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1.
Sensors (Basel) ; 23(18)2023 Sep 06.
Article in English | MEDLINE | ID: mdl-37765737

ABSTRACT

Sourdough can improve bakery products' shelf life, sensory properties, and nutrient composition. To ensure high-quality sourdough, the fermentation has to be monitored. The characteristic process variables for sourdough fermentation are pH and the degree of acidity measured as total titratable acidity (TTA). The time- and cost-intensive offline measurement of process variables can be improved by utilizing online gas measurements in prediction models. Therefore, a gas sensor array (GSA) system was used to monitor the fermentation process of sourdough online by correlation of exhaust gas data with offline measurement values of the process variables. Three methods were tested to utilize the extracted features from GSA to create the models. The most robust prediction models were achieved using a PCA (Principal Component Analysis) on all features and combined two fermentations. The calibrations with the extracted features had a percentage root mean square error (RMSE) from 1.4% to 12% for the pH and from 2.7% to 9.3% for the TTA. The coefficient of determination (R2) for these calibrations was 0.94 to 0.998 for the pH and 0.947 to 0.994 for the TTA. The obtained results indicate that the online measurement of exhaust gas from sourdough fermentations with gas sensor arrays can be a cheap and efficient application to predict pH and TTA.

2.
Biotechnol Bioeng ; 120(10): 2925-2939, 2023 10.
Article in English | MEDLINE | ID: mdl-37350126

ABSTRACT

Online fluorescence monitoring has become a key technology in modern bioprocess development, as it provides in-depth process knowledge at comparably low costs. In particular, the technology is widely established for high-throughput microbioreactor cultivation systems, due to its noninvasive character. For microtiter plates, previously also multi-wavelength 2D fluorescence monitoring was developed. To overcome an observed limitation of fluorescence sensitivity, this study presents a modified spectroscopic setup, including a tunable emission monochromator. The new optical component enables the separation of the scattered and fluorescent light measurements, which allows for the adjustment of integration times of the charge-coupled device detector. The resulting increased fluorescence sensitivity positively affected the performance of principal component analysis for spectral data of Escherichia coli batch cultivation experiments with varying sorbitol concentration supplementation. In direct comparison with spectral data recorded at short integration times, more biologically consistent signal dynamics were calculated. Furthermore, during partial least square regression for E. coli cultivation experiments with varying glucose concentrations, improved modeling performance was observed. Especially, for the growth-uncoupled acetate concentration, a considerable improvement of the root-mean-square error from 0.25 to 0.17 g/L was achieved. In conclusion, the modified setup represents another important step in advancing 2D fluorescence monitoring in microtiter plates.


Subject(s)
Bioreactors , Escherichia coli , Fluorescence , Technology
3.
J Biol Eng ; 17(1): 12, 2023 Feb 13.
Article in English | MEDLINE | ID: mdl-36782293

ABSTRACT

BACKGROUND: Non-invasive online fluorescence monitoring in high-throughput microbioreactors is a well-established method to accelerate early-stage bioprocess development. Recently, single-wavelength fluorescence monitoring in microtiter plates was extended to measurements of highly resolved 2D fluorescence spectra, by introducing charge-coupled device (CCD) detectors. Although introductory experiments demonstrated a high potential of the new monitoring technology, an assessment of the capabilities and limits for practical applications is yet to be provided. RESULTS: In this study, three experimental sets introducing secondary substrate limitations of magnesium, potassium, and phosphate to cultivations of a GFP-expressing H. polymorpha strain were conducted. This increased the complexity of the spectral dynamics, which were determined by 2D fluorescence measurements. The metabolic responses upon growth limiting conditions were assessed by monitoring of the oxygen transfer rate and extensive offline sampling. Using only the spectral data, subsequently, partial least-square (PLS) regression models for the key parameters of glycerol, cell dry weight, and pH value were generated. For model calibration, spectral data of only two cultivation conditions were combined with sparse offline sampling data. Applying the models to spectral data of six cultures not used for calibration, resulted in an average relative root-mean-square error (RMSE) of prediction between 6.8 and 6.0%. Thus, while demanding only sparse offline data, the models allowed the estimation of biomass accumulation and glycerol consumption, even in the presence of more or less pronounced secondary substrate limitation. CONCLUSION: For the secondary substrate limitation experiments of this study, the generation of data-driven models allowed a considerable reduction in sampling efforts while also providing process information for unsampled cultures. Therefore, the practical experiments of this study strongly affirm the previously claimed advantages of 2D fluorescence spectroscopy in microtiter plates.

