Filtern
Erscheinungsjahr
Dokumenttyp
- Zeitschriftenartikel (56)
- Vortrag (50)
- Beitrag zu einem Tagungsband (26)
- Beitrag zu einem Sammelband (5)
- Posterpräsentation (5)
- Buchkapitel (3)
- Sonstiges (1)
- Forschungsbericht (1)
Schlagworte
- LTCC (35)
- Ferrite (7)
- Co-firing (5)
- Keramische Multilayer (5)
- Sintering (5)
- Keramik (4)
- Pressure-assisted sintering (4)
- Calcination (3)
- Capacitor (3)
- Dielectric properties (3)
Organisationseinheit der BAM
Eingeladener Vortrag
- nein (50)
Determination of pore sizes on sintered ceramic materials using image analysis and X-ray refraction
(1997)
Co-firing of low temperature co-fired ceramics (LTCC) and functional ceramics like ferrites is a promising approach to increase the level of integration in future microsystems, and to create new applications for LTCC technology. Besides the development of compatible material combinations, the configuration of the sintering process is an important issue for successful co-firing. A method is presented to derive the linear shrinkage mismatch of a material combination based on density data calculated from the master sintering curves (MSCs) of the individual materials. The influence of the firing profile on the constraint in the combined multilayer can be anticipated using this method. To investigate and improve the co-firing of ferrite and dielectric tape, the shrinkage mismatch with respect to heating rate was studied. A significant reduction of shrinkage mismatch was found for increased heating rates. The calculated results are verified by lateral shrinkage measurements on combined laminates.
Recent advances in the development of high gauge factor thin films for strain gauges prompt the research on advanced substrate materials. A glass ceramic composite has been developed in consideration of a high coefficient of thermal expansion (9.4 ppm/K) and a low modulus of elasticity (82 GPa) for the application as support material for thin-film sensors. In the first part, constantan foil strain gauges were fabricated from this material by tape casting, pressure-assisted sintering, and subsequent lamination of the metal foil on the planar ceramic substrates. The accuracy of the assembled load cells corresponds to accuracy class C6. That qualifies the load cells for the use in automatic packaging units and confirms the applicability of the low-temperature co-fired ceramic (LTCC) substrates for fabrication of accurate strain gauges. In the second part, to facilitate the deposition of thin-film sensor structures to the LTCC substrates, pressure-assisted sintering step is modified using smooth setters instead of release tapes, which resulted in fabrication of substrates with low average surface roughness of 50 nm. Titanium thin films deposited on these substrates as test coatings exhibited low surface resistances of 850 Ω comparable to thin films on commercial alumina thin-film substrates with 920 Ω. The presented material design and advances in manufacturing technology are important to promote the development of high-performance thin-film strain gauges.
Integration of magnetic functional components in LTCC Circuit boards calls for co-firing of dielectric and ferrite tapes. Ni-Cu-Zn ferrites with permeability of p=900 were developed which can be fully densified at the Standard LTCC sintering temperature of 900 °C. Successful co-firing of this ferrite with dielectric tapes requires the adaptation of the shrinkage behavior of the materials as well as the thermal expansion during the cooling period - especially in the temperature range below the transformation point of the glassy phase of the dielectric tape. To match these preconditions, a new dielectric LTCC material with steep sintering curve and high thermal expansion coefficient was designed. Sintered multilayer composed of Ni-Cu-Zn ferrite and tailored dielectric tapes are free of cracks and possess no open porosity. No significant interdiffusion between the ferrite and dielectric tapes was found by EDX measurements. Compared to pure ferrite laminates the permeability of co-sintered Ni-Cu-Zn ferrite layers is drastically reduced to 400, i.e. a decrease of more than 50 %.
To investigate the origin of this permeability reduction, Ni-Cu-Zn ferrite laminates were sintered separately, and in combination with alumina release tapes or dielectric tapes, respectively. SEM and EDX analysis of co-fired laminates reveal differences in the ferrite grain growth behavior. Ferrite laminates with homogeneous microstructure and grain size up to 50 pm exhibit large permeability. However, growth of ferrite grains does not take place near the interface between ferrite and release or dielectric tapes. There is a strong correlation between high permeability and volume fraction of large ferrite grains. Regions of fine and coarse grains inside the ferrite layers show different bismuth concentration; the Bi-content is larger in regions of fine ferrite grains.
