立方晶
International Journal of Pharmaceutics 396 (2010) 179–187
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International Journal of
Pharmaceutics
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Pharmaceutical Nanotechnology
Self-assembled liquid crystalline nanoparticles as a novel ophthalmic delivery system for dexamethasone:Improving preocular retention and ocular bioavailability
Li Gan a ,1,Shun Han a ,1,Jinqiu Shen b ,Jiabi Zhu b ,Chunliu Zhu a ,Xinxin Zhang a ,Yong Gan a ,?
a Shanghai Institute of Materia Medica,Chinese Academy of Sciences,555Zuchongzhi Road,Shanghai 201203,China b
School of Pharmacy,China Pharmaceutical University,Nanjing 210009,China
a r t i c l e i n f o Article history:
Received 17March 2010
Received in revised form 12May 2010Accepted 9June 2010
Available online 15 June 2010Keywords:Cubosome
Dexamethasone
Ocular bioavailability Ophthalmic delivery Preocular retention
a b s t r a c t
The object of this study was to design novel self-assembled liquid crystalline nanoparticles (cubosomes)as an ophthalmic delivery system for dexamethasone (DEX)to improve its preocular retention and ocu-lar bioavailability.DEX cubosome particles were produced by fragmenting a cubic crystalline phase of monoolein and water in the presence of stabilizer Poloxamer 407.Small angle X-ray diffraction (SAXR)pro?les revealed its internal structure as Pn 3m space group,indicating the diamond cubic phase.In vitro,the apparent permeability coef?cient of DEX administered in cubosomes exhibited a 4.5-fold (F1)and 3.5-fold (F2)increase compared to that of Dex-Na phosphate eye drops.Preocular retention studies revealed that the retention of cubosomes was signi?cantly longer than that of solution and carbopol gel,with AUC 0→180min of Rh B cubosomes being 2–3-fold higher than that of the other two formulations.In vivo pharmacokinetics in aqueous humor was evaluated by microdialysis,which indicated a 1.8-fold (F1)increase in AUC 0→240min of DEX administered in cubosomes relative to that of Dex-Na phosphate eye drops,with about an 8-fold increase compared to that of DEX suspension.Corneal cross-sections after incubation with DEX cubosomes demonstrated an unaffected corneal structure and tissue integrity,which indicated the good biocompatibility of DEX cubosomes.In conclusion,self-assembled liquid crystalline nanoparticles might represent a promising vehicle for effective ocular drug delivery.
Crown Copyright ? 2010 Published by Elsevier B.V. All rights reserved.
1.Introduction
Ocular diseases are usually treated with topical application of drug solutions (eye drops).However,the rapid and extensive pre-corneal losses caused by drainage and high tear ?uid turnover limit drug ocular bioavailability.Meanwhile,for drugs entering the ocu-lar tissue,the cornea is the major route of anterior drug absorption.The lipophilicity and tight conjunction of the corneal epithelium make it the major limiting barrier in corneal drug absorption;con-sequently,lipophilic (log D 2–3)drugs have a higher permeability than hydrophilic ionized drugs (Mannermaa et al.,2006).
To improve ocular bioavailability,several ophthalmic drug delivery systems have been proposed,such as emulsions (Yamaguchi et al.,2005),nanoparticles (Zimmer and Kreuter,1995)and liposomes (Meisner and Mezei,1995).These systems might be able to enhance drug bioavailability by facilitating transcorneal/transconjunctival penetration (Tamilvanan and
?Corresponding author.Tel.:+862150806600x2122;fax:+862150806600x2122.
E-mail address:simm2122@https://www.wendangku.net/doc/454339160.html, (Y.Gan).1
These authors contributed equally to this paper.
Benita,2004).Nevertheless,their potential in ocular drug delivery is limited by rapid clearance from the precorneal region,as the same rapid drainage has been observed as for aqueous eye drops.In order to enhance adherence to the corneal/conjunctival surface,dispersion of these vesicular systems into mucoadhesive gels has been proposed (Aggarwal and Kaur,2005;Gan et al.,2009).However,the high gel viscosity might adversely accelerate the blinking frequency,leading to a feeling of discomfort.
Monoolein (MO),as a nontoxic,biodegradable and biocompati-ble material classi?ed as GRAS (generally recognized as safe),show the mesomorphic phase,important in making more comprehensi-ble the potential pharmaceutical application of the lipid.It may exist in several different phases depending on temperature and hydration.The phase sequence at room temperature when adding water is as follows:lamellar crystalline phase (Lc)in coexistence with a L2phase,lamellar liquid crystalline phase (L ?phase)and the inverted bicontinuous cubic phase (C).What is perhaps the most intriguing is the ability of cubic phases to exist in equilibrium with excess water and can be dispersed to form cubosomes.
Liquid crystalline phases of MO,such as cubic phases,present interesting properties for a topical delivery system (Carr et al.,1997;Lee and Kellaway,2000a,b ),as they (i)are bioadhesive,(ii)present a permeation enhancer as the structure forming lipid (MO),and
0378-5173/$–see front matter.Crown Copyright ? 2010 Published by Elsevier B.V. All rights reserved.doi:10.1016/j.ijpharm.2010.06.015
立方晶
180L.Gan et al./International Journal of Pharmaceutics396 (2010) 179–187
(iii)afford the ability to incorporate compounds independently of their solubility,protecting them from physical and enzymatic degradation,and to sustain their delivery(Shah et al.,2001).The emulsi?cation of cubic lipid phases in water results in the pro-duction of cubosomes,which can be de?ned as nanoparticulate dispersion systems.It has been demonstrated that the dispersed particles retain the internal structure of the bulk phase and its prop-erties(Nakano et al.,2002;Siekmann et al.,2002;Boyd,2003).In comparison with the bulk gel,the dispersions present some advan-tages,such as larger surface area and high?uidity(low viscosity), and can be incorporated into other product formulations(Lopes et al.,2006).
Despite the amazing properties of cubosomes as innovative drug carriers,little research has thus far been performed to demon-strate their potential as ophthalmic drug delivery systems(Lee et al.,2004;Leesajakul et al.,2004;Esposito et al.,2005).The aim of this work was to study the performance of cubosomes as innova-tive ocular delivery systems for dexamethasone,chosen as a model drug.
DEX is a lipophilic glucocorticoid steroid,which is similar to the natural steroid hormone made by the adrenal glands in the body.It is known to be an effective anti-in?ammatory drug for the treatment of acute and chronic posterior segment eye dis-eases such as uvetis(Phillips and Katz,2005).In the generally used clinical product,Dex-Na phosphate eye drops,DEX exists in a hydrophilic ionized form which cannot effectively penetrate the lipophilic corneal epithelium.Therefore,it needs to be instilled3–4 times per day.It is reported that continuous application of eye drops of0.1%dexamethasone for extended periods of time could cause glaucoma accompanied by optic nerve damage,defects in visual acuity and?elds of vision,and posterior subcapsular cataract for-mation and thinning of the cornea or sclera(Kim and Chauhan, 2008).
In this study,DEX-containing monoolein cubosomes were pre-pared,and their internal structure was further characterized by SAXR and cryo-TEM.An in vitro penetration study was performed using freshly excised rabbit cornea.Ocular tolerance was evaluated by corneal cross-sections after incubation.A noninvasive?uores-cence imaging system was utilized to assess the preocular retention of the cubosomes.Finally,in vivo aqueous humor pharmacokinetics was investigated using the microdialysis method.
2.Materials and methods
2.1.Materials
Dexamethasone was purchased from Zhejiang Xianju Pharma-ceutical Co.Ltd.(Zhejiang,China).Monoolein(MO,RYLOTM MG19) was kindly gifted by Danisco Ingredients(Brabrand,Denmark). Poloxamer407(Lutrol?F127)was obtained from BASF(Lud-wigshafen,Germany)and CMC-Na(600–1000mPa s)from Shanhe Medicinal Excipients(Anhui,China).Carbopol974was kindly donated by Lubrizol Specialty Chemicals Manufacturing Co.Ltd. (Shanghai,China).Ethyl Rhodamine B was bought from Sinopharm Chemical Reagent Co.Ltd.(Shanghai,China).Bidistilled water was made using Milli-Q(Gradient).All other reagents were of analytical grade.The microdialysis probe(CMA/20,10mm)used for aque-ous humor sampling was purchased from CMA/AB Microdialysis (Stockholm,Sweden).
Male New Zealand albino rabbits weighing2–3kg were pro-vided by the Animal Experimental Center of Shanghai Institute of Materia Medica.The animals were housed in standard cages in a light-controlled room at19±1?C and50±5%RH and were fed a standard pellet diet and water ad libitum.All studies were approved by the Department of Laboratory Animal Research at Shanghai Institute of Materia Medica.Procedures involving animals were reviewed and approved by the Animal Ethics Committee at Shanghai Institute of Materia Medica.
2.2.Preparation of DEX cubosomes,micelles and suspension
Production of the dispersion was based on the emulsi?cation of MO and Poloxamer407in water as described by Cortesi et al. (Esposito et al.,2005;Kuntsche et al.,2008).In all experiments, the MO/Poloxamer ratio was9:1(w/w).MO and Poloxamer were ?rstly heated to70?C,and then DEX(0.05%)was added to the molten MO/Poloxamer solution and solubilized before adding to the aqueous phase.Afterwards,the oil phase was dropped into the water phase and the components were emulsi?ed using a high-shear dispersing emulsi?er(T25basic,IKA Guangzhou,China)at 10,000rpm for5min.After equilibration for12h at room temper-ature,the crude emulsion was homogenized7times(Panda2000, GEA Niro Soavi S.P.A.,Italy)at350bar.Finally,glycerol was used to adjust the osmotic pressure to physiological conditions.
DEX micelles(0.05%)were prepared by dissolving10mg DEX in 20ml Poloxamer407solution(5%,w/v),with glycerol being used to adjust the osmotic pressure.
To prepare a suspension,10mg DEX were manually milled with a pestle in20ml0.1%(w/v)CMC-Na solution for30min until uni-form,and then the osmotic pressure was adjusted with glycerol.
2.3.Characterization of DEX cubosomes
2.3.1.Particle size analysis
The particle size(PS)and polydispersity index(PI)of the cubo-somes were analyzed at25?C using a dynamic light-scattering par-ticle size analyzer(Particle Sizing System,Nicomp388/ZetaPALS, Santa Barbara,USA)after100-fold dilution with bidistilled water.
