression of the small T antigen of Lymphotropic Papovavirus is sufficient to transform primary mouse embryo fibroblasts

Polyomaviruses induce cell proliferation and transformation through different oncoproteins encoded within the early region (ER): large T antigen (LT), small T antigen (sT) and, in some cases, additional components. Each virus utilizes different mechanisms to achieve transformation. For instance, the LTs of Simian virus 40 (SV40), BK and/or JC virus can induce transformation; but Merkel Cell Polyomavirus (MCPyV) requires expression of sT. Lymphotropic Papovavirus (LPV) is closely related to Human Polyomavirus 9 (HuPyV9) and, under similar conditions, mice expressing LPV.ER exhibit higher rates of tumor formation than mice expressing SV40.ER. We have investigated the contributions of individual LPV.ER components to cell transformation. In contrast to SV40, LPV.ER transforms mouse embryonic fibroblasts (MEFs), but expression of LPV LT is insufficient to transform MEFs. Furthermore, LPV sT induces immortalization and transformation of MEFs. Thus, in the case of LPV, sT is the main mediator of oncogenesis. - Highlights: • Characterization of early region products from the Lymphotropic Polyomavirus (LPV). • On its own, sT immortalizes and transforms mouse primary cells, and is able to block p53 activation. • Combined LT and sT expression induces a greater rate of proliferation than either LT or sT alone.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SWAP-70 contributes to spontaneous transformation of mouse embryo fibroblasts

Mouse embryo fibroblasts (MEFs) grow slowly after cultivation from animals, however, after an extended period of cultivation, their growth accelerates. We found that SWAP-70 deficient MEFs failed to increase growth rates. They maintain normal growth rates and proliferation cycles for at least 5 years. Complementing SWAP-70 deficiency in one of these MEF clones, MEF1F2, by expressing human SWAP-70 resulted in fast growth of the cells after further cultivation for a long period. The resulting cells show a transformation phenotype, since they grow on top of each other and do not show contact inhibition. This phenotype was reverted when sanguinarine, a putative SWAP-70 inhibitor, was added. Two SWAP-70 expressing clones were examined in detail. Even after cell density became very high their cdc2 and NFκB were still activated suggesting that they do not stop growing. One of the clones formed colonies in soft agar and formed tumors in nude mice. Lately, one more clone became transformed being able to make colonies in soft agar. We maintain 4 human SWAP-70 expressing MEF1F2 cell lines. Three out of 4 clones exhibited transforming phenotypes. The mouse SWAP-70 gene also promoted transformation of MEFs. Taken together our data suggest that SWAP-70 is not a typical oncogene, but is required for spontaneous transformation of MEFs. - Highlights: • Mouse embryo fibroblasts (MEFs) lacking SWAP-70 do not cause spontaneous transform. • Adding back of SWAP-70 to SWAP-70-deficient MEFs induces spontaneous transformation. • SWAP-70 is required for spontaneous transformation of MEFs.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1992

Chromosomal changes in cultured human epithelial cells transformed by low- and high-LET radiation

For a better assessment of radiation risk in space, an understanding of the responses of human cells, especially the epithelial cells, to low- and high-LET radiation is essential. In our laboratory, we have successfully developed techniques to study the neoplastic transformation of two human epithelial cell systems by ionizing radiation. These cell systems are human mammary epithelial cells (H184B5) and human epidermal keratinocytes (HEK). Both cell lines are immortal, anchorage dependent for growth, and nontumorigenic in athymic nude mice. Neoplastic transformation was achieved by irradiating cells successively. Our results showed that radiogenic cell transformation is a multistep process and that a single exposure of ionizing radiation can cause only one step of transformation. It requires, therefore, multihits to make human epithelial cells fully tumorigenic. Using a simple karyotyping method, we did chromosome analysis with cells cloned at various stages of transformation. We found no consistent large terminal deletion of chromosomes in radiation-induced transformants. Some changes of total number of chromosomes, however, were observed in the transformed cells. These transformants provide an unique opportunity for further genetic studies at a molecular level.