4.
Sci Rep ; 13(1): 235, 2023 01 05.
Article in English | MEDLINE | ID: mdl-36604451

ABSTRACT

Makespan dominates the manufacturing expenses in bakery production. The high energy consumption of ovens also has a substantial impact, which bakers may overlook. Bakers leave ovens running until the final product is baked, allowing them to consume energy even when not in use. It results in energy waste, increased manufacturing costs, and CO2 emissions. This paper investigates three manufacturing lines from small and medium-sized bakeries to find optimum makespan and ovens' idle time (OIDT). A hybrid no-wait flow shop scheduling model considering the constraints that are most common in bakeries is proposed. To find optimal solutions, non-dominated sorting genetic algorithm (NSGA-II), strength Pareto evolutionary algorithm (SPEA2), generalized differential evolution (GDE3), improved multi-objective particle swarm optimization (OMOPSO), and speed-constrained multi-objective particle swarm optimization (SMPSO) were used. The experimental results show that the shortest makespan does not always imply the lowest OIDT. Even the optimized solutions have up to 231 min of excess OIDT, while the makespan is the shortest. Pareto solutions provide promising trade-offs between makespan and OIDT, with the best-case scenario reducing OIDT by 1348 min while increasing makespan only by 61 min from the minimum possible makespan. NSGA-II outperforms all other algorithms in obtaining a high number of good-quality solutions and a small number of poor-quality solutions, followed by SPEA2 and GDE3. In contrast, OMOPSO and SMPSO deliver the worst solutions, which become pronounced as the problem complexity grows.


Subject(s)
Algorithms , Commerce
5.
Bioengineering (Basel) ; 9(9)2022 Sep 04.
Article in English | MEDLINE | ID: mdl-36134983

ABSTRACT

Multi-wavelength (2D) fluorescence spectroscopy represents an important step towards exploiting the monitoring potential of microtiter plates (MTPs) during early-stage bioprocess development. In combination with multivariate data analysis (MVDA), important process information can be obtained, while repetitive, cost-intensive sample analytics can be reduced. This study provides a comprehensive experimental dataset of online and offline measurements for batch cultures of Hansenula polymorpha. In the first step, principal component analysis (PCA) was used to assess spectral data quality. Secondly, partial least-squares (PLS) regression models were generated, based on spectral data of two cultivation conditions and offline samples for glycerol, cell dry weight, and pH value. Thereby, the time-wise resolution increased 12-fold compared to the offline sampling interval of 6 h. The PLS models were validated using offline samples of a shorter sampling interval. Very good model transferability was shown during the PLS model application to the spectral data of cultures with six varying initial cultivation conditions. For all the predicted variables, a relative root-mean-square error (RMSE) below 6% was obtained. Based on the findings, the initial experimental strategy was re-evaluated and a more practical approach with minimised sampling effort and elevated experimental throughput was proposed. In conclusion, the study underlines the high potential of multi-wavelength (2D) fluorescence spectroscopy and provides an evaluation workflow for PLS modelling in microtiter plates.

6.
Sensors (Basel) ; 22(15)2022 Jul 26.
Article in English | MEDLINE | ID: mdl-35898085

ABSTRACT

Chemometric models for on-line process monitoring have become well established in pharmaceutical bioprocesses. The main drawback is the required calibration effort and the inflexibility regarding system or process changes. So, a recalibration is necessary whenever the process or the setup changes even slightly. With a large and diverse Raman dataset, however, it was possible to generate generic partial least squares regression models to reliably predict the concentrations of important metabolic compounds, such as glucose-, lactate-, and glutamine-indifferent CHO cell cultivations. The data for calibration were collected from various cell cultures from different sites in different companies using different Raman spectrophotometers. In testing, the developed "generic" models were capable of predicting the concentrations of said compounds from a dilution series in FMX-8 mod medium, as well as from an independent CHO cell culture. These spectra were taken with a completely different setup and with different Raman spectrometers, demonstrating the model flexibility. The prediction errors for the tests were mostly in an acceptable range (<10% relative error). This demonstrates that, under the right circumstances and by choosing the calibration data carefully, it is possible to create generic and reliable chemometric models that are transferrable from one process to another without recalibration.


