Study of anharmonic elastic properties of mixed diatomic crystals AgCl−AgBr and NaCl−NaBr

Summary An interionic-force model has been employed to analyse the anharmonic elastic properties of mixed-diatomic-crystal systems with varying compositions. The interaction system consists of long-range Coulomb and three-body interactions within the framework of Hafemeister-Zarht (HZ) short-range repulsion, effective up to second-neighbour ions. This interionic potential has been used for predicting the third-order elastic constants, the first pressure derivative of second-order elastic constants and the Anderson-Grüneisen (AG) parameter in NaCl−NaBr and AgCl−AgBr mixed crystals. The values of the hardness parameter between nearest neighbours as well as between second nearest neighbours have been evaluated by using the overlap integral method. The results obtained in the present study are generally in good agreement with the available experimental data as compared to those obtained by earlier investigations. The experimental values of the Anderson-Grüneisen parameter have been calculated by using Chang’s relation.

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Riassunto Un modello di forza interionica è stato usato per analizzare le proprietà anarmoniche elastiche di sistemi di cristalli diatomici misti con composizioni variabili. Il sistema d’interazione consiste in interazioni di Coulomb a largo raggio e a tre corpi nell’àmbito della repulsione a corto raggio di Hagemeister-Zorht (HZ), efficaci fino a ioni secondi vicini. Questo potenziale interionico è stato usato per prevedere costanti elastiche di terz’ordine, la prima derivata di pressione delle costanti elastiche di second’ordine e il parametro di Anderson-Grüneisen (AG) in cristalli misti NaCl−NaBr e AgCl−AgBr. I valori del parametro di durezza tra vicini prossimi e tra secondi vicini prossimi sono stati calcolati usando il metodo dell’integrale di sovrapprosizione. I risultati ottenuti in questo studio sono generalmente in buon accordo con i dati sperimentali disponibili se confrontati con quelli ottenuti da precedenti ricerche. I valori sperimentali del parametro di Anderson-Grüneisen sono stati calcolati usando la relazione di Chang.

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Резюме Используется модель междуионной силы для анализа ангармонических упругих свойств смешанных двухатомных кристаллических систем с изменяющимся составом. Взаимодействие системы состоит из длиннодействующего кулоновского взаимодействия и взаимодействий трех тел в рамках короткодействующего отталкивания Хафемайстера-Зарта, с учетом взаимодействий с ионами, следующими за соседями. Предложенный междуионный потенциал используется для предсказания упругих постоянных третьего порядка, первой производной упругих постоянных второго порядка по давлению и параметра Андерсона-Грюнайзена в смешанных кристаллах NaCl−NaBr и AgCl−AgBr. Оцениваются параметры жесткости между соседними ионами, а также между ионами, следующими за соседними. Полученные результаты хорошо согласуются с имеущимися экспериментальными данными. Используя соотношение Чанга, вычисляются экспериментальные значения параметра Андерсона-Грюнайзена.

     

Some anharmonic properties of Caesium halides

The second thermal Grüneisen parameter and isentropic Anderson-Grüneisen parameter for caesium halides are determined at different temperatures employing a pressure dependent shell model of lattice dynamics. A new thermodynamic relation is also proposed to calculate the second thermal Grüneisen parameter using experimentally measurable quantities. The agreement between experimentally estimated and theoretically calculated values is fairly good for the Anderson-Grüneisen parameter while it is very poor for the second thermal Grüneisen parameter.     

Magnetic properties of the alkanediammonium copper halides

Powder magnetic susceptibility and magnetization data have been obtained for the remaining, unreported members of the quasi-two-dimensional series [NH₃(CH₂)_nNH₃] CuX₄ for n=2?10 and X=Cl and Br. Values for J (in-plane), J′ (out-of-plane) and T_c are tabulated for the entire series. An alternation between ferromagnetic and antiferromagnetic behavior for the low temperature phases in the bromine series was found. Several unusual low temperature phases which could not be classified were also seen.     

Dielectric and anharmonic behaviour of mixed alkali halides

Summary In the present paper an analysis of the dielectric behaviour and anharmonic contribution to the dielectric constants has been made of KCl−KBr mixed ionic crystals. The temperature and volume derivatives of static (ε₀), electronic (ε_∞) dielectric constants and energy gap parameter (E _g) have been calculated using the Szigeti and Havinga and Bosman dielectric theories. The anharmonic contributions have been estimated in terms of temperature derivatives of dielectric constants at constant volumes. The modified form of Clausius-Mossotti theory of dielectric polarization has been used for the mixed crystal under study. The calculated quantities have been compared with the available experimental data. A good agreement has been obtained. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Multi-instantons and exact results III: Unification of even and odd anharmonic oscillators