NASA Discipline Number 04-10↗

DOE OSTI2014

In situ X-ray diffraction strain-controlled study of Ti–Nb–Zr and Ti–Nb–Ta shape memory alloys: crystal lattice and transformation features

Phase and structure transformations in biomedical Ti–21.8Nb–6.0Zr (TNZ) and Ti–19.7Nb–5.8Ta (TNT) shape memory alloys (at.%) under and without load in the − 150 to 100 °S temperature range are studied in situ using an original tensile module for a low-temperature chamber of an X-ray diffractometer. Alpha″- and beta-phase lattice parameters, the crystallographic resource of recovery strain, phase and structure transformation sequences, and microstress appearance and disappearance are examined, compared and discussed. For both alloys, the crystallographic resource of recovery strain decreases with temperature increase to become 4.5% for TNZ and 2.5% for TNT alloy (at RT). Loading at low temperatures leads to additional α″-phase formation and reorientation. Heating under load, as compared to strain-free heating, affects the reverse transformation sequence of both alloys in different ways. For TNZ alloy, strain-free heating results in simultaneous ω→β and α″→β transformations, whereas during heating under stress, they are sequential: β + ω→α″ precedes α″→β. For TNT alloy, strain-free heating results in reverse α″→β transformation, whereas during heating under stress, α″→β transformation is preceded by α″-phase reorientation. - Highlights: • Comparative in situ XRD analysis of Ti–Nb–Zr(Ta) shape memory alloys is realized. • Lattice parameters of β- and α″-phases are calculated in the − 150 to + 100 °C range. • The higher the temperature, the lower the α″→β transformation strain. • Loading at low temperatures results in α″-phase formation and reorientation. • Transformation sequences upon heating with and without loading are different.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Graphite to diamond transformation under shock compression: Role of orientational order

To gain insight into the role of orientational order on the shock-induced graphite to diamond phase transformation, three pyrolytic graphite types having different orientational orders were shock-compressed along the average c -axis to peak stresses between 35 and 69 GPa. The materials studied were ZYB-grade highly oriented pyrolytic graphite (HOPG), ZYH-grade HOPG, and as-deposited pyrolytic graphite (PG) having mosaic spreads of 0.8° ± 0.2°, 3.5° ± 1.5°, and ~45°, respectively. Wave profiles, obtained using laser interferometry, show a multiple-wave structure with a distinct, rapid (<10 ns) rise to the high-pressure phase for each graphite type. Multiple-wave profiles, first observed in this study for the less ordered ZYH-grade HOPG and PG samples, show that somewhat poorly oriented pyrolytic graphites also undergo a well-defined phase transformation. Previously, rapid transformation was reported for ZYB-grade but not ZYH-grade HOPG. The measured wave profiles for both HOPG grades are very similar and both grades show a ~22 GPa transformation stress. In contrast, the PG wave profiles are quite different and show a ~46 GPa transformation stress. The continuum results (stress-density states) presented here cannot distinguish between the different high-pressure phases [hexagonal diamond (HD) or cubic diamond] reported in recent x-ray studies. Because ZYB-grade HOPG was recently shown to transform to HD and due to the similar peak states for both HOPG grades, it seems likely that ZYH-grade also transforms into HD. In conclusion, the very different shock responses of PG and HOPG suggest different transformation mechanisms for PG and HOPG, but the high-pressure PG phase remains unclear in the present work.

58 GEOSCIENCES↗

DOE OSTI2024

Reconfigurable unitary transformations of optical beam arrays

Spatial transformations of light are ubiquitous in optics, with examples ranging from simple imaging with a lens to quantum and classical information processing in waveguide meshes. Multi-plane light converter (MPLC) systems have emerged as a platform that promises completely general spatial transformations, i.e., a universal unitary. However, until now, MPLC systems have demonstrated transformations that are far from general, e.g., converting from a Gaussian to Laguerre-Gauss mode. Here, we demonstrate the promise of an MLPC, the ability to impose an arbitrary unitary transformation that can be reconfigured dynamically. Specifically, we consider transformations on superpositions of parallel free-space beams arranged in an array, which is a common information encoding in photonics. We experimentally test the full gamut of unitary transformations for a system of two parallel beams and make a map of their fidelity. We obtain an average transformation fidelity of 0.85 ± 0.03. This high-fidelity suggests that MPLCs are a useful tool for implementing the unitary transformations that comprise quantum and classical information processing.

