Faculty of Science, Engineering and Technology (FSET)

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Formulation of Schrödinger Equation Using The Hilbert Space Operators Approach
(Chuka University, 2019-09) Mbatha, Elizabeth
Operators in Hilbert space have properties which are useful in the study of mathematical abstract areas such as approximation theory, Banach Fixed point theory, the spectral theory as well as Quantum Mechanics. Schrödinger equation is a fundamental entity with many applications in Quantum Mechanics. This equation was initially derived by applying the knowledge of electromagnetic wave function and Einstein theory of relativity. Later, it was derived by applying the knowledge of Newtonian mechanics. It was also derived by extending the wave equation for classical fields to photons and simplified using approximations consistent with generalized non-zero rest mass. However, from the existing literature no study has been done on deriving Schrödinger equation using properties of Hilbert space operators. In this study, Hilbert space operators that include unitary operators, self adjoint operators and compact operators, norms of linear operators, Hilbert Schmidt operator, normal operators together with Lebesque Integral, Neumann Integral and spectrum are used in place of the existing concepts of electromagnetic wave function, Einstein theory of relativity and approximation consistent with generalized non zero mass to derive the Schrödinger equation. Furthermore, this study has established the correlation between the electromagnetic wave function and Einstein theory of relativity in relation with Hilbert space operators. Application of Hilbert space operators on Quantum observables such as position, momentum and energy of a particle has been done in these study. The derivation of Schrödinger enhances equation and its application using Hilbert space operators have enhanced a better understanding of the concept of Schrödinger equation. The results of this work will be useful in quantum mechanics as well as in mathematical operator theory.
Modelling the Effects of Mindfulness Based Stress on Breast Cancer Survival Rate among Women in Meru and Nyeri Counties, Kenya, using Cox Proportional Hazard Model
(Chuka University, 2019-09) Mutwiri, Mwendwa N.
Breast cancer remains the most commonly diagnosed cancer among women, affecting 34 women per every 100,000. This has led to high number of fatalities annually, which need to be mitigated. The main interest among many cancer survivors and their families is establishing other conventional therapies they can engage in to improve their prognosis and survival. Among some of the key therapies is the interest in working on mindfulness-based stress (MBS) that patients undergo after diagnosis as complementary and alternate measures. Regardless of this, there is little that is known about the effects of MBS factors on breast cancer survival. Management of breast cancer can be enhanced through modelling the effects of MBS on breast cancer survival rate. However, there is limited information on accuracy of existing models. This study focused on developing a model to predict the effect MBS factors have on breast cancer survival rate among women in Meru and Nyeri Counties. Both Primary data and Secondary data were used. Primary data was obtained using a structured questionnaire from the breast cancer survivors and the medical practioners while secondary data was obtained from records at Meru teaching and referral hospital and Nyeri level five hospital on the MBS variables (cost burden of treatment, stress on diagnosis, prolonged time taken to access treatment, poor diet, alcohol use, physical activity and lack of awareness) among breast cancer patients for the period 2012 to 2017. Mixed method research design was used in the study. Both quantitative and qualitative data used in the study was analysed using R software. Cox proportional hazard model was used in establishing the survival rates, with the breast cancer survival rate being dependent variable while MBS factors were the independent variables. Kaplain-Meier estimators were used in determining the varying effects which the MBS factors have on survival rate. Log-rank test was used to perform comparisons of survival curves using hypothesis tests on the patients‘ survival rate considering age. The likelihood ratio test showed that MBS factors are significant in predicting hazard rates ( = 66.7, p = 0.0000119). Treatment period was highly statistically significant (p = 0.00014) as compared to other covariates. Lack of awareness (p = 0.0010124), ease of coping with stress (p = 0.000514) and observing the right diet (p = 0.04092) were also found to significantly affect survival rate. Access of treatment immediately after diagnosis, availing the right information to the patients, helping patients to cope easily with stress and observing the right diet were found to be the best estimators in increasing breast cancer survival rate. The study therefore recommends use of the model in predicting breast cancer survival rates which can greatly improve breast cancer prognosis.
Modelling and Application of Response Surface Methodology for Optimization of Weight Gain of Eight Weeks Old Kenbro Served With Pumpkin (Cucurbita Pepo L) Seeds Extract
(Chuka University, 2019-09) Kinyua, Charles Mugendi
Extensive use of synthetic growth promoting antibiotics have become a threat to public health. Therefore, there is a need to search for bioactive phytochemicals that have positive effects on immune, growth and appetite status of the chicken. Such bioactive compounds can be obtained from plants. Pumpkin seeds have been found to be a valuable source of protein and bioactive compounds. Mathematical models have been used to study the effect of pumpkin extracts on the weight gain of chicken. However, most of these studies have focused on the levels of the application of pumpkin extract, rather than on optimising the levels of application on the weight gain of the chicken. Optimization is important since it provides information on the amount of pumpkin seed extracts that should be fed to the chicken without wastage. This study was conducted to evaluate the weight gained by the Kenbro chicken served with pumpkin (Cucurbita pepo L) seeds extract and examined the possible combination of the number of weeks and quantity of pumpkin seed extract that can result in maximum weight gain of the Kenbro chicken. The experiment was conducted using Random Complete Block Design at the poultry demonstration unit of Chuka University. Sixty- day old Kenbro chicks were randomly distributed to five treatments which contained 0, 50, 100, 150 and 200 ml of pumpkin seed extracts per litre of water. Each treatment was replicated three times with four chicken per replicate. The birds were fed with the same diets of finisher and starter feeds. The chickens were provided with enough feeds and water ad libitum in the morning at 8 am. The birds were weighed at the beginning of the experiment and thereafter at an interval of three days for eight weeks. Data was analysed using R statistical software. A Response surface model was fitted to the data and subjected to contour plots to characterize the nature of its turning point and to capture the combination of the number of weeks and quantity of pumpkin seed extract that brings maximum weight gain of the Kenbro chicken. The results showed that the average body weight gained was significant (p < 0.05). The birds served with 200 ml pumpkin seed extract for 4 weeks had the highest weight gain. The fitted Response Surface Model indicated that the number of weeks and quantity of pumpkin seed extract together with their interaction significantly (p < 0.05) determined the weight gain of Kenbro chickens. The study found that the quadratic model fitted using the data had an adjusted R-Squared value of 0.78. The optimal weight gain of 0.23 kg was achieved when the number of weeks was 3.18 with 192.40 ml of pumpkin seed extract. The number of weeks, pumpkin seed extract and their interaction play a key role in obtaining maximum weight gain of the Kenbro chicken. These factors should be put into consideration when developing a feeding system for Kenbro chickens. The study also guides the farmers on the optimization of Kenbro chicken production without incurring an extra cost in the input.