Further miniaturization of electronic packaging calls for integration of magnetic functional components into LTCC modules. For integration of magnetic function into LTCC, low fired MnZn- and NiCuZn-ferrites which can be fully densified at the standard LTCC sintering temperature of 900°C were developed. To co-fire these ferrite tapes with dielectric tapes the sintering shrinkage and the coefficient of thermal expansion of ferrite and dielectric tapes must be matched. For each ferrite material a new LTCC dielectric material was designed. The embedded ferrite tapes into new LTCC dielectric tapes can be sufficiently densified during co-firing at 900°C without any cracking. Compared to separately sintered ferrites the permeability of embedded ferrite tapes is reduced. For embedded NiCuZn ferrites permeabilities between 230 and 570 (at 2 MHz) according to the thickness of the embedded ferrite layer were measured. For embedded MnZn ferrites a permeability of 300 was measured.
Recent advances in the development of high gauge factor thin-films for strain gauges prompt the research on advanced substrate materials. A glass ceramic composite has been developed in consideration of a high coefficient of thermal expansion and a low modulus of elasticity for the application as support material for thin-film sensors. Constantan foil strain gauges were fabricated from this material by tape casting, pressure-assisted sintering and subsequent lamination of the metal foil on the planar ceramic substrates. The sensors were mounted on a strain gauge beam arrangement and load curves and creep behavior were evaluated. The accuracy of the assembled load cells correspond to accuracy class C6. That qualifies the load cells for the use in automatic packaging units and confirms the applicability of the LTCC substrates for fabrication of accurate strain gauges. To facilitate the deposition of thin film sensor structures onto the LTCC substrates, the pressure-assisted sintering technology has been refined. By the use of smooth setters instead of release tapes substrates with minimal surface roughness were fabricated. Metallic thin films deposited on these substrates exhibit low surface resistances comparable to thin films on commercial alumina thin-film substrates. The presented advances in material design and manufacturing technology are important to promote the development of high performance thin-film strain gauges.
Integration of magnetic functional components in LTCC circuit boards calls for co-firing of dielectric and ferrite tapes. Ni-Cu-Zn ferrites with permeability of µ = 900 were fully densified at the standard LTCC sintering temperature of 900°C. Co-firing of this ferrite with dielectric tapes requires the adaptation of the shrinkage behavior of the materials as well as the thermal contraction during the cooling period – especially in the temperature range below the transformation point of the glass phase of the dielectric tape. To match these preconditions, a new dielectric LTCC material with steep sintering curve and high thermal expansion coefficient was designed. Sintered multilayer laminates composed of Ni-Cu-Zn ferrite and tailored dielectric tapes are free of cracks and possess no open porosity. No significant interdiffusion between the ferrite and dielectric tapes was found using microprobe analysis. Pure ferrite laminates show homogeneous microstructure with large grains up to 50 µm in diameter. However, growth of ferrite grains does not take place near the interface between ferrite and release or dielectric tapes. There is a strong correlation between permeability and volume fraction of large ferrite grains. Compared to pure ferrite laminates the permeability of co-sintered Ni-Cu-Zn ferrite layers is drastically reduced to 400, that is a decrease of more than 50%.
We studied sintering of LTCC-type glass matrix composites (GMCs) consisting of small glass and alumina particles of equal size. Primarily, crystals act as rigid inclusions, decelerating the densification rate. In later stages, they also dissolve, partially increasing the viscosity. Release of alumina finally induces crystallization of alumosilicates, which enables post-firing stability. To study both effects, two model GMCs were prepared: an α-Al2O3 + barium alumoborosilicate glass (BABS)GMC, which shows neither significant dissolution nor crystallization, and an α-Al2O3 + calcium alumoborosilicate glass (CABS)GMC, which dissolves readily and promotes crystallization. The kinetics of shrinkage for both GMC were modeled by utilizing Frenkel theory for the early stage and MackenzieShuttleworth theory for the late stage, assuming that sintering is superimposed by the weighted contributions of triparticle glasscrystal clusters, their random occurrence (ideal mixing), and a shrinkage rate controlled by the GMC effective viscosity. In agreement with modeling, the experimental results showed that the shrinkage rate of BABSGMC decreases progressively for crystal volume fractions Φ > 0.15. The attainable shrinkage is reduced by up to 8% for Φ = 0.45. For the CABSGMC with Φ = 0.25, a reduction of Φ to 0.20 was evident due to partial α-Al2O3 dissolution. This effect was found able to increase the sintering temperature by ~5060 K.
