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Dielectric and energy-storage properties of Ba0.85Ca0.15Zr0.10Ti0.90O3 ceramics with BaO-Na2O-Nb2O5-WO3-P2O5 glass addition
Published 21 May 2024 in physics.app-ph and cond-mat.mtrl-sci | (2405.13207v1)
Abstract: Lead-free Ba0.85Ca0.15Zr0.10Ti0.90O3 (BCZT) ceramics with different BaO-Na2O-Nb2O5-WO3-P2O5 (BNNWP) glass content, forming (1-x)BCZT-xBNNWP lead-free ceramics (abbreviated as BCZTx; x=0, 2, 4, 6, and 8wt%) were synthesized using the conventional solid-state processing route. The XRD investigation shows the coexistence of tetragonal and orthorhombic phases in BCZT pure. Likewise, only the tetragonal phase was detected in BCZTx (x = 2-8 wt%) ceramics. The SEM findings indicate that the average grain size decreases as the amount of BNNWP glass additives increases. In addition, BCZT ceramics Amodified with glass additions showed narrower hysteresis loops and a large electric field. The BCZT4 showed the highest recovered energy density of 0.52 J/cm3 at 135kV/cm with an energy storage efficiency of 62.4%, which is increased by 6.6 compared to BCZT0 (0.075 J/cm3). The energy density was also calculated using the Landau-Ginzburg-Devonshire (LGD) theory
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What is this paper about?
This paper is about making safer, better materials for capacitors—devices that store electrical energy quickly, like a “short-term battery.” The researchers worked with a lead-free ceramic called BCZT and mixed in a special phosphate glass (BNNWP) to see if it could store more energy and lose less during charging and discharging.
Why does this matter?
Capacitors are used in things like electric cars, medical defibrillators, and fast electronics. To make these systems smaller, faster, and safer, we need materials that:
- Store a lot of energy in a small space
- Charge and discharge quickly
- Don’t break easily under strong electric fields
- Work without toxic elements like lead
The main questions
The researchers wanted to answer:
- Can adding a small amount of phosphate glass to BCZT improve how much energy it can store?
- How does the glass affect the ceramic’s structure, grain size, and electrical behavior?
- Is there a way to model or predict the energy storage using a simple theory?
How did they do it?
They made several versions of the ceramic by mixing BCZT with different amounts of phosphate glass (0%, 2%, 4%, 6%, and 8%) and heating them to high temperatures to form solid disks.
Then they tested the materials using:
- X-ray diffraction (XRD): Like looking at a material’s “fingerprint” to see what crystal structures it has.
- Scanning electron microscopy (SEM): A super close-up “camera” to see the size and shape of grains (tiny crystals) inside.
- Electrical tests:
- Measuring dielectric constant (how well the material stores electric charge)
- Measuring polarization-electric field (P-E) loops to see how the material responds to electric fields and how much energy it can store and release
They also used a math-based model called Landau-Ginzburg-Devonshire (LGD) theory to estimate energy storage and compare it with the experiments.
Explaining key terms
- Ceramic grains: Imagine the material is made of tiny pebbles packed together. Smaller pebbles can make the material stronger and more uniform.
- Breakdown strength: The maximum electric field a material can handle before it “fails,” like how much air you can pump into a balloon before it pops.
- Dielectric constant: How well the material holds electric charge. Higher means it can store more, but that’s only part of the story.
- P-E hysteresis loop: A graph that shows how the material’s polarization (how its internal charges line up) changes when you apply and remove an electric field. Slimmer loops mean less energy lost and better efficiency.
- Recoverable energy density: How much energy you can store and get back per unit volume (like how much water a sponge can soak up and squeeze out).
- Energy efficiency: What percentage of stored energy you can actually get back (less waste).
What did they find?
- Structure change: Pure BCZT showed a mix of two crystal phases (orthorhombic and tetragonal). Adding the glass pushed it towards a single tetragonal phase. This can change how the material behaves electrically.
- Smaller grains and denser material: With more glass, grain size shrank from about 6.4 micrometers to about 1.25 micrometers. Smaller grains and a denser structure help resist electrical breakdown and allow higher electric fields.
- Dielectric constant decreased: As glass content increased, the ability to hold charge (dielectric constant) went down. This is normal because the glass itself doesn’t store charge as well as the ceramic.
- Better energy storage performance at the right glass amount:
- The sample with 4% glass (called BCZT4) was the best.