LEVELS OF SELECTED PHTHALATES FROM WASTEWATER TREATMENT PLANTS IN LAKE VICTORIA CATCHMENT AREA AND THEIR ADSORPTION ONTO WATER HYACINTH BIOCHAR
(Chuka University, 2020-12) OGORA, ELKANAH NYAKWAMA
Endocrine disrupting chemicals (EDCs) disturb the endocrine system’s functionality causing negative effects on health in an organism and its progeny. They can interfere with natural hormone cycles in humans or animals, potentially affecting metabolism, development, reproduction and growth. Phthalates are among the many examples of EDCs, which have been used as plasticizers for longtime around the world. Due to their extensive usage, they are found in many surface waters, sludge and waste waters. The occurrence of phthalates in water, and their exposure to non-target organisms cause adverse effects such as congenital anomalies, endocrine disruption and chronic toxicity. This study determined residual levels of three phthalates namely; dimethyl phthalate (DMP), benzyl butyl phthalate, (BBP) and bis(2-ethylhexyl) phthalate (BEHP) in wastewater sampled from wastewater treatment plants (WWTPs) of Nyalenda, Homabay and Kisii during wet and dry seasons. The wastewater samples were extracted and cleaned by solid phase extraction cartridges (SPE) ready for high performance liquid chromatography (HPLC) for quantitative analysis. Most of the sites sampled had detectable levels of DMP, BBP and BEHP in wastewater. High concentrations were detected during wet season compared to dry season in all sampled sites. Nyalenda WWTP recorded the highest concentrations of phthalates than Homabay and Kisii WWTPs. The concentrations of all selected phthalates were recorded highest at the inlet sampling points from all WWTPs, in both seasons sampled. Almost all the selected phthalates were below the limit of quantification (LOQ) at the outlet sampling points of Homabay and Kisii WWTPs in both seasons. The residue levels obtained showed significant differences at 5% confidence limits with zcal for all phthalates in all WWTPs less than the critical value (Zcritical = 1.96). Therefore, the null hypothesis was rejected. Consequently, a cost-effective technique of removing DMP, BBP and BEHP from their solutions using water hyacinth biochar (WHB) as an adsorbent was investigated. A mass of 0.1 g of WHB both before and after adsorption was used for characterization process. Elemental analysis of WHB was determined using XRF (EDXRF), the XRD patterns were obtained using bruker operating with Cu Kά(λ = 1.541nm) and samples scanned in coupled TwoTheta/Theta. The FTIR spectra were obtained between 4000cm-1 and 400cm-1 using Shimadzu type. The adsorption process was done using an orbital shaker agitated at 125 rpm and residual levels determined using the HPLC. The optimum conditions obtained from the adsorption of DMP, BBP and BEHP onto WHB were as follows; equilibrium time was 25 minutes, maximum adsorbate concentration adsorbed at 0.1 g of WHB was 4 mg/L, temperature of 298 K was appropriate and 0.8 g of WHB was effective for the adsorption of above 67% of 10 mg/L of each selected phthalate. The kinetic data fitted the pseudo second order model with regression values for DMP, BBP and BEHP found to be 0.9987, 0.9984 and 0.9986, respectively. The Freundlich model demonstrated to be a good model for fitting the adsorption data, which was attributed to heterogenous distribution of charged functional groups at adsorption sites of WHB’s surface. The calculated thermodynamic parameters, namely; change in Gibb’s free energy (ΔG), change in enthalpy (ΔH) and change in entropy (ΔS) showed that the adsorption process was favorable, exothermic, spontaneous and of a physical type. This was due to the fact that all of them were negative values. Dimethyl phthalate was the most effectively removed by WHB as adsorbent. The removal efficiency decreased with increasing molecular weight of the phthalates. The findings demonstrated that WHB is a good low cost and environmentally adsorbent for removal of phthalates from water.
ON CHARACTERIZATION OF PERMUTATION GRAPHS
(Chuka University, 2020-12) Nyabate, Nyabuto Fancy
Graph theory is an area in discrete mathematics with numerous theoretical developments and many applications to practical problems in computer science, chemistry, biology and operational research. As a result, it has attracted much attention to researchers in many dimensions including graph labeling, graph coloring, combinatorics, graph isomorphism, matroid theory and graph representations among others. Many researchers in this area have also worked on permutation graphs paying attention to the properties of cyclic permutation graphs, including crossing numbers and isomorphism. So far isomorphism between two cyclic permutation graphs has been determined by positive and negative natural isomorphism. However, construction of other classes of permutations graphs and establishing an alternative approach for determining isomorphism between permutation graphs as well as finding some properties of permutation graphs would be of significance. The aim of this study was to develop a class of permutations, determine algebraic properties of the permutations, construct permutation graphs and establish some properties of the constructed graphs including isomorphism. A class of [nxk - permutations was first obtained by coming up with a bijection on a finite set, which resulted into permutations. Some algebraic properties were established, in particular, the permutations resulted in an abelian group as well as it formed a subgroup. Graphs were then constructed from these permutations and some properties including symmetry, unique, connectedness, distance and isomorphism determined by enumeration. The results of this research are of significance in other practical areas of application of graphs, including computer science, chemistry, biology, operational research and combinatorics.
