Iris Publishers-Open access Journal of Dentistry & Oral Health | A Novel Technique for Orthodontic Gap Closure with Access through the Maxillary Sinus

 

Authored by I Boujoual*,

Abstract

Introduction: Temporomandibular dysfunction is a benign pathology, with polymorphic expression and subject to multiple factors that participate in its etiology, which makes the diagnosis of certainty difficult. A wide range of therapeutic options are available, including splints, physical therapy, pharmacotherapy (analgesics, muscle relaxants, anxiolytics, antidepressants, etc.)

Objective: The aim of our work is to conduct a systematic review evaluating the clinical efficacy of muscle relaxants and paralyzers in the treatment of temporomandibular disorders in the light of Evidence Based Dentistry.

Methods: The collection of data from the scientific literature was carried out among the production that appeared during the period from 2000 to 2021. The literature search was carried out by exploiting databases accessible via the Internet, namely Medline through its search engine Pubmed, Elsevier, Google scholar, Research for life and Web of science. A bottom-up manual search covering the same study period was carried out in order to expand our bibliography. The writing of this systematic review followed the guidelines of PRISMA Statement (Preferred Reporting Items for Systematic Reviews and Meta-Analyses).

Results: 9 relevant articles were retained after critical reading guided by CASP-type reading grids. The articles were then classified into 3 categories according to the type of molecule administered:
-Administration of centrally acting muscle relaxants
-Administration of anxiolytics with muscle relaxant properties
-Administration of muscle paralyzer
The articles were classified in tables according to the PICO criteria (Participants/Interventions/Comparison/Outcomes). The results of our study showed a decrease in pain intensity after administration of muscle relaxants and anxiolytics with muscle relaxant properties. Botulinum toxin injection also has the advantage of being a minimally invasive procedure and an effective treatment method in patients who do not respond to the most conservative treatments.

Discussion: The results of our studies regarding the efficacy of muscle relaxants and paralytics in the management of temporomandibular disorders are supported by other systematic reviews and meta-analyses. However, new research with a longer observation period, a large sample size and a correct methodology is still needed.

Conclusion: The disparity of the results of the studies and the absence of scientific evidence that would lead to a consensus on the efficacy of muscle relaxants and paralytics in the treatment of TMD do not allow for clear-cut conclusions. In addition, the small size of the populations studied makes it impossible to extrapolate the results, which is why more in-depth studies are needed.

Keywords: Temporomandibular joint disorders, Neuromuscular agents, Cyclobenzaprine, Botulinum toxins

Introduction

The manducatory apparatus is a system formed by several elements; a passive articular component (temporomandibular and occlusal) and an active muscular component, which maintain reciprocal relations of influence between them, in coordination with the neuromuscular system [1].

These different components cannot be dissociated from each other, their harmony conditions the efficiency of the manducatory apparatus, and any alteration could disrupt the balance of the whole, manifesting in a craniomandibular dysfunction. Defined as a mechanical attack on the TMJs, of multifactorial etiology, craniomandibular dysfunction can manifest locally at the TMJs or a distance from them [2].

The most characteristic symptoms of these diseases are pain, joint noises, and dyskinesias. The latter is related to abnormal muscular activity: the masticatory muscles are the most affected and the pain can be related to damage to muscle fibers, fascia insertions, or tendons [3].

The overall treatment aims to reduce pain, improve function and act on the psyche. To achieve this, various therapeutic approaches are available, such as maxillofacial physiotherapy [4], cognitive-behavioral therapies, hypnosis [5], occlusal orthoses [6], and pharmacological therapies (muscle relaxants, analgesics, anxiolytics, NSAIDs, etc.).

Muscle relaxants act directly on the skeletal muscles due to a selective chemical action on the central nervous system. The principal molecules are Cyclobenzaprine, Tetrazepam, Thiocolchicoside and Baclofen [7].