47 OTHER INSTRUMENTATION↗

DOE OSTI2019

HEMP Transformer Defense Through Power Electronics

High altitude electromagnetic pulse (HEMP) generated by exoatmospheric nuclear burst has the ability to affect the electric power grid. The main power grid components, cables and transformers, act as large antennas that have current induced in them from the HEMP. These currents are called geomagneticallyinduced currents (GIC), and they can occur during geomagnetic disturbances from HEMP or solar flares. HEMPs produce pulses with high electric field strengths that breakdown the dielectric of most electronics and, it is broken into three stages: E1 pulse with a microsecond width, E2 the falling trail of the pulse, and E3 a constant DC component. Oak Ridge National Laboratory has proven that transformers fitted with lightning arrestors do not receive damage from E1 and E2 pulses. However, the DC component of the E3 causes the transformer’s core to saturate and induce rapid heating that damages the transformer. SRNL is developing a power electronic system that is connected to the neutral of the high voltage side of large power transformers (LPT). This system will inject the inverse of the DC effect from the HEMP into the primary side of the transformer canceling out the E3 waveform and protecting the transformer from half-cycle-saturation. This year SRNL successfully simulated removing the DC injected and accurately simulated saturation on the transformer.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2007

Effects of Stoichiometry on Transformation Temperatures and Actuator-Type Performance of NiTiPd and NiTiPdX High-Temperature Shape Memory Alloys

High-temperature shape memory NiTiPd and NiTiPdX (X=Au, Pt, Hf) alloys were produced with titanium equivalent (Ti+Hf) compositions of 50.5, 50.0, 49.5, and 49.0 at.%. Thermo-mechanical testing in compression was used to evaluate the transformation temperatures, transformation strain, work output, and permanent deformation behavior of each alloy to study the effects of quaternary alloying and stoichiometry on high-temperature shape memory alloy behavior. Microstructural evaluation showed the presence of second phases for all alloy compositions. No load transformation temperatures in the stoichiometric alloys were relatively unchanged by Au and Pt substitutions, while the substitution of Hf for Ti causes a drop in transformation temperatures. The NiTiPd, NiTiPdAu and NiTiPdHf alloys exhibited transformation temperatures that were highest in the Ti-rich compositions, slightly lower at stoichiometry, and significantly reduced when the Ti equivalent composition was less than 50 at.%. For the NiTiPdPt alloy, transformation temperatures were highest for the Ti-rich compositions, lowest at stoichiometry, and slightly higher in the Ni-rich composition. When thermally cycled under constant stresses of up to 300 MPa, all of the alloys had transformation strains, and therefore work outputs, which increased with increasing stress. In each series of alloys, the transformation strain and thus work output was highest for stoichiometric or Ti-rich compositions while permanent strain associated with the constant-load thermal cycling was lowest for alloys with Ni-equivalent-rich compositions. Based on these results, basic rules for optimizing the composition of NiTiPd alloys for actuator performance will be discussed.

Bigelow, Glen S.↗

DOE OSTI2019

Methods of resolving artifacts in Hadamard-transformed data

Apparatus and methods are disclosed for processing data transformed according to an invertible transform (e.g., using a Hadamard transform) multiplexing scheme. In one example of the disclosed technology, a computer-implemented method includes generating transformed data by applying a Hadamard transform to intensity data generated by modulating input of analytes into a mass spectrometer according to a pseudorandom sequence (PRS). The exemplary method further includes identifying at least one pair of symmetric intensity peaks in the transformed data based on the PRS and removing data associated with the pair of symmetric peaks from the transformed data to produce modified data, which can be used to identify, characterize, and/or quantify the composition of the sample. In some examples, the exemplary method further includes validating peaks in the transformed data based on comparing the location of peaks in the untransformed intensity data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Transformation-induced plasticity in bulk metallic glass composites evidenced by in-situ neutron diffraction