Subject(s)
Chemometrics , Spectrum Analysis, Raman , Animals , CHO Cells , Calibration , Cricetinae , Cricetulus , Least-Squares Analysis
7.
Foods ; 11(8)2022 Apr 18.
Article in English | MEDLINE | ID: mdl-35454758

ABSTRACT

There is increasing demand for cereal-based probiotic fermented beverages as an alternative to dairy-based products due to their limitations. However, analyzing and monitoring the fermentation process is usually time consuming, costly, and labor intensive. This research therefore aims to apply two-dimensional (2D)-fluorescence spectroscopy coupled with partial least-squares regression (PLSR) and artificial neural networks (ANN) for the on-line quantitative analysis of cell growth and concentrations of lactic acid and glucose during the fermentation of a teff-based substrate. This substrate was inoculated with mixed strains of Lactiplantibacillus plantarum A6 (LPA6) and Lacticaseibacillus rhamnosus GG (LCGG). The fermentation was performed under two different conditions: condition 1 (7 g/100 mL substrate inoculated with 6 log cfu/mL) and condition 2 (4 g/100 mL substrate inoculated with 6 log cfu/mL). For the prediction of LPA6 and LCGG cell growth, the relative root mean square error of prediction (pRMSEP) was measured between 2.5 and 4.5%. The highest pRMSEP (4.5%) was observed for the prediction of LPA6 cell growth under condition 2 using ANN, but the lowest pRMSEP (2.5%) was observed for the prediction of LCGG cell growth under condition 1 with ANN. A slightly more accurate prediction was found with ANN under condition 1. However, under condition 2, a superior prediction was observed with PLSR as compared to ANN. Moreover, for the prediction of lactic acid concentration, the observed values of pRMSEP were 7.6 and 7.7% using PLSR and ANN, respectively. The highest error rates of 13 and 14% were observed for the prediction of glucose concentration using PLSR and ANN, respectively. Most of the predicted values had a coefficient of determination (R2) of more than 0.85. In conclusion, a 2D-fluorescence spectroscopy combined with PLSR and ANN can be used to accurately monitor LPA6 and LCGG cell counts and lactic acid concentration in the fermentation process of a teff-based substrate. The prediction of glucose concentration, however, showed a rather high error rate.

8.
Foods ; 10(8)2021 Aug 04.
Article in English | MEDLINE | ID: mdl-34441575

ABSTRACT

Chia oil is a valuable source of omega-3-fatty acids and other nutritional components. However, it is expensive to produce and can therefore be easily adulterated with cheaper oils to improve the profit margins. Spectroscopic methods are becoming more and more common in food fraud detection. The aim of this study was to answer following questions: Is it possible to detect chia oil adulteration by spectroscopic analysis of the oils? Is it possible to identify the adulteration oil? Is it possible to determine the amount of adulteration? Two chia oils from local markets were adulterated with three common food oils, including sunflower, rapeseed and corn oil. Subsequently, six chia oils obtained from different sites in Kenya were adulterated with sunflower oil to check the results. Raman, NIR and fluorescence spectroscopy were applied for the analysis. It was possible to detect the amount of adulterated oils by spectroscopic analysis, with a minimum R2 of 0.95 for the used partial least square regression with a maximum RMSEPrange of 10%. The adulterations of chia oils by rapeseed, sunflower and corn oil were identified by classification with a median true positive rate of 90%. The training accuracies, sensitivity and specificity of the classifications were over 90%. Chia oil B was easier to detect. The adulterated samples were identified with a precision of 97%. All of the classification methods show good results, however SVM were the best. The identification of the adulteration oil was possible; less than 5% of the adulteration oils were difficult to detect. In summary, spectroscopic analysis of chia oils might be a useful tool to identify adulterations.