This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin, U.D. Jentschura, Ann. Phys. (N.Y.) 313 (2004) 197 and 269], we here focus on simple even and odd anharmonic oscillators for arbitrary magnitude and complex phase of the coupling parameter. A unification is achieved by the use of PT-symmetry inspired dispersion relations and generalized quantization conditions that include instanton configurations. Higher-order formulas are provided for the oscillators of degrees 3 to 8, which lead to subleading corrections to the leading factorial growth of the perturbative coefficients describing the resonance energies. Numerical results are provided, and higher-order terms are found to be numerically significant. The resonances are described by generalized expansions involving intertwined nonanalytic exponentials, logarithmic terms and power series. Finally, we summarize spectral properties and dispersion relations of anharmonic oscillators, and their interconnections. The purpose is to look at one of the classic problems of quantum theory from a new perspective, through which we gain systematic access to the phenomenologically significant higher-order terms.     

Optical deformation potentials of the copper halides

The absolute Raman scattering efficiency of the copper-halides is determined in the energy range from 2 to 3.1 eV. From it the absolute values of the deformation potentials d_o are deduced. They are anomalously small (|d_o|<5 eV). This is explained theoretically with the help of a tight binding model in which the special nature of the valence band (obtained by a mixing of the 3d-Cu and p-halogen orbitals) is taken into account.     

Magnetic properties of ternary compounds

Summary At present magnetism is becoming a more and more fundamental science. On the other hand, the solid-state chemists are able to prepare easily many new ?magnetic? phases with a more or less complex crystal structure. There results a conflicting situation between the ideal expected models and the true behaviour of the real crystal. A strategy to tackle this important problem is suggested. Illustrations are given by analysing the properties of ternary compounds with different structural arrangements of their magnetic carriers such as chains or layers. Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16, 1982.     

The piezobirefringence in copper halides

Summary We present new experimental results on the piezobirefringence (PBR) of CuCl, CuBr, CuI, as a function of strain in the directions [100] and [111]. The three crystals show similar dependences of PBR on frequency when this is much lower than the exciton energy, but behave differently as the frequency approach threshold. This is interpreted in terms of the effect of stress on the band structure and on the excitons. Fittings of experimental data give appropriate values for the deformation potentials.

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Riassunto Si presentano nuovi risultati sperimentali sulla piezobirifrangenza (PBR) di CuCl, CuBr, e CuI in funzione della deformazione nelle direzioni [100] e [111]. I tre cristalli mostrano simili dipendenze di PBR dalla frequenza quando questa è molto più bassa dell'energia dell'eccitone, ma si comportano in maniere differenti secondo come la frequenza raggiunge la soglia. Ciò è interpretato in termini di effetto di stress sulla struttura di banda e sugli eccitoni. Approssimazioni dei dati sperimentali danno valori appropriati dei potenziali di deformazione.

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Резюме Предложены новые экспериментальные результаты по двойиому лучепреломлению, обусловленному внешними мехабическими напряжениями (пьезоэффект) в CuCl, CuBr и CuI для двух различных ориентций, [111] и [100]. Все три кристслла оьнаруживают сложую частотхую зависимостя пьезоэффекта вдали от экситонной энергии, одннако, существенно разные сьойства вблизи экситона. Интерпретция результатов основана на предствлении о воздействии давления на зонную структуру и зкситон. Спавнение экспериментальных результатов и теории позволфет определить деформационные потенциалы.

     

Spatial discrimination in dimensional analysis and the reduction of variables in the equations of fluid physics

Summary Dimensional analysis with spatial discrimination is used to lower the number of unknowns in the equations governing Newtonian fluids. The authors of this paper have agreed to not receive the proofs for corection.     

Cu低维体系的结构和电子性质

基于密度泛函理论，选择generalized gradient approximation(缩写为GGA)交换作用势，使用自洽场全势的线性缀加平面波方法，计算了Cu原子组成的5种不同体系，包括面心立方晶体，两种原子面和两种原子链.结果显示，平面正六边形晶格要比正方形晶格从能量上更加稳定，原子最近邻距离稍长；而平面锯齿形原子链与直线形原子链相比也有类似的计算结果.计算还发现，锯齿形原子链中的电子态密度表现异常，能带出现间隙.另外，对比不同体系的态密度和结构，分析了量子限制和原子构型对体系电子性质的影响. 关键词： 原子链 电子结构 平面波方法 密度泛函理论     

Theory of the vibrational spectra of transition h.c.p. metals

Summary A semi-first principle (SFM) model using the concept of a rigid-shell moving relative to its nucleus to simulate the response of thed-electrons has been proposed for studying lattice dynamics of transition metals which belong to the h.c.p. structure. The long-range interaction between ion-ion as well as shell-shell via conduction electrons is described using the screened potential and the short-range interaction is described using two-body and three-body unpaired forces between cores as well as shells. Elastic constants, phonon dispersion curves and thermal properties,e.g. lattice specific heat, Debye characteristic temperature of three prominent transition metals (Zr, Hf, Ti) have been calculated and compared with the experimental results.