INCIDENCE AND PREVALENCE OF FUSARIUM WILT AND PHYTOCHEMICAL ANALYSIS OF CRUDE EXTRACTS OF Tithonia diversifolia (Hemsl.) A.Gray AND Kigelia africana (Lam.) Benth AND THEIR ANTIMICROBIAL ACTIVITIES AGAINST Fusarium oxysporum IN TOMATOES
(Chuka University, 2020-12) Awere, Collince Omondi
Kenya is one of the leading countries in Africa in tomato production. Production of tomato is 14% of the total vegetable and 6.72% of the horticultural crops produced in the country. It is a source of food, foreign exchange earnings and source of employment and income. The major factor that reduces the growth and yield of tomato production in Kenya are pathogenic microorganisms. For instance, Fusarium oxysporum is among the fungal pathogens that destroy the xylem of the plant hence causing Fusarium wilt due to poor transportation of water to various parts of the plant. Besides, it persists in the soil environment for a long period thus continuously infecting healthy plants grown in the site. The management practices that are mostly used to control the pathogen are ineffective and environmentally unfriendly. Therefore, plant products with antimicrobial properties present an affordable alternative solution to control such persistent pathogens. The objective of this study was to determine the incidence and prevalence of Fusarium wilt and the phytochemical composition of Tithonia diversifolia and Kigelia africana and their antimicrobial activity against fungal pathogen F. oxysporum in tomatoes. Tithonia diversifolia and Kigelia africana plants were selected because of their wide medicinal use, distribution and availability. A preliminary survey was carried out in Mwea, Kirinyaga County which is among the most common areas where tomatoes are grown. Questionnaires were used to evaluate the farmers` knowledge, perception and management practices of Fusarium wilt disease. A total of 80 respondents were interviewed. K. africana and T. diversifolia plant samples were collected for phytochemical analysis. The samples were ground into a fine powder and extracted using water. Phytochemical screening of the crude extract was done. Soil was used for F. oxysporum pathogen isolation. Antimicrobial test disc soaked with plant extract was placed on to the media cultured with F. oxysporum and incubated at 28 oC for a week to allow growth. Analysis of the collected data was done using SAS version 9.4 for analysis of variance and further subjected to a post adhoc test with 𝛼 = 0.05 being considered significant. The results showed that the Rio Grande was the tomato variety widely grown; the preference for this variety was attributed due to its high marketability, high production, high quality, and early maturity. From the response, 92.5 % of the farmers had seen the symptoms of the pathogen while the rest had not seen the symptoms of the pathogen in tomatoes. The application of chemicals was widely used to control the pathogen, which contributes to environmental pollution. Screening of the plant extract revealed the presence of tannins, alkaloids, flavonoids, saponins, terpenoids, and glycosides. Each of the plant extract used had antimicrobial activity against F. oxysporum; this was due to the presence of phytochemicals that had an effect on the growth of the pathogen. K. africana exhibited the highest zone of inhibition while T. diversifolia had the lowest zones of inhibition. When each crude extract was used singly and in combination against the F. oxysporum, the zone of inhibition was found to be statistically significant at P< 0.05. The combined crude extract showed an increased antimicrobial activity against F. oxysporum. The results provide a potential application of the crude extract as an antifungal agent against F. oxysporum. It also provides scientific evidence that K. africana and T. diversifolia extract possess antifungal activity that can be used as a broad-spectrum in managing microbial diseases.
ASSESSMENT OF QUALITY OF SHALLOW WELLS WATER IN CHUKA SUB-COUNTY, KENYA
(Chuka University, 2020-12) Rugendo, Edith Mwende
Groundwater from shallow wells is an important source of water for domestic and agricultural uses in Chuka Sub-County. However, most shallow wells in Chuka Sub-County are undocumented because approval is not required to sink a shallow well. Groundwater from these shallow wells is therefore susceptible to contamination by both geogenic and anthropogenic sources. This study was conducted to determine the quality of shallow wells water in Chuka Sub-County. Samples were collected from twenty shallow wells in Chuka Sub-County during the dry and wet seasons. The temperature, pH and conductivity were determined in situ using a conductivity meter. The concentration of cations in the water samples was determined using an Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) system. The concentration of chloride and nitrate ions in the water samples were determined using the argentometric and the spectrophotometric method, respectively. The concentration of sulphate ions was determined using a turbidimetric method while the concentration of phosphate ions was determined using a colorimetric method. The data obtained were subjected to ANOVA to test the significance differences using R-3.5.2. Mean comparison was achieved through LSD. The temperatures of the waters were significantly higher during the dry season. The pH of water in most shallow wells during the wet season was within the limits set by KEBS and WHO. However, shallow well water at Karandini (T15) was highly acidic (pH of 3.95) during the wet season. During the dry season, the shallow well waters were slightly acidic (4.42 - 6.44) except for the shallow wells at Ndagani market (T11), whose water was alkaline (pH = 8.75). The shallow wells water at site T11 had remarkably higher conductivities than the other shallow wells in the study area during both the wet (1150 μs/cm) and the dry (1208 μs/cm) seasons. The concentrations of macro-cations (Ca2+ and Mg2+) were higher during the dry season. The concentrations of the trace and toxic cations differed significantly across sites and seasons but were within the limits set by KEBS and WHO. The concentrations of anions (NO3-, SO42-, Cl- and PO43-) were within the limits set by KEBS and WHO for portable water. Groundwater from most shallow wells in Chuka Sub-County is generally safe for domestic uses but regular monitoring for quality is recommended because, the concentration of nitrate in several wells during the dry season was within the range that causes chronic health effects including colorectal, ovarian, thyroid, kidney and bladder cancers.
SECURE CLOUD BASED APPROACH FOR MOBILE DEVICES USER DATA
(Chuka University, 2022-02) Mbae, Oscar
ABSTRACT In this era characterized by rapid technological innovations, mobile devices such as tablets and smartphones have become inevitable due to the variety of services they offer. As a result, computing capacity as well as storage needs of these devices are increasing tremendously. To ensure users continue to enjoy the portability, flexibility and accessibility that these devices continue to provide, there is need for a secure and user friendly data storage solution. However, despite the benefits of this technology, there are increased risks to the information that is accessible from the mobile devices. The main problem is the risk of private and confidential data being exposed to unauthorized persons and the risk of permanent loss or damage of that data. These problems are escalated by the fact that most information is stored in the devices’ internal memory, making them easily accessible. Mobile devices are susceptible to loss and the pins and patterns used as security controls are easy to by-pass because they have minimal encryptions. In the event of human error whereby the user forgets to delete downloaded confidential content from cloud-based platforms, it remains in the mobile device from where it can be accessed easily. This creates a need for secure ways of storing data in a cost-effective and convenient manner. The objective of this study was to design, implement and validate a secure cloud based approach for mobile devices’ user data. The study adopted design and development methodology which followed the entire design and development process from analyses to evaluation. From this methodology, the research employed the strategy of mixed method using a systematic process of collecting data, at first during prototype and then throughout the rest of study. This method allowed for continued development and implementation of the product. The solution was prototyped in an android based environment and developed using Java programming language together with MySQL for the database. The mobile data privacy solution proposed by this study provides a security solution to users to be able to store sensitive data and access it on their mobile devices. The solution focuses on securing the data on the mobile devices by storing it in an encrypted format and uploading it to the cloud. In addition, the downloaded data is timed to self-destruct after user consumption, eliminating unauthorized person or application from reading the information without a decryption key. The developed solution was able to provide security for the users’ confidential data while making it available. The tool enabled its users to store the selected sensitive files from their mobile devices in an encrypted format. To achieve this, we used the algorithm AES 256 to encrypt the data with a key only known to the user and upload it to the cloud for secure storage. The secure mobile tool was developed and fulfilled the requirements specification successfully. It met all the security parameters stated hence optimizing mobile user data storage security.