2.3.2.Viscosity
The viscosity of the prepared formulations was determined at different angular velocities at25?C using a rotary viscometer(DV-III,Brook?eld,USA).The rotation speed was20rpm,with spin18 #.The average of two readings was used to calculate the viscosity.
2.3.3.Drug encapsulation ef?ciency
The drug encapsulation ef?ciency was determined by ultra-?ltration.A500-?l aliquot of DEX cubosomes was transferred to the upper chamber of a centrifuge tube?tted with an ultra-?lter(Vivaspin500,Sartorius,MWCO10kDa),which was then centrifuged at4000rpm for30min.The amount of DEX loaded in the cubosomes was calculated as the difference between the total amount used in preparation of the cubosomes and the amount in the?ltrate,as determined by HPLC.The drug encapsulation ef?-ciency was calculated according to:
Q w=
W total?W free
W total
×100%≈
C total?C free
C total
×100%
where Q w is the drug encapsulation ef?ciency;W total is the total amount of drug in the cubosomes;W free is the amount of drug in the?ltrate;C total is the concentration of drug in the cubosomes;
C free is the concentration of drug in the?ltrate(Gan et al.,2009).
2.3.4.Small angle X-ray scattering(SAXS)measurement
The SAXS measurements were carried out using NanoStar (Bruker AXS GmbH,Germany),which consisted of a‘Hi-Star’2D-detector,3collimator SAXS system,3kW high voltage generator, cross-coupled Goebel mirrors,copper X-ray radiation at5000W ( =0.154nm)and1mbar vacuum chamber.The scattering angle (2?)ranged from0.2?to2.8?.The sample was transferred to a0.5-mm diameter quartz capillary and sealed.The measurement was
L.Gan et al./International Journal of Pharmaceutics396 (2010) 179–187181 carried out in a vacuum at25?C,with exposure time of0.5h and
sample-to-detector distance of10.7cm.
2.3.5.Cryo-transmission electron microscopy(cryo-TEM)
For cryo-TEM,4?l of sample were applied to a holey carbon
?lm grid(R1.2/1.3Quantifoil Micro Tools GmbH,Jena,Germany),
and were absorbed by?lter paper(#1,Whatman)for about3s.
After absorption,the grid was immediately plunged into pre-cooled
liquid ethane to fast freeze it.The cryo-grid was held in a Gatan
626Cryo-Holder(Gatan,USA)and transferred into a JEOL JEM-
2010(200kv LaB6?lament)TEM at?172?C.The sample was
searched and observed under minimal dose conditions at?172?C.
The micrographs were recorded by a Gatan832CCD camera at a
magni?cation of10,000–50,000×and at a defocus of1.80–4.46?m.
2.4.In vitro corneal penetration study
In vitro corneal penetration studies were carried out using a
modi?ed Franz diffusion cell with a diffusion area of0.785cm2.
Rabbits were killed by injection of an overdose of air into the
marginal ear vein.The corneas were excised from the globes and
mounted onto the ring of the perfusion apparatus.The corneas were
gently rinsed with saline,and extreme care was taken not to pro-
duce any wrinkles or folding of the membrane before mounting.
Glutathione bicarbonate ringer(GBR)buffer(2ml)preadjusted to
a temperature of37?C was placed into the receptor chambers of
the apparatus with magnetic stirring throughout the entire exper-
iment.DEX formulation(100?l)was placed in the donor chamber,
which was then sealed to avoid evaporation.A mixture of O2:CO2
(95:5)was bubbled through the chambers.
Samples(200?l)were taken at30,60,90,120,150,180,210,
240,270and300min after beginning the experiment and replaced
with fresh GBR buffer.The amount of drug that permeated across
the cornea was assayed by HPLC.
The HPLC system(Agilent1100series)used comprised an
autosampler(G1313A ALS),a pump(G1311A Quatpump),a column
oven(G1316A Column),a UV detector(G1314A VWD)and data
processing software(HP Chemstation Rev.A.10.01).A C18column
(Zorbax?SB,150mm×4.6mm,5?m)was used for DEX analysis
with acetonitrile–water(40:60)as the mobile phase at a?ow rate
of1.0ml/min at25?C.Detection was performed at240nm.
The hydration level of the cornea,which indicates the corneal
condition,was measured according to a method previously
reported(Suhonen et al.,1991).
The amounts of drug that permeated the corneal epithelium
were plotted versus time for each formula and the slope of the linear
portion of the graph was calculated.The apparent corneal perme-
ability coef?cient(cm/s)was determined according to Muchtar et
al.(1997):
P app=
Q
t·C0·A·60
where Q/ t is the linear portion of the slope(?g min?1),60is the conversion of minutes to seconds,A is the corneal surface area (in this study,0.785cm2),and C0is the initial drug concentration (?g cm?3).
2.5.Ocular tolerance evaluation
To examine the effects on corneal structure and integrity,the corneas were removed from fresh rabbit eyes and incubated at 37?C for2h in the DEX cubosome formulations.PBS and a sodium dodecylsulfate(SDS)solution in PBS0.1%(w/w)were taken as ref-erences.
After incubation,the corneas were washed with PBS,and imme-diately?xed with a formalin solution8%(w/w).The material was dehydrated with an alcohol gradient,put in melted paraf?n and solidi?ed in block form.Cross-sections(<1?m)were cut,stained with haematoxyline and eosine(H and E)and microscopically observed for any pathological modi?cations(Baydoun et al.,2004).
2.6.Preocular retention of cubosomes
Preocular retention of the DEX cubosomes was evaluated using a noninvasive?uorescence imaging system(Fx Pro,Kodak In-Vivo Imaging System,USA).Albino rabbits(n=9)were used in the study and each rabbit was restrained and positioned in front of the cam-era.
The cubosome formulation was labeled by adding a speci?ed amount of ethyl rhodamine B(Rh B)in the oil phase and then processed via the same method as for preparation of DEX cubo-somes.Rh B carbopol gel was prepared by?rstly dissolving Rh B in water,and then carbopol974(0.25%,w/v)was added to the solu-tion and stirred overnight.Finally,pH(6–7)and osmotic pressure (0.27–0.33osmol/kg)were adjusted.The viscosity of Rh B carbopol gel was88.6±0.59mPa s(DV-III,Brook?eld,USA).Rh B directly dissolved in PBS as Rh B solution was taken as reference.
Exactly5?l of?uorescence-labeled test formulation(?nal Rh B concentration was0.2?mol/ml)were instilled directly into the lower fornix of the conjunctival sac of the left eye and the eye was manually closed for10s to distribute the formulation over the cornea.Rabbits were under conscious condition.Just before the time of imaging,they were anesthetized with i.v.injection of pen-tobarbital(30mg kg?1)through ear vein.Imaging was carried out at0,5,10,30,60,90,120,150and180min after administration. Regions of interest(ROI)were created around the resulting images of the ocular and non-ocular areas to estimate residual?uorescence activity using a data acquisition,processing and quanti?cation pro-gram(Kodak MI SE4.5).The amount(%)of activity remaining in the ROI versus time pro?le was evaluated with regard to different for-mulations.Remaining intensity(R)was calculated according to the equation:R=(A?B)/C×100%.Where A was the intensity of ROI,B was the background?uorescence intensity and C was the intensity of ROI at0min.
2.7.Aqueous humor pharmacokinetics
Aqueous humor sampling to assess the ocular absorption of DEX was carried out using microdialysis.
The rabbits were kept under anesthesia throughout the exper-iment using sodium pentobarbital(30mg/kg)injected into the marginal ear vein.Pupils were dilated by topical instillation of1% tropicamide prior to probe implantation.The microdialysis probe (CMA/20)was implanted in the anterior chamber using a22G nee-dle.It was inserted carefully across the cornea,preventing any damage to the iris–ciliary body.The needle was then removed and the probe was placed immediately and adjusted such that the mem-brane resided in the anterior chamber.The probe was perfused with PBS buffer with a?ow rate of2?l/min using a microinjection pump (MD-1001,BAS,USA).After probe implantation,the animals were allowed to stabilize for at least2h before administering any agent. This time period has been shown to be suf?cient for the restoration of intraocular pressure and replenishment of the aqueous humor lost during probe implantation(Anand et al.,2006).
2.7.1.Probe recovery
Probe recovery was evaluated by the retrodialysis method.A series of DEX solutions of known concentrations(20,85,150,650 and1500ng/ml)were used as the perfusates with a?ow rate of 2.0?l/min.All dialysates were collected for15min at0.5h after changing the perfusate.
182L.Gan et al./International Journal of Pharmaceutics 396 (2010) 179–187
Table 1
Physico-chemical properties of DEX cubosomes (n =3).Formulations Mean diameter (nm)Polydispersity index Viscosity (mPa s)Encapsulation ef?ciency (%)F110%oil 214.1±41.10.144±0.0210.96±0.2298.8±2.6F2
20%oil
226.3±55.6
0.176±0.014
10.0±1.53
98.5±5.4
Recovery (R )is the ratio between drug concentration in the dialysate (C d )and in the tissue (C m ),which is calculated according to the following equation (Burngay et al.,1990):R =
C d ?C p C m ?C p
(1)
where C p is the drug concentration in the perfusate.R is the value of the slope for the plot of C d ?C p versus C p.
2.7.2.Aqueous humor sample
50?l of each formulation was instilled into the eye.Dialysates were collected every 10min for the ?rst hour,every 20min during the second hour and every 30min during the third and fourth hours after instillation.All dialysate samples were kept frozen ?20?C until analyzed.2.8.Statistical analysis
Statistical analysis of the results was performed using one-way analysis of variances (ANOVA),referring to a level of p <0.05.This statistical analysis was computed using Origin ?software.3.Results
3.1.Characterization of DEX cubosomes
3.1.1.Particle size,viscosity and encapsulation ef?ciency
As can be seen in Table 1,the mean diameter of F1was 214.1±41.1nm (PI 0.144±0.021)and of F2was 226.3±55.6nm (PI 0.176±0.014).There was no signi?cant effect of oil content on the particle size and polydispersity index of the DEX cubosomes.The viscosity of DEX cubosomes F2was about 10mPa s,10-fold higher than that of DEX cubosomes F1,which might be due to the higher oil content.As for the DEX micelles and suspension,the viscosities were 1.03±0.15and 1.58±0.26mPa s,respectively.Because of its lipophilicity,the encapsulation ef?ciency of DEX in the cubosomes was above 98%,which meant most of the drug was encapsulated in the cubic nanoparticles.
