Vol. 43 No. 6
SCIENCE IN CHINA (Series D)
Self-organized genesis of Lunijianlaite and its apparent
KONG Youhua (孔佑华)1,2, WU Fengmin (吴锋民)1, HUANG Hui (黄 辉)1,
JIANG Lu (姜 璐)3 & WANG Jianghai (王江海)4
1. Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310014, China;
2. Zhejiang Institute of Geology and Mineral Products, Hangzhou 310007, China;
3. Department of Physics, Beijing Normal University, Beijing 100875, China;
4. Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640, China
Correspondence should be addressed to Wu Fengmin (email: email@example.com)
Received October 30, 1999
Abstract From the structure of layer stacking of Lunijianlaite and its host and theory of nonequilib-
rium thermodynamics, a nonlinear dynamical model named
under the condition of nonequilibrium. The numerical results have been successfully used to ex-
plain the self-organized ordering phenomenon at two levels in the apparent single-crystal. Hence,
the latter has been confirmed as crystallization product of the supersaturated silicate solution, who-
se chemical composition is between that of cookeite and pyrophyllite, under the conditions of non-
equilibrium and nonlinearity.
Shenkuoator has been presented
Keywords: Lunijianlaite, apparent single-crystal, nonlinear, nonequilibrium thermodynamics, Shenkuoator, self-orga-
nizd ordering structure at molecular level.
Over a century’s study on interstratified minerals has confirmed that two kinds of unit struc-
ture layers for 2:1 typical phyllosilicate minerals can form regular alternate or random stacking.
The former has been generally recognized as independent mineral species, because it has defi-
nite chemical formula and one-dimensional diffraction pattern. It has been known that this type of
mineral always exists as lamellar crystallite or domain with 10 “cells” in thickness, by calculation
of their one-dimensional diffraction pattern[2,3] and observation of lattice image[4
kinds of 2:1 typical phyllosilicate minerals with different thermodynamic constants form regular
alternate stack by their unit structure layer? What are physicochemical conditions for the inter-
stratification to form? These questions are always puzzling in clay academic circles.
Kong et al.[6,7] have discovered a kind of special crystal, which shows perfect lathlike crystal
form under stereomicroscopy and homogeneity in composition and structure by means of the
maximum resolution for electron probe. It does not provide any single-crystal diffraction spot. But
its powder provides nice mixed Debye-Sherrer pattern of cookeite and Lunijianlaite. This kind of
crystal is tentatively named “the apparent single-crystal”. It has been defined after the study of
lattice image that two phases within the crystal exist as lamellar domains, whose C*-axes are
parallel to each other, as seen in fig. 1. If A and B indicate cookeite and pyrophyllite layers con-
6]. Why can two
No. 6SELF-ORGANIZED GENESIS OF LUNIJIANLAITE & ITS APPARENT SINGLE-CRYSTAL639
stituting Lunijianlaite domain respectively, there is the rhythmic layer sequence modeled as
in the common direction of C* axis of the
apparent single-crystal, in which “AAA”
and Lunijianlaite domain.
From thermodynamic viewpoint, Nicolis
and Prigogine have divided order structure
in nature into two kinds: equilibrium and
dissipative. The former is the ordering struc-
ture at molecular level characterized by the
intermolecular action distance; the latter is
the structure with macro time-space order
(self-organized order structure). From this
definition, the domain-alternated structure in
the apparent single-crystal is incorporated
into self-organized ordering one, because ref.
 has confirmed that the thickness of Luni-
jianlaite and cookeite domain is about 20
Truely, the equispaced based fringes in Lunijianlaite domain can be understood as a reflec-
tion of C* axial length of a completely new structure, under normal conditions. However, the ex-
periment results of the domain only provide the diffuse two-dimensional, h (or k) =1 SAED and its
lattice images. It indicates that the alternate stack can only lead to epitaxy at layer itself and keep
original structure state stipulated by respective interatomic action distances. Hence this domain
structure that is formed by epitaxy of two kinds of the two-dimensional equilibrium crystals with
unit cell-sized in thickness, should also belong to that of the self-organized ordering structure. The
basic reason existing in this special structure is the bonding force within 2:1 layer to be far greater
than the interlayer action force.