Multilayer ceramic devices based on low-temperature co-fired ceramics (LTCC) materials provide a very promising technology. Most LTCC tapes available today contain considerable fractions of glass powders to lower the sintering temperature. However, the glassy phases offer more possibilities to set a proper sintering behavior, on the one hand, and to tailor the desired properties of the final LTCC substrate, on the other. The exploitation of demixing and subsequent crystallizing glass compositions was shown on an example of a low-permittivity (4.4)low-loss (1.5 × 103) LTCC with a high quartz content. In another LTCC material, undesired demixing could be restricted and the crystal phase anorthite could be triggered by partial dissolution of alumina in the liquid phase during sintering. To estimate the effect of silver diffusion in the latter material, the surroundings of a pure silver via were studied. A silver-contaminated range of 50 µm was detected. Using model glasses containing silver oxide, a strong influence of dissolved silver on viscosity and crystallization behavior of the liquid phase was demonstrated. The dielectric properties of the sintered substrates were not degraded.
New applications of ceramic multilayers, for example, in biotechnology, sensor technology, and chemical micro-reaction technique, call for cavities with complex geometries. Hot embossing offers a promising, cost-effective way to generate these structures on the surfaces of green tapes or laminates. Cavities inside low-temperature co-fired ceramic multilayer were manufactured by a combination of hot embossing, lamination by a special adhesive technique, and zero shrinkage sintering. The edge and surface quality in the green state as well as the sintered multilayers with surface structures and cavities were extensively characterized by laser surface scanning, optical and ultrasound microscopy. Sintering shrinkage of hot-embossed laminates could be reduced in the x and y directions to less than 0.5%.
Über das Sintern von LTCC
(2007)
For co-firing of MnZn-ferrite tapes and LTCC dielectric tapes, the sintering shrinkage curves and the coefficient of thermal expansion of ferrite and dielectric tapes were matched. Highly densified embedded ferrite without any cracks could be manufactured by co-firing at 900 °C in nitrogen atmosphere. However, the permeability of MnZn-ferrite co-fired between dielectric tapes is significantly reduced (µ´=100) compared to that of the separately sintered ferrite (µ´=500). Changes in the phase stability and microstructure of MnZn-ferrite were investigated to explain the permeability reduction in the embedded ferrite. It is supposed that early densification of the dielectric tapes on the top and bottom of the ferrite layer prevent the gas exchange during sintering which is necessary for (Mn,Zn)Fe2O4 spinel formation. As a result, high amount of Fe2O3 secondary phase and a Mn-rich spinel phase with low permeability remain in the embedded ferrite layer.
Silver in LTCC - Interfacial Reactions, Tranpsort Processes and Influence on Properties of Ceramics
(2009)
LTCC-Modules with integrated ferrite layers - Strategies for material development and co-sintering
(2009)
The integration of passive components (resistors, capacitors, inductors) into LTCC modules is a challenging task in multilayer ceramics technology. We report on multilayer assemblies consisting of combined layers of ferrite and dielectric LTCC tapes. Ni-Cu-Zn ferrites with maximum shrinkage at 900°C were processed to green tapes and laminated with dielectric LTCC tapes. Cosintering at 900°C led to multilayers with different defects such as incomplete densification of the ferrite layers, cracks, and warpage. Since ferrite tapes do not really allow compositional changes without deterioration of magnetic properties, the dielectric tape was modified with the following objectives: (i) matching of the shrinkage curves of dielectric and ferrite materials, (ii) adjusting the coefficients of thermal expansion to avoid cracking during cooling, and (iii) controlling of interface reactions. Using this concept we fabricated dense and defect-free multilayers consisting of dielectric and ferrite layers. However, compositional changes of the individual ferrite tapes require the development of a specific dielectric tape material with tailored properties.
Presented are results of an inter-laboratory study (ILS) for measurements of the particle size distribution of fine powders in wet dispersion by laser diffraction. In this proficiency test 32 participants from four countries took part. They utilized 13 different devices from 7 manufacturers.
Three commercial powders (glass spheres and two silicon carbide powders) showing a median diameter of about 30, 10 and 1 µm (volume distribution), respectively, were chosen for the procedure. A homogeneity study was carried out after the units had been separated and bottled.