3.1.2.Small angle X-ray diffraction
SAXR was performed to determine the structural organization of the cubosome formulations.Several Bragg peaks can be seen in Fig.1.The spacing ratio of re?ections was √2:√3:√4:√6:√8:√9,in accordance with the Pn 3m space group,indicating a diamond cubic phase (Siekmann et al.,2002).
Fig.2shows the diffraction pro?les of blank cubosomes (A)and DEX cubosomes F1(B).Noticeable is the fact that,in the absence and in the presence of DEX,the samples exhibit similar cubic unit cell dimensions,which indicates that the addition of DEX does not substantially affect the cubic structure.
3.1.3.Cryo-transmission electron microscopy (cryo-TEM)
Cryo-TEM observations were in full agreement
with the SAXR qualitative results,which revealed mostly square cubosomes with a clear inner periodicity.The diameters observed in the cryo-TEM images were about 200nm,which was also consistent with those determined by dynamic light-scattering particle size analyzer (Fig.3).
Fig.1.Small angle X-ray diffraction pro?les of ophthalmic DEX cubosomes F1.
3.2.In vitro corneal penetration
Fig.4illustrates the in vitro corneal penetration experimental results of the three different dosage forms,DEX cubosomes,DEX micelles and Dex-Na phosphate eye drops.Following a lag time,a linear relationship between accumulative permeated DEX and time could be seen.The apparent permeability coef?cients (P app )of DEX in cubosomes F1,cubosomes F2,DEX micelles and Dex-Na phosphate eye drops were 2.16×10?6,1.67×10?6,1.27×10?6and 0.48×10?6cm/s,https://www.wendangku.net/doc/454339160.html,pared with Dex-Na phosphate eye drops,DEX formulated in cubosomes exhibited 4.5-fold (F1)and 3.5-fold (F2)increase in P app ,which indicated the enhanced penetration achieved with cubosomes.P app of DEX in cubosomes F1was also 1.7-fold higher than that in DEX micelles.
Careful handling of the isolated cornea and maintenance of its physical activity throughout the experiment is very important for reproducibility of the results.The corneal hydration level
is a parameter frequently used to evaluate damage of this tissue.Generally,the normal cornea has a hydration level of 76–80%,while an 83–92%hydration level denotes damage of the epithelium and/or endothelium (Saettone et al.,1996).In this study,the corneal
Fig.2.SAXS pro?les from (A)the blank cubosomes and (B)the DEX cubosomes F1.
L.Gan et al./International Journal of Pharmaceutics 396 (2010) 179–187
183
Fig.3.Photographs of DEX ophthalmic cubosomes by cryo-TEM:(1)F1,(2)F2.
hydration level of all corneas ranged between 79.01±0.01%(DEX cubosome F2)and 82.76±1.09%(Dex-Na phosphate eye drops),and did not exceed 83.0%,which indicated the integrity of the corneas throughout the experiments.
3.3.Ocular tolerance evaluation
Fig.5presents corneal cross-sections after incubation of freshly excised rabbit corneas with various preparations to investigate their in?uence on corneal cell structure and tissue integrity.After incubation in a PBS solution (Fig.5A),the epithelium (EP)and stroma (ST)structure is maintained.A typical strati?ed epithe-lial layer can be recognized by the appearance of a bulge at the nuclei of the basal columnar cells and the squamous surface cells.When the corneal epithelium is exposed to SDS (Fig.5B),previ-ously narrow intercellular spaces are clearly widened,cells and nuclei are deformed and super?cial epithelial cells are detached from tissue assembly.Treatments of corneas with DEX cubosome formulations are exempli?ed in Fig.5C and D,showing a cornea cross-section after incubation in F1and F2,which leaves the corneal structure and integrity almost visibly unaffected.The above results indicated the good corneal biocompatibility of DEX cubosome for-
mulations.
Fig.4.In vitro transcorneal permeation pro?les of DEX in various dosage forms (n =3).
3.4.Preocular retention of cubosomes
After administration,rapid clearance could be seen in the Rh B solution group (Fig.6A).Up to 90min,almost no ?uorescence intensity resided in the ROI,with only a little intensity remaining in the nasolacrimal duct.As for the Rh B carbopol gel,the images were very similar to that of Rh B solution,therefore it is not illustrated in Fig.6.When instilled with Rh B cubosomes,a stable liquid ?lm was formed at the cornea/conjuctiva surface (Fig.6B),which indicated the good wettability and spreadability of the cubosomes.At 90min,a relatively strong intensity still could be seen in the ROI.
Fig.7illustrates the amount (%)of activity remaining in the ROI versus time pro?les for Rh B solution,Rh B carbopol gel and cubo-somes F1.For all formulations,the pro?les consisted of a rapid initial clearance phase followed by a slower basal drainage phase.
A summary of statistical analysis is shown in Table 2.The AUC 0→180min of cubosome formulation was signi?cantly higher than that of solution and carbopol gel.In fact,there was about a 3.5-fold increase in AUC 0→180min of Rh
B cubosomes F1compared to that of Rh B solution,with a 2.5-fold increase compared to that of Rh B carbopol gel.The clearance of Rh B cubosomes in the initial phase was much slower,as the clearance rate (k )was signi?cantly lower than that of the other two formulations.Activity remaining in the ROI at 90min after administration was de?ned as A 90.A 90of Rh B cubosomes was about 40%,which was signi?cantly higher than that of Rh B solution/Rh B carbopol gel.Moreover,no signi?cant differences in precorneal clearance parameters between the Rh B carbopol gel formulation and Rh B solution was found in Table 2.It was therefore not evaluated as reference dosage forms in the in vivo aqueous humor pharmacokinetics study (Table 3).3.5.Aqueous humor pharmacokinetics
In vivo probe recoveries were usually determined before the experiments to ensure the proper functioning of the probe,the value of which ranged from 10%to 40%as reported (Rittenhouse et al.,1998;Katragadda et al.,2008).In this study,it was approx-Table 2
Precorneal clearance parameters (n =3).Sample
AUC 0→180min (%min)k (min ?1)A 90(%)Rh B solution 2196.7±920.10.031±0.00810.4±5.7Rh B carbopol gel 3104.3±1267.90.026±0.01514.2±8.8Rh B cubosome F1
7715.8±1050.9a ,b
0.013±0.002a ,b
37.8±2.8a ,b
a p <0.05,statistically signi?cant difference from Rh B solution.b
p <0.05,statistically signi?cant difference from Rh B carbopol gel.
184L.Gan et al./International Journal of Pharmaceutics
396 (2010) 179–187
Fig.5.Histological cross-sections of excised rabbit cornea showing epithelium (EP)and stroma (ST),stained with hematoxylin-eosin (scale bar 20?m)after incubation at 37?C.
imately 34.75%,and it remained constant throughout the whole experiment.
Concentration–time pro?les of DEX in rabbit aqueous humor are shown in Fig.8,while the pharmacokinetic parameters have been summarized in Table 2.The area under the curve (AUC 0→240min )values of DEX administered in DEX cubosomes F1,micelles,Dex-Na phosphate eye drops and DEX suspen-sion were 24023.5±9899.7,5362.6±1887.6,13505.8±3234.3and 3005.1±1559.6ng ml ?1min,respectively.The AUC 0→240min of DEX administered in cubosomes exhibited a 1.8-fold increase com-pared to that of the Dex-Na phosphate eye drops,with about an 8-fold increase compared to that of the DEX suspension.Cmax for DEX in cubosomes also exhibited a remarkable increment rela-tive to Dex-Na phosphate eye drops and DEX suspension (p <0.05).However,no signi?cant differences could be seen in Tmax.MRT of DEX administered in cubosomes also increased signi?cantly,com-pared with DEX suspension.4.Discussion
SAXR and cryo-TEM are usually used to characterize the inter-nal structure of dispersed cubic particles (Gustafsson et al.,1997).The cryo-TEM images in this study showed a typical ordered cubic
texture and inner periodicity which was further con?rmed by SAXR.Introduction of guest molecules generally in?uences the self-assembly structure properties.The more hydrophilic ones would induce a transition to the lamellar phase,while the more lipophilic ones would induce a transition to the hexagonal phase (Sagalowicz et al.,2006).The similarity of SAXR pro?les between blank cubo-somes and DEX cubosomes F1indicated that the addition of 0.05%DEX did not change the internal structure of the dispersed cubic particles.
Reports on the nanodispersion of MO and oleic acid as a topical delivery system have shown that it was non-irritant to the skin of hairless mice (Lopes et al.,2006).Therefore,it might be considered feasible to utilize nanodispersions of MO as an ocular drug deliv-ery system.Histologically,cross-sections of rabbit corneas after incubation with cubosome formulations showed that the corneal structure and integrity were almost visibly unaffected.It was there-fore concluded that MO cubosomes will not result in histological impairment as vehicles for ocular drug delivery.
Preocular retention of cubosomes was evaluated using a nonin-vasive ?uorescence imaging system.Identifying ROI and de?ning them as ocular and non-ocular allowed the quanti?cation of the remaining activity in these regions at different time points.The non-ocular ROI represent the inner canthus and nasolacrimal duct
Table 3
Pharmacokinetic parameters of DEX in rabbit aqueous humor after instillation of various dosage forms (n =3).Samples
AUC 0→240min Cmax Tmax MRT (ng ml ?1min)(ng ml ?1)(min)(min)Dex cubosome F124023.5±9899.7a ,b 336.8±187.6a ,b 23.3±5.874.8±20.8b Dex micelle
5362.6±1887.6392.1±89.813.3±5.734.9±10.9Dex-Na phosphate eye drops 13505.8±3234.3233.1±56.626.7±15.361.7±15.6Dex suspension
3005.1
±
1559.6
136.7
±
75.6
11.5
±9.3
28.5
±19.2
a p <0.05statistically signi?cant difference from Dex-Na phosphate eye drops.b
p <0.05statistically signi?cant difference from Dex suspension.
L.Gan et al./International Journal of Pharmaceutics 396 (2010) 179–187
185
Fig.6.Fluorescence images of rabbit eyes after administration of (A)Rhodamin B solution,(B)Rhodamin B cubosomes F1(10%oil content);(C)white light image of rabbit eye.1:intensity reference standard,2:ocular ROI,3:non-ocular ROI (inner canthus and nasolacrimal duct region).
and were therefore not considered relevant to precorneal resi-dence.As illustrated in Fig.6,only two ROI were created,ocular and non-ocular,with an intensity reference standard used to esti-mate the residual ?uorescence activity.The ?uorescence
reference Fig.7.Precorneal clearance of various formulations (n =3),Rh B cubosomes F1(10%oil content).in Fig.6was used for better identifying the position of rabbit eyes.About 100?l Rh B solution (10?4?mol/ml)was put in a small glass tube to be used as reference.Therefore,the ?uorescence intensity seems far lower than that of the ocular ROI and non-ocular
ROI.