A CONVOLUTIONAL NEURAL NETWORKS AND SUPPORT VECTOR MACHINES HYBRID MODEL FOR NUMBER PLATE RECOGNITION
(Chuka University, 2022-03) Kibaara, Peter
ABSTRACT Automatic Number Plate Recognition (ANPR) systems are applied in many fields such as automatic electronic toll collection, car park management and access control, logistics and vehicle tracking, traffic law enforcement and crime resolution amongst others. Motion blur, plate orientation, lighting changes and image noise severely lower the detection speed and recognition accuracy of these systems. The incorporation of machine learning algorithms in ANPRs has seen Convolutional Neural Network (CNN) being used to develop ANPR models with improved performance in license plate detection. CNNs are best suited for image data where the number of features is large such as license plate detection. This is attributed to their design architecture which enables them to perform feature extraction automatically. However, their speed of execution is slow as the model has to learn a lot of features. Support Vector Machine (SVM) is a supervised machine learning algorithm suitable for classification and regression problems with datasets that have a small number of features. It doesn’t scale up well for large datasets with many features. It has demonstrated high speed and accuracy when used for classification in small datasets such as character recognition. The final stage in ANPR is a character recognition phase and involves few features. These two algorithms have been deployed independently, however the concept of combining the two algorithms for ANPR models remains highly unexplored. The research therefore combines the two models (CNN and SVM) to come up with an efficient hybrid ANPR system with improved number plate recognition accuracy. The two models were developed using a deep cascade framework; a CNN with a SoftMax classifier and a hybrid CNN with a SVM classifier. The Universidade Federal do Paraná (UFPR-ALPR) dataset was used to train validate and test the models. Recognition accuracy, precision, recall and F1 score metrics were used to evaluate the model. The hybrid CNN-SVM model had a recognition accuracy of 91.25% against 89.07 % from the pure CNN model. The weighted average precision, recall, and F1-score of the hybrid CNN-SVM was 92%, 91% and 91% respectively, which was better compared to that of pure CNN. The hybrid model was tested for external validity using the Smart Sense Laboratory (SSIG) dataset. The hybrid CNN-SVM model had a recognition accuracy of 91% against 89 % from the pure CNN model. The weighted average precision, recall, and F1 score of the hybrid CNN-SVM was 91%, 91% and 91% respectively which was better compared to that of pure CNN, which had 90%, 89% and 89% respectively.
STRUCTURAL, OPTICAL, AND SURFACE POTENTIAL CHARACTERIZATION OF NICKEL, ZINC DOPED MAGNESIUM FERRITES SYNTHESIZED USING SOL-GEL AUTO-COMBUSTION METHOD
(Chuka University, 2022-09) ALEX, NJOROGE
Nano-sized spinel ferrites have attracted heightened scientific focus due to their interesting structural, morphological, magnetic, optical, and electrical properties. Metal substitution in the structural equation of the spinel ferrite (MFe2O4) plays important roles in the modification of its physical properties in order to suits specific applications, like gas sensing. Recently, air pollution has greatly increased, e.g., leakage of liquid petroleum gas (LPG). This lead to deaths, fire outbreaks and other health complication. As a result, there is demand for effective gas sensors with lower limits of detection. Sensing material especially the ferrites are limited in their sensitivity and operate at high temperatures. Among the ferrites, Mg-Zn ferrites are most important magnetic oxide due to their properties. Substitution of any magnetic ion by replacing Zn2+ in Mg-Zn ferrite plays an important role in modifying its properties and hence enhancing its sensing properties. This work, aimed at contributing to the effort focused to improve ferrite sensing properties and overcome these limitations by ternary ionic substitution. Consequently, NixZn0.5-xMg0.5Fe2O4 (x = 0, 0.1, 0.3 and 0.5) ferrite nanoparticles were synthesized by Citra gel auto-combustion method at a pH 7 and characterized for their structural, elemental composition, electronic and optical properties. Pre-elemental analysis by x-ray fluorescence revealed the expected stoichiometry of the synthesized nanoferrites with low amount of impurities. X-ray Diffraction analysis confirmed cubic spinel nature of the samples with crystalline size between 26.90-43.34 nm using Debye Scherrer equation, 8.94 – 26.38 nm using Modified Debye Scherrer plots and 11.60 – 23.86 nm using Halder Wagner plots. The most intense peak was at a miller indices (311), which is a characteristic of a spinel ferrites. Nickel substitution brought variation in the lattice constants which were in the range of 8.3436 – 8.4149 Å. Both Williamson – Hall and Halder- Wagner plots revealed all sample to possess compressive micro strain. Further structural properties by Fourier transform spectroscopy showed prominent peak at range of 350 – 450 cm-1 which are vibration of metal oxygen bond in octahedral sites while vibrations at 500 – 600 cm-1 which are vibration in tetrahedral sites, a characteristics of spinel ferrites with metal oxygen bond stretching. Optical properties by UV-Vis showed the samples optical band gap in the range of 4.19 – 4.21 eV, refractive index in the range of 2.048 – 2.562 and optical dielectric constant in the range 5.062 – 5.070. Kelvin probe scans revealed a low potential material and more interesting was the negative surface potential. The work function for the area scan was in the range 4.536 – 4.588 eV while for the line scan was in the range 4.341 – 4.5673 eV. Electrical conductivities of the samples were found to increase with increase in nickel content, this was determined from the calculation of length jump which was found to decrease from 2.975 Å to 2.942 Å. Similar results of variation of electrical conductivity were found by calculation of unshared edges which were found to decrease with nickel content from 6.9773 – 6.9181 Å. In summary, the synthesized nanoferrites have properties which could find their applications in fabrications of effective gas sensors, based on their size, band gap, length jump, and surface potential obtained.