- It reached a high electric field of 135 kV/cm (much higher than pure BCZT’s ~25 kV/cm).
- It achieved a recoverable energy density of about 0.52 J/cm³ and an efficiency of about 62%.
- That’s roughly 6.6 times more energy than pure BCZT (which had ~0.075 J/cm³).
- Slimmer P-E loops: With glass, the loops became narrower and more “relaxor-like,” meaning less energy was lost and the material handled stronger fields better.
- The math model matched reality: The LGD theory gave energy storage values close to the measured ones, which helps predict performance in future designs.
Why are these results important?
- Even though the dielectric constant dropped, the material’s ability to handle much higher electric fields mattered more. Energy stored in a capacitor depends on both the material properties and the maximum field it can withstand. Here, boosting the breakdown strength and reducing losses led to better overall energy storage.
- The best performance came from balancing the amount of glass: too little didn’t help much, too much started to hurt performance. The “sweet spot” was 4% glass.
What could this mean in the real world?
- Safer, lead-free capacitors: These materials avoid toxic lead and still perform well.
- Better energy storage for fast electronics: Higher energy density and good efficiency can make devices smaller and more powerful.
- Practical manufacturing: The glass helps make the ceramic denser at lower temperatures, which is useful for production.
- Predictable design: Since the theory matched experiments, engineers can use it to design new materials more quickly.
In short, by adding just the right amount of phosphate glass to BCZT, the researchers created a lead-free ceramic that stores more energy, wastes less, and can handle stronger electric fields—making it a promising material for future high-performance capacitors.
Knowledge Gaps
Knowledge gaps, limitations, and open questions
The following points summarize what remains uncertain or unexplored and could guide future research:
- Composition optimization:
- Only five glass contents (0–8 wt% in coarse 2 wt% steps) were tested; the reported optimum at 4 wt% needs finer compositional mapping (e.g., 3–5 wt% in 0.5 wt% steps) and exploration beyond 8 wt% to confirm global optima.
- The BNNWP glass itself is fixed in composition; the roles and optimal ratios of BaO, Na2O, Nb2O5, WO3, and P2O5 within the glass remain unstudied.
- Phase identification and chemistry:
- Secondary phases appearing after glass addition (peaks ~2θ = 25–35°) are neither identified nor quantified; their structure, composition, and volume fraction and how they affect dielectric/leakage properties are unknown.
- The mechanism behind the O+T to T phase transformation with glass addition is unclear (true lattice substitution vs. elastic strain vs. intergranular stress); no direct evidence of cation interdiffusion from the glass into the perovskite lattice.
- No chemical/structural mapping at grain boundaries; absence of EDS/EPMA/TEM/PFIB data to confirm glass distribution, thickness, continuity, interfacial reaction layers, or core–shell structures.
- Microstructure–property correlations:
- Grain size reduction is reported, but the method, statistics, and uncertainty of grain-size measurements are not provided; no quantitative correlation (e.g., EBDS ∝ G−b with fitted b) is established.
- The hypothesized performance degradation at higher glass content (coarsened/discontinuous glass at grain boundaries) is speculative; no microstructural metrics (e.g., grain-boundary film thickness distributions) substantiate this claim.
- Relative densities and porosity are not quantified against theoretical density; densification mechanisms and sintering kinetics (e.g., shrinkage curves, activation energies) are not analyzed.
- Electrical breakdown and reliability:
- True dielectric breakdown strength (BDS) is not measured; reported Emax appears to be the maximum applied field rather than a statistically evaluated breakdown field.
- No Weibull analysis or sample-size statistics to establish breakdown reliability, scatter, and failure modes.
- Leakage current characteristics (I–E, temperature dependence) are absent; the origins of energy loss (leakage vs. hysteretic loss) are not deconvolved.
- Operating conditions and stability:
- Energy storage performance (Wrec, η) is evaluated only at room temperature and 100 Hz; behavior across temperature (below/above Tc), frequency (kHz–MHz), and under dc bias remains unknown.
- No thermal stability of Wrec and η (e.g., 25–150°C), thermal cycling, or thermal aging data.
- Charge–discharge rate capability, efficiency at high dE/dt, and pulse power metrics are not assessed.
- Cycling endurance/fatigue (104–106 cycles), humidity sensitivity, and long-term stability are not investigated.