To sum up, according to thermodynamic viewpoint, the idealized rhythmic structure in the
apparent single-crystal should belong to the self-organized ordering at domain- and layer-level,
whose mechanism of formation should be probed by application of the nonequilibrium thermody-
namic viewpoint and method.
” correspond to cookeite
1 Building of Shenkuoator
1.1 Mineralizing solution and its evolution
In order to reveal the mechanism of formation of Lunijianlaite and its host, the apparent sin-
gle-crystal, the correlative mineralizing solution must be made clear. According to ref. , before
Fig. 1. Lattice image of Lunijianlaite domain with regularly
alternative stacking for 8 times. 1,The alternative period is 2.34
nm; 2, cookeite is on the sides of this domain with the same
distance 1.42 nm.
640SCIENCE IN CHINA (Series D) Vol. 43
crystallizing the apparent single-crystal, there has existed the Al-rich Si-poor mineralizing solu-
tion transformed from the volcanic hydrothermal solution in lithophysae of the volcanite. When
temperature of the system successively fell down to about 500 and 300
microcrystalline diaspore crystallized out one after another from the solution. Just then, compo-
nents Al2O3 and H2O were unceasingly taken away from the solution, making the latter develop
into the Al-bearing supersaturated silicate solution. It is just the chemical system that crystallizes
out the apparent single-crystal.
According to the chemical composition of the apparent single-crystal, the ionizing constitu-
tion of the system is easily concluded:
[SiO4]4−: [AlOH]2+: [Al(OH)2]+: Li+ = 0.4107: 0.3077: 0.2180: 0.0636
, lumpy corundum and
1.2 The physical model making the system into nonequilibrium
In order to describe emergence of the nonequilibrium system and its crystallization, the
commonly used “twin-cases model” is introduced here. It can be considered that when tempera-
ture of the system falls further down from 300
crystallization front of the solution (on surface of diaspore) and its crystallization rate is far greater
than diffusion rate of every ion. Consequently, there will be the gradient in both concentration and
polymerized state of ions in space between the front and the far-front. So a “semipermeable parti-
tion” can be put up at the suitable position of the above-mentioned space and the subspace be-
tween “semipermeable partition” and the front is called the interface region, then another one is
the far-interface region, in which the ions have not polymerized each other and are in Brownian
movement. So these ions are in homogeneous disordering state and can continuously come into
the interface region through the “semipermeable partition” with their original concentration rate,
because of smaller ion radius value. These ions entering the interface region as reactants will par-
ticipate in a variety of chemical reactions. These chemical reactions will lead to the solution in the
interface region to make the chemical oscillation happen and then form rhythmic crystallization of
A- and B-layer. Such crystallization is making the front with the “semipermeable partition” move
forward to the far-interface region before the system disappears. It is obvious that the rhythmic
structure shown in space of the apparent single-crystal has been regarded as an authentic record of
the oscillation history occurring in the remnant solution that had occurred in pyrophyllilization
process of the volcanite in late Jura.
, the crystallization of gibbsite can happen at the
1.3 Chemical reactions happening in the interface region and Shenkuoator
Since the apparent single-crystal is regarded as the product of nonlinear crystallization
caused by the interfacial chemical reactions with oscillatory characteristics, we must provide those
reactions. Obviously, the reactants and the resultants are four kinds of ions from the far-interface
region and two structural formulae corresponding to A- and B-layer. To consider structures of sili-
cate melt (or solution) and two kinds of layers, polymerized anion-groups [Si3AlO10]5−, [Si4O10]4−
and complex cation [Al2.19Li0.73 (OH)5.70O0.30]+ will appear in the reaction process. These larger
No. 6SELF-ORGANIZED GENESIS OF LUNIJIANLAITE & ITS APPARENT SINGLE-CRYSTAL641
ion-groups can exist more stably in the solution as short-range ordering state and can be regarded