The lack of consensus concerning the place of muscle relaxants and paralyzers in the management of disorders of the manducatory apparatus means that practitioners are confused about the use of these molecules.

The objective of this article is to evaluate, based on literature data, the clinical effectiveness of these molecules in the management of dysfunctions of the manducatory apparatus.

Materials and Methods

A literature search was performed in the international databases Medline, and Elsevier, by their search engines; respectively PubMed, and ScienceDirect. we also consulted Google Scholar.
The electronic search strategy was based on Boolean equations using MESH words related to the topic:
- “Temporomandibular joint disorder” (Mesh) And ”Neuromuscular agents” (Mesh)
- “Temporomandibular joint disorder” (Mesh) And “Cyclobenzaprine” (Mesh)
- “Temporomandibular joint disorders” (Mesh) And “Botulinum toxins” (Mesh)

Inclusion criteria

Controlled clinical trials and randomized clinical trials, conducted in humans, with identical follow-up between groups, published between 2000 and 2021 and written in French or English were included in our review.

Exclusion criteria

It was excluded from this review: Studies with publication dates before 2000, studies conducted in animals, case series, retrospective studies, literature reviews, and studies funded by manufacturers.

After searching the database, the bibliographic references of the selected articles were examined for other articles on the same topic. The scientific articles were independently checked by two authors (B.I. and F.K.), who assessed the methodological quality of all included articles using the Critical Appraisals Skills Program (CASP).

Results

The results of our search are presented using a flow chart showing the selection of articles. A general description of the studies will be listed in a table and the articles will be classified in tables according to PICO criteria (Participants/Interventions/ Comparison/Outcomes) (Figure 1).

The studies were classified into three principal categories according to the type of molecule administered:
- Administration of centrally acting muscle relaxants
- Administration of anxiolytics with muscle relaxant properties
- Administration of muscle paralytics
The description of the articles included in our review was carried out according to the PICO criteria (Participants/ Intervention/ Comparison/ Outcomes). For each article, the variables studied and their measurement tools as well as the most significant results were summarised in the form of a table (Table 1).

Table 1:

*VAS Visual Analogue Scale
*PSQI Pittsburgh Sleep Quality Index
*SSI Symptom Severity Index

Discussion

Regarding the effect of centrally acting muscle relaxants on the management of MAD

To evaluate the effect of muscle relaxants in pain management all authors used the visual analog scale to identify pain intensity.

The study by Alencar F, et al. [8] concluded that there was an eventual improvement in symptoms for all groups: Cyclobenzaprine, Tizanidine, and placebo groups, between pre-treatment and post-treatment, but no statistically significant difference could be observed between the active groups.

However, another study by Cory R Herman, et al. [9], evaluating the effect of Cyclobenzaprine on patients with waking myofascial pain, comparing it with Clonazepam and placebo, concluded that Cyclobenzaprine is more effective than the anxiolytic (Clonazepam) in the treatment of temporomandibular disorders when combined with patient education and a home self-care program for pain management.

In the trial by Alpaslan C, et al. [10], all four groups of patients who received muscle relaxants (Chlorzoxazone, Phenprobamate, Mephenoxalone, Baclofen) had pain reduction and improved mandibular function during the follow-up period. Nevertheless, in terms of symptom resolution, the final results were comparable between the groups. Muscle relaxants in the four groups for active treatment were no more effective than no active treatment. These results show that symptoms may resolve over time, even if no treatment is given in TMD.

However, the response of patients may differ in the treated and control groups. The complex biopsychosocial factors in the etiology of TMDs may lead to variable treatment outcomes. In most cases, it appears that no medication is needed as the natural course shows the resolution of symptoms.

A muscle relaxant may be prescribed for severe pain and dysfunction, while follow-up may be recommended for mild symptoms, remembering that myofascial pain symptoms tend to resolve with or without medication.

Regarding the efficacy of anxiolytics with muscle relaxant properties in the management of DAM Through the clinical trial conducted by Pramod GV, et al. [11], we concluded that the reduction in pain score was better in the diazepam group (72%) than in the placebo group (65%).