FACTORS AFFECTING ADOPTION OF MANURE ON BANANA YIELDS IN SMALLHOLDER FARMS IN MAARA SUB COUNTY, THARAKA NITHI COUNTY, KENYA
(Chuka University, 2022-09) Kimetto, Jerono
ABSTRACT Banana (Musa ssp) is a widely distributed fruit and which is contributing greatly towards food security in the developing countries. In Kenya, banana is among the major food and cash crop produced by smallholder farmers as a source of income and food security. However, it has been associated with low productivity and income. Currently, banana production in Kenya is 14 t/ha-1yr-1, which is below the global average of 20.5 t/ha-1 yr1. The low production has been attributed to various factors such as poor agronomic practices, low soil fertility, poor markets, lack of farming capital and sociodemographic factors. Despite studies on most of these factors, information on dynamics of socio-economic factors on banana farming by smallholder farmers is ever changing due to change in climate and lifestyles. Therefore, there is need to continuously monitor and study the effect of these factors on productivity and income of banana farming. The study, therefore determined the effect of manure adoption on banana production in smallholder farms in Maara Sub County, Tharaka-Nithi County. Descriptive research design was used in the study. The study targeted 34,779 smallholder banana farmers. A structured questionnaire, open and closed ended, were used to collect the data. Data was collected on demographic socio economic, institutional factors and banana production. Data obtained was analysed using the SPSS version 26. Descriptive statistics were employed in the presentation of the results. The study revealed that majority of the banana farmers are above 53 years and majority (54.8%) of the farmers derived their seedlings from their own suckers. About 83.8% of the farmers have adopted manure while 16.2% of the respondents have not. The common variety planted by the farmers is Kampala represented by 30.73%. About 29.7% banana farmers own land sizes between 0.5-1.0 ha of land. The majority (97.3%) of the farmers privately owned their lands while 2.7 3% of the respondents leased the lands for growing bananas. It was established that majority (88.0%) of the adopters received extension services while adopters who had not received any extension services were being represented by 8.0 %. Majority of the farmers who belonged to a farmer group and were adopters of manure being represented by 82.0% respondents while farmers who and were adopters and did not belong to any farmer group were represented by 14.0%. The study sought to determine the socioeconomic factors that affect adoption of manure in smallholder farms in Maara Sub County. Logistic regression model was used to find out whether gender, age, highest level of education of decision maker, access to extension service, participation in a farmer group, labour and land size were significant in the adoption of manure. Education level of decision maker p = 0.007, Gender p = 0.000, land size p = 0.000 and participation in farmer group p = 0.003 and extension services p = 0. 027 were the factors that were found to significantly affect adoption of manure. Multiple regression model was carried out to determine the impact of adoption of manure on banana yield. The result showed that adoption of manure had an association with banana yield and was statically significant at p = 0.000. Most of the respondents were found to be literate. Therefore, illiterate farmers should be enlightened as education boost a farmer’s ability to decode information. Awareness should be created to encourage any member who has not registered to any group as is through such groups the information is disseminated. Extension services should also be well strengthened. The study recommends farmers to adopt manure as a way of increasing banana yields.
CHARACTERIZATION AND SCREENING OF ANTIBACTERIAL PROPERTIES OF Actinomycetes FROM RIVER TANA AND LAKE ELEMENTAITA, KENYA
(Chuka University, 2023-04) SHIKUKU BONFACE OLOO
The increased prevalence of bacterial infections has been a major challenge to human with devastating high mortality and morbidity rates. This situation has been worsened by increasing antibiotic resistant strains of pathogenic bacteria, reduced effectiveness of antibiotics in the market, and the emergence of new bacterial infections. This study aimed at identification of antibacterial Actinomycetes species using biochemical and molecular methods, screening for their antibacterial secondary metabolite and determination of effect of pH, fructose, sucrose, urea and sodium nitrate on their antibacterial activities. The experiments for this study was laid out in Complete Randomized Design and replicated thrice to determine the difference between the inhibition zones (mm) of isolates against the tests organisms and effects of different levels of pH, sucrose and fructose on antbacterial properties of isolates. The resultant data ( zones of inhibition in millmetres) was analysed using One Way Analysis of Variance and Kruskal Wallis test in SAS version 9.4. A total of six antibiotic producing Actinomycetes species were isolated from river Tana and lake Elementaita and identified through morphological, biochemical and molecular methods.There was a significant (p<0.05) different antibacterial activity of Actinomycetes isolates against Staphylococcus aureus, Salmonella typhi and Escherichia coli. The thin layer chromatography profiling for secondary metabolites in extracts revealed a total of 13 different spots with each having a unique retardation factor. The GC-MS analysis of the extracts revealed 140 different metabolites which have been documented to have antibacterial properties from the six Actinomycetes isolates. There was a significant (p<0.05) effects of different levels of pH and concentration of fructose, urea and sodium nitrate on the antibacterial activity of Actinomycetes isolates against Escherichia coli. The study has revealed different secondary metabolites in unique combinations across the six Actinomycetes isolates with antibacterial activities against Staphylococcus aureus, Salmonella typhi and Escherichia coli. The findings of this study can help in developing new or alternative antibiotics that can be used for treatment of pathogenic and resistant bacteria.
SYNTHESIS AND CHARACTERIZATION OF IRISH POTATO PEELS POWDER-NANOSILICA COMPOSITE FOR THE DEGRADATION OF RHODAMINE BLUE AND DICLOFENAC
(Chuka University, 2023-10) MUTIE JOSEPH NZUKU
In today's world, finding safe drinking water has become a major concern. Many contaminants, including dyes and pharmaceuticals, are discharged directly or indirectly into bodies of water without sufficient treatment, rendering the water unsafe for human consumption. To safeguard the environment and human health, harmful toxins must be removed from wastewater. Various technologies have been used to address this issue. Adsorption on activated carbons is a widespread technique in wastewater treatment, but the exorbitant cost of ordinary activated carbons limits its use. Several agricultural waste products are currently being used inefficiently and have the potential to be transformed into important adsorbents such as composites. Because of its nano-sized inorganic filler, nano-silica has exceptional characteristics such as large surface area, mesoporous structure, biocompatibility, versatile pore size, modifiability, and polymer hybridizability over common composites. Irish potato peel powder is a natural binder that works well in composite materials. Since most composite materials are poorly distributed, this study concentrated on utilizing Irish potato peel powder and nano-silica from rice husks to produce a composite of Irish potato peel powder and nano-silica. This study aimed to synthesize, characterize and make Irish potato peel powder/nano-silica composite in the degradation of rhodamine blue and diclofenac. Silica nanoparticles were mixed with Irish potato peel powder in the ratios 1:1, 1:2, 2:1, 4:1, and 5:1, respectively. Glutaraldehyde was added to the mixture as a binder. The following functional groups was detected in the composite's Fourier Infrared spectrum: C=C, O-Si-O, and Si-OH, which corresponded to peaks at 1645.35 cm-1, 1104.29 cm-1, and 3439.23 cm-1, respectively, and are responsible for the adsorption of Rhodamine Blue and Diclofenac. The XRF analysis showed that silica accounted for a large proportion in the composite, which determined the mixing ratio of RHNS and IPPP (4:1). The composite surface area was 100.6328 m2/g, with a single point surface area of 97.4036 m2/g, according to BET-BJH surface characterization. The synthesized composite was amorphous in nature, as shown by the XRD pattern, which has a strong broad peak between 200 and 250 (2θ). The adsorption capacity of RB and DCF by the composite was optimal at pH 4 and 2, respectively, an initial concentration of 1 mg/L and 40 mg/L, respectively, an adsorbent dose of 0.1 g, and a 240 rpm stirring speed. The removal efficiency of the composite was 99.39% for DCF and 97.57% for RB. The rhodamine blue removal best fit the Freundlich isotherm in the used composite adsorbent with R2 = 0.996, while the DCF removal suited the Langmuir isotherm model the best with R2 = 0.901. The kinetic data were pseudo-second-order (R2 = 0.9989 for RB and 0.849 for DCF), which was more suitable for explaining the adsorption rate. Fineness, surface area, and vacancy concentration are all associated with better adsorption capacity.