as independent reaction units to join the concerned chemical reactions. In crystallizing phases,
AlIV-bearing and AlIV-free polymerized anion groups will respectively become the only memble of
tetrahedral sheet in A- and B-layer, and the complex cations will do that of Li-bearing gibbsite
interlayer in A layer. To consider such a fact that the nonlinear alternate crystallization appears in
A- and B-layer of the apparent single-crystal, a self-catalytic reaction is put in the planned chemi-
cal reaction system. The reaction system is as follows:
3[SiO4]4− + [AlOH]2+ → [Si3AlO10]5− + 2O2− + [OH] − (R1)
2.19[Al(OH)2]+ + 0.73Li+ + 1.32[OH] −+ 0.30O2− → [Al2.19Li0.73(OH)5.70O0.30]+ (R2)
2 [AlOH]2+ + [Si3AlO10]5− + [Al2.19Li0.73(OH)5.70O0.30] −
4[SiO4]4− → [Si4O10]4− + 6O2− (R4)
2[Si3AlO10]5− + [Si4O10]4− + 2[OH] − → 2.5[Si4O10]4− + [AlOH]2+ + 5O2− (R5)
[Si4O10]4− + 2[AlOH]2+ → Al2[Si4O10](OH)2 ↓ (R6)
Oxygen might not be excessive in the reaction system because the Si/O rate of the system is
up to about 0.4 (From the chemical composition of the apparent single-crystal in ref.  to be up
to 0.33). If reactants [SiO4]4−, [AlOH]2+, [Al(OH)2]+, Li+; intermediate products [Si3AlO10]5−,
[Si4O10]4−, [Al2.19Li0.73(OH)5.70O0.30]+; resultants Al2.19Li0.73(OH)5.70O0.30
Al2[Si4O10](OH)2 are successively shown by S, L, M, N, X, Y, Z, A and B, then
. 019 . 2
Al2[SiAlO](OH)2 ↓ (R3)
25 . 22
There are the following mass conservation equations of intermediate products X, Y and Z:
,5 . 1
5 . 1
73. 019. 2
where the symbol with square brackets shows the concentration corresponding to reactant, ai and
ki (i =1
6) are reaction rate and its constant respectively. Hence, there are the reaction kinetics
equations of the system:
642SCIENCE IN CHINA (Series D) Vol. 43
,5 . 1d/d
Eqs. (1)(3) are just the mathematical model de-
scribing or controlling crystallization of Lunijianlaite and
the apparent single-crystal. This model is named
“Shenkuoator” to commemorate the great ancient Chinese
scientist, Shen Kuo (1031
Hangzhou. Fig. 2 is its reaction flow diagram.
1095), who was born in
2 Numerical simulation and its result
2.1 The initial and out-of-steady conditions of Shen-
There are stationary equations for eqs. (1) (3):
, 05 . 1
The stationary solution of the system (X0,Y0, Z0) can be
obtained by eqs. (4)
])( 75. 0[
)( 5 . 0
)( 75 . 0
]2)(5 . 1 [
Thus, the initial condition is
The out-of-steady condition has been obtained by the linearized stability analysis of Shenkuoator
a3X0Y0 + 1.5a5
Eq. (5) is substituted into eq. (11) to obtain another expression of the out-of-steady condition:
2.2 Numerical simulation and its result
The simulation results of Shenkuoator that satisfy the out-of-steady condition given by (12)
are shown in fig. 3. The parameters are: a1=0.335, a2=0.169, a3=1.000, a4=0.059, a5=2.766, a6
=0.904 6, and the initial values are set to: X0=0.411 1, Y0=0.177 8, Z0=0.411 1. It can be seen
Fig. 2. The reaction flow diagram of Shen-
kuoator. (The annotation on English alphabets is
seen from the text, the arrows show the reaction
No. 6SELF-ORGANIZED GENESIS OF LUNIJIANLAITE & ITS APPARENT SINGLE-CRYSTAL 643
clearly from these curves that all of the state variables X, Y, Z show oscillation with two levels as
time goes on. If it is understood that it is time that A-layer crystallized when X and Z are at the
wave crests, B-layer crystallized when Y is at the wave crest of curve. It is reasonable that it is
time that Lunijianlaite crystallized in AB region and that is cookeite crystallized in BC region. It
should be especially pointed out that the number of times of the A-B oscillation is consistent with
the base lattice fringe image of Lunijianlaite domain. The stable limited circles in X-Y, Y-Z, X-Z
plates are shown in fig. 4. These simulation results are dependent on the intrinic dynamics of sys-
tem and can repeat for a long time.
3 Conclusion and discussion
From the oscillation solution reflecting the distribution characteristic in space among A- and
B-layers within the apparent single-crystal, we can obtain the following conclusions:
1) The structure of Lunijianlaite and its host, the apparent single-crystal, is truly self-organ-
ized ordering at layer- and domain-level from thermodynamics viewpoint. They are crystallizing
Fig. 3. Vibrational curves of X, Y, Z.