All participants received their test samples including a description of the standard operating procedures based on ISO 13320:2009 – to ensure that experiments were performed in a consistent manner. Results were calculated using the Mie Theory. The general means and the precision of the results were estimated in accordance with ISO 5725-2:2002.
The evaluation showed excellent values of repeatability standard deviation. Values of 4 to 21?% of the reproducibility standard deviation of the results were found in the particle size range above 1 µm. Much larger deviation between the labs was detected in the case of smaller particles. Differences in the design of the analyzers were unambiguously identified as the main reason for the large deviations.
Glass-ceramic composites as insulation material for thermoelectric oxide multilayer generators
(2021)
Thermoelectric generators can be used as energy harvesters for sensor applications.
Adapting the ceramic multilayer technology, their production can be
highly automated. In such multilayer thermoelectric generators, the electrical insulation material, which separates the thermoelectric legs, is crucial for the performance of the device. The insulationmaterial should be adapted to the thermoelectric regarding its averaged coefficient of thermal expansion α and its sintering temperature while maintaining a high resistivity.
In this study, starting from theoretical calculations, a glass-ceramic Composite material adapted for multilayer generators fromcalciummanganate and Calcium cobaltite is developed. The material is optimized towards an α of 11 × 10−6 K−1 (20–500◦C), a sintering temperature of 900◦C, and a high resistivity up to 800◦C.
Calculated and measured α are in good agreement. The chosen glass-ceramic composite with 45 vol.% quartz has a resistivity of 1 × 107 Ωcm and an open porosity of <3%. Sintered multilayer samples from tape-cast thermoelectric oxides and screen-printed insulation show only small reaction layers. It can be concluded that glass-ceramic composites are a well-suited material class for insulation layers as their physical properties can be tuned by varying glass composition or dispersion phases.
Dieses Strategiepapier zielt darauf ab, Akteuren und Entscheidungsträgern den Status der Digitalisierung in der keramischen Fertigung, erfolgreiche Best-Practice-Beispiele aber auch die Herausforderungen nahezubringen, die es nun anzugehen gilt. Es ist die Vision, die Keramikfertigung durchgehend zu digitalisieren und alle Schritte des Produktkreislaufs lückenlos über die gesamte Wertschöpfungs- und Nutzungskette zu vernetzen: also eine Keramikindustrie 4.0 zu etablieren. Das Strategiepapier erfasst zunächst die Spezifität der keramischen Fertigung und nimmt eine Analyse des gegenwärtigen Standes der Digitalisierung in der keramischen Industrie vor, auch anhand einiger ausgewählter Beispiele aus der industriellen Praxis. Auf Basis der wesentlichen Bausteine für eine Fertigungsdigitalisierung werden schließlich die Chancen für Keramikproduzenten sowie der erforderliche Forschungs- und Entwicklungsbedarf aufgezeigt.
The relationship between fracture toughness and Yttria content in modern zirconia ceramics was revised. For that purpose, we evaluated here 10 modern Y2O3-stabilized zirconia (YSZ) materials currently used in biomedical applications, namely prosthetic and implant dentistry. The most relevant range between 2-5 mol% Y2O3 was addressed by selecting from conventional opaque 3 mol% YSZ up to more translucent compositions (4-5 mol% YSZs). A technical 2YSZ was used to extend the range of our evaluation. The bulk mol% Y2O3 concentration was measured by X-Ray Fluorescence Spectroscopy. Phase quantification by Rietveld refinement considered two tetragonal phases or an additional cubic phase. A first-account of the fracture toughness (KIc) of the pre-sintered blocks is given, which amounted to 0.4 – 0.7 MPa√m. In the fully-densified state, an inverse power-law behavior was obtained between KIc and bulk mol% Y2O3 content, whether using only our measurements or including literature data, challenging some established relationships. A linear relationship between KIc and the fraction of the transformable t-phase was established within the range of 30–70 vol%.