Indeed, Basmajian JV [12] compared Cyclobenzaprine with Diazepam and placebo in patients with muscle spasms in the lumbar and neck region. Clinical improvement in signs and symptoms was observed for both drugs and placebo, and there was no statistical difference between the three treatment groups.

Singer and Dionne [13] in their clinical trial of patients with chronic orofacial muscle pain found a significant decrease in pain symptoms in the groups treated with Diazepam alone and the combination of Diazepam and Ibuprofen.

As a result, the use of anxiolytics with muscle relaxant properties in the management of manducatory system disorder allows amelioration, by acting on the underlying anxiety as well as on masticatory muscle spasms.

Regarding the efficacy of botulinum toxin in the management of TMD Studies included in our research concerning muscle paralytics concluded the effectiveness of the latter in improving pain scores. However, this conclusion should be qualified since the tool used to measure pain intensity was the visual analog scale which is a subjective tool.

The study by Ernberg M, et al. [14], showed no significant difference in pain reduction between BTX-A and saline injection into the masseter muscle for patients with persistent myofascial pain associated with MAD.

Other studies by Guarda-Nardini L, et al. [15] reported a 50% reduction after BTX-A administration and 5% after saline administration, while Kurtoglu C, et al. [16] reported a 22% pain reduction for BTX-A and 13% for saline at one-month follow-up. The study by Calis AS, et al. [17] also showed that pain was reduced after BTX injection by 100%.

Finally, the study by Freund and Schwartz concluded that muscle pain in patients with TMD was reduced by 50% after BTX-A administration. It was also observed that the degree of mouth opening increased. Three processes have been recognized concerning the effectiveness of BTX-A injection [18, 19]:

Firstly, muscle relaxation: the reduction in muscle tone is explained by the inhibition of alpha and gamma neurons. Secondly, the mechanism is associated with the reduction of inflammation in the TMJ and muscle. Inflammation of the TMJs limits the movement of the capsules and ligaments. The third process is the relief of pain and the increase in the degree of mouth opening.

Botulinum toxin has the advantage of being a minimally invasive procedure and an effective treatment method in patients who do not respond to the most conservative treatments (gentle diet, non-steroidal anti-inflammatory drugs, and occlusal splints). In addition, the relatively short administration time of botulinum toxin, the low level of pain associated with its application, and the low risk of complication can all be cited as significant advantages [20, 21].

In light of the above, we can conclude that the studies do not seem to be in complete agreement on the efficacy of botulinum toxin in the management of TMD. Hence the need for further studies to judge the actual action of this substance in the treatment of patients.

Conclusion

Dysfunctions of the manducatory apparatus are complex pathologies with a multifactorial etiology and multiple manifestations that complicate their diagnosis and their management.

The diversity of study results and the lack of scientific evidence leading to a consensus make it impossible to reach clear-cut conclusions. In addition, the small size of the populations studied makes it impossible to extrapolate the results.

As a result, further studies are required, with a more extended observation period and larger sample size, to provide a better analysis of the efficacy of muscle relaxants and paralytics in the treatment of TMD.

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Iris Publishers- Open access Journal of Agriculture and Soil Science | Iodine Nutrition Knowledge of Food Handlers: A Capricorn and Waterberg District Study, Limpopo Province, South Africa

 

Authored by Mabapa Ngoako Solomon*,

Opinion

Given the public health importance of eliminating iodine deficiency and its consequences, one can assume that consumers are informed and educated about iodine nutrition and iodine deficiency disorders such as impaired mental function, goitre, hypothyroidism, cretinism, retarded physical development and even child mortality [1]. Salt fortification was an intervention initiated by the government to address iodine deficiency disorders but the community has limited information on the salt fortification and its benefits [2]. Intensive implementation activities of monitoring and evaluation of salt fortification have revealed the limited knowledge of how to translate efficacious interventions into effective programs with relevant mechanisms for program monitoring, quality assurance, and impact evaluation to the beneficiaries of the programme [3].