9.
Sci Rep ; 11(1): 9253, 2021 04 29.
Article in English | MEDLINE | ID: mdl-33927250

ABSTRACT

Chia seeds are becoming more and more popular in modern diets. In this contribution NIR and 2D-fluorescence spectroscopy were used to determine their nutritional values, mainly fat and protein content. 25 samples of chia seeds were analysed, whereof 9 samples were obtained from different regions in Kenya, 16 samples were purchased in stores in Germany and originated mostly from South America. For the purchased samples the nutritional information of the package was taken in addition to the values obtained for fat and protein, which were determined at the Hohenheim Core Facility. For the first time the NIR and fluorescence spectroscopy were used for the analysis of chia. For the spectral evaluation two different pre-processing methods were tested. Baseline correction with subsequent mean-centring lead to the best results for NIR spectra whereas SNV (standard normal variate transformation) was sufficient for the evaluation of fluorescence spectra. When combining NIR and fluorescence spectra, the fluorescence spectra were also multiplied with a factor to adjust the intensity levels. The best prediction results for the evaluation of the combined spectra were obtained for Kenyan samples with prediction errors below 0.2 g/100 g. For all other samples the absolute prediction error was 0.51 g/100 g for fat and 0.62 g/100 g for protein. It is possible to determine the amount of protein and fat of chia seeds by fluorescence and NIR spectroscopy. The combination of both methods is beneficial for the predictions. Chia seeds from Kenya had similar protein and lipid contents as South American seeds.

10.
Eng Life Sci ; 21(3-4): 169, 2021 Mar.
Article in English | MEDLINE | ID: mdl-33716615

ABSTRACT

DOI: 10.1002/elsc.202000058 Successful operation, control and optimization of biotechnological process depend on reliable real-time available measurements of the process variables. Although some hardware sensors are readily available, they often have several drawbacks: cost, sample destruction, discrete-time measurements, processing delay, sterilization, disturbances in the hydrodynamic conditions inside the bioreactor, etc. It is therefore of interest to use software sensors [29, 30]. The central idea behind a soft sensor is to use easily accessible on-line data for the estimation of other process variables that are either difficult to measure or only measured at low frequency [30]. The figure illustrates a software sensor for on-line monitoring of substrate and biomass production in backers yeast cultivation. For details see article DOI 10.1002/elsc.202000058 on page 169.

11.
Eng Life Sci ; 21(3-4): 170-180, 2021 Mar.
Article in English | MEDLINE | ID: mdl-33716616

ABSTRACT

Real-time information about the concentrations of substrates and biomass is the key to accurate monitoring and control of bioprocess. However, on-line measurement of these variables is a challenging task and new measurement systems are still required. An alternative are software sensors, which can be used for state and parameter estimation in bioprocesses. The software sensors predict the state of the process by using mathematical models as well as data from measured variables. The Kalman filter is a type of such sensors. In this paper, we have used the Unscented Kalman Filter (UKF) which is a nonlinear extension of the Kalman filter for on-line estimation of biomass, glucose and ethanol concentration as well as for estimating the growth rate parameters in S. cerevisiae batch cultivation, based on infrequent ethanol measurements. The UKF algorithm was validated on three different cultivations with variability of the substrate concentrations and the estimated values were compared to the off-line values. The results obtained showed that the UKF algorithm provides satisfactory results with respect to estimation of concentrations of substrates and biomass as well as the growth rate parameters during the batch cultivation.

12.
Adv Biochem Eng Biotechnol ; 177: 95-125, 2021.
Article in English | MEDLINE | ID: mdl-33174065

ABSTRACT

In the era of technology and digitalization, the process industries are undergoing a digital transformation. The available process models, advance sensor technologies, enhanced computational power and a broad set of data analytical techniques enable solid bases for digital transformation in the biopharmaceutical industry.Among various data analytical techniques, the Kalman filter and its non-linear extensions are powerful tools for prediction of reliable process information. The combination of the Kalman filter with a virtual representation of the bioprocess, called digital twin, can provide real-time available process information. Incorporation of such variables in process operation can provide improved control performance with enhanced productivity.In this chapter the linear discrete Kalman filter, the extended Kalman filter and the unscented Kalman filters are described and a brief overview of applications of the Kalman filter and its non-linear extensions to bioreactors are presented. Furthermore, in a case study an example of the digital twin of the backer's yeast batch cultivation process is presented. A digital twin of a bioreactor mirrors the processes of the real bioreactor. It contains the physical parts, the process model and prediction algorithm to predict the bioprocess variables. These values could be used for optimization and control of the process.


