C.F. Woensdregt
Utrecht University
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Featured researches published by C.F. Woensdregt.
Journal of Crystal Growth | 1990
Bing Nan Sun; P. Hartman; C.F. Woensdregt; Hans Schmid
The structural morphol. of YBa2Cu3O7-x (YBCO) was investigated by application of the periodic bond chain (PBC) theory. For x = 1, the F forms are {001}, {011}, {013}, {112} and {114}. Attachment energies were calcd. in a broken bond model and in an electrostatic point charge model. For x = 1 the theor. growth habit is tabular to platy {001} with {011} as side faces. For x = 0 {010} also becomes an F form. The habit is isometric with large {001} and {011} and small {010} faces. The outermost layer of {001} contains half of the Cu+ (x = 1) or Cu3+ and O2- (x = 0) ions in an ordered arrangement based on a c(2 * 2) quadratic lattice. For the outermost layer of (010) (x = 0) an ordering scheme of the Cu and O ions is proposed. The occurrence of {010} rather than {011} on grown crystals has to be ascribed to external factors.
Journal of Crystal Growth | 1984
Magdalena Aguiló; C.F. Woensdregt
The Hartman—Perdoktheory enablesone to establishthe order of morphological importance of the ADP (NH4H2PO4) crystal facesfrom its crystal structure.Periodic Bond Chains (PBC’s) havebeenobtained using the N—HN 0 strong bonds betweenthe ionic [NH4]~ and [H2P041 crystallization units. The PBC’sare parallel to 1,which are typical of the so-called tapering,are S faces.
Journal of Crystal Growth | 1988
C.F. Woensdregt; P. Hartman
Abstract The structural morphology of compounds having the PbCl 2 and the closely related SbSI structures has been determined. Based upon the nine-coordination of the Pb atoms the F forms of the PbCl 2 structure are {110}, {020}, {120}, {011}, {200}, {111} , {201}, {121} and {211}. These forms are arranged in an order of increasing attachment energies, that were calculated using a broken bond model. In the SbSI structure type the Sb atom has a seven-coordination with the consequence that {020} becomes a different surface structure and that {120} is an S face. The theoretical habit of PbCl 2 and Pb(OH)Cl is short prismatic, elongated along the c axis, with {011} as terminal form. The appearance of {211} as main form on PbCl 2 when growth takes place from pure aqueous solution is ascribed to the preferential adsorption of OH - ions on that face. The predominance of {020} and {121} on PbCl 2 from solutions containing HCl is explained by adsorption of H 3 O + on these faces. The theoretical habit of the SbSI structure type is slender prismatic {110} with {011} as terminal form.
Journal of Crystal Growth | 1988
M. Van Panhuys-Sigler; P. Hartman; C.F. Woensdregt
Abstract Crystallization of lead chloride, PbCl 2 , from pure aqueous solution produces crystals with dominant {211} and smaller {010} and {100} faces at low supersaturation. Increase of supersaturation yields crystals elongated along the c axis. Growth from a previously prepared saturated solution gives crystals elongated along the c axis with {011} as main terminal faces. This habit also occurs when KCl, NH 4 Cl or CdCl 2 or mixtures of these are added to a freshly prepared supersaturated solution. Only at low additive concentration and at low supersaturation {211} is dominant. The latter habit is supposed to be caused by adsorption of OH - ions on {211}. A deposit of Pb(OH)Cl has been observed. Crystallization from HCl containing solutions enhances the {010} and {121} forms, presumably through preferred adsorption of H + and possibly PbCl - 3 ions. Increasing supersaturation diminishes the effect of the habit modifying process until the stage where dendrites appear.
Journal of Crystal Growth | 1993
M.M.R. Boutz; C.F. Woensdregt
Abstract F forms of natural garnets are {112}, {110}, {123}, {001}, {120} and {332}. For Mg 3 Al 2 (SiO 4 ) 3 , the surface con figurations of the elementary growth layers d 220 and d 240 are bounded by Al ions. For d 220 , a different boundary configuration exists as well, th at of Si and Mg ions, just as the configuration of d 040 . For d 112 two boundary configurations are possible, one with Mg and Al, and another with Al and Si. The attachment energies of the F faces have been calculated in different electrostatic point charge models, in which the point charges of the ions forming the Si-O tetrahedral bonds vary from the completely ionic model with formal charges, [Si 4+ O 2- 4 ], to the covalent one with reduced charges, [Si 0 O - 4 ]. In all models the formal point charges of Al and Mg h ave been used. Because these energies are supposed to be directly proportional to their growth rates for F faces, theoretical growth forms have been constructed. For models with q O = -2‖ e ‖, the growth form consists only of {112}. However, for the more coval ent like models with lower q O , {100} and {110} appear, while at the same time, {211} disappears slowly. If q O = -‖ e ‖ oxv;, the growth form is merely bounded by {110}. Ordering of the boundary ions changes fundametally the growth form only at q O ≈-1.75 ‖ e ‖ producing a growth form with equally important {211}, {110} and {100}. If the mineral growth of garnets proceeds with isolated silicate tetrahedra as building units, the theoretical growth form shows only {112}.