Although some people have knowledge about salt fortification, socio economic factors play a role since most exclusive users of common salt say the price of iodized salt is a little higher that of the common salt [4]. Limited knowledge of iodine nutrition among low socio-economic groups have also been reported in South Africa hence people who have less education and less resources, have the least knowledge about the importance of iodized salt [1]. While people who had some knowledge about importance of iodized salt, minority reported the use of iodized salt indicating a huge gap in knowledge and practice [1].

Generally, the reasons for iodization failing to eliminate iodine deficiency were that a) only about a third of table salt produced in South Africa was iodized; b) unequal distribution of iodized salt favored urban areas; c) price-sensitive rural and low income consumers used cheaper non-iodized salt brands; and d) there was a low awareness of the benefits of iodized salt [4,5]. Most people are not sufficiently informed about the health implications of an inadequate iodine intake, nor were they aware of dietary sources of iodine, or the potential benefits of fortification [6]. Study conducted before introduction of mandatory iodization in the country revealed that despite the price of iodized and non-iodized salt being identical, a low proportion of low socio-economic households (between 4.3 and 25%) used iodized salt [4]. A study in towns of the Northern Cape Province in South Africa showed that only 2% of the mothers correctly knew the health benefits of iodine in iodized salt [5]. Although large nutritional studies have been conducted in South Africa on iodine and its benefits, there is scarcity of data concerning the iodine nutrition knowledge of food handlers in primary schools in particular. In view of this, the study was conducted to assess the iodine nutritional knowledge of food handlers in Capricorn and Waterberg district, Limpopo Province, South Africa.

Of all food handlers 55.3% had no idea what salt fortification was and 34.7% were from Capricorn district as compared to 21.3% in Waterberg district. About, 96.1% of food handlers knew the importance of using iodized salt and majority were from Capricorn district 58.7% as compared to 38.7% in Waterberg district. In addition, 32% in Capricorn district don’t read the labeling when buying salt as compared to 12% in Waterberg district.

Of all food handlers, 17.3% in Capricorn district indicated that iodine was a vitamin as compared to 8% in Waterberg district. In Capricorn district 26.7% indicated that iodine is added to maize meal as a fortificant as compared to 29.3% in Waterberg district. About 25.3% of food handlers in Capricorn district didn’t know what iodine was as compared to 24% in Waterberg district. Only 18.7% of food handlers in the study knew that iodized salt was the sources of iodine. About 12% and 6.7% of participants from Capricorn and Waterberg districts respectively knew the body part that needs iodine for normal functioning. Furthermore the results of the study showed that 5.3% correctly knew the consequences of iodine deficiency [7]. The results of the study appears to be suggesting that while South Africa made good progress as far as the implementation of salt iodization and coverage is concerned, the advocacy and educational aspects are seriously lacking. The results of the study also suggest that nutrition knowledge is inadmissibly low among food handlers. Of particular concern is the finding that the international education strategy to increase public awareness that iodine deficiency is a preventable cause of mental retardation appear to have had little or no impact to most South Africans. The low level of iodine nutrition knowledge requires vigorous public awareness campaigns targeting people from low socio-economic groups.

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Iris Publishers- Open access Journal of Engineering Sciences | Temperature-Dependence of Debye-Waller Factors of Semiconductors Presented in Terms of Cumulant Expansion

 

Authored by Nguyen Van Hung*,

Abstract

This work studies temperature-dependence of Debye-Waller factors of semiconductors presented in terms of cumulant expansion in extended X-ray absorption fine structure (EXAFS). The advances in these studies are succeeded based on further development of the anharmonic correlated Einstein model derived primary for fcc crystals into the one for applying to semiconductors and for creating a method having the advantage that all considered quantities are provided based on only the calculation or measurement of second cumulants. Analytical expressions of three first EXAFS cumulants have been derived. They describe the thermodynamic and anharmonic properties and contribute to accurate structural determination of semiconductors. The theory simplifies the many-body task into the one of one-dimensional model with taking the many-body effects into account based on the first shell near neighbor contributions to the vibration between absorber and backscattered atoms. Morse potential is assumed to describe single-pair atomic interaction. The results calculated using the present theory and those obtained by the created method for Ge having diamond structure are found to be in good agreement with experiment and with those of other theorie.