Subject(s)
Algorithms
13.
ACS Nano ; 14(10): 13127-13136, 2020 Oct 27.
Article in English | MEDLINE | ID: mdl-32960037

ABSTRACT

Highly polar materials are usually preferred over weakly polar ones to study strong electron-phonon interactions and its fascinating properties. Here, we report on the achievement of simultaneous confinement of charge carriers and phonons at the vicinity of a 2D vertical homovalent singularity (antiphase boundary, APB) in an (In,Ga)P/SiGe/Si sample. The impact of the electron-phonon interaction on the photoluminescence processes is then clarified by combining transmission electron microscopy, X-ray diffraction, ab initio calculations, Raman spectroscopy, and photoluminescence experiments. 2D localization and layer group symmetry properties of homovalent electronic states and phonons are studied by first-principles methods, leading to the prediction of a type-II band alignment between the APB and the surrounding semiconductor matrix. A Huang-Rhys factor of 8 is finally experimentally determined for the APB emission line, underlining that a large and unusually strong electron-phonon coupling can be achieved by 2D vertical quantum confinement in an undoped III-V semiconductor. This work extends the concept of an electron-phonon interaction to 2D vertically buried III-V homovalent nano-objects and therefore provides different approaches for material designs, vertical carrier transport, heterostructure design on silicon, and device applications with weakly polar semiconductors.

14.
Science ; 360(6384): 67-70, 2018 04 06.
Article in English | MEDLINE | ID: mdl-29622649

ABSTRACT

Light-induced structural dynamics plays a vital role in the physical properties, device performance, and stability of hybrid perovskite-based optoelectronic devices. We report that continuous light illumination leads to a uniform lattice expansion in hybrid perovskite thin films, which is critical for obtaining high-efficiency photovoltaic devices. Correlated, in situ structural and device characterizations reveal that light-induced lattice expansion benefits the performances of a mixed-cation pure-halide planar device, boosting the power conversion efficiency from 18.5 to 20.5%. The lattice expansion leads to the relaxation of local lattice strain, which lowers the energetic barriers at the perovskite-contact interfaces, thus improving the open circuit voltage and fill factor. The light-induced lattice expansion did not compromise the stability of these high-efficiency photovoltaic devices under continuous operation at full-spectrum 1-sun (100 milliwatts per square centimeter) illumination for more than 1500 hours.

15.
Adv Mater ; 30(5)2018 Feb.
Article in English | MEDLINE | ID: mdl-29226392

ABSTRACT

Hybrid perovskites are on a trajectory toward realizing the most efficient single-junction, solution-processed photovoltaic devices. However, a critical issue is the limited understanding of the correlation between the degree of crystallinity and the emergent perovskite/hole (or electron) transport layer on device performance and photostability. Here, the controlled growth of hybrid perovskites on nickel oxide (NiO) is shown, resulting in the formation of thin films with enhanced crystallinity with characteristic peak width and splitting reminiscent of the tetragonal phase in single crystals. Photophysical and interface sensitive measurements reveal a reduced trap density at the perovskite/NiO interface in comparison with perovskites grown on poly(3,4-ethylene dioxy thiophene) polystyrene sulfonate. Photovoltaic cells exhibit a high open circuit voltage (1.12 V), indicating a near-ideal energy band alignment. Moreover, photostability of photovoltaic devices up to 10-Suns is observed, which is a direct result of the superior crystallinity of perovskite thin films on NiO. These results elucidate the critical role of the quality of the perovskite/hole transport layer interface in rendering high-performance and photostable optoelectronic devices.

16.
J Acoust Soc Am ; 142(4): 2233, 2017 10.
Article in English | MEDLINE | ID: mdl-29092560

ABSTRACT

The field of civil engineering is in need of new methods of non-destructive testing, especially in order to prevent and monitor the serious deterioration of concrete structures. In this work, experimental results are reported on fault detection and characterization in a meter-scale concrete structure using an ultrasonic nonlinear coda wave interferometry (NCWI) method. This method entails the nonlinear mixing of strong pump waves with multiple scattered probe (coda) waves, along with analysis of the net effect using coda wave interferometry. A controlled damage protocol is implemented on a post-tensioned, meter-scale concrete structure in order to generate cracking within a specific area being monitored by NCWI. The nonlinear acoustic response due to the high amplitude of acoustic modulation yields information on the elastic nonlinearities of concrete, as evaluated by two specific nonlinear observables. The increase in nonlinearity level corresponds to the creation of a crack with a network of microcracks localized at its base. In addition, once the crack closes as a result of post-tensioning, the residual nonlinearities confirm the presence of the closed crack. Last, the benefits and applicability of this NCWI method to the characterization and monitoring of large structures are discussed.