This study combines three different approaches to lower the sintering temperature of Sm-doped CaMnO3 to save energy in production and facilitate co-firing with other low-firing oxides or metallization. The surface energy of the powder was increased by fine milling, sintering kinetics were enhanced by additives, and uniaxial pressure during sintering was applied. The shrinkage, density, microstructure, and thermoelectric properties were evaluated. Compared to micro-sized powder, the use of finely ground powder allows us to lower the sintering temperature by 150 K without reduction of the power factor. By screening the effect of various common additives on linear shrinkage of CaMnO3 after sintering at 1100 ○C for 2 h, CuO is identified as the most effective additive. Densification at sintering temperatures below 1000 ○C can be significantly increased by pressure-assisted sintering. The power factor at room temperature of CaMnO3 nano-powder sintered at 1250 ○C was 445 μW/(m K2). Sintering at 1100 ○C reduced the power factor to 130 μW/(m K2) for CaMnO3 nano-powder, while addition of 4 wt.% CuO to the same powder led to ∼290 μW/(m K2). The combination of fine milling, CuO addition, and pressureassisted sintering at 950 ○C resulted in a power factor of ∼130 μW/(m K2). These results show that nano-sized powder and CuO addition are successful and recommendable strategies to produce CaMnO3 with competitive properties at significantly reduced temperatures and dwell times.
Plane LTCC substrates can be produced in zeroshrinkage technology by pressure-assisted sintering. The application of axial pressure during sintering supports densification, enhances cofiring of different materials, and restrains deformation. However, the sintered surfaces are affected by the release tapes and by the setters used in the pressure-assisted sintering process. In this study, the effect of release tape particle size on the surface properties of sintered substrates was investigated. Moreover, the substitution of release tape by the use of a vitreous carbon setter was tested. Surface roughness and sheet resistances of metallic thin films on the respective samples were determined. It was found that the roughness of the substrates is not directly correlated with the adequacy of the surface for thin-film deposition. Compared with a freely sintered sample with an average roughness (Ra) of 0.31 μm, pressure-assisted sintering created smoother surfaces using finegrained release tapes (Ra = 0.18 μm) and rougher surfaces using coarse release tapes (Ra = 0.46 μm). Still, sheet resistances were higher on all sinter-pressed samples. The vitreous carbon setter created unusual trenched surface structures, characterized by varying roughness values and intermediate sheet resistances on the LTCCs tested.
We have studied the integration of Ni-Cu-Zn ferrite spinels as well as substituted hexagonal Co2Y-and M-type ferrites into LTCC (Low Temperature Ceramic Co-firing) modules. The cofiring behavior and the magnetic properties of these materials were investigated and evaluated for multilayer applications. Ni-Cu-Zn ferrites exhibit permeabilities of µ=300–500 for operating frequencies in the MHz range. Cu-substituted Y-type ferrites Ba2Co2-x-yZnxCuyFe12O22 in combination with sintering additives display sufficient shrinkage and densification at 900°C. A permeability of µ=10 is observed; however, substituted Co2Y-type ferrites do not exhibit long-term stability at 900°C. Co/Ti-substituted M-type ferrites BaFe12-2yCoyTiyO19 (y=1.2) with planar magneto-crystalline anisotropy exhibit excellent soft magnetic behavior. Using sintering additives, complete densification is reached at 900°C and a permeability of µ=15 and a resonance frequency of larger than 1?GHz are observed. Integration of ferrite multilayer inductor components into LTCC modules using free and constrained cofiring technologies is demonstrated.
The sintering temperature of BaTiO3 powder was reduced to 900 °C due to the ZnO-B2O3-Li2O-Nb2O5-Co2O3 addition. Excellent densification was achieved after sintering at 900 °C for 2 h. The low sintering temperature of newly developed capacitor materials allows a co-firing with pure silver electrodes. The dielectric constant and the temperature stability of the dielectric constant are strongly correlated with the composition of the ZnO-B2O3-Li2O additives. A high dielectric constant up to 3000 and a dielectric loss less than 0.024 were measured on multilayer capacitors sintered at 900 °C with silver inner electrodes.