Keywords: Temperature dependence; Debye-Waller factor; Cumulant expansion; Anharmonic correlated einstein model; Semiconductor

Introduction

Extended X-ray Absorption Fine Structure (EXAFS) has developed into a powerful technique for providing information on the local atomic structure and thermal effects of substances. The formalism for including anharmonic effects in EXAFS is often based on the cumulant expansion approach [1] from which the expression for anharmonic EXAFS is given by

where F(k) is the real atomic backscattering amplitude, k and λ are the wave number and mean free path of the photoelectron, respectively, ɸ is net phase shift and σ(n) (n = 1, 2, 3, …) are the cumulants describing Debye-Waller factor (DWF).

In this expression of EXAFS the even cumulants contribute to the amplitude, the odd ones to the phase of EXAFS spectra, and they also account for the net thermal expansion (first cumulant), the mean square relative displacement (MSRD) (second cumulant) and the asymmetry of the pair distribution function (third cumulant). Consequently, the lack of the precise DWFs has been one of the biggest limitations not only to accurate structural determinations but also to specifications of the thermodynamic and anharmonic properties of materials from EXAFS data. Therefore, investigation of DWFs is of great interest.

The purpose of this work is to study temperature-dependence of DWFs of semiconductors presented in terms of cumulant expansion in EXAFS. The most advantageous developments in these studies are presented in Section 2. They are succeeded based on the further development of the anharmonic correlated Einstein model (ACEM) [2] derived primary for fcc crystals, into the one for applying to semiconductors and for creating a method having the advantage that all considered quantities are provided based on only the calculation or measurement of second cumulants. Analytical expressions of three first EXAFS cumulants have been derived. They describe the thermodynamic and anharmonic properties and contribute to accurate structural determination of semiconductors. The theory simplifies the many-body task into the one of one-dimensional model with taking the many body effects into account based on the first shell near neighbor contributions to the vibration between absorber and backscattered atoms. Morse potential contained in the derived anharmonic effective potential is assumed to describe the single-pair atomic interaction. In Section 3 the results calculated

using the present theory and those obtained by using the created method, i.e., from the available theoretical [3,4,10] or experimental [5-7] second cumulants of Ge having diamond structure are compared to experiment [5-9], and to those of the other theories [3,4,10], which show good agreement. The conclusions are presented in Section 4.

Formalism

Anharmonic effective potential

To determine EXAFS cumulants of a semiconductor it is necessary to specify its interatomic interaction potential and force constant. Let us consider an anharmonic interatomic effective potential expanded up to the third order around its equilibrium

where keff is the effective local force constant, k3eff is the cubic anharmonic effective parameter giving an asymmetry of the anharmonic effective potential, x is the deviation of the instantaneous bond length r between two immediate neighboring atoms from its equilibrium value r0.

In the present theory the many-body task is simplified into the one of one-dimensional model with taking the many-body effects into account based on including the first shell near-neighbor contributions to the vibrations between absorber and backscattered atoms. Therefore, the anharmonic effective potential Eq. (2) defined based on an assumption in the center-of-mass frame of single bond pair of an absorber and a backscattered has resulted as

where α and D are Morse potential parameters describing respectively the width of the potential and the dissociation energy.

Here the effective local force constant and cubic anharmonic parameter for semiconductors included in Eq. (2) as the parameters of anharmonic effective potential have been defined and given in the following forms

Note that in the derivation of the above expressions we consider the diamond structure, where each atom is bonded to four nearest neighbors and Morse potential is assumed to describe the single pair atomic interaction.