- Dielectric/ferroelectric characterization depth:
- Dielectric relaxation/relaxor behavior is inferred but not rigorously analyzed (no Vogel–Fulcher fitting, no broadening parameters, no Rayleigh analysis).
- P–E loops are measured only at 100 Hz; frequency dependence of hysteresis, coercive field, and energy loss is missing.
- No dc-bias-dependent permittivity or nonlinearity characterization to link to PNR dynamics and field tunability.
- LGD modeling limitations:
- The Landau model fit treats a and b as field- and temperature-independent for each sample; relaxor ferroelectrics typically exhibit strong T and E dependence—this assumption is not validated.
- The physical meaning and units of fitted coefficients (including the sign changes in b for some compositions) are not discussed; potential implications for phase stability and double-well profiles are not examined.
- Agreement between calculated and experimental energies is shown for a single field/rate; sensitivity to measurement noise, fitting range, and discharge vs. charge paths is not addressed.
- Processing constraints and scalability:
- Sintering temperatures (1250–1350°C) remain high for co-firing with base-metal electrodes; the extent to which BNNWP glass lowers firing temperature, and compatibility with multilayer capacitor processing, are not demonstrated.
- The effect of pellet thickness on apparent breakdown field (thickness scaling) is not studied; only ~0.25 mm samples are reported.
- Device-level considerations:
- No measurement of practical charge–discharge efficiency using pulse circuits (e.g., 10–1000 μs discharge), ESR, or Q-factor relevant to pulse power applications.
- Electrode interface effects (e.g., Schottky barriers with Ag, interfacial layers) and their impact on leakage and breakdown are not characterized.
- Benchmarking and context:
- Comparisons to literature span different fields and testing protocols; normalization for electric field, sample thickness, and measurement conditions is lacking, limiting fair benchmarking.
- Despite improved η, the achieved Wrec (0.52 J/cm3 at 135 kV/cm) is modest versus state-of-the-art; routes to push Emax without sacrificing η (e.g., multilayer architectures, core–shell grains, alternative glass chemistries) are not explored.
- Environmental and materials aspects:
- Potential volatility or segregation of Na, P, and W during sintering and their effects on stoichiometry/leakage are not examined.
- No assessment of lead-free environmental benefits vs. any new environmental/health risks introduced by the specific glass composition.
- Reproducibility and uncertainty:
- No error bars, replicate sample data, or batch-to-batch variability are provided for structural, dielectric, or energy storage metrics.
These gaps point to specific follow-ups: comprehensive phase/chemistry analysis at grain boundaries (TEM-EDS/EELS), true breakdown and reliability testing (Weibull), temperature- and frequency-resolved energy storage and leakage studies, rigorous relaxor analysis, expanded compositional and processing optimization (glass chemistry, content, firing profile), and device-relevant pulse testing with endurance and environmental stability assessments.
Practical Applications
Immediate Applications
The following applications can be implemented or piloted with existing materials, equipment, and workflows, drawing directly from the paper’s demonstrated results (notably BCZT with 4 wt% BNNWP glass achieving Wrec ≈ 0.52 J/cm³ at 135 kV/cm and η ≈ 62.4%, reduced sintering temperatures to ~1250–1300°C, refined grain size down to ~1.2 μm, and improved breakdown strength and dielectric stability).
- Lead-free, glass-modified BCZT dielectrics for prototype multilayer ceramic capacitors (MLCCs)
- Sector: Electronics, Power Electronics, Automotive
- Use cases:
- High-temperature snubber and pulse capacitors in gate drivers and compact power modules (e.g., GaN/SiC converters) where polymer films struggle thermally.
- Fast-discharge capacitors in compact pulse circuits requiring slimmer hysteresis and moderate energy density with reasonable efficiency.
- Tools/products/workflows:
- Substitute the ceramic dielectric in small-format MLCC prototypes with (1–x)BCZT–xBNNWP at x ≈ 4 wt% for maximal recoverable energy density and higher Emax.
- Maintain process steps (tape casting, lamination) but adjust co-firing windows to reflect lowered sintering temperatures (1250–1300°C vs 1350°C).
- Assumptions/dependencies:
- Compatibility of the phosphate glass phase with internal electrodes (Ni/Cu) under reducing atmospheres; lab results used Ag electrodes in air.
- Maintain high breakdown strength when scaled to thin layers; defect control critical.