ANALYSIS OF PRODUCTION, SOCIO-ECONOMIC AND INSTITUTIONAL FACTORS AFFECTING TECHNICAL EFFICIENCY OF SMALLHOLDER BANANA PRODUCERS IN KIRINYAGA CENTRAL SUB-COUNTY, KENYA
(Chuka University, 2023-10) MATIVA JACKSON MKENYE
Banana provides food, nutrition security and income for most households and is fourth most popular food crop in the world after wheat, maize and rice. Despite its significance, full potential of banana production in Kenya remains unexploited by smallholder producers. This is as a result of low technical efficiency especially in utilization of farming inputs and producer specific factors like production, socio-economic and institutional factors among others. In Kirinyaga County, the actual banana production is at 4-18 tonnes per acre against the potential of 30-40 tonnes. Due to the limited supply of resources for production, attainment of highest possible levels of technical efficiency is key to achieving sufficiency in banana farming. This study aimed at analyzing the effects of production, socio-economic and institutional factors on technical efficiency of smallholder banana producers in Kirinyaga Central Sub-County, Kenya. The study used a cross-sectional research design and targeted a population of 24,440 smallholder banana producers. Multistage sampling technique was employed where purposive sampling and simple random sampling methods were used in some stages to sample respondents in the study area. A sample of 402 smallholder banana producers were selected. Using a questionnaire, primary data on production, socio-economic and institutional factors affecting technical efficiency of banana production was collected. The data was then analyzed using Stata version 17 and SPSS version 25. Descriptive statistics were used to describe the production, socio-economic and institutional factors of the smallholder banana producers. A stochastic frontier analysis approach was used to model the technical efficiency level using the Cobb-Douglas function. The stochastic production function of the Cobb Douglas function was estimated using the maximum likelihood estimation technique. The study showed that the level of banana production technical efficiency among the smallholder producers varied between 0.9% to 95.5% and average technical efficiency of 83.1%. According to the model parameters calculated, land set aside for production of banana, banana suckers and agrochemicals were significant production factors in banana cultivation at 5% significance level. The study found that agrochemicals and planting materials had positive effects on technical efficiency whereas land size had a negative impact on technical efficiency. This implied that increasing the amount of land set aside for banana production by an acre reduces the amount of banana harvested by 0.438 kgs while increasing the amount of planting materials and agrochemicals used by one unit increases banana production by 1.315 and 0.155 kgs, respectively. The study found that decision makers’ age and size of the household had negative effects on banana production technical efficiency whereas education, experience, producer group membership and market access had positive effects. The study recommends people with high levels of education to venture into banana production. In addition, producer group formation and membership be encouraged for the benefit of increasing technical efficiencies. The inefficient producers are advised to increase their present output by enhancing technical efficiency as a result of the inefficient utilization of their resources throughout production.
IMPACTS OF SHORELINE CHANGE ON THE NEARSHORE MARINE ENVIRONMENT AT GAZI BAY, KENYA; BETWEEN 1989 AND 2020
(Chuka University, 2023-10) MWANGI PAULINE NYAMBURA
Coastal zones are dynamic environments influenced by both human and natural processes. In the current study, the objectives were to estimate change in shoreline at Gazi bay between 1989 and 2020, to identify the spatial-temporal changes of the nearshore marine environment; particularly on mangrove forests and to establish hotspot areas of shoreline change. The study applied both longitudinal and ecological research design. Digital Shoreline Analysis System (DSAS 5.0), a software within ArcGIS Platform computed change statistics along the study area over the study period. Kalman filter model was used to project future shoreline positions. Supervised, and unsupervised classification methods were used in detecting vegetational change. The relationship between shoreline change and mangrove cover change was examined using the Pearson Correlation coefficient. The average End Point Rate (EPR) of shoreline change at Gazi bay was estimated at -1.38 m/y, with the northerner sections of the western creek showing an accretion rate of 2.38 m/y. At least 88.62 hectares of the mangroves had been affected by the sedimentation processes, representing 55% of mangroves in the study site. A hotspot area exhibiting a change of -4.99m/y was observed at the opening of the Mkurumudzi River, where sandspits and sandbars had formed. Other hotspots areas were at the site with introduced artificial rocks to serve as gabions, fish landing sites, and at the northern side of western creek that had enhanced sediment accretions killing mangroves. A negative correlation between shoreline change and mangrove cover loss was observed, though not statistically significant (r=-0.536, p=0.273, α=0.05). Assessing the dynamics and vulnerabilities of the coastal zones is very crucial in understanding sustainable coastal development and management. These findings provide valuable insights on shoreline changes that could contribute towards integrated coastal zone management strategies for the area.
APPLICATION OF QUEUING THEORY FOR OPTIMAL CUSTOMER CENTRICITY TO THE BANKING SECTOR IN KENYA
(Chuka University, 2023-10) JUMA SAMWEL KISIANG’ANI
Long queues and waiting times are common in banks, resulting in customer dissatisfaction and low customer retention. The study applied a descriptive research design to investigate queuing dynamics in a banking hall at a commercial bank in Kenya. A single server system (M/M/1) queuing model was used to estimate the average waiting time, system intensity, service time, and optimal number of staff during peak and off-peak periods (July). The study used secondary data on daily waiting times, service times, the number of customers, and servers for May and July 2019, 2020, and 2021 during working hours between 8.30 a.m. and 4 p.m. on Monday to Friday and 8:30 a.m. and 12 p.m. on Saturdays. Data analysis was done using R and Excel. The research findings indicated that the peak periods (May) recorded an average waiting time (AWT) of 13 minutes, 35 seconds in 2019, 10 minutes, 14 seconds in 2020, and 8 minutes, 36 seconds in May 2021. In the off-peak periods (July), an AWT of 3 minutes, 46 seconds, was registered in 2019, 5 minutes, 12 seconds in 2020, and 7 minutes, 42 seconds in 2021. An average service time (AST) of 1 minute 52 seconds in May 2019, 2 minutes 34 seconds in May 2020, and 2 minutes 27 seconds in May 2021. In the off-peak periods (July), an AST of 3 11 seconds was registered in 2019, 3 4 seconds in July 2020, and 2 43 seconds in July 2021. Overall, the system intensities are low to moderate, with the COVID-19 pandemic severely impacting the peak period more than the off-peak. In the peak periods, the service rates averaged 33, 24, and 25 persons per hour in May 2019, May 2020, and May 2021. The respective system intensities were 0.534, 0.360, and 0.492. In the off-peak periods, the average service rates were 19, 20, and 23 persons per hour in July 2029, July 2020, and July 2021. The respective associated system intensities of 0.535, 0.461, and 0.487. From the pooled data for 2019 and 2021, the study recommends that banks operate with an AWT of 6 minutes, 24 seconds, and an AST of 3 minutes. Further, the study established that a bank could work with an optimal four servers with an AST of 2 minutes, 35 seconds (a service rate of 20 people per hour), and achieve a moderate average service intensity of 0.552.