Fig.8.Concentration–time pro?les of DEX in rabbit aqueous humor after instillation of various dosage forms (n =3).
186L.Gan et al./International Journal of Pharmaceutics396 (2010) 179–187
It was found that the cubosomes formulation exhibited a slow clearance and signi?cantly prolonged residence of?uorescence in the ocular ROI(A90was about40%)compared to solution.The lipid bilayer microstructure may serve to prolong retention.A pos-sible explanation for this could be the non-speci?c interactions (hydrophobic and van der Waals)of the cubosomes with the super-?cial oily layer of the tear?lm(Alany et al.,2006).Moreover, compared with carbopol gel,signi?cant differences were observed in the clearance rate(k)and residence of?uorescence in the ocu-lar ROI at90min(A90).As the viscosity of carbopol gel was about 90mPa s,the relatively high viscosity might adversely accelerate the blinking frequency leading to rapid clearance.It was there-fore considered that cubosomes could be of value as vehicles for ocular applications as they appeared to have prolonged preocular residence with low viscosity.
The cornea consists of three primary layers:the cellular epithe-lium and endothelium are lipophilic,while the gel-like stroma is hydrophilic.The epithelium and endothelium contain100-fold greater amounts of lipid material per unit weight than the stroma (Suhonen et al.,1998).For most topically applied drugs,passive diffusion along their concentration gradient,either transcellularly or paracellularly,is the main permeation mechanism across the cornea.Physico-chemical drug properties,such as lipophilicity,sol-ubility,molecular size and shape,charge and degree of ionization, affect the route and rate of permeation of the cornea(Jarvinen et al., 1995).It has been shown that the optimal lipophilicity for corneal permeation corresponds to log D values of2–3(Mannermaa et al., 2006).
In the in vitro cornea penetration study,P app of DEX formulated in cubosomes exhibited a4.5-fold(F1)and a3.5-fold(F2)increase relative to Dex-Na phosphate eye drops.The phosphate derivative of DEX exists in an ionized form,which is too hydrophilic to pen-etrate through the lipophilic corneal epithelium.Therefore,one of the possible mechanisms for cubosomes in enhancing corneal permeation is to deliver the drug in unionized form.The union-ized species usually penetrates the lipid membranes more easily than the ionized form(Suhonen et al.,1998).Compared with DEX micelles,P app of DEX in cubosomes F1also showed a1.7-fold increase.Some researchers found the periodically curved lipid bilayer of cubosomes was very similar to the microstructure of the cell membrane(Larsson,1989;Giorgione et al.,1998).It is reasonable to suppose the formation of a mix of cubosome MO with corneal epithelium lipid,where the cubosomes might act as a depot from which DEX can be continuously released.This might be another possible mechanism for the penetration enhancement effect of cubosomes.
Results of an in vivo aqueous humor pharmacokinetic study also indicated the1.8-fold and8-fold increase in AUC0→240min of DEX administered in cubosomes compared with Dex-Na phosphate eye drops and DEX suspension,respectively.
Ocular drug absorption from the lacrimal?uid to the anterior ocular tissues via transcorneal absorption is determined by two major factors:ocular contact time of the delivery system and drug permeability in the cornea(Mannermaa et al.,2006).On one hand, an in vitro preocular retention study indicated the prolonged resi-dence of cubosomes in the preocular region,which would improve one of the above-mentioned major factors,ocular contact time. On the other hand,the in vitro cornea penetration study showed that P app of DEX formulated in cubosomes exhibited a4.5-fold(F1) increase relative to Dex-Na phosphate eye drops.Therefore,as has been discussed above,the other major factor affecting drug perme-ability in the cornea might also have been improved.Consequently, as illustrated in the in vivo aqueous humor pharmacokinetic study, DEX formulated in the self-assembled liquid crystalline nanoparti-cles(cubosomes)might exhibit increased ocular bioavailability by improving both of the two important factors.5.Conclusion
In this study,self-assembled liquid crystalline nanoparticles, named cubosomes,were investigated as an ocular drug delivery system.The apparent permeability coef?cient of DEX formulated in cubosomes was signi?cantly enhanced.In addition,the cubosomes (10%oil)with low viscosity were retained in the preocular region much longer.Consequently,the ocular bioavailability of DEX has been greatly improved.On the other hand,MO/Poloxamer cubo-somes might have good ocular biocompatibility as they appeared to exert no deleterious in?uence on corneal structure and integrity in the in vitro ocular tolerance test.In conclusion,cubosomes might represent a promising vehicle for effective ocular drug delivery. Acknowledgements
We thank the National Science&Technology Major Project “Key New Drug Creation and Manufacturing Program”(No. 2009ZX09301-001)for?nancial support.This work was also supported in part by the National Basic Research Program of China(No.2009CB930300)and the National High Technology Research and Development Program of China(863Program)(No. 2007AA021604).
References
Aggarwal,D.,Kaur,I.P.,2005.Improved pharmacodynamics of timolol maleate from
a mucoadhesive niosomal ophthalmic drug delivery system.Int.J.Pharm.290,
155–159.
Alany,R.G.,Rades,T.,Nicoll,J.,Tucker,I.G.,Davies,N.M.,2006.W/O microemulsions for ocular delivery:Evaluation of ocular irritation and precorneal retention.J.
Control.Release111,145–152.
Anand,B.S.,Katragadda,S.,Gunda,S.,Mitra,A.K.,2006.In vivo ocular pharmacoki-netics of acyclovir dipeptide ester prodrugs by microdialysis in rabbits.Mol.
Pharm.3,431–440.
Baydoun,L.,Furrer,P.,Gurny,R.,Muller-Goymann,C.C.,2004.New surface-active polymers for ophthalmic formulations:evaluation of ocular tolerance.Eur.J.
Pharm.Biopharm.58,169–175.
Boyd,B.J.,2003.Characterisation of drug release from cubosomes using the pressure ultra?ltration method.Int.J.Pharm.260,239–247.
Burngay,P.M.,Morrison,P.F.,Dedrick,R.L.,1990.Steady-state theory for quan-titative microdialysis of solutes and water in vivo and in vitro.Life Sci.46, 105–119.
Carr,M.G.,Corish,J.,Corrigan,O.I.,1997.Drug delivery from a liquid crystalline base across Visking and human stratum corneum.Int.J.Pharm.157,35–42. Esposito,E.,Cortesi,R.,Drechsler,M.,Paccamiccio,L.,Mariani,P.,Contado,C.,Stellin,
E.,Menegatti,E.,Bonina,
F.,Puglia,C.,2005.Cubosome dispersions as deliv-
ery systems for percutaneous administration of indomethacin.Pharm.Res.22, 2163–2173.
Gan,L.,Gan,Y.,Zhu,C.L.,Zhang,X.X.,Zhu,J.B.,2009.Novel microemulsion in situ electrolyte-triggered gelling system for ophthalmic delivery of lipophilic cyclosporine A:in vitro and in vivo results.Int.J.Pharm.365,143–149. Giorgione,J.R.,Huang,Z.,Epand,R.M.,1998.Increased activation of protein kinase
C with cubic phase lipid compared with liposomes.Biochem.J.37,2384–2392. Gustafsson,J.,Ljusberg-Wahren,H.,Almgren,M.,Larsson,K.,1997.Submicron par-ticles of reversed lipid phases in water stabilized by a nonionic amphiphilic https://www.wendangku.net/doc/454339160.html,ngmuir13,6964–6971.
Jarvinen,K.,Jarvinen,T.,Urtti,A.,1995.Ocular absorption following topical delivery.
Adv.Drug Deliv.Rev.16,3–19.
Katragadda,S.,Gunda,S.,Hariharan,S.,Mitra,A.K.,2008.Ocular pharmacokinetics of acyclovir amino acid ester prodrugs in the anterior chamber:evaluation of their utility in treating ocular HSV infections.Int.J.Pharm.359,15–24.
Kim,J.,Chauhan,A.,2008.Dexamethasone transport and ocular delivery from poly(hydroxyethyl methacrylate)gels.Int.J.Pharm.353,205–222. Kuntsche,J.,Bunjes,H.,Fahr,A.,Pappinen,A.,Ronkko,S.,Suhonen,M.U.,Urtti,A., 2008.Interaction of lipid nanoparticles with human epidermis and an organ-otypic cell culture model.Int.J.Pharm.354,180–195.
Larsson,K.,1989.Cubic lipid-water phases–structures and biomembrane aspects.
J.Phys.Chem.93,7304–7314.
Lee,J.,Kellaway,I.W.,2000a.Buccal permeation of[d-Ala(2),d-Leu(5)]enkephalin from liquid crystalline phases of glyceryl monooleate.Int.J.Pharm.195, 35–38.
Lee,J.,Kellaway,I.W.,https://www.wendangku.net/doc/454339160.html,bined effect of oleic acid and polyethylene glycol 200on buccal permeation of[d-Ala(2),d-Leu(5)]enkephalin from a cubic phase of glyceryl monooleate.Int.J.Pharm.204,137–144.
Lee,S.-B.,Geroski,D.H.,Prausnitz,M.R.,Edelhauser,H.F.,2004.Drug delivery through the sclera:effects of thickness,hydration,and sustained release systems.Exp.
Eye Res.78,599–607.
L.Gan et al./International Journal of Pharmaceutics396 (2010) 179–187187
Leesajakul,W.,Nakano,M.,Taniguchi,A.,Handa,T.,2004.Interaction of cubo-somes with plasma components resulting in the destabilization of cubosomes in plasma.Colloid.Surf.B34,253–258.
Lopes,L.B.,Ferreira,D.A.,de Paula,D.,Garcia,M.T.J.,Thomazini,J.A.,Fantini,M.C.A., Bentley,M.V.L.B.,2006.Reverse hexagonal phase nanodispersion of monoolein and oleic acid for topical delivery of peptides:in vitro and in vivo skin penetra-tion of cyclosporin A.Pharm.Res.23,1332–1342.
Mannermaa,E.,Vellonen,K.-S.,Urtti,A.,2006.Drug transport in corneal epithelium and blood-retina barrier:emerging role of transporters in ocular pharmacoki-netics.Adv.Drug Deliv.Rev.58,1136–1163.