- Lower-temperature co-sintering routes for BaTiO3-based lead-free dielectrics
- Sector: Advanced Manufacturing, Energy-Efficient Processing
- Use cases:
- Immediate reduction in kiln energy consumption by exploiting BNNWP’s low melting temperature and liquid-phase sintering to densify at 50–100°C lower than pure BCZT.
- Tools/products/workflows:
- Incorporate BNNWP glass frits (2–6 wt%) into BCZT feedstocks; adjust dwell times and ramp profiles to achieve target densification.
- Inline SEM/porosity mapping and Archimedes density checks to lock in high density and fine grains for elevated breakdown strength.
- Assumptions/dependencies:
- Stable glass composition control (BaO–Na2O–Nb2O5–WO3–P2O5) at production scale.
- Moisture and sodium mobility mitigation (e.g., encapsulation, barrier coatings).
- Relaxor-like ferroelectric ceramics with slim hysteresis for power-pulse conditioning
- Sector: Industrial Power Systems, Test & Measurement
- Use cases:
- Capacitive pulse shaping and energy recovery blocks in lab pulsers, compact radar drivers, and non-lethal EMI/ESD test rigs requiring repeatable discharge and moderate η with low tanδ at kHz–MHz.
- Tools/products/workflows:
- Leverage x ≈ 4 wt% BNNWP for slim P–E loops and lower Pr; design capacitor stacks aimed at 10–100 kV/cm operating fields.
- Assumptions/dependencies:
- Adequate thermal management across 25–100°C and controlled humidity to limit leakage.
- Materials design workflow using Landau-Ginzburg-Devonshire (LGD) parameter extraction
- Sector: Academia, R&D, Materials Informatics
- Use cases:
- Rapid screening of glass-additive levels by fitting E–P curves to extract a, b coefficients and predict Wrec/Wtot/η prior to large-scale synthesis.
- Tools/products/workflows:
- Standard ferroelectric testers (e.g., PolyK CPE1701) plus scripted fitting (Python/Matlab) to Equation E = aP + bP³; use Eq. (6) to compute energy metrics.
- Assumptions/dependencies:
- Temperature dependence of a, b in relaxors must be included for accurate device-range predictions.
- Lead-free compliance and green procurement guidance
- Sector: Policy, Corporate Sustainability, Supply Chain
- Use cases:
- Immediate alignment with RoHS and broader lead-reduction policies by substituting PZT-class dielectrics with BCZT-based compositions in non-piezoelectric energy storage roles.
- Tools/products/workflows:
- Procurement specs referencing BCZT+glass dielectric families; supplier audits for lead-free lines.
- Assumptions/dependencies:
- Device performance and reliability meet application-specific standards (e.g., AEC-Q200 for automotive passive components).
Long-Term Applications
The following opportunities require further research, scaling, and/or engineering development to address field strength scaling, reliability, electrode compatibility, and environmental stability.
- High-energy-density lead-free MLCCs for EV powertrains and DC-link buffers
- Sector: Automotive, Energy, Industrial Drives
- Use cases:
- Compact DC-link capacitors operating at elevated temperatures (>125°C) with stable dielectric behavior and fast charge–discharge.
- Potential products:
- Stacked MLCC banks with graded glass content (e.g., 2–4 wt% near electrodes for breakdown strength, lower glass in core for higher εr).
- Dependencies:
- Co-firing compatibility with Ni/Cu electrodes in reducing atmospheres; long-term humidity and Na-ion migration control; thermal cycling and lifetime (THB, HTRB) data.
- Medical pulse delivery (e.g., compact defibrillator modules) with ceramic pulse capacitors
- Sector: Healthcare, Medical Devices
- Use cases:
- Replace bulky electrolytics with robust ceramic banks that offer higher pulse rate capability, better shelf life, and improved thermal tolerance.
- Dependencies:
- Raising Wrec towards ≥1–2 J/cm³ at practical voltages via thinner layers, multilayer stacks, and further BDS enhancement; rigorous biocompatibility and safety standards; shock-cycle endurance.
- Grid and defense pulsed-power conditioning (compact Marx generators, radar, laser drivers)
- Sector: Energy, Defense, Research Infrastructure
- Use cases:
- Modular, robust pulse capacitors less sensitive to temperature, with repeatable discharge and moderate efficiency.
- Dependencies:
- Achieving very high breakdown fields (≥300 kV/cm) comparable to best-in-class relaxor BT systems using glass-assisted grain-boundary engineering (e.g., core–shell, Al2O3/SiO2 coatings, dopant co-segregation).