Transformation-induced plasticity in a strain-softening amorphous matrix consisting of austenite B2 phase was studied by in-situ neutron diffraction, coupled with molecular dynamic simulation. It was found that the martensitic transformation from B2 to B19' upon loading commenced at the macroscopic yielding which increased with the decrease of the fraction of the parent austenite B2 phase, and the threshold lattice strain for the martensitic transformation is almost the same in different samples, suggesting that the martensitic transformation in the current glassy matrix is strain-controlled. Analysis of load partition and strain accommodation unveiled that B2 has elastic anisotropy, and the desirable elastic match between B2 and the amorphous matrix ensures a good cooperative deformation. Additionally, molecular dynamic simulation revealed that atoms at the interface between B2 and the amorphous matrix deviated from the standard B2 lattices and acted as nucleation site for the martensitic transformation, eventually giving rise to the strain-controlled martensitic transformation. Our findings provide new insights into the mechanism of phase transformation-mediated plasticity at the microscopic level, and have useful implications for developing novel, high-performance bulk metallic glass composites.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Continuous activation of Nrf2 and its target antioxidant enzymes leads to arsenite-induced malignant transformation of human bronchial epithelial cells

Long-term exposure to arsenite leads to human lung cancer, but the underlying mechanisms of carcinogenesis remain obscure. The transcription factor of nuclear factor-erythroid-2 p45-related factor (Nrf2)-mediated antioxidant response represents a critical cellular defense mechanism and protection against various diseases. Paradoxically, emerging data suggest that the constitutive activation of Nrf2 is associated with cancer development, progression and chemotherapy resistance. However, the role of Nrf2 in the occurrence of cancer induced by long-term arsenite exposure remains to be fully understood. By establishing transformed human bronchial epithelial (HBE) cells via chronic low-dose arsenite treatment, we showed that, in acquiring this malignant phenotype, continuous low level of ROS and sustained enhancement of Nrf2 and its target antioxidant enzyme levels were observed in the later-stage of arsenite-induced cell transformation. The downregulation of Keap1 level may be responsible for the over-activation of Nrf2 and its target enzymes. To validate these observations, Nrf2 was knocked down in arsenite-transformed HBE cells by SiRNA transfection, and the levels of Nrf2 and its target antioxidant enzymes, ROS, cell proliferation, migration, and colony formation were determined following these treatments. Results showed that blocked Nrf2 expression significantly reduced Nrf2 and its target antioxidant enzyme levels, restored ROS levels, and eventually suppressed cell proliferation, migration, and colony formation of the transformed cells. In summary, the results of the study strongly suggested that the continuous activation of Nrf2 and its target antioxidant enzymes led to the over-depletion of intracellular ROS levels, which contributed to arsenite-induced HBE cell transformation. - Highlights: • Low level, long term arsenite exposure induces malignant transformation in vitro. • Long term arsenite exposure reduces ROS and MDA levels. • Long term arsenite exposure enhances Nrf2-mediated antioxidant levels. • Knockdown of Nrf2 reduces malignant degree of arsenite-transformed cells.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Uncovering the role of nanoscale precipitates on martensitic transformation and superelasticity

Here we characterize the role of coherent nanoscale B2 Ni 50 Al 50 precipitates on the temperature- and stress-induced martensitic phase transformation in nanocrystalline Ni 63 Al 37 shape memory alloys using multi-million-atoms molecular dynamics (MD) simulations. We studied two types of precipitates: one with single crystal precipitates (SXP) and a second where grain boundaries cut through precipitates (PXP). Simulations reveal that the presence of B2 precipitates stabilizes the cyclic flag-shaped stress-strain response, characteristic of superelasticity, and reduces remnant strain. In contrast, single-phase nanocrystalline Ni 63 Al 37 exhibits degradation of the reverse transformation during cyclic loading and, eventually, incomplete reversible transformation within a few cycles. This is consistent with previous experimental findings of ultra-low fatigue in Ni-Ti-Cu alloys with Ti 2 Cu precipitates. The simulations reveal that the presence of precipitates significantly improves the reversibility of the transformation by acting as elastic zones that partially shield the martensitic transformation and drive the reverse transformation. A detailed analysis of the MD trajectories reveals that the martensitic transformation of the matrix induces ultra-large elastic deformation in some of the B2 precipitates (approximately 12%) to the point of resulting in a martensite-like atomic structure.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Quantum decoration transformation for spin models

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