Journal of Crystal Growth | 1987
Magdalena Aguiló; C.F. Woensdregt
The Hartman—Perdok theory enables one to establish the F forms of ammonium dihydrogen phosphate (ADP) as (100} and 011}. Although the 0 kl } forms are theoretically expected to be S faces, they nevertheless exhibit K face characteristics for k 1, which are typical of the so-called tapering of the ADP crystals, are S faces. The attachment energy of a particular face, which is assumed to be directly proportional to its growth rate, can be computed in an electrostatic point charge model. As the ionic charge distribution in the crystallizing units is not known exactly, the calculations have been made in 36 models, with P—Oand N—Hbond varying from purely ionic to completely covalent. The theoretical growth forms comprise always the (011 and sometimes (100)~~The presence of the latter is a function of the ionic charge of the oxygen, q0, and that of the hydrogen H0 belonging to the [H2P04] group, q~0. The form (100) is present, if —0.9<q0 <0, when q~0 varies accordingly between 0 and 0.8. When halving of the elementary growth layer d011is applicable, the theoretical growth forms of all the models show {100} and (011} resulting in a very pronounced prismatic habit. The presence of impurities can explain the occurrence of (031) on the growth forms of all the models, which therefore resemble the so called tapered ADP crystals. The equilibrium forms show always (100) and (011 }. The prismatic habit is more pronounced for models with a low q0 and q~. The hydrogens H0 are situated just on the boundaries of the elementary growth layers. The effect of ordering of these H0 ions on the theoretical growth and equilibrium forms is not substantial.
Journal of Applied Crystallography | 2002
Mirela F. Nicolov; C.F. Woensdregt
The α phase of SiO2 is known as a technologically important material. According to the Hartman–Perdok theory, so-called F forms are present: the hexagonal prism m {10\bar{1}0}, the major rhombohedron r {10\bar{1}1} and the minor rhombohedron z {01\bar{1}1}. F faces grow according to a two-dimensional growth mechanism and are the only forms to be expected on the growth form. Computation of attachment energies, which are considered to be directly related to the growth rates of the corresponding F faces, has been performed using an electrostatic point-charge model, taking into account Born repulsion and van der Waals contributions computed by means of the Gilbert equation or the van Beest and van Santen potential. All the theoretical growth forms are prismatic with the two aforementioned rhombohedra, which are almost equally important and independent of the corrections for the van der Waals and Born interactions. The equilibrium form is prismatic and shorter as a result of the hexagonal prism form being less important. On the atomic scale, the differences in surface topologies between the F forms depend on the variation in depth below the surface boundary of those central Si atoms that are partially unshielded because of the incomplete tetrahedral coordination.
Journal of Crystal Growth | 2001
Carlos M. Pina; C.F. Woensdregt
The trigonal b-LiNaSO4 low temperature polymorph belongs to the family of double sulphates with general formula LiMSO4 (M ¼ Na; NH4, Rb,y), which have very specific electrical properties. In this paper we present the b-LiNaSO4 theoretical growth morphology based on the Hartman–Perdok theory. Therefore, Periodic Bond Chains (PBCs) have been identified in order to determine the influence of the crystal structure on the crystal morphology. The shortest PBC is parallel to /1 00S and consists of a one-step proto-PBC with sulphate(I)–cation–sulphate(I, 1 0 0) strong bonds. All the other PBCs are built up from strong bonds in two or more consecutive steps, e.g., sulphate (I)–cation–sulphate(II)– cation–sulphate (I, u vw). The corresponding F forms are in order of decreasing dhkl : f1 0 %11 0g; f1 0 %11 1g; {0 0 0 2}, f1 0 %11 2g; f1 1 %22 0g ¼ f2 %11 %11 0g; f1 1 %22 2g ¼ f2 %11 %11 2g; y For many F forms several different slice configurations can be defined. Attachment energies have been calculated in electrostatic point charge models with formal charges. In addition, the effect of covalent S–O bonds on the growth forms has been taken into account by decreasing the effective charge on oxygen, qO: The theoretical growth form of b-LiNaSO4 based on attachment energies calculated in the LiNaS6+O42 point charge model shows the hexagonal prism f1 0 %11 0g; the hexagonal pyramid f1 0 %11 1g and the pedion (0 0 0 1). When the influence of the S–O bond decreases (LiNaS4+O4 1.5 model), the habit is slightly less elongated parallel to the c-axis due to the increased relative morphological importance of the pyramid form with respect to the prism. When we assume that the hexagonal prism face grows with halved slices d20%220 and thus using the attachment energies of E20%220 a instead of those of E10%110 a ; the growth forms changes drastically by the absence of the hexagonal prism form in both models. In addition, the trigonal prism f1 1 %22 0g is present as a minor form on this LiNaS4+O4 1.5 model with halved d20%220 slices. Experimentally grown LiNaSO4 crystals show habits that deviate from the theoretical growth forms. This must be due to external factors such as supersaturation and interaction of the crystal surface with the aqueous solutions during the growth. Growth experiments confirm that the growth morphology is strongly influenced by the degree of supersaturation.
Journal of Crystal Growth | 2002
Rob Dekkers; C.F. Woensdregt
Journal of Crystal Growth | 2005
C.F. Woensdregt; Arkady E. Glikin