- Digital twin and inverse design for glass-modified ferroelectrics
- Sector: Materials Informatics, Software
- Use cases:
- Integrate LGD parameter extraction with microstructure descriptors (grain size, porosity, secondary phases) to predict Wrec/η/BDS; guide composition and process windows.
- Tools/products:
- Software plugins for COMSOL/Ansys or open-source Python packages that take E–P loops and SEM/XRD features as inputs to propose optimal x and firing profiles.
- Dependencies:
- Expanded datasets across temperatures/frequencies; standardized E–P acquisition protocols; uncertainty quantification.
- Additive and gradient manufacturing of BCZT+glass dielectrics
- Sector: Advanced Manufacturing, Printed Electronics
- Use cases:
- Inkjet/screen-printable inks with BNNWP-modified BCZT for conformal capacitors; functionally graded glass content to balance εr and BDS across thickness.
- Dependencies:
- Rheology control of ceramic–glass inks; low-temperature densification routes compatible with printed electrodes; microstructural stability in thin films.
- Standards and certification frameworks for lead-free ceramic energy-storage capacitors
- Sector: Policy, Standardization (IEC, JEDEC, AEC)
- Use cases:
- Develop qualification metrics for recoverable energy density, efficiency, breakdown strength, and stability for lead-free relaxor ceramics.
- Dependencies:
- Interlaboratory benchmarks, lifetime and failure-mode studies under bias/temperature/humidity, and application-specific derating rules.
- Consumer electronics power delivery and fast chargers
- Sector: Consumer Electronics
- Use cases:
- Miniaturized pulse/surge suppression and energy buffering with improved thermal headroom vs polymer films.
- Dependencies:
- Scaling to very thin dielectric layers with controlled defects; maintaining low loss (tanδ) across MHz switching frequencies; competitive cost vs polymer MLCCs/films.
Cross-cutting assumptions and risks
- Field scaling and reliability: Demonstrated Emax at 0.25 mm thickness may not directly translate to thin multilayers; defect density and grain-boundary chemistry will govern BDS in production.
- Electrode compatibility: Phosphate glass phases must be made compatible with Ni/Cu co-firing and reducing atmospheres; otherwise, Ag/Pt electrodes add cost.
- Environmental stability: Na-containing phosphate glasses can be moisture sensitive; long-term leakage and drift under humidity/temperature must be mitigated (barrier coatings, encapsulation).
- Performance trade-offs: Increasing glass content lowers εr and can introduce secondary phases; optimization around x ≈ 4 wt% appears best, but application-specific tuning is required.
- Benchmarks: Current Wrec (0.52 J/cm³, η ≈ 62%) is promising but below best-in-class lead-free relaxor ceramics at higher fields; further microstructural and compositional engineering is needed for top-tier applications.
Glossary
- Agate mortar: A hard, non-reactive grinding tool used to mill powders for ceramic synthesis. "then milled in an agate mortar with ethanol."
- Archimedes method: A buoyancy-based technique for measuring the density of solid samples. "The density (d) of the BCZTx was measured at room temperature by Archimedes method."
- Ba0.85Ca0.15Zr0.10Ti0.90O3 (BCZT): A lead-free perovskite ceramic composition engineered for dielectric and piezoelectric properties. "Lead-free Bao.85Cao.15Zro.10Tio.9003 (BCZT) ceramics with different BaO-Na2O-Nb2O5- WO3-P2O5 (BNNWP) glass content"
- BaO-Na2O-Nb2O5-WO3-P2O5 (BNNWP) glass: A phosphate glass system used as a sintering aid and microstructure modifier in ceramics. "BaO-Na2O-Nb2O5- WO3-P2O5 (BNNWP) glass"
- Breakdown strength (BDS): The maximum electric field a dielectric can withstand before electrical failure. "higher breakdown strength (BDS)"
- Curie temperature (Tc): The temperature at which a ferroelectric material transitions to a paraelectric state. "The decrease in the Tc could be attributed to (i) the transition from a long-term order to a short- term order [25]"
- Dielectric constant (Er): The relative permittivity indicating how much electric energy a material can store. "The temperature dependence of the dielectric constant (Er) of BCZTx ceramics at different frequencies is shown in Fig.5."