For further calculation of EXAFS cumulants using quantum thermodynamic perturbation theory in the present theory the anharmonic effective potential Eq. (4) is expressed in the sum of the harmonic contribution and a perturbation d V due to the weak anharmonicity in EXAFS as

EXAFS cumulants

Derivation of EXAFS cumulants in the present theory for semiconductors is based on quantum statistical theory [11] and the anharmonic effective potential derived in the previous Section 2.1. Now we consider the physical quantity which is determined based on an averaging procedure using the canonical partition function Z and statistical density matrix ρ, e.g.,

Atomic vibrations are quantized in terms of phonons, and anharmonicity is the result of phononphonon interaction, that is why we express y in terms of the annihilation and creation operators  respectively

which have the following properties

as well as use the harmonic oscillator state n as the eigenstate with the eigenvalue  respectively

for n being the phonon number, ignoring the zero-point energy for convenience.

Based on the local force constant given by the first equation of Eqs. (5), the correlated Einstein frequency  respectively

Based on the local force constant given by the first equation of Eqs. (5), the correlated Einstein frequency ω E and temperature θE for semiconductors have resulted and given by

where kB is Boltzmann constant m is atomic mass (for monatomic crystal). The canonical partition function in Eq. (8) can be expressed as

Using the above results for the correlated atomic vibration and the procedure depicted by Eqs. (8) - (12), as well as the first-order thermodynamic perturbation theory [11] the temperature-dependent EXAFS cumulants in the present theory for semiconductors have been derived.

Here, based on the procedure depicted by Eq. (8) we derived the even moment expressing the second cumulant or MSRD

and the odd moments expressing the first (m = 1) and third (m = 3) cumulants

Where δV( y) is taken from Eq. (7) and the operations expressed by Eqs. (8) - (10) have been applied to calculate the matrix elements given in Eqs. (13) - (14).

Consequently, the EXAFS cumulants for semiconductors have resulted for the first cumulant describing net thermal expansion or lattice disorder

for the second cumulant describing MSRD

and for the third cumulant describing the mean cubic relative displacement (MCRD) or the asymmetry of the pair distribution function

Here  are zero-point energy contributions to the Cumulants  respectively.

Hence, the EXAFS quantities given by Eqs. (15) – (17) have been described in terms of second cumulant. This is useful not only for reducing the numerical calculations but also for creating a method for obtaining the remain theoretical or experimental EXAFS quantities of the considered semiconductor based on only the calculated (theoretical study) or measured (experimental study) second cumulants.

Note that the derived cumulants describe the thermodynamic and anharmonic properties and based on Fourier transform magnitudes of EXAFS spectra described by Eq. (1) containing these cumulants contribute to accurate structural determination of semiconductors.

Numerical Results and Discussions

Now we apply the expressions derived in the previous sections to numerical calculations for temperature-dependence of EXAFS cumulants of diamond structure type semiconductor Ge using its Morse potential parameters [12] D = 1.63 eV, α = 1.50 Ǻ-1. The calculated values of the local force constant keff, anharmonic cubic parameter keff, correlated Einstein frequency ωE and temperature θE are written in Table 1.

Table 1: Calculated values of  of semiconductor Ge using its Morse potential parameters [12].

Figure 1 illustrates the anharmonic interatomic effective potentials of Ge calculated using the present theory. It is asymmetric due to the anharmonic contribution described by the third order parameter k3eff of the potential. Here, the anharmonic effective potential of Ge is compared to its harmonic effective term to show the rate of its asymmetry due to anharmonicity. This anharmonic effective potential of Ge is used for calculating the considered EXAFS quantities.

Temperature-dependence of second cumulant or MSRD σ2(T) of Ge (Figure 2) calculated using the present theory agrees well with the experimental values of G Dalba, et al. (Expt.) [5,6], and of AE Stern, et al. [7], with the result of FD Vila, et al. [3] and of JJ Rehr, et al. [4] calculated using the LDA (local density approximation), and of NV Hung, et al. [10] calculated using the SMM (statistical moment method) and Stillinger-Weber potentials.