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Riassunto Un modello a principio semiprimo (SFM) che usa il concetto di uno strato rigido con movimento relativo al suo nucleo per simulare la risposta degli elettronid è stato proposto per studiare la dinamica reticolare dei metalli di transizione che appartengono alla struttura h.c.p. Si descrive l’interazione a lungo raggio tra ione-ione e strato-strato via elettroni di conduzione usando il potenziale schermato e l’interazione a corto raggio è descritta usando forze spaiate a due e tre corpi tra i nuclei e gli strati. Sono state calcolate e confrontate con i risultati sperimentali le curve di dispersione dei fononi con costanti elastiche e le proprietà termiche, cioè calore specifico del fononi con costanti elastiche e le proprietà termiche, cioè calore specifico del reticolo, la temperatura caratteristica di Debye di tre importanti metalli di transizione (Zr, Hf, Ti).

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Резюме Для исследования динамики решетки переходных металлов, которые имеют гексагональную с плотной упаковкой структуру, предлагается модель, использующая концепцию жесткой оболочки, движущейся относительно ее ядра, чтобы смоделировать откликd-электронов. Описывается длиннодействующее взаимодействие между ионами, а также между оболочками через электроны проводимости, используя экранированный потенциал. Короткодействующее взаимодействие описывается с помощью двух-частичных и трех-частичных неспаренных сил между остовами и оболочками. Вычисляются упругие постоянные, фононные дисперсионные кривые и тепловые свойства, т.е. удельная теплоемкость решетки, характеристическая температура Дебая для трех переходных металлов решетки, характеристическая температура Дебая для трех переходных металлов (Zr, Hf, Ti). Полученные результаты сравниваются с экспериментальными данными.

     

«Well-posedness» of the magnetoplasmastatic problem with anisotropic stress tensor

Summary It is generally agreed upon that the two-pressure magnetoplasmastatic problem is locally “well posed” if the relevant PDE system does not admit of real characteristic conoid apart from a disk perpendicular to the magnetic lines. The various cases of practical interest are briefly reviewed and the corresponding well-posedness condition is given for each of them.

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Riassunto Generalmente si conviene che il problema magnetoplasmastatico a due pressioni sia localmente ?ben posto? se il sistema differenziale-parziale in oggetto non ammette, come conoide caratteristico reale, che un disco perpendicolare alle linee magnetiche. Si esaminano qui brevemente i casi di maggior interesse pratico e se ne dà la corrispondente condizione di buona posizione.

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Резюме Обычно предполагается, что магнитоплазмостатическая проблема с двумя давлениями локально хорошо сформулирована, если система дифференциальных уравнений в частных производных не допускает вешественного характеристического коноида, за исключением диска, перпендикулярного магнитным силовым линиям. Обсуждаются различные случаи, представляющие практический интерес, и приводятся соответствующие условия для формулировки проблемы в каждом случае.

     

Spin-orbit splitting of the copper halides and its volume dependence

We have investigated theoretically and experimentally the dependence of the spin-orbit splitting of the edge excitons in CuCl, CuBr, and CuI on volume. The results indicate a large contribution of the change in p(halogen)-d(Cu) hybridization with volume, especially for CuCl.     

Thermal properties of cubic metals in anharmonic approximation

Expressions for thermal properties such as thermal expansion, specific heat and melting point are obtained by employing the usual quadratic-quartic form of the potential energy. Computed results for nineteen cubic metals are presented and compared with the experimental values. The model describes the broad features observed in the thermal properties and an estimate of the anharmonicity in cubic metals.     

Systematic theoretical investigation of structure and electronic properties of pure copper and lithium doped copper clusters

The pure copper and lithium-doped copper clusters are studied using the unbiased CALYPSO structure searching method and density function theory to understand the evolution of various structure and electronic properties. Theoretical results show the growth behaviours of doped clusters are organised as follows: Li capped Cu_n clusters or Li substituted Cu_n+1 clusters as well as Cu capped Cu_n-1Li clusters. Moreover, the lowest energy structures of Cu_nLi favour planar structures for n ≤ 3 and three-dimensional structures for n = 4–12. In addition, the calculated averaged binding energies, fragmentation energies and second-order difference of energies exhibit obvious odd–even alternations as cluster size increasing. At last, the highest occupied-lowest unoccupied molecular orbital gaps, molecular orbital energy, magnetic property, natural population analysis, natural electron configurations, electrostatic potential, electron density difference, Infrared and Raman spectra and density of states are also, respectively, operative for characterising and rationalising the electronic properties of doped clusters.