- Dielectric loss (tan δ): A measure of energy dissipation in a dielectric under an alternating electric field. "The temperature-dependence of the dielectric losses (tan 8) of BCZTx ceramics at 1kHz is shown in Fig. 7."
- Energy efficiency (n): The percentage of stored energy that is recoverable during discharge. "Consequently, the energy efficiency (n) can be determined using Eq. (3) [27]."
- Energy storage density: The amount of electrical energy stored per unit volume of a material or device. "The energy storage density is determined by the material's dielectric constant and the electrical breakdown resistance [6]."
- Ferroelectric behavior: Material behavior characterized by spontaneous polarization reversible by an external electric field. "BCZT0 ceramic displays typical ferroelectric behavior"
- Grain boundary: The interface between two grains (crystallites) in a polycrystalline material, influencing transport and mechanical properties. "the liquid glass phase existing between the grains can limit the migration of the grain boundary and prevent grain growth"
- Impedance analyzer (LCR meter): An instrument that measures impedance, capacitance, and resistance over a range of frequencies. "The dielectric properties were measured by using an impedance analyzer (LCR meter hp 4284A 20Hz-1MHz)."
- Landau-Ginzburg-Devonshire (LGD) theory: A phenomenological framework describing ferroelectric phase behavior and energy via Landau expansion. "The energy density was also calculated using the Landau-Ginzburg-Devonshire (LGD) theory."
- Morphotropic phase boundary (MPB): A compositional region where two crystal phases coexist, often enhancing functional properties. "Bao.85Cao.15Zro.10Tio.9003(BCZT) ceramic exhibits excellent dielectric and piezoelectric properties due to the closeness to morphotropic phase boundary (MPB) [11]-[13]."
- Orthorhombic–tetragonal (O–T) phase transition: A structural transformation between orthorhombic and tetragonal crystal phases. "present two obvious polymorphic phase transitions corresponding to the orthorhombic-tetragonal (O-T) and tetragonal-cubic (T-C) transitions, respectively."
- P-E hysteresis loop: The polarization–electric field curve that characterizes ferroelectric switching and energy loss. "The polarization-electric field (P-E) hysteresis loops of a BCZTx ceramics with a thickness of 0.25mm were investigated"
- Permittivity: A material property quantifying its response to an electric field; closely related to the dielectric constant. "BaTiO3-based dielectric ceramics have been widely studied for energy storage devices due to their high permittivity and low energy loss [8]-[10]."
- Polar nanoregions (PNRs): Nanoscale regions with local polarization that contribute to relaxor behavior and slim hysteresis. "which promotes the formation of polar nanoregions (PNRs) [26]"
- Relaxor ferroelectrics: Ferroelectrics with diffuse phase transitions, strong frequency dispersion, and nanoscale polar heterogeneity. "Note that the coefficients a and b are temperature-dependent in relaxor ferroelectrics"
- Remnant polarization (Pr): The residual polarization retained after the external electric field is removed. "the remnant polarization (Pr), the maximum polarization (Pmax) and the maximal electric field (Emax)"
- Rietveld refinement: A method for quantitatively fitting powder XRD patterns to extract crystal structure parameters. "Figure 1 presents Rietveld fitted X- ray difraction patterns"
- Scanning Electron Microscope (SEM): An imaging technique using focused electron beams to resolve microstructure and morphology. "Scanning electron microscope (SEM, Tescan VEGA3) was used to examine the morphology of BCZTx ceramics."
- Sintering temperature: The temperature at which particulate materials are densified by thermal treatment. "The appropriate sintering temperature corresponds to the highest density"
- Solid-state reaction method: A synthesis technique where solid precursors react upon heating to form ceramics. "were prepared by the conventional solid-state reaction method."
- Space group P4mm: A crystallographic symmetry designation for a tetragonal structure. "For all compositions, the results reveal a significant compromise with the tetragonal structure (P4mm)."
- Tetragonal–cubic (T–C) phase transition: A structural transformation between tetragonal and cubic crystal phases. "present two obvious polymorphic phase transitions corresponding to the orthorhombic-tetragonal (O-T) and tetragonal-cubic (T-C) transitions, respectively."
- X-ray diffraction (XRD): A technique for determining crystal structures and phases via diffraction of X-rays. "The phase structure of BCZTx ceramics was analyzed by the X-ray diffraction (XRD, Panalytical™M X-Pert Pro spectrometer) using Cu-Ka radiation (2~1.5406 Å)."
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