Temperature-dependence of the first cumulant or net thermal expansion σ(1)(T) of Ge (Figure 3) calculated using the present theory agrees well with the experimental values of G Dalba, et al. [8], and to those calculated from the experimental (exp.) MSRD of G Dalba, et al. [5], of EA Stern, et al. [7], as well as from the calculated (calc.) MSRD of FD Vila, et al. [3], and of JJ Rehr, et al. [4] calculated using the LDA. Such good agreement is also shown for the third cumulant σ(3)(T) of Ge (Figure 4) calculated using the present theory with the EXAFS experimental values of P Fornasini, et al. [9], as well as to those calculated from the experimental (exp.) MSRD of Dalba, et al. [6], of E Stern, et al. [7] and from the calculated (calc.) MSRD of FD Vila, et al. [3], and of JJ Rehr, et al. [4] calculated using the LDA.

Note that the good agreement of the values calculated from the theoretical and experimental second cumulants or MSRDs of Ge (Figure 2) for the first cumulants presented in Figure 3 and for the third cumulants presented in Figure 4 with experiment confirms not only their validity as the theoretical and experimental EXAFS quantities but also the possibility of getting the other EXAFS parameters if the second cumulants are calculated or measured. This actually also confirms the validity of the above created method which has been used in the present studies.

The above figures show that at high temperatures the first and second cumulants are linearly proportional to temperature T and the third cumulant to T2. They contain zero-point energy contributions at low-temperatures, a quantum effect.

The cumulant ratios are often considered in the anharmonic EXAFS studies [2,13,14]. Figure 5 illustrates temperaturedependence of cumulant ratio σ(1)σ2/σ(3) calculated using the present theory for Ge. Here, σ(1)σ2/σ(3) approaches 3/2 at low-temperatures and the classical value [13,14] of 1/2 at high temperatures beginning from the Einstein temperature (θE = 363.26K for Ge, Table 1) as for the other crystal structures [2]. Hence, it remains to be considered as the standard for studying EXAFS cumulants of semiconductors calculated using the present theory.

Conclusion

In this work a theory has been derived for studies of temperature-dependence of DWFs of semiconductors presented in terms of cumulant expansion in EXAFS. They contribute to accurate structural determination, as well as to valuation of the thermodynamic properties and anharmonic effects accounting for the net thermal expansion, the MSRD, and the asymmetry of the pair distribution function of semiconductors.

The advanced studies are succeeded based on the further development of the ACEM derived primary for fcc crystals into the one applied to semiconductors. Here the many-body task is simplified into the one of one-dimensional model with taking the many-body effects into account based on including the first shell near-neighbor contributions to the vibrations between absorber and backscattered atoms.

The method created in this theory has the advantage that all theoretical and experimental EXAFS quantities are provided based on only the calculation (theoretical study) or measurement (experimental study) of second cumulants. It is useful not only for reducing the numerical calculations or measurements but also for creating a simple way of obtaining the considered quantities.

The theory is successfully applied to valuation of temperaturedependence of three first EXAFS cumulants of semiconductors. At high temperatures the first and second cumulants are linearly proportional to temperature T and the third one to T2. They contain zero-point energy contributions at low-temperatures, a quantum effect. The cumulant ratio σ(1)σ2/σ(3) expresses the same properties as those for the other crystal structures so that it remains to be considered as the standard for EXAFS cumulant studies of semiconductors.

The good agreement of the results calculated using the present theory and of those obtained by using the created method with experiment and with those of other theories for Ge having diamond structure illustrates the simplicity, advantage and efficiency of the present theory and the created method in the theoretical and experimental EXAFS studies of the thermodynamic properties and anharmonic effects of materials having any structure including semiconductors.

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