New applications of low-temperature co-fired ceramics (LTCC), such as pressure sensors or integrated functional layers, require materials that possess higher coefficients of thermal expansion (CTE). To fabricate LTCC with elevated CTE, two methods of material design are examined: firstly, glass ceramic composites (GCC), which consist of >50 vol% glass in the starting powder, and, secondly, glass-bonded ceramics (GBC), where glass is added as a sintering aid only. The CTE of GBC is mainly determined by the crystalline component. For GCC, the CTE can be well predicted, if CTE and elastic data of each phase in the microstructure are known. A nonlinear characteristic of the CTE versus phase composition was found with increasing Ecrystals/Eglass ratio and absolute CTE difference between the components. The glass composition and glass amount can be used to compensate the fixed properties of a crystalline material in a desired way. However, because the CTE and permittivity of a glass cannot be chosen independently, an optimum glass composition has to be found. For a given LTCC, it is possible to control the devitrification by shifting the glass composition. In this way, the resulting CTE values can be predicted more exactly and tailoring becomes possible. Different LTCC materials, based on the crystalline compounds Ba(La,Nd)2Ti4O12, ZrO2 (Y-TZP), SiO2 (quartz), and specially developed glasses, possessing an elevated CTE of around 10 × 10-6 K-1 while showing permittivity εr between 6 and 63, are introduced.
LTCC-modules with integrated ferrite layers - Strategies for material development and co-sintering
(2008)
Novel approaches of tunable devices for millimeter wave applications based on liquid crystal (LC) are presented. In the first part of the paper, a novel concept of a tunable LC phase shifter realized in Low Temperature Cofired Ceramics technology is shown while the second part of the paper deals with a tunable high-gain antenna based on an LC tunable reflectarray. The reflectarray features continuously beam scanning in between ±25°. Also first investigations on radiation hardness of LCs are carried out, indicating that LCs might be suitable for space applications.
Silver in LTCC - Interfacial reactions, transport processes and influence on properties of ceramics
(2009)
Due to addition of minor amounts of suitable additive combinations to BaTiO3 powder the sintering temperature was reduced to 900 °C. Excellent densification (more than 98% of theoretical density) and good dielectric properties were achieved after sintering at 900 °C for 2 hours. Dielectric properties can be improved by modifying the composition of sintering additives and additon of further dopants. The low sintering temperature of newly developed capacitor material allows a co-sintering with pure silver electrodes. No interfacial reaction between silver electrodes and ceramics was observed by microprobe analysis. The dielectric constants of about 1200 to 3000 and the dielectric losses of about 0.008 to 0.02 were measured (f = 1 kHz, T = 25 °C). The temperature dependency of dielectric constant for new capacitor materials is low, almost X7R characteristics. Furthermore, the densification and the dielectric properties of embedded capacitors in LTCC were investigated.
By addition of LiF-containing sintering additives to commercial BaTiO3 powder, more than 98% of the theoretical density was reached at a sintering temperature of 900 °C both on powder compacts and laminates. Dielectric measurements were performed on ceramic samples in the temperature and frequency ranges from -20 °C to 125 °C and from 103 to 106 Hz, respectively. High relative permittivity (εr ~ 3160) and low dielectric loss (tan δ ~ 0.014) were measured for tapes of the favoured material. The breakdown strength for tapes with a thickness of about 80 µm is 30 kV/mm. The microprobe analysis showed, that no interfacial reaction between the dielectric layer and the Ag-electrode had occurred.
The newly developed barium titanate ceramics completely densifying at 900 °C turned out to be promising for integration of buried capacitors in LTCC multilayers.
Sintering of LTCC
(2008)
Low Temperature Co-fired Ceramic materials (LTCC) have attracted growing interest in recent years since they are promising candidates for highly integrated ceramic packaging. This paper surveys materials concepts of related glass ceramic composites (GCC) and discusses unsolved problems and challenges. The densification of GCC based on "viscous sintering" may be affected by steric effects and partial dissolution of dispersed crystal particles, crystallization and phase boundary reactions.
Pressure-assisted sintering (PAS) is an established procedure for the production of low-temperature cofired ceramics (LTCC) without lateral shrinkage and minimal shrinkage tolerances for automotive and high-frequency applications. To develop a feasible model for the prediction of densification during that process, master sintering curves (MSCs) for the commercial LTCC DP951 were generated from thermomechanical analysis (TMA) data in the pressure regime from 2 to 500 kPa. Strain mainly related to creep deformation of the LTCC was identified by evaluation of the strain rate and was discarded for the determination of MSC parameters. It was found that no creep occurred at any pressure up to a relative density of 0.9. Different pressure levels can be modeled with the same activation energy of 400 kJ/mol. Densification curves predicted by the model were in good agreement with experimental data. Based on MSCs, the pressure-assisted master sintering surface was compiled to illustrate the influence of pressure on densification. The results show that the MSC approach is a suitable method to feasibly predict the densification of LTCC during PAS.