Fig. 4. Limited circles.
644SCIENCE IN CHINA (Series D) Vol. 43
substances from the same supersaturated system, whose composition is between those of cookeite
and pyrophyllite, under the conditions of far-equilibrium and nonlinearity.
2) According to the definition of ref. , the structure of Lunijianlaite has been considered as
a new regularly interstratified one by Kong et al.[6,7]. However, its thermodynamic classification
has not been done, because the famous viewpoint of ref.  remains to be noticed by us or even in
academic circles on clay. From the thermodynamic classification of ordering structures, it is
obvious that the structure of cookeite domain belongs to typical equilibrium one and that the alter-
nated two kinds of domains within the apparent single-crystal to typical macroscopic space-time
(or self-organized) ordering one. It should be pointed out that the structure of Lunijianlaite domain
belongs to neither the former nor the latter, because there is no real molecule of Lunijianlaite but
there is the regular alternation at layer (or molecule) level rather than at macroscopic level within
Lunijianlaite domain. Hence, we suggest that it is “at molecule level” behind the term “self-
organized ordering”, so as to indicate the essential distinction between this structure and usually
called self-organized ordering one. In other words, the space-time order is not confined to the
3) Shenkuoator is another satisfying kinetic model based on chemical reaction after Brusse-
lator and Oregonater, because it has not only successfully revealed the crystallization se-
quence of every kind of domain (or layer) in the apparent single-crystal under the control of the
model, but also revealed the details of chemical oscillation in the system, e.g. the chemical be-
haviors of the amphiprotic net work-modifying cation Al3+ to come in to and go out of T-O tetra-
hedral interstice of Si-O polymerized anion-group in the process of depolymerization/ repolymeri-
zation. Hence, Shenkuoator has not only answered the self-organized genesis of Lunijianlaite and
the apparent single-crystal but also enriched some qualities of silicate melt-structure. In addition,
the difference among our model and two above-mentioned models is that the latter successfully
explains B-Z reaction happening before their eyes; our model recovers the chemical oscillatory
phenomenon during crystallization of the apparent single-crystal happened in Jura.
4) As clay mineralogists know very well, there can be the mineral belt formed by random I/S
and/or rectorite in intermediate horizon of depositional smectite-illite sequence. There have been
some models concerning the mechanism transforming from smectite to illite, specially, forming
interstratified I/S. For example, the two-solid-solution model and the fundamental particle
model. Nonequilibrium thermodynamics is not involved in these models. So it is necessary to
provide such a new model that in deposition-diagenism of muddy deposits, the perpendicular
zoning in minerals and the buried conditions determine the zoning of smectite and illite. If the
interaction between original deposits and mineralizers has produced a nonequilibrium silicate
solution at the intermediate horizon of the depositional sequence, there can occur random I/S
and/or rectorite. The ordering degree of these interstratified phases is related to the degree of open
of the system and a variety of factors influencing chemical oscillation of the system.
Owing to the same layer-type and the stack pattern among Lunijianlaite and all other regular
No. 6 SELF-ORGANIZED GENESIS OF LUNIJIANLAITE & ITS APPARENT SINGLE-CRYSTAL645
interstratified minerals, in view of thermodynamics, the structure of all regular interstratified min-
erals should belong to one with the self-organized order at molecule level too. If this viewpoint
can be approved, it should be accepted that the genesis problem on interstratified minerals, which
is puzzling in clay academic circles, has been solved by casting off binding of classical thermody-
namics. The study on applying Shenkuoator to other regular interstratified minerals is already in
Of course, the model (Shenkuoator) does not contain a diffusion term and the case where the
concentration of reactants is probably variable has not been considered. However, besides the
regular oscillation, more complicated kinetics behaviors (such as bifurcation and chaos) seem to
appear under the conditions of some parameters, because of high nonlinearity of the model. The
short-range random alternate with different layers between different domains, which is seen in
lattice images of ref. , should correspond to the condition between the self-organized order and
chaos. The study in this respect is in progress too.
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No.
49672095) and the Key Task Project of Ministry of Geology and Mineral Resources (Grant No. 850-2020).
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