Meisner,D.,Mezei,M.,1995.Liposome ocular delivery systems.Adv.Drug Deliv.
Rev.16,75–93.
Muchtar,S.,Abdulrazik,M.,Frucht-Pery,J.,Benita,S.,1997.Ex-vivo permeation study of indomethacin from a submicron emulsion through albino rabbit cornea.
J.Control.Release44,55–64.
Nakano,M.,Teshigawara,T.,Sugita,A.,Leesajakul,W.,Taniguchi,A.,Kamo,T., Matsuoka,H.,Handa,T.,2002.Dispersions of liquid crystalline phases of the monoolein/oleic acid/Pluronic https://www.wendangku.net/doc/454339160.html,ngmuir18,9283–9288. Phillips,K.,Katz,H.R.,2005.A comparison of the ef?cacy of dexamethasone and loteprednol on endotoxin-induced uveitis in rodents following topical ocular administration.Invest.Ophthalmol.Vis.Sci.46,983.
Rittenhouse,K.D.,Peiffer,R.L.,Pollack,G.M.,1998.Evaluation of microdialysis sam-pling of aqueous humor for in vivo models of ocular absorption and disposition.
J.Pharmaceut.Biomed.16,951–959.Saettone,M.F.,Chetoni,P.,Cerbai,R.,Mazzanti,G.,Braghiroli,L.,1996.Evalu-ation of ocular permeation enhancers:In vitro effects on corneal transport of four[beta]-blockers,and in vitro/in vivo toxic activity.Int.J.Pharm.142, 103–113.
Sagalowicz,L.,Leser,M.E.,Watzke,H.J.,Michel,M.,2006.Monoglyceride self-assembly structures as delivery vehicles.Trend Food Sci.Technol.17, 204–214.
Shah,J.C.,Sadhale,Y.,Chilukuri,D.M.,2001.Cubic phase gels as drug delivery sys-tems.Adv.Drug Deliv.Rev.47,229–250.
Siekmann,B.,Bunjes,H.,Koch,M.H.,Westesen,K.,2002.Preparation and structural investigations of colloidal dispersions prepared from cubic monoglyceride-water phases.Int.J.Pharm.244,33–43.
Suhonen,P.,Jarvinen,T.,Koivisto,S.,Urtti,A.,1998.Different effects of pH on the permeation of pilocarpine and pilocarpine prodrugs across the isolated rabbit cornea.Eur.J.Pharm.Sci.6,169–176.
Suhonen,P.,Jarvinen,T.,Peura,P.,Urtti,A.,1991.Permeability of pilocarpic acid diesters across albino rabbit cornea in vitro.Int.J.Pharm.74,221–228. Tamilvanan,S.,Benita,S.,2004.The potential of lipid emulsion for ocular delivery of lipophilic drugs.Eur.J.Pharm.Biopharm.58,357–368.
Yamaguchi,M.,Yasueda,S.,Isowaki,A.,Yamamoto,M.,Kimura,M.,Inada,K.,Ohtori,
A.,2005.Formulation of an ophthalmic lipid emulsion containing an anti-
in?ammatory steroidal drug,di?uprednate.Int.J.Pharm.301,121–128. Zimmer,A.,Kreuter,J.,1995.Microspheres and nanoparticles used in ocular delivery systems.Adv.Drug Deliv.Rev.16,61–73.
晶体学基础与晶体结构习题与答案
晶体学基础与晶体结构习题与答案 1. 由标准的(001)极射赤面投影图指出在立方晶体中属于[110]晶带轴的晶带，除了已在图2-1中标出晶面外，在下列晶面中哪些属于[110]晶带？(1-12)，(0-12)，(-113)，(1-32)，(-221)。 图2-1 2. 试证明四方晶系中只有简单立方和体心立方两种点阵类型。 3. 为什么密排六方结构不能称作为一种空间点阵？ 4. 标出面心立方晶胞中（111）面上各点的坐标。 5. 标出具有下列密勒指数的晶面和晶向：a)立方晶系(421)，(-123)，(130)，[2-1-1]，[311]； b)六方晶系(2-1-11)，(1-101)，(3-2-12)，[2-1-11]，[1-213]。 6. 在体心立方晶系中画出{111}晶面族的所有晶面。 7. 在立方晶系中画出以[001]为晶带轴的所有晶面。 8. 已知纯钛有两种同素异构体，密排六方结构的低温稳定的α-Ti和体心立方结构的高温稳定的β-Ti，其同素异构转变温度为882.5℃，使计算纯钛在室温(20℃)和900℃时晶体中(112)和(001)的晶面间距(已知aα20℃=0.29506nm，cα20℃=0.46788nm，aα900℃=0.33065nm)。 9. 试计算面心立方晶体的(100)，(110)，(111)，等晶面的面间距和面致密度，并指出面间距最大的面。 10.平面A在极射赤平面投影图中为通过NS及核电0°N，20°E的大圆，平面B的极点在30°N，50°W处，a)求极射投影图上两极点A、B间的夹角；b)求出A绕B顺时针转过40°的位置。 11. a)说明在fcc的(001)标准极射赤面投影图的外圆上，赤道线上和0°经线上的极点的指数各有何特点，b)在上述极图上标出(-110)，(011)，(112)极点。 12. 图2-2为α-Fe的x射线衍射谱，所用x光波长λ=0.1542nm，试计算每个峰线所对应晶面间距，并确定其晶格常数。 图2-2 13. 采用Cu kα(λ=0.15418nm)测得Cr的x射线衍射谱为首的三条2θ=44.4°，64.6°和81.8°，若(bcc)Cr的晶格常数a=0.28845nm，试求对应这些谱线的密勒指数。
晶面间距计算公式
晶面间距计算公式 正交晶系 1/d2=h2/a2+k2/b2+l2/c2 单斜晶系 1/d2={h2/a2+k2sin2β/b2+l2/c2－2hlcosβ/(ac)}/ sin2β 立方晶系 d=a/(h2+k2+l2) 六角晶系 四角晶系 单斜晶系
三斜晶系 If Φ is the angle between plane (h 1 k 1 l 1) and (h 2 k 2 l 2), then for Orthorhombic 2 /12 2222222 22 /12 212 212 2 1221221221)()()(cos ??? ? ??++??? ? ??++++= Φc l b k a h c l b k a h c l l b k k a h h Tetragonal []() 2 /12 2 2222 22 2 /12 21221 21 2 212212 1))/)(cos ??? ? ??++???? ??++++= Φc l a k h c l a k h c l l a k k h h Cubic
()()[] 2 /122 2222 21 21 21 212121cos l k h l k h l l k k h h ++++++= Φ Hexagonal ()() 2 /12222222 222212211212121221221212143434 321 cos ? ????????? ??+++???? ? ?++++++ += Φl c a k h k h l c a k h k h l l c a K h k h k k h h VOLUME: Orthorhombic: =abc Tetragonal: =c a 2 Cubic: =3a Hexagonal: = c a 2 2 3 hcp transition between (UVW) and (uvtw) U=u-t, V=v-t, W=w u=1/3(2U-V), v=1/3(2V-U), t= - (u+v), w=W.
1-2 常见的晶体结构及其原胞、晶胞
§1-2 常见的晶体结构及其原胞、晶胞 1) 简单晶体的简单立方(simple cubic, sc) 它所构成的晶格为布喇菲格子。例如氧、硫固体。基元为单一原子结构的晶体叫简单晶体。 其特点有: 三个基矢互相垂直（），重复间距相等，为a， 亦称晶格常数。其晶胞=原胞；体积= ；配位数(第一近邻数) =6。（见图1-7） 图1-7简单立方堆积与简单立方结构单元 2) 简单晶体的体心立方( body-centered cubic, bcc ) , 例如，Li，K， Na，Rb，Cs,αFe，Cr，Mo，W，Ta，Ba等。其特点有：晶胞基矢, 并且，其惯用原胞基矢由从一顶点指向另外三个体心点的矢量构成：（见图1-9 b） (1-2) 其体积为；配位数=8；（见图1-8）