INDUCTION OF SYSTEMIC ACQUIRED RESISTANCE AGAINST Ralstonia solanacearum IN IRISH POTATO
(Chuka University, 2023-10) ATIENO MARGARET FAITH
Irish potato (Solanum tubesorum) is an economically important crop throughout the world with large-scale production and consumption. Irish potato is rich in carbohydrates, vitamins and minerals, especially iron, magnesium and potassium. Irish potato production has been plagued by constraints such as lack of certified seeds, pests and diseases. Bacterial wilt caused by Ralstonia solanacearum is the major bacterial disease of potato resulting to 50 - 100% crop losses. Management of R. solanacearum is difficult since it has a wide host range and the fact that it is a soil borne pathogen. Several methods including biocontrol, chemical control, cultural practices, host resistance and phytosanitation have been used to manage R. solanacearum. However, there is no method that has been found to effectively control the disease but a combination of different methods have been reported to reduce the impact of the disease. Inducing systemic acquired resistance is another alternative to control bacterial wilt. Systemic acquired resistance is the response of a plant to a pathogen attack and confers long-lasting protection against a broad spectrum of microorganisms. Thus, this study determined the induction of systemic acquired resistance against bacterial wilt in Irish potato through injection of attenuated pathogen and non-pathogens. The ability of Escherichia coli, Saccharomyces cerevisiae and attenuated R. solanacearum to induce systemic acquired resistance against bacterial wilt of Irish potato was tested in the greenhouse. Attenuation assay was conducted using four levels of formaldehyde concentrations and incubation duration for attenuation of R.solanacearum using randomized complete block design. Randomised complete block design was also used to evaluate in-vivo effect of different treatments and varieties on R. solanacearum in the greenhouse. Bacterial wilt symptoms were observed and a rating scale of 0 - 6 was used to score for disease severity. Leaves of the treated plants were collected for salicylic acid quantification in the laboratory. Disease severity, colony count, amount of salicylic acid and tuber yield data were analysed using statistical analysis software version 9.4 to determine induction of systemic acquired resistance. Significant means were separated using Least Significant Difference test at 5% probability level. Result from this study showed that there was statistically significant effect (p < 0.05) of formaldehyde concentrations and incubation duration for attenuation of R. solanacearum. The results from attenuation of R. solanacearum showed that colony count ranged from 0.67 colony forming units (in 0.6% formaldehyde concentration and incubation duration of attenuation of two hours) to 233 colony forming units (in 0% formaldehyde concentration and incubation duration of attenuation of two hours). There was significant (p < 0.05) treatment effect on disease severity, salicylic acid levels and tuber yield of Irish potato. Higher disease severity was recorded in S. cerevisiae treatments (80%) followed by E. coli treatments (40%) while least disease severity was recorded in attenuated R. solanacearum treatments. Attenuated R. solanacearum induced the highest level of salicylic acid (3409.64 mg/kg of Irish potato leaves) while R. solanacearum induced the lowest (1222.74 mg/kg of Irish potato leaves). Irish potato plants with attenuated R. solanacearum treatment had the highest yield of tubers (0.5772 kg/plant) while those treated with S. cerevisiae treatments had the lowest (0.4840 kg/plant). This study concluded that attenuated R. solanacearum and E. coli triggered systemic acquired resistance in Irish potato plants thereby increasing the levels of salicylic acid, which reduced the negative impact of the disease in the plants. Induction of systemic acquired resistance is a viable method for induction of resistance against bacterial wilt in Irish potato. The study recommends the identification of the specific molecules involved in induction of resistance from attenuated R. solanacearum and E. coli and their utilization in the control of bacterial wilt in order to mitigate the huge loses that are caused by this disease.
FIRST PRINCIPLES STUDY ON EFFECTS OF PRESSURE AND NIOBIUM DOPING ON STRUCTURAL AND ELECTRONIC PROPERTIES OF MOLYBDENUM DISULFIDE MONOLAYER
(Chuka University, 2023-10) MUTAVA GABRIEL MUTINDA
Semiconductor materials are dominant in the fabrication of electronic devices. Unlike metals, the presence of an energy band gap makes them ideal for application in optoelectronics nanostructures. Silicon was the most preferred 2D material to be used, but due to its limitations, for example, quantum tunneling effects, graphene was preferred to silicon. However, graphene has no bandgap, and since the bandgap property is very useful in electronics, research is ongoing to replace silicon and graphene with Transition Metal Dichalcogenides (TMDs). TMDs make nanostructures easily with adjustable energy bandgap, hence applicable in optoelectronics. They exhibit various unique optoelectronic characteristics, attracting interest due to distinct features from bulk predecessors and have bandgap characteristics between 1.80 - 2.30 eV, which can be tuned to fabricate Field Effect Transistors (FET) and other optoelectronic devices. Molybdenum disulfide has sparked attention among TMDs because of the potential of tuning the band gap. Up to date, research on the effects of impurities and pressure on the energy band gap of molybdenum disulfide have been studied, resulting in energy band gaps falling between 1.3 - 1.55 eV. There is need to reduce the value of the energy band gap further so as to make the semiconductor applicable at lower energies. Therefore, this study combined the ionic doping and pressure application on MoS2 in an attempt to narrow the energy band gap to a lower value that could accommodate majority of radiations falling under electromagnetic spectrum. Structural optimization of MoS2 monolayer and niobium doped MoS2 was done using the Density Functional Theory (DFT) method as implemented by the Quantum ESPRESSO simulation package. The study utilized PBE-GGA method of approximation and the number of k-points utilized were 8 x 8 x 1. The structure was optimized to a cell dimension of 3.175 Å for 𝑎 = 𝑏 parameters. A vacuum height of 14.971 Å served to minimize artificial interactions between periodic layers. A 4 x 4 x 1 supercell was modelled and had optimized dimensions of 12.57 Å for 𝑎 = 𝑏 and a vacuum height of 14.971 Å. Its band gap energy was found to be 1.70 eV. Upon 8.33% niobium doping of the 4 x 4 x 1 MoS2 supercell, the energy band gap reduced to 1.375 eV. A pressure in the range of −2.852 GPa to 6.832 GPa was applied, which corresponds to strains ranging from 2. 52 % to -2.50 %. The energy band gap for undoped MoS2 monolayer reduced from 1.70 eV to 1.40 eV at a pressure of -2.852 GPa. The energy band gap for the 8.33% Nb doped MoS2 monolayer narrowed from 1.375 eV to 1.25 eV at a pressure of -5.166 GPa. The combined effect decreased the band gap of MoS2 monolayer from 1.70 eV to 1.25 eV. This study concludes that the combined effect of Nb doping and pressure on the structure of molybdenum disulfide can improve its electronic properties by reducing its energy band gap. This property makes it useful in fabricating optoelectronic devices which can work well at lower energies.