17.
Eng Life Sci ; 17(8): 874-880, 2017 Aug.
Article in English | MEDLINE | ID: mdl-32624835

ABSTRACT

The feasibility of using a feed-forward neural network in combination with 2D fluorescence spectroscopy to monitor the state of Saccharomyces cerevisiae fermentation was investigated. The main point is that for the backpropagation training of the neural network, no offline measurement value was used, which is the ordinary approach. Instead, a theoretical model of the process has been applied to simulate the process state (biomass, glucose, and ethanol concentration) at any given time. However, the kinetic parameters of the simulation model are unknown at the beginning of the training. It will be demonstrated that the kinetic parameters of the theoretical process model as well as the parameters of the feed-forward neural network to predict the process state from 2D fluorescence spectra can be acquired from the 2D fluorescence spectra alone. Offline measurements are not actually required. The resulting trained neural network can predict the process state as accurate as a conventionally (with offline measurements) trained neural network. The calculated parameters result in a simulation model that is at least as accurate as a model with parameters acquired by least squares fitting to the offline measurements.

18.
Ultrasonics ; 73: 245-252, 2017 01.
Article in English | MEDLINE | ID: mdl-27693600

ABSTRACT

A nonlinear acoustic method to assess the damage level of a complex medium is discussed herein. Thanks to the highly nonlinear elastic signatures of cracks or, more generally, internal solid contacts, this method is able to distinguish between contributions from linear wave scattering by a heterogeneity and contributions from nonlinear scattering by a crack or unbounded interface. The coda wave interferometry (CWI) technique is applied to reverberated and scattered waves in glass plate samples featuring various levels of damage. The ultrasonic coda signals are recorded in both the absence and presence of an independent and lower-frequency elastic "pump" wave, before being analyzed by CWI. The monitored CWI parameters quantifying changes in these coda signals, which therefore quantify the nonlinear wave-mixing effects between the coda and pump waves, are found to be dependent on the damage level in the sample. A parametric study is also performed to analyze the influence of sensor positions and average temperature on the method's output. The reported results could be applied to the non-destructive testing and evaluation of complex-shape materials and multiple scattering samples, for which conventional ultrasonic methods show strong limitations.

19.
J Phys Chem Lett ; 7(19): 3776-3784, 2016 Oct 06.
Article in English | MEDLINE | ID: mdl-27601100

ABSTRACT

Low frequency dynamics has been studied in a CH3NH3PbBr3 hybrid perovskite single crystal by using four different spectroscopy techniques: coherent inelastic neutron, Raman and Brillouin scatterings, and ultrasound measurements. Sound velocities were measured over five decades in energy to yield the complete set of elastic constants in a hybrid halide perovskite crystal in the pseudocubic plastic phase. The C44 shear elastic constant is very small, leading to a particularly low resistance to shear stress. Brillouin scattering has been used to study the relaxation dynamics of methylammonium cations and to evidence translation-rotation coupling associated with the cubic to tetragonal phase transition at Tc ≈ 230 K. Low frequency and highly damped optical phonons observed using both Raman and inelastic neutron below 18 meV, do not present softening close to Tc. The critical dynamics at Tc ≈ 230 K is compatible with an order-disorder character, dominated by relaxational motions of the molecules.

20.
J Appl Crystallogr ; 48(Pt 3): 702-710, 2015 Jun 01.
Article in English | MEDLINE | ID: mdl-26089763

ABSTRACT

This study is carried out in the context of III-V semiconductor monolithic integration on silicon for optoelectronic device applications. X-ray diffraction is combined with atomic force microscopy and scanning transmission electron microscopy for structural characterization of GaP nanolayers grown on Si. GaP has been chosen as the interfacial layer, owing to its low lattice mismatch with Si. But, microtwins and antiphase boundaries are still difficult to avoid in this system. Absolute quantification of the microtwin volume fraction is used for optimization of the growth procedure in order to eliminate these defects. Lateral correlation lengths associated with mean antiphase boundary distances are then evaluated. Finally, optimized growth conditions lead to the annihilation of antiphase domains within the first 10 nm.

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