图1-8体心立方堆积与体心立方结构单元 图1-9简单立方晶胞(a)与体心立方晶胞、惯用原胞(b) 3) 简单晶体的面心立方( face-centered cubic, fcc ) , 例如，Cu，Ag， Au，Ni，Pd，Pt，Ne, Ar, Xe, Rn, Ca, Sr, Al等。晶胞基矢， 并且每面中心有一格点, 其原胞基矢由从一顶点指向另外三个面心点的矢量构成（见图1-10 b）： (1-3)
其体积=；配位数=12。，（见图1-10） 图1-10面心立方结构(晶胞)(a)与面心立方惯用原胞(b) 4) NaCl结构（Sodium Chloride structure），复式面心立方（互为fcc），配位数=6（图1-11 a)。 表1-1 NaCl结构晶体的常数 5) CsCl结构（Cesuim Chloride structure），复式简单立方（互为sc），配位数=8（图1-11 b）。 表1-2 CsCl结构晶体的常数
六方晶系四指数推导
1.4 晶向指数和晶面指数 一晶向和晶面 1 晶向 晶向：空间点阵中各阵点列的方向（连接点阵中任意结点列的直线方向）。晶体中的某些方向，涉及到晶体中原子的位置，原子列方向，表示的是一组相互平行、方向一致的直线的指向。 2 晶面 晶面：通过空间点阵中任意一组阵点的平面（在点阵中由结点构成的平面）。晶体中原子所构成的平面。 不同的晶面和晶向具有不同的原子排列和不同的取向。材料的许多性质和行为（如各种物理性质、力学行为、相变、X光和电子衍射特性等）都和晶面、晶向有密切的关系。所以，为了研究和描述材料的性质和行为，首先就要设法表征晶面和晶向。为了便于确定和区别晶体中不同方位的晶向和晶面，国际上通用密勒（Miller）指数来统一标定晶向指数与晶面指数。 二晶向指数和晶面指数的确定 1 晶向指数的确定方法 三指数表示晶向指数[uvw]的步骤如图1所示。 (1)建立以晶轴a，b，c为坐标轴的坐标系，各轴上的坐标长度单位分别是晶胞边长a，b，c，坐标原点在待标晶向上。 (2)选取该晶向上原点以外的任一点P(xa，yb，zc)。 (3)将xa，yb，zc化成最小的简单整数比u，v，w，且u∶v∶w = xa∶yb∶zc。 (4)将u，v，w三数置于方括号内就得到晶向指数[uvw]。 图1 晶向指数的确定方法 图2 不同的晶向及其指数 当然，在确定晶向指数时，坐标原点不一定非选取在晶向上不可。若原点不在待标晶向上，那就需要选取该晶向上两点的坐标P(x1，y1，z1)和Q(x2，y2，z2)，然后将(x1-x2)，(y1-y2)，
(z 1-z 2)三个数化成最小的简单整数u ，v ，w ，并使之满足u ∶v ∶w =(x 1-x 2)∶(y 1-y 2)∶(z 1-z 2)。则[uvw ]为该晶向的指数。 显然，晶向指数表示了所有相互平行、方向一致的晶向。若所指的方向相反，则晶向指数的数字相同，但符号相反，如图3中[001]与[010]。 说明： a 指数意义：代表相互平行、方向一致的所有晶向。 b 负值：标于数字上方，表示同一晶向的相反方向。 c 晶向族：晶体中原子排列情况相同但空间位向不同的一组晶向。用
晶面间距及晶包参数计算公式
空间点阵必可选择3个不相平行的连结相邻两个点阵点的单位矢量a，b，c，它们将点阵划分成并置的平行六面体单位，称为晶面间距。空间点阵按照确定的平行六面体单位连线划分，获得一套直线网格，称为空间格子或晶格。点阵和晶格是分别用几何的点和线反映晶体结构的周期性，它们具有同样的意义。 1概述 空间点阵必可选择3个不相平行的连结相邻两个点阵点的单位矢量a，b，c，它们将点阵划分成并置的平行六面体单位，称为晶面间距。空间点阵按照确定的平行六面体单位连线划分，获得一套直线网格，称为空间格子或晶格。点阵和晶格是分别用几何的点和线反映晶体结构的周期性，它们具有同样的意义。 2 计算 不同的{hkl}晶面（标准卡片可读出hkl为衍射指数），其面间距(即相邻的两个平行晶面之间的距离)各不相同。总的来说，低指数的晶 面其面间距较大，而高指数面的面间距小。以图1-22所示的简单立 方点阵为例，可看到其{100}面的晶面间距最大，{120}面的间距较小，而{320}面的间距就更小。但是，如果分析一下体心立方或面心立方 点阵，则它们的最大晶面间距的面分别为{110}或{111}而不是{100}，说明此面还与点阵类型有关。此外还可证明，晶面间距最大的面总是阵点(或原子)最密排的晶面，晶面间距越小则晶面上的阵点排列就越
稀疏。正是由于不同晶面和晶向上的原子排列情况不同，使晶体表现为各向异性。 简单立方点阵晶面间距d与点阵常数之间的关系： 。 面心立方晶体（FCC）晶面间距与点阵常数a之间的关系： 若h、k、l 均为奇数，则 ；否则， 。 体心立方晶体（BCC）晶面间距与点阵常数a之间的关系： 若h+k+l=偶数，则 ；否则，
体心立方晶格与面心立方晶格
体心立方、面心立方晶格主要晶面的原子排列和密度
体心立方、面心立方晶格主要晶向的原子排列和密度 第1章 小结 1．三种常见金属的晶体结构 体心立方晶格（胞）：晶格常数a 、90°，晶胞原子数为2个， 原子半径： ， 致密度为68%，最大空隙半径 r 四=0.29r 原子，配位数为8 面心立方晶格（胞）：晶格常数a 、90°，晶胞原子数为4个，
原子半径： ， 致密度为74%，最大空隙半径r八=0.414r原子，配位数为12。 密排六方晶格（胞）：晶格常数a、c、90°、120°，晶胞原子数为6个， 原子半径：， 致密度为74%，最大空隙半径r八=0.414r原子，配位数为12。 2．晶面与晶向可用晶面指数与晶向指数来表达。不同晶面、不同晶向上的原子排列情况不同。 体心立方晶格的最密面为{110}，最密方向为<111>。 面心立方晶格的最密面为{111}，最密方向为<110>。 密排六方晶格的最密面为{0001}，最密方向为。 3．实际金属中含有点缺陷（空位、间隙原子、异类原子）、线缺陷（位错）、面缺陷（晶界、亚晶界）三类晶体缺陷，位错密度增加，材料强度增加。晶界越多，晶粒越细，金属的强度越高，同时塑性越好（即细晶强化）。 4．合金中有两类基本相：固溶体和金属化合物。固溶强化是金属强化的一种重要形式。细小弥散分布的金属化合物可产生弥散强化或第二相强化。材料的微观组成和微观形貌称组织，材料的组织取决于化学成分和工艺过程。
5．金属材料的性能特点是：强度高，韧性好，塑性变形能力强，综合机械性能好，通过热处理可以大幅度改变机械性能。金属材料导电、导热性好。不同的金属材料耐蚀性相差很大，钛、不锈钢耐蚀性好，碳钢、铸铁耐蚀性差。 6．高分子材料结构由大分子链组成，大分子链之间的相互作用力为分子键，分子链的原子之间、链节之间的相互作用力为共价键。高分子材料的大分子链结构与聚集态及其性能密切相关。高分子的聚集态结构分无定形和晶态两种。线型非晶态高聚物在不同温度下表现三种物理状态：玻璃态、高弹态、粘流态。 高分子材料的性能特点：高聚物轻，其特有的机械性能是高弹性和粘弹性。由于可以处于不同的力学状态，高分子材料可以是硬脆、强硬、强韧、柔韧或软弱的，机械性能不高，刚度小，强度不高，韧性较低。高分子材料耐磨、减摩性能好，绝缘、绝热、绝声，耐蚀性能好，但耐热性不高，存在老化问题。 7. 陶瓷材料的生产过程包括原料的制备、坯料的成形和制品的烧结三大步骤。典型陶瓷的组织由晶体相、玻璃相和气相组成。晶体相是陶瓷的主要组成，决定材料的基本性能。普通陶瓷的晶体相主要是硅酸盐，特种陶瓷的晶体相为氧化物、碳化物、氮化物、硼化物和硅化物，金属陶瓷则还有金属。玻璃相为非均质的酸性和碱性氧化物的非晶态固体，起粘结剂作用。气相是陶瓷组织中残留的孔洞，极大地破坏材料的机械性能。
晶体学习题与答案
一、 名词解释 （1）阵点；（2）（空间）点阵；（3）晶体结构；（4）晶胞；（5）晶带轴； 二、填空 （1）晶体中共有 种空间点阵，属于立方晶系的空间点阵有 三种。 （2）对于立方晶系，晶面间距的计算公式为 。 （3）{110}晶面族包括 等晶面。 （4）{h 1k 1l 1}和{h 2k 2l 2}两晶面的晶带轴指数[u v w]为 。 （5）(110)和(11-0)晶面的交线是 ；包括有[112]和[123]晶向的晶面是 。 三、计算及简答 （1）原子间的结合键共有几种？各自有何特点？ （2）在立方晶系的晶胞中，画出（111）、（112）、（011）、（123）晶面和[111]、[101]、[111-] 晶向。 （3）列出六方晶系{101-2} 晶面族中所有晶面的密勒指数，并绘出（101-0）、（112-0）晶面 和〔112-0〕晶向。 （4）试证明立方晶系的〔111〕晶向垂直于（111）晶面。 （5）绘图指出面心立方和体心立方晶体的（100）、（110）、及（111）晶面，并求其面间距； 试分别指出两种晶体中，哪一种晶面的面间距最大？ （6）在立方晶系中，（1-10）、（3-11）、（1-3- 2）晶面是否属于同一晶带？如果是，请指出其晶 带轴；并指出属于该晶带的任一其他晶面。 （7）写出立方晶系的{111}、{123}晶面族和<112>晶向族中的全部等价晶面和晶向的具体指 数。 （8）计算立方晶系中（111）和〔111-〕两晶面间的夹角。
（9）若采用四轴坐标系标定六方晶体的晶向指数，应该有什么约束条件？为什么？ 答 案 二、填空 (1)14 简单、体心、面心 (2)222hkl d h k l =++ (3) (110)、(101)、(011)、(1-10)、(1-01) 、(01-1) (4)1122k l u k l =；1122l h v l h =；11 22 h k w h k = (5)〔001〕 （111-） 三、简答及计算 （1）略 （2） （3）{101-2}晶面的密勒指数为（101-2）、（1-012）、（01-12）、（011-2）、 （ 1-102）、（11-02）。要求绘出的晶面和晶向如下图1-9所示。
面心立方体结构研究
单质金属物质冷却到固体时，有些原子，像钋，是按照立方体的结构排列的，这样在原子中间有很大的空隙。另一些原子，像铁、钠、钾、钨、铬、钒等就在立方体的中心再嵌一个原子，这样排得更密一点。但是更多的原子是以最紧密的形式排列，像铜、银、金、镍、铝、铅、镁、铍、钛、锌、镉、钴等。如果假象成球形的单个原子没有对相邻的分子有方向或数量的要求，无数个小球组成一个要排列得最紧密的物质，那会排成什么样呢？ 简单一点我们先从二维空间说起。二维空间对称的微粒是圆形的，一个圆的周围正好可以挤满6个同样的圆，一点也不空着，所以填满二维空间就是就是六角排列。 三维的情况要复杂一点，把二维最紧密的结构一层一层最紧密地叠起来，上面一层的小球落在下面三个小球的中间，使层与层之间的距离最近，在三维空间也正好是最紧密的排列【1】。