PHYTOCHEMICAL ANALYSIS, IN VITRO TESTING OF ANTIBACTERIAL PROPERTIES, ANTI-INFLAMMATORY ACTIVITY, AND CYTOTOXICITY OF AQUEOUS AND DICHLOROMETHANE LEAF EXTRACTS OF Solanum incanum AND Tamarindus indica
(Chuka University, 2023-10) NGURARI SAMSON WAINAINA
The prevalence of bacterial infections and inflammatory-related diseases is increasing. As an alternative, the pharmaceutical sector is currently focusing on studying medicinal plants to generate alternative therapies for these health concerns. Solanum incanum and Tamarindus indica are among the plant species utilized in traditional medicine to address these issues. Most conventional drugs used to manage inflammation and bacterial infections have side effects, while some are expensive, hence the need to have alternative plant-based therapies. Additionally, there is limited information on the potency of Solanum incanum and Tamarindus indica, which is vital in process of commercializing its active metabolites to improve disease management. Therefore, this study analyzed phytochemicals present in aqueous and dichloromethane leaf extracts of the two plants and tested their antibacterial, anti-inflammatory, and cytotoxic properties. The phytochemical analysis was done using standard chemical tests followed by Gas Chromatography-Mass Spectroscopy of dichloromethane extracts. The antibacterial activity of the extracts was tested against Escherichia coli, Salmonella typhi, and Staphylococcus aureus using disc diffusion method, minimum inhibitory Concentration, and minimum bactericidal concentrations assays. The anti-inflammatory potency of the extracts was tested using an Erythrocyte stabilization assay, while the toxicity of the extract was tested using brine shrimp lethality tests. Phytochemical analysis indicated presence of flavonoids, tannins, saponins, phenols, and alkaloids in all the plant extracts. Additionally, the T. indica dichloromethane and S. incanum water extracts had no glycosides, while anthraquinones were absent in all the extracts. The antibacterial assay revealed significant difference in antibacterial activity between the plant extracts at different concentrations. The Minimum Inhibitory Concentrations of T. indica extracts ranged between 62.5 μg/mL and 125 μg/mL, while those of S. incanum ranged between 62.5 μg/mL and 250 μg/mL. The Minimum Bactericidal Concentration of both plants ranged between 125 μg/mL and 500 μg/mL. The S. incanum dichloromethane extracts had the highest percentage erythrocyte stabilization at 1000 μg/ml, 57.64 ±13.90%, while S. incanum water extract had the lowest stabilization at 2000 μg/ml, 19.06 ±14.43%. T. indica dichloromethane extract has the highest toxicity (LD50 of 113.57 μg/mL) while S. incanum DCM extract was the least toxic (LD50 of 2341 μg/mL). The plant extracts have demonstrated the potential of being used for therapeutic purposes after further analysis for the identification of the active compounds. Therefore, this research provides preliminary data on their antibacterial and anti-inflammatory activity and cytotoxicity of the extracts, which is foundational for further research.
AB INITIO STUDY OF STRUCTURAL AND PIEZOELECTRIC PROPERTIES OF HAFNIUM DOPED BISMUTH SODIUM POTASSIUM TITANATE
(Chuka University, 2023-10) MWANZIA BONFACE MUTUKU
Piezoelectric materials have gained increased attention in the recent times due to their significant technological applications. These materials are widely used to make ultrasound transducers, sensors, actuators and others are used for energy harvesting. Due to its brilliant piezoelectric properties, Lead Zirconate Titanate (PZT) is mostly used with a piezoelectric constant of 𝑑33 = 374 𝑝𝐶/𝑁 from experimental reports and 306 − 314 𝑝𝐶/𝑁 from theoretical studies. However, due to the toxic nature of lead oxide which is formed when PZT is being manufactured, there is increased effort in development of lead-free materials. Several classes of materials have recently been studied and are now being considered as potential alternatives to PZT. Lead free perovskite systems such as Bismuth Sodium Potassium Titanate (BNKT) have been developed, with a piezoelectric constant 𝑑33 = 157 𝑝𝐶/𝑁 . However, the main drawback of this system is that it is highly corrosive and has a low piezoelectric constant compared to PZT. In the quest to provide suitable alternatives, dopants such as zirconium have been used, which improved the piezoelectric constant of BNKT up to203 𝑝𝐶/𝑁. Hf which possesses similar physico-chemical properties as zirconium has led to an improvement in the piezo electric constant of other piezoelectric systems such as in hafnium doped Barium Titanate (BT). It has an added advantage of being extremely resistant to corrosion, which is expected to mitigate the corrosive nature of BNKT. In this study, hafnium has been incorporated in BNKT so as to engineer an alternative material suitable for piezoelectric applications. Density Functional Theory (DFT) method was used to predict the structural and piezoelectric properties of hafnium doped BNKT, starting with those of Bismuth Sodium Titanate (BNT) and BNKT. The exchange and correlation was taken as the Generalized Gradient Approximation (GGA). The optimal lattice parameters for BNT were found to be 𝑎 = 5.57 Å and 𝑐/𝑎 ratio of 2.50 for the conventional cell, having space group R3c space group number 161. Piezoelectric constant for this system was found to be 97.67 pC/N. This structure was adopted for doping and further calculations. Potassium doped bismuth sodium titanate was modelled using VESTA software and its optimized lattice parameter was found to be 𝑎 = 5.60 Å. Piezoelectric constant for this system was found to be 147.42 pC/N. Hafnium doped BNKT had an improved piezoelectric constant of 205.52 pC/N for 3% hafnium doping, which decreased to 163.22 pC/N at the level of 6% doping. The results shows that small amounts of hafnium improved the piezoelectric constant of BNKT from 147.42 pC/N to 205.52 pC/N. Elastic and elastic compliance full tensors for these systems was also generated with elastic constants of C33 = 286.48 Gpa, 282.13 Gpa, 257.193 Gpa and 276.43 Gpa for BNT, BNKT, 3% Hf doped BNKT and 6% Hf doped BNKT respectively. This study concludes that doping BNKT with hafnium indeed improves the piezoelectric properties of BNKT. This makes this material more useful in energy generation since high piezoelectric constant leads to efficient mechanical – electrical energy conversion in the piezoelectric materials.

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