如果把底层的小球的位置称作A位的话，上一层的位置有两个不同排法，在B位或者C位。如果这一层在B位或在C位可以随便定义的话，那么再上一层的位置是否回到A位就很关键了。于是就有了A-B- A-B- A-B- A-B- A-B- A-B的排列方式和A-B-C- A-B-C- A-B-C- A-B-C 的排列方式。
原子按照A-B- A-B- A-B- A-B- A-B- A-B的方式排列，很显然有六边形的结构，我们把这种排列叫做六角密堆。镁、铍、钛、锌、镉、钴等原子组成的晶体就是六角密堆的。 按照A-B-C- A-B-C- A-B-C- A-B-C的排列，除了有六边形的对称结构外，换一个方向看，还有立方体的结构，仔细分析，就是立方体的每个面上都填着一个原子。所以这种最紧密的排列，叫做面心立方密堆。在面心立方密堆结构的立方体中，与大对角线垂直的平面就是一个 按六边形紧密排列的。
晶格类型 1体心立方
1．晶格类型1体心立方：α—fe Cr W, Mo,V （2）面心立方：r-fe，铜铝，镍，（3）密排立方：Be. Mg. Zn, Cd 2．三种缺陷：（1）点缺陷：空位，置换原子，间隙原子（2）线缺陷：刃型位错（3）面缺陷：金属中的晶界亚晶界产生晶格畸变 3．细化晶粒的方法：（1）增大过冷度（2）变质处理（3）机械振动和搅拌 4．细化晶粒对力学性能的影响：晶粒越小则金属的强度硬度越好，塑性韧性下降 5．固溶强化现象; 溶质溶入溶剂中使晶格产生畸变现象使强度硬度塑性韧性下降6．二元相图建立（1）配制几种成分不同的合金（2）测定上述合金的冷却曲线（3）找上述合金的临界点注：冷却时，是以极其缓慢的速度 7．二元相图：匀晶共晶包晶共析 8．Fe-FeC状态图中各点，线的含义，温度，成分及各区的组织是什么？各组织用什么符号表示？
? ? ?? ? L J N G A A+Fe3C F+Fe3C L+Fe3C L+A + A L J N G A A+Fe3C L+Fe3C L+A F + A 9.。碳钢中常含有哪四种杂质元素？哪些是有益元素哪些是有害元素？
Mn Si S P Mn Si 有益P S 有害 10.过冷奥氏体等温转变曲线包括哪三个转变区域？共析钢等温曲线的转变区温度范围是多少？各转变区在不同温度下的转变产物的名称和符号是什么？ 珠光体转变贝氏体转变马氏体转变 11.退火，正火，淬火，低低温回火的目的是什么？获得的组织是什么？ 退火目的：（1）降低硬度，改善切削加工性（2）消除应力，稳定尺寸（3）细化晶粒，调整组织，消除缺陷，为后续热处理做好组织准备获得铁素体加珠光体冷却方式：空气中冷却正火：细化晶粒，提高其力学性能获得索氏体组织空气冷却淬火：为了获得马氏体，提高钢的强度，硬度和耐磨性油冷或水冷低温回火：降低淬火应力和脆性，多用于处理各种模具或表面淬火的工艺获得回火马氏体 12.合金元素对C曲线位置有何影响？其他元素对C曲线位置的影响？ 1.含碳量的影响：对C曲线位置影响：在正常加热条件下，Wc<0.77%时，含碳量增加，C曲线右移；Wc>0.77%时，含碳量增加，C曲线左移。所以，共析钢的过冷奥氏体最稳定。 2.合金元素的影响：除钴以外，所有的合金元素溶入奥氏体后，都增大过冷奥氏体A的稳定性，使C曲线右移。碳化物含量较多时，对曲线的形状也有影响 13.选用材料：45号钢制造机床主轴的工艺路线：下料—锻造—正火—粗加工—调制—精加工—表面淬火加回火—机械加工锻造后正火的目的：慰劳改善锻造组织，细化晶粒，降低硬度以利于切削加工，并为调制处理做组织准备淬火加回火的目的：提高弹性 简答题 1.金属材料塑性变形的基本方式有几种？物理本质？ 滑移孪生本质：晶体产生滑移晶体产生转动 2．Mn在C钢中的性能形式？ 来自生铁及脱氧剂。溶于铁素体起固溶强化作用，同时还可形成合金渗碳体。锰可降低S 的有害作用，提高加工性能。通常含锰量＜0.8%。 3.晶粒大小对性能的影响？
第一章 金属的晶体结构习题答案
第一章 金属的晶体结构 (一)填空题 3．金属晶体中常见的点缺陷是 空位、间隙原子和置换原子 ，最主要的面缺陷是 。 4．位错密度是指 单位体积中所包含的位错线的总长度 ，其数学表达式为V L =ρ。 5．表示晶体中原子排列形式的空间格子叫做 晶格 ，而晶胞是指 从晶格中选取一个能够完全反应晶格特征的最小几何单元 。 6．在常见金属晶格中，原子排列最密的晶向，体心立方晶格是 [111] ，而面心立方 晶格是 [110] 。 7 晶体在不同晶向上的性能是 不同的 ，这就是单晶体的 各向异性现象。一般结构用金属 为 多 晶体，在各个方向上性能 相同 ，这就是实际金属的 伪等向性 现象。 8 实际金属存在有 点缺陷 、 线缺陷 和 面缺陷 三种缺陷。位错是 线 缺陷。 9．常温下使用的金属材料以 细 晶粒为好。而高温下使用的金属材料在一定范围内以粗 晶粒为好。 10．金属常见的晶格类型是 面心立方、 体心立方 、 密排六方 。 11．在立方晶格中，各点坐标为：A (1，0，1)，B (0，1，1)，C (1，1，1/2)，D(1/2，1，1/2)， 那么AB 晶向指数为10]1[- ，OC 晶向指数为[221] ，OD 晶向指数为 [121] 。 12．铜是 面心 结构的金属，它的最密排面是 ｛111｝ ，若铜的晶格常数a=0.36nm, 那么最密排面上原子间距为 0.509nm 。 13 α-Fe 、γ-Fe 、Al 、Cu 、Ni 、Cr 、V 、Mg 、Zn 中属于体心立方晶格的有 α-Fe 、Cr 、 V ，属于面心立方晶格的有 γ-Fe 、Al 、Cu 、Ni 、 ，属于密排六方晶格的有 Mg 、 Zn 。 14．已知Cu 的原子直径为0．256nm ，那么铜的晶格常数为 。1mm 3Cu 中的原子数 为 。 15．晶面通过(0，0，0)、(1/2、1/4、0)和(1/2，0，1/2)三点，这个晶面的晶面指数为 . 16．在立方晶系中，某晶面在x 轴上的截距为2，在y 轴上的截距为1/2；与z 轴平行，则 该晶面指数为 （140） . 17．金属具有良好的导电性、导热性、塑性和金属光泽主要是因为金属原子具有 金属键 的 结合方式。 18．同素异构转变是指 当外部条件（如温度和压强）改变时，金属内部由一种金属内部由 一种晶体结构向另一种晶体结构的转变 。纯铁在 温度发生 和 多晶型转变。 19．在常温下铁的原子直径为0．256nm ，那么铁的晶格常数为 。 20．金属原子结构的特点是 。 21．物质的原子间结合键主要包括 离子键 、 共价键 和 金属键 三种。 (二)判断题 1．因为单晶体具有各向异性的特征，所以实际应用的金属晶体在各个方向上的性能也是不 相同的。 (N) 2．金属多晶体是由许多结晶位向相同的单晶体所构成。 ( N) 3．因为面心立方晶体与密排六方晶体的配位数相同，所以它们的原子排列密集程度也相同 4．体心立方晶格中最密原子面是｛111｝。 Y 5．金属理想晶体的强度比实际晶体的强度高得多。N 6．金属面心立方晶格的致密度比体心立方晶格的致密度高。 7．实际金属在不同方向上的性能是不一样的。N 8．纯铁加热到912℃时将发生α-Fe 向γ-Fe 的转变。 ( Y ) 9．面心立方晶格中最密的原子面是111}，原子排列最密的方向也是<111>。 ( N ) 10．在室温下，金属的晶粒越细，则其强度愈高和塑性愈低。 ( Y ) 11．纯铁只可能是体心立方结构，而铜只可能是面心立方结构。 ( N ) 12．实际金属中存在着点、线和面缺陷，从而使得金属的强度和硬度均下降。 ( Y ) 13．金属具有美丽的金属光泽，而非金属则无此光泽，这是金属与非金属的根本区别。N
测定晶体的晶面间距 (1)
测定晶体的晶面间距 ——X射线衍射法（布拉格法） 一、前言 X射线的波长非常短，与晶体的晶面间距基本上在同一数量级。因此，若把晶体的晶面间距作为光栅，用X射线照射晶体，就有可能产生衍射现象。科学家们深入研究了X射线在晶体中的衍射现象，得出了著名的劳厄晶体衍射公式、布拉格父子的布拉格定律等等。在他们的带领下，人们的视野深入到了晶体的内部，开辟了X射线理论和应用的广阔天地。他们也因自己的卓越研究，都获得了诺贝尔奖。 今天，X射线的衍射原理和方法在物理、化学、地质学、生命科学、……、尤其是在材料科学等各个领域都有了成熟的应用，而且仍在继续兴旺发展，特别是在材料的微观结构认识与缺陷分析上仍在不断揭示新的奇妙现象，正吸引着科学家们致力于开创新的理论突破！ 二、实验目的： 1）掌握X射线衍射仪分析法（衍射仪法）的基本原理和方法； 2）了解Y-2000型Ｘ射线衍射仪的结构、工作原理和使用方法。 三、实验原理 1912年英国物理学家布拉格父子（W. H. B ragg & W. L. B ragg）通过实验，发现了单色X射线与晶体作用产生衍射的规律。利用这一规律，发明了测定晶格常数（晶面间距）d的方法，这一方法也可以用来测定X射线的波长λ。在用X射线分析晶体结构方面，布拉格父子作出了杰出贡献，因而共同获得1915年诺贝尔物理学奖。 晶面间距与X射线的波长大致在同一数量级。当用一束单色X射线以一定角度θ照射晶体时，会发生什么现象呢？又有何规律呢？见图1： 图1 晶体衍射原理图 用单色X射线照射晶体： 1）会象可见光照射镜面一样发生反射，也遵从反射定律：即入射线、衍（反）射线、法线三线共面；掠射角θ与衍射角相等。 2）但也有不同：可见光在0°~180°都会发生反射，X射线却只在某些角度有较强的反射，而在其余角度则几乎不发生反射，称X射线的这种反射为“选择反射”。 选择性反射实际上是X射线1与X射线2互相干涉加强的结果，如图1（b）所示。当X射线1与2的光程差2 δ是波长λ的整数倍时，即2 δ = n λ（n∈Z﹢）时，会发 生干涉： ∵δ = d Sin θ 2 δ = 2 d Sinθ ∴ 2 d Sin θ = n λ ( 1 ) 此即著名的布拉格公式。 布拉格公式指出，用波长为λ的X射线射向晶体表面时，当在某些角度的光程差正好为波长λ的整数倍时，会发生干涉加强。让试样和计数器同步旋转（即转过扫查角度范围），用记数器记录下单位时间发生衍射的光量子数CPS，用测角仪测出发生衍射的角度（ 2 θ），如图2所示。 图2 测量衍射示意图 用CPS（CPS–C ounts P er S econd ）作纵坐标，2 θ作横坐标，描绘出所记录到的光量子数与角度的关系曲线，就可以得到如下衍射波形图： 图3 S i的衍射波形图 衍射峰对应的横坐标值即测得的2 θ角，而实验中的X射线管发出的X射线的波长λ
如何确定晶面间距
通过HRTEM的高分辨衬度条纹，可以量出相应的晶面间距为0.5nm，可以对材料的PDF 卡片看下这个间距对应的是哪个晶面的晶面间距，这样就可以把条纹所代表的晶面确定下来。最下面的SAED点比较杂乱，可能是所选区处含有多种晶向的晶体，因此可能会得到几种方向斑点重合的的SAED。你所测得的0.297nm或0.387nm都是对的，但是对应于不同的晶面衍射，究竟是对应哪个还是需要对比PDF卡片数据进行指认。 你这里的HRTEM与SAED并没有很明显的对应关系，可能原因是打HRTEM是区域较小，但打SAED时选区包含的晶粒较多，又出现不同取向造成的。或者他们根本就不是在一个地方打的。 FFT结合HRTEM可以进一步确定晶体的晶面及取向信息。 从HRTEM量得的明显的条纹间距就是0.5nm。你也可以用电子尺通过标尺来量取间距。一次可以量10个，然后再平均。正常情况同样晶面得到的晶格条纹间距是应该相等的，如果你量取的值出现与标准值有差别的情况，如果差得不多是正常的，还要再结合SAED指认晶面。或者看FFT的点分布能与什么样的拍摄几何构型对得上。总之当一种图片里信息不好确定情况下，要采用其它佐证。 关键要对FFT中的点进行标定，这也要结合HRTEM，如果测试结果正确，分析过程没问题，HRTEM的晶格条纹是会给出可信的晶面信息的，然后看FFT可以看出晶面的对称信息。从你这个FFT可以看出与电子束入射方向平行的晶面应该是有六方对称存在的，只不过电子束方向在实际测试时并没有与这些晶面都很好地平行，所以测得的HRTEM并不理想，只有一种晶面看得最清楚。 这张图照得很好，可以同时看到两种晶面的信息，竖条的如果是（220），那么横条就是与之成近90度的另一晶面。都需要测量，然后给标定出来，如果横条的与竖条间距一致，那么说明这两个是同一族晶面，正常标定就可以了。 HRTEM所测得的条纹间距，就是相应晶面的晶格间距。SAED打出的六方感觉的点不一定就说明材料是六方相，我们知道对于立方相的（111）方向打SAED就是很完美的六方点，但材料本身是立方相。关键要看电子束是从晶体的哪个面入射的。SAED的多晶环，每个环对应一种晶面，但HRTEM要想照出很好的晶格对电子束与晶体之间的角度是有关系的。所以有时候就算晶体很薄，电子束可以透过，也可能会出现HRTEM打不出晶格的情况，或者只能打出一种晶面的晶格条纹。HRTEM与FFT有对应关系，但与测的SAED除非晶体很完美，如果是纳米晶，一般就很难有完美的对应。 1.L*λ叫相机常数，依赖于不同的仪器。 2. r是用直尺所量的长度 所以，很明显，这是老仪器的套路。 要把图置于真实尺寸下量取距离，带入公式即可计算。 现在是ccd成像，scale bar直接在照片上，量出来的中心点至衍射点的距离，就直接是d值的倒数， 按你的图，即1/nm。 3. 中心点就是圆心。 4. 标衍射点，请先做理论计算或者叫“模拟”，按你的晶体结构jcpds77-2042进行，晶
晶面夹角公式
晶面夹角公式： 设晶面（h 1k 1l 1）和晶面（h 2k 2l 2）的面间距分别为d 1、d 2，则二晶面的夹角ω以下列公式计算（Ｖ为单胞体积）。 立方晶系： cos φ= 正方晶系：121212 22 cos h h k k l l φ++= 六方晶系：( )2 1212122112 213cos a h h k k h k h k l l φ++++= 正交晶系：121212 222cos h h k k l l φ++=菱方晶系： ()()()42212 1212121221122112212cos sin cos cos a d d h h k k l l k l k l l h l h h k h k V φααα??=+++-+++++??单斜晶系：()2122112121212222 2cos sin cos sin l h l h d d h h k k l l a b c ac ββφβ+?? =++-???? 三斜晶系： ()()()12 1112221233122312211312211212212cos d d S h h S k k S l l S k l k l S l h l h S h k h k V φ= ++++++++???? 立方晶系： cos φ= 正方晶系：121212 22 cos h h k k l l φ++=
立方晶系：( )2 1212122112 213cos a h h k k h k h k l l φ++++= 正交晶系：121212 222cos h h k k l l φ++= 菱方晶系： ()()()422 121212121221122112212cos sin cos cos a d d h h k k l l k l k l l h l h h k h k V φααα??=+++-+++++?? 单斜晶系： ()2122112121212222 2cos sin cos sin l h l h d d h h k k l l a b c ac ββφβ+?? =++-???? 三斜晶系： ()()()12 1112221233122312211312211212212cos d d S h h S k k S l l S k l k l S l h l h S h k h k V φ= ++++++++??? ?
《固体物理》课后习题答案
1.1 如果将等体积球分别排列成下列结构，设x 表示钢球所占体积与总体积之比，证明结构x简单立方π/ 6 ≈0.52 体心立方3π/ 8 ≈0.68 面心立方2π/ 6 ≈0.74六方密排2π/ 6 ≈0.74 金刚石3π/16 ≈0.34 解：设钢球半径为r ，根据不同晶体结构原子球的排列，晶格常数a 与r 的关系不同，分别为：简单立方：a = 2r 金刚石：根据金刚石结构的特点，因为体对角线四分之一处的原子与角上的原子紧贴，因此有
1.3 证明：体心立方晶格的倒格子是面心立方；面心立方晶格的倒格子是体心立方。 证明：体心立方格子的基矢可以写为 面心立方格子的基矢可以写为 根据定义，体心立方晶格的倒格子基矢为 同理 与面心立方晶格基矢对比，正是晶格常数为4π/ a的面心立方的基矢，说明体心立方晶格 的倒格子确实是面心立方。注意，倒格子不是真实空间的几何分布，因此该面心立方只是形式上的，或者说是倒格子空间中的布拉菲格子。根据定义，面心立方的倒格子基矢为 同理 而把以上结果与体心立方基矢比较，这正是晶格常数为4πa的体心立方晶格的基矢。 证明：根据定义，密勒指数为的晶面系中距离原点最近的平面ABC 交于基矢的截距分别为 即为平面的法线
根据定义，倒格子基矢为 则倒格子原胞的体积为 1.6 对于简单立方晶格，证明密勒指数为(h, k,l)的晶面系，面间距d 满足 其中a 为立方边长。 解：根据倒格子的特点，倒格子 与晶面族(h, k,l)的面间距有如下关系 因此只要先求出倒格，求出其大小即可。 因为倒格子基矢互相正交，因此其大小为 则带入前边的关系式，即得晶面族的面间距。
晶面指数
引用晶面指数、晶向指数、晶面间距 第二章X射线衍射方向 【教学内容】 1．晶体几何学基础。 2．X射线衍射的概念与布拉格方程（布拉格定律、衍射矢量方程、爱瓦德图解、劳埃方程）。 3．布拉格方程的应用与衍射方法。 【重点掌握内容】 1．晶体几何学的基本概念，包括布拉菲点阵，晶面和晶向指数等。 2．布拉格方程，这是本章的重中之重。 3．关于反射级数，X射线衍射与可见光反射的区别，以及衍射产生的条件及其在实际分析工作应用。 【了解内容】 1．复习晶体几何学的某些概念，如晶体、空间格子、晶带、晶带定律和晶面间距和晶面夹角的计算。 2．布拉格方程的应用和主要的衍射分析方法。 【教学难点】 1．倒易点阵。 2．衍射矢量方程、爱瓦德图解。 【教学目标】 1．熟练掌握X射线衍射的基本原理，尤其是布拉格方程。 2．培养学生善于利用这些理论去指导实际分析工作的能力。 【教学方法】 1．以课堂教学为主，通过多媒体教学手段，使学生掌握较抽象的几何结晶学的概念和布拉格方程。 2．通过做习题加深对X射线衍射理论的理解。 一、X射线衍射的发现 上章已经X射线的波动本质。我们对X射线的应用很大程度依赖于它的波动性。 第一个成功对X射线波动性进行的研究是德国物理学家劳厄（M. V. Laue）(照片)。1912年，劳厄是德国慕尼黑大学非正式聘请的教授。在此之前，人们对光的波动性已经进行了很多的研究，有关的理论已相当成熟。比如，光的衍射作用。人们知道，当光通过与其波长相当的光栅时会发生衍射作用。另一方面，人们对晶体的研究也达到相当的水平，认为晶体内部的质点是规则排列的，且质点间距在1-10A之间。当时，同校的一名博士研究生厄瓦耳（P. P. Eward）正在研究关于“各向同性共振体按各向异排列时的光学散射性质”。一天，他去向劳厄请教问题。劳厄问他，如果波长比晶体的原子间距小，而不象可见光波
晶面间距计算公式
正交晶系 1/d2=h2/a2+k2/b2+l2/c2 单斜晶系 1/d2={h2/a2+k2sin2β/b2+l2/c2－2hlcosβ/(ac)}/ sin2β 立方晶系 d=a/(h2+k2+l2) 六角晶系 四角晶系 单斜晶系
三斜晶系 If Φ is the angle between plane (h 1 k 1 l 1) and (h 2 k 2 l 2), then for Orthorhombic 2 /12222222222 /1221221221221221221)()()(cos ??? ? ??++??? ? ??++++= Φc l b k a h c l b k a h c l l b k k a h h Tetragonal []() 2 /1222222222 /1221221212 2 122121 ))/)(cos ??? ? ??++???? ??++++= Φc l a k h c l a k h c l l a k k h h Cubic ()()[] 2 /122 2222 21 2 1 21 212121cos l k h l k h l l k k h h ++++++= Φ Hexagonal ()() 2 /12222 222 2222122 11212121221221212143434 321 cos ????? ????? ??+++???? ??++++++ += Φl c a k h k h l c a k h k h l l c a K h k h k k h h
VOLUME: Orthorhombic: =abc Tetragonal: =c a2 Cubic: =3a 3 Hexagonal: =c a2 2 hcp transition between (UVW) and (uvtw) U=u-t, V=v-t, W=w u=1/3(2U-V), v=1/3(2V-U), t= - (u+v), w=W.